Download - Precast Prestressed Concrete Horizontally Curved … 1. Precast prestressed concrete horizontally curved bridge beam concepts. Design variable Manufacturing variable Concrete Continuity

Special Report

Precast Prestressed ConcreteHorizontally Curved

Bridge Beamsprepared by

ABAM Engineers Inc.A MEMBER OF THE BERGER GROUP

33301 Ninth Avenue SouthFederal Way, Washington 98003-6395

50

This report discusses the concept, analysis anddesign procedures, design alternatives andfabrication techniques recommended for precastprestressed horizontally curved bridge beams.Comparisons of curved precast bridge super-structures with steel and cast-in-place concretedemonstrate the aesthetic and economic advantagesa precast concrete solution offers to bridge ownersand engineers. Three separate appendixes containplans and details, design charts and a designexample applying the design aids.

CONTENTS

1. Introduction ............................................... 52

2. Concept Description ........................................ 52

3. Cost Comparisons ......................................... 56

4. Analysis and Design ........................................ 58

5. Design Alternatives ......................................... 61

6. Fabrication Techniques ..................................... 62

7. Conclusion ................................................ 64

Reference ................................................... 64Appendix A — Conceptual Drawings and Details .................. 65

AppendixB — Design Charts ................................... 73

AppendixC — Design Example ................................. 87

PCI JOURNAL/September-October 1988 51

1. INTRODUCTIONNew interchanges off limited access

highways often require horizontallycurved medium length bridge beams.These bridge beams have been madealmost exclusively of steel where false-work restrictions preclude cast-in-placeconcrete construction. This report pre-sents results of a project sponsored bythe Prestressed Concrete Institute (PCI)to develop standards for precast pre-stressed horizontally curved bridgebeams.

The idea to develop horizontallycurved bridge beams won PCI's Indus-try Advancement Award in 1985. Thisaward winning idea was developed from

a precast prestressed curved beam proj-ect constructed in Pennsylvania. PCIsubsequently issued a request for pro-posals to develop this idea. ABAM En-gineers of Federal Way, Washington,was selected to pursue this effort.

This report summarizes the concept,analysis and design procedures, and fab-rication techniques recommended forprecast prestressed horizontally curvedbridge beams. Comparisons of curvedprecast bridge superstructures withsteel and cast-in-place concrete demon-strate the aesthetic and economic ad-vantages a precast concrete solution of-fers to bridge owners and engineers.

2. CONCEPT DESCRIPTION

A concept for horizontally curved pre-cast prestressed concrete beams is pre-sented. The concept uses the basic ideathat won PCI's Industry AdvancementAward for 1985. Several alternatives tothis basic idea for materials, fabricationand erection procedures, beamgeometry, and beam cross sections wereevaluated. Descriptions of these alter-natives are listed in Table 1. Concept 8,a trapezoidal box beam, was selected fordevelopment in this report. Designcharts and conceptual drawings arepresented for 5 and 6 ft (1.52 and 1.83 m)deep precast box beams. These chartsare intended to present preliminary pre-stressing strand and concrete strengthcriteria for various spans and beamspacings. Appendix A contains concep-tual design plans and details.

The concept uses long precast con-crete beams spanning between sup-ports. Chorded sections [20 ft (6.10 m)long] are used to approximate curvedgeometry (Figs. 1 and 2). Diaphragmsare provided at angle points betweenthese chorded sections. This chordlength produces a 2 in. (51 mm) offset on

a 300 ft (91.5 m) radius curve. Thebeams are chorded in plan and in pro-file. Individual precast beams arepost-tensioned together in the field toform continuous structures.

Trapezoidal box beams are used toproduce a torsionally rigid section that isaesthetically pleasing (Fig. 3). Span todepth ratios for bridge superstructuresconstructed with 5 ft (1.52 m) deep pre-cast box beam elements can be 27 to 1for interior spans and 23 to 1 for exteriorspans. These span to depth ratios arecomparable to bridges constructed fromcomposite welded steel girders andfrom cast-in-place post-tensioned boxgirders.

Post-tensioning tendons are placedinside the beam void and are deflectedhorizontally and vertically at dia-phragms between chorded sections. Thetendons, therefore, form a string poly-gon that approximates a parabolic shapein profile and the curve radius in plan(Fig. 4). Tendons are bonded to thecross section at each diaphragm but arenot continuously bonded along the ten-don length.

52

BEAM LENGTH

DIAPHRAGMS

PLAN OR ELEVATION

Fig. 1. Chorded geometry.

BEAM LINE 1

P►ER P ER

BEAM LINE 2 IBEAM LINE 3 I

TYP 20' CHORD

Fig. 2. Schematic layout.

•o •0 4 5nic

O 1 5'

4'-0'Fig. 3. Typical section.

I I ^ I Ij II I I I I

STRING POLYGONGONA

INTENDONS

II I I j PLAN & ELEVATION

Fig. 4. Tendon profile.


Table 1. Precast prestressed concrete horizontally curved bridge beam concepts.

Design variable Manufacturing variable

Concrete Continuity Numberdensity* at center Casting of beams

Concept Cross section (pcf) pier methodt Void form* per project1 Rectangular box 160 Yes Full length Expendable polystyrene 242 Rectangular box 160 Yes Full length Steel and wood 243 Rectangular box 160 Yes Segmental Steel and wood 244 Rectangular box 160 No Full length Steel and wood 245 Rectangular box 160 Yes Full length Steel and wood 66 Rectangular box 160 Yes Segmental Steel and wood 67 Rectangular box 125 Yes Full length Steel and wood 248 Trapezoidal box 160 Yes Full length Steel and wood 24

* Density includes reinforcement.

Full length casting: Chorded sections and diaphragms are cast monolithically.Segmental casting: Chorded segments are cast separately then moved to an assembly area for integration into full length beams.

Expendable polystyrene void: Solid sacrificial expendable polystyrene forms entire void.Steel and wood forms: Reusable steel forms for the sides of the interior; sacrificial wood forms for the soffit of the top flange. This is a two-stage casting.

ELEVATION

STAGE 1 • FABRICATE BEAMFIELD TENDONSSTAGE 2 • STRESS PLANTFIELD TENDONS TENDONS

PLANT TENDONSCROSS-SECTION

Fig. 5. Step 1.

• ERECT BEAMS

• CAST CLOSURE POURS • •

• STRESS STAGE 1 TENDONS

Fig. 6. Step 2.

ELEVATIONCIPCK

• CAST CROSSBEAMS

• CAST DECK IN PLACE

0 0 • STRESS• • STAGE 2 TENDONS

CROSSBEAM

CROSS-SECTION

Fig. 7. Step 3.

The concept allows individual beamlines to be bent horizontally to specificdesign radii and to provide differentprofiles for individual beam lines tobuild in vertical curves and varyingsuperelevations. A table of precast beam

geometry would be developed for eachproject.

Construction of a bridge made fromprecast prestressed horizontally curvedbeams involves three basic steps, illus-trated in Figs. 5, 6 and 7.

PCI JOURNALJSeptember-October 1988 55

• Step 1 (Fig. 5): Beams are fabri-cated full length in the plant in speciallydesigned formwork. Beams are cast intwo stages. Stage 1 includes the soffitand webs of the chorded sections, enddiaphragms, and diaphragms betweenchorded segments. Ducts are providedby plant post-tensioning tendons and forStage 1 and Stage 2 field post-tensioningtendons. The beam deck is cast in Stage2. Beam casting is complete prior to re-moving the beam from the form. Beamsare lifted out of the form and transportedto a yard storage/stressing area as rein-forced concrete members. Plant post-tensioning tendons are stressed.

• Step 2 (Fig. 6): Beams are trans-ported to the site and erected. Ducts forStage 1 and Stage 2 field post-tensioningtendons are spliced over interior sup-ports. Closure pours are made betweenbeams over interior supports. Stage 1tendons are stressed, creating continu-ous beams.

• Step 3 (Fig. 7): Cross beams arecast at the midpoint or at the third pointsalong the span at the nearest diaphragmlocations. The bridge deck is cast. Stage2 tendons are stressed, placing the deckinto compression. Traffic barriers,overlays, and expansion joints are

placed, completing the bridge construc-tion.

This horizontally curved prestressedprecast beam concept was selected overthe other concepts (see Table 1) becauseit generally:

• Improved quality• Reduced costs• Improved aestheticsQuality was enhanced using a two-

stage casting with removable innerforms for Stage 1. Inner surfaces andthicknesses of the beam soffit and webscan be inspected and positioning ofpost-tensioning tendons can be carefullyestablished and verified.

Labor costs to produce full lengthbeams are reduced by minimizing fabri-cation steps. Also, sloping sides deletethe requirement to move back beamside forms to lift beams from the form.Material costs are reduced by eliminat-ing costly inner void forms.

Aesthetics are improved by utilizingsloping beam sides in lieu of verticalsides.

Alternative design and fabricationvariations of this concept may be appro-priate for specific project conditions.These variations are discussed later inthis report.

3. COST COMPARISONSCost estimates were developed for

bridge superstructures of precast con-crete, cast-in-place concrete, and struc-tural steel. The precast alternative in-cludes the cost of cast-in-place concretecross beams, bridge deck, and trafficbarriers. The steel alternative includesthe cost of a concrete bridge deck andtraffic barriers.

A 24-beam project was assumed forthis cost comparison. Projects requiringfewer beams will be more costly persquare foot for the precast alternative.

The unit superstructure cost range(per square foot) for the precast conceptversus the cast-in-place concrete design

and the steel girder bridge design isshown in Fig. 8. This figure shows thatthe precast beam concept is cost com-petitive with the steel beam designwhen the unit steel price, in place andpainted, is more than $1 per pound($2000 per ton). Typical unit prices oncurved steel girders range from $1.00 to$1.50 per pound.

Precast beams are competitive withcast-in-place concrete box girders whenthe in-place unit concrete price exceeds$530 per cubic yard. Typical cast-in-place concrete bridges will cost be-tween $400 and $700 per cubic yard(complete with reinforcing bars and

56

post-tensioning). Difficult shoring con-ditions will add to this cost. Also, certainprojects will not allow shoring and willtherefore exclude cast-in-place concretedesigns.

Horizontally curved bridges made

from precast concrete beams are com-petitive with steel girder bridges andcast-in-place concrete bridges. Theamount of competitive edge will varywith local project and market condi-tions.

4. ANALYSIS AND DESIGN

Design of the curved precast beamsaddresses flexure, shear, torsion, distor-tion, and tendon anchoring and deflec-tion forces. A computer model was de-veloped for a 120 ft (36.6 m) span 5 ft(1.52 m) deep girder on a 300 ft (91.5 m)radius to better understand beam be-havior. The beams, cross beams, anddeck were modeled using a grillage ofone-dimensional elements. From this

model, analysis techniques were de-veloped for preliminary design.

Flexure and shear forces can be com-puted as if the beam were tangent, giv-ing consideration to the extra length ofthe outside beam line that results fromhorizontal curvature (Fig. 9). Criticalstress conditions are identified for eachstep of the construction process.

The beam is post-tensioned at the

DESIGN AS A TANGENT BMCONSIDER EXTRA LENGTH DUE TO CURVE

—^— BEAM LENGTH

Fig. 9. Flexure and shear design.

• ERECTED POSITION

TENSION AT MIDSPAN • STORED POSITION

LEVEL BEAM

U Li

Fig. 10. Critical stress condition (at plant).

58

• AT STAGE 1 POST-TENSIONING

TENSION INBEAM SOFFIT

• WITH DECK IN PLACET O^ TOP T

SOFFIT CMIDSPAN AT PIER

Fig. 11. Critical stress condition (Stage 1).

• AT STAGE 2 POST-TENSIONING WITH FULLDEAD LOAD & LIVE LOAD

TOP T

.f — --► TOP C

BOTTOM C

AT PIER MIDSPAN

Fig. 12. Critical stress condition (Stage 2).

plant to carry its own weight (Fig. 10). Inthis condition, long beams generally ex-perience downward deflection. Due tothe beam curvature, the bunking, trans-portation, and lifting locations are po-sitioned inward from the ends of thebeam over an appropriate diaphragm toprovide overturning stability. The beamprestressing is also adjusted to minimizecamber growth in the stored position.The beam profile in the form is adjustedfor the vertical geometry and for ex-pected elastic and creep deflections.

The critical stress condition due tostressing Stage 1 tendons is tension inthe beam soffit over interior supports(Fig. 11). Temporary tension at this lo-

cation is resisted by a positive momentconnection between beams. Uponplacing the cross beams and deck, thecritical stress condition becomes com-pression in the soffit over the piers.Tension stresses in the top of the beamsover the piers and compressive stressesin the top of the beams near midspancan also control the design.

The critical stress conditions at Stage2, with the full superimposed dead loadand live load in place, are tension in thebridge deck and compression in thebeam soffit over interior supports andcompression in the top of the beam nearmidspan (Fig. 12). The compressivestress at midspan is theoretically large in


P - C C TANZh

T T TAN4h

Fig. 13. Radial forces due to turning flexural forces.

RADIAL BENDING FORCE

\ ^/ TORSION

DISTORTION

Fig. 14. Torsion/distortion forces.

the girder top flange and small in theadjacent cast-in-place deck. Creep ef-fects, however, will redistribute thelarge compressive stress from the beaminto the deck. Because the creep effectis not considered in the preliminary cal-culations, the beams designed in thisreport use a maximum compressivestress of 0.5 f,' in the top flange of theprecast beam at midspan. Compressionin the beam soffit near interior supportsgenerally determines the required con-crete compressive stress, based on anallowable compressive stress of 0.4f.

An ultimate strength check is re-quired. It is recommended that thecomputation be done using the capacityof unbonded post-tensioned tendons.Additional mild steel can be added toachieve the required flexural strength.Mild steel reinforcement is used acrossall cold joints along the beam length.

This controls cracking and improvesductility, which is especially attractivein seismic risk areas.

Other considerations need to be ac-counted for in horizontally curved pre-cast prestressed concrete bridge beams.At each horizontal angle point, betweenchorded sections, the internal flexuralforces resisting the vertical bendingmoment turns through a horizontalangle (Fig. 13). Angular deflection ofthese forces places horizontal forces inthe top and bottom surfaces of thebeams. These in-plane forces can bebroken into torsional and distortioncomponents (Fig. 14). The torsionalcomponent is reacted by the box sectionand the distortion component is resistedby the diaphragm between chordedsegments.

Significant beam torsions are pro-duced only by the beam self weight

60

1 /

O^— O FIELD PT

PLANT PT

Fig. 15. Reinforcement at typical section.

acting on a simple span and by thebridge deck dead load acting on a con-tinuous beam. Subsequent twisting ofthe curved beams is resisted by thebridge deck and cross beams.

Shear and torsion design is performedby distributing the torsional resistanceinto individual web shears and addingweb shears reacting vertical forces.Thickening of webs may be required forlonger beams.

Tendon deflection and anchoringforces are reacted by the end blocks andthe diaphragms between chorded seg-ments.

Beam span charts have been de-veloped that show the required number

of post-tensioning strands per beam forvarious spans and beam spacings. Re-quired concrete strengths for the designare also shown. High concrete strengthscan be used to increase girder spacing.Bridge horizontal curvature has littleinfluence on post-tensioning require-ments. Therefore, designers can use de-sign charts for any bridge having thesame outside beam length. Designcharts use HS-20 live load. Beam chartsare included in Appendix B and a designexample using the charts is included inAppendix C.

Typical reinforcement and post-ten-sioning (PT) placement are shown inFig. 15.

5. DESIGN ALTERNATIVES

Situations are presented that require aconcept to offer flexibility to suit theparticular requirements of an owner,bridge engineer, or precaster. Severalvariations in design can be employed toenhance the usefulness of horizontallycurved precast concrete beams.

in lieu of a trapezoidal box section. De-sign curves for trapezoidal box crosssections may be used if rectangular crosssections have properties similar totrapezoidal cross sections shown.

Thickening of Soffit Slab atInterior Piers

Cross SectionA rectangular box section can be used p

The soffit of the beam near the sup-ort can be thickened to reduce com-


pressive stresses and therefore the re-quired concrete compressive stress. De-sign Chart 11 can be compared to De-sign Chart 2 (Appendix B) to determinethe amount of this reduction. Similarly,the thickness of the top flange of theprecast beam could be increased in themidspan region to reduce compressivestresses near midspan.

Elimination of the Second Stage ofField Post-Tensioning

The second stage of field post-ten-sioning can be eliminated. Additionalmild steel is placed in the deck over thepiers to control cracking and provide ul-

timate moment strength. This alterna-tive is especially attractive for areaswhere the requirement to totally removethe concrete deck for future replace-ment exists. Comparison of DesignCharts 12 and 2 shows the effect this al-ternative has on the number of pre-stressing strands and on the requiredconcrete compressive strength.

Use of Lightweight Concrete

Lightweight or semi-lightweight con-crete can be used to reduce beam trans-portation and erection weight. Reduc-tions in beam weight can be seen inCharts 7 and 10 (Appendix B).

6. FABRICATION TECHNIQUES

Form Concept

A forming concept for fabricating fullspan length chorded beams was de-veloped. The segments move and rotatealong guide beams to provide the hori-zontal curvature (Fig. 16). The eleva-tions of the guide beams can be adjustedusing jacks to provide the vertical pro-file (Fig. 17). The segments are nottwisted or warped. These variations canbe accommodated in the cast-in-placedeck.

Beam Weight

The weight of precast concrete beamsis a major concern. A maximum shippingweight of 314,000 lb (142,430 kg) (haul-ing equipment plus beam) was selectedto identify limiting span lengths. Thisweight is equal to the P13 permit designload used on California's highway sys-tem.

Shipping these large loads requiresspecial transporters (Fig. 18). There areunits that have been used to transportgirders of similar size. For instance, 13-axle transporters are available on the

west coast. The 318,000 lb (144,245 kg)shipping weight places an axle load of24 kips (107 kN) on axles 41/2 ft (1.37 m)apart.

This is similar to the axle loads forthe AASHTO military loading. Themaximum shipping weight translatesinto an effective beam transportationweight of 254,000 lb (115,214 kg). Thisbeam weight limits the shipping lengthof the 6 ft (1.83 m) deep section to 130 ft(39.6 m) and the 5 ft (1.52 m) deep sec-tion to 150 ft (45.7 m).

Alternative Production Methods

Alternative production techniquesalso were investigated.

Individual 20 ft (6.10 m) long chordedbeam segments could be fabricated andthen assembled into span length beamsat the plant. This option reduces beamforming costs but increases the numberof production steps. This alternativemay be advantageous on projects re-quiring a small number of beams.

Optional void materials could beused. The concept was designed arounda two-pour beam casting using steel

62

Fig. 16. Plan view of forming concept.

REF LINE

Fig. 17. Elevation of forming concept.

Fig. 18. Beam transporter.

inner forms with an expendable wooddeck soffit form. Polystyrene or woodforms could be used. However, produc-tion problems with these expendable

voids need to be carefully considered.Beams can also be spliced in the field

to reduce shipping weight and to pro-duce longer spans.


7. CONCLUSIONA concept has been developed for

precast prestressed concrete horizon-tally curved bridge beams. 'The conceptuses trapezoidal box beams made ofchorded segments to approximatecurved plan and profile geometries.Tendons are placed inside the void ofthe beams. High strength concrete canbe used to increase the beam spacing.Shipping restrictions limit practicalbeam span lengths, especially for 6 ft(1.83 m) deep units. Lightweight con-crete or spliced beams can be used toovercome this limitation. Precast pre-stressed bridge beams can be a viable

option for horizontally curved bridges,giving bridge owners and engineers analternative to steel girders and to cast-in-place concrete structures.

REFERENCEBarnofi, Robert, M.; Nagle, Gordon;Suarez, Mario, G.; Geschwindner, Louis,F., Jr.; Merz, H. William, Jr.; and West,Harry, H.; "Design, Fabrication, andErection of a Curved Prestressed Con-crete Bridge With Continuous Girders,"Transportation Research Record 950,1985, pp. 136-140.

NOTE: Discussion of this report is invited. Please submityour comments to PCI Headquarters by May 1, 1989.

64

APPENDIX• APPENDIX A - CONCEPTUAL DRAWINGS AND DETAILS

• APPENDIX B - DESIGN CHARTS

• APPENDIX C - DESIGN EXAMPLE

APPENDIX A - CONCEPTUAL DRAWINGSAND DETAILS


rnrn

gBOX BEAM

PIER CROSS BEAM

40' MAXIMUM SPACING 1 -s, 38'-0' 1'-g•

1/2 BEAM_S_PACING BEA M SPACING _i/2OFUBEAM T END ABUTMENT END BEAM —^ BEAM

q { OF BEAM SPACIN BRIDGE 7SPACING

9a gPG 1 _L T SPAN 2 BEAMS^,oSPAN ^1^\ eqGo_ 1 RADIUS 'R'

PLAN SECTION A-A

PIER

i

ELEVATION

Fig. Al. Precast prestressed concrete horizontally curved bridge beams (typical bridge layout).

C)C-

0CMZ

CD

CD3QCD

O0QCD

CoCo

^^POS i SOFFIT

O

P J ^NZ ENO SYMM ABT SPAN ;' 112.5

2o'!—i (((^^^

l^D Mil ! I PIER

' BEAM LENGTH

PLAN-PRECAST BEAM ' a -o•

SECTION

FIELD P/T (STAGE 1)MAX 2-31 STRAND

DIAPH, TYP ISYMM TENDONS I

PLANT P/T FIELD PT (STAGE 2)MAX 2-31 STRAND MAX 2-31 STRANDTENDONS TENDONS

PRECAST BEAM ELEVATION - P/T

4 Fig. A2. Precast prestressed concrete horizontally curved bridge beams 15 ft (1.52 m) beam].

0)

PIER1277

LiJFIELD P/T (STAGE o SECTIONMAX 2-31 STRANDDIAPH, TYP1 SYMM7// TENDONS

PLANT P/T FIELD P/T (STAGE 2)TENDONS STRAND

TENDONS STRAND}

PRECAST BEAMELEVATiON - PIT

Fig. A3. Precas prestressed concrete horizontally curved bridge beams [6 ft (1.83 m) beam].

C)C-

0C11z

CD

CD

3QCD

O0Q<D

toco

BRIDGE flt4 ^J STIRRUP♦8 CONT SETS a 8' OC

♦4 A^

♦5, TOP gEAM

TENDONSOR P/T BARS

-o \ J "

14' ABUTMENT^-F 10' p INT DIAPH

#5,BOTTOM

SECTION A-A (AT LAP)TYPICAL CROSS BEAM ELEVATION

& END DIAPHRAGM AT ABUTMENT

CD Fig. A4. Precast prestressed concrete horizontally curved bridge beams (cross beam details).

v0

BRIDGE DECK t5 STIRRUPSTYPICAL TRAFFIC t6 CONT., TYP @ 8" O.C.BARRIER -

t4TOP & BOTTOM BEAM

TOP & BOTTOM 0 0

1 1

\ \\

II I t1`

I I COUNTINUOUS \ 1

1 ^l

illI LL LL

U) wPOLYSTYRENE VOID,THICKNESS VARIES 1 1 i i\\ 11

.\ \, / WITH VERTICAL CURVE 1111 I J

PRECAST^_____ BEAM,

BEYONDPIER BETWEENSPANS

SECTION @ BRIDGE DECK SECTION @ CONTINUOUS ENDDIAPHRAGM

Fig. A5. Precast prestressed concrete horizontally curved bridge beams (deck and pier diaphragm details).

STEEL PIPE SCHED 40DIAPHRAGM c JOINT

(PRE-BENT)---_., B PVC PIPE SCHED 40

-- --- - ---_- --{- I_^- ---, i5. TYP

5•B

PLAN AT TYP INTERIOR DIAPHRAGM SECTION B - B

FIELD BEND I

1__ #4 TYP TYP#5, TYP \ t4 d

-FIELD P/T STAGE 2

FIELD P/T STAGE 1

VARIES PLANT P/T

MIN 1/2'5 EO SPA. 7 1/2'MIDSPAN

SECTION A - A REINFORCEMENT AT TYP SECTION

1 Fig. A6. Precast prestressed concrete horizontally curved bridge beams (typical cross section and tendon deflection details).

VN

Ii1-+ -+ FIELD P/T

G PLANT P/T

m U^--1 3/8 . 0 THREAD BAR- F_ F (tpu = 150 ksi)IL m TORSION RESTRAINTID D

ELEVATION AT BEAM END

1 - 2 I FIELD P/T

+ PLANT P/Ti

m m m m ^'------1 3/8 0 THREAD BARi- f- ►- i- (fpu = 150 ksi)LL LL u_ u_ TORSION RESTRAINTN m N m

ELEVATION AT CONTINUOUS END

4'-10•1'-4• 10• 1'-4•END BLOCK

=flflflflp!illff 11,11

• ^■ii■•■■il

ANCHOR DETAIL DETAIL AT END BLOCK CONTINUOUS END

Fig. A7. Precast prestressed concrete horizontally curved bridge beams (sections and details).

APPENDIX B - DESIGN CHARTS

GENERALFig. B. Key plan, sections, and notes to be used with charts.

5 FT (1.52 M) DEEP BOX BEAM

Chart 1. Total post-tensioned strand requirement (interior span beam).

Chart 2. Total post-tensioned strand requirement (exterior span beam).

Chart 3. Post-tensioned strand requirement (interior span beam, beam spacing = 13 ft).

Chart 4. Post-tensioned strand requirement (exterior span beam, beam spacing = 8 ft).



Chart 7. Beam shipping weight.

6 FT (1.83 M) DEEP BOX BEAMChart 8. Total post-tensioned strand requirement (interior span beam).

Chart 9. Total post-tensioned strand requirement (exterior span beam).

Chart 10. Beam shipping weight.

DESIGN ALTERNATIVES, 5 FT (1.52 M) DEEP BOX BEAM

Chart 11. Total post-tensioned strand requirement (exterior span beam, thickenedbottom slab).Chart 12. Total post-tensioned strand requirement (exterior span beam, no Stage 2post-tensioning).


PIER (i BOX BEAMCROSS BEAM40 MAXIMUM SPACINGOUTSIDE ABUTMENT END BEAM AOf BEAM ^ _ ^ ^ Ct PIER

y 4iA ee

9. 0PG EXTEH\OR SPAN INTERIO SPAN # &G

PLANSPAN LENGTH IS AT 5j BRIDGE.NOTE THAT DESIGN CHARTS AREBASED ON MOMENTS IN THEOUTSIDE GIRDER.VFIELD

I1'-6' -1 38-0' 1'-6'1/2 BEAM SPACING BEAM SPACING 1/2BEAM BEAMPACING BRIDGE SPACING1_0 CIP BRIDGE iDECK2)CROSSBEAMm o RADIUS 'R'SECTION A-A DETAIL 1ONOTES:• POST-TENSIONED (PT) TENDONS COMPROMISE 1/20-270K STRANDS.• EFFECTIVE STRESS IN THE STRANDS AFTER CONSIDERING ALL LOSSES IS 160 KSI.• STAGE 1 PT IS JACKED BEFORE THE CIP DECK IS PLACED.• STAGE 2 PT IS JACKED AFTER THE CIP DECK IS PLACED.• HS-20 LIVE LOAD.

Fig. B. Key plan, sections, and notes to be used with charts.

74

C)C-0CzDI-

NW3a-

O0a-

mm

160• 5F• INTI

150

140

1302wm120

wa-

110zC

100LL0w 90I

Z 80J

F0 70

60

5090 100

Fig. B1. Design chart.

110 120 130 140 150

SPAN LENGTH (FT)

CHART 1 — TOTAL PT STRAND REQUIREMENT

160 170

-9K5x

8 Kg(' G

- -I ks^

6 Kaif' G

CG

60

5090 100


110 120 130 140 150 160

SPAN LENGTH (FT)

CHART 2 — TOTAL PT STRAND REQUIREMENT

170

1600)

150

140

130

wm 120

wa-

110z

100w0w 90

z 80JF-0 70

0 K5^

fG '/

9 K5^

,

• 5 FT BEAM DEPTH• EXTERIOR SPAN BEAM

65-o • 5 FT BEAM DEPTHC- • INTERIOR SPAN BEAMo0

60 • S 13 FTX

z

55CD

m

B 50m Q

Om 45

CD w Q^a ^^0 40 Q^,Pz

35

o

cr 30 S^ PG 2 P^

S^ PG`cZ 25

20

15

1090 100 110 120 130 140 150 160 170

SPAN LENGTH (FT)

V

V

Fig. B3. Design chart. CHART 3 — PT STRAND REQUIREMENT

50

wC0 45IwnU) 402I

35U-0CE 30I

z 25

PLANT PT

STAGE 1 PT

110 120 130 140 150

SPAN LENGTH (FT)

---- STAGE 2 PT

20

15

1090

65co

60

55

• 5 FT BEAM DEPTH• EXTERIOR SPAN BEAM• S=8FT

160 170

Fig. B4. Design chart. CHART 4 — PT STRAND REQUIREMENT

C)

C-0Cwz

CD

CD36N

aC,0QCD

Cow

• 5 FT BEAM DEPTH

• EXTERIOR SPAN BEAM

• S 10 FT

PLANT PT

STAGE 1 PT

STAGE 2 PT

0

15

0

90 100

110 120 130 140 150

160 1/U

SPAN LENGTH (FT)

Fig. 65. Design chart. CHART 5 — PT STRAND REQUIREMENT

65

60

55

50

wm 45Iwa

0 40z

I35

Ow 30I

Z 25

2

1

160 170

wm 45

w3-

40z

m35

U-0

30m

z 25

20

15

10

90 100


110 120 130 140 150

SPAN LENGTH (FT)

CHART 6 - PT STRAND REQUIREMENT

Co 650

60

55

50

• 5 FT BEAM DEPTH

• EXTERIOR SPAN BEAM

• S=13 FTPLANT & STAGE 1 PT

STAGE 2 PT

0C-0Cz

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350

300

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150

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• 5 FT BEAM DEPTH• OUTSIDE BEAM• ROAD WIDTH = 38 FT, 3 BEAMS

160 pcf

NGREC^ O^NS\̂ ^ ^4o Pci

GO 16 = A30 pci

90 100

110 120 130 140 150 IOU '(U

SPAN LENGTH (FT)

Co Fig. B7. Design chart. CHART 7 — BEAM SHIPPING WEIGHT

CoN • 6 FT BEAM DEPTH• INTERIOR SPAN BEAM

150

14C

13C

wm 120

wd

0 110zI

100U-OW 90m

z 80J

0 70

60

5090 100 110

Fig. B8. Design chart. CH/

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150

140

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• 6 FT BEAM DEPTH

• EXTERIOR SPAN BEAMg ks^

9 K5^1 Ks^

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. 6 K5^EG

5 v'sfc "

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50 I I I II '

90 100 110 120 130 140 150 160 170

SPAN LENGTH (FT)

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W Fig. B9. Design chart. CHART 9 — TOTAL PT STRAND REQUIREMENT

OD

- 35• 6 FT BEAM DEPTH• OUTSIDE BEAM

301

• ROAD WIDTH = 38 FT, 3 BEAMS

ENS^^y ^' ,60 pct

25I-I0w

w 20,m

150

10090 100


110 120 130 140 150

SPAN LENGTH (FT)

CHART 10 – BEAM SHIPPING WEIGHT

160 170

0 120 130 14U uuu

SPAN LENGTH (FT)

CHART 11 — TOTAL PT STRAND REQUIREMENT00(TIFig. Bi 1. Design chart.

0 100 11

0• 5 FT BEAM DEPTH• EXTERIOR SPAN BEAM

0 • BOTTOM SLAB 10 • THICKAT INTERIOR SUPPORT

0

'0

10

30

30

70

60

50

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30

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0

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12 Ks%(si

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/ c 8 ks^

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90 100 110 120 130 140 150 160

170

SPAN LENGTH (FT)

Fig. B12. Design chart. CHART 12 — TOTAL PT STRAND REQUIREMENT

APPENDIX C-DESIGN EXAMPLE


APPENDIX C - DESIGN EXAMPLE

Perform PreliminaryFlexural Design

Bridge length = 380 ft '(116 m)Roadway width W = 38 ft (11.6m)Roadway radius R = 300 ft (91.5 m)Use beam depth = 5 ft (1.52 m)Number of spans: 380/3 = 127 ft (38.7 m)avgTry three spans.380/4 = 95 ft (29.0 m) avg

The number of beams, N,, (or beamspacing, S), can be determined from thedesign charts.

Try three beams [spacing = 13 ft (3.92m)].

To optimize the post-tensioning de-sign, enter 5 ft (1.52 m) beam depthcharts (exterior and interior span beams)with plot of strand required versus spanfor three beams (see Figs. C1 and C2).

Piers p-1 P-2

Find the combination of exterior andinterior span lengths that add up to thetotal bridge length and that has the samenumber of strands required for eachstage of field post-tensioning.

The plant post-tensioning supportsthe beam as a simple span and is notcontinuous; therefore, the requirednumber of strands will be greater for thelonger interior spans. It does not controlthe ratio of spans.

Stage 1 field post-tensioning is tosupport the cast-in-place bridge deckdead load and is continuous acrossinterior supports. The number of strandsis the same in the tendon. There will besome difference in the final stresses ofthe strand along the span from the endanchor to the center of the bridge (as-suming stressing is done from both endsof the bridge) due to losses.

P-3 P-4

Initial Stres:

After Seatin

Final Stress

veragetress50 ksi

TENDON STRESS ALONG BEAM LINE

From the charts, find the spans thatadd up to the total length for the samenumber of strands in Stage 1:

Req'd. No.Span of strands

Exterior 118.0 x 2 = 236 ft 34.5Interior 144.0 x 1 = 144 ft 34.5

380 ft

Using the same charts, similar calcu-lations are done for determining thespans for Stage 2 post-tensioning:

Req'd. No.Span of strands

Exterior 122.5x2 = 245 ft 33.0Interior 135.0 x 1 = 135 ft 33.0

380 ft

The vertical lines plotted on the quire a few more strands.charts will bracket an efficient design By inspection, use:solution. Any choice in between will re- Span = 120 + 140 + 120 = 380 ft (116 m)

88

120' 140' 120'

BRIDGE ELEVATION

Strand Required (Figs. C3 and C4):

AdjustedBy chart strandstrand require-

required ment

Exterior span:5 ft beam depth,three beams (S = 13 ft)

Plant post-tension 36

36Stage 1 post-tension 36

36

Stage 2 post-tension 32

36*104

108

Interior span: 5 ft beam depth,three beams (S = 13 ft)

Plant post-tension 49

49Stage 1 post-tension 33

36*

Stage 2 post-tension 36

36

118

121*Increase

Required 28-Day CompressiveStrength (see Figs. C3 and C4)

Exterior span: fc = 7300 psi (50.4 MPa)Interior span: fc = 7200 psi (49.7 MPa)

Say: f,' = 7500 psi (51.7 MPa)This requirement can be significantly

reduced by thickening the bottom slabnear the interior continuous supports,because the compressive strength re-quirements shown on the charts aregenerally governed by compression inthe bottom slab at the interior support(see Fig. C5).

There are significant compressivestresses at the top of the bare beam atmidspan prior to casting the deck; how-ever, service level stresses in the deckare relatively low, allowing creep effectsto reduce the compressive stress in thebeam.f,' might be reduced to 6000 psi (41.4

MPa).Exterior span = 4500 psi (31.0 MPa)

Beam Shipping Weight (see Fig. C6)

Exterior span beam shipping weight =210 kips (934 kN)

Interior span beam shipping weight =240 kips (1067 kN)

CIP Deck Thickness

Precast Beam Depth

Stress After Creep

Initial StressDistribution

COMPRESSIVE STRESS AT MIDSPAN


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60' INTERIOR SPAN BEAM

• S=13 FT

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50

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40 g^P

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33.030 ZPC

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20

15

1090 100 110 120 130 Vv 140 150 160 170

SPAN LENGTH (FT)

Fig. C1. Design Example. CHART 3 — PT STRAND REQUIREMENT

C)C-0CzD

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65

60

55

50

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20

15

10

• 5 FT BEAM DEPTH• EXTERIOR SPAN BEAM• S = 13 FT PLANT & STAGE 1 PT

STAGE 2 PT

PLOTTED FROM THEINTERIOR SPANBEAM CHART

34.5

3 3.0

90 100

110 120 '" ' 130 140 150 160 170

SPAN LENGTH (FT)

Fig. 02. Design Example CHART 6 — PT STRAND REQUIREMENT

160coN

150

140

130

wm 120crwa

110z

100U-0W 90m

z 80J

0 70

60

SPAN LENGTH (FT)

Fig. 03. Design Example. CHART 1 — TOTAL PT STRAND REQUIREMENT

160• 5 FT BEAM DEPTH

C- • EXTERIOR SPAN BEAM t c '150

z

17 140

a K5^, gCD

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70

60 KS^

5090 100 110 120 130 140 150 160 170

SPAN LENGTH (FT)

cD

W Fig. 04. Design Example CHART 2 — TOTAL PT STRAND REQUIREMENT

• 5 FT BEAM DEPTH• EXTERIOR SPAN BEAM• BOTTOM SLAB 10 THICK

AT INTERIOR SUPPORT6 ks^

5 KS%

A K5^

3Kai/ (G

150

140

130

wm 120Ltwa-

110z

100U-0w 90m

Z 80JF-0 70

60

il

5090 100

110 120 130 140 150 160 170

SPAN LENGTH (FT)

Fig. C5. Design Example CHART 11 — TOTAL PT STRAND REQUIREMENT

350

cii

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250I-Iw

w 200m

n

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240 k ,60 pct

NGRES^ ^^NSt̂ y ^ ' S ao p°t210 k GO ^,

1S = A30 Pit

150

10090 100

110 120 130 140 150 160 170

SPAN LENGTH (FT)

Fig. C6. Design Example. CHART 7 — BEAM SHIPPING WEIGHT