Mathcad - Footing F-4

Calculation Sheet

8D ISOLATED FOOTING, F-1

REFERENCE

Reference:C:\Users\Bong\Desktop\01 MathCad\Utilities.mcd(R)

DESCRIPTION

This section provides the design of ISOLATED FOOTING

PAGE CONTENTS

2 A. DIMENSIONS

2 B. MATERIAL PROPERTIES

4 C. DESIGN LOADS

5 C. ANALYSIS RESULTS

11 D. FACTORED SOIL BEARING PRESSURE

13 E. CHECK SHEAR

22 F. REINFORCEMENT DESIGN

25 G. SUMMARY/DETAILS

Footing F-4.xmcd LNT - Page 1 of 41

Calculation Sheet

C Jun 11 LNT VKJ

Rev Date By CheckedRev Date By CheckedRev Date By Checked

Elec File Location \ENG\ST\CA\References\MB\MATHCAD\

Project File Location J:\ONSHORE\04811225 Page 2 of 26

Calculation Title KFIP BERTH-22 MAINTENANCE BUILDING Phase/CTR

Project Title JUBAIL EXPORT REFINERY (PACKAGE-8) Calc No SA-JER-PI903-GCCC-070113Customer SATORP Proj No 04811179

A. DIMENSIONS

A.1 FOOTING AND PIER DATA

FOOTING DATA

Footing Length, L = 5.000 m

Footing Width, B = 6.000 m

Footing Thickness, T = 0.500 m

Concrete Unit Wt., Yc = 24.000 kN/m

Soil Depth, D = 0.800 m

Soil Unit Wt., Ys = 18.000 kN/m

Pass. Press. Coef., Kp = 3.000

Coef. of Base Friction, = 0.400

Uniform Surcharge, Q = 0.000 kPa

Net Allow. SB Pressure, qs = 100 kPa

PIER DATANumber of Piers = 3

Nomenclature

Pier #1 Pier #2 Pier #3

Xp (m) = 0.000 0.000 0.000

Zp (m) = -2.000 0.000 2.000

Lpx (m) = 0.500 0.500 0.500

Lpz (m) = 0.500 0.500 0.500

h (m) = 1.000 1.000 1.000

B. MATERIALS PROPERTIES

B.1 CONCRETE

Compressive Strength fc 30MPa:=Modulus of Elasticity Ec 4700 fc MPa:= Ec 25743 MPa=Concrete strain c 0.003:=Concrete Protection cov 75mm:=

B.2 REBARSYield Strength of Steel fy 414MPa:= Modulus of Elasticity Es 2 105MPa:=


Calculation Sheet

BAR DESIGNATIONS, SIZES AND AREAS

TableNo 0 1 2 3 4 5 6 7 8 9 10db (mm) 0 0 8 10 12 16 20 22 25 28 32As (mm) 0 0 50 79 113 201 314 380 491 616 804

No NoT:= dia dbT mm:= As AsT mm2:= Example for bar at bar 4:= Nobar 4=

Bar diameter is: diabar 12 mm=Area of bar is: Asbar 113 mm

2=

SKETCH PLAN

cL Z-AXIS

cL X

-AXI

S


Calculation Sheet

C. DESIGN LOADS From STAAD Analysis and Design Output

ASD LOAD COMBINATIONS

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

k 0 Npier 1..:=Node_Nok

9810

:=

rk match Node_Nok ASD0 , := NLC rows ASD_Comb( ):=

FXk ASD_Data 2 rk, ( ) kN:= MXk ASD_Data 5 rk, ( ) kN m:=FYk ASD_Data 3 rk, ( ) kN:= MYk ASD_Data 6 rk, ( ) kN m:=FZk ASD_Data 4 rk, ( ) kN:= MZk ASD_Data 7 rk, ( ) kN m:=

FX1 k 0

Fk FXi( )jk k 1+

j 0 NLC 1..fori 0 Npier 1..for

F

:= FY1 k 0

Fk FYi( )jk k 1+


F

:= FZ1 k 0

Fk FZi( )jk k 1+


F

:=

MX1 k 0

Fk MXi( )jk k 1+


F

:= MY1 k 0

Fk MYi( )jk k 1+


F

:= MZ1 k 0

Fk MZi( )jk k 1+


F

:=

LOAD1 k 0

Fk ASD_Combjk k 1+


F

:= NODE1 k 0

Fk Node_Noi mod k NLC, ( ) 0=ifFk " " otherwisek k 1+


F

:=


Calculation Sheet

ASD LOAD COMBINATIONS

SUPPORT REACTIONS ALL UNITS ARE IN -- KN METER

NODE LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM-Z

9 100 0.20 441.82 -2.75 -7.62 -2.30 0.30 101 8.95 406.58 -2.33 -5.24 -0.97 28.40 102 -0.22 386.44 32.87 79.41 -1.18 -1.16 103 6.58 420.57 -2.12 -4.95 -1.18 20.75 104 -0.29 405.46 24.28 58.54 -1.33 -1.42 105 9.10 235.58 -1.48 -3.31 -0.39 29.01 106 -0.06 215.43 33.72 81.35 -0.59 -0.558 100 -2.94 799.73 -5.24 -12.30 -0.35 -4.44 101 7.26 640.25 -2.57 -5.53 -0.14 28.06 102 -2.32 647.81 21.87 71.80 0.38 -4.01 103 4.14 719.18 -3.75 -7.98 -0.18 18.68 104 -3.05 724.85 14.58 50.01 0.21 -5.37 105 8.16 352.34 -1.55 -3.35 -0.06 29.49 106 -1.42 359.89 22.89 73.98 0.46 -2.58

10 100 -0.53 574.79 8.52 16.41 -0.82 -1.42 101 8.95 472.30 5.80 11.70 -0.62 28.63 102 -0.37 499.49 35.73 85.73 0.85 -1.00 103 6.43 539.38 8.25 16.52 -0.65 20.66 104 -0.56 559.77 30.70 72.04 0.46 -1.57 105 9.22 274.88 3.52 7.09 -0.41 29.41 106 -0.10 302.06 33.46 81.12 1.07 -0.22


Calculation Sheet

LRFD COMBINATIONS

rk match Node_Nok LRFD0 , := NLC rows LRFD_Comb( ):=

FXUk LRFD_Data 2 rk, ( ) kN:= MXUk LRFD_Data 5 rk, ( ) kN m:=FYUk LRFD_Data 3 rk, ( ) kN:= MYUk LRFD_Data 6 rk, ( ) kN m:=FZUk LRFD_Data 4 rk, ( ) kN:= MZUk LRFD_Data 7 rk, ( ) kN m:=

FXU1 k 0

Fk FXUi( )jk k 1+


F

:= FYU1 k 0

Fk FYUi( )jk k 1+


F

:= FZU1 k 0

Fk FZUi( )jk k 1+


F

:=

MXU1 k 0

Fk MXUi( )jk k 1+


F

:= MYU1 k 0

Fk MYUi( )jk k 1+


F

:= MZU1 k 0

Fk MZUi( )jk k 1+


F

:=

LOAD1 k 0

Fk LRFD_Combjk k 1+


F

:= NODE1 k 0

Fk Node_Noi mod k NLC, ( ) 0=ifFk " " otherwisek k 1+


F

:=

LRFD COMBINATIONS


Calculation Sheet

SUPPORT REACTIONS ALL UNITS ARE IN -- KN METER

NODE LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM-Z

9 200 -0.55 598.50 -2.98 -6.78 -2.04 -2.14 201 0.48 535.91 -3.55 -10.26 -3.10 1.09 202 7.95 519.17 -3.71 -10.58 -2.71 25.03 203 0.62 503.05 24.45 57.14 -2.88 1.39 204 15.06 493.84 -3.50 -9.23 -1.81 47.88 205 0.40 461.61 52.82 126.21 -2.14 0.58 206 14.59 351.27 -2.24 -5.00 -0.53 46.51 207 -0.07 319.04 54.07 130.45 -0.86 -0.788 200 -3.16 1007.71 -3.55 -7.61 -0.29 -5.00 201 -3.80 991.65 -7.36 -17.50 -0.48 -5.67 202 3.82 928.02 -7.39 -17.58 -0.43 19.63 203 -3.85 934.07 12.17 44.29 -0.01 -6.02 204 11.84 816.43 -5.80 -13.53 -0.29 45.45 205 -3.49 828.52 33.31 110.20 0.54 -5.86 206 13.20 520.55 -2.34 -5.04 -0.08 47.39 207 -2.14 532.64 36.77 118.69 0.75 -3.92

10 200 -0.95 691.00 7.96 16.15 -0.75 -2.73 201 -0.58 722.24 11.36 21.64 -1.09 -1.49 202 7.12 705.23 11.46 21.78 -1.16 22.98 203 -0.33 726.97 35.40 81.00 0.02 -0.73 204 14.74 639.48 9.84 18.99 -1.06 47.13 205 -0.17 682.97 57.74 137.43 1.30 -0.29 206 14.79 410.19 5.30 10.65 -0.62 47.18 207 -0.11 453.68 53.19 129.09 1.74 -0.23


Calculation Sheet

D. ANALYSIS RESULTSD.1 WEIGHTS AND LOADS

FOUNDATION CENTROID:

Xc 0m:= Yc 0m:= FOUNDATION, SOIL AND SURCHARGE:

Base weight: Wtbase L B T c:= Wtbase 360.0 kN=

Soil weight: Wtsoil L B D s:= Wtsoil 432.0 kN=

Surcharge wt: Wtsurc L B Q:= Wtsurc 0.0 kN=

Total wt: WTotal Wtbase Wtsoil+ Wtsurc+:= WTotal 792.0 kN= PIER WEIGHTS AND LOADS:

Excess Pier Weights ExcessPier_wtn Lpxn Lpzn hn c s( ) hn DifLpxn Lpzn D c s( ) hn D( ) c+ otherwise

:=

ExcessPier_wtT 2.4 2.4 2.4( ) kN=

Applied load + Excess pier weight Ptyn Pyn ExcessPier_wtn+:= TOTAL VERTICAL LOAD:

PTotal WTotal

n

Ptyn+:=

CALCULATE FOOTING STABILITY

D.3 CHECK STABILITY

SLIDING CHECK:

Passive Soil Pressure

Passivex T B Kp( ) s D T+( ) Kp s D( )+ 0.5:= Passivex 170.1 kN=Passivez T L Kp( ) s D T+( ) Kp s D( )+ 0.5:= Passivez 141.8 kN=

Friction Forces

Frictionxj 0kN PTotalj 0kNif PTotalj Wtsurc( ) otherwise

:= Frictionzj 0kN PTotalj 0kNif PTotalj Wtsurc( ) otherwise

:=

Factor of Safety:

FSSL.xj

Passivex Frictionxj+

n

Fxn jround

n

Fxn j1kN

3,

0kNif

"INFINITY" otherwise

:=


Calculation Sheet

Check_FSSLxj "N.A." FSSL.xj "INFINITY"=if

"OK,Safe against sliding @ X" FSSL.xj 1.5if"N.G. Redesign" otherwise

otherwise

:=

SLIDING ALONG X-DIRECTION

Comb Passive + Ff Sum FX FS Sliding Remarks

100 1216.32 3.27 371.96 OK,Safe against sliding @ X101 1097.43 -25.16 43.62 OK,Safe against sliding @ X102 1103.28 2.91 379.13 OK,Safe against sliding @ X103 1161.43 -17.15 67.72 OK,Safe against sliding @ X104 1165.81 3.90 298.93 OK,Safe against sliding @ X105 834.90 -26.48 31.53 OK,Safe against sliding @ X106 840.73 1.58 532.11 OK,Safe against sliding @ X

FSSL.zj

Passivez Frictionzj+

n

Fzn jround

n

Fzn j1kN

3,

0kNif


:=

Check_FSSLzj "N.A." FSSL.zj "INFINITY"=if

"OK,Safe against sliding @ Z" FSSL.zj 1.5if"N.G. Redesign" otherwise

otherwise

:=

SLIDING ALONG Z-DIRECTION

Comb Passive + Ff Sum FZ FS Sliding Remarks

100 1187.97 0.53 2241.45 OK,Safe against sliding @ Z101 1069.08 0.90 1187.87 OK,Safe against sliding @ Z102 1074.93 90.47 11.88 OK,Safe against sliding @ Z103 1133.08 2.38 476.08 OK,Safe against sliding @ Z104 1137.46 69.56 16.35 OK,Safe against sliding @ Z105 806.55 0.49 1646.02 OK,Safe against sliding @ Z106 812.38 90.07 9.02 OK,Safe against sliding @ Z

UPLIFT CHECK:

Upward Loads Py.upnUpj if Pyn( )j 0 kN> Pyn( )j, 0 kN, Upliftn Up

j 0 6..for

Upliftn

:=

Pty.upliftjn

Py.upn j:=


Calculation Sheet

Pty.downj PTotaljn

Py.upn j+ Wtsurc:=Downward Loads

Factor of Safety:

FSULj

Pty.downjPty.upliftj

Pty.upliftj 0kN>if


:=

Check_FSULj "N.A." FSULj "INFINITY"=if

"> 1.2, OK,Safe against sliding @ X" FSULj 1.2if"< 1.2, N.G. Redesign" otherwise

otherwise

:=

UPLIFT

Comb Downward F Uplift F FS Uplift Remarks

100 2615.54 0.00 INFINITY N.A.101 2318.33 0.00 INFINITY N.A.102 2332.94 0.00 INFINITY N.A.103 2478.33 0.00 INFINITY N.A.104 2489.28 0.00 INFINITY N.A.105 1662.00 0.00 INFINITY N.A.106 1676.58 0.00 INFINITY N.A.

OVERTURNING ABOUT X-AXIS CHECK:

Moment due to Py: Mexn Ptyn Zpn:=

Due to Fz and Mx: Moxn Fzn hn T+( ) Mxn+:=

Eccentricity: ezj

n

Mexn j nMoxn j

+

PTotalj:=

Overturning Moment due to Py:

Mot.xn

OTj Ptyn( )j B2 Zpn Zpn 0 mif

OTj Ptyn( )j B2 ezj 0mif

Zpn 0m=if

Ptyn( )j 0 kN

Calculation Sheet

Total Overturning Moment about X-axis: MOT.x

n

Moxnn

Mot.xn+:=Resisting Moment about X-axis due to Py: Mrm.xn

OTj Ptyn( )j B2 Zpn+ MOT.xj 0 kN m>ifOTj Ptyn( )j B2 Zpn MOT.xj 0 kN mif

OTj 0 kN m otherwise

j 0 6..for

OT

:=

Total Resisting Moment about X-axis: MRM.x

n

Mrm.xn Wtbase Wtsoil+( ) B2+:=

Factor of Safety: FSOT.xj

MRM.xjMOT.xj

MOT.xj 0 kN mif


:=

Check_FSOTxj "N.A." FSOT.xj "INFINITY"=if

"> 1.5, OK,Safe against overturning @ X" FSOT.xj 1.5if"< 1.5, N.G. Redesign" otherwise

otherwise

:=

OVERTURNING MOMENT ABOUT X

Comb RM OM FS OT Remarks

100 8112.56 2.72 2988.05 > 1.5, OK,Safe against overturning @ X101 6823.55 -2.28 2992.79 > 1.5, OK,Safe against overturning @ X102 6772.72 -372.65 18.17 > 1.5, OK,Safe against overturning @ X103 7197.37 -7.16 1005.22 > 1.5, OK,Safe against overturning @ X104 7159.22 -284.93 25.13 > 1.5, OK,Safe against overturning @ X105 4907.40 -1.17 4212.36 > 1.5, OK,Safe against overturning @ X106 4856.48 -371.56 13.07 > 1.5, OK,Safe against overturning @ X

OVERTURNING ABOUT Z-AXIS CHECK:

Moment due to Py: Mezn Ptyn Xpn:=

Due to Fx and Mz: Mozn Fxn hn T+( ) Mzn+:=

Eccentricity: exj

n

Mezn j nMozn j

+

PTotalj:=


Calculation Sheet

Overturning Moment due to Py: Total Overturning Moment about X-axis:

Mot.zn

OTj Ptyn( )j L2 Xpn Xpn 0 mif

OTj Ptyn( )j L2 ezj 0mif

Xpn 0m=if

Ptyn( )j 0 kNifOTj Ptyn( )j L2 Xpn+ MOT.zj 0 kN mif

OTj 0 kN m otherwise

j 0 6..for

OT

:= MRM.zn

Mrm.zn Wtbase Wtsoil+( ) L2+:=

Factor of Safety:

FSOT.zj

MRM.zjMOT.zj

MOT.zj 0 kN mif


:= Check_FSOTzj "N.A." FSOT.zj "INFINITY"=if

"> 1.5, OK,Safe against overturning @ Z" FSOT.zj 1.5if"< 1.5, N.G. Redesign" otherwise

otherwise

:=

OVERTURNING MOMENT ABOUT Z

Comb RM OM FS OT Remarks

100 6538.85 -0.66 9982.98 > 1.5, OK,Safe against overturning @ Z101 5795.83 47.35 122.40 > 1.5, OK,Safe against overturning @ Z102 5832.35 -1.81 3231.22 > 1.5, OK,Safe against overturning @ Z103 6195.83 34.37 180.29 > 1.5, OK,Safe against overturning @ Z104 6223.20 -2.51 2479.36 > 1.5, OK,Safe against overturning @ Z105 4155.00 48.19 86.22 > 1.5, OK,Safe against overturning @ Z106 4191.45 -0.98 4276.99 > 1.5, OK,Safe against overturning @ Z

CALCULATE FOOTING STABILITY


Calculation Sheet

NET SOIL BEARING PRESSURE:

MAX NET SOIL BEARING PRESSURE

Comb P Total(kN)ex

(m)ez

(m) K CoeffP max(kPa)

P max.net(kPa) Remarks

100 2615.54 0.000 0.101 1.10 95.99 72.59 < qs = 100 kPa, O.K.!101 2318.33 0.020 0.058 1.08 83.63 60.23 < qs = 100 kPa, O.K.!102 2332.94 -0.001 0.257 1.26 97.80 74.40 < qs = 100 kPa, O.K.!103 2478.33 0.014 0.099 1.12 92.14 68.74 < qs = 100 kPa, O.K.!104 2489.28 -0.001 0.238 1.24 102.86 79.46 < qs = 100 kPa, O.K.!105 1662.00 0.029 0.048 1.08 59.99 36.59 < qs = 100 kPa, O.K.!106 1676.58 -0.001 0.325 1.33 74.09 50.69 < qs = 100 kPa, O.K.!

CRITICAL LOAD COMBINATION ASD_CombSL 104=


Py (kN) = -405.5 -724.9 -559.8

Fx (kN) = 0.3 3.1 0.6

Fz (kN) = 24.3 14.6 30.7

Mx (kNm) = -58.5 -50.0 -72.0

Mz (kNm) = -1.4 -5.4 -1.6

CALCULATE SOIL BEARING PRESSURE


Calculation Sheet

BEARING AREA:

Dist x dx "N.A."=

Dist z dz "N.A."=Brg. L1 L1 5.000m=Brg. L2 L2 6.000m=

%Brg. Area Brg_Area 100.00 %=

Biaxial Case Case "N.A."=

GROSS SOIL BEARING CORNER PRESSURES:

MAXIMUM NET SOIL PRESSURE:

Pmax.net max P( ) s D T+( ):=P1 63.09 kPa= P3 102.86 kPa=Pmax.net 79.46 kPa=

P2 102.66 kPa= P4 63.29 kPa= Check_qs if Pmax.net qs "OK, q max < q allowable", "N.G. Redesign", ( ):=Check_qs "OK, q max < q allowable"= Pmax.net

Calculation Sheet

Moment due to Py: Muezn Putyn Xpn:=

Due to Fx and Mz: Muozn Vuxn hn T+( ) Muzn+:=

Eccentricity: euxj

n

Muezn j nMuozn j

+

PuTotalj:=

CALCULATE ULTIMATE LOADS

CALCULATE ULTIMATE SOIL BEARING

MAX NET ULTIMATE SOIL BEARING PRESSURE

Comb Pu Total(kN)e ux(m)

e uz(m) K Coeff

Pu max(kPa)

Pu 1(kPa)

Pu 2(kPa)

Pu 3(kPa)

Pu 4(kPa)

200 3416.09 -0.001 0.055 1.06 120.28 107.46 120.05 120.28 107.69201 3368.68 0.000 0.109 1.11 124.54 100.04 124.52 124.54 100.06202 3271.30 0.012 0.112 1.13 122.82 98.41 122.82 119.68 95.26203 3282.97 0.000 0.225 1.22 134.04 84.82 134.04 134.04 84.82204 3068.63 0.025 0.094 1.12 115.02 95.80 115.02 108.78 89.56205 3091.98 0.000 0.334 1.33 137.51 68.63 137.45 137.51 68.68206 2400.89 0.032 0.050 1.09 87.10 79.13 87.10 80.93 72.96207 2424.24 -0.001 0.356 1.36 109.65 51.96 109.54 109.65 52.08

CRITICAL LOAD COMBINATION LRFD_CombFL 205=


Puy (kN) = -461.6 -828.5 -683.0

Vux (kN) = -0.4 3.5 0.2

Vuz (kN) = 52.8 33.3 57.7

Mux (kNm) = -126.2 -110.2 -137.4

Muz (kNm) = 0.6 -5.9 -0.3

CALCULATE SOIL BEARING PRESSURE

TOTAL RESULTANT ULTIMATE LOAD AND ECCENTRICITIES:

Total Vertical Load PuTotalFL 3092.0 kN=Eccentricity along X-axis euxFL 0.000 m=Eccentricity along Z-axis euzFL 0.334m=

ULTIMATE SOIL BEARING CORNER PRESSURES:


Calculation Sheet

Pu1 68.63 kPa=

Pu2 137.45 kPa=

Pu3 137.51 kPa=

Pu4 68.68 kPa=

F. CHECK SHEAR

F.1 FOOTING ANALYSIS ALONG X-DIRECTIONS

L 5m=

quLPu3 Pu4+

2:= quR

Pu1 Pu2+2

:=

quL 103.1 kPa= quR 103.0 kPa=

qx CALCULATIONS

Effective length of bearing:

Brgx2 PuTotalFL

maxPu3 Pu4+

2

Pu1 Pu2+2

,

Bmin

Pu3 Pu4+2

Pu1 Pu2+2

,

0kPa=if

L otherwise

:= Brgx 5m=

Effective length of bearing:

Brgz2 PuTotalFL

maxPu1 Pu4+

2

Pu3 Pu2+2

,

Lmin

Pu1 Pu4+2

Pu3 Pu2+2

,

0kPa=if

B otherwise

:= Brgz 6m=

q at critical sections:

qquL quR

Brgx:= q 0.011 kPam=


Calculation Sheet

q x( )

quL 1x

Brgx

x Brgxif0kPa otherwise

quR 0kPa=if

quR 1x LBrgx

+ x L Brgx( )if

0kPa otherwise

quL 0kPa=if

min quL quR, ( ) q Brgx x( ) quL quR>ifx otherwise

+ otherwise

:=

d6n maxL2

Xpn+Lpxn

2 de 0m,

:= d6

T 1.835 1.835 1.835( ) m=

d5n maxL2

Xpn+Lpxn

2 de

2 0m,

:= d5

T 2.042 2.042 2.042( ) m=

d4n maxL2

Xpn+Lpxn

2 0m,

:= d4

T 2.25 2.25 2.25( ) m=

d3n minL2

Xpn+Lpxn

2+ L,

:= d3

T 2.75 2.75 2.75( ) m=

d2n minL2

Xpn+Lpxn

2+ de

2+ L,

:= d2

T 2.957 2.957 2.957( ) m=

d1n minL2

Xpn+Lpxn

2+ de+ L,

:= d1

T 3.165 3.165 3.165( ) m=

box d2 d5:= boxT 0.915 0.915 0.915( ) m=

qx CALCULATIONS


q d1n( )103.1103.1103.1

kPa= q d6n( )

103.1103.1103.1

kPa= q d2n( )

103.1103.1103.1

kPa= q d5n( )

103.1103.1103.1

kPa= q d3n( )

103.1103.1103.1

kPa= q d4n( )

103.1103.1103.1

kPa=


Calculation Sheet

Diagrams

xp n( )

L2

Xpn+Lpxn

2

L2

Xpn+Lpxn

2+

L2

Xpn+Lpxn

2+

L2

Xpn+Lpxn

2

L2

Xpn+Lpxn

2

:= y1p

T

T

T 0.5m+T 0.5m+

T

:= xf

0m

L

L

0m

0m

:= yf

0m

0m

T

T

0m

:=yp n( )

T

T

T hn+T hn+

T

:=

Moment due to Py: Shear due to Py:

Vp_ x n, ( ) 0kN x L2 Xpn+

Calculation Sheet

TOTAL SHEAR: TOTAL MOMENT:

V x( ) 0 kN x 0 m=( ) x L=( )+ifVsbp x( ) Vssf x( )+ Vp_ x( )+ otherwise

:= M x( ) 0 kN m x 0 m=( ) x L=( )+ifMssf x( ) Msbp x( )+ Mp_ x( )+ otherwise

:=

a 1000:=

Let x 0mLa

, L..:=

M1

M1i Mi La

i 0 a..for

M1

:= V1Mi V

i La

i 0 a..for

M

:=

X c( ) matchmax c( )

mmc

mm,

0 L1a

:=

m1 100 ceil 0.011M X M1( )( )

kN m

:= v1 100 ceil 0.011M X M1( )( )

kN m

:=

m1 0= v1 0=

y10.25m1

0.25 m1

:= x1L2

L2

:=

m1 100 ceil 0.011max yp 0( ) yp 1( ), yp 2( ), ( )

mm

:=

m1 1.7 103=

qx.5n q d5n( ):= qx.2n q d2n( ):=

Diagrams


Calculation Sheet

0 2 103 4 103 6 103

Soil Bearing Pressure Diagram

L (mm)

qu (

kPa)



Calculation Sheet

0 2 103 4 103 6 103

Shear Diagram

L (mm)

Vu (

kN)


Calculation Sheet

0 2 103 4 103 6 103

Moment Diagram

L (mm)

Mu

(kN

-m)


Calculation Sheet

Max Beam Shear & Bending Moment

Beam Shear along Z-axis at d distance from face of col: Bending moment about Z-axis at critical sections:

V d1n( )727.6727.6727.6

kN= V d6n( )

-728.0-728.0-728.0

kN= M d3n( )

-1003.7-1003.7-1003.7

kN m= M d4n( )

-1004.3-1004.3-1004.3

kN m=

Mupos.z max M1( ):=

MuRz

mi M d3i( )i 0 Npier 1..for

min m( )

:=VuRz

vi V d1i( )i 0 Npier 1..for

max v( )

:= VuRz 727.6 kN=

MuRz 1003.7 kN m=

MuLz


min m( )

:=VuLz


max v( )

:=

MuLz 1004.3 kN m=VuLz 728.0 kN= Muneg.z if min MuLz MuRz, ( ) 0kN m 0kN m, min MuLz MuRz, ( ), ( ):=


Wide-beam shear along Z direction Max negative moment at face of support Muneg.z 1004.3 kN m=

VuLz 728.0 kN= VuRz 727.6 kN= Max positive moment: Mupos.z 0.0 kN m=

F.2 FOOTING ANALYSIS ALONG Z-DIRECTIONS


Calculation Sheet

B 6m=

quLPu1 Pu4+

2:= quR

Pu3 Pu2+2

:=


qz CALCULATIONS


qquL quR

Brgz:= q 11.471 kPam=

q x( )

quL 1x

Brgz

x Brgzif0kPa otherwise

quR 0kPa=if

quR 1x BBrgz

+ x B Brgz( )if

0kPa otherwise

quL 0kPa=if

min quL quR, ( ) q Brgz x( ) quL quR>ifx otherwise

+ otherwise

:=

d6n maxB2

Zpn+Lpzn

2 de 0m,

:= d6

T 0.335 2.335 4.335( ) m=

d5n maxB2

Zpn+Lpzn

2 de

2 0m,

:= d5

T 0.542 2.542 4.543( ) m=


Calculation Sheet

d4n maxB2

Zpn+Lpzn

2 0 m,

:= d4

T 0.75 2.75 4.75( ) m=

d3n minB2

Zpn+Lpzn

2+ B,

:= d3

T 1.25 3.25 5.25( ) m=

d2n minB2

Zpn+Lpzn

2+ de

2+ B,

:= d2

T 1.458 3.458 5.457( ) m=

d1n minB2

Zpn+Lpzn

2+ de+ B,

:= d1

T 1.665 3.665 5.665( ) m=

boz d2 d5:= bozT 0.915 0.915 0.915( ) m=

WzR Brgx d1:= WzRT 3.335 1.335 0.665( ) m=

WzL d6:= WzLT 0.335 2.335 4.335( ) m=

azL d4:= azLT 0.75 2.75 4.75( ) m=

azR Brgz d3:= azRT 4.75 2.75 0.75( ) m=

qz CALCULATIONS


q d1n( )87.8

110.7133.6

kPa= q d6n( )

72.595.4

118.4

kPa= q d2n( )

85.4108.3131.3

kPa= q d5n( )

74.997.8

120.8

kPa= q d3n( )

83.0105.9128.9

kPa= q d4n( )

77.3100.2123.1

kPa=


Calculation Sheet

Diagrams

xp n( )

B2

Zpn+Lpzn

2

B2

Zpn+Lpzn

2+

B2

Zpn+Lpzn

2+

B2

Zpn+Lpzn

2

B2

Zpn+Lpzn

2

:= xf

0m

B

B

0m

0m

:= yf

0m

0m

T

T

0m

:=

Moment due to Py:

Shear due to Py:

Mp_ x n, ( ) 0kN m x B2 Zpn+

Calculation Sheet

TOTAL SHEAR: TOTAL MOMENT:

V x( ) 0 kN x 0 m=( ) x B=( )+ifVsbp x( ) Vssf x( )+ Vp_ x( )+ otherwise

:= M x( ) 0 kN m x 0 m=( ) x B=( )+ifMssf x( ) Msbp x( )+ Mp_ x( )+ otherwise

:=

a 1000:=

Let x 0mBa

, B..:= Ba

6 mm=

x1

B2

B2

:=

M1

M1i Mi Ba

i 0 a..for

M1

:= V1Mi V

i Ba

i 0 a..for

M

:=

X c( ) matchmax c( )

mmc

mm,

0 B1a

:=

qz.5n q d5n( ):= qz.2n q d2n( ):=

Diagrams


Calculation Sheet

0 2 103 4 103 6 103

Soil Bearing Pressure Diagram

B (mm)

qu (

kPa)



Calculation Sheet

0 2 103 4 103 6 103

Shear Diagram

B (mm)

Vu (

kN)


Calculation Sheet

0 2 103 4 103 6 103

Moment Diagram

B (mm)

Mu

(kN

-m)


Calculation Sheet


Beam Shear along X-axis at d distance from face of col: Bending moment about X-axis at critical sections:

V d1n( )121.6330.9165.1

kN= V d6n( )

-56.3-61.471.0

kN= M d3n( )

-231.7-276.5-137.3

kN m= M d4n( )

-48.6-189.8

21.6

kN m=

VuRx


max v( )

:=Mupos.x max M1( ):=

MuRx


min m( )

:=VuRx 389.3 kN=

VuLx


max v( )

:=MuRx 276.5 kN m=

MuLx


min m( )

:=

VuLx 109.5 kN=

MuLx 189.8 kN m=

Muneg.x if min MuLx MuRx, ( ) 0kN m 0kN m, min MuLx MuRx, ( ), ( ):=Max Beam Shear & Bending Moment

Wide-beam shear along X direction Max negative moment at face of support Muneg.x 276.5 kN m=VuLx 109.5 kN= VuRx 389.3 kN= Max positive moment: Mupos.x 34.1 kN m=

F.4 PUNCHING SHEAR

Capacity reduction factor v 0.85:= Shear strength provided

Vc v 0.33 fc MPa( ) box boz+( ) de:=VcT 1167 1167 1167( ) kN=

Punching Shear

Perimeter around column/pier:

Along x-direction boxT 0.915 0.915 0.915( ) m=

Along z-direction bozT 0.915 0.915 0.915( ) m=

Area of Punching Shear:


Calculation Sheet

Apn boxn bozn:= ApT 0.837 0.837 0.837( ) m2=

Total force from column/pier:

Puyn Putyn( )FL LF Apn T c D s+ Q+( ) +:=Puy

T 495.9 862.8 717.3( ) kN=q at d/2 distance from supports:

Along x-directionqx.2

T 103.1 103.1 103.1( ) kPa=

qx.5T 103.1 103.1 103.1( ) kPa=

Along z-directionqz.2

T 85.4 108.3 131.3( ) kPa=

qz.5T 74.9 97.8 120.8( ) kPa=

Total force acting on punched area

Rqn12

max qx.5n qx.2n+ qz.5n qz.2n+, ( ) Apn:=Rq

T 86.3 86.3 105.5( ) kN=Net punching shear:

Vupn Puyn Rqn:=

VupT 409.6 776.5 611.8( ) kN=

Check if shear strength provided by concrete is greater than the maximum shear force.

ACI31811.3.1.1.Eq.11.3.p if min Vc( ) max Vup( )> "OK,shear strength provided > Vu.", "NG!", ( ):=ACI31811.3.1.1.Eq.11.3.p "OK,shear strength provided > Vu."= min Vc( ) >=? max Vup( ) "YES!.. SATISFACTORY"=

F.5 WIDE BEAM SHEAR

Wide-beam shear along Z direction

VuLz 728.0 kN= VuRz 727.6 kN=

Shear strength provided Vnb v 0.17 fc MPa B de( ):= Vnb 1970.7 kN=Check if shear strength provided by concrete is greater than the maximum shear force.

ACI31811.3.1.1.Eq.11.3.bsz if Vnb max VuLz VuRz, ( )> "OK,shear strength provided > Vu.", "NG!", ( ):=ACI31811.3.1.1.Eq.11.3.bsz "OK,shear strength provided > Vu."= Vnb >=? max VuLz VuRz, ( ) "YES!.. SATISFACTORY"= Wide-beam shear along X direction

VuLx 109.5 kN= VuRx 389.3 kN=

( )Footing F-4.xmcd LNT - Page 32 of 41

Calculation Sheet

Shear strength provided Vnb v 0.17 fc MPa L de( ):= Vnb 1642.3 kN=Check if shear strength provided by concrete is greater than the maximum shear force.

ACI31811.3.1.1.Eq.11.3.bsx if Vnb max VuLx VuRx, ( )> "OK,shear strength provided > Vu.", "NG!", ( ):=ACI31811.3.1.1.Eq.11.3.bsx "OK,shear strength provided > Vu."= Vnb >=? max VuLx VuRx, ( ) "YES!.. SATISFACTORY"=

G. REINFORCEMENT DESIGN

G.1 DESIGN MOMENT FOR BOTTOM BARS

Capacity reduction factor f 0.90:= Moment at face of pedestal X-direction Muneg.z 1004.3 kN m= Moment at face of pedestal Z-direction Muneg.x 276.5 kN m=

G.2 BOTTOM REINFORCEMENTS

Temp steel reinforcement ratio temp 0.0018:= [ACI 318 7.12.2]

min temp:=Minimum steel reinf ratio [ACI 318 10.5.4]

min 0.0018= Bars in X-direction

Factored resistance Mr f As fy ds 12As fy

0.85 fc b

=Mr max Muneg.z 0.001 kN m, ( ):= Mr 1004.3 kN m= b B:=Reinforcement provided

Size of bar barx 6 Bar diameter diabarx 20 mm=

Proposed bar spacing Sx.bot 200mm:= Bar area Asbarx 314 mm2=

Area of steel provided As

Asbarxb

Sx.bot:= As 9420 mm2=

Distance from extreme compressive fiberto centroid of reinforcing steel

d T cov 0.5 diabarx:= d 415 mm=

Solve the quadratic equation for the areaof steel required

Given Mr f As fy d 12As fy

0.85 fc b

=

As.reqd Find As( ):= As.reqd 6638 mm2=Minimum reinforcement As.min min min b d

43

As.reqd, := As.min 4482 mm

2=

Temperature reinforcement As.temp temp bT2

:= As.temp 2700 mm2=

Reinforcing steel required As.reqd max As.reqd As.min, As.temp, ( ):= As.reqd 6638 mm2=Check As provided As >=? As.reqd "YES!.. SATISFACTORY"=

Bars in Z-direction


Calculation Sheet


0.85 fc b

=Mr max Muneg.x 0.001 kN m, ( ):= Mr 276.5 kN m= b L:=Reinforcement provided

Size of bar barz 6 Bar diameter diabarz 20 mm=

Proposed bar spacing Sz.bot 200mm:= Bar area Asbarz 314 mm2=


Asbarzb

Sz.bot:= As 7850 mm2=


d T cov diabarx 0.5 diabarz:= d 395 mm=



0.85 fc b

=As.reqd Find As( ):= As.reqd 1893 mm2=

Minimum reinforcement As.min min min b d43


2=




G.3 TOP REINFORCEMENTS

Bars in X-direction


0.85 fc b

=Mr max Mupos.z 0.001 kN m, ( ):= Mr 0.0 kN m= b B:=Reinforcement provided

Size of bar barx.top 5:= Bar diameter diabarx.top 16 mm=

Proposed bar spacing Sx.top 300mm:= Bar area Asbarx.top 201 mm2=


Asbarx.topb

Sx.top:= As 4020 mm2=


d T cov 0.5 diabarx.top:= d 417 mm=



0.85 fc b

=

As.reqd Find As( ):= As.reqd 0 mm2=Minimum reinforcement As.min min min b d

43


2=



Reinforcing steel required As.reqd max As.reqd As.min, As.temp, ( ):= As.reqd 2700 mm2=


Calculation Sheet

Check As provided As >=? As.reqd "YES!.. SATISFACTORY"= Bars in Z-direction


0.85 fc b

=Mr max Mupos.x 0.001 kN m, ( ):= Mr 34.1 kN m= b L:=Reinforcement provided

Size of bar barz.top 5:= Bar diameter diabarz.top 16 mm=

Proposed bar spacing Sz.top 300mm:= Bar area Asbarz.top 201 mm2=


Asbarz.topb

Sz.top:= As 3350 mm2=


d T cov diabarx.top 0.5 diabarz.top:= d 401 mm=



0.85 fc b

=As.reqd Find As( ):= As.reqd 228 mm2=

Minimum reinforcement As.min min min b d43


2=




H. SUMMARY/DETAILS

PLAN REINFORCEMENTS

Bot_BarsParallel.L concat num2strdiabarx

mm

"mm at ", num2str

Sx.botmm

, "mm O.C.",

:=

Top_BarsParallel.L concat num2strdiabarx.top

mm

"mm at ", num2str

Sx.topmm

, "mm O.C.",

Sx.top 0mmif

"Rebars Not Required" otherwise

:=

Bot_BarsParallel.B concat num2strdiabarz

mm

"mm at ", num2str

Sz.botmm

, "mm O.C.",

:=


Calculation Sheet

Top_BarsParallel.B concat num2strdiabarz.top

mm

"mm at ", num2str

Sz.topmm

, "mm O.C.",

Sz.top 0mmif

"Rebars Not Required" otherwise

:=

Center lines:y1

0m

0m

:= x1

Scale 2 max L B, ( )2

1.2 L2

:= y3

B 2cov5

down mdown m

:=

y2

1.2 B2

1.2 B2

:= x2 0m

0m

:= y4

B 2cov4

up mup m

:=

Footing: xf

L2

L2

L2

L2

L2

:= yf

B2

B2

B2

B2

B2

:=

Rebars: x1rebar

L 2cov2

L 2cov2

:= y2rebar

B 2cov2

B 2cov2

:=

y1rebar

B 2cov4

B 2cov4

:= x2rebar

L 2cov4

L 2cov4

:=


Calculation Sheet

Columns/pedestal: xp n( )

Xpn

Lpxn2

Xpn

Lpxn2

+

Xpn

Lpxn2

+

Xpn

Lpxn2

Xpn

Lpxn2

:= yp n( )

Zpn

Lpzn2

Zpn

Lpzn2

Zpn

Lpzn2

+

Zpn

Lpzn2

+

Zpn

Lpzn2

:=

PLAN REINFORCEMENTS

cL X

-Axi

s

L 5.000m=

BARS PARALLEL TO 'L'

B 6.000m=

BARS PARALLEL TO 'B'


Calculation Sheet

cL Z-Axis

SUMMARY OF REINFORCEMENTS:

Bot_BarsParallel.L "20mm at 200mm O.C."= Bot_BarsParallel.B "20mm at 200mm O.C."=Top_BarsParallel.L "16mm at 300mm O.C."= Top_BarsParallel.B "16mm at 300mm O.C."=

FOOTING DIMENSIONS: L 5.000m= B 6.000m= T 0.500m=ELEVATION ALONG X-AXIS

T cov diabarx+ 1 +

Center lines:y1

0m

0m

:= x1

1.2 L2

1.2 L2

:= y3

T cov diabarx+ 1 diab+

cov diabarx+ 1 diaba+

down mdown m

:=


Calculation Sheet

y2

1.2 max h T+( )T2

:= x2 0m

0m

:= y4

cov 0.5 diabarx+

T cov 0.5 diabarx+

up mup m

:=

Footing: xf

L2

L2

L2

L2

L2

:= yf

0m

0m

T

T

0m

:=

Rebars: x1rebar

L 2cov2

L 2cov2

:= y2rebar

T cov 0.5 diabarx+

T cov 0.5 diabarx+

:=

y1rebar

cov 0.5diabarx+

cov 0.5 diabarx+

:= x2rebar

L 2cov2

L 2cov2

:=

x3rebar

L 3cov2

L 3cov2

L 3cov2

L 3cov2

L 3cov2

:= y3rebar

cov diabarx+ 1 diabarz+


T cov diabarx+ 1 diabarz+

T cov diabarx+ 1 diabarz+


:=


Calculation Sheet

Columns/pedestal: xp n( )

Xpn

Lpxn2

Xpn

Lpxn2

+

Xpn

Lpxn2

+

Xpn

Lpxn2

Xpn

Lpxn2

:= yp n( )

T

T

T hn+T hn+

T

:=

ELEVATION ALONG X-AXIS

BARS PARALLEL TO 'L'

T 0.500m=

BARS PARALLEL TO 'B'

L 5.000m=


Calculation Sheet

END OF FTG DESIGN


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