cp-manual

CONCRETEPIPE

DESIGNMANUAL

www.concrete-pipe.org

http://www.concrete-pipe.org

ii

Copyright 2007AmeriCAn ConCrete PiPe AssoCiAtion

All rights reserved.

this book or any part thereof must not be reproduced in any form without the written permission of the American Concrete Pipe Association.

Library of Congress catalog number 78-58624

Printed in the United states of America FirstprintingFebruary,1970 EighteenthprintingSeptember,2006 15,000copies 1,000copies SecondprintingJuly,1970 NineteenthprintingApril,2007 15,000copies 5,000copies Thirdprinting(revised)February,1974 15,000copies Fourthprinting(revised)June,1978 10,000copies Fifthprinting(revised)June,1980 15,000copies Sixthprinting(revised)February,1985 10,000copies Seventhprinting(revised)October,1987 10,000copies EighthprintingMarch,1990 5,000copies NinthprintingNovember,1992 5,000copies TenthprintingMarch,1995 2,500copies EleventhprintingNovember,1996 2,500copies TwelfthprintingAugust,1998 2,500copies Thirteenthprinting(revised)June,2000 4,000copies FourteenthprintingFebruary,2001 3,000copies FifteenthprintingFebruary,2002 3,000copies Sixteenthprinting(revised)May,2004 2,000copies SeventeenthprintingMarch,2005 2,000copies

technical programs of the American Concrete Pipe Association, since its founding in 1907, have been designed to compile engineering data on the hydraulics, loads and supporting strengths and design of concrete pipe. information obtained is disseminated to producers and consumers of concrete pipe through technical literature and promotional handbooks. other important activities of the Association include development of product specifications, government relations, participation in related trade and professional societies, advertising and promotion, an industry safety program and educational training. these services are made possible by the financial support of member companies located throughout the United states, Canada, and in almost 30 foreign countries.

American Concrete Pipe Assoication • www.concrete-pipe.org

FOREWORD the principal objective in compiling the material for this CONCRETE PIPE

DESIGN MANUAL was to present data and information on the design of concrete

pipe systems in a readily usable form. the Design manual is a companion volume

to the CONCRETE PIPE HANDBOOK which provides an up-to-date compilation

of the concepts and theories which form the basis for the design and installation of

precast concrete pipe sewers and culverts and explanations for the charts, tables

and design procedures summarized in the Design manual.

special recognition is acknowledged for the contribution of the staff of the

American Concrete Pipe Association and the technical review and assistance

of the engineers of the member companies of the Association in preparing this

Design manual. Also acknowledged is the development work of the American

Association of state Highway and transportation officials, American society

of Civil engineers, U. s. Army Corps of engineers, U. s. Federal Highway

Administration, Bureau of reclamation, iowa state University, natural resources

Conservation service, Water environment Federation, and many others. Credit for

much of the data in this manual goes to the engineers of these organizations and

agencies. every effort has been made to assure accuracy, and technical data are

considered reliable, but no guarantee is made or liability assumed.

iiiAmerican Concrete Pipe Assoication • www.concrete-pipe.org

American Concrete Pipe Association • www.concrete-pipe.org

FOREWORD.......................................................... .................................. ........... iii

Chapter 1. INTRODUCTION ................................................................................ 1

Chapter 2. HYDRAULICS OF SEWERSSanitary Sewers............................................................................................... 3

Determination of Sewer System Type ........................................................ 3Determination of Design Flow .................................................................... 3

Average Flow ........................................................................................ 3Peak Flow ............................................................................................. 3Minimum Flow ....................................................................................... 4

Selection of Pipe Size ................................................................................ 4Manning’s Formula ............................................................................... 4Manning’s “n” Value .............................................................................. 4Full Flow Graphs ................................................................................... 5Partially Full Flow Graphs ..................................................................... 5

Determination of Flow Velocity ................................................................... 5Minimum Velocity .................................................................................. 5Maximum Velocity ................................................................................. 5

Storm Sewers .................................................................................................. 5Determination of Sewer System Type ........................................................ 5Determination of Design Flow .................................................................... 5

Runoff Coefficient.................................................................................. 6Rainfall Intensity .................................................................................... 6Time of Concentration ........................................................................... 6Runoff Area ........................................................................................... 6

Selection of Pipe Size ................................................................................ 7Manning’s Formula ............................................................................... 7Manning’s “n” Value .............................................................................. 7

Determination of Flow Velocity ................................................................... 7Minimum Velocity .................................................................................. 7Maximum Velocity ................................................................................. 7

Example Problems ..................................................................................... 82-1 Storm Sewer Flow .......................................................................... 82-2 Required Sanitary Sewer Size ........................................................ 82-3 Storm Sewer Minimum Slope ......................................................... 92-4 Sanitary Sewer Design ................................................................... 92-5 Storm Sewer Design ..................................................................... 112-6 Sanitary Sewer Design ................................................................. 13

Chapter 3. HYDRAULICS OF CULVERTSDetermination of Design Flow........................................................................ 15Factors Affecting Culvert Discharge .............................................................. 15

INDEX OF CONTENTS

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Concrete Pipe Design Manual


Inlet Control .............................................................................................. 15Outlet Control ........................................................................................... 16Critical Depth ............................................................................................ 16

Selection of Culvert Size................................................................................ 17Culvert Capacity Chart Procedure............................................................ 17Nomograph Procedure ............................................................................. 18Example Problems ................................................................................... 203-1 Culvert Capacity Chart Procedure ..................................................... 203-2 Nomograph Procedure ....................................................................... 223-3 Culvert Design.................................................................................... 233-4 Culvert Design ................................................................................... 24

Chapter 4. LOADS AND SUPPORTING STRENGTHSTypes of Installations ..................................................................................... 27

Trench ...................................................................................................... 27Positive Projecting Embankment .............................................................. 27Negative Projecting Embankment ............................................................ 27Jacked or Tunneled .................................................................................. 27

Background.................................................................................................... 29Introduction .................................................................................................... 29Four Standard Installations ............................................................................ 30Load Pressures.............................................................................................. 34Determination of Earth Load .......................................................................... 34

Embankment Soil Load ............................................................................ 34Trench Soil Load ...................................................................................... 36Negative Projecting Embankment Soil Load ............................................ 37Jacked or Tunneled Soil Load .................................................................. 38

Fluid Load ...................................................................................................... 39Determination of Live Load ............................................................................ 39

Load Distribution ...................................................................................... 41Average Pressure Intensity ...................................................................... 44Total Live Load ......................................................................................... 44Total Live Loads in Pounds per Linear Foot ............................................. 44Airports ..................................................................................................... 46Rigid Pavements ...................................................................................... 46Flexible Pavements .................................................................................. 47Railroads .................................................................................................. 48Construction Loads .................................................................................. 49

Selection of Bedding ...................................................................................... 49Bedding Factors............................................................................................. 49

Determination of Bedding Factor .............................................................. 51Application of Factor of Safety ................................................................. 53

Selection of Pipe Strength ............................................................................. 54Example Problems

4-1 Trench Installation .............................................................................. 584-2 Positive Projecting Embankment Installation ..................................... 604-3 Negative Projecting Embankment Installation ................................... 63

Index of Contents vii


4-4 Jacked or Tunneled Installation ......................................................... 654-5 Wide Trench Installation..................................................................... 674-6 Positive Projecting Embankment

Installation Vertical Elliptical Pipe....................................................... 694-7 Highway Live Load............................................................................. 714-8 Aircraft Live Load - Rigid Pavement ................................................... 734-9 Aircraft Live Load - Flexible Pavement .............................................. 764-10 Railroad Live Load ........................................................................... 80

Chapter 5. SUPPLEMENTAL DATACircular Concrete Pipe................................................................................... 83Elliptical Concrete Pipe .................................................................................. 83

Horizontal Elliptical Pipe ........................................................................... 83Vertical Elliptical Pipe ............................................................................... 86

Concrete Arch Pipe ........................................................................................ 86Concrete Box Sections .................................................................................. 89Special Sections ............................................................................................ 91

Precast Concrete Manhole Sections ........................................................ 92Flat Base Pipe .......................................................................................... 93

Standard Specifications for Concrete Pipe .................................................... 93Pipe Joints ..................................................................................................... 98Jacking Concrete Pipe ................................................................................. 103

Required Characteristics of Concrete Jacking Pipe ............................... 103The Jacking Method ............................................................................... 103

Bends and Curves ....................................................................................... 104Deflected Straight Pipe........................................................................... 104Radius Pipe ............................................................................................ 105Bends and Special Sections................................................................... 107

Significance of Cracking .............................................................................. 108

TABLES

Table 1 Sewage Flows Used For Design....................................................... 112Table 2 Sewer Capacity Allowances For Commercial And Industrial Areas .. 113Table 3 Full Flow Coefficient Values - Circular Concrete Pipe....................... 114Table 4 Full Flow Coefficient Values - Elliptical Concrete Pipe ...................... 115Table 5 Full Flow Coefficient Values - Concrete Arch Pipe ............................ 115Table 6 Full Flow Coefficient Values - Precast Concrete Box Sections ......... 116Table 7 Slopes Required for V = 2 fps at Full and Half Full Flow .................. 117Table 8 Runoff Coefficients for Various Areas ............................................... 118Table 9 Rainfall Intensity Conversion Factors ............................................... 118Table 10 Recurrence Interval Factors.............................................................. 118Table 11 Nationwide Flood-Frequency Projects .............................................. 119Table 12 Entrance Loss Coefficients ............................................................... 119Table 13 Transition Widths - 12 inch Circular Pipe .......................................... 120

viii Concrete Pipe Design Manual


Table 14 Transition Widths - 15 inch Circular Pipe .......................................... 121Table 15 Transition Widths - 18 inch Circular Pipe .......................................... 122Table 16 Transition Widths - 21 inch Circular Pipe .......................................... 123Table 17 Transition Widths - 24 inch Circular Pipe .......................................... 124Table 18 Transition Widths - 27 inch Circular Pipe .......................................... 125Table 19 Transition Widths - 30 inch Circular Pipe .......................................... 126Table 20 Transition Widths - 33 inch Circular Pipe .......................................... 127Table 21 Transition Widths - 36 inch Circular Pipe .......................................... 128Table 22 Transition Widths - 42 inch Circular Pipe .......................................... 129Table 23 Transition Widths - 48 inch Circular Pipe .......................................... 130Table 24 Transition Widths - 54 inch Circular Pipe .......................................... 131Table 25 Transition Widths - 60 inch Circular Pipe .......................................... 132Table 26 Transition Widths - 66 inch Circular Pipe .......................................... 133Table 27 Transition Widths - 72 inch Circular Pipe .......................................... 134Table 28 Transition Widths - 78 inch Circular Pipe .......................................... 135Table 29 Transition Widths - 84 inch Circular Pipe .......................................... 136Table 30 Transition Widths - 90 inch Circular Pipe .......................................... 137Table 31 Transition Widths - 96 inch Circular Pipe .......................................... 138Table 32 Transition Widths - 102 inch Circular Pipe ........................................ 139Table 33 Transition Widths - 108 inch Circular Pipe ........................................ 140Table 34 Transition Widths - 114 inch Circular Pipe ........................................ 141Table 35 Transition Widths - 120 inch Circular Pipe ........................................ 142Table 36 Transition Widths - 126 inch Circular Pipe ........................................ 143Table 37 Transition Widths - 132 inch Circular Pipe ........................................ 144Table 38 Transition Widths - 138 inch Circular Pipe ........................................ 145Table 39 Transition Widths - 144 inch Circular Pipe ........................................ 146Table 40 Design Values of Settlement Ratio ................................................... 147Table 41 Design Values of Coefficient of Cohesion ......................................... 147Table 42 Highway Loads on Circular Pipe ....................................................... 148Table 43 Highway Loads on Horizontal Elliptical Pipe ..................................... 149Table 44 Hghway Loads on Vertical Elliptical Pipe .......................................... 150Table 45 Highway Loads on Arch Pipe ............................................................ 151Table 46 Pressure Coefficients for a Single Load ............................................ 152Table 47 Pressure Coefficients for Two Loads Spaced 0.8Rs Apart ............... 153Table 48 Pressure Coefficients for Two Loads Spaced 1.6Rs Apart ............... 154Table 49 Pressure Coefficients for Two Loads Spaced 2.4Rs Apart ............... 155Table 50 Pressure Coefficients for Two Loads Spaced 3.2Rs Apart ............... 156Table 51 Pressure Coefficients for a Single Load Applied on

Subgrade or Flexible Pavement ........................................................ 157Table 52 Values of Radius of Stiffness ............................................................ 158Table 53 Aircraft Loads on Circular Pipe ......................................................... 159Table 54 Aircraft Loads on Horizontal Elliptical Pipe ....................................... 160Table 55 Aircraft Loads on Arch Pipe .............................................................. 161Table 56 Railroad Loads on Circular Pipe ....................................................... 162Table 57 Railroad Loads on Horizontal Elliptical Pipe ..................................... 163

Index of Contents ix


Table 58 Railroad Loads on Arch Pipe ............................................................ 164Table 59 Bedding Factors for Vertical Elliptical Pipe —

Positive Projecting Embankment Installation .................................... 165Table 60 Bedding Factors for Horizonal Elliptical Pipe —

Positive Projecting Embankment Installation .................................... 166Table 61 Bedding Factors for Arch Pipe —

Positive Projecting Embankment Installation .................................... 167Table 62 Type I Fill Height Table - 1 ft. through 15 ft. ...................................... 168Table 63 Type I Fill Height Table - 16 ft. through 30 ft. .................................... 169Table 64 Type I Fill Height Table - 31 ft. through 45 ft. .................................... 170Table 65 Type I Fill Height Table - 46 ft. through 60 ft. .................................... 171Table 66 Type 2 Fill Height Table - 1 ft. through 15 ft. ..................................... 172Table 67 Type 2 Fill Height Table - 16 ft. through 30 ft. ................................... 173Table 68 Type 2 Fill Height Table - 31 ft. through 45 ft. ................................... 174Table 69 Type 3 Fill Height Table - 1 ft. through 18 ft. ..................................... 175Table 70 Type 3 Fill Height Table - 19 ft. through 35 ft. ................................... 176Table 71 Type 4 Fill Height Table - 1 ft. through 15 ft. ..................................... 177Table 72 Type 4 Fill Height Table - 16 ft. through 23 ft. ................................... 178

FIGURES

Figure 1 Ratio of Extreme Flows to Average Daily Flow ................................. 180Figure 2 Flow for Circular Pipe Flowing Full ......................... n=0.010 ........... 181Figure 3 Flow for Circular Pipe Flowing Full ......................... n=0.011............ 182Figure 4 Flow for Circular Pipe Flowing Full ......................... n=0.012 ........... 183Figure 5 Flow for Circular Pipe Flowing Full ......................... n=0.013 ........... 184Figure 6 Flow for Horizontal Elliptical Pipe Flowing Full ....... n=0.010 ........... 185Figure 7 Flow for Horizontal Elliptical Pipe Flowing Full ....... n=0.011............ 186Figure 8 Flow for Horizontal Elliptical Pipe Flowing Full ....... n=0.012 ........... 187Figure 9 Flow for Horizontal Elliptical Pipe Flowing Full ....... n=0.013 ........... 188Figure 10 Flow for Vertical Elliptical Pipe Flowing Full ............ n=0.010 ........... 189Figure 11 Flow for Vertical Elliptical Pipe Flowing Full ............ n=0.011............ 190Figure 12 Flow for Vertical Elliptical Pipe Flowing Full ............ n=0.012 ........... 191Figure 13 Flow for Vertical Elliptical Pipe Flowing Full ............ n=0.013 ........... 192Figure 14 Flow for Arch Pipe Flowing Full ............................... n=0.010 ........... 193Figure 15 Flow for Arch Pipe Flowing Full ............................... n=0.011............ 194Figure 16 Flow for Arch Pipe Flowing Full ............................... n=0.012 ........... 195Figure 17 Flow for Arch Pipe Flowing Full ............................... n=0.013 ........... 196Figure 18 Flow for Box Sections Flowing Full ......................... n=0.012 ........... 197Figure 19 Flow for Box Sections Flowing Full ......................... n=0.013 ........... 199Figure 20 Relative Velocity and Flow in Circular Pipe for

Any Depth of Flow............................................................................. 201Figure 21 Relative Velocity and Flow in Horizontal Elliptical

Pipe for Any Depth of Flow ............................................................... 202

x Concrete Pipe Design Manual


Figure 22 Relative Velocity and Flow in Vertical Elliptical Pipefor Any Depth of Flow........................................................................ 203

Figure 23 Relative Velocity and Flow in Arch Pipe for Any Depth of Flow ........ 204Figure 24 Relative Velocity and Flow in Precast Concrete Box

Sections for Any Depth of Flow ......................................................... 205Figure 25 2-Year, 30 Minute Rainfall Intensity Map........................................... 214Figure 26 Intensity-Duration Curve ................................................................... 214Figure 27 California Chart “A” for Calculation of Design Discharges ................ 215Figure 28 Critical Depth Circular Pipe ............................................................... 216Figure 29 Critical Depth Horizontal Elliptical Pipe ............................................. 217Figure 30 Critical Depth Vertical Elliptical Pipe ................................................. 218Figure 31 Critical Depth Arch Pipe .................................................................... 219Figure 32 Critical Depth Precast Concrete Box Sections.................................. 221Figure 33 Headwater Depth for Circular Concrete Pipe

Culverts with Inlet Control ................................................................. 222Figure 34 Headwater Depth for Horizontal Elliptical Concrete

Pipe Culverts with Inlet Control ......................................................... 223Figure 35 Headwater Depth for Vertical Elliptical Concrete

Pipe Culverts with Inlet Control ......................................................... 224Figure 36 Headwater Depth for Arch Concrete Pipe Culverts

with Inlet Control ............................................................................... 225Figure 37 Headwater Depth for Concrete Box Culverts with

Inlet Control ....................................................................................... 226Figure 38 Head for Circular Concrete Culverts Flowing Full ............................. 227Figure 39 Head for Elliptical Concrete Culverts Flowing Full ............................ 228Figure 40 Head for Concrete Arch Culverts Flowing Full .................................. 229Figure 41 Head for Concrete Box Culverts Flowing Full ................................... 230Figure 42 Culvert Capacity 12-Inch Diameter Pipe ...................................... 231Figure 43 Culvert Capacity 15-Inch Diameter Pipe ...................................... 232Figure 44 Culvert Capacity 18-Inch Diameter Pipe ...................................... 233Figure 45 Culvert Capacity 21-Inch Diameter Pipe ...................................... 234Figure 46 Culvert Capacity 24-Inch Diameter Pipe ...................................... 235Figure 47 Culvert Capacity 27-Inch Diameter Pipe ...................................... 236Figure 48 Culvert Capacity 30-Inch Diameter Pipe ...................................... 237Figure 49 Culvert Capacity 33-Inch Diameter Pipe ...................................... 238Figure 50 Culvert Capacity 36-Inch Diameter Pipe ...................................... 239Figure 51 Culvert Capacity 42-Inch Diameter Pipe ...................................... 240Figure 52 Culvert Capacity 48-Inch Diameter Pipe ...................................... 241Figure 53 Culvert Capacity 54-Inch Diameter Pipe ...................................... 242Figure 54 Culvert Capacity 60-Inch Diameter Pipe ...................................... 243Figure 55 Culvert Capacity 66-Inch Diameter Pipe ...................................... 244Figure 56 Culvert Capacity 72-Inch Diameter Pipe ...................................... 245Figure 57 Culvert Capacity 78-Inch Diameter Pipe ...................................... 246Figure 58 Culvert Capacity 84-Inch Diameter Pipe ...................................... 247Figure 59 Culvert Capacity 90-Inch Diameter Pipe ...................................... 248

Index of Contents xi


Figure 60 Culvert Capacity 96-Inch Diameter Pipe ...................................... 249Figure 61 Culvert Capacity 102-Inch Diameter Pipe .................................... 250Figure 62 Culvert Capacity 108-Inch Diameter Pipe .................................... 251Figure 63 Culvert Capacity 114-Inch Diameter Pipe .................................... 252Figure 64 Culvert Capacity 120-Inch Diameter Pipe .................................... 253Figure 65 Culvert Capacity 132-Inch Diameter Pipe .................................... 254Figure 66 Culvert Capacity 144-Inch Diameter Pipe .................................... 255Figure 67 Culvert Capacity 14 x 23-Inch Horizontal

Ellipitical Equivalent 18-Inch Circular ................................................ 256Figure 68 Culvert Capacity 19 x 30-Inch Horizontal

Elliptical Equivalent 24-Inch Circular ................................................. 257Figure 69 Culvert Capacity 24 x 38-Inch Horizontal


Elliptical Equivalent 36-Inch Circular ................................................. 259Figure71 Culvert Capacity 34 x 54-Inch Horizontal








Elliptical Equivalent 84-Inch Circular ................................................. 267Figure 79 Culvert Capacity 72 x 113 -Inch Horizontal



Elliptical Equivalent 102-Inch Circular ............................................... 270Figure 82 Culvert Capacity 87 x 136-Inch Horizontal


Elliptical Equivalent 114-Inch Circular ............................................... 272Figure 84 Culvert Capacity 97 x 151 -Inch Horizontal


Elliptical Equivalent 132-Inch Circular ............................................... 274

xii Concrete Pipe Design Manual


Figure 86 Culvert Capacity 116 x 180-Inch HorizontalElliptical Equivalent 144-Inch Circular ............................................... 275

Figure 87 Culvert Capacity 11 x 18-Inch ArchEquivalent 15-Inch Circular ............................................................... 276






Figure 93 Culvert Capacity 31 x 51 -Inch ArchEquivalent 42-Inch Circular ............................................................... 282







Figure 100 Culvert Capacity 77 x 122-Inch ArchEquivalent 96-Inch Circular ............................................................ 289

Figure 101 Culvert Capacity 87 x 138-Inch ArchEquivalent 108-Inch Circular .......................................................... 290



Figure 104 Culvert Capacity 3 x 2-Foot Box Equivalent 33-Inch Circular ... 293Figure 105 Culvert Capacity 3 x 3-Foot Box Equivalent 39-Inch Circular ... 294Figure 106 Culvert Capacity 4 x 2-Foot Box Equivalent 36-Inch Circular ... 295Figure 107 Culvert Capacity 4 x 3-Foot Box Equivalent 42-Inch Circular ... 296Figure 108 Culvert Capacity 4 x 4-Foot Box Equivalent 54-Inch Circular ... 297Figure 109 Culvert Capacity 5 x 3-Foot Box Equivalent 48-Inch Circular ... 298Figure 110 Culvert Capacity 5 x 4-Foot Box Equivalent 60-Inch Circular ... 299Figure 111 Culvert Capacity 5 x 5-Foot Box Equivalent 66-Inch Circular ... 300Figure 112 Culvert Capacity 6 x 3-Foot Box Equivalent 57-Inch Circular ... 301

Index of Contents xiii


Figure 113 Culvert Capacity 6 x 4-Foot Box Equivalent 66-Inch Circular ... 302Figure 114 Culvert Capacity 6 x 5-Foot Box Equivalent 75-Inch Circular ... 303Figure 115 Culvert Capacity 6 x 6-Foot Box Equivalent 81-Inch Circular ... 304Figure 116 Culvert Capacity 7 x 4-Foot Box Equivalent 71-Inch Circular ... 305Figure 117 Culvert Capacity 7 x 5-Foot Box Equivalent 79-Inch Circular .... 306Figure 118 Culvert Capacity 7 x 6-Foot Box Equivalent 87-Inch Circular .... 307Figure 119 Culvert Capacity 7 x 7-Foot Box Equivalent 94-Inch Circular .... 308Figure 120 Culvert Capacity 8 x 4-Foot Box Equivalent 76-Inch Circular .... 309Figure 121 Culvert Capacity 8 x 5-Foot Box Equivalent 85-Inch Circular .... 310Figure 122 Culvert Capacity 8 x 6-Foot Box Equivalent 93-Inch Circular .... 311Figure 123 Culvert Capacity 8 x 7-Foot Box Equivalent 101-Inch Circular ...... 312Figure 124 Culvert Capacity 8 x 8-Foot Box Equivalent 108-Inch Circular ...... 313Figure 125 Culvert Capacity 9 x 5-Foot Box Equivalent 90-Inch Circular......... 314Figure 126 Culvert Capacity 9 x 6-Foot Box Equivalent 99-Inch Circular......... 315Figure 127 Culvert Capacity 9 x 7-Foot Box Equivalent 107-Inch Circular ...... 316Figure 128 Culvert Capacity 9 x 8-Foot Box Equivalent 114-Inch Circular ....... 317Figure 129 Culvert Capacity 9 x 9-Foot Box Equivalent 121-Inch Circular ...... 318Figure 130 Culvert Capacity 10 x 5-Foot Box Equivalent 94-inch Circular ....... 319Figure 131 Culvert Capacity 10 x 6-Foot Box Equivalent 104-Inch Circular .... 320Figure 132 Culvert Capacity 10 x 7-Foot Box Equivalent 112-Inch Circular ..... 321Figure 133 Culvert Capacity 10 x 8-Foot Box Equivalent 120-Inch Circular .... 322Figure 134 Culvert Capacity 10 x 9-Foot Box Equivalent 128-Inch Circular .... 323Figure 135 Culvert Capacity 10 x 10-Foot Box Equivalent 135-Inch Circular... 324Figure 136 Culvert Capacity 11 x 4-Foot Box Equivalent 88-Inch Circular ....... 325Figure 137 Culvert Capacity 11 x 6-Foot Box Equivalent 109-Inch Circular ..... 326Figure 138 Culvert Capacity 11 x 8-Foot Box Equivalent 126-Inch Circular ..... 327Figure 139 Culvert Capacity 11 x 10-Foot Box Equivalent 141-Inch Circular ... 328Figure 140 Culvert Capacity 11 x 11-Foot Box Equivalent 148-Inch Circular ... 329Figure 141 Culvert Capacity 12 x 4-Foot Box Equivalent 92-Inch Circular ...... 330Figure 142 Culvert Capacity 12 x 6-Foot Box Equivalent 113-Inch Circular ..... 331Figure 143 Culvert Capacity 12 x 8-Foot Box Equivalent 131-Inch Circular .... 332Figure 144 Culvert Capacity 12 x 10-Foot Box Equivalent 147-Inch Circular... 333Figure 145 Culvert Capacity 12 x 12-Foot Box Equivalent 161-Inch Circular... 334Figure 146 Essential Features of Types of Installations ................................ 335Figure 147 Earth Loads on Jacked or Tunneled Installations

Sand and Gravel Trench Term..................................................... 336Figure 148 Earth Loads on Jacked or Tunneled Installations

Sand and Gravel Cohesion Term ................................................ 337Figure 149 Earth Loads on Jacked or Tunneled Installations

Saturated Top Soil Trench Term .................................................. 338Figure 150 Earth Loads on Jacked or Tunneled Installations

Saturated Top Soil Cohesion Term .............................................. 339Figure 151 Earth Loads on Jacked or Tunneled Installations

Ordinary Clay Trench Term.......................................................... 340

xiv Concrete Pipe Design Manual


Figure 152 Earth Loads on Jacked or Tunneled InstallationsOrdinary Clay Cohesion Term ..................................................... 341

Figure 153 Earth Loads on Jacked or Tunneled InstallationsSaturated Clay Trench Term ........................................................ 342

Figure 154 Earth Loads on Jacked or Tunneled InstallationsSaturated Clay Cohesion Term.................................................... 343

Figure 155 Trench Backfill Loads on Vertical Elliptical PipeSand and Gravel (Fill Height = 2 to 10 ft) ................................... 344

Figure 156 Trench Backfill Loads on Vertical Elliptical PipeSand and Gravel (Fill Height = 10 to 50 ft) ................................. 345

Figure 157 Trench Backfill Loads on Vertical Elliptical PipeSaturated Top Soil (Fill Height = 2 to 10 ft) ................................. 346

Figure 158 Trench Backfill Loads on Vertical Elliptical PipeSaturated Top Soil (Fill Height = 10 to 50) .................................. 347

Figure 159 Trench Backfill Loads on Vertical Elliptical PipeOrdinary Clay (Fill Height = 2 to 10 ft) ........................................ 348

Figure 160 Trench Backfill Loads on Vertical Elliptical PipeOrdinary Clay (Fill Height = 10 to 50) ......................................... 349

Figure 161 Trench Backfill Loads on Vertical Elliptical PipeSaturated Clay (Fill Height = 2 to 10 ft) ....................................... 350

Figure 162 Trench Backfill Loads on Vertical Elliptical PipeSaturated Clay (Fill Height = 10 to 50 ft) ..................................... 351

Figure 163 Trench Backfill Loads on Horizontal Elliptical PipeSand and Gravel (Fill Height = 2 to 10 ft) ................................... 352

Figure 164 Trench Backfill Loads on Horizontal Elliptical PipeSand and Gravel (Fill Height = 10 to 50 ft) ................................. 353

Figure 165 Trench Backfill Loads on Horizontal Elliptical PipeSaturated Top Soil (Fill Height = 2 to 10 ft) ................................. 354

Figure 166 Trench Backfill Loads on Horizontal Elliptical PipeSaturated Top Soil (Fill Height = 10 to 50 ft) ............................... 355

Figure 167 Trench Backfill Loads on Horizontal Elliptical PipeOrdinary Clay (Fill Height = 2 to 10 ft) ........................................ 356

Figure 168 Trench Backfill Loads on Horizontal Elliptical PipeOrdinary Clay (Fill Height = 10 to 50 ft) ...................................... 357

Figure 169 Trench Backfill Loads on Horizontal Elliptical PipeSaturated Clay (Fill Height = 2 to 10 ft) ....................................... 358

Figure 170 Trench Backfill Loads on Horizontal Elliptical PipeSaturated Clay (Fill Height = 10 to 50 ft) ..................................... 359

Figure 171 Trench Backfill Loads on Arch Pipe Sand andGravel (Fill Height = 2 to 10 ft) .................................................... 360

Figure 172 Trench Backfill Loads on Arch Pipe Sand andGravel (Fill Height = 10 to 50 ft) .................................................. 361

Figure 173 Trench Backfill Loads on Arch Pipe SaturatedTop Soil (Fill Height = 2 to 10 ft) .................................................. 362

Index of Contents xv


Figure 174 Trench Backfill Loads on Arch Pipe SaturatedTop Soil (Fill Height = 10 to 50 ft) ................................................ 363

Figure 175 Trench Backfill Loads on Arch Pipe OrdinaryClay (Fill Height = 2 to 10 ft) ....................................................... 364

Figure 176 Trench Backfill Loads on Arch Pipe OrdinaryClay (Fill Height = 10 to 50 ft) ..................................................... 365

Figure 177 Trench Backfill Loads on Arch Pipe SaturatedClay (Fill Height = 2 to 10 ft) ....................................................... 366

Figure 178 Trench Backfill Loads on Arch Pipe SaturatedClay (Fill Height = 10 to 50 ft) ..................................................... 367

Figure 179 Embankment Fill Loads on Vertical EllipticalPipe Positive Projecting rsdp = 0 ................................................. 368

Figure 180 Embankment Fill Loads on Vertical EllipticalPipe Positive Projecting rsdp = 01 ............................................... 369

Figure 181 Embankment Fill Loads on Vertical EllipticalPipe Positive Projecting rsdp = 0.3 .............................................. 370



Figure 184 Embankment Fill Loads on Horizontal EllipticalPipe Positive Projecting rsdp = 0 ................................................. 373

Figure 185 Embankment Fill Loads on Horizontal EllipticalPipe Positive Projecting rsdp = 0.1 .............................................. 374



Figure 188 Embankment Fill Loads on Horizontal Elliptical PipePositive Projecting rsdp = 1.0....................................................... 377

Figure 189 Embankment Fill Loads on Arch Pipe PositiveProjecting rsdp = 0 ....................................................................... 378

Figure 190 Embankment Fill Loads on Arch Pipe PositiveProjecting rsdp = 0.1 .................................................................... 379




Figure 194 Embankment Fill Loads on Circular Pipe NegativeProjecting p’ = 0.5 rsd = 0 ............................................................ 383

Figure 195 Embankment Fill Loads on Circular Pipe NegativeProjecting p’ = 0.5 rsd = -0.1 ........................................................ 384

xvi Concrete Pipe Design Manual





Figure 199 Embankment Fill Loads on Circular Pipe NegativeProjecting p’ = 1.0 rsd = 0 ............................................................ 388

Figure 200 Embankment Fill Loads on Circular PipeNegative Projecting p’ = 1.0 rsd = -0.1 ......................................... 389




Figure 204 Embankment Fill Loads on Circular PipeNegative Projecting p’ = 1.5 rsd = 0 ............................................. 393





Figure 209 Embankment Fill Loads on Circular PipeNegative Projecting p’ = 2.0 rsd = 0 ............................................. 398





Figure 214 Load Coefficient Diagram for Trench Installations ...................... 403

APPENDIX A

Table A-1 Square Roots of Decimal Number (S1/2 in Manning’s Formula) ..... 406Table A-2 Three-Eighths Powers of Numbers ................................................ 407Table A-3 Two-Thirds Powers of Numbers ..................................................... 408Table A-4 Eight-Thirds Powers of Numbers ................................................... 409Table A-5 Square Roots and Cube Roots of Numbers ................................... 410

Index of Contents xvii


Table A-6 Decimal Equivalents of Inches and Feet ........................................ 411Table A-7 Various Powers of Pipe Diameters ................................................. 412Table A-8 Areas of Circular Sections (Square Feet)....................................... 413Table A-9 Areas of Circular Segments ........................................................... 414Table A-10 Area, Wetted Perimeter and Hydraulic Radius

of Partially Filled Circular Pipe ....................................................... 415Table A-11 Headwater Depth for Circular Pipe Culverts with Inlet Control....... 416Table A-12 Trigonometric Formulas ................................................................. 417Table A-13 Properties of the Circle ................................................................... 418Table A-14 Properties of Geometric Sections................................................... 419Table A-15 Properties of Geometric Sections and Structural Shapes .............. 425Table A-16 Four Place Logarithm Tables.......................................................... 426Table A-17 Frequently Used Conversion Factors ............................................. 427Table A-18 Metric Conversion of Diameter ....................................................... 430Table A-19 Metric Conversion of Wall Thickness .............................................. 430

APPENDIX B Marston/Spangler Design Procedure

Types of Installations......................................................................................... 431Trench ..................................................................................................... 431Positive Projecting Embankment ................................................................. 432Negative Projecting Embankment ............................................................... 433

Selection of Bedding ......................................................................................... 435Determination of Bedding Factor ...................................................................... 436Application of Factor of Safety .......................................................................... 438Selection of Pipe Strength................................................................................. 438Example Problems ............................................................................................ 439

B-1 Trench Installation ................................................................................. 439B-2 Positive Projecting Embankment Installation ........................................ 441B-3 Negative Projecting Embankment Installation....................................... 443B-4 Wide Trench Installation ........................................................................ 445B-5 Positive Projecting Embankment Installation

Vertical Elliptical Pipe ............................................................................ 447B-6 Highway Live Load ................................................................................ 449

APPENDIX B - TABLES AND FIGURES........................................................... 451

GLOSSARY OF TERMS................................................................................... 533

CONDENSED BIBLIOGRAPHY....................................................................... 537

xviii Concrete Pipe Design Manual

1

CHAPTER 1

INTRODUCTION

The design and construction of sewers and culverts are among the mostimportant areas of public works engineering and, like all engineering projects, theyinvolve various stages of development. The information presented in this manualdoes not cover all phases of the project, and the engineer may need to consultadditional references for the data required to complete preliminary surveys.

This manual is a compilation of data on concrete pipe, and it was planned toprovide all design information needed by the engineer when he begins to considerthe type and shape of pipe to be used. All equations used in developing thefigures and tables are shown along with limited supporting theory. A condensedbibliography of literature references is included to assist the engineer who wishesto further study the development of these equations.

Chapters have been arranged so the descriptive information can be easilyfollowed into the tables and figures containing data which enable the engineer toselect the required type and size concrete pipe without the lengthy computationspreviously required. All of these design aids are presently published inengineering textbooks or represent the computer analysis of involved equations.Supplemental data and information are included to assist in completing thisimportant phase of the project, and illustrative example problems are presented inChapters 2 through 4. A review of these examples will indicate the relative easewith which this manual can be used.

The revised Chapter 4 on Loads and Supporting Strengths incorporates theStandard Installations for concrete pipe bedding and design. The standardInstallations are compatible with today's methods of installation and incorporatethe latest research on concrete pipe. In 1996 the B, C, and D beddings,researched by Anson Marston and Merlin Spangler, were replaced in the AASHTOBridge Specifications by the Standard Installations. A description of the B, C, andD beddings along with the appropriate design procedures are included inAppendix B of this manual to facilitate designs still using these beddings.

3

CHAPTER 2

HYDRAULICS OF SEWERSThe hydraulic design procedure for sewers requires:

1. Determination of Sewer System Type2. Determination of Design Flow3. Selection of Pipe Size4. Determination of Flow Velocity

SANITARY SEWERS

DETERMINATION OF SEWER SYSTEM TYPESanitary sewers are designed to carry domestic, commercial and industrial

sewage with consideration given to possible infiltration of ground water. All typesof flow are designed on the basis of having the flow characteristics of water.

DETERMINATION OF DESIGN FLOWIn designing sanitary sewers, average, peak and minimum flows are

considered. Average flow is determined or selected, and a factor applied to arriveat the peak flow which is used for selecting pipe size. Minimum flows are used todetermine if specified velocities can be maintained to prevent deposition of solids.

Average Flow. The average flow, usually expressed in gallons per day, is ahypothetical quantity which is derived from past data and experience. Withadequate local historical records, the average rate of water consumption can berelated to the average sewage flow from domestic, commercial and industrialsources. Without such records, information on probable average flows can beobtained from other sources such as state or national agencies. Requirements forminimum average flows are usually specified by local or state sanitary authoritiesor local, state and national public health agencies. Table 1 lists design criteria fordomestic sewage flows for various municipalities. Commercial and industrialsewage flows are listed in Table 2. These tables were adapted from the “Designand Construction of Sanitary and Storm Sewers,” published by American Societyof Civil Engineers and Water Pollution Control Federation. To apply flow criteria inthe design of a sewer system, it is necessary to determine present and futurezoning, population densities and types of business and industry.

Peak Flow. The actual flow in a sanitary sewer is variable, and many studieshave been made of hourly, daily and seasonal variations. Typical results of onestudy are shown in Figure I adapted from “Design and Construction of Sanitaryand Storm Sewers,” published by the American Society of Civil Engineers andWater Pollution Control Federation. Maximum and minimum daily flows are usedin the design of treatment plants, but the sanitary sewer must carry the peak flow

4 Concrete Pipe Design Manual


that will occur during its design life. This peak flow is defined as the mean rate ofthe maximum flow occurring during a 15-minute period for any 12-month periodand is determined by multiplying average daily flow by an appropriate factor.Estimates of this factor range from 4.0 to 5.5 for design populations of onethousand, to a factor of 1.5 to 2.0 for design population of one million. Tables 1and 2 list minimum peak loads used by some municipalities as a basis for design.

Minimum Flow. A minimum velocity of 2 feet per second, when the pipe isflowing full or half full, will prevent deposition of solids. The design should bechecked using the minimum flow to determine if this self-cleaning velocity ismaintained.

SELECTION OF PIPE SIZEAfter the design flows have been calculated, pipe size is selected using

Manning’s formula. The formula can be solved by selecting a pipe roughnesscoefficient, and assuming a pipe size and slope. However, this trial and errormethod is not necessary since nomographs, tables, graphs and computerprograms provide a direct solution.

Manning’s Formula. Manning’s formula for selecting pipe size is:

Q = AR S (1)1.486 2/3 1/2n

A constant C1 = AR1.486 2/3n which depends only on the geometry and

characteristics of the pipe enables Manning’s formula to be written as:

Q = C1S (2)1/2

Tables 3, 4, 5 and 6 list full flow values of C1 for circular pipe, ellipticalpipe, arch pipe, and box sections. Table A-1 in the Appendix lists values ofS1/2.

Manning’s “n” Value. The difference between laboratory test values ofManning’s “n” and accepted design values is significant. Numerous tests by publicand other agencies have established Manning’s “n” laboratory values. However,these laboratory results were obtained utilizing clean water and straight pipesections without bends, manholes, debris, or other obstructions. The laboratoryresults indicated the only differences were between smooth wall and rough wallpipes. Rough wall, or corrugated pipe, have relatively high “n” values which areapproximately 2.5 to 3 times those of smooth wall pipe.

All smooth wall pipes, such as concrete and plastic, were found to have “n”values ranging between 0.009 and 0.010, but, historically, engineers familiar withsewers have used 0.012 and 0.013. This “design factor” of 20-30 percent takesinto account the difference between laboratory testing and actual installedconditions. The use of such design factors is good engineering practice, and, tobe consistent for all pipe materials, the applicable Manning’s “ ” laboratory value

Hydraulics of Sewers 5


should be increased a similar amount in order to arrive at design values.Full Flow Graphs. Graphical solutions of Manning’s formula are presented

for circular pipe in Figures 2 through 5 and for horizontal elliptical pipe, verticalelliptical pipe, arch pipe and box sections in Figures 6 through 19. When flow,slope and roughness coefficient are known, pipe size and the resulting velocity forfull flow can be determined.

Partially Full Flow Graphs. Velocity, hydraulic radius and quantity and areaof flow vary with the depth of flow. These values are proportionate to full flowvalues and for any depth of flow are plotted for circular pipe, horizontal ellipticalpipe, vertical elliptical pipe, arch pipe, and box sections in Figures 20 through 24.

DETERMINATION OF FLOW VELOCITYMinimum Velocity. Slopes required to maintain a velocity of 2 feet per

second under full flow conditions with various “n” values are listed in Table 7 forcircular pipe. The slopes required to maintain velocities other than 2 feet persecond under full flow conditions can be obtained by multiplying the tabulatedvalues by one-fourth of the velocity squared or by solving Manning’s formula usingFigures 2 through 19.

Maximum Velocity. Maximum design velocities for clear effluent in concretepipe can be very high. Unless governed by topography or other restrictions, pipeslopes should be set as flat as possible to reduce excavation costs andconsequently velocities are held close to the minimum.

STORM SEWERS

DETERMINATION OF SEWER SYSTEM TYPEStorm sewers are designed to carry precipitation runoff, surface waters and,

in some instances, ground water. Storm water flow is analyzed on the basis ofhaving the flow characteristics of water.

DETERMINATION OF DESIGN FLOWThe Rational Method is widely used for determining design flows in urban and

small watersheds. The method assumes that the maximum rate of runoff for agiven intensity occurs when the duration of the storm is such that all parts of thewatershed are contributing to the runoff at the interception point. The formula usedis an empirical equation that relates the quantity of runoff from a given area to thetotal rainfall falling at a uniform rate on the same area and is expressed as:

Q = CiA (3)The runoff coefficient “C” and the drainage area “A” are both constant for a

given area at a given time. Rainfall intensity “ i “, however, is determined by usingan appropriate storm frequency and duration which are selected on the basis ofeconomics and engineering judgment. Storm sewers are designed on the basisthat they will flow full during storms occurring at certain intervals. Storm frequencyis selected through consideration of the size of drainage area, probable flooding,



possible flood damage and projected development schedule for the area.Runoff Coefficient. The runoff coefficient “C” is the ratio of the average rate

of rainfall on an area to the maximum rate of runoff. Normally ranging betweenzero and unity, the runoff coefficient can exceed unity in those areas where rainfalloccurs in conjunction with melting snow or ice. The soil characteristics, such asporosity, permeability and whether or not it is frozen are important considerations.Another factor to consider is ground cover, such as paved, grassy or wooded. Incertain areas, the coefficient depends upon the slope of the terrain. Duration ofrainfall and shape of area are also important factors in special instances. Averagevalues for different areas are listed in Table 8.

Rainfall Intensity. Rainfall intensity “ i “ is the amount of rainfall measured ininches per hour that would be expected to occur during a storm of a certainduration. The storm frequency is the time in years in which a certain storm wouldbe expected again and is determined statistically from available rainfall data.

Several sources, such as the U. S. Weather Bureau, have published tablesand graphs for various areas of the country which show the relationship betweenrainfall intensity, storm duration and storm frequency. To illustrate theserelationships, the subsequent figures and tables are presented as examples only,and specific design information is available for most areas. For a 2-year frequencystorm of 30-minute duration, the expected rainfall intensities for the United Statesare plotted on the map in Figure 25. These intensities could be converted tostorms of other durations and frequencies by using factors as listed in Tables 9and 10 and an intensity-duration-frequency curve constructed as shown in Figure26.

Time of Concentration. The time of concentration at any point in a sewersystem is the time required for runoff from the most remote portion of the drainagearea to reach that point. The most remote portion provides the longest time ofconcentration but is not necessarily the most distant point in the drainage area.Since a basic assumption of the Rational Method is that all portions of the areaare contributing runoff, the time of concentration is used as the storm duration incalculating the intensity. The time of concentration consists of the time of flow fromthe most remote portion of the drainage area to the first inlet (called the inlet time)and the time of flow from the inlet through the system to the point underconsideration (called the flow time). The inlet time is affected by the rainfallintensity, topography and ground conditions. Many designers use inlet timesranging from a minimum of 5 minutes for densely developed areas with closelyspaced inlets to a maximum of 30 minutes for flat residential areas with widelyspaced inlets. If the inlet time exceeds 30 minutes, then a detailed analysis isrequired because a very small inlet time will result in an overdesigned systemwhile conversely for a very long inlet time the system will be underdesigned.

Runoff Area. The runoff area “A” is the drainage area in acres served by thestorm sewer. This area can be accurately determined from topographic maps orfield surveys.



SELECTION OF PIPE SIZEManning’s Formula. Manning’s formula for selecting pipe size is:

Q = AR S (1)1.486 2/3 1/2n

A constant C1 = AR1.486 2/3n which depends only on the geometry and

characteristics of the pipe enables Manning’s formula to be written as:

Q = C1S (2)1/2

Tables 3, 4, 5 and 6 for circular pipe, elliptical pipe, arch pipe, and boxsections with full flow and Table A-1 in the Appendix for values of C1 and S1/2

respectively are used to solve formula (2). Graphical solutions of Manning’sformula (1) are presented in Figures 2 through 5 for circular pipe, and Figures 6through 19 for horizontal elliptical pipe, vertical elliptical pipe, arch pipe and boxsections under full flow conditions.

Partial flow problems can be solved with the proportionate relationshipsplotted in Figure 20 through 24.

Manning’s “n” Value. The difference between laboratory test values ofManning’s “n” and accepted design values is significant. Numerous tests by publicand other agencies have established Manning’s “n” laboratory values. However,these laboratory results were obtained utilizing clean water and straight pipesections without bends, manholes, debris, or other obstructions. The laboratoryresults indicated the only differences were between smooth wall and rough wallpipes. Rough wall, or corrugated pipe, have relatively high “n” values which areapproximately 2.5 to 3 times those of smooth wall pipe.

All smooth wall pipes, such as concrete and plastic, were found to have “n”values ranging between 0.009 and 0.010, but, historically, engineers familiar withsewers have used 0.012 or 0.013. This “design factor” of 20-30 percent takes intoaccount the difference between laboratory testing and actual installed conditions.The use of such design factors is good engineering practice, and, to be consistentfor all pipe materials, the applicable Manning’s “n” laboratory value should beincreased a similar amount in order to arrive at design values.

DETERMINATION OF FLOW VELOCITYMinimum Velocity. The debris entering a storm sewer system will generally

have a higher specific gravity than sanitary sewage, therefore a minimum velocityof 3 feet per second is usually specified. The pipe slopes required to maintain thisvelocity can be calculated from Table 7 or by solving Manning’s formula usingFigures 2 through 19.

Maximum Velocity. Tests have indicated that concrete pipe can carry clearwater of extremely high velocities without eroding. Actual performance records ofstorm sewers on grades up to 45 percent and carrying high percentages of solidsindicate that erosion is seldom a problem with concrete pipe.



EXAMPLE PROBLEMSEXAMPLE 2 - 1

STORM SEWER FLOW

Given: The inside diameter of a circular concrete pipe storm sewer is 48inches, “n” = 0.012 and slope is 0.006 feet per foot.

Find: The full flow capacity, “Q”.

Solution: The problem can be solved using Figure 4 or Table 3.

Figure 4 The slope for the sewer is 0.006 feet per foot or 0.60 feet per 100 feet.Find this slope on the horizontal axis. Proceed verticaly along the 0.60line to the intersection of this line and the curve labelled 48 inches.Proceed horizontally to the vertical axis and read Q = 121 cubic feet persecond.

Table 3 Enter Table 3 under the column n = 0.012 for a 48-inch diameter pipeand find C1, = 1556. For S = 0.006, find S1/2 = 0.07746 in Table A-1.Then Q = 1556 X 0.07746 or 121 cubic feet per second.

Answer: Q = 121 cubic feet per second..

EXAMPLE 2 - 2REQUIRED SANITARY SEWER SIZE

Given: A concrete pipe sanitary sewer with “n” = 0.013, slope of 0.6 percentand required full flow capacity of 110 cubic feet per second.

Find: Size of circular concrete pipe required.

Solution: This problem can be solved using Figure 5 or Table 3.

Figure 5 Find the intersection of a horizontal line through Q = 110 cubic feet persecond and a slope of 0.60 feet per 100 feet. The minimum size seweris 48 inches.

Table 3 For Q = 110 cubic feet per second and S1/2 = 0.07746

C1 = = = 1420 1100.07746

Q1/2S

In the table, 1436 is the closest value of C1, equal to or larger than1420, so the minimum size sewer is 48 inches.



Answer: A 48-inch diameter circular pipe would have more than adequatecapacity.

EXAMPLE 2 - 3STORM SEWER MINIMUM SLOPE

Given: A 48-inch diameter circular concrete pipe storm sewer, “n” = 0.012 andflowing one-third full.

Find: Slope required to maintain a minimum velocity of 3 feet per second.

Solution: Enter Figure 20 on the vertical scale at Depth of Flow = 0.33 and projecta horizontal line to the curved line representing velocity. On thehorizontal scale directly beneath the point of intersection read a value of0.81 which represents the proportional value to full flow.

= 0.81VVfull

0.81VVfull =

0.813 =

= 3.7

Enter Figure 4 and at the intersection of the line representing 48-inchdiameter and the interpolated velocity line of 3.7 read a slope of 0.088percent on the horizontal scale.

Answer: The slope required to maintain a minimum velocity of 3 feet per secondat one-third full is 0.088 percent.

EXAMPLE 2 - 4SANITARY SEWER DESIGN

General: A multi-family housing project is being developed on 350 acres of rollingto flat ground. Zoning regulations establish a population density of 30persons per acre. The state Department of Health specifies 100 gallonsper capita per day as the average and 500 gallons per capita per day asthe peak domestic sewage flow, and an infiltration allowance of 500gallons per acre per day.

Circular concrete pipe will be used, “n”= 0.013, designed to flow full atpeak load with a minimum velocity of 2 feet per second at one-thirdpeak flow. Maximum spacing between manholes will be 400 feet.



Given: Population Density = 30 persons per acreAverage Flow = 100 gallons per capita per dayPeak Flow = 500 gallons per capita per dayInfiltration = 500 gallons per acre per dayManning’s Roughness = 0.0 13 (See discussion of Manning’s

Coefficient “n” Value)Minimum Velocity = 2 feet per second @ 1/3 peak flow

Find: Design the final 400 feet of pipe between manhole Nos. 20 and 21,which serves 58 acres in addition to carrying the load from the previouspipe which serves the remaining 292 acres.

Solution: 1. Design Flow

Population-Manhole 1 to 20 = 30 X 292 = 8760Population-Manhole 20 to 21 = 30 X 58 = 1740Total population 10,500 personsPeak flow-Manhole

1 to 20 = 500 X 8760 = 4,380,000 gallons per dayInfiltration-Manhole

1 to 20 - 500 X 292 = 146,000 gallons per dayPeak flow-Manhole

20 to 21 = 500 X 1740 = 870,000 gallons per dayInfiltration-Manhole

20 to 21 = 500 X 58 = 29,000 gallons per day

Total Peak flow = 5,425,000 gallons per dayuse 5,425,000 gallons per day or 8.4 cubic feet per second

2. Selection of Pipe Size

In designing the sewer system, selection of pipe begins at the firstmanhole and proceeds downstream. The section of pipe preceding thefinal section is an 18-inch diameter, with slope = 0.0045 feet per foot.Therefore, for the final section the same pipe size will be checked andused unless it has inadequate capacity, excessive slope or inadequatevelocity.

Enter Figure 5, from Q = 8.4 cubic feet per second on the vertical scaleproject a horizontal line to the 18-inch diameter pipe, read velocity = 4.7feet per second.

From the intersection, project a vertical line to the horizontal scale, readslope = 0.63 feet per 100 feet.



3. Partial Flow

Enter Figure 20, from Proportion of Value for Full Flow = 0.33 on thehorizontal scale project a line vertically to “flow” curve, from intersectionproject a line horizontally to “velocity” curve, from intersection project aline vertically to horizontal scale, read Proportion of Value for Full Flow -0.83.

Velocity at minimum flow = 0.83 X 4.7 = 3.9 feet per second.

Answer: Use 18-inch diameter concrete pipe with slope of 0.0063 feetper foot.

The preceding computations are summarized in the followingtabular forms, Illustrations 2.1 and 2.2.

Illustration 2.1 - Population and Flow

Illustration 2.2 - Sanitary Sewer Design Data

EXAMPLE 2 - 5STORM SEWER DESIGN

General: A portion of the storm sewer system for the multi-family developmentis to serve a drainage area of about 30 acres. The state Departmentof Health specifies a 10-inch diameter minimum pipe size.

ManholeManhole SEWER Flow-line Elevations

Flow Length Slope Pipe Velocity FallNo. Sta. cfs ft. ft./ft. Dia. in. fps ft. In Out

19 46 7.0 389.51

20 50 8.4 400 0.0045 18 4.0 1.80 387.71 387.71

21 54 400 0.0063 18 4.7 2.52 385.19

DRAINAGE AREA PEAK-FLOW - MGD Cum.Manhole Ultimate Indus- Infil- Cum. Flow

No. Zoning Acres Population Domestic trial tration Total Total cfs.

19 From Preceeding Computations................................................................... 4.53 7.0

Multi-20 family 58 1740 .087 – 0.03 0.90 5.43 8.4

21 Trunk Sewer Interceptor Manhole



Circular concrete pipe will be used,”n” = 0.011, with a minimumvelocity of 3 feet per second when flowing full. Minimum time ofconcentration is 10 minutes with a maximum spacing betweenmanholes of 400 feet.

Given: Drainage Area A = 30 acres (total)Runoff Coefficient C = 0.40Rainfall Intensity i as shown in Figure 26Roughness Coefficient n = 0.0 11 (See discussion of Manning’s

“n” Value)Velocity V = 3.0 feet per second (minimum at

full flow)

Find: Design of the storm system as shown in Illustration 2.3, “Plan forStorm Sewer Example,” adapted from “Design and Construction ofConcrete Sewers,” published by the Portland Cement Association.

Solution: The hydraulic properties of the storm sewer will be entered as theyare determined on the example form Illustration 2.4, “ComputationSheet for Hydraulic Properties of Storm Sewer.” The design of thesystem begins at the upper manhole and proceeds downstream.

The areas contributing to each manhole are determined, enteredincrementally in column 4, and as cumulative totals in column 5. Theinitial inlet time of 10 minutes minimum is entered in column 6, line 1,and from Figure 26 the intensity is found to be 4.2 inches per hourwhich is entered in column 8, line 1. Solving the Rational formula,Q = 1.68 cubic feet per second is entered in column 9, line 1. EnterFigure 3, for V = 3 feet per second and Q = 1.68 cubic feet persecond, the 10-inch diameter pipe requires a slope = 0.39 feet per100 feet. Columns 10, 12, 13, 14, 15 and 16, line 1, are now filled in.The flow time from manhole 7 to 6 is found by dividing the length(300 feet) between manholes by the velocity of flow (3 feet persecond) and converting the answers to minutes (1.7 minutes) whichis entered in column 7, line 1. This time increment is added to the10-minute time of concentration for manhole 7 to arrive at 11.7minutes time of concentration for manhole 6 which is entered incolumn 6, line 2.From Figure 26, the intensity is found to be 4.0 inches per hour for atime of concentration of 11.7 minutes which is entered in column 8,line 2. The procedure outlined in the preceding paragraph is repeatedfor each section of sewer as shown in the table.

Answer: The design pipe sizes, slopes and other properties are as indicated inIllustration 2.4.



Illustration 2.3-Plan for Storm Sewer Example

Illustration 2.4-Computation Sheet for Hydraulic Properties of Storm Sewer

EXAMPLE 2 - 6SANITARY SEWER DESIGN

Given: A concrete box section sanitary sewer with “n” = 0.013, slope of 1.0%and required full flow capacity of 250 cubic feet per second.

204

204

206208

208

208

208

210

210

206

206

206

1

2

34567

BlackRiver

Flow

9.00 acres

300' 300' 300'300'

7.40 acres

3.18 acres2.96 acres

Franklin

Adams Street

Street

300'

Str

eet

250'

2nd

2.40 acres2.28 acres

1.0 acres

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 Adams 7 6 1.00 1.00 10.0 1.7 4.2 1.68 0.39 10 1.7 3.0 300 200.00 198.83

2 Adams 6 5 2.28 3.28 11.7 1.7 4.0 5.25 0.18 18 5.3 3.0 300 198.16 197.62

3 Adams 5 4 2.40 5.68 13.4 1.3 3.8 8.63 0.23 21 8.65 3.8 300 197.37 196.68

4 Adams 4 3 2.96 8.64 14.7 1.2 3.7 12.0 0.23 24 13.0 4.1 300 196.43 195.74

5 2nd 3 2 3.18 11.82 15.9 0.9 3.6 17.0 0.23 27 17.0 4.5 250 195.49 194.91

6 2nd 2 1 17.84 29.66 16.8 - 3.5 41.6 0.30 36 42.0 6.1 300 194.41 193.51

Line

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TRIBU- TIMESEWER TARY OF FLOW

LOCATION AREA (minutes) SEWER DESIGN PROFILE

Elevationof Invert



Find: Size of concrete box section required for full flow.

Solution: This problem can be solved using Figure 19 or Table 6.

Figure 19 Find the intersection of a horizontal line through Q = 250 cubic feetper second and a slope of 1.0 feet per 100 feet. The minimum sizebox section is either a 6 foot span by 4 foot rise or a 5 foot span by 5foot rise.

Table 6 For Q = 250 cubic feet per second and S1/2 = 0. 100

C1 = = = 2,5000.100250

1/2

QS

In Table 6, under the column headed n = 0.013, 3,338 is the first valueof C1, equal to or larger than 2,500, therefore a box section with a 5foot span X a 5 foot rise is adequate. Looking further in the samecolumn, a box section with a 6 foot span and a 4 foot rise is found tohave a C1, value of 3,096, therefore a 6 X 4 box section is alsoadequate.

Answer: Either a 5 foot X 5 foot or a 6 foot X 4 foot box section would have afull flow capacity equal to or greater than Q = 250 cubic feet persecond.

15

CHAPTER 3

HYDRAULICS OF CULVERTSThe hydraulic design procedure for culverts requires:

1. Determination of Design Flow2. Selection of Culvert Size3. Determination of Outlet Velocity

DETERMINATION OF DESIGN FLOWThe United States Geological Survey has developed a nationwide series of

water-supply papers titled the “Magnitude and Frequency of Floods in the UnitedStates.” These reports contain tables of maximum known floods and charts forestimating the probable magnitude of floods of frequencies ranging from 1. 1 to 50years. Table 11 indicates the Geological Survey regions, USGS district andprincipal field offices and the applicable water-supply paper numbers. Most stateshave adapted and consolidated those parts of the water-supply papers whichpertain to specific hydrologic areas within the particular state. The hydrologicdesign procedures developed by the various states enable quick and accuratedetermination of design flow. It is recommended that the culvert design flow bedetermined by methods based on USGS data.

If USGS data are not available for a particular culvert location, flow quantitiesmay be determined by the Rational Method or by statistical methods usingrecords of flow and runoff. An example of the latter method is a nomographdeveloped by California and shown in Figure 27.

FACTORS AFFECTING CULVERT DISCHARGEFactors affecting culvert discharge are depicted on the culvert cross section

shown in Illustration 3.1 and are used in determining the type of discharge control.Inlet Control. The control section is located at or near the culvert entrance,

and, for any given shape and size of culvert, the discharge is dependent only onthe inlet geometry and headwater depth. Inlet control will exist as long as watercan flow through the barrel of the culvert at a greater rate than water can enter theinlet. Since the control section is at the inlet, the capacity is not affected by anyhydraulic factors beyond the culvert entrance such as slope, length or surfaceroughness. Culverts operating under inlet control will always flow partially full.



Illustration 3.1 - Factors Affecting Culvert DischargeD = Inside diameter for circular pipe

HW = Headwater depth at culvert entranceL = Length of culvertn = Surface roughness of the pipe wall, usually expressed in terms of

Manning’s nSo = Slope of the culvert pipe

TW = Tailwater depth at culvert outlet

Outlet Control. The control section is located at or near the culvert outlet andfor any given shape and size of culvert, the discharge is dependent on all of thehydraulic factors upstream from the outlet such as shape, slope, length, surfaceroughness, tailwater depth, headwater depth and inlet geometry. Outlet control willexist as long as water can enter the culvert at a greater rate than water can flowthrough it. Culverts operating under outlet control can flow either full or partiallyfull.

Critical Depth. Critical flow occurs when the sum of the kinetic energy(velocity head) plus the potential energy (static or depth head equal to the depthof the flow) for a given discharge is at a minimum. Conversely, the dischargethrough a pipe with a given total energy head will be maximum at critical flow. Thedepth of the flow at this point is defined as critical depth, and the slope required toproduce the flow is defined as critical slope. Capacity of a culvert with anunsubmerged outlet will be established at the point where critical flow occurs.Since under inlet control, the discharge of the culvert is not reduced by as manyhydraulic factors as under outlet control, for a given energy head, a culvert willhave maximum possible discharge if it is operating at critical flow with inlet control.The energy head at the inlet control section is approximately equal to the head atthe inlet minus entrance losses. Discharge is not limited by culvert roughness oroutlet conditions but is dependent only on the shape and size of the culvertentrance. Although the discharge of a culvert operating with inlet control is notrelated to the pipe roughness, the roughness does determine the minimum slope(critical slope) at which inlet control will occur. Pipe with a smooth interior can beinstalled on a very flat slope and still have inlet control. Pipe with a rough interiormust be installed on a much steeper slope to have inlet control. Charts of criticaldepth for various pipe and box section sizes and flows are shown in Figures 28through 32.

D

HW

So n

TW

L

InletGeometry

Hydraulics of Culverts 17


SELECTION OF CULVERT SIZEThe many hydraulic design procedures available for determining the

required size of a culvert vary from empirical formulas to a comprehensivemathematical analysis. Most empirical formulas, while easy to use, do not lendthemselves to proper evaluation of all the factors that affect the flow of waterthrough a culvert. The mathematical solution, while giving precise results, is timeconsuming. A systematic and simple design procedure for the proper selection ofa culvert size is provided by Hydraulic Engineering Circular No. 5, “HydraulicCharts for the Selection of Highway Culverts” and No. 10, “Capacity Charts for theHydraulic Design of Highway Culverts,” developed by the Bureau of Public Roads.The procedure when selecting a culvert is to determine the headwater depth fromthe charts for both assumed inlet and outlet controls. The solution which yields thehigher headwater depth indicates the governing control. When this procedure isfollowed, Inlet Control Nomographs, Figures 33 through 37, and Outlet ControlNomographs, Figures 38 through 41, are used.

An alternative and simpler method is to use the Culvert Capacity Charts,Figures 42 through 145. These charts are based on the data given in CircularNo. 5 and enable the hydraulic solution to be obtained directly without using thedouble solution for both inlet and outlet control required when the nomographs areused.

Culvert Capacity Chart Procedure. The Culvert Capacity Charts are aconvenient tool for selection of pipe sizes when the culvert is installed withconditions as indicated on the charts. The nomographs must be used for othershapes, roughness coefficients, inlet conditions or submerged outlets.

List Design DataA. Design discharge Q, in cubic feet per second, with average return period

(i.e., Q25 or Q50, etc.).B. Approximate length L of culvert, in feet.C. Slope of culvert.D. Allowable headwater depth, in feet, which is the vertical distance from the

culvert invert (flow line) at the entrance to the water surface elevationpermissible in the headwater pool or approach channel upstream from theculvert.

E. Mean and maximum flood velocities in natural stream.F. Type of culvert for first trial selection, including barrel cross sectional

shape and entrance type.

Select Culvert SizeA. Select the appropriate capacity chart, Figures 42 to 145, for the culvert

size approximately equal to the allowable headwater depth divided by 2.0.B. Project a vertical line from the design discharge Q to the inlet control

curve. From this intersection project a line horizontally and read theheadwater depth on the vertical scale. If this headwater depth is more



than the allowable, try the next larger size pipe. If the headwater depth isless than the allowable, check the outlet control curves.

C. Extend the vertical line from the design discharge to the outlet controlcurve representing the length of the culvert. From this intersection projecta line horizontally and read the headwater depth plus SoL on the verticalscale. Subtract SoL from the outlet control value to obtain the headwaterdepth. If the headwater depth is more than the allowable, try the nextlarger size pipe. If the headwater depth is less than the allowable, checkthe next smaller pipe size following the same procedure for both inletcontrol and outlet control.

D. Compare the headwater depths for inlet and outlet control. The higherheadwater depth indicates the governing control.

Determine Outlet VelocityA. If outlet control governs, the outlet velocity equals the flow quantity divided

by the flow cross sectional area at the outlet. Depending upon thetailwater conditions, this flow area will be between that corresponding tocritical depth and the full area of the pipe. If the outlet is not submerged, itis usually sufficiently accurate to calculate the flow area based on a depthof flow equal to the average of the critical depth and the vertical height ofthe pipe.

B. If inlet control governs, the outlet velocity may be approximated byManning’s formula using Figures 2 through 19 for full flow values andFigures 20 through 24 for partial flow values.

Record SelectionRecord final selection of culvert with size, type, required headwater andoutlet velocity.

Nomograph Procedure. The nomograph procedure is used for selection ofculverts with entrance conditions other than projecting or for submerged outlets.

List Design DataA. Design discharge Q, in cubic feet per second, with average return period

(i.e., Q25 or Q,50, etc.).B. Approximate length L of culvert, in feet.C. Slope of culvert.D. Allowable headwater depth, in feet, which is the vertical distance from the

culvert invert (flow line) at the entrance to the water surface elevationpermissible in the headwater pool or approach channel upstream from theculvert.

E. Mean and maximum flood velocities in natural stream.F. Type of culvert for first trial selection, including barrel cross sectional

shape and entrance type.



Select Trial Culvert SizeSelect a trial culvert with a rise or diameter equal to the allowableheadwater divided by 2.0.

Find Headwater Depth for Trial CulvertA. Inlet Control

(1) Given Q, size and type of culvert, use appropriate inlet controlnomograph Figures 33 through 37 to find headwater depth:(a) Connect with a straightedge the given culvert diameter or height

(D) and the discharge Q; mark intersection of straightedge onHW/D scale marked (1).

(b) HW/D scale marked (1) represents entrance type used, read HW/Don scale (1). If another of the three entrance types listed on thenomograph is used, extend the point of intersection in (a)horizontally to scale (2) or (3) and read HW/D.

(c) Compute HW by multiplying HW/D by D.(2) If HW is greater or less than allowable, try another trial size until HW is

acceptable for inlet control.

B. Outlet Control(1) Given Q, size and type of culvert and estimated depth of tailwater TW,

in feet, above the invert at the outlet for the design flood condition inthe outlet channel:(a) Locate appropriate outlet control nomograph (Figures 38 through

41) for type of culvert selected. Find ke, for entrance type fromTable 12.

(b) Begin nomograph solution by locating starting point on length scalefor proper ke.

(c) Using a straightedge, connect point on length scale to size ofculvert barrel and mark the point of crossing on the “turning line.”

(d) Pivot the straightedge on this point on the turning line and connectgiven discharge rate. Read head in feet on the head (H) scale.

(2) For tailwater TW elevation equal to or greater than the top of theculvert at the outlet set ho equal to TW and find HW by the followingequation:

HW = H + ho - SoL (3)

(3) For tailwater TW elevations less than the top of the culvert at the

outlet, use ho = dc + D

2 or TW, whichever is the greater, where dc, the

critical depth in feet is determined from the appropriate critical depthchart (Figures 28 through 32).



C. Compare the headwaters found in paragraphs A (Inlet Control) and B(Outlet Control). The higher headwater governs and indicates the flowcontrol existing under the given conditions for the trial size selected.

D. If outlet control governs and the HW is higher than acceptable, select alarger trial size and find HW as instructed under paragraph B. Inlet controlneed not be checked, if the smaller size was satisfactory for this control asdetermined under paragraph A.

Try Another CulvertTry a culvert of another size or shape and repeat the above procedure.

Determine Outlet VelocityA. If outlet control governs, the outlet velocity equals the flow quantity divided

by the flow cross sectional area at the outlet. Depending upon thetailwater conditions, this flow area will be between that corresponding tocritical depth and the full area of the pipe. If the outlet is not submerged, itis sufficiently accurate to calculate flow area based on a depth of flowequal to the average of the critical depth and vertical height of the pipe.

B. If inlet control governs, the outlet velocity may be approximated byManning’s formula using Figures 2 through 19 for full flow values andFigures 20 through 24 for partial flow values.

Record SelectionRecord final selection of culvert with size, type, required headwater andoutlet velocity.

EXAMPLE PROBLEMSEXAMPLE 3 - I

CULVERT CAPACITY CHART PROCEDURE

List Design DataA. Q25 = 180 cubic feet per second

Q50 = 225 cubic feet per secondB. L = 200 feetC. So = 0.01 feet per footD. Allowable HW = 10 feet for 25 and 50-year stormsE. TW = 3.5 feet for 25-year storm

TW = 4.0 feet for 50-year stormF. Circular concrete culvert with a projecting entrance, n = 0.0 12

Select Culvert Size

A. Try D = =HW2.0

102.0 = 5 feet or 60 inch diameter as first trial size.

B. In Figure 54, project a vertical line from Q = 180 cubic feet per second



to the inlet control curve and read horizontally HW = 6.2. Since HW =6.2 is considerably less than the allowable try a 54 inch diameter.In Figure 53, project a vertical line from Q = 180 cubic feet per secondto the inlet control curve and read horizontally HW = 7.2 feet.In Figure 53, project a vertical line from Q = 225 cubic feet per secondto the inlet control curve and read horizontally HW = 9.6 feet.

C. In Figure 53, extend the vertical line from Q = 180 cubic feet persecond to the L = 200 feet outlet control curve and read horizontallyHW + SoL = 8.0 feet.In Figure 53, extend the vertical line from Q = 225 cubic feet persecond to the L = 200 feet outlet control curve and read horizontallyHW + SoL = 10.2 feet.SoL = 0.01 X 200 = 2.0 feet.Therefore HW = 8.0 - 2.0 = 6.0 feet for 25-year storm

HW = 10.2 - 2.0 = 8.2 feet for 50-year stormD. Since the calculated HW for inlet control exceeds the calculated HW

for outlet control in both cases, inlet control governs for both the 25and 50-year storm flows.

Determine Outlet VelocityB. Enter Figure 4 on the horizontal scale at a pipe slope of 0.01 feet per

foot (1.0 feet per 100 feet). Project a vertical line to the linerepresenting 54-inch pipe diameter. Read a full flow value of 210 cubicfeet per second on the vertical scale and a full flow velocity of 13.5 feet

per second. Calculate = = 1.07.Q50

QFull

225210

Enter Figure 20 at 1.07 on the horizontal scale and project a verticalline to the “flow” curve. At this intersection project a horizontal line tothe “velocity” curve. Directly beneath this intersection read

V50

VFull = 1.12 on the horizontal scale. Calculate V50 = 1.12 VFull = 1.12 X

13.5 = 15.1 feet per second.

Record SelectionUse a 54-inch diameter concrete pipe with allowable HW = 10.0 feet andactual HW = 7.2 and 9.6 feet respectively for the 25 and 50 year stormflows, and a maximum outlet velocity of 15.1 feet per second.



EXAMPLE 3 - 2NOMOGRAPH PROCEDURE

List Design DataA. Q25 = 180 cubic feet per second

Q50 = 225 cubic feet per secondB. L = 200 feetC. So = 0.01 feet per footD. Allowable HW = 10 feet for 25 and 50-year stormsE. TW = 3.5 feet for 25-year storm

TW = 4.0 feet for 50-year stormF. Circular concrete culvert with a projecting entrance, n = 0.012

Select Trial Culvert Size

D = = = 5 feetHW2.0

102.0

Determine Trial Culvert Headwater DepthA. Inlet Control

(1) For Q = 180 cubic feet per second and D = 60 inches, Figure 33indicates HW/D = 1.25. Therefore HW = 1.25 X 5 =6.2 feet.

(2) Since HW = 6.2 feet is considerably less than allowable try a 54-inch pipe.For Q = 180 cubic feet per second and D = 54 inches, Figure 33indicates HW/D = 1.6. Therefore HW = 1.6 X 4.5 = 7.2 feet.For Q = 225 cubic feet per second and D = 54 inches, Figure 33indicates HW/D = 2.14. Therefore HW 2.14 X 4.5 = 9.6 feet.

B. Outlet Control(I) TW = 3.5 and 4.0 feet is less than D = 4.5 feet.(3) Table 12, ke, = 0.2.

For D = 54 inches, Q = 180 cubic feet per second, Figure 28indicates dc, 3.9 feet which is less than D = 4.5 feet. Calculate

ho = = = 4.2 feet.dc + D

23.9 + 4.5

2

For D = 54 inches, Q = 180 cubic feet per second, ke. = 0.2 and L =200 feet.Figure 38 indicates H = 3.8 feet.Therefore HW = 3.8 + 4.2 - (0.01 X 200) = 6.0 feet (Equation 3).For D = 54 inches, Q = 225 cubic feet per second, Figure 28indicates dc, = 4.2 feet which is less than D = 4.5 feet. Calculate

ho = = = 4.3 feet.dc + D

24.2 + 4.5

2



For D = 54 inches, Q = 225 cubic feet per second, ke, = 0.2 and L =200 feet.Figure 38 indicates H = 5.9 feet.Therefore HW = 5.9 + 4.3 - (0.01 X 200) = 8.2 feet (Equation 3).

C. Inlet control governs for both the 25 and 50-year design flows.

Try Another CulvertA 48-inch culvert would be sufficient for the 25-year storm flow but for the50-year storm flow the HW would be greater than the allowable.

Determine Outlet VelocityB. Enter Figure 4 on the horizontal scale at a pipe slope of 0.01 feet per

foot (1.0 feet per 100 feet). Project a vertical line to the linerepresenting 54-inch pipe diameter. Read a full flow value of 210 cubicfeet per second on the vertical scale and a full flow velocity of 13.5 feetper second. Calculate

= = 1.07.Q50

QFull

225210

Enter Figure 20 at 1.07 on the horizontal scale and project a verticalline to the “flow” curve. At this intersection project a horizontal line tothe “velocity” curve. Directly beneath this intersection read

V50

VFull = 1.12 on the horizontal scale. Calculate V50 = 1.12 VFull = 1.12 X

13.5 = 15.1 feet per second.

Record SelectionUse a 54-inch diameter concrete pipe with allowable HW = 10.0 feet andactual HW = 7.2 and 9.6 feet respectively for the 25 and 50-year stormflows, and a maximum outlet velocity of 15.1 feet per second.

EXAMPLE 3 - 3CULVERT DESIGN

General: A highway is to be constructed on embankment over a creekdraining 400 acres. The embankment will be 41-feet high with 2:1side slopes and a top width of 80 feet. Hydraulic design criteriarequires a circular concrete pipe, n = 0.012, with the inlet projectingfrom the fill. To prevent flooding of upstream properties, theallowable headwater is 10.0 feet, and the design storm frequency is25 years.

Given: Drainage Area A = 400 acresRoughness Coefficient n = 0.012 (See discussion of Manning’s

“n” Value)Headwater HW = 10 feet (allowable)



Find: The required culvert size.

Solution: 1. Design FlowThe design flow for 400 acres should be obtained using USGSdata. Rather than present an analysis for a specific area, thedesign flow will be assumed as 250 cubic feet per second for a25-year storm.

2. Selection of Culvert SizeThe culvert will be set on the natural creek bed which has a onepercent slope. A cross sectional sketch of the culvert andembankment indicates a culvert length of about 250 feet. Noflooding of the outlet is expected.

Trial diameter HW/D = 2.0 feet D = = 5 feet. 102

Enter Figure 54, from Q = 250 cubic feet per second project aline vertically to the inlet control curve, read HW = 8.8 feet on thevertical scale. Extend the vertical line to the outlet control curvefor L = 250 feet, read H + SoL = 9.6 on the vertical scale. SoL =250 X 0.01 = 2.5 feet. Therefore, outlet control HW = 9.6 - 2.5 =7.1 feet and inlet control governs.Enter Figure 53, from Q = 250 cubic feet per second project aline vertically to the inlet control curve, read HW = 10.8 feetwhich is greater than the allowable.

3. Determine Outlet VelocityFor inlet control, the outlet velocity is determined from Manning’sformula. Entering Figure 4, a 60-inch diameter pipe with So = 1.0foot per 100 feet will have a velocity = 14.1 feet per secondflowing full and a capacity of 280 cubic feet per second.Enter Figure 20 with a Proportion of Value for Full Flow =

250280 or 0.9, read Depth of Flow = 0.74 and

Velocity Proportion = 1.13. Therefore, outlet velocity = 1.13 X14.1 = 15.9 feet per second.

Answer: A 60-inch diameter circular pipe would be required.

EXAMPLE 3 - 4CULVERT DESIGN

General: An 800-foot long box culvert with an n = 0.012 is to be installed ona 0.5% slope. Because utility lines are to be installed in theembankment above the box culvert, the maximum rise is limited to



8 feet. The box section is required to carry a maximum flow of1,000 cubic feet per second with an allowable headwater depth of15 feet.

List Design DataA. Q = 1,000 cubic feet per secondB. L = 800 feetC. So = 0.5% = 0.005 feet per footD. Allowable HW = 15 feetE. Box culvert with projecting entrance and n = 0.012

Select Culvert SizeInspecting the box section culvert capacity charts for boxes with riseequal to or less than 8 feet, it is found that a 8 X 8 foot and a 9 X 7 footbox section will all discharge 1,000 cubic feet per second with aheadwater depth equal to or less than 15 feet under inlet control.Therefore, each of the two sizes will be investigated.

Determine Headwater Depth8 X 8 foot Box SectionA. Inlet Control

Enter Figure 124, from Q = 1,000 project a vertical line to the inletcontrol curve. Project horizontally to the vertical scale and read aheadwater depth of 14.8 feet for inlet control.

B. Outlet ControlContinue vertical projection from Q = 1,000 to the outlet control curvefor L = 800 feet. Project horizontally to vertical scale and read a valuefor (HW + SoL) = 17.5 feet. Then HW = 17.5 - SoL = 17.5 - (0.005 X800) = 13.5 feet for outlet control.

Therefore inlet control governs.

9 X 7 - foot Box SectionEntering Figure 127, and proceeding in a similar manner, find aheadwater depth of 14.7 for inlet control and 13.1 feet for outlet controlwith inlet control governing.

Determine Outlet VelocityEntering Table 6, find area and C1, value for each size box section andTable A-1 find value of S1/2 for So, = 0.005, then Qfull = C1S1/2.

For 8 X 8 - foot Box SectionQfull = 12700 X 0.07071 = 898 cubic feet per secondVfull = Q/A = 899 ÷ 63.11 = 14.2 feet per second.



Then

= = 1.11.Qpartial

Qfull

1000899

Entering Figure 24.9 on the horizontal scale at 1.11, project a verticalline to intersect the flow curve. From this point, proceed horizontally tothe right and intersect the velocity curve. From this point drop verticallyto the horizontal scale and read a value of 1.18 for Vpartial/Vfull ratio.

ThenVpartial = 1.18 X 14.2 = 16.8 feet per second

Proceeding in a similar manner for the 9 X 7 foot box section, Figure24.7, find a Vpartial = 16.9 feet per second.

Record SelectionUse either a 8 X 8 foot box section with an actual HW of 14.8 feetand an outlet velocity of 16.8 feet per second or a 9 X 7 foot boxsection with an actual HW of 14.7 feet and an outlet velocity of 16.9feet per second.

27

CHAPTER 4

LOADS AND SUPPORTINGSTRENGTHS

The design procedure for the selection of pipe strength requires:

I . Determination of Earth Load2. Determination of Live Load3. Selection of Bedding4. Determination of Bedding Factor5. Application of Factor of Safety6. Selection of Pipe Strength

TYPES OF INSTALLATIONSThe earth load transmitted to a pipe is largely dependent on the type of

installation. Three common types are Trench, Positive Projecting Embankment,and Negative Projecting Embankment. Pipelines are also installed by jacking ortunneling methods where deep installations are necessary or where conventionalopen excavation and backfill methods may not be feasible. The essential featuresof each of these installations are shown in Illustration 4.1.

Trench. This type of installation is normally used in the construction ofsewers, drains and water mains. The pipe is installed in a relatively narrow trenchexcavated in undisturbed soil and then covered with backfill extending to theground surface.

Positive Projecting Embankment. This type of installation is normally usedwhen the culvert is installed in a relatively flat stream bed or drainage path. Thepipe is installed on the original ground or compacted fill and then covered by anearth fill or embankment.

Negative Projecting Embankment. This type of installation is normally usedwhen the culvert is installed in a relatively narrow and deep stream bed ordrainage path. The pipe is installed in a shallow trench of such depth that the topof the pipe is below the natural ground surface or compacted fill and then coveredwith an earth fill or embankment which extends above the original ground level.

Jacked or Tunneled. This type of installation is used where surfaceconditions make it difficult to install the pipe by conventional open excavation andbackfill methods, or where it is necessary to install the pipe under an existingembankment. A jacking pit is dug and the pipe is advanced horizontallyunderground.



Illustration 4.1 Essential Features of Types of Installations

Do

Bd

Do

Bt

H

Trench

GROUND SURFACE

GROUND SURFACETOP OF EMBANKMENT

TOP OF EMBANKMENT

Do

Bd

H

p'Bd

pBC

Negative ProjectingEmbankment

Jacked orTunneled

H

Do

Positive ProjectingEmbankment

H

Loads and Supporting Strengths 29


BACKGROUNDThe classic theory of earth loads on buried concrete pipe, published in 1930

by A. Marston, was developed for trench and embankment conditions.In later work published in 1933, M. G. Spangler presented three bedding

configurations and the concept of a bedding factor to relate the supportingstrength of buried pipe to the strength obtained in a three-edge bearing test.

Spangler’s theory proposed that the bedding factor for a particular pipelineand, consequently, the supporting strength of the buried pipe, is dependent on twoinstallation characteristics:

1. Width and quality of contact between the pipe and bedding.2. Magnitude of lateral pressure and the portion of the vertical height of the

pipe over which it acts.For the embankment condition, Spangler developed a general equation for

the bedding factor, which partially included the effects of lateral pressure. For thetrench condition, Spangler established conservative fixed bedding factors, whichneglected the effects of lateral pressure, for each of the three beddings. Thisseparate development of bedding factors for trench and embankment conditionsresulted in the belief that lateral pressure becomes effective only at trench widthsequal to or greater than the transition width. Such an assumption is notcompatible with current engineering concepts and construction methods. It isreasonable to expect some lateral pressure to be effective at trench widths lessthan transition widths. Although conservative designs based on the work ofMarston and Spangler have been developed and installed successfully for years,the design concepts have their limitations when applied to real world installations.

The limitations include:• Loads considered acting only at the top of the pipe.• Axial thrust not considered.• Bedding width of test installations less than width designated in his bedding

configurations.• Standard beddings developed to fit assumed theories for soil support rather

than ease of and methods of construction.• Bedding materials and compaction levels not adequately defined.This section discusses the Standard Installations and the appropriate indirect

design procedures to be used with them. The Standard Installations are the mostrecent beddings developed by ACPA to allow the engineer to take into considerationmodern installation techniques when designing concrete pipe. For more informationon design using the Marston/Spangler beddings, see Appendix B.

INTRODUCTIONIn 1970, ACPA began a long-range research program on the interaction of

buried concrete pipe and soil. The research resulted in the comprehensive finiteelement computer program SPIDA, Soil-Pipe Interaction Design and Analysis, forthe direct design of buried concrete pipe.

Since the early 1980’s, SPIDA has been used for a variety of studies,including the development of four new Standard Installations, and a simplifiedmicrocomputer design program, SIDD, Standard Installations Direct Design.

The procedure presented here replaces the historical A, B, C, and Dbeddings used in the indirect design method and found in the appendix of thismanual, with the four new Standard Installations, and presents a state-of-the-art



method for determination of bedding factors for the Standard Installations. Pipeand installation terminology as used in the Standard Installations, and thisprocedure, is defined in Illustration 4.2.

Illustration 4.2 Pipe/Installation Terminology

FOUR STANDARD INSTALLATIONSThrough consultations with engineers and contractors, and with the results of

numerous SPIDA parameter studies, four new Standard Installations weredeveloped and are presented in Illustration 4.4. The SPIDA studies wereconducted for positive projection embankment conditions, which are the worst-case vertical load conditions for pipe, and which provide conservative results forother embankment and trench conditions.

The parameter studies confirmed ideas postulated from past experience andproved the following concepts:

• Loosely placed, uncompacted bedding directly under the invert of the pipesignificantly reduces stresses in the pipe.

• Soil in those portions of the bedding and haunch areas directly under thepipe is difficult to compact.

• The soil in the haunch area from the foundation to the pipe springlineprovides significant support to the pipe and reduces pipe stresses.

• Compaction level of the soil directly above the haunch, from the pipespringline to the top of the pipe grade level, has negligible effect on pipestresses. Compaction of the soil in this area is not necessary unlessrequired for pavement structures.

Do

Di

Invert

Bottom

Foundation(Existing Soil or Compacted Fill)

Bedding

OverfillH

Top

Crown

Haunch

Lower SideSpringline



• Installation materials and compaction levels below the springline have asignificant effect on pipe structural requirements.

The four Standard Installations provide an optimum range of soil-pipeinteraction characteristics. For the relatively high quality materials and highcompaction effort of a Type 1 Installation, a lower strength pipe is required.Conversely, a Type 4 Installation requires a higher strength pipe, because it wasdeveloped for conditions of little or no control over materials or compaction.

Generic soil types are designated in Illustration 4.5. The Unified SoilClassification System (USCS) and American Association of State Highway andTransportation Officials (AASHTO) soil classifications equivalent to the genericsoil types in the Standard Installations are also presented in Illustration 4.5.

Illustration 4.3 Standard Trench/Embankment Installation

The SPIDA design runs with the Standard Installations were made withmedium compaction of the bedding under the middle-third of the pipe, and withsome compaction of the overfill above the springline of the pipe. This middle-thirdarea under the pipe in the Standard Installations has been designated as looselyplaced, uncompacted material. The intent is to maintain a slightly yielding beddingunder the middle-third of the pipe so that the pipe may settle slightly into thebedding and achieve improved load distribution. Compactive efforts in the middle-third of the bedding with mechanical compactors is undesirable, and could

DoDo/6 (Min.)

Do (Min.)

Do/3

Di

Middle Bedding loosely placed uncompacted bedding except Type 4 Outer bedding materials

and compaction each side, same requirements as

haunch

Foundation

BeddingSee Illustrations 4.4 & 4.5

H

Haunch - SeeIllustration 4.4

Lower Side - SeeIllustration 4.4

Springline

Overfill SoilCategory I, II, III



Illustration 4.4 Standard Installations Soil and Minimum CompactionRequirements

Installation Bedding Haunch and Lower SideType Thickness Outer Bedding

Type 1 Do/24 minimum, not 95% Category I 90% Category I,less than 75 mm (3"). 95% Category II,If rock foundation, use orDo/12 minimum, not 100% Category IIIless than 150 mm (6").

Type 2 Do/24 minimum, not 90% Category I 85% Category I,less than 75 mm (3"). or 90% Category II,If rock foundation, use 95% Category II orDo/12 minimum, not 95% Category lIlless than 150 mm (6").

Type 3 Do/24 minimum, not 85% Category I, 85% Category I,less than 75 mm (3"). 90% Category II, 90% Category II,If rock foundation, use or orDo/12 minimum, not 95% Category III 95% Category IIIless than 150 mm (6") .

Type 4 No bedding No compaction No compactionrequired, except required, except required, except ifif rock foundation, use if Category III, Category III,Do/12 minimum, not use 85% use 85%less than 150 mm (6"). Category III Category III

Notes:1. Compaction and soil symbols - i.e. “95% Category I”- refers to Category I soil material with minimum

standard Proctor compaction of 95%. See Illustration 4.5 for equivalent modified Proctor values.2. Soil in the outer bedding, haunch, and lower side zones, except under the middle1/3 of the pipe, shall be

compacted to at least the same compaction as the majority of soil in the overfill zone.3. For trenches, top elevation shall be no lower than 0.1 H below finished grade or, for roadways, its top

shall be no lower than an elevation of 1 foot below the bottom of the pavement base material.4. For trenches, width shall be wider than shown if required for adequate space to attain the specified

compaction in the haunch and bedding zones.5. For trench walls that are within 10 degrees of vertical, the compaction or firmness of the soil in the trench

walls and lower side zone need not be considered.6. For trench walls with greater than 10 degree slopes that consist of embankment, the lower side shall be

compacted to at least the same compaction as specified for the soil in the backfill zone.7. Subtrenches

7.1 A subtrench is defined as a trench with its top below finished grade by more than 0.1 H or, forroadways, its top is at an elevation lower than 1ft. below the bottom of the pavement base material.

7.2 The minimum width of a subtrench shall be 1.33 Do or wider if required for adequate space to attainthe specified compaction in the haunch and bedding zones.

7.3 For subtrenches with walls of natural soil, any portion of the lower side zone in the subtrench wallshall be at least as firm as an equivalent soil placed to the compaction requirements specified for thelower side zone and as firm as the majority of soil in the overfill zone, or shall be removed andreplaced with soil compacted to the specified level.



produce a hard flat surface, which would result in highly concentrated stresses inthe pipe invert similar to those experienced in the three-edge bearing test. Themost desirable construction sequence is to place the bedding to grade; install thepipe to grade; compact the bedding outside of the middle-third of the pipe; andthen place and compact the haunch area up to the springline of the pipe. Thebedding outside the middle-third of the pipe may be compacted prior to placingthe pipe.

As indicated in Illustrations 4.3 and 4.4, when the design includes surfaceloads, the overfill and lower side areas should be compacted as required tosupport the surface load. With no surface loads or surface structure requirements,these areas need not be compacted.

SELECTION OF STANDARD INSTALLATIONThe selection of a Standard Installation for a project should be based on an

evaluation of the quality of construction and inspection anticipated. A Type 1Standard Installation requires the highest construction quality and degree ofinspection. Required construction quality is reduced for a Type 2 StandardInstallation, and reduced further for a Type 3 Standard Installation. A Type 4Standard Installation requires virtually no construction or quality inspection.Consequently, a Type 4 Standard Installation will require a higher strength pipe,and a Type I Standard Installation will require a lower strength pipe for the samedepth of installation.

Representative Soil Types Percent Compaction

Standard Standard ModifiedSIDD Soil USCS, AASHTO Proctor Proctor

Gravelly SW, SP, A1,A3 100 95Sand GW, GP 95 90(Category 1) 90 85

85 8080 7561 59

Sandy GM, SM, ML, A2, A4 100 95Silt Also GC, SC 95 90(Category II) with less than 20% 90 85

passing #200 sieve 85 8080 7549 46

Silty CL, MH, A5, A6 100 90Clay GC, SC 95 85(Category III) 90 80

85 7580 7045 40

Illustration 4.5 Equivalent USCS and AASHTO Soil Classifications for SIDD SoilDesignations



LOAD PRESSURESSPIDA was programmed with the Standard Installations, and many design

runs were made. An evaluation of the output of the designs by Dr. Frank J. Hegerproduced a load pressure diagram significantly different than proposed byprevious theories. See Illustration 4.6. This difference is particularly significantunder the pipe in the lower haunch area and is due in part to the assumption ofthe existence of partial voids adjacent to the pipe wall in this area. SIDD uses thispressure data to determine moments, thrusts, and shears in the pipe wall, andthen uses the ACPA limit states design method to determine the requiredreinforcement areas to handle the pipe wall stresses. Using this method, eachcriteria that may limit or govern the design is considered separately in theevaluation of overall design requirements. SIDD, which is based on the fourStandard Installations, is a stand-alone program developed by the AmericanConcrete Pipe Association.

The Federal Highway Administration, FHWA, developed a microcomputerprogram, PIPECAR, for the direct design of concrete pipe prior to thedevelopment of SIDD. PIPECAR determines moment, thrust, and shearcoefficients from either of two systems, a radial pressure system developed byOlander in 1950 and a uniform pressure system developed by Paris in the 1920’s,and also uses the ACPA limit states design method to determine the requiredreinforcement areas to handle the pipe wall stresses. The SIDD system has beenincorporated into PIPECAR as a state-of-the-art enhancement.

DETERMINATION OF EARTH LOADEmbankment Soil Load. Concrete pipe can be installed in either an

embankment or trench condition as discussed previously. The type of installationhas a significant effect on the loads carried by the rigid pipe. Although narrowtrench installations are most typical, there are many cases where the pipe isinstalled in a positive projecting embankment condition, or a trench with a widthsignificant enough that it should be considered a positive projecting embankmentcondition. In this condition the soil along side the pipe will settle more than the soilabove the rigid pipe structure, thereby imposing additional load to the prism of soildirectly above the pipe. With the Standard Installations, this additional load isaccounted for by using a Vertical Arching Factor, VAF. This factor is multiplied bythe prism load, PL, (weight of soil directly above the pipe) to give the total load ofsoil on the pipe.

W = VAF x PL (4.1)

Unlike the previous design method used for the Marston/Spangler beddingsthere is no need to assume a projection or settlement ratio. The Vertical ArchingFactors for the Standard Installations are as shown in Illustration 4.7. Theequation for soil prism load is shown below in Equation 4.2.

The prism load, PL, is further defined as:

PL = w H Do (4.2)Do(4 - π)

8+



Illustration 4.6 Arching Coefficients and Heger Earth Pressure Distributions

InstallationType VAF HAF A1 A2 A3 A4 A5 A6 a b c e f u v

1 1.35 0.45 0.62 0.73 1.35 0.19 0.08 0.18 1.40 0.40 0.18 0.08 0.05 0.80 0.80

2 1.40 0.40 0.85 0.55 1.40 0.15 0.08 0.17 1.45 0.40 0.19 0.10 0.05 0.82 0.70

3 1.40 0.37 1.05 0.35 1.40 0.10 0.10 0.17 1.45 0.36 0.20 0.12 0.05 0.85 0.60

4 1.45 0.30 1.45 0.00 1.45 0.00 0.11 0.19 1.45 0.30 0.25 0.00 - 0.90 -

Notes:1. VAF and HAF are vertical and horizontal arching factors. These coefficients represent non-

dimensional total vertical and horizontal loads on the pipe, respectively. The actual totalvertical and horizontal loads are (VAF) X (PL) and (HAF) X (PL), respectively, where PL is theprism load.

2. Coefficients A1 through A6 represent the integration of non-dimensional vertical and horizontalcomponents of soil pressure under the indicated portions of the component pressure diagrams(i.e. the area under the component pressure diagrams). The pressures are assumed to varyeither parabolically or linearly, as shown, with the non-dimensional magnitudes at governingpoints represented by h1, h2, uh1, vh2, a and b. Non-dimensional horizontal and verticaldimensions of component pressure regions are defined by c, d, e, vc, vd, and f coefficients.

3. d is calculated as (0.5-c-e).h1 is calculated as (1.5A1) / (c) (1+u).h2 is calculated as (1.5A2) / [(d) (1+v) + (2e)]

where:w = soil unit weight, (lbs/ft3)H = height of fill, (ft)Do = outside diameter, (ft)

A4

A5

A6

A3

HAF

VAF

Dm = 1 b

a

e

f

d

f

b

h2hI

cuc vd

vh2uhl

A22A2

A4

A5

A6

AF

A12



Illustration 4.7 Vertical Arching Factor (VAF)

Standard Installation Minimum Bedding Factor, Bfo

Type 1 1.35Type 2 1.40Type 3 1.40Type 4 1.45

Note:1. VAF are vertical arching factors. These coefficients represent nondimensional total vertical loads on the pipe. The

actual total vertical loads are (VAF) X (PL), where PL is the prism load.

Trench Soil Load. In narrow or moderate trench width conditions, theresulting earth load is equal to the weight of the soil within the trench minus theshearing (frictional) forces on the sides of the trench. Since the new installedbackfill material will settle more than the existing soil on the sides of the trench,the friction along the trench walls will relieve the pipe of some of its soil burden.The Vertical Arching Factors in this case will be less than those used forembankment design. The backfill load on pipe installed in a trench condition iscomputed by the equation:

Wd = CdwBd + w (4.3)22

8Do (4 - π)

The trench load coefficient, Cd, is further defined as:

Cd = (4.4)2Kµ'

1 – e – 2Kµ'HBd

where:Bd = width of trench, (ft)K = ratio of active lateral unit pressure to vertical unit pressurem' = tan ø', coefficient of friction between fill material and sides of trench

The value of Cd can be calculated using equation 4.4 above, or read fromFigure 214 in the Appendix.

Typical values of Kµ' are:Kµ' = .1924 Max. for granular materials without cohesionKµ' = .165 Max for sand and gravelKµ' = .150 Max. for saturated top soilKµ' = .130 Max. for ordinary clayKµ' = .110 Max for saturated clay

As trench width increases, the reduction in load from the frictional forces isoffset by the increase in soil weight within the trench. As the trench widthincreases it starts to behave like an embankment, where the soil on the side of thepipe settles more than the soil above the pipe. Eventually, the embankmentcondition is reached when the trench walls are too far away from the pipe to helpsupport the soil immediately adjacent to it. The transition width is the width of atrench at a particular depth where the trench load equals the embankment load.



Once transition width is reached, there is no longer any benefit from frictionalforces along the wall of the trench. Any pipe installed in a trench width equal to orgreater than transition width should be designed for the embankment condition.

Tables 13 through 39 are based on equation (4.2) and list the transitionwidths for the four types of beddings with various heights of backfill.

Negative Projection Embankment Soil Load. The fill load on a pipeinstalled in a negative projecting embankment condition is computed by theequation:

Wn = CnwBd (4.5)2

The embankment load coefficient Cn is further defined as:

Cn = when H ≤ He (4.6)

Cn = + + e when H > He (4.7)

– 2Kµ'

– 2Kµ' Bd

H

Bd

He

e – 1– 2Kµ' HBd

He

Bde – 1– 2Kµ'– 2Kµ'

He

Bd

The settlements which influence loads on negative projecting embankmentinstallations are shown in Illustration 4.8.

Illustration 4.8 Settlements Which Influence Loads Negative ProjectionEmbankment Installation

TOP OF EMBANKMENT

Bc

Bd

Plane of Equal Settlement

H'

H =

H' +

p'B

d

H'e

p'Bd

Sf + dc

SgSd + Sf + dc

Sf

Ground Surface

Shearing ForcesInduced BySettlement

Initial ElevationFinal Elevation



The settlement ratio is the numerical relationship between the pipe deflectionand the relative settlement between the prism of fill directly above the pipe andadjacent soil. It is necessary to define the settlement ratio for negative projectionembankment installations. Equating the deflection of the pipe and the totalsettlement of the prism of fill above the pipe to the settlement of the adjacent soil,the settlement ratio is:

rsd = (4.8)Sd

Sg – (Sd + Sf +dc)

Recommended settlement ratio design values are listed in Table 40. Theprojection ratio (p’) for this type of installation is the distance from the top of thepipe to the surface of the natural ground or compacted fill at the time of installationdivided by the width of the trench. Where the ground surface is sloping, theaverage vertical distance from the top of the pipe to the original ground should beused in determining the projection ratio (p’). Figures 194 through 213 present fillloads in pounds per linear foot for circular pipe based on projection ratios of 0.5,1.0, 1.5, 2.0 and settlement ratios of 0, -0.1, -0.3, -0.5 and -1.0. The dashed H =p’Bd line represents the limiting condition where the height of fill is at the sameelevation as the natural ground surface. The dashed H = He line represents thecondition where the height of the plane of equal settlement (He) is equal to theheight of fill (H).

Jacked or Tunneled Soil Load. This type of installation is used wheresurface conditions make it difficult to install the pipe by conventional openexcavation and backfill methods, or where it is necessary to install the pipe underan existing embankment. The earth load on a pipe installed by these methods iscomputed by the equation:

Wt = CtwBt – 2cCtBt (4.9)2

where:Bt = width of tunnel bore, (ft)

The jacked or tunneled load coefficient Ct is further defined as:

Ct = (4.10)– 2Kµ'

1 – e – 2Kµ'

HBt

In equation (4.9) the Ctw Bt2 term is similar to the Negative Projection

Embankment equation (4.5) for soil loads and the 2cCtBt term accounts for thecohesion of undisturbed soil. Conservative design values of the coefficient ofcohesion for various soils are listed in Table 41. Figures 147, 149, 151 and 153present values of the trench load term (Ctw Bt

2) in pounds per linear foot for a soildensity of 120 pounds per cubic foot and Km’ values of 0.165, 0.150, 0.130 and0.110. Figures 148, 150, 152 and 154 present values of the cohesion term(2cCtBt) divided by the design values for the coefficient of cohesion (c). To obtainthe total earth load for any given height of cover, width of bore or tunnel and typeof soil, the value of the cohesion term must be multiplied by the appropriate



coefficient of cohesion (c) and this product subtracted from the value of the trenchload term.

FLUID LOADFluid weight typically is about the same order of magnitude as pipe weight

and generally represents a significant portion of the pipe design load only for largediameter pipe under relatively shallow fills. Fluid weight has been neglected in thetraditional design procedures of the past, including the Marston Spangler designmethod utilizing the B and C beddings. There is no documentation of concretepipe failures as a result of neglecting fluid load. However, some specifyingagencies such as AASHTO and CHBDC, now require that the weight of the fluidinside the pipe always be considered when determining the D-load.

The Sixteenth Edition of the AASHTO Standard Specifications For HighwayBridges states: “The weight of fluid, Wf, in the pipe shall be considered in designbased on a fluid weight of 62.4 lbs/cu.ft, unless otherwise specified.”

DETERMINATION OF LIVE LOADTo determine the required supporting strength of concrete pipe installed

under asphalts, other flexible pavements, or relatively shallow earth cover, it isnecessary to evaluate the effect of live loads, such as highway truck loads, inaddition to dead loads imposed by soil and surcharge loads.

If a rigid pavement or a thick flexible pavement designed for heavy duty trafficis provided with a sufficient buffer between the pipe and pavement, then the liveload transmitted through the pavement to the buried concrete pipe is usuallynegligible at any depth. If any culvert or sewer pipe is within the heavy duty traffichighway right-of-way, but not under the pavement structure, then such pipe shouldbe analyzed for the effect of live load transmission from an unsurfaced roadway,because of the possibility of trucks leaving the pavement.

The AASHTO design loads commonly used in the past were the HS 20 with a32,000 pound axle load in the Normal Truck Configuration, and a 24,000 poundaxle load in the Alternate Load Configuration.

The AASHTO LRFD designates an HL 93 Live Load. This load consists ofthe greater of a HS 20 with 32,000 pound axle load in the Normal TruckConfiguration, or a 25,000 pound axle load in the Alternate Load Configuration. Inaddition, a 640 pound per linear foot Lane Load is applied across a 10 foot widelane at all depths of earth cover over the top of the pipe, up to a depth of 8 feet.This Lane Load converts to an additional live load of 64 pounds per square foot,applied to the top of the pipe for any depth of burial less than 8 feet. The averagepressure intensity caused by a wheel load is calculated by Equation 4.12. TheLane Load intensity is added to the wheel load pressure intensity in Equation4.13.

The HS 20, 32,000 pound and the Alternate Truck 25,000 pound design axleare carried on dual wheels. The contact area of the dual wheels with the ground isassumed to be rectangle, with dimensions presented in Illustration 4.9.



Illustration 4.9 AASHTO Wheel Load Surface Contact Area (Foot Print)

Illustration 4.10 AASHTO Wheel Loads and Wheel Spacings

Impact Factors. The AASHTO LRFD Standard applies a dynamic loadallowance, sometimes called Impact Factor, to account for the truck load beingnon-static. The dynamic load allowance, IM, is determined by Equation 4.11:

IM = (4.11)33(1.0 - 0125H)

100

HS 20 Load LRFD Alternate Load

4000 lb. 4000 lb.

6 ft.

6 ft. 6 ft.4 ft.

14 ft.

14 ft.to

30 ft.

H 20 Load

4000 lb. 4000 lb.

HS 20 & Alternate Loads

16000 lb. 16000 lb. 16000 lb. 16000 lb.

12000 lb. 12000 lb.

12000 lb. 12000 lb.

16000 lb. 16000 lb.

6 ft. 14 ft.

4 ft.

a

b

16000 lb. HS 20 Load12500 lb. LRFD Altemate Load

1.67 ft.(20 in.)

0.83 ft.(10 in.)



where:H = height of earth cover over the top of the pipe, ft.

Load Distribution. The surface load is assumed to be uniformly spread onany horizontal subsoil plane. The spread load area is developed by increasing thelength and width of the wheel contact area for a load configuration as shown inIllustration 4.13 for a dual wheel. On a horizontal soil plane, the dimensionalincreases to the wheel contact area are based on height of earth cover over thetop of the pipe as presented in Illustration 4.11 for two types of soil.

Illustration 4.11 Dimensional Increase Factor, AASHTO LRFD

Soil Type Dimensional Increase Factor

LRFD select granular 1.15H

LRFD any other soil 1.00H

As indicated by Illustrations 4.14 and 4.15, the spread load areas fromadjacent wheels will overlap as height of earth cover over the top of the pipeincreases. At shallow depths, the maximum pressure will be developed by an HS20 dual wheel, since at 16,000 pounds it applies a greater load than the 12,500pound Alternate Load. At intermediate depths, the maximum pressure will bedeveloped by the wheels of two HS 20 trucks in the passing mode, since at16,000 pounds each, the two wheels apply a greater load than the 12,500 poundsof an Alternate Load wheel. At greater depths, the maximum pressure will bedeveloped by wheels of two Alternate Load configuration trucks in the passingmode, since at 12,500 pounds each, the four wheels apply the greatestload(50,000 pounds). Intermediate depths begin when the spread area of dualwheels of two HS 20 trucks in the passing mode meet and begin to overlap.Greater depths begin when the spread area b of two single dual wheels of twoAlternate Load configurations in the passing mode meet and begin to overlap.

Since the exact geometric relationship of individual or combinations ofsurface wheel loads cannot be anticipated, the most critical loading configurationsalong with axle loads and rectangular spread load area are presented inIllustration 4.12 for the two AASHTO LRFD soil types.



H, ft P, lbs Spread a, ft Spread b, ft Illustration

H < 2.03 16,000 a + 1.15H b + 1.15H 4.13

2.03 ≤ H < 2.76 32,000 a + 4 + 1.15H b + 4 + 1.15H 4.14

2.76 ≤ H 50,000 a + 4 + 1.15H b + 4 + 1.15H 4.15

Select Granular Soil Fill

H, ft P, lbs Spread a, ft Spread b, ft Illustration

H < 2.33 16,000 a + 1.00H b + 1.00H 4.13

2.33 ≤ H < 3.17 32,000 a + 4 + 1.00H b + 4 + 1.00H 4.14

3.17 ≤ H 50,000 a + 4 + 1.00H b + 4 + 1.00H 4.15

Other Soils

Illustration 4.12 LRFD Critical Wheel Loads and Spread Dimensions at the Top of the Pipe for:

a=1.67'

Spread a

H ft.

b=0.83'

Spread b

Direction of Travel

Spread Load Area

Wheel Load Area

Illustration 4.13 Spread Load Area - Single Dual Wheel



a4.0 ft.

Spread a

a

H ft.

b

Spread b

Direction of Travel

Distributed Load Area

WheelLoad Areas

Wheel Load Areas

Illustration 4.14 Spread Load Area - Two Single Dual Wheels of Trucks in Passing Mode

a

4.0 ft.

Spread a

a

H ft.

b

b

4.0 ft.

Spread b

Direction of Travel

Distributed Load Area

WheelLoad Areas

Wheel Load Areas

Illustration 4.15 Spread Load Area - Two Single Dual Wheels of Two Alternate Loads in Passing Mode



Average Pressure Intensity. The wheel load average pressure intensity onthe subsoil plane at the outside top of the concrete pipe is:

w = (4.12)P(1 + IM)

Awhere:

w = wheel load average pressure intensity, pounds per square footP = total live wheel load applied at the surface, poundsA = spread wheel load area at the outside top of the pipe, square feetIM = dynamic load allowance

From the appropriate Table in Illustration 4.12, select the critical wheel loadand spread dimensions for the height of earth cover over the outside top of thepipe, H. The spread live load area is equal to Spread a times Spread b. Select theappropriate dynamic load allowance, using Equation 4.11.

Total Live Load. A designer is concerned with the maximum possible loads,which occur when the distributed load area is centered over the buried pipe.Depending on the pipe size and height of cover, the most critical loadingorientation can occur either when the truck travels transverse or parallel to thecenterline of the pipe. Illustration 4.16 shows the dimensions of the spread loadarea, A, as related to whether the truck travel is transverse or parallel to thecenterline of the pipe.

Illustration 4.16 Spread Load Area Dimensions vs Direction of Truck

Unless you are certain of the pipeline orientation, the total live load in pounds,WT, must be calculated for each travel orientation, and the maximum calculatedvalue must be used in Equation 4.14 to calculate the live load on the pipe in

Spread a

Pipe

Pipe Centerline

Spread b

Spread a

Spread b

Direction of Travel

Dir

ecti

on

of

Tra

vel



pounds per linear foot.The LRFD requires a Lane Load, LL, of 64 pounds per square foot on the top

of the pipe at any depth less than 8 feet.The total live load acting on the pipe is:

WT = (w + LL) L SL (4.13)where:

WT = total live load, poundsw = wheel load average pressure intensity, pounds per square

foot (at the top of the pipe)LL = lane loading if AASHTO LRFD is used, pounds per square

foot0≤H<8, LL = 64, pounds per square footH≥8, LL = 0L = dimension of load area parallel to the longitudinal axis of

pipe, feetSL = outside horizontal span of pipe, Bc, or dimension of load

area transverse to the longitudinal axis of pipe, whichever isless, feet

Total Live Load in Pounds per Linear Foot. The total live load in poundsper linear foot, WL, is calculated by dividing the Total Live Load, WT, by theEffective Supporting Length, Le (See Illustration 4.17), of the pipe:

WL = (4.14)WT

Le

where:WL = live load on top of pipe, pounds per linear footLe = effective supporting length of pipe, feet

The effective supporting length of pipe is:

Le = L + 1.75(3/4RO)

where:RO = outside vertical Rise of pipe, feet

Illustration 4.17 Effective Supporting Length of Pipe

Wheel Surface Contact Area

Pipe Centerline

Le = L + 1.75 (3/4Ro)

3Ro

H L

Ro



Airports. The distribution of aircraft wheel loads on any horizontal plane inthe soil mass is dependent on the magnitude and characteristics of the aircraftloads, the aircraft’s landing gear configuration, the type of pavement structure andthe subsoil conditions. Heavier gross aircraft weights have resulted in multiplewheel undercarriages consisting of dual wheel assemblies and/or dual tandemassemblies. The distribution of wheel loads through rigid pavement are shown inIllustration 4.18.

If a rigid pavement is provided, an aircraft wheel load concentration isdistributed over an appreciable area and is substantially reduced in intensity at thesubgrade. For multi-wheeled landing gear assemblies, the total pressure intensityis dependent on the interacting pressures produced by each individual wheel. Themaximum load transmitted to a pipe varies with the pipe size under consideration,the pipe’s relative location with respect to the particular landing gear configurationand the height of fill between the top of the pipe and the subgrade surface.

For a flexible pavement, the area of the load distribution at any plane in thesoil mass is considerably less than for a rigid pavement. The interaction ofpressure intensities due to individual wheels of a multi-wheeled landing gearassembly is also less pronounced at any given depth of cover.

In present airport design practices, the aircraft’s maximum takeoff weight isused since the maximum landing weight is usually considered to be about threefourths the takeoff weight. Impact is not considered, as criteria are not yetavailable to include dynamic effects in the design process.

Rigid Pavement.

Illustration 4.18 Aircraft Pressure Distribution, Rigid Pavement

Fill Height H = 2 Feet

Fill Height H = 6 Feet



The pressure intensity is computed by the equation:

p(H,X) = (4.15)2Rs

CP

where:P = Load at the surface, poundsC = Load coefficient, dependent on the horizontal distance (X), the

vertical distance (H), and RsRs = Radius of Stiffness of the pavement, feet

Rs is further defined as:

Rs = (4.16)4

12 (1 – µ2) k

(Eh)3

where:E = modulus of elasticity of the pavement, pounds per square inchh = pavement thickness, inchesµ = Poisson’s ratio (generally assumed 0.15 for concrete pavement)k = modulus of subgrade reaction, pounds per cubic inch

Tables 46 through 50 present pressure coefficients in terms of the radius ofstiffness as developed by the Portland Cement Association and published in thereport “Vertical Pressure on Culverts Under Wheel Loads on Concrete PavementSlabs.” 3

Values of radius of stiffness are listed in Table 52 for pavement thickness andmodulus of subgrade reaction.

Tables 53 through 55 present aircraft loads in pounds per linear foot forcircular, horizontal elliptical and arch pipe. The Tables are based on equations4.15 and 4.16 using a 180,000 pound dual tandem wheel assembly, 190 poundsper square inch tire pressure, 26-inch spacing between dual tires, 66-inch spacingbetween tandem axles, k value of 300 pounds per cubic inch, 12-inch, thickconcrete pavement and an Rs, value of 37.44 inches. Subgrade and subbasesupport for a rigid pavement is evaluated in terms of k, the modulus of subgradereaction. A k value of 300 pounds per cubic inch was used, since this valuerepresents a desirable subgrade or subbase material. In addition, because of theinteraction between the pavement and subgrade, a lower value of k (representingreduced subgrade support) results in less load on the pipe.

Although Tables 53 through 55 are for specific values of aircraft weights andlanding gear configuration, the tables can be used with sufficient accuracy for allheavy commercial aircraft currently in operation. Investigation of the design loadsof future jets indicates that although the total loads will greatly exceed presentaircraft loads, the distribution of such loads over a greater number of landinggears and wheels will not impose loads on underground conduits greater than bycommercial aircraft currently in operation. For lighter aircrafts and/or different rigidpavement thicknesses, it is necessary to calculate loads as illustrated in Example4.10.

Flexible Pavement. AASHTO considers flexible pavement as an unpaved



surface and therefore live load distributions may be calculated as if the load werebearing on soil. Cover depths are measured from the top of the flexible pavement,however, at least one foot of fill between the bottom of the pavement and top ofthe pipe should be provided.

Railroads. In determining the live load transmitted to a pipe installed underrailroad tracks, the weight on the locomotive driver axles plus the weight of thetrack structure, including ballast, is considered to be uniformly distributed over anarea equal to the length occupied by the drivers multiplied by the length of ties.

The American Railway Engineering and Maintenance of Way Association(AREMA) recommends a Cooper E80 loading with axle loads and axle spacing asshown in Illustration 4.19. Based on a uniform load distribution at the bottom ofthe ties and through the soil mass, the live load transmitted to a pipe undergroundis computed by the equation:

WL = CpoBcIf (4.19)

where:C = load coefficientpo = tire pressure, pounds per square footBc = outside span of the pipe, feetIf = impact factor

Tables 56 through 58 present live loads in pounds per linear foot based onequation (4.18) with a Cooper E80 design loading, track structure weighing 200pounds per linear foot and the locomotive load uniformly distributed over an area8 feet X 20 feet yielding a uniform live load of 2025 pounds per square foot. Inaccordance with the AREMA “Manual of Recommended Practice” an impact factorof 1.4 at zero cover decreasing to 1.0 at ten feet of cover is included in the Tables.

Illustration 4.19 Cooper E 80 Wheel Loads and Axel Spacing

Based on a uniform load distribution at the bottom of the ties and through thesoil mass, the design track unit load, WL, in pounds per square foot, is determinedfrom the AREMA graph presented in Figure 215. To obtain the live loadtransmitted to the pipe in pounds per linear foot, it is necessary to multiply the unitload, WL, from Figure 215, by the outside span, Bc, of the pipe in feet.

Loadings on a pipe within a casing pipe shall be taken as the full dead load,plus live load, plus impact load without consideration of the presence of the casing

3 Op. cit., p. 284 Equation (21) is recommended by WPCF-ASCE Manual, The Design and Construction of Sanitary

Storm Sewers.

8,000 lbper lin ft

8' 5' 5' 5' 9' 5' 6' 5' 8' 8' 5' 5' 5' 9' 5' 6' 5' 5'

40,0

00

80,0

00

80,0

00

80,0

00

80,0

00

52,0

00

52,0

00

52,0

00

52,0

00

40,0

00

80,0

00

80,0

00

80,0

00

80,0

00

52,0

00

52,0

00

52,0

00

52,0

00



pipe, unless the casing pipe is fully protected from corrosion.Culvert or sewer pipe within the railway right-of-way, but not under the track

structure, should be analyzed for the effect of live loads because of the possibilityof train derailment.

Construction Loads. During grading operations it may be necessary forheavy construction equipment to travel over an installed pipe. Unless adequateprotection is provided, the pipe may be subjected to load concentrations in excessof the design loads. Before heavy construction equipment is permitted to crossover a pipe, a temporary earth fill should be constructed to an elevation at least 3feet over the top of the pipe. The fill should be of sufficient width to preventpossible lateral displacement of the pipe.

SELECTION OF BEDDINGA bedding is provided to distribute the vertical reaction around the lower

exterior surface of the pipe and reduce stress concentrations within the pipe wall.The load that a concrete pipe will support depends on the width of the beddingcontact area and the quality of the contact between the pipe and bedding. Animportant consideration in selecting a material for bedding is to be sure thatpositive contact can be obtained between the bed and the pipe. Since mostgranular materials will shift to attain positive contact as the pipe settles, an idealload distribution can be attained through the use of clean coarse sand, well-rounded pea gravel or well-graded crushed rock.

BEDDING FACTORSUnder installed conditions the vertical load on a pipe is distributed over its

width and the reaction is distributed in accordance with the type of bedding. Whenthe pipe strength used in design has been determined by plant testing, beddingfactors must be developed to relate the in-place supporting strength to the moresevere plant test strength. The bedding factor is the ratio of the strength of thepipe under the installed condition of loading and bedding to the strength of thepipe in the plant test. This same ratio was defined originally by Spangler as theload factor. This latter term, however, was subsequently defined in the ultimatestrength method of reinforced concrete design with an entirely different meaning.To avoid confusion, therefore, Spangler’s term was renamed the bedding factor.The three-edge bearing test as shown in Illustration 4.20 is the normally acceptedplant test so that all bedding factors described in the following pages relate the in-place supporting strength to the three-edge bearing strength.



Illustration 4.20 Three-Edge Bearing Test

Although developed for the direct design method, the Standard Installationsare readily applicable to and simplify the indirect design method. The StandardInstallations are easier to construct and provide more realistic designs than thehistorical A, B, C, and D beddings. Development of bedding factors for theStandard Installations, as presented in the following paragraphs, follows theconcepts of reinforced concrete design theories. The basic definition of beddingfactor is that it is the ratio of maximum moment in the three-edge bearing test tothe maximum moment in the buried condition, when the vertical loads under eachcondition are equal:

Bf = (20)MTEST

MFIELD

where:Bf = bedding factorMTEST = maximum moment in pipe wall under three-edge bearing test

load, inch-poundsMFIELD = maximum moment in pipe wall under field loads, inch-pounds

Consequently, to evaluate the proper bedding factor relationship, the verticalload on the pipe for each condition must be equal, which occurs when thespringline axial thrusts for both conditions are equal. In accordance with the lawsof statics and equilibrium, MTEST and MFIELD are:

MTEST = [0.318NFS] x [D + t] (21)

MFIELD = [MFI] - [0.38tNFI] - [0.125NFI x c] (22)

where:NFS = axial thrust at the springline under a three-edge bearing test load,

pounds per footD = inside pipe diameter, inchest = pipe wall thickness, inchesMFI = moment at the invert under field loading, inch-pounds/ftNFI = axial thrust at the invert under field loads, pounds per footc = thickness of concrete cover over the inner reinforcement, inches

Rigid Steel

Member

BearingStrips



Substituting equations 4.21 and 4.22 into equation 4.20.

Bf = (23)[0.318NFS] x [D + t]

[MFI] - [0.38tNFI] - [0.125NFI x C]

Using this equation, bedding factors were determined for a range of pipediameters and depths of burial. These calculations were based on one inch coverover the reinforcement, a moment arm of 0.875d between the resultant tensileand compressive forces, and a reinforcement diameter of 0.075t. Evaluationsindicated that for A, B and C pipe wall thicknesses, there was negligible variationin the bedding factor due to pipe wall thickness or the concrete cover, c, over thereinforcement. The resulting bedding factors are presented in Illustration 4.21.

Illustration 4.21 Bedding Factors, Embankment Conditions, Bfe

Pipe Standard InstallationDiameter Type 1 Type 2 Type 3 Type 4

12 in. 4.4 3.2 2.5 1.7

24 in. 4.2 3.0 2.4 1.7

36 in. 4.0 2.9 2.3 1.7

72 in. 3.8 2.8 2.2 1.7

144 in. 3.6 2.8 2.2 1.7

Notes:1. For pipe diameters other than listed in Illustration 4.21, embankment condition factors, Bfe can

be obtained by interpolation.2. Bedding factors are based on the soils being placed with the minimum compaction specified in

Illustration 4.4 for each standard installation.

Determination of Bedding Factor. For trench installations as discussedpreviously, experience indicates that active lateral pressure increases as trenchwidth increases to the transition width, provided the sidefill is compacted. A SIDDparameter study of the Standard Installations indicates the bedding factors areconstant for all pipe diameters under conditions of zero lateral pressure on thepipe. These bedding factors exist at the interface of the pipewall and the soil andare called minimum bedding factors, Bfo, to differentiate them from the fixedbedding factors developed by Spangler. Illustration 4.22 presents the minimumbedding factors.



Illustration 4.22 Trench Minimum Bedding Factors, Bfo

Standard Installation Minimum Bedding Factor, Bfo

Type 1 2.3

Type 2 1.9

Type 3 1.7

Type 4 1.5

Note:1. Bedding factors are based on the soils being placed with the minimum compaction specified in

Illustration 4.4 for each Standard Installation.2. For pipe installed in trenches dug in previously constructed embankment, the load and the

bedding factor should be determined as an embankment condition unless the backfill placedover the pipe is of lesser compaction than the embankment.

A conservative linear variation is assumed between the minimum beddingfactor and the bedding factor for the embankment condition, which begins attransition width.

Illustration 4.23 Variable Bedding Factor

The equation for the variable trench bedding factor, is:

Bfv = + Bfo (24)[Bfe – Bfo][Bd – Bc]

[Bdt – Bc]

where:Bc = outside horizontal span of pipe, feetBd = trench width at top of pipe, feet

Bc

Bfe

Bfo

Bc

Bd

Bdt



Bdt = transition width at top of pipe, feetBfe = bedding factor, embankmentBfo = minimum bedding factor, trenchBfv = variable bedding factor, trench

Transition width values, Bdt are provided in Tables 13 through 39.

For pipe installed with 6.5 ft or less of overfill and subjected to truck loads, thecontrolling maximum moment may be at the crown rather than the invert.Consequently, the use of an earth load bedding factor may produceunconservative designs. Crown and invert moments of pipe for a range ofdiameters and burial depths subjected to HS20 truck live loadings were evaluated.Also evaluated, was the effect of bedding angle and live load angle (width ofloading on the pipe). When HS20 or other live loadings are encountered to asignificant value, the live load bedding factors, BfLL,, presented in Illustration 4.24are satisfactory for a Type 4 Standard Installation and become increasinglyconservative for Types 3, 2, and 1. Limitations on BfLL are discussed in the sectionon Selection of Pipe Strength.

Illustration 4.24 Bedding Factors, BfLL, for HS20 Live Loadings

Fill Pipe Diameter, InchesHeight,Ft. 12 24 36 48 60 72 84 96 108 120 1440.5 2.2 1.7 1.4 1.3 1.3 1.1 1.1 1.1 1.1 1.1 1.1

1.0 2.2 2.2 1.7 1.5 1.4 1.3 1.3 1.3 1.1 1.1 1.11.5 2.2 2.2 2.1 1.8 1.5 1.4 1.4 1.3 1.3 1.3 1.12.0 2.2 2.2 2.2 2.0 1.8 1.5 1.5 1.4 1.4 1.3 1.32.5 2.2 2.2 2.2 2.2 2.0 1.8 1.7 1.5 1.4 1.4 1.33.0 2.2 2.2 2.2 2.2 2.2 2.2 1.8 1.7 1.5 1.5 1.43.5 2.2 2.2 2.2 2.2 2.2 2.2 1.9 1.8 1.7 1.5 1.44.0 2.2 2.2 2.2 2.2 2.2 2.2 2.1 1.9 1.8 1.7 1.54.5 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.0 1.9 1.8 1.75.0 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.0 1.9 1.8

Application of Factor of Safety. The indirect design method for concretepipe is similar to the common working stress method of steel design, whichemploys a factor of safety between yield stress and the desired working stress. Inthe indirect method, the factor of safety is defined as the relationship between theultimate strength D-load and the 0.01inch crack D-load. This relationship isspecified in the ASTM Standards C 76 and C 655 on concrete pipe. Therelationship between ultimate D-load and 0.01-inch crack D-load is 1.5 for 0.01inch crack D-loads of 2,000 or less; 1.25 for 0.01 inch crack D loads of 3,000 ormore; and a linear reduction from 1.5 to 1.25 for 0.01 inch crack D-loads betweenmore than 2,000 and less than 3,000. Therefore, a factor of safety of 1.0 shouldbe applied if the 0.01 inch crack strength is used as the design criterion rather



than the ultimate strength. The 0.01 inch crack width is an arbitrarily chosen testcriterion and not a criteri for field performance or service limit.

SELECTION OF PIPE STRENGTHThe American Society for Testing and Materials has developed standard

specifications for precast concrete pipe. Each specification contains design,manufacturing and testing criteria.

ASTM Standard C 14 covers three strength classes for nonreinforcedconcrete pipe. These classes are specified to meet minimum ultimate loads,expressed in terms of three-edge bearing strength in pounds per linear foot.

ASTM Standard C 76 for reinforced concrete culvert, storm drain and sewerpipe specifies strength classes based on D-load at 0.01-inch crack and/or ultimateload. The 0.01-inch crack D-load (D0.01) is the maximum three-edge-bearing testload supported by a concrete pipe before a crack occurs having a width of 0.01inch measured at close intervals, throughout a length of at least 1 foot. Theultimate D-load (Dult) is the maximum three-edge-bearing test load supported by apipe divided by the pipe’s inside diameter. D-loads are expressed in pounds perlinear foot per foot of inside diameter.

ASTM Standard C 506 for reinforced concrete arch culvert, storm drain, andsewer pipe specifies strengths based on D-load at 0.01-inch crack and/or ultimateload in pounds per linear foot per foot of inside span.

ASTM Standard C 507 for reinforced concrete elliptical culvert, storm drainand sewer pipe specifies strength classes for both horizontal elliptical and verticalelliptical pipe based on D-load at 0.01-inch crack and/or ultimate load in poundsper linear foot per foot of inside span.

ASTM Standard C 655 for reinforced concrete D-load culvert, storm drain andsewer pipe covers acceptance of pipe designed to meet specific D-loadrequirements.

ASTM Standard C 985 for nonreinforced concrete specified strength culvert,storm drain, and sewer pipe covers acceptance of pipe designed for specifiedstrength requirements.

Since numerous reinforced concrete pipe sizes are available, three-edgebearing test strengths are classified by D-loads. The D-load concept providesstrength classification of pipe independent of pipe diameter. For reinforced circularpipe the three-edge-bearing test load in pounds per linear foot equals D-loadtimes inside diameter in feet. For arch, horizontal elliptical and vertical ellipticalpipe the three-edge bearing test load in pounds per linear foot equals D-loadtimes nominal inside span in feet.

The required three-edge-bearing strength of non-reinforced concrete pipe isexpressed in pounds per linear foot, not as a D-load, and is computed by theequation:

T.E.B = + x F.S. (25)WE + WF

Bf

WL

BfLL

The required three-edge bearing strength of circular reinforced concrete pipeis expressed as D-load and is computed by the equation:



D-load = + x (26)WL

BfLL

F.S.

D

WE + WF

Bf

The determination of required strength of elliptical and arch concrete pipe iscomputed by the equation:

D-load = + x (27)WL

BfLL

F.S.

S

WE + WF

Bf

where:

S = inside horizontal span of pipe, ft.

When an HS20 truck live loading is applied to the pipe, use the live loadbedding factor, BfLL, as indicated in Equations 4.25 – 4.27, unless the earth loadbedding factor, Bf, is of lesser value in which case, use the lower Bf value in placeof BfLL. For example, with a Type 4 Standard Installation of a 48 inch diameter pipeunder 1.0 feet of fill, the factors used would be Bf = 1.7 and BfLL = 1.5; but under2.5 feet or greater fill, the factors used would be Bf= 1.7 and BfLL, = 1.7 rather than2.2. For trench installations with trench widths less than transition width, BfLL wouldbe compared to the variable trench bedding factor, Bfv. Although their loads aregenerally less concentrated, the live load bedding factor may be conservativelyused for aircraft and railroad loadings.

The use of the six-step indirect design method is illustrated by examples onthe following pages.



EXAMPLE PROBLEMS



EXAMPLE PROBLEMS

EXAMPLE 4-1Trench Installation

Given: A 48 inch circular pipe is to be installed in a 7 foot wide trench with 10 feetof cover over the top of the pipe. The pipe will be backfilled with sand andgravel weighing 110 pounds per cubic foot. Assume a Type 4 Installation.

Find: The required pipe strength in terms of 0.01 inch crack D-load.

1. Determination of Earth Load (WE)To determine the earth load, we must first determine if the installation isbehaving as a trench installation or an embankment installation. Sincewe are not told what the existing in-situ material is, conservativelyassume a Km' value between the existing soil and backfill of 0.150.

From Table 23, The transition width for a 48 inch diameter pipe with aKµ' value of 0.150 under 10 feet of fill is:

Bdt = 8.5 feet

Transition width is greater than the actual trench width, therefore theinstallation will act as a trench. Use Equations 4.3 and 4.4 to determinethe soil load.

w = 110 pounds per cubic footH = 10 feetBd = 7 feetKµ' = 0.150

Do =

Do = 4.83 feet

48 + 2 (5)12

Note: Wall thickness for a 48 inch inside diameter pipe with a B wall is 5-inches per ASTM C 76.

Bc

Bd

H



The value of Cd can be obtained from Figure 214, or calculated usingEquation 4.4.

Cd = Equation 4.4

Cd = 1.16

1 - e(2) (0.150)

107

-2 (0.150)

Wd = (1.16)(110)(7)2 + (110) Equation 4.3

Wd = 6,538 pounds per linear foot

We = Wd WE = 6,538 earth load in pounds per linear foot

8

(4.83)2 (4 - π)

Fluid Load, WF = 62.4 lbs/ft3

2. Determination of Live Load (WL)From Table 42, live load is negligible at a depth of 10 feet.

3. Selection of BeddingBecause of the narrow trench, good compaction of the soil on the sidesof the pipe would be difficult, although not impossible. Therefore a Type4 Installation was assumed.

4. Determination of Bedding Factor, (Bfv)The pipe is installed in a trench that is less than transition width.Therefore, Equation 4.24 must be used to determine the variablebedding factor.

Bc = Do Bc = 4.83 outside diameter of pipe in feet Bd = 7 width of trench in feet Bdt = 8.5 transition width in feetBfe = 1.7 embankment bedding factorBfo = 1.5 minimum bedding factor

Bfv = 1.62

Bfv = + 1.5 Equation 4.248.5 - 4.83

(1.7 - 1.5) (7 - 4.83)

5. Application of Factor of Safety (F.S.)A factor of safety of 1.0 based on the 0.01 inch crack will be applied.

6. Selection of Pipe StrengthThe D-load is given by Equation 4.26



WE = 6,538 earth load in pounds per linear footWF = 62.4 fluid load in pounds per cubic footWL = 0 live load is negligibleBf = Bfv Bf = 1.62 earth load bedding factorBfLL = N/A live load bedding factor is not applicableD = 4 inside diameter of pipe in feet

D0.01 = 1,009 pounds per linear foot per foot of diameter

D0.01 = Equation 4.261.62 4

6,538 + 62.4 1.0

Answer: A pipe which would withstand a minimum three-edge bearing test loadfor the 0.01 inch crack of 1,009 pounds per linear foot per foot of insidediameter would be required.

EXAMPLE 4-2Positive Projection Embankment Installation

Given: A 48 inch circular pipe is to be installed in a positive projectingembankment condition using a Type 1 installation. The pipe will becovered with 35 feet of 120 pounds per cubic foot overfill.

Find: The required pipe strength in terms of 0.01 inch D-load

1. Determination of Earth Load (WE)Per the given information, the installation behaves as a positiveprojecting embankment. Therefore, use Equation 4.2 to determine thesoil prism load and multiply it by the appropriate vertical arching factor.

Do

Di

H



Do = 4.83 outside diameter of pipe in feet

w = 120 unit weight of soil in pounds per cubic foot

H = 1 height of cover in feet

PL = 880 pounds per linear foot

Do = 12

48 + 2 (5) Note: The wall thickness for a 48-inch pipe with a B wall is 5-inches per ASTM C76.

PL = 120 35 + 4.83 Equation 4.2 8

4.83 (4 - π)

Immediately listed below Equation 4.2 are the vertical arching factors(VAFs) for the four types of Standard Installations. Using a VAF of 1.35for a Type 1 Installation, the earth load is:

WE = 1.35 x 20,586

WE = 27,791 pounds per linear foot Equation 4.1



3. Selection of BeddingA Type 1 Installation will be used for this example

4. Determination of Bedding Factor, (Bfe)The embankment bedding factor for a Type 1 Installation may beinterpolated from Illustration 4.21

Bfe36 = 4.0Bfe72 = 3.8

Bfe48 = (4.0 - 3.8) + 3.8

Bfe48 = 3.93

72 - 48

72 - 36





WE = 27,791 earth load in pounds per linear footWF = 62.4 fluid load in pounds per cubic footWL = 0 live load is negligibleBf = Bfe Bf = 3.93 earth load bedding factorBfLL = N/A live load bedding factor is not applicableD = 4 inside diameter of pipe in feet


D0.01 = Equation 4.263.93 4

27,791 + 62.4 1.0

Answer: A pipe which would withstand a minimum three-edge bearing test forthe 0.01 inch crack of 1,768 pounds per linear foot per foot of insidediameter would be required.

EXAMPLE 4-3Negative Projection Embankment Installation

Given: A 72 inch circular pipe is to be installed in a negative projectingembankment condition in ordinary soil. The pipe will be covered with 35feet of 120 pounds per cubic foot overfill. A 10 foot trench width will beconstructed with a 5 foot depth from the top of the pipe to the naturalground surface.

Find: The required pipe strength in terms of 0.01 inch D-load

1. Determination of Earth Load (WE)A settlement ratio must first be assumed. The negative projection ratioof this installation is the height of soil from the top of the pipe to the topof the natural ground (5 ft) divided by the trench width (10 ft). Thereforethe negative projection ratio of this installation is p' = 0.5. From Table40, for a negative projection ratio of p' = 0.5, the design value of thesettlement ratio is -0.1.

Bc

Bd

H



Enter Figure 195 on the horizontal scale at H = 35 feet. Proceedvertically until the line representing Bd = 10 feet is intersected. At thispoint the vertical scale shows the fill load to be 27,500 pounds perlinear foot for 100 pounds per cubic foot fill material. Increase the load20 percent for 120 pound material since Figure 195 shows values for100 pound material.

Wn = 1.20 x 27,500Wn = 33,000 pounds per linear footWE = Wn WE = 33,000 earth load in pounds per linear foot



3. Selection of BeddingNo specific bedding was given. Assuming the contractor will putminimal effort into compacting the soil, a Type 3 Installation is chosen.

4. Determination of Bedding Factor, (Bfv)The variable bedding factor will be determined using Equation 4.24 inthe same fashion as if the pipe were installed in a trench.

Bc = 7.17 outside diameter of pipe in feet

Bd = 10 trench width in feet

Bdt = 14.1 transition width for a Type 3 Installation with Kµ'=0.150

Bfe = 2.2 embankment bedding factor (taken from Illustration 4.21)

Bfo = 1.7 minimum bedding factor (taken from Illustration 4.22)

Bfv = 1.9

Bc = 12

72 + 2 (7) Note: The wall thickness for a 72-inch pipe with a B wall is 7-inches per ASTM C 76.

Bfv = + 1.7 Equation 4.2414.1 - 7.17

(2.2 - 1.7) (10 - 7.17)







D0.01 = Equation 4.261.9 6

33,000 + 62.4 1.0

Answer: A pipe which would withstand a minimum three-edge bearing test loadfor the 0.01 inch crack of 28,95 pounds per linear foot per foot of insidediameter would be required.

EXAMPLE 4-4Jacked or Tunneled Installation

Given: A 48 inch circular pipe is to be installed by the jacking method ofconstruction with a height of cover over the top of the pipe of 40 feet. Thepipe will be jacked through ordinary clay material weighing 110 poundsper cubic foot throughout its entire length. The limit of excavation will be 5feet.


1. Determination of Earth Load (WE)A coefficient of cohesion value must first be assumed. In Table 41,values of the coefficient of cohesion from 40 to 1,000 are given for clay.A conservative value of 100 pounds per square foot will be used.

Enter Figure 151, Ordinary Clay, and project a horizontal line from H =40 feet on the vertical scale and a vertical line from Bt = 5 feet on thehorizontal scale. At the intersection of these two lines interpolate

Bc

Bt

H



between the curved lines for a value of 9,500 pounds per linear foot,which accounts for earth load without cohesion. Decrease the load inproportion to 110/120 for 110 pound material since Figure 151 showsvalues for 120 pound material.

Wt = x 9,500

Wt = 8,708 pounds per linear foot

110120

Enter Figure 152, Ordinary Clay, and project a horizontal line from H =40 feet on the vertical scale and a vertical line from Bt = 5 feet on thehorizontal scale. At the intersection of these two lines interpolatebetween the curved lines for a value of 33, which accounts for thecohesion of the soil. Multiply this value by the coefficient of cohesion, c= 100, and subtract the product from the 8,708 value obtained fromfigure 151.

Wt = 8,708 –100 (33)Wt = 5,408 pounds per linear footWE = Wt WE = 5,408 earth load in pounds per linear foot

Note: If the soil properties are not consistent, or sufficient information onthe soil is not available, cohesion may be neglected and a conservativevalue of 8,708 lbs/ft used.


2. Determination of Live Load (WL)From Table 42, live load is negligible at 40 feet.

3. Selection of BeddingThe annular space between the pipe and limit of excavation will be filledwith grout.

4. Determination of Bedding Factor (Bfv)Since the space between the pipe and the bore will be filled with grout,there will be positive contact of bedding around the periphery of thepipe. Because of this beneficial bedding condition, little flexural stressshould be induced in the pipe wall. A conservative variable beddingfactor of 3.0 will be used.


6. Selection of Pipe StrengthThe D-load is given by Equation 4.26.




D0.01 = 451 pounds per linear foot per foot of diameter

D0.01 = Equation 4.263.0 4

5,408 + 62.4 1.0

Answer: A pipe which would withstand a minimum three-edge bearing test loadfor the 0.01 inch crack of 451 pounds per linear foot per foot of insidediameter would be required.

EXAMPLE 4-5Wide Trench Installation

Given: A 24 inch circular non reinforced concrete pipe is to be installed in a 5 footwide trench with 10 feet of cover over the top of the pipe. The pipe will bebackfilled with ordinary clay weighing 120 pounds per cubic foot.

Find: The required three-edge bearing test strength for nonreinforced pipe andthe ultimate D-load for reinforced pipe.

1. Determination of Earth Load (WE)To determine the earth load, we must first determine if the installation isbehaving as a trench installation or an embankment installation.Assume that since the pipe is being backfilled with clay that they areusing in-situ soil for backfill. Assume a Kµ’ value between the existingsoil and backfill of 0.130. We will assume a Type 4 Installation for thisexample.

From Table 17, the transition width for a 24 inch diameter pipe with aKµ’ value of 0.130 under 10 feet of fill is:Bdt = 4.8

Bc

Bd

H



Since the transition width is less than the trench width, this installationwill act as an embankment. Therefore calculate the prism load perEquation 4.2 and multiply it by the appropriate vertical arching factor(VAF).

Do = 2.5 outside diameter of pipe in feet w = 120 unit weight of soil in pounds per cubic footH = 10 height of cover in feet

PL = 3,080 pounds per linear foot

Do = 12


PL = 120 10 + 2.5 Equation 4.2 8

2.5 (4 - π)

Immediately listed below Equation 4.2 are the vertical arching factors(VAF) for the four types of Standard Installations. Using a VAF of 1.45for a Type 4 Installation, the earth load is:

WE = 1.45 x 3,080WE = 4,466 pounds per linear foot Equation 4.1



3. Selection of BeddingA Type 4 Installation has been chosen for this example

4. Determination of Bedding Factor, (Bfe)Since this installation behaves as an embankment, an embankmentbedding factor will be chosen. From Illustration 4.21, the embankmentbedding factor for a 24 inch pipe installed in a Type 4 Installation is:

Bfe = 1.7


6. Selection of Pipe StrengthThe D-load is given by Equation 4.26.



TEB = 1.5 Equation 4.25

TEB = 3,941 pounds per linear foot

The D-load for reinforced concrete pipe is given by Equation 2.46.

D0.01 = Equation 4.26


1.7 21.0 4,466 + 62.4

1.7

4,466 + 62.4

WE = 4,466 earth load in pounds per linear footWF = 62.4 fluid load in pounds per cubic footWL = 0 live load is negligibleBf = Bfe Bf = 1.7 earth load bedding factorBfLL = N/A live load bedding factor is not applicableD = 2 inside diameter of pipe in feet

The ultimate three-edge bearing strength for nonreinforced concrete pipeis given by Equation 4.25

Answer: A nonreinforced pipe which would withstand a minimum three-edgebearing test load of 3,941 pounds per linear foot would be required.

EXAMPLE 4-6Positive Projection Embankment Installation

Vertical Elliptical Pipe

Given: A 76 inch x 48 inch vertical elliptical pipe is to be installed in a positiveprojection embankment condition in ordinary soil. The pipe will be coveredwith 50 feet of 120 pounds per cubic foot overfill.

pB'CB'c

H




1. Determination of Earth Load (WE)Note: The Standard Installations were initially developed for circularpipe, and their benefit has not yet been established for elliptical andarch pipe. Therefore, the traditional Marston/Spangler design methodusing B and C beddings is still conservatively applied for these shapes.

A settlement ratio must first be assumed. In Table 40, values ofsettlement ratio from +0.5 to +0.8 are given for positive projectinginstallation on a foundation of ordinary soil. A value of 0.7 will be used.The product of the settlement ratio and the projection ratio will be 0.49(rsdp approximately 0.5).

Enter Figure 182 on the horizontal scale at H = 50 feet. Proceedvertically until the line representing R x S = 76" x 48" is intersected. Atthis point the vertical scale shows the fill load to be 41,000 pounds perlinear foot for 100 pounds per cubic foot fill material. Increase the load20 percent for 120 pound material.Wc = 1.20 x 41,000Wc = 49,200 per linear footWE = Wc WE = 49,200 earth load in pounds per linear foot



3. Selection of BeddingDue to the high fill height you will more than likely want good supportaround the pipe, a Class B bedding will be assumed for this example.

4. Determination of Bedding Factor (Bfe)First determine the H/Bc ratio.

H = 50

Bc =

Bc = 5.08 outside diameter of pipe in feet

H/Bc = 9.84

48 + 2 (6.5)12

Note: the wall thickness for a 72" x 48" elliptical pipe is 6.5" per ASTM C507.

From Table 59, for an H/Bc ratio of 9.84, rsdp value of 0.5, p value of 0.7,and a Class B bedding, an embankment bedding factor of 2.71 isobtained.

Bfe = 2.71





WE = 49,200 earth load in pounds per linear footWF = 62.4 fluid load in pounds per cubic footWL = 0 live load is negligibleBf = Bfe Bf = 2.71 earth load bedding factorBfLL = N/A live load bedding factor is not applicableS = 4 inside diameter of pipe in feet


D0.01 = Equation 4.272.71 4

49,200 + 62.4 1.0

Answer: A pipe which would withstand a minimum three-edge bearing test loadfor the 0.01 inch crack of 4,539 pounds per linear foot per foot of insidehorizontal span would be required.

EXAMPLE 4-7Highway Live Load

Given: A 24 inch circular pipe is to be installed in a positive projectionembankment under an unsurfaced roadway and covered with 2.0 feet of120 pounds per cubic foot backfill material.


1. Determination of Earth Load (WE)Per the given information, the installation behaves as a positiveprojecting embankment. Therefore, use Equation 4.2 to determine thesoil prism load and multiply it by the appropriate vertical arching factor.

Bc

B





Do = 12


PL = 120 2 + 2.5 Equation 4.2 8

2.5 (4 - π)

Assume a Type 2 Standard Installation and use the appropriate verticalarching factor listed below Equation 4.2.

VAF = 1.4

WE = 1.40 x 680

WE = 952 pounds per linear foot Equation 4.1


2. Determination of Live Load (WL)Since the pipe is being installed under an unsurfaced roadway withshallow cover, a truck loading based on AASHTO will be evaluated.From Table 42, for D = 24 inches and H = 2.0 feet, a live load of 1,780pounds per linear foot is obtained. This live load value includes impact.WL = 1,780 pounds per linear foot

3. Selection of BeddingA Type 2 Standard Installation will be used for this example.

4. Determination of Bedding Factor, (Bfe)a.) Determination of Embankment Bedding Factor

From Illustration 4.21, the earth load bedding factor for a 24 inchpipe installed in a Type 2 positive projecting embankment conditionis 3.0.

Bfe = 3.0

b.) Determination of Live Load Bedding Factor, (BfLL)From Illustration 4.24, the live load bedding factor for a 24 inch pipeunder 2 feet of cover is 2.2.

BfLL = 2.2




6. Selection of Pipe StrengthThe D-load is given by equation 4.26

WE = 952 earth load in pounds per linear footWF = 62.4 fluid load in pounds per cubic footWL = 1,780 live load in pounds per linear footBf = Bfe Bf = 3 earth load bedding factorBfLL = 2.2 live load bedding factor is not applicableD = 2 inside diameter of pipe in feet

D0.01 = 597.3 pounds per linear foot per foot of diameter

D0.01 = Equation 4.263.0 2.2 4

952 + 62.4 1,780 1.0 +

Answer: A pipe which would withstand a minimum three-edge bearing test forthe 0.01 inch crack of 563 pounds per linear foot per foot of insidediameter would be required.

EXAMPLE 4-8Highway Live Load per AASHTO LRFD

Given: A 30-inch diameter, B wall, concrete pipe is to be installed as a stormdrain under a flexible pavement and subjected to AASHTO highwayloadings. The pipe will be installed in a 6 ft wide trench with a minimum of2 feet of cover over the top of the pipe. The AASHTO LRFD Criteria will beused with Select Granular Soil and a Type 3 Installation.

Find: The maximum 0.01” Dload required of the pipe.

1. Determination of Earth Load (WE)Per review of Table 19, the 6 ft. trench is wider than transition width.Therefore, the earth load is equal to the soil prism load multiplied by theappropriate vertical arching factor.

Bc

B





Do = 12

30 + 2 (3.5) Note: The wall thickness for a 30-inch pipe with a B wall is 3.5-inches per ASTM C76.

PL = 120 2 + 3.08 8

3.08 (4 - π)

Illustration 4.7 lists the vertical arching factors (VAFs) for the four typesof Standard Installations. Using a VAF of 1.40 for a Type 3 Installation,the earth load is:

WE = 1.40 x 861 Equation 4.1WE = 1,205 pounds per linear foot

The weight of concrete pavement must be included also. Assuming 150pounds per cubic foot unit weight of concrete, the total weight of soiland concrete is:WE = 1,205 + 150 x 1.0 x 3.08WE = 1,655 pounds per linear foot


2. Review project data.A 30-inch diameter, B wall, circular concrete pipe has a wall thickness of3.5 inches, per ASTM C76 therefore

Bc = 3.08

Bc = 12

30 + 2 (3.5)

And Ro, the outside height of the pipe, is 3.08 feet. Height of earth coveris 2 feet. Use AASHTO LRFD Criteria with Select Granular Soil Fill.

2. Calculate average pressure intensity of the live load on the plane at theoutside top of the pipe.From Illustration 4.12, the critical load, P, is 16,000 pounds from an HS20 single dual wheel, and the Spread Area is:

A = (Spread a)(Spread b)A = (1.67 + 1.15x2)(0.83 + 1.15x2)A = (3.97)(3.13)A = 12.4 square feet

I.M. = 33(1.0-0.125H)/100I.M. = 0.2475 (24.75%)w = P(1+IM)/Aw = 16,000(1+0.2475)/12.4w = 1,610 lb/ft2



3. Calculate total live load acting on the pipe.

WT = (w + LL)LSL

Assuming truck travel transverse to pipe centerline.

LL = 64L = Spread a = 3.97 feetSpread b = 3.13 feetBc = 3.08 feet, which is less than Spread b,

thereforeSL = 3.08 feetWT = (1,610 + 64) 3.97 x 3.08 = 20,500 pounds

Assuming truck travel parallel to pipe centerline.LL = 64Spread a = 3.97 feetL = Spread b = 3.13 feetBc = 3.08 feet, which is less than Spread a,

thereforeSL = 3.08 feetWT = (1,610 + 64) 3.08 x 3.13 = 16,100 pounds

WT Maximum = 20,500 pounds; and truck travel istransverse to pipe centerline

4. Calculate live load on pipe in pounds per linear foot, (WL)

Ro = 3.08 feetLe = L + 1.75 (3/4Ro)Le = 3.97 + 1.75(.75 x 3.08) = 8.01 feetWL = WT/LeWL = 20,500/8.01 = 2,559 pounds per linear foot

The pipe should withstand a maximum live load of 2,559 pounds perlinear foot.

5. Determination of Bedding Factor, (Bfe)

a) Determination of Embankment Bedding FactorThe embankment bedding factor for a Type 3 Installation may beinterpolated from Illustration 4.21

Bfe24 = 2.4Bfe36 = 2.3

Bfe30 = (2.4 - 2.3) + 2.3

Bfe30 = 2.334 - 24

36 - 30

3.97

3.13

3.13

3.97



b) Determination of Live Load Bedding Factor

From Illustration 4.24, the live load bedding factor for a 30 inch pipeunder 3 feet of cover (one foot of pavement and two feet of soil) canbe interpolated

BfLL24 = 2.4BfLL36 = 2.2Therefore BfLL30 = 2.3


7. Selection of Pipe Strength

WE = 1,655 earth load in pounds per linear footWF = 62.4 fluid load in pounds per cubic footWL = 2,559 live load in pounds per linear footBf = Bfe Bf = 2.35 earth load bedding factorBfLL = 2.3 live load bedding factor is not applicableD = 2.5 inside diameter of pipe in feet

D0.01 = Equation 4.262.35 2.3 2.5

1,655 + 62.4 2,559 1.0


+

Answer: A pipe which would withstand a minimum three-edge bearing test forthe 0.01 inch crack of 727 pounds per linear foot per foot of insidediameter would be required.

EXAMPLE 4-9Aircraft Live LoadRigid Pavement

Given: A 12 inch circular pipe is to be installed in a narrow trench, Bd = 3ft undera 12 inch thick concrete airfield pavement and subject to heavy

Bc

H



commercial aircraft loading. The pipe will be covered with 1.0 foot(measured from top of pipe to bottom of pavement slab) of sand andgravel material weighing 120 pounds per cubic foot.


1. Determination of Earth Load (WE)Per review of Table 13, the 3 ft. trench is wider than transition width.Therefore, the earth load is equal to the soil prism load multiplied by theappropriate vertical arching factor.


Do = 12


PL = 120 1 + 1.33 Equation 4.2 8

1.33 (4 - π)


Immediately listed below Equation 4.2 are the vertical arching factors(VAFs) for the four types of Standard Installations. Using a VAF of 1.40for a Type 2 Installation, the earth load is:

WE = 1.40 x 182 Equation 4.1WE = 255 pounds per linear foot

The weight of concrete pavement must be included also. Assuming 150pounds per cubic foot unit weight of concrete, the total weight of soiland concrete is:WE = 255 + 150 x 1.0 x 1.33WE = 455 pounds per linear foot


2. Determination of Live Load (WL)It would first be necessary to determine the bearing value of the backfilland/or subgrade. A modulus of subgrade reaction, k = 300 pounds percubic inch will be assumed for this example. This value is used in Table53A and represents a moderately compacted granular material, which isin line with the Type 2 Installation we are using.

Based on the number of undercarriages, landing gear configurationsand gross weights of existing and proposed future aircrafts, theConcorde is a reasonable commercial aircraft design loading for pipeplaced under airfields. From Table 53A, for D = 12 inches and H = 1.0foot, a live load of 1,892 pounds per linear foot is obtained.WL = 1892 pounds per linear foot



3. Selection of BeddingSince this installation is under an airfield, a relatively good installation isrequired, therefore use a Type 2 Installation.


From Illustration 4.21, the embankment bedding factor for a 12 inchpipe installed in a positive projecting embankment condition is 3.2.

Bfe = 3.2

b.) Determination of Live Load Bedding Factor

From Illustration 4.24, the live load bedding factor for a 12 inch pipeunder 2 feet of cover (one foot of pavement and one foot of soil) is2.2.

BfLL = 2.2



WE = 455 earth load in pounds per linear footWF = 62.4 fluid load in pounds per cubic footWL = 1,892 live load in pounds per linear footBf = Bfe Bf = 3.2 earth load bedding factorBfLL = 2.2 live load bedding factor is not applicableD = 1 inside diameter of pipe in feet

D0.01 = Equation 4.263.2 2.2 4

455 + 62.4 1,892 1.0


+

Answer: A pipe which would withstand a minimum three-edge bearing test forthe 0.01 inch crack of 1,002 pounds per linear foot per foot of insidediameter would be required.



EXAMPLE 4-10Aircraft Live LoadRigid Pavement

Given: A 68 inch x 106 inch horizontal elliptical pipe is to be installed in a positiveprojecting embankment condition under a 7 inch thick concrete airfieldpavement and subject to two 60,000 pound wheel loads spaced 20 feet,center to center. The pipe will be covered with 3-feet (measured from topof pipe to bottom of pavement slab) of sand and gravel material weighing120 pounds per cubic foot.


1. Determination of Earth Load (WE)Note: The Standard Installations were initially developed for circularpipe, and their benefit has not yet been established for elliptical andarch pipe. Therefore, the traditional Marston/Spangler design methodusing B and C beddings is still conservatively applied for these shapes.

A settlement ratio must first be assumed. In Table 40, values ofsettlement ratio from +0.5 to +0.8 are given for positive projectinginstallations on a foundation of ordinary soil. A value of 0.7 will beused. The product of the settlement ratio and the projection ratio will be0.49 (rsdp approximately 0.5).

Enter Figure 187 on the horizontal scale at H = 3 ft. Proceed verticallyuntil the line representing R x S = 68" x 106" is intersected. At this pointthe vertical scale shows the fill load to be 3,400 pounds per linear footfor 100 pounds per cubic foot fill material. Increase the load 20 percentfor 120 pound material.Wd = 3,400 x 1.2Wd = 4,080 pounds per linear footoutside span of pipe is:

H 20'

Bc = 10.25'

p1 = 943psf

p2 = 290psf 290psf



Bc = 10.25 feet Assuming 150 pounds per cubic foot concrete, the weight of the pavement is:Wp = 150 x 7/12 x 10.25 Wp = 897 pounds per linear footWE = Wd + Wp WE = 4,977 pounds per linear foot

Bc = 12

106 + 2 (8.5) Note: The wall thickness for a 68"x106" ellipitical pipe is 8.5-inches per ASTM C76.


2. Determination of Live Load (WL)

Assuming a modulus of subgrade reaction of k = 300 pounds per cubicinch and a pavement thickness of h = 7 inches, a radius of stiffness of24.99 inches (2.08 feet) is obtained from Table 52. The wheel spacingin terms of the radius of stiffness is 20/2.08 = 9.6 Rs, therefore themaximum live load on the pipe will occur when one wheel is directlyover the centerline of the pipe and the second wheel disregarded. Thepressure intensity on the pipe is given by Equation 4.15:

P(X,H) = C x P

Rs2

The pressure coefficient (C) is obtained from Table 46 at x = 0 and H =3 feet.

For x/Rs = 0 and H/Rs = 3/2.08 = 1.44, C = 0.068 by interpolationbetween H/Rs = 1.2 and H/Rs = 1.6 in Table 46.

p1 = Equation 4.15(0.068)(60,000)

(2.08)2

p1 = 943 pounds per square foot

In a similar manner pressure intensities are calculated at convenientincrements across the width of the pipe. The pressure coefficients andcorresponding pressures in pounds per square foot are listed in theaccompanying table.

x/Rs

Point 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8PressureCoefficient C 0.068 0.064 0.058 0.050 0.041 0.031 0.022 0.015Pressure psf 943 887 804 693 568 430 305 208

For convenience of computing the load in pounds per linear foot, thepressure distribution can be broken down into two components; a



uniform load and a parabolic load.

The uniform load occurs where the minimum load is applied to the pipeat:

xRs Rs

Bc

xRs

12 5.13

2.5

2.08=

=

=

The pressure, p2, is then interpolated between the points 2.4 and 2.8from the chart x/Rs above, and equal to 290 pounds per square foot.

The parabolic load (area of a parabola = 2/3ab, or in this case 2/3 (p1-p2)Bc has a maximum pressure of 653 pounds per foot.

Therefore the total love load, (WL) is equal to:

WL = p2 x Bc + 2/3 (p1-p2)BcWL = 290 x 10.25 + 2/3(943-290)10.25WL = 7,435 pounds per linear foot

3. Selection of BeddingA Class B bedding will be assumed for this example.


From Table 60, a Class B bedding with p = 0.7, H/Bc = 3 ft/10.25 ft. =0.3, and rsdp = 0.5, an embankment bedding factor of 2.42 isobtained.

Bfe = 2.42

b.) Determination of Live Load Bedding FactorLive Load Bedding Factors are given in Illustration 4.24 for circularpipe. These factors can be applied to elliptical pipe by using thespan of the pipe in place of diameter. The 106" span for the ellipticalpipe in this example is very close to the 108" pipe diameter value inthe table. Therefore, from Illustration 4.24, the live load beddingfactor for a pipe with a span of 108 inches, buried under 3.5 feet offill (3 feet of cover plus 7 inches of pavement is approx. 3.5 feet) is1.7.

BfLL = 1.7




6. Selection of pipe strengthThe D-load given is given by Equation 4.27

WE = 49,277 earth load in pounds per linear footWF = 62.4 fluid load in pounds per cubic footWL = 7,435 live load in pounds per linear footBf = Bfe Bf = 2.42 earth load bedding factorBfLL = 1.7 live load bedding factorS = 106/12 S = 8.83 inside span of pipe in feet


D0.01 = Equation 4.272.42 1.7 8.83

4,977 + 62.4 7,435 1.0 +

Answer: A pipe which would withstand a minimum three-edge bearing test loadfor the 0.01 inch crack of 728 pounds per linear foot per foot of insidehorizontal span would be required.

EXAMPLE 4-11Railroad Live Load

Given: A 48 inch circular pipe is to be installed under a railroad in a 9 foot widetrench. The pipe will be covered with 1.0 foot of 120 pounds per cubic footoverfill (measured from top of pipe to bottom of ties).


1. Determination of Earth Load (WE)The transition width tables do not have fill heights less than 5 ft. Withonly one foot of cover, assume an embankment condition. Aninstallation directly below the tracks such as this would probably requiregood granular soil well compacted around it to avoid settlement of thetracks. Therefore assume a Type 1 Installation and multiply the soil

BL

H



prism load by a vertical arching factor of 1.35.


Do = 12


PL = 120 1 + 4.83 Equation 4.2 8

4.83 (4 - π)


PL = 880 pounds per linear footImmediately listed below Equation 4.2 are the vertical arching factors(VAFs) for the four types of Standard Installations. Using a VAF of 1.35for a Type 1 Installation, the earth load is:

WE = 1.35 x 880WE = 1,188 pounds per linear foot Equation 4.1


83

CHAPTER 5

SUPPLEMENTAL DATA

CIRCULAR CONCRETE PIPEIllustration 5.2 includes tables of dimensions and approximate weights of

most frequently used types of circular concrete pipe. Weights are based onconcrete weighing 150 pounds per cubic foot. Concrete pipe may be producedwhich conforms to the requirements of the respective specifications but withincreased wall thickness and different concrete density.

ELLIPTICAL CONCRETE PIPEElliptical pipe, shown in Illustration 5.1, installed with the major axis horizontal

or vertical, represents two different products from the stand-point of structuralstrength, hydraulic characteristics and type of application. Illustration 5.3 includesthe dimensions and approximate weights of elliptical concrete pipe.

Illustration 5.1 Typical Cross Sections of Horizontal Elliptical and VerticalElliptical Pipe

Horizontal Elliptical (HE) Pipe. Horizontal elliptical concrete pipe is installedwith the major axis horizontal and is extensively used for minimum coverconditions or where vertical clearance is limited by existing structures. It offers thehydraulic advantage of greater capacity for the same depth of flow than mostother structures of equivalent water-way area. Under most embankmentconditions, its wide span results in greater earth loadings for the same height ofcover than for the equivalent size circular pipe and, at the same time, there is areduction in effective lateral support due to the smaller vertical dimension of thesection. Earth loadings are normally greater than for the equivalent circular pipe in

RIS

E RIS

ESPAN

HORIZONTAL ELLIPTICAL VERTICAL ELLIPTICAL

SPAN



Illustration 5.2 Dimensions and Approximate Weights of Concrete Pipe

These tables are based on concrete weighing 150 pounds per cubic foot and will vary with heavieror lighter weight concrete.

ASTM C 14 - Nonreinforced Sewer and Culvert Pipe, Bell and Spigot Joint.CLASS 1 CLASS 2 CLASS 3

Minimum Approx. Minimum Approx. Minimum Approx.Internal Wall Weight, Wall Weight, Wall Weight,

Diameter, Thickness, pounds Thickness, pounds Thickness, poundsinches inches per foot inches per foot inches per foot

4 5/8 9.5 3/4 13 7/8 15

6 5/8 17 3/4 20 1 24

8 3/4 27 7/8 31 1 1/8 36

10 7/8 37 1 42 1 1/4 50

12 1 50 1 3/8 68 1 3/4 90

15 1 1/4 80 1 5/8 100 1 7/8 120

18 1 1/2 110 2 160 2 1/4 170

21 1 3/4 160 2 1/4 210 2 3/4 260

24 2 1/8 200 3 320 3 3/8 350

27 3 1/4 390 3 3/4 450 3 3/4 450

30 3 1/2 450 4 1/4 540 4 1/4 540

33 3 3/4 520 4 1/2 620 4 1/2 620

36 4 580 4 3/4 700 4 3/4 700

ASTM C 76 - Reinforced Concrete Culvert, Storm Drain and Sewer Pipe,Bell and Spigot Joint.

WALL A WALL B

Internal Minimum Wall Approximate Minimum Wall ApproximateDiameter, Thickness Weight, pounds Thickness, Weight,pounds

inches inches per foot inches per foot

12 1 3/4 90 2 110

15 1 7/8 120 2 1/4 150

18 2 160 2 1/2 200

21 2 1/4 210 2 3/4 260

24 2 1/2 270 3 330

27 2 5/8 310 3 1/4 390

30 2 3/4 360 3 1/2 450

Supplemental Data 85


Illustration 5.2 (Continued) Dimensions and Approximate Weights ofConcrete Pipe

ASTM C 76 - Reinforced Concrete Culvert, Storm Drain and Sewer Pipe,Tongue and Groove Joints

WALL A WALL B WALL C

Minimum Approximate Minimum Approximate Minimum ApproximateInternal Wall Weight, Wall Weight, Wall Weight,

Diameter Thickness, pounds Thickness, pounds Thickness, poundsinches inches per foot inches per foot inches per foot

12 1 3/4 79 2 93 — —

15 1 7/8 103 2 1/4 127 — —

18 2 131 2 1/2 168 — —

21 2 1/4 171 2 3/4 214 — —

24 2 1/2 217 3 264 3 3/4 366

27 2 5/8 255 3 1/4 322 4 420

30 2 3/4 295 3 1/2 384 4 1/4 476

33 2 7/8 336 3 3/4 451 4 1/2 552

36 3 383 4 524 4 3/4 654

42 3 1/2 520 4 1/2 686 5 1/4 811

48 4 683 5 867 5 3/4 1011

54 4 1/2 864 5 1/2 1068 6 1/4 1208

60 5 1064 6 1295 6 3/4 1473

66 5 1/2 1287 6 1/2 1542 7 1/4 1735

72 6 1532 7 1811 7 3/4 2015

78 6 1/2 1797 7 1/2 2100 8 1/4 2410

84 7 2085 8 2409 8 3/4 2660

90 7 1/2 2395 8 1/2 2740 9 1/4 3020

96 8 2710 9 3090 9 3/4 3355

102 8 1/2 3078 9 1/2 3480 10 1/4 3760

108 9 3446 10 3865 10 3/4 4160



These tables are based on concrete weighing 150 pounds per cubic foot and will vary with heavieror lighter weight concrete.

the trench condition, since a greater trench width is usually required for HE pipe.For shallow cover, where live load requirements control the design, loading isalmost identical to that for an equivalent size circular pipe with the same invertelevation.

Vertical Elliptical (VE) Pipe. Vertical elliptical concrete pipe is installed withthe major axis vertical and is useful where minimum horizontal clearances areencountered or where unusual strength characteristics are desired. Hydraulically,it provides higher flushing velocities under minimum flow conditions and carriesequal flow at a greater depth than equivalent HE or circular pipe. For trenchconditions the smaller span requires less excavation than an equivalent sizecircular pipe and the pipe is subjected to less vertical earth load due to thenarrower trench. The structural advantages of VE pipe are particularly applicablein the embankment condition where the greater height of the section increases theeffective lateral support while the vertical load is reduced due to the smaller span.

CONCRETE ARCH PIPEArch pipe, as shown in Illustration 5.4, is useful in minimum cover situations

or other conditions where vertical clearance problems are encountered. It offersthe hydraulic advantage of greater capacity for the same depth of flow than mostother structures of equivalent water-way area. Structural characteristics are

Large Sizes of Pipe Tongue and Groove JointInternal Internal Wall Approximate

Diameter Diameter Thickness Weight, poundsInches Feet Inches per foot

114 9 1/2 9 1/2 3840

120 10 10 4263

126 10 1/2 10 1/2 4690

132 11 11 5148

138 11 1/2 11 1/2 5627

144 12 12 6126

150 12 1/2 12 1/2 6647

156 13 13 7190

162 13 1/2 13 1/2 7754

168 14 14 8339

174 14 1/2 14 1/2 8945

180 15 15 9572

Illustration 5.2 (Continued) Dimensions and Approximate Weights ofConcrete Pipe



similar to those of horizontal elliptical pipe in that under similar cover conditions itis subject to the same field load as a round pipe with the same span. Forminimum cover conditions where live load requirements control the design, theloading to which arch pipe is subjected is almost identical to that for an equivalentsize circular pipe with the same invert elevation. Illustration 5.5 includes thedimensions and approximate weights of concrete arch pipe.

Illustration 5.3 Dimensions and Approximate Weights of EllipticalConcrete Pipe

ASTM C 507-Reinforced Concrete Elliptical Culvert,Storm Drain and Sewer Pipe

Equivalent Minor Major Minimum Wall Water-Way ApproximateRound Size, Axis, Axis, Thickness, Area, Weight, pounds

inches inches inches inches square feet per foot

18 14 23 2 3/4 1.8 195

24 19 30 3 1/4 3.3 300

27 22 34 3 1/2 4.1 365

30 24 38 3 3/4 5.1 430

33 27 42 3 3/4 6.3 475

36 29 45 4 1/2 7.4 625

39 32 49 4 3/4 8.8 720

42 34 53 5 10.2 815

48 38 60 5 1/2 12.9 1000

54 43 68 6 16.6 1235

60 48 76 6 1/2 20.5 1475

66 53 83 7 24.8 1745

72 58 91 7 1/2 29.5 2040

78 63 98 8 34.6 2350

84 68 106 8 1/2 40.1 2680

90 72 113 9 46.1 3050

96 77 121 9 1/2 52.4 3420

102 82 128 9 3/4 59.2 3725

108 87 136 10 66.4 4050

114 92 143 10 1/2 74.0 4470

120 97 151 11 82.0 4930

132 106 166 12 99.2 5900

144 116 180 13 118.6 7000



Illustration 5.4 Typical Cross Section of Arch Pipe

Illustration 5.5 Dimensions and Approximate Weights ofConcrete Arch Pipe

ASTM C 506 - Reinforced Concrete Arch Culvert, Storm Drain and Sewer PipeMinimum Approximate

Equivalent Minimum Minimum Wall Water-Way Weight,Round Size, Rise, Span, Thickness, Area, pounds

inches inches inches inches square feet per foot

15 11 18 2 1/4 1.1 —

18 13 1/2 22 2 1/2 1.65 170

21 15 1/2 26 2 3/4 2.2 225

24 18 28 1/2 3 2.8 320

30 22 1/2 36 1/4 3 1/2 4.4 450

36 26 5/8 43 3/4 4 6.4 595

42 31 5/16 51 1/8 4 1/2 8.8 740

48 36 58 1/2 5 11.4 880

54 40 65 5 1/2 14.3 1090

60 45 73 6 17.7 1320

72 54 88 7 25.6 1840

84 62 102 8 34.6 2520

90 72 115 8 1/2 44.5 2750

96 77 1/4 122 9 51.7 3110

108 87 1/8 138 10 66.0 3850

120 96 7/8 154 11 81.8 5040

132 106 1/2 168 3/4 10 99.1 5220

RIS

E

SPAN



Illustration 5.6 Typical Cross Section of Precast Concrete Box Sections

CONCRETE BOX SECTIONSPrecast concrete box sections, as shown in Illustration 5.6, are useful in

minimum cover and width situations or other conditions where clearance problemsare encountered, for special waterway requirements, or designer preference.Illustration 5.7 includes the dimensions and approximate weights of standardprecast concrete box sections. Special design precast concrete box sections maybe produced which conform to the requirements of the respective specificationsbut in different size and cover conditions.

TWALL

SPAN

RISE

TWALL

TTOP SLABSymmetrical

TBOTTOM SLAB



ASTM C1433 - PRECAST REINFORCED CONCRETE BOX SECTIONSWaterway Approx.

Thickness (in.) Area Weigh†Span (Ft.) Rise (Ft.) Top Slab Bot. Slab Wall (Sq. Feet) (lbs/ft)

3 2 7 6 4 5.8 8303 3 7 6 4 8.8 9304 2 7 1/2 6 5 7.7 11204 3 7 1/2 6 5 11.7 12404 4 7 1/2 6 5 15.7 13705 3 8 7 6 14.5 16505 4 8 7 6 19.5 18005 5 8 7 6 24.5 19506 3 8 7 7 17.3 19706 4 8 7 7 23.3 21506 5 8 7 7 29.3 23206 6 8 7 7 35.3 25007 4 8 8 8 27.1 26007 5 8 8 8 34.1 28007 6 8 8 8 41.1 30007 7 8 8 8 48.1 32008 4 8 8 8 31.1 28008 5 8 8 8 39.1 30008 6 8 8 8 47.1 32008 7 8 8 8 55.1 34008 8 8 8 8 63.1 36009 5 9 9 9 43.9 36609 6 9 9 9 52.9 38809 7 9 9 9 61.9 41109 8 9 9 9 70.9 43309 9 9 9 9 79.9 4560

10 5 10 10 10 48.6 438010 6 10 10 10 58.6 463010 7 10 10 10 68.6 488010 8 10 10 10 78.6 513010 9 10 10 10 88.6 538010 10 10 10 10 98.6 563011 4 11 11 11 42.3 488011 6 11 11 11 64.3 543011 8 11 11 11 86.3 598011 10 11 11 11 108.3 653011 11 11 11 11 119.3 681012 4 12 12 12 46.0 570012 6 12 12 12 70.0 630012 8 12 12 12 94.5 690012 10 12 12 12 118.0 750012 12 12 12 12 142.0 8100

Illustration 5.7 Dimensions and Approximate Weights ofConcrete Box Sections



SPECIAL SECTIONS

Precast Concrete Manhole Sections. Precast manholes offer significantsavings in installed cost over cast-in-place concrete, masonry or brick manholesand are universally accepted for use in sanitary or storm sewers. Precast,reinforced concrete manhole sections are available throughout the United Statesand Canada, and are generally manufactured in accordance with the provisions ofAmerican Society for Testing and Materials Standard C 478.

The typical precast concrete manhole as shown in Illustration 5.8 consists ofriser sections, a top section and grade rings and, in many cases, precast basesections or tee sections. The riser sections are usually 48 inches in diameter, butare available from 36 inches up to 72 inches and larger. They are of circular crosssection, and a number of sections may be joined vertically on top of the base orjunction chamber. Most precast manholes employ an eccentric or a concentriccone section instead of a slab top. These reinforced cone sections affect thetransition from the inside diameter of the riser sections to the specified size of thetop opening. Flat slab tops are normally used for very shallow manholes andconsist of a reinforced circular slab at least 6-inches thick for risers up to 48inches in diameter and 8-inches thick for larger riser sizes. The slab which restson top of the riser sections is cast with an access opening.

Precast grade rings, which are placed on top of either the cone or flat slab topsection, are used for close adjustment of top elevation. Cast iron manhole coverassemblies are normally placed on top of the grade rings.

The manhole assembly may be furnished with or without steps inserted intothe walls of the sections. Reinforcement required by ASTM Standard C 478 isprimarily designed to resist handling stresses incurred before and duringinstallation, and is more than adequate for that purpose. Such stresses are moresevere than those encountered in the vertically installed manhole. In normalinstallations, the intensity of the earth loads transmitted to the manhole risers isonly a fraction of the intensity of the vertical pressure.

The maximum allowable depth of a typical precast concrete manhole withregard to lateral earth pressures is in excess of 300 feet or, for all practicalpurposes, unlimited, Because of this, the critical or limiting factor for manholedepth is the supporting strength of the base structure or the resistance to crushingof the ends of the riser section. This phenomena, being largely dependent on therelative settlement of the adjacent soil mass, does not lend itself to preciseanalysis. Even with extremely conservative values for soil weights, lateralpressure and friction coefficients, it may be concluded several hundred feet canbe safely supported by the riser sections without end crushing, based on theassumption that provision is made for uniform bearing at the ends of the risersections and the elimination of localized stress concentrations.



Illustration 5.8 Typical Configuration of Precast Manhole Sections

standardman holeframe andcover

grade ringsor brickflat slab top

base


grade ringsor brick

eccentriccone

base


grade ringsor brick

eccentriccone

transitionsection

base


grade ringsor brick

eccentriccone

transitionsection

base


grade ringsor brick

concentriccone

base

base


grade ringsor brick

concentriccone

riser

riser

riser riser

riser



When confronted with manhole depths greater than those commonlyencountered, there may be a tendency to specify additional circumferentialreinforcement in the manhole riser sections. Such requirements are completelyunnecessary and only result in increasing the cost of the manhole structure.

A number of joint types may be used for manhole risers and tops, includingmortar, mastic, rubber gaskets or combinations of these three basic types forsealing purposes. Consideration should be given to manhole depth, the presenceof groundwater and the minimum allowable leakage rates in the selection ofspecific joint requirements.

Flat Base Pipe. Flat base pipe as shown in Illustration 5.9 has been used ascattle passes, pedestrian underpasses and utility tunnels. It is normally furnishedwith joints designed for use with mortar or mastic fillers and may be installed bythe conventional open trenching method or by jacking.

Although not covered by any existing national specification, standard designshave been developed by various manufacturers which are appropriate for a widerange of loading conditions.

Illustration 5.9 Typical Cross Sections of Flat Base Pipe

STANDARD SPECIFICATIONS FOR CONCRETE PIPENationally accepted specifications covering concrete pipe along with the

applicable size ranges and scopes of the individual specifications are included inthe following list.

AMERICAN SOCIETY FOR TESTING AND MATERIALS (ASTM)

ASTM C 14 Concrete Sewer, Storm Drain and Culvert Pipe: Coversnonreinforced concrete pipe intended to be used for theconveyance of sewage, industrial wastes, storm water, and for theconstruction of culverts in sizes from 4 inches through 36 inches indiameter.



ASTM C 76 Reinforced Concrete Culvert, Storm Drain, and Sewer Pipe:Covers reinforced concrete pipe intended to be used for theconveyance of sewage, industrial wastes, and storm waters, andfor the construction of culverts. Class I - 60 inches through 144inches in diameter; Class II, III, IV and V - 12 inches through 144inches in diameter. Larger sizes and higher classes are availableas special designs.

ASTM C 118 Concrete Pipe for Irrigation or Drainage: Covers concrete pipeintended to be used for the conveyance of irrigation water underlow hydrostatic heads, generally not exceeding 25 feet, and for usein drainage in sizes from 4 inches through 24 inches in diameter.

ASTM C 361 Reinforced Concrete Low-Head Pressure Pipe: Covers reinforcedconcrete pipe intended to be used for the construction of pressureconduits with low internal hydrostatic heads generally notexceeding 125 feet in sizes from 12 inches through 108 inches indiameter.

ASTM C 412 Concrete Drain Tile: Covers nonreinforced concrete drain tile withinternal diameters from 4 inches to 24 inches for Standard Quality,and 4 inches to 36 inches for Extra-Quality, Heavy-Duty Extra-Quality and Special Quality Concrete Drain Tile.

ASTM C 443 Joints for Circular Concrete Sewer and Culvert Pipe, with RubberGaskets: Covers joints where infiltration or exfiltration is a factor inthe design, including the design of joints and the requirements forrubber gaskets to be used therewith for pipe conforming in all otherrespects to ASTM C 14 or ASTM C 76.

ASTM C 444 Perforated Concrete Pipe: Covers perforated concrete pipeintended to be used for underdrainage in sizes 4 inches and larger.

ASTM C 478 Precast Reinforced Concrete Manhole Sections: Covers precastreinforced concrete manhole risers, grade rings and tops to beused to construct manholes for storm and sanitary sewers.

ASTM C 497 Standard Test Methods for Concrete Pipe, Manhole Sections, orTile: Covers procedures for testing concrete pipe and tile.

ASTM C 505 Nonreinforced Concrete Irrigation Pipe With Rubber Gasket Joints:Covers pipe to be used for the conveyance of irrigation water withworking pressures, including hydraulic transients, of up to 30 feetof head. Higher pressures may be used up to a maximum of 50feet for 6 inch through 12 inch diameters, and 40 feet for 15 inchthrough 18 inch diameters by increasing the strength of the pipe.



ASTM C 506 Reinforced Concrete Arch Culvert, Storm Drain, and Sewer Pipe:Covers pipe to be used for the conveyance of sewage, industrialwaste, and storm water and for the construction of culverts in sizesfrom 15 inch through 132 inch equivalent circular diameter. Largersizes are available as special designs.

ASTM C 507 Reinforced Concrete Elliptical Culvert, Storm Drain, and SewerPipe: Covers reinforced elliptically shaped concrete pipe to beused for the conveyance of sewage, industrial waste and stormwater, and for the construction of culverts. Five standard classes ofhorizontal elliptical, 18 inches through 144 inches in equivalentcircular diameter and five standard classes of vertical elliptical, 36inches through 144 inches in equivalent circular diameter areincluded. Larger sizes are available as special designs.

ASTM C 655 Reinforced Concrete D-load Culvert, Storm Drain and Sewer Pipe:Covers acceptance of pipe design and production pipe based uponthe D-load concept and statistical sampling techniques forconcrete pipe to be used for the conveyance of sewage, industrialwaste and storm water and construction of culverts.

ASTM C 822 Standard Definitions and Terms Relating to Concrete Pipe andRelated Products: Covers words and terms used in concrete pipestandards.

ASTM C 877 External Sealing Bands for NonCircular Concrete Sewer, StormDrain and Culvert Pipe: Covers external sealing bands to be usedfor noncircular pipe conforming to ASTM C 506, C 507, C 789 andC 850.

ASTM C 923 Resilient Connectors Between Reinforced Concrete ManholeStructures and Pipes: Covers the minimum performance andmaterial requirements for resilient connections between pipe andreinforced concrete manholes conforming to ASTM C 478.

ASTM C 924 Testing Concrete Pipe Sewer Lines by Low-Pressure Air TestMethod: Covers procedures for testing concrete pipe sewer lineswhen using the low-pressure air test method to demonstrate theintegrity of the installed material and construction procedures.

ASTM C 969 Infiltration and Exfiltration Acceptance Testing of Installed PrecastConcrete Pipe Sewer Lines: Covers procedures for testinginstalled precast concrete pipe sewer lines using either waterinfiltration or exfiltration acceptance limits to demonstrate theintegrity of the installed materials and construction procedure.



ASTM C 985 Nonreinforced Concrete Specified Strength Culvert, Storm Drain,and Sewer Pipe: Covers nonreinforced concrete pipe designed forspecified strengths and intended to be used for the conveyance ofsewage, industrial wastes, storm water, and for the construction ofculverts.

ASTM C 990 Joints for Concrete Pipe, Manholes, and Precast Box SectionsUsing Preformed Flexible Sealants: Covers joints for precastconcrete pipe, box, and other sections using preformed flexiblejoint sealants for use in storm sewers and culverts which are notintended to operate under internal pressure, or are not subject toinfiltration or exfiltration limits.

ASTM C 1103 Joint Acceptance Testing of Installed Precast Concrete Pipe SewerLines: Covers procedures for testing the joints of installed precastconcrete pipe sewer lines, when using either air or water under lowpressure to demonstrate the integrity of the joint and constructionprocedure.

ASTM C 1131 Least Cost (Life Cycle) Analysis of Concrete Culvert, StormSewer, and Sanitary Sewer Systems: Covers procedures for leastcost (life cycle) analysis (LCA) of materials, systems, or structuresproposed for use in the construction of concrete culvert, stormsewer and sanitary sewer systems.

ASTM C 1214 Test Method for Concrete Pipe Sewerlines by Negative AirPressure (Vacuum) Test Method: Covers procedures for testingconcrete pipe sewerlines, when using the negative air pressure(vacuum) test method to demonstrate the integrity of the installedmaterial and the construction procedures.

ASTM C 1244 Test Method for Concrete Sewer Manholes by the Negative AirPressure (Vacuum) Test: Covers procedures for testing precastconcrete manhole sections when using the vacuum test method todemonstrate the integrity of the installed materials and theconstruction procedures.

ASTM C 1417 Manufacture of Reinforced Concrete Sewer, Storm Drain, andCulvert Pipe for Direct Design: Covers the manufacture andacceptance of precast concrete pipe designed to conform to theowner’s design requirements and to ASCE 15-93 (Direct DesignStandard) or an equivalent design specification.

ASTM C 1433 Precast Reinforced Concrete Box Sections for Culverts, StormDrains, and Sewers: Covers single-cell precast reinforced concretebox sections intended to be used for the construction of culverts



for the conveyance of storm water and industrial wastes andsewage.

AMERICAN ASSOCIATION OF STATE HIGHWAY ANDTRANSPORTATION OFFICIALS (AASHTO)

AASHTO M 86 Concrete Sewer, Storm Drain, and Culvert Pipe: Similar toASTM C 14.

AASHTO M 170 Reinforced Concrete Culvert, Storm Drain, and Sewer Pipe:Similar to ASTM C 76.

AASHTO M 175 Perforated Concrete Pipe: Similar to ASTM C 444.

AASHTO M 178 Concrete Drain Tile: Similar to ASTM C 412.

AASHTO M 198 Joints for Circular Concrete Sewer and Culvert Pipe, UsingFlexible Watertight Gaskets: Similar to ASTM C 990.

AASHTO M 199 Precast Reinforced Concrete Manhole Sections: Similar toASTM C 478.

AASHTO M 206 Reinforced Concrete Arch Culvert, Storm Drain, and SewerPipe: Similar to ASTM C 506.

AASHTO M 207 Reinforced Concrete Elliptical Culvert, Storm Drain, and SewerPipe: Similar to ASTM C 507.

AASHTO M 242 Reinforced Concrete D-Load Culvert, Storm Drain, and SewerPipe: Similar to ASTM C 655.

AASHTO M 259 Precast Reinforced Concrete Box Sections for Culverts, StormDrains and Sewers: Similar to ASTM C 789.

AASHTO M 262 Concrete Pipe and Related Products: Similar to ASTM C 882.

AASHTO M 273 Precast Reinforced Box Section for Culverts, Storm Drains, andSewers with less than 2 feet of Cover Subject to HighwayLoadings: Similar to ASTM C 850.

AASHTO T 280 Methods of Testing Concrete Pipe, Sections, or Tile: Similar toASTM C 497.

AASHTO M 315 Joints for Circular Concrete Sewer and Culvert Pipe, UsingRubber Gaskets: Similar to ASTM C 443.



PIPE JOINTS

Pipe joints perform a variety of functions depending upon the type of pipe andits application. To select a proper joint, determine which of the followingcharacteristics are pertinent and what degree of performance is acceptable.

Joints are designed to provide:1. Resistance to infiltration of ground water and/or backfill material.2. Resistance to exfiltration of sewage or storm water.3. Control of leakage from internal or external heads.4. Flexibility to accommodate lateral deflection or longitudinal movement

without creating leakage problems.5. Resistance to shear stresses between adjacent pipe sections without

creating leakage problems.6. Hydraulic continuity and a smooth flow line.7. Controlled infiltration of ground water for subsurface drainage.8. Ease of installation.

The actual field performance of any pipe joint depends primarily upon theinherent performance characteristics of the joint itself, the severity of theconditions of service, and the care with which it is installed.

Since economy is important, it is usually necessary to compare the installedcost of several types of joints against pumping and treatment costs resulting fromincreased or decreased amounts of infiltration.

The concrete pipe industry utilizes a number of different joints, listed below, tosatisfy a broad range of performance requirements. These joints vary in cost, aswell as in inherent performance characteristics. The field performance of all isdependent upon proper installation procedures.

• Concrete surfaces, either bell and spigot or tongue and groove, with somepacking such as cement mortar, a preformed mastic compound, or a trowelapplied mastic compound, as shown in Illustration 5.10. These joints haveno inherent watertightness but depend exclusively upon the workmanshipof the contractor. Field poured concrete diapers or collars are sometimesused with these joints to improve performance. Joints employing mortarjoint fillers are rigid, and any deflection or movement after installation willcause cracks permitting leakage. If properly applied, mastic joint fillersprovide a degree of flexibility without impairing watertightness. These jointsare not generally recommended for any internal or external head conditionsif leakage is an important consideration. Another jointing system used withthis type joint is the external sealing band type rubber gasket conforming toASTM C 877. Generally limited to straight wall and modified tongue andgroove configurations, this jointing system has given good results inresisting external heads of the magnitude normally encountered in sewerconstruction.



Illustration 5.10 Typical Cross Sections of Joints With Mortar or MasticPacking

• Concrete surfaces, with or without shoulders on the tongue or the groove,with a compression type rubber gasket as shown in Illustration 5.11.Although there is wide variation in joint dimensions and gasket crosssection for this type joint, most are manufactured in conformity with ASTMC 443. This type joint is primarily intended for use with pipe manufacturedto meet the requirements of ASTM C 14 or ASTM C 76 and may be usedwith either bell and spigot or tongue and groove pipe.

Illustration 5.11 Typical Cross Sections of Basic Compression Type RubberGasket Joints

• Concrete surfaces with opposing shoulders on both the bell and spigot foruse with an 0-ring, or circular cross section, rubber gasket as shown inIllustration 5.12. Basically designed for low pressure capability, these jointsare frequently used for irrigation lines, waterlines, sewer force mains, andgravity or low head sewer lines where infiltration or exfiltration is a factor inthe design. Meeting all of the requirements of ASTM C 443, these typejoints are also employed with pipe meeting the requirements of ASTM C361. They provide good inherent watertightness in both the straight anddeflected positions, which can be demonstrated by plant tests.

MORTOR PACKING MASTIC PACKING



Illustration 5.12 Typical Cross Sections of Opposing Shoulder Type JointWith 0-ring Gasket

• Concrete surfaces with a groove on the spigot for an 0-ring rubber gasket,as shown in Illustration 5.13. Also referred to as a confined 0-ring type joint,these are designed for low pressure capabilities and are used for irrigationlines, water lines, sewer force mains, and sewers where infiltration orexfiltration is a factor in the design. This type joint, which provides excellentinherent watertightness in both the straight and deflected positions, may beemployed to meet the joint requirements of ASTM C 443 and ASTM C 361.

Illustration 5.13 Typical Cross Section of Spigot Groove Type JointWith 0-ring Gasket

• Steel bell and spigot rings with a groove on the spigot for an 0-ring rubbergasket, as shown in Illustration 5.14. Basically a high pressure jointdesigned for use in water transmission and distribution lines, these are alsoused for irrigation lines, sewer force mains, and sewers where infiltration or



exfiltration is a factor in the design. This type of joint will meet the jointrequirements of ASTM C 443 and ASTM C 361. Combining great shearstrength and excellent inherent watertightness and flexibility, this type jointis the least subject to damage during installation.

Illustration 5.14 Typical Cross Section of Steel End Ring Joint With SpigotGroove and 0-ring Gasket

Since both field construction practices and conditions of service are subject tovariation, it is impossible to precisely define the field performance characteristicsof each of the joint types. Consultation with local concrete pipe manufacturers willprovide information on the availability and cost of the various joints. Based on thisinformation and an evaluation of groundwater conditions, the specifications shoulddefine allowable infiltration or exfiltration rates and/or the joint types which areacceptable.

JACKING CONCRETE PIPE

Concrete pipelines were first jacked in place by the Northern Pacific Railroadbetween 1896 and 1900. In more recent years, this technique has been applied tosewer construction where intermediate shafts along the line of the sewer are usedas jacking stations.

Reinforced concrete pipe as small as 18-inch inside diameter and as large as132-inch inside diameter have been installed by jacking.

Required Characteristics of Concrete Jacking Pipe. Two types of loadingconditions are imposed on concrete pipe installed by the jacking method; the axialload due to the jacking pressures applied during installation, and the earth loadingdue to the overburden, with some possible influence from live loadings, which willgenerally become effective only after installation is completed.

It is necessary to provide for relatively uniform distribution of the axial loadaround the periphery of the pipe to prevent localized stress concentrations. This isaccomplished by keeping the pipe ends parallel within the tolerances prescribedby ASTM C 76, by using a cushion material, such as plywood or hardboard,



between the pipe sections, and by care on the part of the contractor to insure thatthe jacking force is properly distributed through the jacking frame to the pipe andparallel with the axis of the pipe. The cross sectional area of the concrete pipewall is more than adequate to resist pressures encountered in any normal jackingoperation. For projects where extreme jacking pressures are anticipated due tolong jacking distances or excessive unit frictional forces, higher concretecompressive strength may be required, along with greater care to avoid bearingstress concentrations. Little or no gain in axial crushing resistance is provided byspecifying a higher class of pipe.

For a comprehensive treatment of earth loads on jacked pipe see Chapter 4.The earth loads on jacked pipe are similar to loads on a pipe installed in a trenchwith the same width as the bore with one significant difference. In a jacked pipeinstallation the cohesive forces within the soil mass in most instances areappreciable and tend to reduce the total vertical load on the pipe. Thus the verticalload on a jacked pipe will always be less than on a pipe in a trench installationwith the same cover and, unless noncohesive materials are encountered, can besubstantially less.

With the proper analysis of loadings and selection of the appropriate strengthclass of pipe, few additional characteristics of standard concrete pipe need beconsidered. Pipe with a straight wall, without any increase in outside diameter atthe bell or groove, obviously offers fewer problems and minimizes the requiredexcavation. Considerable quantities of modified tongue and groove pipe havebeen jacked, however, and presented no unusual problems.

The Jacking Method. The usual procedure in jacking concrete pipe is toequip the leading edge with a cutter, or shoe, to protect the pipe. As succeedinglengths of pipe are added between the lead pipe and the jacks, and the pipejacked forward, soil is excavated and removed through the pipe. Material istrimmed with care and excavation does not precede the jacking operation morethan necessary. Such a procedure usually results in minimum disturbance of thenatural soils adjacent to the pipe.

Contractors occasionally find it desirable to coat the outside of the pipe with alubricant, such as bentonite, to reduce the frictional resistance. In some instances,this lubricant has been pumped through special fittings installed in the wall of thepipe.

Because of the tendency of jacked pipe to “set” when forward movement isinterrupted for as long as a few hours, resulting in significantly increased frictionalresistance, it is desirable to continue jacking operations until completed.

In all jacking operations it is important that the direction of jacking be carefullyestablished prior to beginning the operation. This requires the erection of guiderails in the bottom of the jacking pit or shaft. In the case of large pipe, it isdesirable to have such rails carefully set in a concrete slab. The number andcapacity of the jacks required depend primarily upon the size and length of thepipe to be jacked and the type of soil encountered.



Illustration 5.15 Steps in Jacking Concrete Pipe

1. Pits are excavated oneach side. The jacks willbear against the back ofthe left pit so a steel orwood abutment is addedfor reinforcement. Asimple track is added toguide the concrete pipesection. The jack(s) arepositioned in place onsupports.

2. A section of concretepipe is lowered into thepit.

3. The jack(s) are operatedpushing the pipe sectionforward.

4. The jack ram(s) areretracted and a “spacer” isadded between the jack(s)and pipe.

5. The jack(s) are operatedand the pipe is pushedforward again.

6. It may becomenecessary to repeat theabove steps 4 and 5several times until the pipeis pushed forward enoughto allow room for the nextsection of pipe. It isextremely important,therefore, that the strokesof the jacks be as long aspossible to reduce thenumber of spacersrequired and therebyreduce the amount of timeand cost. The idealsituation would be to havethe jack stroke longer thanthe pipe to completelyeliminate the need forspacers.

7. The next section of pipeis lowered into the pit andthe above steps repeated.The entire process aboveis repeated until theoperation is complete.

Track

Jack

Spacer

Jack SupportAbutment

Pipe

Pipe

Pipe

Pipe

Pipe Pipe

Pipe Pipe Pipe Pipe

2

3

4

5

6

7

1



Backstops for the jacks must be strong enough and large enough to distributethe maximum capacity of the jacks against the soil behind the backstops. A typicalinstallation for jacking concrete pipe is shown in Illustration 5.15.

BENDS AND CURVES

Changes in direction of concrete pipe sewers are most commonly effected atmanhole structures. This is accomplished by proper location of the inlet and outletopenings and finishing of the invert in the structure to reflect the desired angularchange of direction.

In engineering both grade and alignment changes in concrete pipelines it isnot always practical or feasible to restrict such changes to manhole structures.Fortunately there are a number of economical alternatives.

Deflected Straight Pipe. With concrete pipe installed in straight alignmentand the joints in a home (or normal) position, the joint space, or distance betweenthe ends of adjacent pipe sections, will be essentially uniform around theperiphery of the pipe. Starting from this home position any joint may be opened upto a maximum permissible joint opening on one side while the other side remainsin the home position. The difference between the home and opened joint space isgenerally designated as the pull. This maximum permissible opening retains somemargin between it and the limit for satisfactory function of the joint. It varies fordifferent joint configurations and is best obtained from the pipe manufacturer.

Opening a joint in this manner effects an angular deflection of the axis of thepipe, which, for any given pull is a function of the pipe diameter. Thus, given thevalues of any two of the three factors; pull, pipe diameter, and deflection angle,the remaining factor may be readily calculated.

The radius of curvature which may be obtained by this method is a function ofthe deflection angle per joint and the length of the pipe sections. Thus, longerlengths of pipe will provide a longer radius for the same pull than would beobtained with shorter lengths.The radius of curvature is computed by theequation:

R = L

N∆2(tan 1/2 x )

where:R = Radius of curvature, feetL = Average laid length of pipe sections measured along the centerline, feet∆ = Total deflection angle of curve, degreesN = Number of pipe with pulled joints∆ = Total deflection of each pipe, degreesN



Using the deflected straight pipe method, Illustration 5.16 shows that the P.C.(point of curve) will occur at the midpoint of the last undeflected pipe and the P.T.(point of tangent) will occur at the midpoint of the last pulled pipe.

Illustration 5.16 Curved Alignment Using Deflected Straight Pipe

Radius Pipe. Sharper curvature with correspondingly shorter radii can beaccommodated with radius pipe than with deflected straight pipe. This is due tothe greater deflection angle per joint which may be used. In this case the pipe ismanufactured longer on one side than the other and the deflection angle is built inat the joint. Also referred to as bevelled or mitered pipe, it is similar in severalrespects to deflected straight pipe. Thus, shorter radii may be obtained withshorter pipe lengths; the maximum angular deflection which can be obtained ateach joint is a function of both the pipe diameter and a combination of thegeometric configuration of the joint and the method of manufacture.

These last two factors relate to how much shortening or drop can be appliedto one side of the pipe. The maximum drop for any given pipe is best obtainedfrom the manufacturer of the pipe since it is based on manufacturing feasibility.

The typical alignment problem is one in which the total ∆ angle of the curveand the required radius of curvature have been determined. The diameter anddirection of laying of the pipe are known. To be determined is whether the curvecan be negotiated with radius pipe and, if so, what combination of pipe lengthsand drop are required. Information required from the pipe manufacturer is themaximum permissible drop, the wall thicknesses of the pipe and the standardlengths in which the pipe is available. Any drop up to the maximum may be usedas required to fit the curve.

Values obtained by the following method are approximate, but are within arange of accuracy that will permit the pipe to be readily installed to fit the requiredalignment.

RADIUSNormal

Directi

on of

Layin

g

P. C. P. T.

L

L2

P.I.

∆/N

∆/N

∆/N

∆/N

∆/N

∆/N ∆/N

∆

∆



The tangent of the deflection angle, N∆ required at each joint is computed by

the equation:

tan = LN∆

R + D/2 + t

where:∆ = Total deflection angle of curve, degreesN = Number of radius pipeL = The standard pipe length being used, feetR = Radius of curvature, feetD = Inside diameter of the pipe, feett = Wall thickness of the pipe, feet

The required drop in inches to provide the deflection angle, N∆ computed

by the equation:

Drop = 12(D + 2t) tanN∆

The number of pieces of radius pipe required is equal to the length of thecircular curve in feet divided by the centerline length of the radius pipe(L - 1/2 Drop). Minor modifications in the radius are normally made so this quotientwill be a whole number.

If the calculated drop exceeds the maximum permissible drop, it will benecessary to either increase the radius of curvature or to use shorter pipe lengths.Otherwise special fittings must be used as covered in the next section.

It is essential that radius pipe be oriented such that the plane of the droppedjoint is at right angles to the theoretical circular curve. For this reason lifting holesin the pipe must be accurately located, or, if lifting holes are not provided, the topof the pipe should be clearly and accurately marked by the manufacturer so thatthe deflection angle is properly oriented.

It should also be noted that a reasonable amount of field adjustment ispossible by pulling the radius pipe joints in the same manner as with deflectedstraight pipe.



Illustration 5.17 Curved Alignment Using Radius Pipe

As indicated in Illustration 5.17, the P.C. (point of curve) falls at the midpointof the last straight pipe and the P.T. (point of tangent) falls one half of the standardpipe length back from the straight end of the last radius pipe. To assure that theP.C. will fall at the proper station it is generally necessary that a special shortlength of pipe be installed in the line, ahead of the P.C.

Bends and Special Sections. Extremely short radius curves cannot benegotiated with either deflected straight pipe or with conventional radius pipe.Several alternatives are available through the use of special precast sections tosolve such alignment problems.

Sharper curves can be handled by using special short lengths of radius piperather than standard lengths. These may be computed in accordance with themethods discussed for radius pipe.

Certain types of manufacturing processes permit the use of a dropped jointon both ends of the pipe, which effectively doubles the deflection. Special bends,

L

N∆

D

Direct

ion

of L

ayin

g

Drop

90°90° +

t

N∆

L2

∆P.T

.

L

L2

P.C.

Radius

True Radius Point

Projection of joints do not convergeat common point, but are tangentsto a common circle whose diameteris equal to pipe length.Common method of

manufacturing radius pipe.

L2

∆



or elbows can be manufactured to meet any required deflection angle and somemanufacturers produce standard bends which provide given angular deflectionper section.

One or more of these methods may be employed to meet the most severealignment problems. Since manufacturing processes and local standards vary,local concrete pipe manufacturers should be consulted to determine theavailability and geometric configuration of special sections.

SIGNIFICANCE OF CRACKING

The occurrence, function and significance of cracks have probably been thesubject of more misunderstanding and unnecessary concern by engineers thanany other phenomena related to reinforced concrete pipe.

Reinforced concrete pipe, like reinforced concrete structures in general, aremade of concrete reinforced with steel in such a manner that the highcompressive strength of the concrete is balanced by the high tensile strength ofthe steel. In reinforced concrete pipe design, no value is given to the tensilestrength of the concrete. The tensile strength of the concrete, however, isimportant since all parts of the pipe are subject to tensile forces at some timesubsequent to manufacture. When concrete is subjected to tensile forces inexcess of its tensile strength, it cracks.

Unlike most reinforced concrete structures, reinforced concrete sewer andculvert pipe is designed to meet a specified cracking load rather than a specifiedstress level in the reinforcing steel. This is both reasonable and conservativesince reinforced concrete pipe may be pretested in accordance with detailednational specifications.

In the early days of the concrete pipe industry, the first visible crack observedin a three-edge bearing test was the accepted criterion for pipe performance.However, the observation of such cracks was subject to variations dependingupon the zeal and eyesight of the observer. The need soon became obvious for acriterion based on a measurable crack of a specified width. Eventually the 0.01-inch crack, as measured by a feeler gage of a specified shape, became theaccepted criterion for pipe performance.

The most valid basis for selection of a maximum allowable crack width is theconsideration of exposure and potential corrosion of the reinforcing steel. If acrack is sufficiently wide to provide access to the steel by both moisture andoxygen, corrosion will be initiated. Oxygen is consumed by the oxidation processand in order for corrosion to be progressive there must be a constantreplenishment.

Bending cracks are widest at the surface and get rapidly smaller as theyapproach the reinforcing steel. Unless the crack is wide enough to allowcirculation of the moisture and replenishment of oxygen, corrosion is unlikely.Corrosion is even further inhibited by the alkaline environment resulting from thecement.



While cracks considerably in excess of 0.01-inch have been observed after aperiod of years with absolutely no evidence of corrosion, 0.01-inch is aconservative and universally accepted maximum crack width for design ofreinforced concrete pipe.

• Reinforced concrete pipe is designed to crack. Cracking under loadindicates that the tensile stresses have been transferred to the reinforcingsteel.

• A crack 0.01-inch wide does not indicate structural distress and is notharmful.

• Cracks much wider than 0.01-inch should probably be sealed to insureprotection of the reinforcing steel.

• An exception to the above occurs with pipe manufactured with greater than1 inch cover over the reinforcing steel. In these cases acceptable crackwidth should be increased in proportion to the additional concrete cover.

Tables

111



Table 1

Tables 113


Table 2



Table 3

Tables 115


Table 4

Table 5



Table 6

Tables 117


Table 7



Table 8

Table 9

Table 10

Tables 119


Table 11

Table 12



Table 13

52.

52.

62.

62.

62.

42.

52.

52.

62.

42.

42.

42.

52.

32.

42.

42.

46

2.6

2.7

2.7

2.8

2.5

2.6

2.6

2.7

2.5

2.5

2.5

2.6

2.4

2.5

2.5

2.5

72.

72.

82.

82.

92.

62.

72.

72.

82.

62.

62.

62.

72.

52.

52.

52.

68

2.8

2.9

2.9

3.0

2.7

2.8

2.8

2.9

2.6

2.7

2.7

2.8

2.5

2.6

2.6

2.7

92.

93.

03.

03.

12.

82.

92.

93.

02.

72.

82.

82.

92.

62.

72.

72.

710

3.0

3.1

3.1

3.2

2.9

3.0

3.0

3.1

2.8

2.9

2.9

2.9

2.7

2.7

2.7

2.8

113.

13.

23.

23.

23.

03.

13.

13.

22.

92.

92.

93.

02.

72.

82.

82.

912

3.2

3.3

3.3

3.3

3.1

3.2

3.2

3.2

2.9

3.0

3.0

3.1

2.8

2.9

2.9

3.0

133.

33.

33.

33.

43.

23.

23.

23.

33.

03.

13.

13.

22.

92.

92.

93.

014

3.4

3.4

3.4

3.5

3.2

3.3

3.3

3.4

3.1

3.2

3.2

3.2

2.9

3.0

3.0

3.1

153.

43.

53.

53.

63.

33.

43.

43.

53.

23.

23.

23.

33.

03.

13.

13.

216

3.5

3.6

3.6

3.7

3.4

3.5

3.5

3.6

3.2

3.3

3.3

3.4

3.1

3.1

3.1

3.2

173.

63.

73.

73.

83.

53.

63.

63.

63.

33.

43.

43.

53.

13.

23.

23.

318

3.7

3.8

3.8

3.8

3.5

3.6

3.6

3.7

3.4

3.4

3.4

3.5

3.2

3.3

3.3

3.3

193.

73.

83.

83.

93.

63.

73.

73.

83.

43.

53.

53.

63.

23.

33.

33.

420

3.8

3.9

3.9

4.0

3.7

3.8

3.8

3.9

3.5

3.6

3.6

3.7

3.3

3.4

3.4

3.5

213.

94.

04.

04.

13.

83.

83.

83.

93.

63.

63.

63.

73.

33.

43.

43.

522

4.0

4.0

4.0

4.1

3.8

3.9

3.9

4.0

3.6

3.7

3.7

3.8

3.4

3.5

3.5

3.6

234.

04.

14.

04.

23.

94.

04.

04.

13.

73.

83.

83.

83.

53.

53.

53.

624

4.1

4.2

4.2

4.3

3.9

4.0

4.0

4.1

3.7

3.8

3.8

3.9

3.5

3.6

3.6

3.7

254.

24.

34.

34.

34.

04.

14.

14.

23.

83.

93.

94.

03.

63.

63.

63.

726

4.2

4.3

4.3

4.4

4.1

4.2

4.2

4.3

3.9

3.9

3.9

4.0

3.6

3.7

3.7

3.8

274.

34.

44.

44.

54.

14.

24.

24.

33.

94.

04.

04.

13.

73.

83.

83.

828

4.4

4.5

4.5

4.6

4.2

4.3

4.3

4.4

4.0

4.1

4.1

4.1

3.7

3.8

3.8

3.9

294.

44.

54.

54.

64.

34.

44.

44.

44.

04.

14.

14.

23.

83.

93.

93.

930

4.4

4.5

4.5

4.6

4.3

4.4

4.4

4.4

4.0

4.1

4.1

4.2

3.8

3.9

3.9

3.9

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 12

"

Height of Backfill H Above Top of Pipe, Feet

Tables 121


Table 14

52.

93.

03.

03.

12.

93.

03.

03.

02.

82.

92.

93.

02.

72.

82.

82.

96

3.0

3.1

3.1

3.2

3.0

3.1

3.1

3.2

2.9

3.0

3.0

3.1

2.8

2.9

2.9

3.0

73.

13.

23.

23.

33.

13.

23.

23.

33.

03.

13.

13.

22.

93.

03.

03.

18

3.3

3.3

3.3

3.4

3.2

3.3

3.3

3.4

3.1

3.2

3.2

3.2

3.0

3.0

3.0

3.1

93.

43.

43.

43.

53.

33.

43.

43.

53.

23.

23.

23.

33.

03.

13.

13.

210

3.5

3.5

3.5

3.6

3.4

3.5

3.5

3.5

3.2

3.3

3.3

3.4

3.1

3.2

3.2

3.3

113.

63.

63.

63.

73.

53.

53.

53.

63.

33.

43.

43.

53.

23.

33.

33.

412

3.6

3.7

3.7

3.8

3.5

3.6

3.6

3.7

3.4

3.5

3.5

3.6

3.2

3.3

3.3

3.4

133.

73.

83.

83.

93.

63.

73.

73.

83.

53.

63.

63.

73.

33.

43.

43.

514

3.8

3.9

3.9

4.0

3.7

3.8

3.8

3.9

3.6

3.6

3.6

3.7

3.4

3.5

3.5

3.6

153.

94.

04.

04.

13.

83.

93.

94.

03.

63.

73.

73.

83.

53.

53.

53.

616

4.0

4.1

4.1

4.2

3.9

4.0

4.0

4.1

3.7

3.8

3.8

3.9

3.5

3.6

3.6

3.7

174.

14.

24.

24.

34.

04.

04.

04.

13.

83.

93.

94.

03.

63.

73.

73.

818

4.2

4.3

4.3

4.4

4.0

4.1

4.1

4.2

3.8

3.9

3.9

4.0

3.6

3.7

3.7

3.8

194.

24.

34.

34.

44.

14.

24.

24.

33.

94.

04.

04.

13.

73.

83.

83.

920

4.3

4.4

4.4

4.5

4.2

4.3

4.3

4.4

4.0

4.1

4.1

4.2

3.8

3.9

3.9

4.0

214.

44.

54.

54.

64.

34.

44.

44.

54.

04.

14.

14.

23.

83.

93.

94.

022

4.5

4.6

4.6

4.7

4.3

4.4

4.4

4.5

4.1

4.2

4.2

4.3

3.9

4.0

4.0

4.1

234.

64.

74.

74.

84.

44.

54.

54.

64.

24.

34.

34.

43.

94.

04.

04.

124

4.6

4.7

4.7

4.8

4.5

4.6

4.6

4.7

4.2

4.3

4.3

4.4

4.0

4.1

4.1

4.2

254.

74.

84.

84.

94.

54.

64.

64.

74.

34.

44.

44.

54.

14.

24.

24.

226

4.8

4.9

4.9

5.0

4.6

4.7

4.7

4.8

4.4

4.5

4.5

4.6

4.1

4.2

4.2

4.3

274.

85.

05.

05.

14.

74.

84.

84.

94.

44.

54.

54.

64.

24.

34.

34.

428

4.9

5.0

5.0

5.1

4.7

4.8

4.8

4.9

4.5

4.6

4.6

4.7

4.2

4.3

4.3

4.4

295.

05.

15.

15.

24.

84.

94.

95.

04.

54.

64.

64.

84.

34.

44.

44.

530

5.0

5.1

5.1

5.2

4.8

4.9

4.9

5.0

4.5

4.6

4.6

4.8

4.3

4.4

4.4

4.5

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 15

"




Table 15

53.

43.

53.

53.

63.

33.

43.

43.

53.

23.

33.

33.

43.

13.

23.

23.

36

3.5

3.6

3.6

3.7

3.4

3.5

3.5

3.6

3.3

3.4

3.4

3.5

3.2

3.3

3.3

3.4

73.

63.

73.

73.

83.

53.

63.

63.

73.

43.

53.

53.

63.

33.

43.

43.

58

3.7

3.8

3.8

3.9

3.6

3.7

3.7

3.8

3.5

3.6

3.6

3.7

3.4

3.5

3.5

3.6

93.

83.

93.

94.

03.

73.

83.

83.

93.

63.

73.

73.

83.

53.

63.

63.

710

3.9

4.0

4.0

4.1

3.8

3.9

3.9

4.0

3.7

3.8

3.8

3.9

3.5

3.6

3.6

3.7

114.

04.

14.

14.

23.

94.

04.

04.

13.

83.

93.

94.

03.

63.

73.

73.

812

4.1

4.2

4.2

4.3

4.0

4.1

4.1

4.2

3.8

3.9

3.9

4.1

3.7

3.8

3.8

3.9

134.

24.

34.

34.

44.

14.

24.

24.

33.

94.

04.

04.

13.

83.

93.

94.

014

4.3

4.4

4.4

4.5

4.2

4.3

4.3

4.4

4.0

4.1

4.1

4.2

3.8

3.9

3.9

4.0

154.

44.

54.

54.

64.

34.

44.

44.

54.

14.

24.

24.

33.

94.

04.

04.

116

4.5

4.6

4.6

4.7

4.3

4.4

4.4

4.6

4.2

4.3

4.3

4.4

4.0

4.1

4.1

4.2

174.

64.

74.

74.

84.

44.

54.

54.

64.

24.

34.

34.

44.

04.

14.

14.

218

4.6

4.8

4.8

4.9

4.5

4.6

4.6

4.7

4.3

4.4

4.4

4.5

4.1

4.2

4.2

4.3

194.

74.

84.

85.

04.

64.

74.

74.

84.

44.

54.

54.

64.

24.

34.

34.

420

4.8

4.9

4.9

5.0

4.7

4.8

4.8

4.9

4.4

4.6

4.6

4.7

4.2

4.3

4.3

4.4

214.

95.

05.

05.

14.

74.

94.

95.

04.

54.

64.

64.

74.

34.

44.

44.

522

5.0

5.1

5.1

5.2

4.8

4.9

4.9

5.0

4.6

4.7

4.7

4.8

4.3

4.5

4.5

4.6

235.

15.

25.

25.

34.

95.

05.

05.

14.

74.

84.

84.

94.

44.

54.

54.

624

5.1

5.3

5.3

5.4

5.0

5.1

5.1

5.2

4.7

4.8

4.8

5.0

4.5

4.6

4.6

4.7

255.

25.

35.

35.

55.

05.

25.

25.

34.

84.

94.

95.

04.

54.

64.

64.

826

5.3

5.4

5.4

5.5

5.1

5.2

5.2

5.3

4.9

5.0

5.0

5.1

4.6

4.7

4.7

4.8

275.

45.

55.

55.

65.

25.

35.

35.

44.

95.

05.

05.

24.

64.

84.

84.

928

5.4

5.6

5.6

5.7

5.3

5.4

5.4

5.5

5.0

5.1

5.1

5.2

4.7

4.8

4.8

4.9

295.

55.

65.

65.

85.

35.

45.

45.

65.

05.

25.

25.

34.

84.

94.

95.

030

5.5

5.6

5.6

5.8

5.3

5.4

5.4

5.6

5.0

5.2

5.2

5.3

4.8

4.9

4.9

5.0

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 18

"


Tables 123


Table 16

53.

83.

93.

94.

03.

73.

83.

84.

03.

63.

83.

83.

93.

63.

73.

73.

86

3.9

4.0

4.0

4.1

3.8

3.9

3.9

4.1

3.7

3.9

3.9

4.0

3.6

3.8

3.8

3.9

74.

04.

14.

14.

23.

94.

14.

14.

23.

83.

93.

94.

13.

73.

83.

84.

08

4.1

4.2

4.2

4.4

4.0

4.2

4.2

4.3

3.9

4.0

4.0

4.2

3.8

3.9

3.9

4.0

94.

24.

44.

44.

54.

14.

34.

34.

44.

04.

14.

14.

33.

94.

04.

04.

110

4.3

4.5

4.5

4.6

4.2

4.4

4.4

4.5

4.1

4.2

4.2

4.3

4.0

4.1

4.1

4.2

114.

44.

64.

64.

74.

34.

54.

54.

64.

24.

34.

34.

44.

04.

24.

24.

312

4.5

4.7

4.7

4.8

4.4

4.6

4.6

4.7

4.3

4.4

4.4

4.5

4.1

4.2

4.2

4.4

134.

64.

84.

84.

94.

54.

64.

64.

84.

44.

54.

54.

64.

24.

34.

34.

414

4.7

4.9

4.9

5.0

4.6

4.7

4.7

4.9

4.4

4.6

.46

4.7

4.3

4.4

4.4

4.5

154.

85.

05.

05.

14.

74.

84.

85.

04.

54.

64.

64.

84.

34.

54.

54.

616

4.9

5.1

5.1

5.2

4.8

4.9

4.9

5.0

4.6

4.7

4.7

4.8

4.4

4.5

4.5

4.6

175.

05.

25.

25.

34.

95.

05.

05.

14.

74.

84.

84.

94.

54.

64.

64.

718

5.1

5.2

5.2

5.4

5.0

5.1

5.1

5.2

4.8

4.9

4.9

5.0

4.5

4.7

4.7

4.8

195.

25.

35.

35.

55.

15.

25.

25.

34.

85.

05.

05.

14.

64.

74.

74.

920

5.3

5.4

5.4

5.6

5.1

5.3

5.3

5.4

4.9

5.0

5.0

5.2

4.7

4.8

4.8

4.9

215.

45.

55.

55.

65.

25.

35.

35.

55.

05.

15.

15.

24.

74.

94.

95.

022

5.5

5.6

5.6

5.7

5.3

5.4

5.4

5.6

5.1

5.2

5.2

5.3

4.8

4.9

4.9

5.1

235.

55.

75.

75.

85.

45.

55.

55.

65.

15.

35.

35.

44.

95.

05.

05.

124

5.6

5.8

5.8

5.9

5.4

5.6

5.6

5.7

5.2

5.3

5.3

5.5

4.9

5.1

5.1

5.2

255.

75.

85.

86.

05.

55.

75.

75.

85.

35.

45.

45.

55.

05.

15.

15.

226

5.8

5.9

5.9

6.1

5.6

5.7

5.7

5.9

5.3

5.5

5.5

5.6

5.1

5.2

5.2

5.3

275.

96.

06.

06.

15.

75.

85.

85.

95.

45.

55.

55.

75.

15.

25.

25.

428

6.0

6.1

6.1

6.2

5.7

5.9

5.9

6.0

5.5

5.6

5.6

5.7

5.2

5.3

5.3

5.4

296.

06.

26.

26.

35.

86.

06.

06.

15.

55.

75.

75.

85.

25.

45.

45.

530

6.0

6.2

6.2

6.3

5.8

6.0

6.0

6.1

5.5

5.7

5.7

5.8

5.2

5.4

5.4

5.5

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 21

"




Table 17

54.

24.

34.

34.

54.

14.

34.

34.

44.

14.

24.

24.

34.

04.

14.

14.

26

4.3

4.5

4.5

4.6

4.2

4.4

4.4

4.5

4.2

4.3

4.3

4.4

4.1

4.2

4.2

4.3

74.

44.

64.

64.

74.

44.

54.

54.

64.

34.

44.

44.

54.

14.

34.

34.

48

4.6

4.7

4.7

4.8

4.5

4.6

4.6

4.7

4.3

4.5

4.5

4.6

4.2

4.4

4.4

4.5

94.

74.

84.

84.

94.

64.

74.

74.

84.

44.

64.

64.

74.

34.

44.

44.

610

4.8

4.9

4.9

5.0

4.7

4.8

4.8

4.9

4.5

4.7

4.7

4.8

4.4

4.5

4.5

4.6

114.

95.

05.

05.

24.

84.

94.

95.

04.

64.

84.

84.

94.

54.

64.

64.

712

5.0

5.1

5.1

5.3

4.9

5.0

5.0

5.1

4.7

4.8

4.8

5.0

4.5

4.7

4.7

4.8

135.

15.

25.

25.

45.

05.

15.

15.

24.

84.

94.

95.

14.

64.

74.

74.

914

5.2

5.3

5.3

5.5

5.1

5.2

5.2

5.3

4.9

5.0

5.0

5.2

4.7

4.8

4.8

5.0

155.

35.

45.

45.

65.

25.

35.

35.

45.

05.

15.

15.

24.

84.

94.

95.

016

5.4

5.5

5.5

5.7

5.2

5.4

5.4

5.5

5.0

5.2

5.2

5.3

4.8

5.0

5.0

5.1

175.

55.

65.

65.

85.

35.

55.

55.

65.

15.

35.

35.

44.

95.

05.

05.

218

5.6

5.7

5.7

5.9

5.4

5.6

5.6

5.7

5.2

5.3

5.3

5.5

5.0

5.1

5.1

5.3

195.

75.

85.

86.

05.

55.

75.

75.

85.

35.

45.

45.

65.

05.

25.

25.

320

5.8

5.9

5.9

6.1

5.6

5.7

5.7

5.9

5.4

5.5

5.5

5.6

5.1

5.3

5.3

5.4

215.

96.

06.

06.

15.

75.

85.

86.

05.

45.

65.

65.

75.

25.

35.

35.

522

5.9

6.1

6.1

6.2

5.8

5.9

5.9

6.0

5.5

5.7

5.7

5.8

5.3

5.4

5.4

5.5

236.

06.

26.

26.

35.

86.

06.

06.

15.

65.

75.

75.

95.

35.

55.

55.

624

6.1

6.3

6.3

6.4

5.9

6.1

6.1

6.2

5.7

5.8

5.8

5.9

5.4

5.5

5.5

5.7

256.

26.

36.

36.

56.

06.

26.

26.

35.

75.

95.

96.

05.

45.

65.

65.

726

6.3

6.4

6.4

6.6

6.1

6.2

6.2

6.4

5.8

5.9

5.9

6.1

5.5

5.7

5.7

5.8

276.

46.

56.

56.

76.

26.

36.

36.

55.

96.

06.

06.

25.

65.

75.

75.

928

6.4

6.6

6.6

6.8

6.2

6.4

6.4

6.5

5.9

6.1

6.1

6.2

5.6

5.8

5.8

5.9

296.

56.

76.

76.

86.

36.

56.

56.

66.

06.

26.

26.

35.

75.

85.

86.

030

6.5

6.7

6.7

6.8

6.3

6.5

6.5

6.6

6.0

6.2

6.2

6.3

5.7

5.8

5.8

6.0

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 24

"


Tables 125


Table 18

54.

64.

84.

84.

94.

64.

74.

74.

94.

54.

64.

64.

84.

44.

54.

54.

76

4.7

4.9

4.9

5.0

4.7

4.8

4.8

5.0

4.6

4.7

4.7

4.9

4.5

4.6

4.6

4.8

74.

95.

05.

05.

24.

84.

94.

95.

14.

74.

84.

85.

04.

64.

74.

74.

98

5.0

5.1

5.1

5.3

4.9

5.0

5.0

5.2

4.8

4.9

4.9

5.1

4.6

4.8

4.8

4.9

95.

15.

25.

25.

45.

05.

15.

15.

34.

95.

05.

05.

24.

74.

94.

95.

010

5.2

5.4

5.4

5.5

5.1

5.2

5.2

5.4

5.0

5.1

5.1

5.3

4.8

5.0

5.0

5.1

115.

35.

55.

55.

65.

25.

45.

45.

55.

05.

25.

25.

34.

95.

05.

05.

212

5.4

5.6

5.6

5.7

5.3

5.5

5.5

5.6

5.1

5.3

5.3

5.4

5.0

5.1

5.1

5.3

135.

55.

75.

75.

85.

45.

65.

65.

75.

25.

45.

45.

55.

05.

25.

25.

314

5.6

5.8

5.8

5.9

5.5

5.7

5.7

5.8

5.3

5.5

5.5

5.6

5.1

5.3

5.3

5.4

155.

75.

95.

96.

05.

65.

75.

75.

95.

45.

55.

55.

75.

25.

35.

35.

516

5.8

6.0

6.0

6.1

5.7

5.8

5.8

6.0

5.5

5.6

5.6

5.8

5.3

5.4

5.4

5.6

175.

96.

16.

16.

25.

85.

95.

96.

15.

65.

75.

75.

95.

35.

55.

55.

618

6.0

6.2

6.2

6.3

5.9

6.0

6.0

6.2

5.6

5.8

5.8

6.0

5.4

5.6

5.6

5.7

196.

16.

36.

36.

46.

06.

16.

16.

35.

75.

95.

96.

05.

55.

65.

65.

820

6.2

6.4

6.4

6.5

6.0

6.2

6.2

6.4

5.8

6.0

6.0

6.1

5.6

5.7

5.7

5.9

216.

36.

56.

56.

66.

16.

36.

36.

55.

96.

06.

06.

25.

65.

85.

85.

922

6.4

6.6

6.6

6.7

6.2

6.4

6.4

6.5

6.0

6.1

6.1

6.3

5.7

5.8

5.8

6.0

236.

56.

76.

76.

86.

36.

56.

56.

66.

06.

26.

26.

45.

85.

95.

96.

124

6.6

6.7

6.7

6.9

6.4

6.5

6.5

6.7

6.1

6.3

6.3

6.4

5.8

6.0

6.0

6.1

256.

76.

86.

87.

06.

56.

66.

66.

86.

26.

36.

36.

55.

96.

16.

16.

226

6.8

6.9

6.9

7.1

6.6

6.7

6.7

6.9

6.3

6.4

6.4

6.6

6.0

6.1

6.1

6.3

276.

87.

07.

07.

26.

66.

86.

87.

06.

36.

56.

56.

76.

06.

26.

26.

328

6.9

7.1

7.1

7.3

6.7

6.9

6.9

7.0

6.4

6.6

6.6

6.7

6.1

6.2

6.2

6.4

297.

07.

27.

27.

46.

87.

07.

07.

16.

56.

66.

66.

86.

26.

36.

36.

530

7.0

7.2

7.2

7.4

6.8

7.0

7.0

7.1

6.5

6.6

6.6

6.8

6.2

6.3

6.3

6.5

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 27

"




Table 19

55.

05.

25.

25.

45.

05.

15.

15.

34.

95.

15.

15.

24.

85.

05.

05.

16

5.2

5.3

5.3

5.5

5.1

5.3

5.3

5.4

5.0

5.2

5.2

5.3

4.9

5.1

5.1

5.2

75.

35.

45.

45.

65.

25.

45.

45.

55.

15.

35.

35.

45.

05.

15.

15.

38

5.4

5.6

5.6

5.7

5.3

5.5

5.5

5.6

5.2

5.4

5.4

5.5

5.1

5.2

5.2

5.4

95.

55.

75.

75.

85.

45.

65.

65.

75.

35.

45.

45.

65.

15.

35.

35.

510

5.6

5.8

5.8

6.0

5.5

5.7

5.7

5.9

5.4

5.5

5.5

5.7

5.2

5.4

5.4

5.5

115.

75.

95.

96.

15.

65.

85.

86.

05.

55.

65.

65.

85.

35.

55.

55.

612

5.9

6.0

6.0

6.2

5.7

5.9

5.9

6.1

5.6

5.7

5.7

5.9

5.4

5.5

5.5

5.7

136.

06.

16.

16.

35.

86.

06.

06.

25.

75.

85.

86.

05.

55.

65.

65.

814

6.1

6.2

6.2

6.4

5.9

6.1

6.1

6.3

5.7

5.9

5.9

6.1

5.5

5.7

5.7

5.9

156.

26.

36.

36.

56.

06.

26.

26.

45.

86.

06.

06.

25.

65.

85.

85.

916

6.3

6.4

6.4

6.6

6.1

6.3

6.3

6.5

5.9

6.1

6.1

6.2

5.7

5.9

5.9

6.0

176.

46.

66.

66.

76.

26.

46.

46.

66.

06.

26.

26.

35.

85.

95.

96.

118

6.5

6.7

6.7

6.8

6.3

6.5

6.5

6.7

6.1

6.3

6.3

6.4

5.8

6.0

6.0

6.2

196.

66.

86.

86.

96.

46.

66.

66.

76.

26.

36.

36.

55.

96.

16.

16.

320

6.7

6.9

6.9

7.0

6.5

6.7

6.7

6.8

6.2

6.4

6.4

6.6

6.0

6.2

6.2

6.3

216.

86.

96.

97.

16.

66.

86.

86.

96.

36.

56.

56.

76.

16.

26.

26.

422

6.9

7.0

7.0

7.2

6.7

6.8

6.8

7.0

6.4

6.6

6.6

6.8

6.1

6.3

6.3

6.5

237.

07.

17.

17.

36.

86.

96.

97.

16.

56.

76.

76.

86.

26.

46.

46.

524

7.1

7.2

7.2

7.4

6.8

7.0

7.0

7.2

6.6

6.7

6.7

6.9

6.3

6.4

6.4

6.6

257.

17.

37.

37.

56.

97.

17.

17.

36.

66.

86.

87.

06.

36.

56.

56.

726

7.2

7.4

7.4

7.6

7.0

7.2

7.2

7.4

6.7

6.9

6.9

7.1

6.4

6.6

6.6

6.7

277.

37.

57.

57.

77.

17.

37.

37.

56.

87.

07.

07.

16.

56.

66.

66.

828

7.4

7.6

7.6

7.8

7.2

7.4

7.4

7.5

6.9

7.0

7.0

7.2

6.5

6.7

6.7

6.9

297.

57.

77.

77.

97.

37.

47.

47.

66.

97.

17.

17.

36.

66.

86.

86.

930

7.5

7.7

7.7

7.9

7.3

7.4

7.4

7.6

6.9

7.1

7.1

7.3

6.6

6.8

6.8

6.9

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 30

"


Tables 127


Table 20

55.

55.

65.

65.

85.

45.

65.

65.

85.

35.

55.

55.

75.

25.

45.

45.

66

5.6

5.8

5.8

5.9

5.5

5.7

5.7

5.9

5.4

5.6

5.6

5.8

5.3

5.5

5.5

5.7

75.

75.

95.

96.

15.

65.

85.

86.

05.

55.

75.

75.

95.

45.

65.

65.

88

5.8

6.0

6.0

6.2

5.7

5.9

5.9

6.1

5.6

5.8

5.8

6.0

5.5

5.7

5.7

5.8

95.

96.

16.

16.

35.

86.

06.

06.

25.

75.

95.

96.

15.

65.

75.

75.

910

6.1

6.2

6.2

6.4

5.9

6.1

6.1

6.3

5.8

6.0

6.0

6.2

5.6

5.8

5.8

6.0

116.

26.

46.

46.

56.

16.

26.

26.

45.

96.

16.

16.

35.

75.

95.

96.

112

6.3

6.5

6.5

6.7

6.2

6.3

6.3

6.5

6.0

6.2

6.2

6.3

5.8

6.0

6.0

6.2

136.

46.

66.

66.

86.

36.

46.

46.

66.

16.

36.

36.

45.

96.

16.

16.

214

6.5

6.7

6.7

6.9

6.4

6.5

6.5

6.7

6.2

6.3

6.3

6.5

6.0

6.1

6.1

6.3

156.

66.

86.

87.

06.

56.

66.

66.

86.

36.

46.

46.

66.

06.

26.

26.

416

6.7

6.9

6.9

7.1

6.6

6.7

6.7

6.9

6.3

6.5

6.5

6.7

6.1

6.3

6.3

6.5

176.

87.

07.

07.

26.

76.

86.

87.

06.

46.

66.

66.

86.

26.

46.

46.

618

6.9

7.1

7.1

7.3

6.8

6.9

6.9

7.1

6.5

6.7

6.7

6.9

6.3

6.5

6.5

6.6

197.

07.

27.

27.

46.

87.

07.

07.

26.

66.

86.

87.

06.

36.

56.

56.

720

7.1

7.3

7.3

7.5

6.9

7.1

7.1

7.3

6.7

6.9

6.9

7.1

6.4

6.6

6.6

6.8

217.

27.

47.

47.

67.

07.

27.

27.

46.

87.

07.

07.

16.

56.

76.

76.

922

7.3

7.5

7.5

7.7

7.1

7.3

7.3

7.5

6.9

7.0

7.0

7.2

6.6

6.7

6.7

6.9

237.

47.

67.

67.

87.

27.

47.

47.

66.

97.

17.

17.

36.

66.

86.

87.

024

7.5

7.7

7.7

7.9

7.3

7.5

7.5

7.7

7.0

7.2

7.2

7.4

6.7

6.9

6.9

7.1

257.

67.

87.

88.

07.

47.

67.

67.

87.

17.

37.

37.

56.

87.

07.

07.

126

7.7

7.9

7.9

8.1

7.5

7.7

7.7

7.9

7.2

7.4

7.4

7.5

6.8

7.0

7.0

7.2

277.

88.

08.

08.

27.

67.

87.

87.

97.

27.

47.

47.

66.

97.

17.

17.

328

7.9

8.1

8.1

8.3

7.6

7.8

7.8

8.0

7.3

7.5

7.5

7.7

7.0

7.1

7.2

7.4

298.

08.

28.

28.

47.

77.

97.

98.

17.

47.

67.

67.

87.

17.

27.

27.

430

8.0

8.2

8.2

8.4

7.7

7.9

7.9

8.1

7.4

7.6

7.6

7.8

7.1

7.2

7.2

7.4

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 33

"




Table 21

55.

96.

16.

16.

35.

86.

06.

06.

25.

75.

95.

96.

15.

65.

85.

86.

06

6.0

6.2

6.2

6.4

5.9

6.1

6.1

6.3

5.8

6.0

6.0

6.2

5.7

5.9

5.9

6.1

76.

16.

36.

36.

56.

06.

26.

26.

45.

96.

16.

16.

35.

86.

06.

06.

28

6.2

6.4

6.4

6.6

6.2

6.3

6.3

6.5

6.0

6.2

6.2

6.4

5.9

6.1

6.1

6.3

96.

46.

66.

66.

86.

36.

56.

56.

76.

16.

36.

36.

56.

06.

26.

26.

410

6.5

6.7

6.7

6.9

6.4

6.6

6.6

6.8

6.2

6.4

6.4

6.6

6.1

6.3

6.3

6.4

116.

66.

86.

87.

06.

56.

76.

76.

96.

36.

56.

56.

76.

16.

36.

36.

512

6.7

6.9

6.9

7.1

6.6

6.8

6.8

7.0

6.4

6.6

6.6

6.8

6.2

6.4

6.4

6.6

136.

87.

07.

07.

26.

76.

96.

97.

16.

56.

76.

76.

96.

36.

56.

56.

714

6.9

7.1

7.1

7.3

6.8

7.0

7.0

7.2

6.6

6.8

6.8

7.0

6.4

6.6

6.6

6.8

157.

07.

27.

27.

46.

97.

17.

17.

36.

76.

96.

97.

16.

56.

76.

76.

916

7.2

7.4

7.4

7.6

7.0

7.2

7.2

7.4

6.8

7.0

7.0

7.2

6.5

6.7

6.7

6.9

177.

37.

57.

57.

77.

17.

37.

37.

56.

97.

17.

17.

36.

66.

86.

87.

018

7.4

7.6

7.6

7.8

7.2

7.4

7.4

7.6

6.9

7.1

7.1

7.3

6.7

6.9

6.9

7.1

197.

57.

77.

77.

97.

37.

57.

57.

77.

07.

27.

27.

46.

87.

07.

07.

220

7.6

7.8

7.8

8.0

7.4

7.6

7.6

7.8

7.1

7.3

7.3

7.5

6.9

7.0

7.0

7.2

217.

77.

97.

98.

17.

57.

77.

77.

97.

27.

47.

47.

66.

97.

17.

17.

322

7.8

8.0

8.0

8.2

7.6

7.8

7.8

8.0

7.3

7.5

7.5

7.7

7.0

7.2

7.2

7.4

237.

98.

18.

18.

37.

77.

97.

98.

17.

47.

67.

67.

87.

17.

37.

37.

524

8.0

8.2

8.2

8.4

7.7

8.0

8.0

8.2

7.5

7.7

7.7

7.9

7.1

7.3

7.3

7.5

258.

18.

38.

38.

57.

88.

08.

08.

27.

57.

77.

77.

97.

27.

47.

47.

626

8.2

8.4

8.4

8.6

7.9

8.1

8.1

8.3

7.6

7.8

7.8

8.0

7.3

7.5

7.5

7.7

278.

28.

58.

58.

78.

08.

28.

28.

47.

77.

97.

98.

17.

47.

67.

67.

828

8.3

8.6

8.6

8.8

8.1

8.3

8.3

8.5

7.8

8.0

8.0

8.2

7.4

7.6

7.6

7.8

298.

48.

68.

68.

98.

28.

48.

48.

67.

88.

18.

18.

37.

57.

77.

77.

930

8.4

8.6

8.6

8.9

8.2

8.4

8.4

8.6

7.8

8.1

8.1

8.3

7.5

7.7

7.7

7.9

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 36

"


Tables 129


Table 22

56.

77.

07.

07.

26.

76.

96.

97.

16.

66.

86.

87.

06.

56.

76.

77.

06

6.9

7.1

7.1

7.3

6.8

7.0

7.0

7.2

6.7

6.9

6.9

7.1

6.6

6.8

6.8

7.0

77.

07.

27.

27.

46.

97.

17.

17.

36.

87.

07.

07.

26.

66.

96.

97.

18

7.1

7.3

7.3

7.5

7.0

7.2

7.2

7.5

6.9

7.1

7.1

7.3

6.7

7.0

7.0

7.2

97.

27.

47.

47.

77.

17.

37.

37.

67.

07.

27.

27.

46.

87.

07.

07.

310

7.3

7.6

7.6

7.8

7.2

7.4

7.4

7.7

7.1

7.3

7.3

7.5

6.9

7.1

7.1

7.3

117.

47.

77.

77.

97.

37.

67.

67.

87.

27.

47.

47.

67.

07.

27.

27.

412

7.6

7.8

7.8

8.0

7.4

7.7

7.7

7.9

7.2

7.5

7.5

7.7

7.1

7.3

7.3

7.5

137.

77.

97.

98.

17.

57.

87.

88.

07.

37.

67.

67.

87.

17.

47.

47.

614

7.8

8.0

8.0

8.3

7.6

7.9

7.9

8.1

7.4

7.7

7.7

7.9

7.2

7.5

7.5

7.7

157.

98.

18.

18.

47.

78.

08.

08.

27.

57.

87.

88.

07.

37.

57.

57.

816

8.0

8.2

8.2

8.5

7.9

8.1

8.1

8.3

7.6

7.9

7.9

8.1

7.4

7.6

7.6

7.8

178.

18.

48.

48.

68.

08.

28.

28.

47.

77.

97.

98.

27.

57.

77.

77.

918

8.2

8.5

8.5

8.7

8.1

8.3

8.3

8.5

7.8

8.0

8.0

8.3

7.5

7.8

7.8

8.0

198.

38.

68.

68.

88.

28.

48.

48.

67.

98.

18.

18.

47.

67.

97.

98.

120

8.4

8.7

8.7

8.9

8.3

8.5

8.5

8.7

8.0

8.2

8.2

8.4

7.7

7.9

7.9

8.2

218.

68.

88.

89.

08.

48.

68.

68.

88.

18.

38.

38.

57.

88.

08.

08.

222

8.7

8.9

8.9

9.1

8.4

8.7

8.7

8.9

8.2

8.4

8.4

8.6

7.9

8.1

8.1

8.3

238.

89.

09.

09.

28.

58.

88.

89.

08.

28.

58.

58.

77.

98.

28.

28.

424

8.9

9.1

9.1

9.3

8.6

8.9

8.9

9.1

8.3

8.6

8.6

8.8

8.0

8.2

8.2

8.5

259.

09.

29.

29.

48.

79.

09.

09.

28.

48.

68.

68.

98.

18.

38.

38.

526

9.1

9.3

9.3

9.5

8.8

9.1

9.1

9.3

8.5

8.7

8.7

9.0

8.2

8.4

8.4

8.6

279.

29.

49.

49.

68.

99.

19.

19.

48.

68.

88.

89.

08.

28.

58.

58.

728

9.3

9.5

9.5

9.7

9.0

9.2

9.2

9.5

8.7

8.9

8.9

9.1

8.3

8.5

8.5

8.8

299.

39.

69.

69.

89.

19.

39.

39.

68.

79.

09.

09.

28.

48.

68.

68.

830

9.3

9.6

9.6

9.8

9.1

9.3

9.3

9.6

8.7

9.0

9.0

9.2

8.4

8.6

8.6

8.8

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 42

"




Table 23

57.

57.

87.

88.

07.

47.

77.

78.

07.

37.

67.

67.

97.

27.

57.

57.

86

7.6

7.9

7.9

8.1

7.5

7.8

7.8

8.0

7.4

7.7

7.7

7.9

7.3

7.6

7.6

7.8

77.

78.

08.

08.

27.

67.

97.

98.

27.

57.

87.

88.

07.

47.

67.

67.

98

7.8

8.1

8.1

8.4

7.7

8.0

8.0

8.3

7.6

7.9

7.9

8.1

7.5

7.7

7.7

8.0

98.

08.

28.

28.

57.

88.

18.

18.

47.

78.

08.

08.

27.

57.

87.

88.

110

8.1

8.3

8.3

8.6

8.0

8.2

8.2

8.5

7.8

8.1

8.1

8.3

7.6

7.9

7.9

8.1

118.

28.

58.

58.

78.

18.

38.

38.

67.

98.

28.

28.

47.

78.

08.

08.

212

8.3

8.6

8.6

8.8

8.2

8.4

8.4

8.7

8.0

8.2

8.2

8.5

7.8

8.1

8.1

8.3

138.

48.

78.

79.

08.

38.

58.

58.

88.

18.

38.

38.

67.

98.

18.

18.

414

8.5

8.8

8.8

9.1

8.4

8.7

8.7

8.9

8.2

8.4

8.4

8.7

8.0

8.2

8.2

8.5

158.

78.

98.

99.

28.

58.

88.

89.

08.

38.

58.

58.

88.

08.

38.

38.

616

8.8

9.0

9.0

9.3

8.6

8.9

8.9

9.1

8.4

8.6

8.6

8.9

8.1

8.4

8.4

8.6

178.

99.

29.

29.

48.

79.

09.

09.

28.

58.

78.

79.

08.

28.

58.

58.

718

9.0

9.3

9.3

9.5

8.8

9.1

9.1

9.3

8.6

8.8

8.8

9.1

8.3

8.5

8.5

8.8

199.

19.

49.

49.

68.

99.

29.

29.

48.

68.

98.

99.

28.

48.

68.

68.

920

9.2

9.5

9.5

9.7

9.0

9.3

9.3

9.5

8.7

9.0

9.0

9.3

8.4

8.7

8.7

9.0

219.

39.

69.

69.

99.

19.

49.

49.

68.

89.

19.

19.

38.

58.

88.

89.

022

9.4

9.7

9.7

10.0

9.2

9.5

9.5

9.7

8.9

9.2

9.2

9.4

8.6

8.9

8.9

9.1

239.

59.

89.

810

.19.

39.

69.

69.

89.

09.

39.

39.

58.

78.

98.

99.

224

9.6

9.9

9.9

10.2

9.4

9.7

9.7

9.9

9.1

9.4

9.4

9.6

8.8

9.0

9.0

9.3

259.

710

.010

.010

.39.

59.

89.

810

.09.

29.

49.

49.

78.

89.

19.

19.

426

9.8

10.1

10.1

10.4

9.6

9.9

9.9

10.1

9.3

9.5

9.5

9.8

8.9

9.2

9.2

9.4

279.

910

.210

.210

.59.

710

.010

.010

.29.

39.

69.

69.

99.

09.

29.

29.

528

10.0

10.3

10.3

10.6

9.8

10.1

10.1

10.3

9.4

9.7

9.7

10.0

9.1

9.3

9.3

9.6

2910

.110

.410

.410

.79.

910

.210

.210

.49.

59.

89.

810

.09.

19.

49.

49.

730

10.1

10.4

10.4

10.7

9.9

10.2

10.2

10.4

9.5

9.8

9.8

10.0

9.1

9.4

9.4

9.7

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 48

"


Tables 131


Table 24

58.

38.

68.

68.

98.

38.

68.

68.

98.

28.

58.

58.

88.

18.

48.

48.

76

8.4

8.7

8.7

9.0

8.4

8.7

8.7

9.0

8.3

8.6

8.6

8.9

8.2

8.5

8.5

8.8

78.

68.

98.

99.

28.

58.

88.

89.

18.

48.

68.

68.

98.

28.

58.

58.

88

8.7

9.0

9.0

9.3

8.6

8.9

8.9

9.2

8.4

8.7

8.7

9.0

8.3

8.6

8.6

8.9

98.

89.

19.

19.

48.

79.

09.

09.

38.

58.

88.

89.

18.

48.

78.

79.

010

8.9

9.2

9.2

9.5

8.8

9.1

9.1

9.4

8.6

8.9

8.9

9.2

8.5

8.8

8.8

9.0

119.

09.

39.

39.

68.

99.

29.

29.

58.

79.

09.

09.

38.

58.

88.

89.

112

9.2

9.5

9.5

9.7

9.0

9.3

9.3

9.6

8.8

9.1

9.1

9.4

8.6

8.9

8.9

9.2

139.

39.

69.

69.

99.

19.

49.

49.

78.

99.

29.

29.

58.

79.

09.

09.

314

9.4

9.7

9.7

10.0

9.2

9.5

9.5

9.8

9.0

9.3

9.3

9.6

8.8

9.1

9.1

9.4

159.

59.

89.

810

.19.

39.

69.

69.

99.

19.

49.

49.

78.

99.

29.

29.

516

9.6

9.9

9.9

10.2

9.5

9.7

9.7

10.0

9.2

9.5

9.5

9.8

9.0

9.3

9.3

9.5

179.

710

.010

.010

.39.

69.

99.

910

.19.

39.

69.

69.

99.

09.

39.

39.

618

9.9

10.2

10.2

10.4

9.7

10.0

10.0

10.2

9.4

9.7

9.7

10.0

9.1

9.4

9.4

9.7

1910

.010

.310

.310

.69.

810

.110

.110

.49.

59.

89.

810

.19.

29.

59.

59.

820

10.1

10.4

10.4

10.7

9.9

10.2

10.2

10.5

9.6

9.9

9.9

10.2

9.3

9.6

9.6

9.9

2110

.210

.510

.510

.810

.010

.310

.310

.69.

710

.010

.010

.39.

49.

79.

79.

922

10.3

10.6

10.6

10.9

10.1

10.4

10.4

10.7

9.8

10.1

10.1

10.3

9.4

9.7

9.7

10.0

2310

.410

.710

.711

.010

.210

.510

.510

.89.

910

.110

.110

.49.

59.

89.

810

.124

10.5

10.8

10.8

11.1

10.3

10.6

10.6

10.9

9.9

10.2

10.2

10.5

9.6

9.9

9.9

10.2

2510

.610

.910

.911

.210

.410

.710

.711

.010

.010

.310

.310

.69.

710

.010

.010

.326

10.7

11.0

11.0

11.3

10.5

10.8

10.8

11.1

10.1

10.4

10.4

10.7

9.8

10.1

10.1

10.3

2710

.811

.111

.111

.410

.610

.910

.911

.210

.210

.510

.510

.89.

810

.110

.110

.428

10.9

11.2

11.2

11.5

10.7

11.0

11.0

11.3

10.3

10.6

10.6

10.9

9.9

10.2

10.2

10.5

2911

.011

.311

.311

.610

.811

.111

.111

.410

.410

.710

.711

.010

.010

.310

.310

.630

11.0

11.3

11.3

11.6

10.8

11.1

11.1

11.4

10.4

10.7

10.7

11.0

10.0

10.3

10.3

10.6

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 54

"




Table 25

59.

29.

59.

59.

99.

19.

59.

59.

89.

09.

49.

49.

78.

99.

39.

39.

66

9.3

9.6

9.6

10.0

9.2

9.6

9.6

9.9

9.1

9.4

9.4

9.8

9.0

9.3

9.3

9.7

79.

49.

79.

710

.19.

39.

69.

610

.09.

29.

59.

59.

99.

19.

49.

49.

78

9.5

9.9

9.9

10.2

9.4

9.8

9.8

10.1

9.3

9.6

9.6

9.9

9.1

9.5

9.5

9.8

99.

610

.010

.010

.39.

59.

99.

910

.29.

49.

79.

710

.09.

29.

59.

59.

910

9.8

10.1

10.1

10.4

9.6

10.0

10.0

10.3

9.5

9.8

9.8

10.1

9.3

9.6

9.6

9.9

119.

910

.210

.210

.59.

810

.110

.110

.49.

69.

99.

910

.29.

49.

79.

710

.012

10.0

10.3

10.3

10.6

9.9

10.2

10.2

10.5

9.7

10.0

10.0

10.3

9.5

9.8

9.8

10.1

1310

.110

.410

.410

.810

.010

.310

.310

.69.

810

.110

.110

.49.

69.

99.

910

.214

10.2

10.6

10.6

10.9

10.1

10.4

10.4

10.7

9.9

10.2

10.2

10.5

9.6

10.0

10.0

10.3

1510

.410

.710

.711

.010

.210

.510

.510

.810

.010

.310

.310

.69.

710

.010

.010

.416

10.5

10.8

10.8

11.1

10.3

10.6

10.6

10.9

10.1

10.4

10.4

10.7

9.8

10.1

10.1

10.4

1710

.610

.910

.911

.210

.410

.710

.711

.010

.110

.510

.510

.89.

910

.210

.210

.518

10.7

11.0

11.0

11.4

10.5

10.8

10.8

11.2

10.2

10.6

10.6

10.9

10.0

10.3

10.3

10.6

1910

.811

.211

.211

.510

.610

.910

.911

.310

.310

.710

.711

.010

.010

.410

.410

.720

10.9

11.3

11.3

11.6

10.7

11.0

11.0

11.4

10.4

10.8

10.8

11.1

10.1

10.4

10.4

10.8

2111

.111

.411

.411

.710

.811

.211

.211

.510

.510

.810

.811

.210

.210

.510

.510

.822

11.2

11.5

11.5

11.8

10.9

11.3

11.3

11.6

10.6

10.9

10.9

11.3

10.3

10.6

10.6

10.9

2311

.311

.611

.611

.911

.011

.411

.411

.710

.711

.011

.011

.410

.410

.710

.711

.024

11.4

11.7

11.7

12.0

11.1

11.5

11.5

11.8

10.8

11.1

11.1

11.4

10.5

10.8

10.8

11.1

2511

.511

.811

.812

.111

.211

.611

.611

.910

.911

.211

.211

.510

.510

.810

.811

.226

11.6

11.9

11.9

12.3

11.3

11.7

11.7

12.0

11.0

11.3

11.3

11.6

10.6

10.9

10.9

11.2

2711

.712

.012

.012

.411

.411

.811

.812

.111

.111

.411

.411

.710

.711

.011

.011

.328

11.8

12.1

12.1

12.5

11.5

11.9

11.9

12.2

11.2

11.5

11.5

11.8

10.8

11.1

11.1

11.4

2911

.912

.212

.212

.611

.612

.012

.012

.311

.211

.611

.611

.910

.811

.211

.211

.530

11.9

12.2

12.2

12.6

11.6

12.0

12.0

12.3

11.2

11.6

11.6

11.9

10.8

11.2

11.2

11.5

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 60

"


Tables 133


Table 26

510

.110

.410

.410

.810

.010

.410

.410

.79.

910

.310

.310

.79.

810

.210

.210

.66

10.2

10.5

10.5

10.9

10.1

10.4

10.4

10.8

10.0

10.3

10.3

10.7

9.9

10.2

10.2

10.6

710

.310

.610

.611

.010

.210

.510

.510

.910

.010

.410

.410

.89.

910

.310

.310

.68

10.4

10.7

10.7

11.1

10.3

10.6

10.6

11.0

10.1

10.5

10.5

10.9

10.0

10.3

10.3

10.7

910

.510

.810

.811

.210

.410

.710

.711

.110

.210

.610

.610

.910

.110

.410

.410

.810

10.6

11.0

11.0

11.3

10.5

10.8

10.8

11.2

10.3

10.7

10.7

11.0

10.1

10.5

10.5

10.9

1110

.711

.111

.111

.410

.610

.910

.911

.310

.410

.810

.811

.110

.210

.610

.610

.912

10.8

11.2

11.2

11.6

10.7

11.1

11.1

11.4

10.5

10.9

10.9

11.2

10.3

10.7

10.7

11.0

1311

.011

.311

.311

.710

.811

.211

.211

.510

.611

.011

.011

.310

.410

.710

.711

.114

11.1

11.4

11.4

11.8

10.9

11.3

11.3

11.6

10.7

11.1

11.1

11.4

10.5

10.8

10.8

11.2

1511

.211

.611

.611

.911

.011

.411

.411

.710

.811

.111

.111

.510

.610

.910

.911

.316

11.3

11.7

11.7

12.0

11.1

11.5

11.5

11.8

10.9

11.2

11.2

11.6

10.6

11.0

11.0

11.3

1711

.411

.811

.812

.211

.311

.611

.612

.011

.011

.311

.311

.710

.711

.111

.111

.418

11.6

11.9

11.9

12.3

11.4

11.7

11.7

12.1

11.1

11.4

11.4

11.8

10.8

11.2

11.2

11.5

1911

.712

.012

.012

.411

.511

.811

.812

.211

.211

.511

.511

.910

.911

.211

.211

.620

11.8

12.1

12.1

12.5

11.6

11.9

11.9

12.3

11.3

11.6

11.6

12.0

11.0

11.3

11.3

11.7

2111

.912

.312

.312

.611

.712

.012

.012

.411

.411

.711

.712

.111

.011

.411

.411

.722

12.0

12.4

12.4

12.7

11.8

12.1

12.1

12.5

11.5

11.8

11.8

12.2

11.1

11.5

11.5

11.8

2312

.112

.512

.512

.811

.912

.212

.212

.611

.611

.911

.912

.311

.211

.611

.611

.924

12.2

12.6

12.6

13.0

12.0

12.3

12.3

12.7

11.6

12.0

12.0

12.4

11.3

11.6

11.6

12.0

2512

.412

.712

.713

.112

.112

.512

.512

.811

.712

.112

.112

.411

.411

.711

.712

.126

12.5

12.8

12.8

13.2

12.2

12.6

12.6

12.9

11.8

12.2

12.2

12.5

11.5

11.8

11.8

12.2

2712

.612

.912

.913

.312

.312

.712

.713

.011

.912

.312

.312

.611

.511

.911

.912

.228

12.7

13.0

13.0

13.4

12.4

12.8

12.8

13.1

12.0

12.4

12.4

12.7

11.6

12.0

12.0

12.3

2912

.813

.213

.213

.512

.512

.912

.913

.212

.112

.512

.512

.811

.712

.012

.012

.430

12.8

13.2

13.2

13.5

12.5

12.9

12.9

13.2

12.1

12.5

12.5

12.8

11.7

12.0

12.0

12.4

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 66

"




Table 27

510

.911

.311

.311

.810

.911

.311

.311

.710

.811

.211

.211

.610

.711

.111

.111

.56

11.0

11.4

11.4

11.8

10.9

11.3

11.3

11.7

10.8

11.2

11.2

11.6

10.7

11.1

11.1

11.5

711

.111

.511

.511

.911

.011

.411

.411

.810

.911

.311

.311

.710

.811

.211

.211

.68

11.2

11.6

11.6

12.0

11.1

11.5

11.5

11.9

11.0

11.4

11.4

11.8

10.8

11.2

11.2

11.6

911

.311

.711

.712

.111

.211

.611

.612

.011

.111

.511

.511

.810

.911

.311

.311

.710

11.5

11.8

11.8

12.2

11.3

11.7

11.7

12.1

11.2

11.5

11.5

11.9

11.0

11.4

11.4

11.8

1111

.612

.012

.012

.311

.411

.811

.812

.211

.211

.611

.612

.011

.111

.411

.411

.812

11.7

12.1

12.1

12.5

11.5

11.9

11.9

12.3

11.3

11.7

11.7

12.1

11.1

11.5

11.5

11.9

1311

.812

.212

.212

.611

.712

.012

.012

.411

.411

.811

.812

.211

.211

.611

.612

.014

11.9

12.3

12.3

12.7

11.8

12.2

12.2

12.5

11.5

11.9

11.9

12.3

11.3

11.7

11.7

12.1

1512

.112

.412

.412

.811

.912

.312

.312

.611

.612

.012

.012

.411

.411

.811

.812

.116

12.2

12.6

12.6

12.9

12.0

12.4

12.4

12.8

11.7

12.1

12.1

12.5

11.5

11.9

11.9

12.2

1712

.312

.712

.713

.112

.112

.512

.512

.911

.812

.212

.212

.611

.611

.911

.912

.318

12.4

12.8

12.8

13.2

12.2

12.6

12.6

13.0

11.9

12.3

12.3

12.7

11.6

12.0

12.0

12.4

1912

.512

.912

.913

.312

.312

.712

.713

.112

.012

.412

.412

.811

.712

.112

.112

.520

12.6

13.0

13.0

13.4

12.4

12.8

12.8

13.2

12.1

12.5

12.5

12.9

11.8

12.2

12.2

12.6

2112

.813

.113

.113

.512

.512

.912

.913

.312

.212

.612

.613

.011

.912

.312

.312

.622

12.9

13.3

13.3

13.6

12.6

13.0

13.0

13.4

12.3

12.7

12.7

13.1

12.0

12.3

12.3

12.7

2313

.013

.413

.413

.812

.713

.113

.113

.512

.412

.812

.813

.212

.112

.412

.412

.824

13.1

13.5

13.5

13.9

12.8

13.2

13.2

13.6

12.5

12.9

12.9

13.3

12.1

12.5

12.5

12.9

2513

.213

.613

.614

.013

.013

.313

.313

.712

.613

.013

.013

.412

.212

.612

.613

.026

13.3

13.7

13.7

14.1

13.1

13.4

13.4

13.8

12.7

13.1

13.1

13.4

12.3

12.7

12.7

13.1

2713

.413

.813

.814

.213

.213

.513

.513

.912

.813

.213

.213

.512

.412

.812

.813

.128

13.5

13.9

13.9

14.3

13.3

13.6

13.6

14.0

12.9

13.2

13.2

13.6

12.5

12.8

12.8

13.2

2913

.714

.014

.014

.413

.413

.713

.714

.113

.013

.313

.313

.712

.512

.912

.913

.330

13.7

14.0

14.0

14.4

13.4

13.7

13.7

14.1

13.0

13.3

13.3

13.7

12.5

12.9

12.9

13.3

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 72

"


Tables 135


Table 28

511

.812

.312

.312

.711

.712

.212

.212

.611

.612

.112

.112

.511

.512

.012

.012

.56

11.9

12.3

12.3

12.8

11.8

12.2

12.2

12.7

11.7

12.1

12.1

12.6

11.6

12.0

12.0

12.5

712

.012

.412

.412

.811

.912

.312

.312

.711

.712

.212

.212

.611

.612

.112

.112

.58

12.1

12.5

12.5

12.9

12.0

12.4

12.4

12.8

11.8

12.3

12.3

12.7

11.7

12.1

12.1

12.5

912

.212

.612

.613

.012

.112

.512

.512

.911

.912

.312

.312

.811

.712

.212

.212

.610

12.3

12.7

12.7

13.1

12.2

12.6

12.6

13.0

12.0

12.4

12.4

12.8

11.8

12.2

12.2

12.7

1112

.412

.812

.813

.312

.312

.712

.713

.112

.112

.512

.512

.911

.912

.312

.312

.712

12.5

13.0

13.0

13.4

12.4

12.8

12.8

13.2

12.2

12.6

12.6

13.0

12.0

12.4

12.4

12.8

1312

.713

.113

.113

.512

.512

.912

.913

.312

.312

.712

.713

.112

.112

.512

.512

.914

12.8

13.2

13.2

13.6

12.6

13.0

13.0

13.4

12.4

12.8

12.8

13.2

12.1

12.6

12.6

13.0

1512

.913

.313

.313

.712

.713

.113

.113

.512

.512

.912

.913

.312

.212

.612

.613

.016

13.0

13.4

13.4

13.9

12.8

13.2

13.2

13.7

12.6

13.0

13.0

13.4

12.3

12.7

12.7

13.1

1713

.113

.613

.614

.012

.913

.413

.413

.812

.713

.113

.113

.512

.412

.812

.813

.218

13.3

13.7

13.7

14.1

13.0

13.5

13.5

13.9

12.8

13.2

13.2

13.6

12.5

12.9

12.9

13.3

1913

.413

.813

.814

.213

.213

.613

.614

.012

.913

.313

.313

.712

.613

.013

.013

.420

13.5

13.9

13.9

14.3

13.3

13.7

13.7

14.1

13.0

13.4

13.4

13.8

12.6

13.0

13.0

13.5

2113

.614

.014

.014

.413

.413

.813

.814

.213

.113

.513

.513

.912

.713

.113

.113

.522

13.7

14.1

14.1

14.6

13.5

13.9

13.9

14.3

13.1

13.6

13.6

14.0

12.8

13.2

13.2

13.6

2313

.814

.314

.314

.713

.614

.014

.014

.413

.213

.713

.714

.112

.913

.313

.313

.724

14.0

14.4

14.4

14.8

13.7

14.1

14.1

14.5

13.3

13.8

13.8

14.2

13.0

13.4

13.4

13.8

2514

.114

.514

.514

.913

.814

.214

.214

.613

.413

.813

.814

.313

.113

.513

.513

.926

14.2

14.6

14.6

15.0

13.9

14.3

14.3

14.7

13.5

13.9

13.9

14.4

13.1

13.5

13.5

14.0

2714

.314

.714

.715

.114

.014

.414

.414

.813

.614

.014

.014

.413

.213

.613

.614

.028

14.4

14.8

14.8

15.2

14.1

14.5

14.5

14.9

13.7

14.1

14.1

14.5

13.3

13.7

13.7

14.1

2914

.514

.914

.915

.414

.214

.614

.615

.113

.814

.214

.214

.613

.413

.813

.814

.230

14.5

14.9

14.9

15.4

14.2

14.6

14.6

15.1

13.8

14.2

14.2

14.6

13.4

13.8

13.8

14.2

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 78

"




Table 29

512

.613

.113

.113

.612

.513

.013

.013

.512

.412

.912

.913

.412

.312

.812

.813

.36

12.6

13.1

13.1

13.6

12.6

13.0

13.0

13.5

12.4

12.9

12.9

13.4

12.3

12.8

12.8

13.3

712

.713

.213

.213

.712

.613

.113

.113

.612

.513

.013

.013

.412

.412

.812

.813

.38

12.8

13.3

13.3

13.8

12.7

13.2

13.2

13.7

12.6

13.0

13.0

13.5

12.4

12.9

12.9

13.4

912

.913

.413

.413

.912

.813

.313

.313

.712

.713

.113

.113

.612

.513

.013

.013

.410

13.0

13.5

13.5

14.0

12.9

13.4

13.4

13.8

12.7

13.2

13.2

13.7

12.6

13.0

13.0

13.5

1113

.213

.613

.614

.113

.013

.513

.513

.912

.813

.313

.313

.712

.613

.113

.113

.512

13.3

13.7

13.7

14.2

13.1

13.6

13.6

14.0

12.9

13.4

13.4

13.8

12.7

13.2

13.2

13.6

1313

.413

.913

.914

.313

.213

.713

.714

.113

.013

.513

.513

.912

.813

.213

.213

.714

13.5

14.0

14.0

14.4

13.3

13.8

13.8

14.2

13.1

13.6

13.6

14.0

12.9

13.3

13.3

13.8

1513

.614

.114

.114

.513

.513

.913

.914

.413

.213

.713

.714

.113

.013

.413

.413

.816

13.8

14.2

14.2

14.7

13.6

14.0

14.0

14.5

13.3

13.8

13.8

14.2

13.0

13.5

13.5

13.9

1713

.914

.314

.314

.813

.714

.114

.114

.613

.413

.913

.914

.313

.113

.613

.614

.018

14.0

14.5

14.5

14.9

13.8

14.2

14.2

14.7

13.5

13.9

13.9

14.4

13.2

13.7

13.7

14.1

1914

.114

.614

.615

.013

.914

.314

.314

.813

.614

.014

.014

.513

.313

.713

.714

.220

14.2

14.7

14.7

15.1

14.0

14.5

14.5

14.9

13.7

14.1

14.1

14.6

13.4

13.8

13.8

14.3

2114

.414

.814

.815

.314

.114

.614

.615

.013

.814

.214

.214

.713

.513

.913

.914

.322

14.5

14.9

14.9

15.4

14.2

14.7

14.7

15.1

13.9

14.3

14.3

14.8

13.5

14.0

14.0

14.4

2314

.615

.015

.015

.514

.314

.814

.815

.214

.014

.414

.414

.913

.614

.114

.114

.524

14.7

15.2

15.2

15.6

14.4

14.9

14.9

15.3

14.1

14.5

14.5

15.0

13.7

14.1

14.1

14.6

2514

.815

.315

.315

.714

.615

.015

.015

.414

.214

.614

.615

.113

.814

.214

.214

.726

14.9

15.4

15.4

15.8

14.7

15.1

15.1

15.6

14.3

14.7

14.7

15.2

13.9

14.3

14.3

14.8

2715

.115

.515

.516

.014

.815

.215

.215

.714

.414

.814

.815

.314

.014

.414

.414

.828

15.2

15.6

15.6

16.1

14.9

15.3

15.3

15.8

14.5

14.9

14.9

15.3

14.0

14.5

14.5

14.9

2915

.315

.715

.716

.215

.015

.415

.415

.914

.615

.015

.015

.414

.114

.614

.615

.030

15.3

15.7

15.7

16.2

15.0

15.4

15.4

15.9

14.6

15.0

15.0

15.4

14.1

14.6

14.6

15.0

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 84

"


Tables 137


Table 30

513

.514

.014

.014

.513

.413

.913

.914

.513

.313

.813

.814

.413

.213

.713

.714

.36

13.5

14.0

14.0

14.5

13.4

13.9

13.9

14.5

13.3

13.8

13.8

14.4

13.2

13.7

13.7

14.3

713

.614

.114

.114

.613

.514

.014

.014

.513

.413

.913

.914

.413

.213

.713

.714

.38

13.7

14.2

14.2

14.7

13.6

14.1

14.1

14.6

13.4

13.9

13.9

14.4

13.3

13.8

13.8

14.3

913

.814

.314

.314

.813

.714

.214

.214

.713

.514

.014

.014

.513

.313

.813

.814

.310

13.9

14.4

14.4

14.9

13.8

14.3

14.3

14.7

13.6

14.1

14.1

14.6

13.4

13.9

13.9

14.4

1114

.014

.514

.515

.013

.914

.414

.414

.813

.714

.214

.214

.713

.514

.014

.014

.512

14.1

14.6

14.6

15.1

14.0

14.5

14.5

14.9

13.8

14.3

14.3

14.7

13.6

14.0

14.0

14.5

1314

.214

.714

.715

.214

.114

.614

.615

.013

.914

.314

.314

.813

.614

.114

.114

.614

14.4

14.8

14.8

15.3

14.2

14.7

14.7

15.2

14.0

14.4

14.4

14.9

13.7

14.2

14.2

14.7

1514

.515

.015

.015

.414

.314

.814

.815

.314

.114

.514

.515

.013

.814

.314

.314

.816

14.6

15.1

15.1

15.6

14.4

14.9

14.9

15.4

14.1

14.6

14.6

15.1

13.9

14.4

14.4

14.8

1714

.715

.215

.215

.714

.515

.015

.015

.514

.214

.714

.715

.214

.014

.414

.414

.918

14.8

15.3

15.3

15.8

14.6

15.1

15.1

15.6

14.3

14.8

14.8

15.3

14.0

14.5

14.5

15.0

1915

.015

.415

.415

.914

.715

.215

.215

.714

.414

.914

.915

.414

.114

.614

.615

.120

15.1

15.6

15.6

16.0

14.9

15.3

15.3

15.8

14.5

15.0

15.0

15.5

14.2

14.7

14.7

15.2

2115

.215

.715

.716

.215

.015

.415

.415

.914

.615

.115

.115

.614

.314

.814

.815

.222

15.3

15.8

15.8

16.3

15.1

15.5

15.5

16.0

14.7

15.2

15.2

15.7

14.4

14.8

14.8

15.3

2315

.415

.915

.916

.415

.215

.715

.716

.114

.815

.315

.315

.814

.514

.914

.915

.424

15.6

16.0

16.0

16.5

15.3

15.8

15.8

16.2

14.9

15.4

15.4

15.9

14.5

15.0

15.0

15.5

2515

.716

.216

.216

.615

.415

.915

.916

.415

.015

.515

.516

.014

.615

.115

.115

.626

15.8

16.3

16.3

16.8

15.5

16.0

16.0

16.5

15.1

15.6

15.6

16.1

14.7

15.2

15.2

15.7

2715

.916

.416

.416

.915

.616

.116

.116

.615

.215

.715

.716

.214

.815

.315

.315

.728

16.0

16.5

16.5

17.0

15.7

16.2

16.2

16.7

15.3

15.8

15.8

16.3

14.9

15.3

15.3

15.8

2916

.116

.616

.617

.115

.816

.316

.316

.815

.415

.915

.916

.315

.015

.415

.415

.930

16.1

16.6

16.6

17.1

15.8

16.3

16.3

16.8

15.4

15.9

15.9

16.3

15.0

15.4

15.4

15.9

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 90

"




Table 31

514

.314

.914

.915

.514

.314

.914

.915

.414

.214

.814

.815

.314

.114

.714

.715

.26

14.4

14.9

14.9

15.5

14.3

14.9

14.9

15.4

14.2

14.8

14.8

15.3

14.1

14.7

14.7

15.2

714

.515

.015

.015

.514

.414

.914

.915

.514

.214

.814

.815

.314

.114

.714

.715

.28

14.5

15.1

15.1

15.6

14.4

15.0

15.0

15.5

14.3

14.8

14.8

15.4

14.1

14.7

14.7

15.2

914

.615

.215

.215

.714

.515

.115

.115

.614

.414

.914

.915

.414

.214

.714

.715

.310

14.7

15.3

15.3

15.8

14.6

15.1

15.1

15.7

14.4

15.0

15.0

15.5

14.3

14.8

14.8

15.3

1114

.915

.415

.415

.914

.715

.215

.215

.814

.515

.015

.015

.614

.314

.814

.815

.412

15.0

15.5

15.5

16.0

14.8

15.3

15.3

15.9

14.6

15.1

15.1

15.6

14.4

14.9

14.9

15.4

1315

.115

.615

.616

.114

.915

.415

.416

.014

.715

.215

.215

.714

.515

.015

.015

.514

15.2

15.7

15.7

16.2

15.0

15.5

15.5

16.1

14.8

15.3

15.3

15.8

14.6

15.1

15.1

15.6

1515

.315

.815

.816

.415

.115

.715

.716

.214

.915

.415

.415

.914

.615

.115

.115

.716

15.4

16.0

16.0

16.5

15.3

15.8

15.8

16.3

15.0

15.5

15.5

16.0

14.7

15.2

15.2

15.7

1715

.616

.116

.116

.615

.415

.915

.916

.415

.115

.615

.616

.114

.815

.315

.315

.818

15.7

16.2

16.2

16.7

15.5

16.0

16.0

16.5

15.2

15.7

15.7

16.2

14.9

15.4

15.4

15.9

1915

.816

.316

.316

.815

.616

.116

.116

.615

.315

.815

.816

.315

.015

.515

.516

.020

15.9

16.4

16.4

17.0

15.7

16.2

16.2

16.7

15.4

15.9

15.9

16.4

15.0

15.5

15.5

16.1

2116

.116

.616

.617

.115

.816

.316

.316

.815

.516

.016

.016

.515

.115

.615

.616

.122

16.2

16.7

16.7

17.2

15.9

16.4

16.4

16.9

15.6

16.1

16.1

16.6

15.2

15.7

15.7

16.2

2316

.316

.816

.817

.316

.016

.516

.517

.015

.716

.216

.216

.715

.315

.815

.816

.324

16.4

16.9

16.9

17.4

16.1

16.6

16.6

17.2

15.8

16.3

16.3

16.8

15.4

15.9

15.9

16.4

2516

.517

.017

.017

.516

.216

.816

.817

.315

.916

.416

.416

.915

.516

.016

.016

.526

16.6

17.2

17.2

17.7

16.4

16.9

16.9

17.4

16.0

16.5

16.5

17.0

15.5

16.0

16.0

16.5

2716

.817

.317

.317

.816

.517

.017

.017

.516

.016

.616

.617

.115

.616

.116

.116

.628

16.9

17.4

17.4

17.9

16.6

17.1

17.1

17.6

16.1

16.6

16.6

17.2

15.7

16.2

16.2

16.7

2917

.017

.517

.518

.016

.717

.217

.217

.716

.216

.716

.717

.215

.816

.316

.316

.830

17.0

17.5

17.5

18.0

16.7

17.2

17.2

17.7

16.2

16.7

16.7

17.2

15.8

16.3

16.3

16.8

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 96

"


Tables 139


Table 32

515

.215

.915

.916

.515

.215

.815

.816

.415

.115

.715

.716

.315

.015

.615

.616

.26

15.3

15.9

15.9

16.5

15.2

15.8

15.8

16.4

15.1

15.7

15.7

16.3

15.0

15.6

15.6

16.2

715

.315

.915

.916

.515

.215

.815

.816

.415

.115

.715

.716

.315

.015

.615

.616

.28

15.4

16.0

16.0

16.6

15.3

15.9

15.9

16.4

15.2

15.7

15.7

16.3

15.0

15.6

15.6

16.2

915

.516

.116

.116

.615

.415

.915

.916

.515

.215

.815

.816

.315

.115

.615

.616

.210

15.6

16.2

16.2

16.7

15.5

16.0

16.0

16.6

15.3

15.9

15.9

16.4

15.1

15.7

15.7

16.2

1115

.716

.316

.316

.815

.616

.116

.116

.715

.415

.915

.916

.515

.215

.715

.716

.312

15.8

16.4

16.4

16.9

15.7

16.2

16.2

16.8

15.5

16.0

16.0

16.6

15.2

15.8

15.8

16.3

1315

.916

.516

.517

.015

.816

.316

.316

.915

.516

.116

.116

.615

.315

.915

.916

.414

16.1

16.6

16.6

17.2

15.9

16.4

16.4

17.0

15.6

16.2

16.2

16.7

15.4

15.9

15.9

16.5

1516

.216

.716

.717

.316

.016

.516

.517

.115

.716

.316

.316

.815

.516

.016

.016

.616

16.3

16.8

16.8

17.4

16.1

16.6

16.6

17.2

15.8

16.4

16.4

16.9

15.6

16.1

16.1

16.6

1716

.417

.017

.017

.516

.216

.716

.717

.315

.916

.516

.517

.015

.616

.216

.216

.718

16.5

17.1

17.1

17.6

16.3

16.9

16.9

17.4

16.0

16.6

16.6

17.1

15.7

16.3

16.3

16.8

1916

.717

.217

.217

.716

.417

.017

.017

.516

.116

.716

.717

.215

.816

.316

.316

.920

16.8

17.3

17.3

17.9

16.5

17.1

17.1

17.6

16.2

16.8

16.8

17.3

15.9

16.4

16.4

17.0

2116

.917

.417

.418

.016

.617

.217

.217

.716

.316

.816

.817

.416

.016

.516

.517

.022

17.0

17.6

17.6

18.1

16.8

17.3

17.3

17.8

16.4

16.9

16.9

17.5

16.0

16.6

16.6

17.1

2317

.117

.717

.718

.216

.917

.417

.417

.916

.517

.017

.017

.616

.116

.716

.717

.224

17.3

17.8

17.8

18.3

17.0

17.5

17.5

18.1

16.6

17.1

17.1

17.7

16.2

16.7

16.7

17.3

2517

.417

.917

.918

.517

.117

.617

.618

.216

.717

.217

.217

.816

.316

.816

.817

.426

17.5

18.0

18.0

18.6

17.2

17.7

17.7

18.3

16.8

17.3

17.3

17.9

16.4

16.9

16.9

17.4

2717

.618

.218

.218

.717

.317

.817

.818

.416

.917

.417

.418

.016

.517

.017

.017

.528

17.7

18.3

18.3

18.8

17.4

18.0

18.0

18.5

17.0

17.5

17.5

18.1

16.5

17.1

17.1

17.6

2917

.818

.418

.418

.917

.518

.118

.118

.617

.117

.617

.618

.216

.617

.217

.217

.730

17.8

18.4

18.4

18.9

17.5

18.1

18.1

18.6

17.1

17.6

17.6

18.2

16.6

17.2

17.2

17.7

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 10

2"




Table 33

516

.116

.816

.817

.416

.116

.716

.717

.416

.016

.616

.617

.315

.916

.516

.517

.26

16.1

16.8

16.8

17.4

16.1

16.7

16.7

17.4

16.0

16.6

16.6

17.3

15.9

16.5

16.5

17.2

716

.216

.816

.817

.416

.116

.716

.717

.416

.016

.616

.617

.315

.916

.516

.517

.28

16.3

16.9

16.9

17.5

16.2

16.8

16.8

17.4

16.0

16.6

16.6

17.3

15.9

16.5

16.5

17.2

916

.417

.017

.017

.616

.216

.816

.817

.416

.116

.716

.717

.315

.916

.516

.517

.210

16.5

17.1

17.1

17.7

16.3

16.9

16.9

17.5

16.1

16.7

16.7

17.3

16.0

16.6

16.6

17.2

1116

.617

.217

.217

.716

.417

.017

.017

.616

.216

.816

.817

.416

.016

.616

.617

.212

16.7

17.3

17.3

17.8

16.5

17.1

17.1

17.7

16.3

16.9

16.9

17.5

16.1

16.7

16.7

17.3

1316

.817

.417

.418

.016

.617

.217

.217

.816

.417

.017

.017

.616

.216

.716

.717

.314

16.9

17.5

17.5

18.1

16.7

17.3

17.3

17.9

16.5

17.1

17.1

17.6

16.2

16.8

16.8

17.4

1517

.017

.617

.618

.216

.817

.417

.418

.016

.617

.217

.217

.716

.316

.916

.917

.516

17.1

17.7

17.7

18.3

16.9

17.5

17.5

18.1

16.7

17.2

17.2

17.8

16.4

17.0

17.0

17.5

1717

.317

.817

.818

.417

.017

.617

.618

.216

.817

.317

.317

.916

.517

.017

.017

.618

17.4

18.0

18.0

18.5

17.2

17.7

17.7

18.3

16.9

17.4

17.4

18.0

16.6

17.1

17.1

17.7

1917

.518

.118

.118

.617

.317

.817

.818

.417

.017

.517

.518

.116

.617

.217

.217

.820

17.6

18.2

18.2

18.8

17.4

18.0

18.0

18.5

17.1

17.6

17.6

18.2

16.7

17.3

17.3

17.9

2117

.718

.318

.318

.917

.518

.118

.118

.617

.117

.717

.718

.316

.817

.417

.417

.922

17.9

18.4

18.4

19.0

17.6

18.2

18.2

18.7

17.2

17.8

17.8

18.4

16.9

17.4

17.4

18.0

2318

.018

.618

.619

.117

.718

.318

.318

.917

.317

.917

.918

.517

.017

.517

.518

.124

18.1

18.7

18.7

19.2

17.8

18.4

18.4

19.0

17.4

18.0

18.0

18.6

17.0

17.6

17.6

18.2

2518

.218

.818

.819

.417

.918

.518

.519

.117

.518

.118

.118

.717

.117

.717

.718

.326

18.3

18.9

18.9

19.5

18.0

18.6

18.6

19.2

17.6

18.2

18.2

18.8

17.2

17.8

17.8

18.3

2718

.519

.019

.019

.618

.118

.718

.719

.317

.718

.318

.318

.917

.317

.917

.918

.428

18.6

19.1

19.1

19.7

18.3

18.8

18.8

19.4

17.8

18.4

18.4

19.0

17.4

17.9

17.9

18.5

2918

.719

.319

.319

.818

.418

.918

.919

.517

.918

.518

.519

.117

.518

.018

.018

.630

18.7

19.3

19.3

19.8

18.4

18.9

18.9

19.5

17.9

18.5

18.5

19.1

17.5

18.0

18.0

18.6

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 10

8"


Tables 141


Table 34

517

.017

.717

.718

.417

.017

.717

.718

.416

.917

.617

.618

.316

.817

.517

.518

.26

17.0

17.7

17.7

18.4

17.0

17.7

17.7

18.4

16.9

17.6

17.6

18.3

16.8

17.5

17.5

18.2

717

.117

.717

.718

.417

.017

.717

.718

.416

.917

.617

.618

.316

.817

.517

.518

.28

17.1

17.8

17.8

18.4

17.0

17.7

17.7

18.4

16.9

17.6

17.6

18.3

16.8

17.5

17.5

18.2

917

.217

.917

.918

.517

.117

.717

.718

.416

.917

.617

.618

.316

.817

.517

.518

.210

17.3

17.9

17.9

18.6

17.2

17.8

17.8

18.4

17.0

17.6

17.6

18.3

16.8

17.5

17.5

18.2

1117

.418

.018

.018

.717

.317

.917

.918

.517

.117

.717

.718

.316

.917

.517

.518

.212

17.5

18.1

18.1

18.8

17.4

18.0

18.0

18.6

17.2

17.8

17.8

18.4

16.9

17.6

17.6

18.2

1317

.618

.318

.318

.917

.518

.118

.118

.717

.217

.917

.918

.517

.017

.617

.618

.214

17.7

18.4

18.4

19.0

17.6

18.2

18.2

18.8

17.3

17.9

17.9

18.6

17.1

17.7

17.7

18.3

1517

.918

.518

.519

.117

.718

.318

.318

.917

.418

.018

.018

.617

.217

.817

.818

.416

18.0

18.6

18.6

19.2

17.8

18.4

18.4

19.0

17.5

18.1

18.1

18.7

17.2

17.8

17.8

18.4

1718

.118

.718

.719

.317

.918

.518

.519

.117

.618

.218

.218

.817

.317

.917

.918

.518

18.2

18.8

18.8

19.4

18.0

18.6

18.6

19.2

17.7

18.3

18.3

18.9

17.4

18.0

18.0

18.6

1918

.319

.019

.019

.618

.118

.718

.719

.317

.818

.418

.419

.017

.518

.118

.118

.720

18.5

19.1

19.1

19.7

18.2

18.8

18.8

19.4

17.9

18.5

18.5

19.1

17.6

18.2

18.2

18.8

2118

.619

.219

.219

.818

.318

.918

.919

.518

.018

.618

.619

.217

.618

.218

.218

.822

18.7

19.3

19.3

19.9

18.4

19.0

19.0

19.6

18.1

18.7

18.7

19.3

17.7

18.3

18.3

18.9

2318

.819

.419

.420

.018

.619

.219

.219

.818

.218

.818

.819

.417

.818

.418

.419

.024

18.9

19.5

19.5

20.2

18.7

19.3

19.3

19.9

18.3

18.9

18.9

19.5

17.9

18.5

18.5

19.1

2519

.119

.719

.720

.318

.819

.419

.420

.018

.419

.019

.019

.618

.018

.618

.619

.226

19.2

19.8

19.8

20.4

18.9

19.5

19.5

20.1

18.5

19.1

19.1

19.7

18.0

18.6

18.6

19.2

2719

.319

.919

.920

.519

.019

.619

.620

.218

.619

.219

.219

.818

.118

.718

.719

.328

19.4

20.0

20.0

20.6

19.1

19.7

19.7

20.3

18.7

19.3

19.3

19.9

18.2

18.8

18.8

19.4

2919

.520

.120

.120

.719

.219

.819

.820

.418

.819

.419

.420

.018

.318

.918

.919

.530

19.5

20.1

20.1

20.7

19.2

19.8

19.8

20.4

18.8

19.4

19.4

20.0

18.3

18.9

18.9

19.5

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 11

4"




Table 35

517

.818

.618

.619

.317

.818

.518

.519

.317

.718

.418

.419

.217

.618

.318

.319

.16

17.8

18.6

18.6

19.3

17.8

18.5

18.5

19.3

17.7

18.4

18.4

19.2

17.6

18.3

18.3

19.1

717

.818

.618

.619

.317

.818

.518

.519

.317

.718

.418

.419

.217

.618

.318

.319

.18

17.9

18.6

18.6

19.3

17.8

18.5

18.5

19.3

17.7

18.4

18.4

19.2

17.6

18.3

18.3

19.1

918

.018

.718

.719

.317

.918

.518

.519

.317

.718

.418

.419

.217

.618

.318

.319

.110

18.1

18.7

18.7

19.4

17.9

18.6

18.6

19.3

17.8

18.4

18.4

19.2

17.6

18.3

18.3

19.1

1118

.218

.818

.819

.518

.018

.718

.719

.317

.818

.518

.519

.217

.618

.318

.319

.112

18.3

18.9

18.9

19.6

18.1

18.8

18.8

19.4

17.9

18.6

18.6

19.2

17.7

18.3

18.3

19.1

1318

.419

.019

.019

.718

.218

.918

.919

.518

.018

.618

.619

.317

.818

.418

.419

.114

18.5

19.1

19.1

19.8

18.3

19.0

19.0

19.6

18.1

18.7

18.7

19.4

17.8

18.5

18.5

19.1

1518

.619

.319

.319

.918

.419

.119

.119

.718

.218

.818

.819

.517

.918

.518

.519

.216

18.7

19.4

19.4

20.0

18.5

19.2

19.2

19.8

18.3

18.9

18.9

19.5

18.0

18.6

18.6

19.3

1718

.819

.519

.520

.118

.619

.319

.319

.918

.319

.019

.019

.618

.018

.718

.719

.318

19.0

19.6

19.6

20.3

18.7

19.4

19.4

20.0

18.4

19.1

19.1

19.7

18.1

18.8

18.8

19.4

1919

.119

.719

.720

.418

.919

.519

.520

.118

.519

.219

.219

.818

.218

.818

.819

.520

19.2

19.8

19.8

20.5

19.0

19.6

19.6

20.2

18.6

19.3

19.3

19.9

18.3

18.9

18.9

19.6

2119

.320

.020

.020

.619

.119

.719

.720

.318

.719

.419

.420

.018

.419

.019

.019

.622

19.4

20.1

20.1

20.7

19.2

19.8

19.8

20.5

18.8

19.5

19.5

20.1

18.5

19.1

19.1

19.7

2319

.620

.220

.220

.819

.319

.919

.920

.618

.919

.619

.620

.218

.519

.219

.219

.824

19.7

20.3

20.3

21.0

19.4

20.0

20.0

20.7

19.0

19.6

19.6

20.3

18.6

19.2

19.2

19.9

2519

.820

.420

.421

.119

.520

.120

.120

.819

.119

.719

.720

.418

.719

.319

.320

.026

19.9

20.6

20.6

21.2

19.6

20.3

20.3

20.9

19.2

19.8

19.8

20.5

18.8

19.4

19.4

20.0

2720

.020

.720

.721

.319

.720

.420

.421

.019

.319

.919

.920

.618

.919

.519

.520

.128

20.2

20.8

20.8

21.4

19.8

20.5

20.5

21.1

19.4

20.0

20.0

20.7

19.0

19.6

19.6

20.2

2920

.320

.920

.921

.620

.020

.620

.621

.219

.520

.120

.120

.819

.019

.719

.720

.330

20.3

20.9

20.9

21.6

20.0

20.6

20.6

21.2

19.5

20.1

20.1

20.8

19.0

19.7

19.7

20.3

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 12

0"


Tables 143


Table 36

518

.819

.519

.520

.318

.719

.519

.520

.318

.619

.419

.420

.218

.519

.319

.320

.16

18.8

19.5

19.5

20.3

18.7

19.5

19.5

20.3

18.6

19.4

19.4

20.2

18.5

19.3

19.3

20.1

718

.819

.519

.520

.318

.719

.519

.520

.318

.619

.419

.420

.218

.519

.319

.320

.18

18.8

19.5

19.5

20.3

18.7

19.5

19.5

20.3

18.6

19.4

19.4

20.2

18.5

19.3

19.3

20.1

918

.819

.619

.620

.318

.719

.519

.520

.318

.619

.419

.420

.218

.519

.319

.320

.110

18.9

19.6

19.6

20.3

18.8

19.5

19.5

20.3

18.6

19.4

19.4

20.2

18.5

19.3

19.3

20.1

1119

.019

.719

.720

.418

.919

.619

.620

.318

.719

.419

.420

.218

.519

.319

.320

.112

19.1

19.8

19.8

20.5

19.0

19.7

19.7

20.4

18.8

19.4

19.4

20.2

18.5

19.3

19.3

20.1

1319

.219

.919

.920

.619

.119

.819

.820

.418

.819

.519

.520

.218

.619

.319

.320

.114

19.3

20.0

20.0

20.7

19.2

19.8

19.8

20.5

18.9

19.6

19.6

20.3

18.7

19.4

19.4

20.1

1519

.520

.120

.120

.819

.319

.919

.920

.619

.019

.719

.720

.418

.719

.419

.420

.116

19.6

20.3

20.3

20.9

19.4

20.0

20.0

20.7

19.1

19.8

19.8

20.4

18.8

19.5

19.5

20.2

1719

.720

.420

.421

.019

.520

.220

.220

.819

.219

.919

.920

.518

.919

.619

.620

.218

19.8

20.5

20.5

21.2

19.6

20.3

20.3

20.9

19.3

20.0

20.0

20.6

19.0

19.6

19.6

20.3

1919

.920

.620

.621

.319

.720

.420

.421

.019

.420

.020

.020

.719

.019

.719

.720

.420

20.1

20.7

20.7

21.4

19.8

20.5

20.5

21.1

19.5

20.1

20.1

20.8

19.1

19.8

19.8

20.5

2120

.220

.820

.821

.519

.920

.620

.621

.319

.620

.220

.220

.919

.219

.919

.920

.522

20.3

21.0

21.0

21.6

20.0

20.7

20.7

21.4

19.7

20.3

20.3

21.0

19.3

20.0

20.0

20.6

2320

.421

.121

.121

.820

.120

.820

.821

.519

.820

.420

.421

.119

.420

.020

.020

.724

20.5

21.2

21.2

21.9

20.2

20.9

20.9

21.6

19.9

20.5

20.5

21.2

19.5

20.1

20.1

20.8

2520

.721

.321

.322

.020

.421

.021

.021

.720

.020

.620

.621

.319

.520

.220

.220

.926

20.8

21.4

21.4

22.1

20.5

21.1

21.1

21.8

20.0

20.7

20.7

21.4

19.6

20.3

20.3

20.9

2720

.921

.621

.622

.220

.621

.221

.221

.920

.120

.820

.821

.519

.720

.420

.421

.028

21.0

21.7

21.7

22.3

20.7

21.4

21.4

22.0

20.2

20.9

20.9

21.6

19.8

20.4

20.4

21.1

2921

.121

.821

.822

.520

.821

.521

.522

.120

.321

.021

.021

.719

.920

.520

.521

.230

21.1

21.8

21.8

22.5

20.8

21.5

21.5

22.1

20.3

21.0

21.0

21.7

19.9

20.5

20.5

21.2

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 12

6"




Table 37

519

.720

.520

.521

.319

.620

.420

.421

.319

.520

.320

.321

.319

.420

.220

.221

.16

19.7

20.5

20.5

21.3

19.6

20.4

20.4

21.3

19.5

20.3

20.3

21.2

19.4

20.2

20.2

21.1

719

.720

.520

.521

.319

.620

.420

.421

.319

.520

.320

.321

.219

.420

.220

.221

.18

19.7

20.5

20.5

21.3

19.6

20.4

20.4

21.3

19.5

20.3

20.3

21.2

19.4

20.2

20.2

21.1

919

.720

.520

.521

.319

.620

.420

.421

.319

.520

.320

.321

.219

.420

.220

.221

.110

19.8

20.5

20.5

21.3

19.7

20.4

20.4

21.3

19.5

20.3

20.3

21.2

19.4

20.2

20.2

21.1

1119

.920

.620

.621

.419

.720

.520

.521

.319

.520

.320

.321

.219

.420

.220

.221

.112

20.0

20.7

20.7

21.4

19.8

20.6

20.6

21.3

19.6

20.3

20.3

21.2

19.4

20.2

20.2

21.1

1320

.120

.820

.821

.519

.920

.620

.621

.419

.720

.420

.421

.219

.520

.220

.221

.114

20.2

20.9

20.9

21.6

20.0

20.7

20.7

21.5

19.8

20.5

20.5

21.2

19.5

20.2

20.2

21.1

1520

.321

.021

.021

.720

.120

.820

.821

.519

.920

.620

.621

.319

.620

.320

.321

.116

20.4

21.1

21.1

21.8

20.2

20.9

20.9

21.6

19.9

20.7

20.7

21.4

19.7

20.4

20.4

21.1

1720

.521

.221

.222

.020

.321

.021

.021

.720

.020

.720

.721

.419

.720

.420

.421

.118

20.7

21.4

21.4

22.1

20.4

21.1

21.1

21.8

20.1

20.8

20.8

21.5

19.8

20.5

20.5

21.2

1920

.821

.521

.522

.220

.521

.221

.221

.920

.220

.920

.921

.619

.920

.620

.621

.320

20.9

21.6

21.6

22.3

20.6

21.3

21.3

22.1

20.3

21.0

21.0

21.7

20.0

20.7

20.7

21.4

2121

.021

.721

.722

.420

.821

.521

.522

.220

.421

.121

.121

.820

.020

.720

.721

.422

21.1

21.8

21.8

22.5

20.9

21.6

21.6

22.3

20.5

21.2

21.2

21.9

20.1

20.8

20.8

21.5

2321

.322

.022

.022

.721

.021

.721

.722

.420

.621

.321

.322

.020

.220

.920

.921

.624

21.4

22.1

22.1

22.8

21.1

21.8

21.8

22.5

20.7

21.4

21.4

22.1

20.3

21.0

21.0

21.7

2521

.522

.222

.222

.921

.221

.921

.922

.620

.821

.521

.522

.220

.421

.121

.121

.826

21.6

22.3

22.3

23.0

21.3

22.0

22.0

22.7

20.9

21.6

21.6

22.3

20.5

21.1

21.1

21.8

2721

.722

.422

.423

.121

.422

.122

.122

.821

.021

.721

.722

.420

.521

.221

.221

.928

21.9

22.6

22.6

23.3

21.5

22.2

22.2

22.9

21.1

21.8

21.8

22.5

20.6

21.3

21.3

22.0

2922

.022

.722

.723

.421

.622

.322

.323

.021

.221

.921

.922

.620

.721

.421

.422

.130

22.0

22.7

22.7

23.4

21.6

22.3

22.3

23.0

21.2

21.9

21.9

22.6

20.7

21.4

21.4

22.1

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 13

2"


Tables 145


Table 38

520

.621

.521

.522

.320

.521

.421

.422

.320

.421

.321

.322

.220

.321

.221

.221

.16

20.6

21.5

21.5

22.3

20.5

21.4

21.4

22.3

20.4

21.3

21.3

22.2

20.3

21.2

21.2

22.1

720

.621

.521

.522

.320

.521

.421

.422

.320

.421

.321

.322

.220

.321

.221

.222

.18

20.6

21.5

21.5

22.3

20.5

21.4

21.4

22.3

20.4

21.3

21.3

22.2

20.3

21.2

21.2

22.1

920

.621

.521

.522

.320

.521

.421

.422

.320

.421

.321

.322

.220

.321

.221

.222

.110

20.7

21.5

21.5

22.3

20.5

21.4

21.4

22.3

20.4

21.3

21.3

22.2

20.3

21.2

21.2

22.1

1120

.721

.521

.522

.320

.621

.421

.422

.320

.421

.321

.322

.220

.321

.221

.222

.112

20.8

21.6

21.6

22.4

20.7

21.4

21.4

22.3

20.5

21.3

21.3

22.2

20.3

21.2

21.2

22.1

1320

.921

.721

.722

.520

.821

.521

.522

.320

.521

.321

.322

.220

.321

.221

.222

.114

21.0

21.8

21.8

22.6

20.9

21.6

21.6

22.4

20.6

21.4

21.4

22.2

20.4

21.2

21.2

22.1

1521

.221

.921

.922

.721

.021

.721

.722

.520

.721

.421

.422

.220

.421

.221

.222

.116

21.3

22.0

22.0

22.8

21.1

21.8

21.8

22.6

20.8

21.5

21.5

22.3

20.5

21.2

21.2

22.1

1721

.422

.122

.122

.921

.221

.921

.922

.720

.921

.621

.622

.420

.621

.321

.322

.118

21.5

22.2

22.2

23.0

21.3

22.0

22.0

22.8

21.0

21.7

21.7

22.4

20.6

21.4

21.4

22.1

1921

.622

.422

.423

.121

.422

.122

.122

.921

.121

.821

.822

.520

.721

.521

.522

.220

21.7

22.5

22.5

23.2

21.5

22.2

22.2

23.0

21.1

21.9

21.9

22.6

20.8

21.5

21.5

22.3

2121

.922

.622

.623

.321

.622

.322

.323

.121

.222

.022

.022

.720

.921

.621

.622

.322

22.0

22.7

22.7

23.4

21.7

22.4

22.4

23.2

21.3

22.1

22.1

22.8

21.0

21.7

21.7

22.4

2322

.122

.822

.823

.621

.822

.622

.623

.321

.422

.222

.222

.921

.021

.821

.822

.524

22.2

23.0

23.0

23.7

21.9

22.7

22.7

23.4

21.5

22.3

22.3

23.0

21.1

21.9

21.9

22.6

2522

.323

.123

.123

.822

.022

.822

.823

.521

.622

.422

.423

.121

.221

.921

.922

.726

22.5

23.2

23.2

23.9

22.1

22.9

22.9

23.6

21.7

22.5

22.5

23.2

21.3

22.0

22.0

22.7

2722

.623

.323

.324

.022

.323

.023

.023

.721

.822

.522

.523

.321

.422

.122

.122

.828

22.7

23.4

23.4

24.2

22.4

23.1

23.1

23.8

21.9

22.6

22.6

23.4

21.5

22.2

22.2

22.9

2922

.823

.623

.624

.322

.523

.223

.223

.922

.022

.722

.723

.521

.522

.322

.323

.030

22.8

23.6

23.6

24.3

22.5

23.2

23.2

23.9

22.0

22.7

22.7

23.5

21.5

22.3

22.3

23.0

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 13

8"




Table 39

521

.522

.422

.423

.421

.422

.422

.423

.321

.422

.322

.323

.221

.322

.222

.223

.16

21.5

22.4

22.4

23.4

21.4

22.4

22.4

23.3

21.4

22.3

22.3

23.2

21.3

22.2

22.2

23.1

721

.522

.422

.423

.421

.422

.422

.423

.321

.422

.322

.323

.221

.322

.222

.223

.18

21.5

22.4

22.4

23.4

21.4

22.4

22.4

23.3

21.4

22.3

22.3

23.2

21.3

22.2

22.2

23.1

921

.522

.422

.423

.421

.422

.422

.423

.321

.422

.322

.323

.221

.322

.222

.223

.110

21.5

22.4

22.4

23.4

21.4

22.4

22.4

23.3

21.4

22.3

22.3

23.2

21.3

22.2

22.2

23.1

1121

.622

.422

.423

.421

.522

.422

.423

.321

.422

.322

.323

.221

.322

.222

.223

.112

21.7

22.5

22.5

23.4

21.5

22.4

22.4

23.3

21.4

22.3

22.3

23.2

21.3

22.2

22.2

23.1

1321

.822

.622

.623

.421

.622

.422

.423

.321

.422

.322

.323

.221

.322

.222

.223

.114

21.9

22.7

22.7

23.5

21.7

22.5

22.5

23.3

21.5

22.3

22.3

23.2

21.3

22.2

22.2

23.1

1522

.022

.822

.823

.621

.822

.622

.623

.421

.522

.322

.323

.221

.322

.222

.223

.116

22.1

22.9

22.9

23.7

21.9

22.7

22.7

23.5

21.6

22.4

22.4

23.2

21.3

22.2

22.2

23.1

1722

.223

.023

.023

.822

.022

.822

.823

.621

.722

.522

.523

.321

.422

.222

.223

.118

22.3

23.1

23.1

23.9

22.1

22.9

22.9

23.7

21.8

22.6

22.6

23.4

21.5

22.3

22.3

23.1

1922

.523

.223

.224

.022

.223

.023

.023

.821

.922

.722

.723

.421

.622

.322

.323

.120

22.6

23.4

23.4

24.1

22.3

23.1

23.1

23.9

22.0

22.8

22.8

23.5

21.6

22.4

22.4

23.2

2122

.723

.523

.524

.222

.423

.223

.224

.022

.122

.922

.923

.621

.722

.522

.523

.322

22.8

23.6

23.6

24.4

22.6

23.3

23.3

24.1

22.2

22.9

22.9

23.7

21.8

22.6

22.6

23.3

2322

.923

.723

.724

.522

.723

.423

.424

.222

.323

.023

.023

.821

.922

.622

.623

.424

23.1

23.8

23.8

24.6

22.8

23.5

23.5

24.3

22.4

23.1

23.1

23.9

22.0

22.7

22.7

23.5

2523

.223

.923

.924

.722

.923

.623

.624

.422

.523

.223

.224

.022

.022

.822

.823

.626

23.3

24.1

24.1

24.8

23.0

23.8

23.8

24.5

22.6

23.3

23.3

24.1

22.1

22.9

22.9

23.6

2723

.424

.224

.225

.023

.123

.923

.924

.622

.723

.423

.424

.222

.223

.023

.023

.728

23.5

24.3

24.3

25.1

23.2

24.0

24.0

24.7

22.8

23.5

23.5

24.3

22.3

23.0

23.0

23.8

2923

.724

.424

.425

.223

.324

.124

.124

.822

.923

.623

.624

.422

.423

.123

.123

.930

23.7

24.4

24.4

25.2

23.3

24.1

24.1

24.8

22.9

23.6

23.6

24.4

22.4

23.1

23.1

23.9

Tran

siti

on

Wid

ths

(FT

)

Ku’

= 0

.165

Ku’

= 0

.150

Ku’

= 0

.130

Ku’

= 0

.110

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Type

1Ty

pe 2

Type

3Ty

pe 4

Pip

e S

ize

= 14

4"


Tables 147


Table 40

Table 41



Table 42

Tables 149


Table 43



Table 44

Tables 151


Table 45



Table 46

Tables 153


Table 47



Table 48

Tables 155


Table 49



Table 50

Tables 157


Table 51



Table 52

Tables 159


Air

craf

t L

oad

s O

n C

ircu

lar

Pip

e U

nd

er R

igid

Pav

emen

t P

ound

s P

er L

inea

r F

oot

Hei

ght o

f Fill

Mea

sure

d Fr

om T

op o

f Pip

e To

Sur

face

of S

ubgr

ade

Hei

ght o

f Fill

H A

bove

Top

of G

rade

Pipe Size – Inside Diameter D In Inches

180,

000

Poun

d Du

al-T

ande

m G

ear A

ssem

bly.

190

pou

nds

per s

quar

e in

ch ti

re p

ress

ure.

26-

inch

c/c

spa

cing

bet

wee

n du

al ti

res.

66-

inch

c/

c sp

acin

g be

twee

n fo

r and

aft

tand

em ti

res.

k-3

00 p

ound

s pe

r cub

ic fo

ot. R

S-37

.44

inch

es. h

-12

inch

es. E

-4,0

00,0

00 p

ound

s pe

r sq

uare

inch

. u-0

.15.

Inte

rpol

ate

for i

nter

med

iate

fill

heig

ths.

12 15 18 21 24 27 30 33 36 42 48 54 60 66 72 78 84 90 96 102

108

114

120

126

138

144

1

2 3

4 5

6 7

8 9

10

1892

17

89

1623

14

53

1266

11

30

998

877

773

686

23

04

2154

19

75

1779

15

42

1377

12

16

1069

94

2 83

5

2714

25

37

2327

20

84

1817

16

22

1433

12

60

1111

98

4

3122

29

18

2677

23

97

2091

18

65

1649

14

51

1279

10

90

35

27

3297

30

25

2709

23

63

2110

18

63

1640

14

47

1280

3932

35

67

3371

29

31

2635

23

52

2076

18

29

1615

14

27

43

33

4049

37

14

3328

29

05

2592

22

88

2016

17

82

1575

4732

44

21

4055

36

36

3175

28

32

2498

22

03

1949

17

22

51

28

4790

43

95

3941

34

42

3069

27

07

2388

21

15

1868

5912

55

20

5065

45

46

3973

35

40

3120

27

55

2446

21

60

66

82

6237

57

25

5142

44

96

4003

35

28

3118

27

74

2449

7437

69

40

6371

57

26

5010

44

59

3930

34

77

3097

27

35

81

74

7628

70

04

6297

55

12

4905

43

25

3831

34

15

3018

8892

82

98

7621

68

55

6002

53

41

4714

41

80

3729

32

97

95

88

8948

82

20

7396

64

80

5767

50

95

4522

40

37

3571

1

0260

95

77

8799

79

21

6943

61

83

5468

48

57

4338

38

40

109

00

1018

0 93

58

8427

73

92

6587

58

31

5184

46

32

4105

1

1520

10

760

9894

89

16

7827

69

80

6186

55

03

4920

43

65

121

00

1131

0 10

410

9385

82

46

7362

65

31

5813

51

99

4620

1

2660

11

840

1090

0 98

37

8615

77

32

6867

61

16

5471

48

70

131

90

1234

0 11

370

1027

0 90

42

8090

71

93

6409

57

35

5112

1

3540

12

680

1169

0 10

560

9312

83

38

7419

66

14

5919

52

79

140

10

1312

0 12

110

1096

0 96

76

8674

77

27

6892

61

70

5507

1

4450

13

540

1251

0 11

340

1002

0 89

98

8024

71

62

6413

57

26

152

30

1430

0 13

240

1203

0 10

680

9607

85

83

7672

68

77

6143

1

5580

14

640

1356

0 12

340

1098

0 98

89

8842

79

10

7095

63

42

Table 53



Air

craf

t L

oad

s H

ori

zon

al E

llip

tica

l Pip

e U

nd

er R

igid

Pav

emen

t P

ound

s P

er L

inea

r F

oot

Hei

ght o

f Fill

Mea

sure

d Fr

om T

op o

f Pip

e To

Sur

face

of S

ubgr

ade

Hei

ght o

f Fill

H A

bove

Top

of G

rade

Pipe Size – Inside Rise x Span R x S In Inches

180,

000

Poun

d Du

al-T

ande

m G

ear A

ssem

bly.

190

pou

nds

per s

quar

e in

ch ti

re p

ress

ure.

26-

inch

c/c

spa

cing

bet

wee

n du

al ti

res.

66-

inch

c/

c sp

acin

g be

twee

n fo

r and

aft

tand

em ti

res.

k-3

00 p

ound

s pe

r cub

ic fo

ot. R

S-37

.44

inch

es. h

-12

inch

es. E

-4,0

00,0

00 p

ound

s pe

r sq

uare

inch

. u-0

.15.

Inte

rpol

ate

for i

nter

med

iate

fill

heig

ths.

14x2

3 19

x30

22x3

424

x38

27x4

229

x45

32x4

934

x53

38x6

043

x68

48x7

653

x83

58x9

163

x98

68x1

0672

x113

77x1

2182

x128

87x1

3692

x143

97x1

5110

6x16

611

6x18

0

1

2 3

4 5

6 7

8 9

10

3354

31

36

2875

25

76

2247

20

06

1771

15

60

1375

12

16

42

76

3996

36

64

3285

28

67

2559

22

58

2989

17

59

1554

4789

44

74

4104

36

79

3213

28

66

2528

22

29

1973

17

42

52

97

4949

45

38

4072

35

57

3172

27

98

2467

21

87

1931

5745

53

65

4922

44

17

3660

34

40

3032

26

77

2376

20

97

62

44

5829

53

49

4803

41

99

3739

32

95

2911

25

87

2284

6737

62

88

5772

51

85

4533

40

36

3557

31

44

2797

24

69

72

23

6741

61

88

5561

48

64

4329

38

16

3375

30

05

2654

8070

75

30

6914

62

17

5441

48

42

4269

37

81

3370

29

78

89

93

8392

77

07

6933

60

71

5403

47

69

4229

37

73

3336

9879

92

21

8471

76

23

6680

59

47

5256

46

67

4167

36

87

106

30

9925

91

21

8212

72

02

6415

56

77

5045

45

07

3992

1

1430

10

680

9819

88

47

7765

69

25

6136

54

58

4879

43

24

121

00

1131

0 10

410

9385

82

46

7362

65

31

5813

51

99

4620

1

2810

11

980

1104

0 99

63

8765

78

36

6962

62

00

5547

49

40

134

00

1254

0 11

560

1045

0 92

05

8240

73

30

6532

58

46

5213

1

4010

13

120

1211

0 10

690

9676

86

74

7727

68

92

6170

55

07

144

80

1357

0 12

540

1136

0 10

040

9021

80

45

7181

64

30

5741

1

4970

14

040

1299

0 11

790

1045

0 93

96

8389

74

95

6715

59

97

153

90

1445

0 13

380

1216

0 10

810

9730

86

96

7875

69

71

6229

1

5810

14

860

1378

0 12

550

1118

0 10

080

9019

80

72

7245

64

81

164

90

1552

0 14

440

1321

0 11

830

1069

0 95

74

8586

77

29

6931

1

7000

16

030

1496

0 13

740

1235

0 11

180

1004

0 10

925

8145

73

23

Table 54

Tables 161


Pipe Size – Inside Rise x Span R x S In InchesA

ircr

aft

Lo

ads

On

Arc

h P

ipe

Un

der

Rig

id P

avem

ent

Pou

nds

Per

Lin

ear

Foo

tH

eigh

t of F

ill M

easu

red

From

Top

of P

ipe

To S

urfa

ce o

f Sub

grad

e

Hei

ght o

f Fill

H A

bove

Top

of G

rade

180,

000

Poun

d Du

al-T

ande

m G

ear A

ssem

bly.

190

pou

nds

per s

quar

e in

ch ti

re p

ress

ure.

26-

inch

c/c

spa

cing

bet

wee

n du

al ti

res.

66-

inch

c/

c sp

acin

g be

twee

n fo

r and

aft

tand

em ti

res.

k-3

00 p

ound

s pe

r cub

ic fo

ot. R

S-37

.44

inch

es. h

-12

inch

es. E

-4,0

00,0

00 p

ound

s pe

r sq

uare

inch

. u-0

.15.

Inte

rpol

ate

for i

nter

med

iate

fill

heig

ths.

11x1

813

-1 / 2x22

15-1 / 2x

2618

x28-

1 / 2 22

-1 / 2x36

-1 / 426

-5 / 8x43

-3 / 431

-5 / 16x5

1-1 / 8

36x5

8-1 / 2

40x6

545

x73

54x8

862

x102

72x1

1577

-1 / 4x12

287

-1 / 8x13

896

-7 / 8x15

410

6-1 / 2x

168-

3 / 4

1

2 3

4 5

6 7

8 9

10

2656

24

83

2277

20

39

1778

15

88

1403

12

34

1087

96

2

3180

29

73

2727

24

42

2130

19

08

1679

14

78

1303

11

53

37

01

3460

31

73

2843

24

81

2214

19

55

1722

15

19

1343

4047

37

82

3469

31

09

2712

24

21

2137

18

82

1663

14

70

50

43

4698

43

22

3876

33

85

3019

26

62

2348

21

04

1836

5954

55

59

5136

46

10

4030

35

90

3164

27

94

2482

21

91

69

14

6452

59

23

5321

46

53

4142

36

50

3228

28

72

2536

7808

72

86

6689

60

14

5262

46

83

4122

36

54

3257

28

78

85

87

8013

73

58

6617

57

94

5155

45

48

4031

35

95

3178

9490

88

57

8135

73

20

6412

57

07

5040

44

74

3993

35

32

110

80

1035

0 95

13

8569

75

18

6701

59

34

5276

47

15

4180

1

2420

11

620

1069

0 96

45

8479

75

75

6724

59

87

5355

47

64

134

70

1261

0 11

620

1051

0 92

58

8289

73

74

6573

58

82

5246

1

4010

13

120

1211

0 10

960

9676

86

74

7727

68

92

6170

55

07

150

80

1415

0 13

090

1188

0 10

540

9481

84

68

7567

67

80

6056

1

5940

14

990

1391

0 12

680

1130

0 10

190

9122

81

67

7334

65

62

164

40

1548

0 14

390

1317

0 11

780

1064

0 95

35

8551

76

95

6899

Table 55



Table 56

Tables 163


Table 57



Table 58

Tables 165


Table 59



Table 60

Tables 167


Table 61



Table 62

Typ

e 1

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

12

34

56

78

910

1112

1314

15

1211

2560

042

537

537

540

040

047

550

055

057

562

567

572

575

0

1510

5057

540

037

537

540

042

545

050

052

557

562

565

070

075

0

1810

0055

040

037

537

540

042

545

050

052

557

560

065

070

075

0

2195

052

537

535

037

540

042

545

047

552

557

560

065

070

075

0

2492

552

537

535

037

540

042

545

047

552

557

562

565

070

075

0

2787

550

037

535

037

540

042

545

050

052

557

562

567

570

075

0

3082

550

037

535

037

540

042

545

050

052

557

562

567

572

577

5

3377

547

537

535

037

540

042

545

050

052

557

562

567

572

577

5

3675

047

535

035

037

540

042

545

050

055

060

062

567

572

577

5

4265

047

535

035

037

540

042

545

050

055

060

065

067

572

577

5

4860

045

035

035

037

540

042

545

050

055

060

065

070

075

080

0

5457

540

035

035

037

540

042

547

550

055

060

065

070

075

080

0

6055

040

035

035

037

540

042

547

550

055

060

065

070

075

080

0

6652

537

532

535

037

540

042

547

552

557

562

565

070

075

080

0

7252

537

532

535

037

540

042

547

552

557

562

567

572

577

582

5

7847

537

532

535

037

542

545

047

552

557

562

567

572

577

582

5

8445

037

532

535

037

542

545

047

552

557

562

567

572

577

582

5

9040

037

532

535

037

542

545

050

052

560

062

567

572

577

582

5

9637

537

532

535

037

542

545

050

055

060

065

070

075

080

085

0

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n

Tables 169


Table 63

Typ

e 1

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

1617

1819

2021

2223

2425

2627

2829

30

1280

085

090

095

010

0010

5011

0011

5012

0012

5013

0013

5014

0014

5015

00

1580

085

090

095

097

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

75

1880

085

090

092

597

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

75

2180

085

090

092

597

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

50

2480

085

090

095

097

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

75

2780

085

090

095

010

0010

2510

7511

2511

7512

2512

7513

2513

7514

2514

75

3080

085

090

095

010

0010

5011

0011

5012

0012

5013

0013

2513

7514

2514

75

3380

085

090

095

010

0010

5011

0011

5012

0012

5013

0013

5014

0014

5015

00

3682

587

592

597

510

2510

5011

0011

5012

0012

5013

0013

5014

0014

5015

00

4282

587

592

597

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

7515

25

4882

587

592

597

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

7515

25

5482

587

592

597

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

7515

25

6085

090

095

010

0010

5011

0011

5012

0012

5013

0013

5014

0014

5015

0015

50

6685

090

095

010

0010

5011

0011

5012

0012

5013

0013

5014

0014

5015

0015

50

7285

092

595

010

0010

5011

0011

5012

0012

5013

0013

7514

2514

7515

2515

75

7887

592

597

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

7515

2515

75

8487

592

597

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

7515

2515

75

9087

592

597

510

2510

7511

2511

7512

2512

7513

2513

7514

2514

7515

2516

00

9687

592

597

510

2510

7511

2511

7512

5013

0013

5014

0014

5015

0015

5016

00

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n



Table 64

Typ

e 1

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

3132

3334

3536

3738

3940

4142

4344

45

12

1550

1600

1650

1700

1725

1775

1825

1875

1925

1975

2025

2075

2125

2175

2225

1515

2515

7516

2516

7517

2517

5018

0018

5019

0019

5020

0020

5021

0021

5022

00

1815

0015

5016

0016

5017

0017

5018

0018

5019

0019

5020

0020

5021

0021

5022

00

2115

0015

5016

0016

5017

0017

5018

0018

5019

0019

5020

0020

5021

0021

5021

75

2415

2515

7516

0016

5017

0017

5018

0018

5019

0019

5020

0020

5021

0021

5022

00

2715

2515

7516

2516

7517

2517

7518

2518

7519

0019

5020

0020

5021

0021

5022

00

3015

2515

7516

2516

7517

2517

7518

2518

7519

2519

7520

2520

7521

2521

7522

25

3315

5016

0016

5017

0017

5018

0018

5019

0019

5019

7520

2520

7521

2521

7522

25

3615

5016

0016

5017

0017

5018

0018

5019

0019

5020

0020

5021

0021

5022

0022

50

4215

7516

2516

7517

0017

5018

0018

5019

0019

5020

0020

5021

0021

5022

0022

50

4815

7516

2516

7517

2517

7518

2518

7519

2519

7520

2520

7521

2521

7522

2522

75

5415

7516

2516

7517

2517

7518

2518

7519

2519

7520

2520

7521

2521

7522

2522

75

6016

0016

5017

0017

5018

0018

5019

0019

5020

0020

5021

0021

5022

0022

5023

00

6616

0016

5017

0017

5018

0018

5019

0019

5020

0020

5021

0021

5022

0022

5023

25

7216

2516

7517

2517

7518

2518

7519

2519

7520

2520

7521

2521

7522

2522

7523

25

7816

2516

7517

2517

7518

2518

7519

2519

7520

2520

7521

2521

7522

2523

0023

50

8416

2516

7517

2517

7518

2519

0019

5020

0020

5021

0021

5022

0022

5023

0023

50

9016

5017

0017

5018

0018

5019

0019

5020

0020

5021

0021

5022

0022

5023

0023

50

9616

5017

0017

5018

0018

5019

0019

5020

0020

5021

0021

7522

2522

7523

2523

75

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n

Tables 171


Table 65

Typ

e 1

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

4647

4849

5051

5253

5455

5657

5859

60

1222

7523

2523

7524

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

2529

75

1522

5023

0023

5024

0024

5025

0025

5026

0026

5027

0027

2527

7528

2528

7529

25

1822

2522

7523

2523

7524

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

25

2122

2522

7523

2523

7524

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

25

2422

5023

0023

5023

7524

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

25

2722

5023

0023

5024

0024

5025

0025

5026

0026

5027

0027

5027

7528

2528

7529

25

3022

7523

2523

7524

2524

5025

0025

5026

0026

5027

0027

5028

0028

5029

0029

50

3322

7523

2523

7524

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

2529

75

3623

0023

5024

0024

5025

0025

5026

0026

5027

0027

5028

0028

5029

0029

5030

00

4223

0023

5024

0024

5025

0025

5026

0026

5027

0027

5028

0028

5029

0029

5030

00

4823

2523

7524

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

2529

7530

25

5423

2523

7524

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

2529

7530

25

6023

5024

0024

5025

0025

5026

0026

5027

0027

5028

0028

5029

0029

5030

0030

50

6623

7524

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

2529

7530

2530

75

7223

7524

2524

7525

2525

7526

2526

7527

5028

0028

5029

0029

5030

0030

5031

00

7824

0024

5025

0025

5026

0026

5027

0027

5028

0028

5029

0029

5030

0030

5031

00

8424

0024

5025

0025

5026

0026

5027

0027

5028

0028

5029

0029

7530

2530

7531

25

9024

0024

5025

2525

7526

2526

7527

2527

7528

2528

7529

2529

7530

2530

7531

25

9624

2524

7525

2525

7526

2526

7527

2527

7528

2528

7529

2529

7530

5031

0031

50

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n



Table 66

Typ

e 2

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

12

34

56

78

910

1112

1314

15

1211

5065

047

547

550

052

557

565

070

075

082

590

095

010

2511

00

1510

7562

547

545

047

552

557

562

570

075

082

587

595

010

2510

75

1810

2560

045

045

047

552

557

562

570

075

082

587

595

010

2510

75

2110

0057

545

045

047

552

557

562

570

075

082

587

595

010

2510

75

2495

057

545

045

047

552

557

565

070

077

582

590

095

010

2511

00

2790

055

045

045

047

552

557

565

070

077

582

590

097

510

2511

00

3085

055

045

045

047

552

557

565

070

077

582

590

097

510

2511

00

3380

055

042

545

047

552

557

565

070

077

585

090

097

510

5011

00

3677

552

542

545

047

552

560

065

072

577

585

090

097

510

5011

25

4267

552

542

545

047

552

560

065

072

577

585

092

597

510

5011

25

4862

550

042

545

047

555

060

065

072

577

585

092

597

510

5011

25

5460

047

542

545

050

055

060

065

072

580

085

092

510

0010

5011

25

6057

545

042

545

050

055

060

067

572

580

085

092

510

0010

7511

25

6657

545

040

045

050

055

060

067

572

580

087

595

010

0010

7511

50

7257

545

040

045

050

055

060

067

575

080

087

595

010

2510

7511

50

7852

545

040

045

050

055

062

567

575

080

087

595

010

2510

7511

50

8447

542

540

045

050

055

062

567

575

082

587

595

010

2510

7511

50

9045

042

540

045

050

055

062

567

575

082

587

595

010

2511

0011

50

9642

542

540

045

050

055

062

567

575

082

587

595

010

2511

0011

75

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n

Tables 173


Table 67

Typ

e 2

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

1617

1819

2021

2223

2425

2627

2829

30

1211

5012

2512

7513

5014

2515

0015

5016

2517

0017

5018

2519

0019

7520

5021

25

1511

5012

0012

7513

2514

0014

7515

5016

2516

7517

5018

2518

7519

5020

2521

00

1811

5012

0012

7513

5014

0014

7515

5016

0016

7517

5018

2518

7519

5020

2521

00

2111

5012

0012

7513

5014

0014

7515

5016

2516

7517

5018

2519

0019

7520

2521

00

2411

5012

2513

0013

5014

2515

0015

5016

2517

0017

7518

5019

0019

7520

5021

25

2711

5012

2513

0013

5014

2515

0015

7516

2517

0017

7518

5019

2519

7520

5021

25

3011

5012

2513

0013

5014

2515

0015

7516

5017

0017

7518

5019

2520

0020

5021

25

3311

5012

2513

0013

7514

2515

0015

7516

5017

2518

0018

5019

2520

0020

7521

50

3611

7512

5013

0013

7514

5015

2516

0016

5017

2518

0018

7519

5020

0020

7521

50

4211

7512

5013

2513

7514

5015

2516

0016

7517

2518

0018

7519

5020

2520

7521

50

4811

7512

5013

2514

0014

5015

2516

0016

7517

2518

0018

7519

5020

2521

0021

50

5411

7512

5013

2514

0014

5015

2516

0016

7517

5018

2518

7519

5020

2521

0021

75

6012

0012

5013

2514

0014

7515

5016

0016

7517

5018

2519

0019

7520

5021

0021

75

6612

0012

7513

5014

0014

7515

5016

2517

0017

7518

2519

0019

7520

5021

2522

00

7212

0012

7513

5014

2515

0015

5016

2517

0017

7518

5019

2520

0020

5021

2522

00

7812

0012

7513

5014

2515

0015

7516

2517

0017

7518

5019

2520

0020

5021

2522

00

8412

2512

7513

5014

2515

0015

7516

2517

0017

7518

5019

2520

0020

7521

2522

00

9012

2512

7513

5014

2515

0015

7516

5017

0017

7518

5019

2520

0020

7521

2522

00

9612

2513

0013

5014

2515

0015

7516

5017

0017

7518

5019

2520

0020

7521

5022

00

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n



Table 68

Typ

e 2

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

3132

3334

3536

3738

3940

4142

4344

45

1221

7522

5023

2524

0024

5025

2526

0026

7527

5028

0028

7529

5030

2531

0031

50

1521

5022

2523

0023

7524

5025

0025

7526

5027

2527

7528

5029

2530

0030

7531

25

1821

5022

2523

0023

7524

5025

0025

7526

5027

2527

7528

5029

2530

0030

5031

25

2121

7522

5023

0023

7524

5025

2526

0026

5027

2528

0028

7529

2530

0030

7531

50

2422

0022

5023

2524

0024

7525

5026

0026

7527

5028

2529

0029

5030

2531

0031

75

2722

0022

7523

2524

0024

7525

50 2

625

2675

2750

2825

2900

2975

3025

3100

3175

3022

0022

7523

5024

0024

7525

5026

2527

0027

5028

2529

0029

7530

5031

2531

75

3322

0022

7523

5024

2525

0025

7526

2527

0027

7528

5029

2529

7530

5031

2532

00

3622

2523

0023

7524

2525

0025

7526

5027

2528

0028

5029

2530

0030

7531

5032

25

4222

2523

0023

7524

5025

0025

7526

5027

2528

0028

5029

2530

0030

7531

5032

25

4822

2523

0023

7524

5025

2525

7526

5027

2528

0028

7529

5030

0030

7531

5032

25

5422

5023

0023

7524

5025

2526

0026

7527

2528

0028

7529

5030

2531

0031

7532

25

6022

5023

2524

0024

7525

2526

0026

7527

5028

2529

0029

7530

2531

0031

7532

50

6622

7523

2524

0024

7525

5026

2527

0027

7528

2529

0029

7530

5031

2532

0032

75

7222

7523

5024

2525

0025

7526

2527

0027

75 2

850

2925

3000

3075

3125

3200

3275

7822

7523

5024

2525

0025

7526

2527

0027

7528

5029

2530

0030

7531

2532

0032

75

8422

7523

5024

2525

0025

7526

2527

0027

7528

5029

2530

0030

7531

2532

0032

75

9022

7523

5024

2525

0025

7526

2527

0027

7528

5029

2530

0030

7531

2532

0032

75

9622

7523

5024

2525

0025

7526

2527

0027

7528

5029

2530

0030

7531

2532

0032

75

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n

Tables 175


Table 69

Typ

e 3

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

12

34

56

78

910

1112

1314

1516

1718

1211

7570

055

055

060

065

072

580

087

595

010

5011

2512

0013

0013

7514

7515

5016

50

1511

0067

552

555

057

565

070

077

587

595

010

2511

0012

0012

7513

7514

5015

2516

00

1810

5065

052

552

557

565

070

077

585

095

010

2511

0012

0012

7513

5014

2515

2516

00

2110

0062

550

052

557

565

070

077

585

095

010

2511

0012

0012

7513

5014

2515

2516

00

2497

560

050

052

557

565

070

077

585

095

010

2511

0012

0012

7513

5014

5015

2516

00

2792

560

050

052

557

565

070

080

087

595

010

2511

2512

0012

7513

7514

5015

2516

00

3087

560

050

052

557

565

072

580

087

595

010

5011

2512

0013

0013

7514

5015

2516

25

3382

557

550

052

557

565

072

580

087

595

010

5011

2512

2513

0013

7514

5015

5016

25

3680

057

550

052

557

565

072

580

087

597

510

5011

5012

2513

0014

0014

7515

5016

50

4270

057

550

052

560

065

072

580

090

097

510

5011

5012

2513

2514

0014

7515

7516

50

4865

055

050

052

560

065

072

582

590

097

510

7511

5012

5013

2514

2514

7515

7516

50

5462

552

550

052

560

067

575

082

590

010

0010

7511

5012

5013

5014

2515

0015

7516

75

6062

550

050

052

560

067

575

082

592

510

0010

7511

7512

5013

5014

2515

0016

0017

00

6660

050

047

555

060

067

575

085

092

510

0011

0011

7512

7513

5014

5015

2516

0017

00

7260

050

047

555

060

067

577

585

092

510

2511

0012

0012

7513

7514

5015

2516

2517

25

7855

050

047

555

060

067

577

585

092

510

2511

0012

0013

0013

7514

7515

5016

2517

25

8452

550

047

555

062

570

077

585

095

010

2511

0012

0013

0013

7514

7515

5016

2517

25

9047

550

047

555

062

570

077

585

095

010

2511

2512

0013

0013

7514

7515

5016

2517

25

9645

047

547

555

062

570

077

585

095

010

2511

2512

0013

0013

7514

7515

5016

5017

25

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n



Table 70

Typ

e 3

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

1920

2122

2324

2526

2728

2930

3132

3334

35

1217

2518

2519

0020

0020

7521

7522

5023

5024

2525

2526

0027

0028

0028

7529

7530

5031

50

1517

0017

7518

7519

5020

5021

2522

2523

0024

0024

7525

7526

7527

5028

5029

2530

2531

00

1816

7517

7518

5019

5020

2521

2522

0023

0023

7524

7525

5026

5027

2528

2529

0030

0030

75

2116

7517

7518

5019

5020

2521

2522

0023

0023

7524

7525

5026

5027

5028

2529

0030

0030

75

2417

0017

7518

7519

5020

2521

2522

0023

0023

7524

7525

5026

5027

2528

2529

0030

0030

75

2717

0017

7518

7519

5020

5021

2522

2523

0024

0024

7525

7526

5027

5028

2529

2530

0031

00

3017

0018

0018

7519

7520

5021

5022

2523

2524

0025

0025

7526

7527

5028

5029

5030

2531

25

3317

2518

0019

0019

7520

7521

5022

5023

5024

2525

2526

0027

0027

7528

7529

5030

5031

25

3617

5018

2519

2520

0021

0021

7522

7523

5024

5025

2526

2527

2528

0029

0029

7530

7531

50

4217

5018

2519

2520

0021

0021

7522

7523

7524

5025

5026

2527

2528

0029

0030

0030

7531

75

4817

5018

5019

2520

2521

0022

0022

7523

7524

7525

5026

5027

2528

2529

0030

0031

0031

75

5417

5018

5019

5020

2521

2522

0023

0024

0024

7525

7526

5027

5028

5029

2530

2531

0032

00

6017

7518

7519

5020

5021

2522

2523

2524

0025

0025

7526

7527

7528

5029

5030

2531

2532

25

6618

0018

7519

7520

5021

5022

5023

2524

2525

2526

0027

0027

7528

7529

7530

5031

5032

50

7218

0019

0020

0020

7521

7522

5023

5024

5025

2526

2527

2528

0029

0030

0030

7531

7532

50

7818

0019

0020

0020

7521

7522

5023

5024

5025

2526

2527

2528

0029

0030

0030

7531

7532

50

8418

0019

0020

0020

7521

7522

7523

5024

5025

2526

2527

2528

0029

0030

0030

7531

7532

75

9018

2519

0020

0020

7521

7522

7523

5024

5025

5026

2527

2528

0029

0030

0030

7531

7532

75

9618

2519

0020

0021

0021

7522

7523

5024

5025

5026

2527

2528

0029

0030

0030

7531

7532

75

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n

Tables 177


Table 71

Typ

e 4

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

12

34

56

78

910

1112

1314

15

1215

5095

075

080

087

595

010

7512

0013

2514

5015

7517

0018

2519

5021

00

1514

5090

075

077

585

095

010

5011

5012

7514

0015

2516

5017

7519

0020

50

1813

7585

072

575

082

592

510

5011

5012

5013

7515

0016

2517

5019

0020

25

2113

2585

070

075

082

592

510

2511

2512

5013

7515

0016

0017

5018

7520

00

2412

7582

570

072

580

090

010

0011

2512

5013

5014

7516

0017

2518

5019

75

2711

5080

070

072

580

090

010

0011

2512

2513

5014

7516

0017

2518

5019

75

3010

2580

067

572

580

090

010

0011

0012

2513

5014

7516

0017

0018

5019

50

3392

577

567

572

580

090

010

0011

0012

2513

5014

7516

0017

0018

2519

50

3685

075

067

572

580

090

010

0011

0012

2513

5014

5015

7517

0018

2519

50

4275

075

065

072

580

090

010

0011

0012

2513

5014

5015

7517

0018

2519

50

4870

067

565

072

580

090

010

0011

0012

2513

5014

5015

7517

0018

2519

50

5467

562

565

072

580

090

010

0011

0012

2513

5014

5015

7517

0018

2519

50

6067

560

065

070

080

090

010

0011

0012

2513

5014

5015

7517

0018

2519

50

6665

057

562

570

080

090

010

0011

2512

2513

5014

7516

0017

0018

2519

50

7265

057

560

070

080

090

010

0011

2512

2513

5014

7516

0017

0018

2519

50

7862

557

560

070

080

090

010

0011

2512

5013

5014

7516

0017

0018

2519

50

8457

557

560

070

080

090

010

2511

2512

5013

5014

7516

0017

2518

5019

50

9055

057

560

070

080

090

010

2511

2512

5013

7514

7516

0017

2518

5019

50

9652

557

560

070

080

092

510

2511

5012

5013

7515

0016

0017

2518

5019

75

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n



Table 72

Typ

e 4

Bed

din

g

Fill

Hei

gh

t (f

eet)

Pip

e i.d

.(i

nch

es)

1617

1819

2021

2223

1222

2523

5025

0026

2527

7527

0030

2531

75

1521

7523

0024

5025

5027

0028

2529

5031

00

1821

2522

7524

0025

2526

5027

7529

0030

50

2121

2522

5023

7525

0026

2527

5028

7530

00

2421

0022

2523

5024

7526

0027

2528

5029

75

2720

7522

0023

2524

5025

7527

0028

2529

50

3020

7522

0023

2524

5025

7527

0028

2529

50

3320

7522

0023

2524

5025

7527

0028

2529

50

3620

7522

0023

2524

5025

5026

7528

0029

25

4220

5021

7523

0024

2525

5026

7528

0029

25

4820

5021

7523

0024

2525

5026

7528

0029

25

5420

5021

7523

0024

2525

5026

7528

0029

25

6020

5021

7523

0024

2525

5026

5027

7529

00

6620

5021

7523

0024

2525

5026

7527

7529

00

7220

5021

7523

0024

2525

5026

7528

0029

00

7820

7521

7523

0024

2525

5026

7528

0029

00

8420

7522

0023

0024

2525

5026

7528

0029

25

9020

7522

0023

2524

2525

5026

7528

0029

25

9620

7522

0023

2524

5025

5026

7528

0029

25

Cla

ss I

Cla

ss IV

Cla

ss II

Cla

ss V

Cla

ss II

IS

peci

al D

esig

n

Fill

Hei

gh

t Ta

ble

s ar

e b

ased

on

:1.

A s

oil w

eigh

t of 1

20 lb

s/ft3

2.A

AS

HT

O H

S20

live

load

3.E

mba

nkm

ent i

nsta

llatio

n

Figures

179



Figure 1

Figures 181


Figure 2



Figure 3

Figures 183


Figure 4



Figure 5

Figures 185


Figure 6



Figure 7

Figures 187


Figure 8



Figure 9

Figures 189


Figure 10



Figure 11

Figures 191


Figure 12



Figure 13

Figures 193


Figure 14



Figure 15

Figures 195


Figure 16



Figure 17

Figures 197


Figure 18.1



Figure 18.2

Figures 199


Figure 19.1



Figure 19.2

Figures 201


Figure 20



Figure 21

Figures 203


Figure 22



Figure 23

Figures 205


Figure 24.1



Figure 24.2

Figures 207


Figure 24.3



Figure 24.4

Figures 209


Figure 24.5



Figure 24.6

Figures 211


Figure 24.7



Figure 24.8

Figures 213


Figure 24.9



Figure 25

Figure 26

Figures 215


Figure 27



Figure 28

Figures 217


Figure 29



Figure 30

Figures 219


Figure 31.1



Figure 31.2

Figures 221


Figure 32



Figure 33

Figures 223


Figure 34



Figure 35

Figures 225


Figure 36



Figure 37

Figures 227


Figure 38



Figure 39

Figures 229


Figure 40



Figure 41

Figures 231


Figure 42



Figure 43

Figures 233


Figure 44



Figure 45

Figures 235


Figure 46



Figure 47

Figures 237


Figure 48



Figure 49

Figures 239


Figure 50



Figure 51

Figures 241


Figure 52



Figure 53

Figures 243


Figure 54



Figure 55

Figures 245


Figure 56



Figure 57

Figures 247


Figure 58



Figure 59

Figures 249


Figure 60



Figure 61

Figures 251


Figure 62



Figure 63

Figures 253


Figure 64



Figure 65

Figures 255


Figure 66



Figure 67

Figures 257


Figure 68



Figure 69

Figures 259


Figure 70



Figure 71

Figures 261


Figure 72



Figure 73

Figures 263


Figure 74



Figure 75

Figures 265


Figure 76



Figure 77

Figures 267


Figure 78



Figure 79

Figures 269


Figure 80



Figure 81

Figures 271


Figure 82



Figure 83

Figures 273


Figure 84



Figure 85

Figures 275


Figure 86



Figure 87

Figures 277


Figure 88



Figure 89

Figures 279


Figure 90



Figure 91

Figures 281


Figure 92



Figure 93

Figures 283


Figure 94



Figure 95

Figures 285


Figure 96



Figure 97

Figures 287


Figure 98



Figure 99

Figures 289


Figure 100



Figure 101

Figures 291


Figure 102



Figure 103

Figures 293


Figure 104



Figure 105

Figures 295


Figure 106



Figure 107

Figures 297


Figure 108



Figure 109

Figures 299


Figure 110



Figure 111

Figures 301


Figure 112



Figure 113

Figures 303


Figure 114



Figure 115

Figures 305


Figure 116



Figure 117

Figures 307


Figure 118



Figure 119

Figures 309


Figure 120



Figure 121

Figures 311


Figure 122



Figure 123

Figures 313


Figure 124



Figure 125

Figures 315


Figure 126



Figure 127

Figures 317


Figure 128



Figure 129

Figures 319


Figure 130



Figure 131

Figures 321


Figure 132



Figure 133

Figures 323


Figure 134



Figure 135

Figures 325


Figure 136



Figure 137

Figures 327


Figure 138



Figure 139

Figures 329


Figure 140



Figure 141

Figures 331


Figure 142



Figure 143

Figures 333


Figure 144



Figure 145

Figures 335


Figure 146



Figure 147

Figures 337


Figure 148



Figure 149

Figures 339


Figure 150



Figure 151

Figures 341


Figure 152



Figure 153

Figures 343


Figure 154



Figure 155

Figures 345


Figure 156



Figure 157

Figures 347


Figure 158



Figure 159

Figures 349


Figure 160



Figure 161

Figures 351


Figure 162



Figure 163

Figures 353


Figure 164



Figure 165

Figures 355


Figure 166



Figure 167

Figures 357


Figure 168



Figure 169

Figures 359


Figure 170



Figure 171

Figures 361


Figure 172



Figure 173

Figures 363


Figure 174



Figure 175

Figures 365


Figure 176



Figure 177

Figures 367


Figure 178



Figure 179

Figures 369


Figure 180



Figure 181

Figures 371


Figure 182



Figure 183

Figures 373


Figure 184



Figure 185

Figures 375


Figure 186



Figure 187

Figures 377


Figure 188



Figure 189

Figures 379


Figure 190



Figure 191

Figures 381


Figure 192



Figure 193

Figures 383


Figure 194



Figure 195

Figures 385


Figure 196



Figure 197

Figures 387


Figure 198



Figure 199

Figures 389


Figure 200



Figure 201

Figures 391


Figure 202



Figure 203

Figures 393


Figure 204



Figure 205

Figures 395


Figure 206



Figure 207

Figures 397


Figure 208



Figure 209

Figures 399


Figure 210



Figure 211

Figures 401


Figure 212



Figure 213

Figures 403


Figure 214



0 2 4 6 8 10 12 14

3000

2500

2000

1500

1000

500

0

UnfactoredLive Load Including Impact

Unit E

arth

Loa

d*

1.40

x w

H

Uni

t Loa

d O

n To

p of

Pip

e, P

ound

s P

er S

quar

e F

oot (

WL

& W

D)

Height of Cover, H, Above Top of Pipe, Feet

Figure 215 Loads on Concrete Pipe Installed Under Railways

“Part 10 Reinforced Concrete Culvert Pipe, Chapter 8, Concrete Structures and Foundations, AREMA Manual of RailwayEngineering”, American Railway Engineering and Maintenance-of-Way Association, 1999.

* Fill for embankment installations DL/Bc = 1.40wH with

w = 120pcf 1.40 = Vertical Arching Factor

Appendix A

405



Table A-1

Appendix A 407


Table A-2



Table A-3

Appendix A 409


Table A-4



Table A-5

Appendix A 411


Table A-6



Table A-7

Appendix A 413


Table A-8



Table A-9

Appendix A 415


Table A-10



Table A-11

Appendix A 417


Table A-12



Table A-13

Appendix A 419


Table A-14a



Table A-14b

Appendix A 421


Table A-14c



Table A-14d

Appendix A 423


Table A-14e



Table A-14f

Appendix A 425


Table A-15



Table A-16

Appendix A 427


Table A-17a



Table A-17b

Appendix A 429


Table A-17c



Table A-17d

431

APPENDIX B

LOADS AND SUPPORTINGSTRENGTHS

Based on Marston/Spangler Design Procedure

The design procedure for the selection of pipe strength requires:

I . Determination of Earth Load2. Determination of Live Load3. Selection of Bedding4. Determination of Bedding Factor5. Application of Factor of Safety6. Selection of Pipe Strength

TYPES OF INSTALLATIONS

The earth load transmitted to a pipe is largely dependent on the type ofinstallation, and the three common types are Trench, Positive ProjectingEmbankment, and Negative Projecting Embankment. Pipe are also installed byjacking or tunneling methods where deep installations are necessary or whereconventional open excavation and backfill methods may not be feasible. Theessential features of each of these installations are shown in Figure 146.

Trench. This type of installation is normally used in the construction ofsewers, drains and water mains. The pipe is installed in a relatively narrow trenchexcavated in undisturbed soil and then covered with backfill extending to theground surface.

Wd = CdwBd B12

Cd is further defined as:

Cd = B22Kµ'

1 – e – 2Kµ'HBd

Note: In 1996 AASHTO adopted the Standard Installations as presented in Chapter 4 of this manual, and eliminatedthe use of the Marston/Spangler beddings and design procedure for circular concrete pipe. The Standard Installations andthe design criteria in Chapter 4 are the preferred method of ACPA. The older and less quantitative Marston/Spanglerbeddings and the design method associated with them are presented in this Appendix for those agencies and individualsstill using this method.



Tables B1 through B30 are based on equation (B1) and list backfill loads inpounds per linear foot for various heights of backfill and trench widths. There arefour tables for each circular pipe size based on Kµ' = 0.165, 0.150, 0.130 and0.110. The “Transition Width” column gives the trench width at which the backfillload on the pipe is a maximum and remains constant regardless of any increasein the width of the trench. For any given height of backfill, the maximum load atthe transition width is shown by bold type.

Figures B1 through B8 also present backfill loads for circular pipe installed ina trench condition. For elliptical and arch pipe, Figures 155 through 178 in themain body of the manual may be used. The solid lines represent trench widthsand the dashed lines represent pipe size for the evaluation of transition widthsand maximum backfill loads. If, when entering the figures from the horizontal axis,the dashed line representing pipe size is interesected before the solid linerepresenting trench width, the actual trench width is wider than the transition widthand the maximum backfill load should be read at the intersection of the height ofbackfill and the dashed line representing pipe size.

Positive Projecting Embankment. This type of installation is normally usedwhen the culvert is installed in a relatively flat stream bed or drainage path. Thepipe is installed on the original ground or compacted fill and then covered by anearth fill or embankment. The fill load on a pipe installed in a positive projectingembankment condition is computed by the equation:

Wc = CcwBc B32

C, is further defined as:

Cc = when H ≤ He B4

Cc = + – e when H > He B5

and

2Kµ

2Kµ' Bc

H

Bc

He

e – 12Kµ HBc

e – 12KµHe

Bc 2KµHe

Bc

The settlements which influence loads on positive projecting embankmentinstallations are shown in Illustration B1. To evaluate the He term in equation (B5),it is necessary to determine numerically the relationship between the pipedeflection and the relative settlement between the prism of fill directly above thepipe and the adjacent soil. This relationship is defined as a settlement ratio,expressed as:

rsd = B6Sm

(Sm + Sg) - (Sf +dc)

1. Pipe widths are based on a wall thickness equivalent to thicknesses indicated for Wall B in ASTM C 76 and designatedthicknesses in other applicable ASTM Standards. Loads corresponding to these wall thicknesses are sufficientlyaccurate for the normal range of pipe widths for any particular pipe size. For extra heavy wall thicknesses, resulting in apipe width considerably in excess of the normal range, interpolation within the Tables and Figures may be necessary.

Marston/Spangler Design Procedure 433


The fill load on a pipe installed in a positive projecting embankment conditionis influenced by the product of the settlement ratio (rsd) and the projection ratio (p).The projection ratio (p) is the vertical distance the pipe projects above the originalground divided by the outside vertical height of the pipe (B'c). Recommendedsettlement ratio design values are listed in Table B-31.

Figures B-9 through B-13 include fill loads in pounds per linear foot forcircular pipe under various fill heights and pipe sizes based on rsdp values of 0,0.1, 0.3, 0.5 and 1.0. For elliptical pipe, Figures 179 through 193 in the main bodyof the manual may be used. The dashed H = He line represents the conditionwhere the height of the plane of equal settlement (He) is equal to the height of fill(H).

Negative Projecting Embankment. This type of installation is normally usedwhen the culvert is installed in a relatively narrow and deep stream bed ordrainage path. The pipe is installed in a shallow trench of such depth that the topof the pipe is below the natural ground surface or compacted fill and then coveredwith an earth fill or embankment which extends above the original ground level.The fill load on a pipe installed in a negative projecting embankment condition iscomputed by the equation:

Illustration B.1 Settlements Which Influence LoadsPositive Projecting Embankment Installation

TOP OF EMBANKMENT

Bc


He

H

H - He

pB'cB'c

Sf + dc

Sg

Sm + Sg

Sf

Critical Plane

Ground Surface





Wn = CnwBd B72

Cn is further defined as:

Cn = when H ≤ He B8

Cn = + – e when H > He B9

and

( )– 2Kµ

– 2Kµ' Bd

H

Bd

He

e – 1 – 2Kµ HBd

e – 1– 2KµHe

Bd – 2KµHe

Bd

When the material within the subtrench is densely compacted, equation (B7)can be expressed as Wn = CnwBdB'd where B'd is the average of the trench widthand the outside diameter of the pipe.

The settlements which influence loads on negative projecting embankmentinstallations are shown in Illustration B2. As in the case of the positive projectingembankment installation, it is necessary to define the settlement ratio. Equating

Illustration B.2 Settlements Which Influence LoadsNegative Projecting Embankment Installation

TOP OF EMBANKMENT

Bc

Bd


H'

H =

H' +

p'B

d

H'e

p'Bd

Sf + dc

SgSd + Sf + dc

Sf

Ground Surface





the deflection of the pipe and the total settlement of the prism of fill above the pipeto the settlement of the adjacent soil:

rsd = B10Sd

Sg – (Sd+ Sf + dc)

Recommended settlement ratio design values are listed in Table B-31. Theprojection ratio (p') for this type of installation is the distance from the top of thepipe to the surface of the natural ground or compacted fill at the time of installationdivided by the width of the trench. Where the ground surface is sloping, theaverage vertical distance from the top of the pipe to the original ground should beused in determining the projection ratio (p'). Figures 194 through 213 present fillloads in pounds per linear foot for circular pipe based on projection ratios of 0.5,1.0, 1.5, 2.0 and settlement ratios of 0, -0.1, -0.3, -0.5 and -1.0. The dashed H =p'Bd line represents the limiting condition where the height of fill is at the sameelevation as the natural ground surface. The dashed H = He, line represents thecondition where the height of the plane of equal settlement (He) is equal to theheight of fill (H).

SELECTION OF BEDDING

A bedding is provided to distribute the vertical reaction around the lowerexterior surface of the pipe and reduce stress concentrations within the pipe wall.The load that a concrete pipe will support depends on the width of the beddingcontact area and the quality of the contact between the pipe and bedding. Animportant consideration in selecting a material for bedding is to be sure thatpositive contact can be obtained between the bed and the pipe. Since mostgranular materials will shift to attain positive contact as the pipe settles an idealload distribution can be attained through the use of clean coarse sand, well-rounded pea gravel or well-graded crushed rock.

Trench Beddings. Four general classes of bedding for the installation ofcircular pipe in a trench condition are illustrated in Figure B-14. Trench bedding forhorizontal elliptical, arch and vertical elliptical pipe are shown in Figure B-15.

Embankment Beddings. Four general classes of bedding for the installationof circular pipe in an embankment condition are shown in Figure B-16.Embankment beddings for horizontal elliptical, arch and vertical elliptical pipe areshown in Figure B-17. Class A through D bedding classifications are presented asa guideline which should be reasonably attainable under field conditions. Toassure that the in-place supporting strength of the pipe is adequate, the width ofthe band of contact between the pipe and the bedding material should be inaccordance with the specified class of bedding. With the development ofmechanical methods for subgrade preparation, pipe installation, backfilling andcompaction, the flat bottom trench with granular foundation is generally the morepractical method of bedding. If the pipe is installed in a flat bottom trench, it is



essential that the bedding material be uniformly compacted under the haunches ofthe pipe.

DETERMINATION OF BEDDING FACTOR

Under installed conditions the vertical load on a pipe is distributed over itswidth and the reaction is distributed in accordance with the type of bedding. Whenthe pipe strength used in design has been determined by plant testing, beddingfactors must be developed to relate the in-place supporting strength to the moresevere plant test strength. The bedding factor is the ratio of the strength of thepipe under the installed condition of loading and bedding to the strength of thepipe in the plant test. This same ratio was defined originally by Spangler as theload factor. This latter term, however, was subsequently defined in the ultimatestrength method of reinforced concrete design with an entirely different meaning.To avoid confusion, therefore, Spangler’s term was renamed the bedding factor.The three-edge bearing test as shown in Illustration B.3 is the normally acceptedplant test so that all bedding factors described below relate the in-placesupporting strength to the three-edge bearing strength.

The bedding factor for a particular pipeline, and consequently the supportingstrength of the buried pipe, depends upon two characteristics of the installation:

• Width and quality of contact between the bedding and the pipe• Magnitude of the lateral pressure and the portion of the vertical area of the

pipe over which it is effective

Since the sidefill material can be more readily compacted for pipe installed ina positive projection embankment condition, the effect of lateral pressure isconsidered in evaluating the bedding factor. For trench installations, the effect of

Illustration B.3 Three-Edge Bearing Test

Rigid Steel

Member

BearingStrips



lateral pressure was neglected in development of bedding factors. Instead of ageneral theory as for the embankment condition, Spangler, from analysis of testinstallations, established conservative fixed bedding factors for each of thestandard classes of bedding used for trench installations.

Trench Bedding Factors. Conservative fixed bedding factors for pipeinstalled in a narrow trench condition are listed below the particular classes ofbeddings shown in Figures B-14 and B-15.

Both Spangler and Schlick, in early Iowa Engineering Experiment Stationspublications, postulate that some active lateral pressure is developed in trenchinstallations before the transition width is reached. Experience indicates that theactive lateral pressure increases as the trench width increases from a very narrowwidth to the transition width, provided the sidefill is compacted. Defining thenarrow trench width as a trench having a width at the top of the pipe equal to orless than the outside horizontal span plus one foot, and assuming a conservativelinear variation, the variable trench bedding factor can be determined by:

Bfv = ( Bfe – Bft) + Bft B11Bd – (Bc+ 1.0)Bdt – (Bc+ 1.0)

Where:Bc = outside horizontal span of pipe, feetBd = trench width at top of pipe, feetBdt = transition width at top of pipe, feetBfe = bedding factor, embankmentBft = fixed bedding factor, trenchBfv = variable bedding factor, trench

A six-step design procedure for determining the trench variable beddingfactor is:

• Determine the trench fixed bedding factor, Bft

• Determine the trench width, Bd

• Determine the transition width for the installation conditions, Bdt

• Determine H/Bc ratio, settlement ratio, rsd, projection ratio, p, and theproduct of the settlement and projection ratios, rsdp

• Determine positive projecting embankment bedding factor, Bfe

• Calculate the trench variable bedding factor, Bfv

Positive Projecting Embankment Bedding Factors. For pipe installed in apositive projecting embankment condition, active lateral pressure is exertedagainst the sides of the pipe. Bedding factors for this type of installation arecomputed by the equation:

Bf = B12N – xq

A



For circular pipe q is further defined as:

q = + ≤ 0.33 B132

pK HCc Bc

p

For elliptical and arch pipe q is further defined as:

q = H + ≤ 0.33 B1422

pB'cK pB'c

CcBc

The value of q, as determined by equations B13 and B 14, shall not exceed0.33.

Tables B32 and B33 list bedding factors for circular pipe. For elliptical andarch pipe bedding factors may be found in Tables 59 through 61 in the main bodyof the manual.

Negative Projecting Embankment Bedding Factors. The methodsdescribed for determining trench bedding factors should be used for negativeprojecting embankment installations.

APPLICATION OF FACTOR OF SAFETY

The total earth and live load on a buried concrete pipe is computed andmultiplied by a factor of safety to determine the pipe supporting strength required.The safety factor is defined as the relationship between the ultimate strength D-load and the 0.01-inch crack D-load. This relationship is specified in the ASTMstandards on reinforced concrete pipe. Therefore, for reinforced concrete pipe afactor of safety of 1.0 should be applied if the 0.01-inch crack strength is used asthe design criterion. For nonreinforced concrete pipe a factor of safety of 1.25 to1.5 is normally used.

SELECTION OF PIPE STRENGTH

Since numerous reinforced concrete pipe sizes are available, three-edgebearing test strengths are classified by D-loads. The D-load concept providesstrength classification of pipe independent of pipe diameter. For reinforced circularpipe the three-edge bearing test load in pounds per linear foot equals D-load Xinside diameter in feet. For arch, horizontal elliptical and vertical elliptical pipe thethree-edge bearing test load in pounds per linear foot equals D-load X nominalinside span in feet.

The required three-edge bearing strength of non-reinforced concrete pipe isexpressed in pounds per linear foot, not as a D-load, and is computed by theequation:

T.E.B. = X F.S. B15Bf

WL + WE



The required three-edge bearing strength of circular reinforced concrete pipeis expressed as D-load and is computed by the equation:

D-load = x F.S. B16Bf x D

WL + WE

The determination of required strength of elliptical and arch concrete pipe iscomputed by the equation:

D-load = x F.S. B17Bf x S

WL + WE

EXAMPLE PROBLEMS

EXAMPLE B-1Trench Installation

Given: A 48 inch circular pipe is to be installed in a 7 foot wide trenchwith 35 feet of cover over the top of the pipe. The pipe will bebackfilled with sand and gravel weighing 110 pounds per cubicfoot.


Bc

Bc

H



Solution: 1. Determination of Earth Load (WE)From Table B-14A, Sand and Gravel, the backfill load based on100 pounds per cubic foot backfill is 12,000 pounds per linear foot.Increase the load 10 percent for 110 pound backfill material.

Wd = 1.10 X 12,000Wd = 13,200 pounds per linear foot


3. Selection of BeddingA Class B bedding will be assumed for this example. In actualdesign, it may be desirable to consider other types of bedding inorder to arrive at the most economical overall installation.

4. Determination of Bedding Factor (Bf)The trench variable bedding factor, Bfv is given by Equation B11:

Bfv = (Bfe – Bft) + BftBd – (Bc+ 1.0)Bdt – (Bc+ 1.0)

Step 1. From Figure B-14, for circular pipe installed on a Class Bbedding, the trench fixed bedding factor, Bft, is 1.9.

Step 2. A trench width, Bd, of 7 feet is specified.

Step 3. The transition width, Bdt, determined from Table B-14A is 11.4feet.

Step 4. H/Bc = 35/4.8 = 7.3From Table B-31, the rsd design range of values for ordinarysoil is +0.5 to +0.8. Assume an rsd value of +0.5. For agranular Class B bedding p = 0.5, then rsdp = 0.5 x 0.5 = 0.25.

Step 5. From Table B-32 for H/Bc = 7.3, p = 0. 5, rsdp = 0.25 and aClass B bedding, Bfe = 2.19.

Step 6. The trench variable bedding factor is:

Bfv = (2.19 – 1.9) + 1.9

Bfv = 1.96

7 – (4.8 + 1.0)11.4 – (4.8 + 1.0)



Use a variable bedding factor, Bfv of 1.96 to determine the requiredD-load pipe strength.

5. Application of Factor of Safety (F.S.)A factor of safety of 1.0 based on the 0.01-inch crack will beapplied.

6. Selection of Pipe StrengthThe D-load is given by Equation B16:

WL + WE = Wd = 13,200 pounds per linear foot

D0.01 = 1684 pounds per linear foot per foot of inside diameter

D0.01 = x F.S.WL + WE

Bf x D

D0.01 = x 1.013,200

1.96 x 4.0


EXAMPLE B-2Positive Projecting Embankment Installation

Given: A 48 inch circular pipe is to be installed in a positive projectingembankment condition in ordinary soil. The pipe will be covered with35 feet of 110 pounds per cubic foot overfill.

pBC

Bc

H




Solution: 1. Determination of Earth Load (WE)A settlement ratio must first be assumed. In Table B-31 values ofsettlement ratio from +0.5 to +0.8 are given for positive projectinginstallations on a foundation of ordinary soil. A conservative valueof 0.7 will be used with an assumed projection ratio of 0.7. Theproduct of the settlement ratio and the projection ratio will be 0.49(rsdp = 0.5).

Enter Figure B-12 on the horizontal scale at H = 35 feet. Proceedvertically until the line representing D = 48 inches is intersected. Atthis point the vertical scale shows the fill load to be 25,300 poundsper linear foot for 100 pounds per cubic foot fill material. Increasethe load 10 percent for 110 pound material.

Wc = 1.10 X 25,300Wc = 27,830 pounds per linear foot



4. Determination of Bedding Factor (Bf)The outside diameter for a 48 inch diameter pipe is 58 inches =4.83 feet. From Table B-32, from an H/Bc ratio of 7.25, rsdp value of0.5, p value of 0.7 and Class B bedding, a bedding factor of 2.34 isobtained.

5. Application of Factor of Safety (F.S.)A factor of safety of 1.0 based on the 0.01 inch crack will beapplied.

6. Selection of Pipe StrengthThe D-load is given by equation B16:



WL + WE = Wc = 27,800 pounds per linear foot


D0.01 = x F.S.WL + WE

Bf x D

D0.01 = x 1.027,800

2.34 x 4.0


EXAMPLE B-3Negative Projecting Embankment Installation

Given: A 48 inch circular pipe is to be installed in a negative projectingembankment condition in ordinary soil. The pipe will be covered with35 feet of 110 pounds per cubic foot overfill. A 7 foot trench width willbe constructed with a 7 foot depth from the top of the pipe to thenatural ground surface.


Bc

Bd

H



Solution: 1. Determination of Earth Load (WE)A settlement ratio must first be assumed. In Table B-31, for anegative projection ratio, p' = 1.0, the design value of thesettlement ratio is -0.3.

Enter Figure 201 on the horizontal scale at H = 35 feet. Proceedvertically until the line representing Bd = 7 feet is intersected. At thispoint the vertical scale shows the fill load to be 15,800 pounds perlinear foot for 100 pounds per cubic foot fill material. Increase theload 10 percent for 110 pound material.

Wn = 1.10 X 15,800Wn = 17,380 pounds per linear foot



4. Determination of Bedding Factor (Bf)The trench variable bedding factor, Bf, is given by Equation B11:

Bfv = ( Bfe – Bft) + BftBd – (Bc+ 1.0)Bdt – (Bc+ 1.0)

Step 1. From Figure B-14, for circular pipe installed on a Class Bbedding, the trench fixed bedding factor, Bft, is 1.9.

Step 2. A trench width, Bd, of 7 feet is specified.

Step 3. The transition width, Bdt, determined from Table B-14 is11.4 feet.

Step 4. H/Bc = 35/4.8 = 7.3From Table B-31, the rsd design range of values forordinary soil is +0.5 to +0.8. Assume an rsd value of +0.5.For a granular Class B bedding p = 0.5, then rsdp = 0.5 x0.5 = 0.25.

Step 5. From Table B-32, for H/Bc = 7.3, p = 0.5, rsdp = 0.25 and aClass B bedding, Bfe = 2.19.

Step 6. The trench variable bedding factor is:



Bfv = (2.19 – 1.9) + 1.9

Bfv = 1.96

7 – (4.8 + 1.0)11.4 – (4.8 + 1.0)

Use a variable bedding factor, Bfv, of 1.96 to determine the requiredD-load pipe strength.



WL + WE = Wn = 17,380 pounds per linear foot


D0.01 = x F.S.WL + WE

Bf x D

D0.01 = x 1.017,380

1.96 x 4.0


EXAMPLE B-4Wide Trench Installation

Bc

Bd

H



Given: A 24 inch circular pipe is to be installed in a 5 foot wide trenchwith 9 feet of cover over the top of the pipe. The pipe will bebackfilled with ordinary clay weighing 120 pounds per cubic foot.

Find: The required three-edge bearing test strength for nonreinforcedpipe and the ultimate D-load for reinforced pipe.

Solution: 1. Determination of Earth Load (WE)From Table B-8C, the transition width for H = 9 feet is 4'-8". Sincethe actual 5 foot trench width exceeds the transition width, thebackfill load based on 100 pounds per cubic foot backfill is 3,331pounds per linear foot as given by the bold type. Increase the load20 percent for 120 pound backfill material.

Wd = 1.20 X 3,331Wd = 3,997 pounds per linear foot

2. Determination of Live Load (WL)From Table 42, the live load is 240 pounds per linear foot.

3. Selection of BeddingA Class C bedding will be assumed for this example.

4. Determination of Bedding Factor (Bf)Since the trench is beyond transition width, a bedding factor for anembankment condition is required.

The outside diameter for a 24 inch diameter pipe is 30 inches = 2.5feet. H/Bc = 3.6. From Table B-31, the rsd design range of values forordinary soil is +0.5 to +0.8. Assume an rsd value of +0.5. Forshaped Class C bedding p = 0.9, then rsdp = 0.5 x 0.9 = 0.45. FromTable B-33, a bedding factor of 2.07 is obtained.

5. Application of Factor of Safety (F.S.)A factor of safety of 1.5 based on the three-edge bearing strengthfor nonreinforced pipe and ultimate D-load for reinforced pipe willbe applied.

6. Selection of Pipe Strength The three-edge bearing strength fornonreinforced pipe is given by equation B15:



T.E.B. = X F.S.

WL + WE = Wd = 4,237 pounds per linear foot

T.E.B. = X 1.5

T.E.B. = 3,070 pounds per linear foot

Bf

2.07

WL + WE

4,237

The D-load for reinforced pipe is given by equation B16:

Dult. = 1,535 pounds per linear foot per foot of inside diameter

Dult. = x F.S.WL + WE

Bf x D

Dult. = x 1.54,237

2.07 x 2.0

Answer: A nonreinforced pipe which would withstand a minimum threeedge bearing test load of 3,070 pounds per linear foot would berequired.

A reinforced pipe which would withstand a minimum three-edgebearing test load for the ultimate load of 1,535 pounds per linearfoot per foot inside diameter would be required.

EXAMPLE B-5Positive Projecting Embankment Installation

Vertical Elliptical Pipe

pB'C

B'c

H



Given: A 76 inch X 48 inch vertical elliptical pipe is to be installed in a positiveprojecting embankment condition in ordinary soil. The pipe will becovered with 50 feet of 120 pounds per cubic foot overfill.


Solution: 1. Determination of Earth Load (WE)A settlement ratio must first be assumed. In Table B-31 values ofsettlement ratio from +0.5 to +0.8 are given for positive projectinginstallations on a foundation of ordinary soil. A value of 0.5 will beused. The product of the settlement ratio and the projection ratiowill be 0.35 (rsdp = 0.3).

Enter Figure 181 on the horizontal scale at H = 50 feet. Proceedvertically until the line representing R X S = 76" X 48" isintersected. At this point the vertical scale shows the fill load to be37,100 pounds per linear foot for 100 pounds per cubic foot fillmaterial. Increase the load 20 percent for 120 pound material.

Wc = 1.20 X 37,100Wc = 44,520 pounds per linear foot


3. Selection of BeddingA Class B bedding will be assumed for this example.

4. Determination of Bedding Factor (Bf)From Table 59, for an H/Bc, ratio of 9.84, rsdp value of 0.3, p valueof 0.7 and a Class B bedding, a bedding factor of 2.80 is obtained.





WL + WE = Wc = 44,520 pounds per linear foot

D0.01 = 3,975 pounds per linear foot per foot of inside horizonal span

D0.01 = x F.S.WL + WE

Bf x S

D0.01 = x 1.044,520

2.80 x 4.0

Answer: A pipe which would withstand a minimum three-edge bearing test loadfor the 0.01 inch crack of 3,975 pounds per linear foot per foot of insidehorizontal span would be required.

EXAMPLE B-6Highway Live Load

Given: A 12 inch circular pipe is to be installed in a narrow trench Bd ≤ (Bc +1.0), under an unsurfaced roadway and covered with 1.0 foot of 120pounds per cubic foot backfill material.


Solution: 1. Determination of Earth Load (WE)For pipe installed with less than 3 feet of cover, it is sufficientlyaccurate to calculate the backfill or fill load as being equal to theweight of the prism of earth on top of the pipe.

Wd = wHBc

Wd = 120 X 1.0 X 1.33Wd = 160 pounds per linear foot

Bc

Bd



2. Determination of Live Load (WL)Since the pipe is being installed under an unsurfaced roadway withshallow cover, a truck loading based on legal load limitationsshould be evaluated. From Table 42, for D = 12 inches, H = 1.0 footand AASHTO loading, a live load of 2,080 pounds per linear foot isobtained. This live load value includes impact.

3. Selection of BeddingA Class C bedding will be assumed for this example.

4. Determination of Bedding Factor (Bf)From Figure B-14, for circular pipe installed on a Class C bedding,a bedding factor of 1.5 is obtained.


6. Selection of Pipe Strength The D-load is given by equation B16:

D0.01 = 1,493 pounds per linear foot per foot of inside diameter

D0.01 = x F.S.WL + WE

Bf x D

D0.01 = x 1.02,080 + 160

1.5 x 1.0

Answer: A pipe which would withstand a minimum three-edge bearing test loadfor the 0.01-inch crack of 1,493 pounds per linear foot per foot ofinside diameter would be required.



Appendix BTables

&Figures



Table B-1



Table B-1 Continued



Table B-2



Table B-2 Continued



Table B-3



Table B-3 Continued



Table B-4



Table B-4 Continued



Table B-5



Table B-5 Continued



Table B-6



Table B-6 Continued



Table B-7



Table B-7 Continued



Table B-8



Table B-8 Continued



Table B-9



Table B-9 Continued



Table B-10



Table B-10 Continued



Table B-11



Table B-12



Table B-13



Table B-14



Table B-15



Table B-16



Table B-17



Table B-18



Table B-19



Table B-20



Table B-21



Table B-22



Table B-23



Table B-24



Table B-25



Table B-26



Table B-27



Table B-28



Table B-29



Table B-30



Table B-31



Table B-32



Table B-33



Figure B-1



Figure B-2



Figure B-3



Figure B-4



Figure B-5



Figure B-6



Figure B-7



Figure B-8



Figure B-9



Figure B-10



Figure B-11



Figure B-12



Figure B-13



Figure B-14



Figure B-15



Figure B-16



Figure B-17

533

Glossaryof Terms



GLOSSARY OF HYDRAULIC TERMS(Chapters 2 and 3)

A ............ cross-sectional area of flow, square feet

A ............ drainage area, acres

AHW ...... allowable headwater depth at culvert entrance, feet

C............ coefficient of runoff which is a function of the characteristics of the drainage area

C1 ............. constant in Manning’s Formula for full flow

D............ height of culvert opening or diameter of pipe, inches or feet

dc .............. critical depth, feet

H............ head loss, feet (the difference between the elevation of the entrance pool surface and theoutlet tailwater surface)

HW ........ headwater depth at culvert inlet measured from invert of pipe, feet

ho .............. vertical distance between the culvert invert at the outlet and the hydraulic grade line, feet

ke .............. entrance head loss coefficient

i ............. rainfall intensity, inches per hour

L ............ length of culvert, feet

n ............ Manning’s coefficient of roughness

Q ........... flow in sewer or culvert discharge, cubic feet per second

R............ hydraulic radius, equals area of flow divided by wetted perimeter, feet

R............ inside vertical rise of elliptical, arch pipe, or boxes, feet or inches

S ............ inside horizontal span of elliptical, arch pipe, or boxes, feet or inches

S ............ slope of sewer, feet per foot

So ............. slope of culvert, feet per foot

TW......... tailwater depth at culvert outlet measured from invert of pipe, feet

V ............ velocity, feet per second

GLOSSARY OF LOAD TERMS(Chapter 4 and Appendix B)

A ............ a constant corresponding to the shape of the pipe

ALL .................. distributed live load area on subsoil plane at outside top of pipe, square feet

As .................... area of transverse steel in a cradle expressed as a percentage of the area of concrete inthe cradle at the invert

Bc .................... outside horizontal span of the pipe, feet

B’c ................... outside vertical height of the pipe, feet

Bd .................... width of trench at top of pipe, feet

Bdt ................... transition width at top of pipe, feet

Bf ..................... bedding factor

Bfe ................... bedding factor, embankment

BfLL ................. bedding factor for live load

Bfo ................... minimum bedding factor, trench

Bfv ................... variable bedding factor, trench

Bt ..................... maximum width of excavation ahead of pipe or tunnel, feet

Glossary of Terms 535


C............ pressure coefficient for live loads

Cc ............. load coefficient for positive projecting embankment installations

Cd ............. load coefficient for trench installations

Cn ............. load coefficient for negative projecting embankment installations

Ct .............. load coefficient for jacked or tunneled installations

c ............ thickness of concrete cover over the inner reinforcement, inches

c ............ coefficient of cohesion of undisturbed soil, pounds per square foot

Di .............. inside diameter of pipe, inches

Do ............. outside diameter of pipe, inches

D............ inside diameter of circular pipe, feet or inches

D-load.... the supporting strength of a pipe loaded under three-edge-bearing test conditionsexpressed in pounds per linear foot per foot of inside diameter or horizontal span

D0.01 ........ the maximum three-edge-bearing test load supported by a concrete pipe before a crackoccurs having a width of 0.01 inch measured at close intervals throughout a length of atleast 1 foot, expressed as D-Load.

Dult. .......... The maximum three-edge-bearing test load supported by a pipe, expressed as D-load.

d ............ depth of bedding material below pipe, inches

dc .............. deflection of the vertical height of the pipe

E ............ modulus of elasticity of concrete, pounds per square inch (4,000,000 psi)

e ............ base of natural logarithms (2.718)

F.S. ........ factor of safety

H............ height of backfill or fill material above top of pipe, feet

HAF ....... horizontal arching factor, dimensionless

He ............. height of the plane of equal settlement above top of pipe, feet

h ............ thickness of rigid pavement

If ................ impact factor for live loads

K ............ ratio of active lateral unit pressure to vertical unit pressure

k ............ modulus of subgrade reaction, pounds per cubic inch

L ............ length of ALL parallel to longitudinal axis of pipe, feet

Le .............. effective live load supporting length of pipe, feet

MFI ........... moment at the invert under field loading, inch-pounds/ft

MFIELD .... maximum moment in pipe wall under field loads, inch-pounds/ft

MTEST ..... maximum moment in pipe wall under three-edge bearing test load, inch-pounds/ft

µ ..............coefficient of internal friction of fill material

µ’ ........... coefficient of sliding friction between the backfill material and the trench walls

N............ a parameter which is a function of the distribution of the vertical load and vertical reaction

NFI ............ axial thrust at the invert under field loads, pounds per foot

NFS .......... axial thrust at the springline under a three-edge bearing test load, pounds per foot

N’ ........... a parameter which is a function of the distribution of the vertical load and the verticalreaction for the concrete cradle method of bedding

PL .......... prism load, weight of the column of earth cover over the pipe outside diameter, poundsper linear foot



p ............ wheel load, pounds

p ............ projection ratio for positive projecting embankment installation; equals vertical distancebetween the top of the pipe and the natural ground surface divided by the outside verticalheight of the pipe

p’ ........... projection ratio for negative projecting installations; equals vertical distance between thetop of the pipe and the top of the trench divided by the trench width

po .............. live load pressure at the surface, pounds per square inch or pounds per square foot

P(H,X) ....... pressure intensity at any vertical distance, H, and horizontal distance, X, pounds persquare inch or pounds per square foot

π ............ 3.1416

q ............ the ratio of total lateral pressure to the total vertical load

R............ inside vertical rise of elliptical, arch pipe, or boxes feet or inches

Rs ............. radius of stiffness of the concrete pavement, inches or feet

r ............. radius of the circle of pressure at the surface, inches

rsd ............. settlement ratio

S ............ inside horizontal span of elliptical, arch pipe, or boxes feet or inches

SL ............. outside horizontal span of pipe (BC) or width of A

LL transverse to longitudinal axis of pipe,

whichever is less, feet

sd .............. compression of the fill material in the trench within the height p’Bd for negative projecting

embankment installations

sf ............... settlement of the pipe into its bedding foundation

sg .............. settlement of the natural ground or compacted fill surface adjacent to the pipe

T.E.B. .... three-edge bearing strength, pounds per linear foot

t ............. pipe wall thickness, inches

u ............ Poisson’s ratio of concrete (0.15)

VAF ....... vertical arching factor, dimensionless

Wc ............ fill load for positive projecting embankment installations, pounds per linear foot

Wd ............ backfill load for trench installations, pounds per linear foot

WE ........... earth load, pounds per linear foot

WL ............ live load on pipe, pounds per linear foot

Wn ............ fill load for negative projecting embankment installations, pounds per linear foot

Wp ............ weight of pavement, pounds per linear foot

WT ............ total live load on pipe, pounds

Wt ............. earth load for jacked or tunneled installations, pounds per linear foot

w ............... unit weight of backfill or fill material, pounds per cubic foot

wL ............. average pressure intensity of live load on subsoil plane at outside top of pipe, pounds persquare foot

x ............ a parameter which is a function of the area of the vertical projection of the pipe overwhich active lateral pressure is effective

x’ ............ a parameter which is a function of the effective lateral support provided by the concretecradle method of bedding

537

CondensedBibliography

Condensed Bibliography 539


Engineersresponsibleforthedesignandspecificationofprecastconcretepipeforsanitarysewer,stormdrainandculvertapplicationswillfindtheConcretePipeDesignManualanindispensableaidinselectingthetype,sizeandstrengthrequirementsofpipe.Revisedtoincludethemostcurrentdesignprocedures,theConcretePipeDesignManualisnowavailableinanelectronicformat.ThissearchableCDincludesthesametextinformationasthehardboundmanualandprovidesquickaccessto: • StandardInstallationsusingtheindirectdesignmethodtofacilitatethedesignofacost-

effectiveconcretepipe. • Morethan330pagesoftablesandfigurescoveringhydraulicsofsewersandculverts,live

loadsandearthloads,supportingstrengthsandsupplementaldesigndata. • Detailedexampleproblemsofspecificapplicationsillustratingtheproperuseofthetime-

savingdesignaidsincludedintheConcretePipeDesignManual. Inadditiontonewstate-of-the-artbeddingsdevelopedovermanyyearsofinvestigationandresearchintothebehaviorofconcretepipeintheburiedcondition,theConcretePipeDesignManualCDcontainstheprovenMarston/Spanglerdesignprocedureandbeddings. YouwillneedAdobeAcrobatReaderSoftware.AlinktotheAdobewebsiteforthisFREEsoftwareislocatedintheGET ACROBAT READER.doconthisCD.

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