Mathcad - Footing F-2

7/22/2019 Mathcad - Footing F-2

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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-2.mcd LNT - Page 1 o


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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-07011

Customer SATORP Proj No 04811179

A. DIMENSIONS

A.1 FOOTING AND PIER DATA

FOOTING DATA

Footing Length, L = 4.000 m

Footing Width, B = 3.000 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 = 140 kPa

PIER DATA

Number of Piers = 1

Nomenclature

Pier #1

Xp (m) = 0.000

Zp (m) = 0.500

Lpx (m) = 0.500

Lpz (m) = 0.500

h (m) = 0.000

B. MATERIALS PROPERTIES

B.1 CONCRETE

Compressive Strength fc 30MPa:=

Modulus of Elasticity Ec 4700 f c MPa:= Ec 25743MPa=

Concrete strain c 0.003:=

Concrete Protection cov 75mm:=

B.2 REBARS

Yield Strength of Steel fy 414MPa:= Modulus of Elasticity Es 2 105MPa:=



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Calculation Sheet

BAR DESIGNATIONS, SIZES AND AREAS

Table

No 0 1 2 3 4 5 6 7 8 9 10

db (mm) 0 0 8 10 12 16 20 22 25 28 32

As(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

12mm=

Area of bar is: Asbar

113mm2

=

SKETCH PLAN

cL Z-AXIS

cLX-AXIS



4/38


5/38

Calculation Sheet

D. ANALYSIS RESULTS

100D.1 SERVICE LOADS LOAD NUMBER

Pier #1

Py (kN) = -799.7

Fx (kN) = 2.9

Fz (kN) = -5.2

Mx (kNm) = -12.3

Mz (kNm) = -4.4

Npier

PyT( )

0

kN

FxT( )

0

kN

FzT( )

0

kN

MxT( )

0

kN m

MzT( )

0

kN m

CALCULATE FOOTING STABILITY

D.2 WEIGHTS AND LOADS

FOUNDATION CENTROID:

Xc 0m:= Yc 0m:=

FOUNDATION, SOIL AND SURCHARGE:

Base weight: Wtbase L B T c:= Wtbase 144.0kN=

Soil weight: Wtsoil L B D s:= Wtsoil 172.8kN=

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

Total wt: WTotal Wtbase Wtsoil+ Wtsurc+:= WTotal 316.8kN=

PIER WEIGHTS AND LOADS:

Excess Pier Weights ExcessPier_wtnLpxn

Lpzn h

n c s( ) hn Dif

LpxnLpzn

D c s( ) hn D( ) c+ otherwise

:=

ExcessPier_wtT

0.0( ) kN=

Applied load + Excess pier weight PtynPy

n ExcessPier_wtn

+:=

TOTAL VERTICAL LOAD:

PTotal WTotal

n

Ptyn+:=

PTotalT

1116.5 957.1 964.6 1036.0 1041.7 669.1 676.7( ) kN=



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Calculation Sheet

D.3 CHECK STABILITY j 0 rows ASD_Comb( ) 1..:=

SLIDING CHECK:

Passive Soil Pressure

Passivex T B Kp( ) s D T+( ) Kp s D( )+ 0.5:= Passivex 85.1kN=

Passivez T L Kp( ) s D T+( ) Kp s D( )+ 0.5:= Passivez 113.4kN=

Friction Forces

Frictionxj0kN PTotalj

0kNif

PTotaljWtsurc( ) otherwise

:=

FrictionxT

446.6 382.8 385.8 414.4 416.7 267.7 270.7( ) kN=

Frictionzj0kN PTotalj

0kNif

PTotalj Wtsurc( ) otherwise

:=

FrictionzT

446.6 382.8 385.8 414.4 416.7 267.7 270.7( ) kN=

Factor of Safety:

FSSL.xj

Passivex Frictionxj+

n

Fxn

j

round

n

Fxn

j

3,

0kNif

"INFINITY" otherwise

:=

n

Fxn

j

FSSL.x

T

=FSSL.x

Check_FSSLxj"N.A." FSSL.xj

"INFINITY"=if

"OK,Safe against sliding @ X" FSSL.xj1.5if

"N.G. Redesign" otherwise

otherwise

:= FSSL.x Check_FSSLx=Check_FSSLx

FSSL.zj

Passivez Frictionzj+

n

Fzn

j

round

n

Fzn

j

3,

0kNif


:=

n

Fzn

j

FSSL.zT

=FSSL.z



7/38

Calculation Sheet

Check_FSSLzj"N.A." FSSL.zj

"INFINITY"=if

"OK,Safe against sliding @ Z" FSSL.zj1.5if


otherwise

:= FSSL.z Check_FSSLz=Check_FSSLz

UPLIFT CHECK:

Upward Loads

Py.upnUp

jif Py

n( )j0 kN> Py

n( )j, 0 kN,

Upliftn

Up

j 0 6..for

Upliftn

:=

Py.upT

0.0

0.0

0.0

0.0

0.0

0.0

0.0

kN=

Downward Loads

Pty.downjPTotalj

n

Py.upn

j

+ Wtsurc:=

Pty.downT

1116.5 957.1 964.6 1036.0 1041.7 669.1 676.7( ) kN=

Pty.upliftj

n

Py.upn

j

:=

Pty.upliftT

0.0 0.0 0.0 0.0 0.0 0.0 0.0( ) kN=

Factor of Safety:

FSULj

Pty.downj

Pty.upliftjPty.upliftj 0kN>if


:= FSUL"INFINITY"

"INFINITY"

"INFINITY"

"INFINITY"

"INFINITY"

"INFINITY"

"INFINITY"

=



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Calculation Sheet

Check_FSULj"N.A." FSULj

"INFINITY"=if

"OK,Safe against sliding @ X" FSULj1.2if


otherwise

:= Check_FSUL"N.A."

"N.A."

"N.A."

"N.A."

"N.A."

"N.A."

"N.A."

=

OVERTURNING ABOUT X-AXIS CHECK:

Moment due to Py:

MexnPtyn

Zpn:=

n

Mexn

399.87

320.13

323.90

359.59

362.43

176.17

179.94

kN m=Mex

T

399.87

320.13

323.90359.59

362.43

176.17

179.94

kN m=

Due to Fz and Mx:

MoxnFz

n h

nT+( ) Mxn+:=

MoxT

9.68

4.25

60.86

6.10

42.72

2.57

62.54

kN m=

n

Moxn

9.68

4.25

60.86

6.10

42.72

2.57

62.54

kN m=

Eccentricity:

ezj

n

Mexn

j n

Moxn

j

+

PTotalj

:=

ezT

0.367 0.339 0.273 0.353 0.307 0.267 0.174( ) m=



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Calculation Sheet

Overturning Moment due to Py:

Mot.xn

OTj

Ptyn( )jB

2Zpn

Zpn0 mif

OTj

Ptyn( )j

B

2

ezj0mif

Zpn0m=if

Ptyn( )j0 kNif

OTj

Ptyn( )jB2

Zpn

MOT.xj0 kN mif

OTj

0 kN m otherwise

j 0 6..for

OT

:=



10/38

Calculation Sheet

Mrm.x

T

799.7

640.3

1295.6

719.21449.7

352.3

719.8

kN m=

nMrm.xn

799.7

640.3

1295.6

719.21449.7

352.3

719.8

kN m=

Total Resisting Moment about X-axis:

MRM.x

n

Mrm.xn Wtbase Wtsoil+( )B

2+:=

MRM.xT

1274.9 1115.5 1770.8 1194.4 1924.9 827.5 1195.0( ) kN m=

Factor of Safety:

FSOT.xj

MRM.xj

MOT.xj

MOT.xj0 kN mif


:=

FSOT.xT

131.7 262.8 29.1 195.6 45.1 321.4 19.1( )=

Check_FSOTxj"N.A." FSOT.xj

"INFINITY"=if

"OK,Safe against overturning @ X" FSOT.xj1.5if


otherwise

:=

Check_FSOTx"OK,Safe against overturning @ X"

"OK,Safe against overturning @ X"






=

OVERTURNING ABOUT Z-AXIS CHECK:

Moment due to Py:

MeznPtyn

Xpn:=



11/38

Calculation Sheet

MezT

0.00

0.00

0.00

0.00

0.000.00

0.00

kN m=

n

Mezn

0.00

0.00

0.00

0.00

0.000.00

0.00

kN m=

Due to Fx and Mz:

MoznFx

nhn

T+( ) Mzn+:=

MozT

3.0

24.4

2.9

16.6

3.8

25.4

1.9

kN m=

n

Mozn

3.0

24.4

2.9

16.6

3.8

25.4

1.9

kN m=

Eccentricity:

exj

n

Mezn

j n

Mozn

j

+

PTotalj

:=

ex

T

0.003 0.026 0.003 0.016 0.004 0.038 0.003( ) m=



12/38

Calculation Sheet

Overturning Moment due to Py:

Mot.zn

OTj

Ptyn( )j

L

2Xpn

Xpn0 mif

OTj

Ptyn( )j

L

2

ezj0mif

Xpn0m=if

Ptyn( )j 0 kNif

OTj

Ptyn( )jL

2Xpn

+

MOT.zj0 kN mif

OTj

0 kN m otherwise

j 0 6..for

OT

:=



13/38

Calculation Sheet

Mrm.z

T

1599.5

1280.5

1295.6

1438.41449.7

704.7

719.8

kN m=n

Mrm.zn

1599.5

1280.5

1295.6

1438.41449.7

704.7

719.8

kN m=

Total Resisting Moment about X-axis:

MRM.z

n

Mrm.zn Wtbase Wtsoil+( )L

2+:=

MRM.zT

2233.1 1914.1 1929.2 2072.0 2083.3 1338.3 1353.4( ) kN m=

Factor of Safety:

FSOT.zj

MRM.zj

MOT.zj

MOT.zj0 kN mif


:=

FSOT.zT

751.872 78.350 676.919 124.742 541.821 52.667 723.733( )=

Check_FSOTzj"N.A." FSOT.zj

"INFINITY"=if

"OK,Safe against overturning @ Z" FSOT.zj1.5if


otherwise

:=

Check_FSOTz"OK,Safe against overturning @ Z"

"OK,Safe against overturning @ Z"






=

CALCULATE FOOTING STABILITY



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Calculation Sheet

TOTAL RESULTANT LOAD AND ECCENTRICITIES:

Total Vertical Load PTotalT

1116.5 957.1 964.6 1036.0 1041.7 669.1 676.7( ) kN=

Eccentricity along X-axisex

T

0.003

0.026 0.003

0.016 0.004

0.038 0.003

( ) m=

Eccentricity along Z-axis ezT

0.367 0.339 0.273 0.353 0.307 0.267 0.174( ) m=

K Coefficient

Using K coefficient

ex

L0.012=

ez

B0.268=

Kj

1.754

1.737

1.574

1.748

1.648

1.612

1.356

=

hence qmax = Kj

PTotalj

B L

163.21

138.51

126.54

150.95

143.03

89.90

76.45

kPa

=

OVERTURNING CHECK:

Resisting Moment about X-axis MRM.xT

1274.9 1115.5 1770.8 1194.4 1924.9 827.5 1195.0( ) kN m=

Overturning Moment about X-axis MOT.xT

9.7 4.2 60.9 6.1 42.7 2.6 62.5( ) kN m=

Factor of Safety FSOT.xT

131.708 262.768 29.094 195.64 45.059 321.375 19.109( )=

FSOT.xj

131.7

262.8

29.1

195.6

45.1

= FSOT.xj>=? 1.5

"YES!.. SATISFACTORY"







=



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Calculation Sheet

.

19.1

Resisting Moment about Z-axis MRM.zT 2233.1 1914.1 1929.2 2072.0 2083.3 1338.3 1353.4( ) kN m=

Overturning Moment about Z-axis MOT.zT

3.0 24.4 2.9 16.6 3.8 25.4 1.9( ) kN m=

Factor of Safety FSOT.zT

751.87 78.35 676.92 124.74 541.82 52.67 723.73( )=

FSOT.zj

751.9

78.4

676.9

124.7

541.8

52.7

723.7

= FSOT.zj>=? 1.5








=

SLIDING CHECK:

Passive Soil Pressure along X-axis Passivex 85.1kN=

Friction Force along X-axis FrictionxT

446.6 382.8 385.8 414.4 416.7 267.7 270.7( ) kN=

Factor of Safety FSSL.xj=FSSL.x FSSL.xj

>=? 1.5=FSSL.x

Passivez 113.4kN=Passive Soil Pressure along Z-axis

FrictionzT

446.6 382.8 385.8 414.4 416.7 267.7 270.7( ) kN=Friction Forces along Z-axis

Factor of Safety FSSL.zj=FSSL.z FSSL.zj

>=? 1.5=FSSL.z



16/38

Calculation Sheet

UPLIFT CHECK:

Downward Force Pty.downT

1116.5 957.1 964.6 1036.0 1041.7 669.1 676.7( ) kN=

Uplift Force Pty.upliftT

0.0 0.0 0.0 0.0 0.0 0.0 0.0( ) kN=

Factor of Safety FSULj

"INFINITY"

"INFINITY"

"INFINITY"

"INFINITY"

"INFINITY"

"INFINITY"

"INFINITY"

= FSULj>=? 1.2

"N.A."

"N.A."

"N.A."

"N.A."

"N.A."

"N.A."

"N.A."

=



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Calculation Sheet

CALCULATE SOIL BEARING PRESSURE

NO OF BEARING CORNERS

b a( )

1

6

a2

6

a3

12+

1 aa2

3+

:=

NBCj

topez b

4exj

L

B

topex b

4ezj

B

L

3 exjtopex ezj

topez ezjB

Lexj

L

6+>if

4 ezj

B

L exjL

6+if

1 ezj

B

4 exj

L

4if

2 otherwise

:= NBCT

4 4 4 4 4 4 4( )=

Solution for Biaxial Resultant Eccentricity for 1, 2, or 3 Corners with Zero Pressure ( when: ABS(6*ex/L)+ABS(6*ey/B) > 1.0 )

BIAX2

Check Ecc.: 0.351 ABS(6*ex/L)+ABS(6*ey/B)


18/38

Calculation Sheet

P1j

P2j

P3j

P4j

P1

j

PTotalj

L B1

6 exj

L+

6 ezj

B+

P2j

PTotalj

L B1

6 exj

L+

6 ezj

B+

P3j

PTotalj

L B1

6 exj

L

6 ezj

B+

P4j

PTotalj

L B1

6 exj

L

6 ezj

B+

Eccj1if

P1j

P1jkPa

P2j

P2jkPa

P3j

P3jkPa

P4j

P4jkPa

otherwise

exj0 m( ) ezj 0 m( )if

P1j

max

PTotalj

L B1

6 exj

L+

6 ezj

B+

0 kPa,

P2j

max

PTotalj

L B1

6 exj

L+

6 ezj

B+

0 kPa,

P3j

max

PTotalj

L B1

6 exj

L

6 ezj

B+

0 kPa,

P4j

max

PTotalj

L B1

6 exj

L

6 ezj

B+

0 kPa,

otherwise

P1j

P2j

P3j

P4j

:=P1

j

P2j

P3j

P4j

T24.42 160.93 161.67 25.16( )

28.75 136.87 130.76 22.64( )

36.19 123.87 124.58 36.9( )

27.46 149.36 145.2 23.31( )33.04 139.61 140.57 34( )

29.15 88.73 82.38 22.79( )

36.59 75.73 76.19 37.06( )

kPa=



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Calculation Sheet

Casej

dx dxjm

dz dzj m

Casej

1 dx L>( ) dz B>( )if

Casej

2 dx L>( ) dz B( )if

Casej

3 dx L( ) dz B>( )if

Casej

4 dx L( ) dz B( )if

Eccj1.0>if

Casej

"N.A." otherwise

exj0m( ) ezj 0m( )if

Casej

"N.A." otherwise

:=

dz

Case=Case

dxj

dzj

"N.A."

"N.A."

Casej

"N.A."=if

dxjm

dzjm

otherwise

:= Casedxj

dzj

T

=dx



20/38

Calculation Sheet

L1j

L2j

L1j

L

L2j

B

Casej

"N.A."=if

L1jdzj

B( )dxj

dzj

L2jdxj

L( )dzj

dxj

Case 1=if

L1jdxj

L( )dzj

dxj

L2j dzj

Case 2=if

L1jdzj

B( )dxj

dzj

L2jdxj

Case 3=if

L1jdxj

L2jdzj

Case 4=if

otherwise

L1j

L2j

:= Case

L1j

L2j

T

=

L1

Brg_Areaj

100% Casej

"N.A."=if

L BL L1j

( ) B L2j( )2

L B100 % Case

j1=if

L L1jL2j

+( )2

L B100 % Case

j2=if

B L1j L2j+( )2

L B100 % Case

j3=if

dxjdzj

2

L B100 % Case

j4=if

otherwise

:= Case



21/38

Calculation Sheet

Brg_Planj

"Case NA" Casej

"N.A."=if

"Case 1" Casej

1=if

"Case 2" Case

j

2=if

"Case 3" Casej

3=if

"Case 4" Casej

4=if

otherwise

:= Case

Brg_PlanT

=Brg_Plan

CaseT

=Case

P kPa=Pdx

dz

T

m=dx L1

L2

T

m=L1

P_Eqnj

"P 1" Eccj1if

"P 2" otherwise

exj0 m( ) ezj 0 m( )if

"P 3" exj

0 m

( )ezj

0 m=

( ) ex

j

0 m=

( )ezj

0 m

( )+if

"P 4" otherwise

:=

P_EqnT

"P 1" "P 1" "P 1" "P 1" "P 1" "P 1" "P 1"( )=



22/38

Calculation Sheet

CALCULATE SOIL BEARING PRESSURE

BEARING AREA:

Dist x dxT

=dx

Dist z dzT

=dz

Brg. L1 L1T =L1

Brg. L2 L2T

=L2

%Brg. Area Brg_AreaT

%=Brg_Area

Biaxial Case CaseT

=Case

GROSS SOIL BEARING CORNER PRESSURES:

P1T

24.42 28.75 36.19 27.46 33.04 29.15 36.59( ) kPa=

P2T

160.93 136.87 123.87 149.36 139.61 88.73 75.73( ) kPa=

P3T

161.67 130.76 124.58 145.20 140.57 82.38 76.19( ) kPa=

P1j

24.42

28.75

kPa

= P2j

160.93

136.87

kPa

= P3j

161.67

130.76

kPa

= P4j

25.16

22.64

kPa

=



23/38

Calculation Sheet

.

27.46

33.04

29.15

36.59

.

149.36

139.61

88.73

75.73

.

145.20

140.57

82.38

76.19

.

23.31

34.00

22.79

37.06

MAXIMUM NET SOIL PRESSURE:

Pmax.netjmax P1

jP2

j, P3

j, P4

j,( ) s D T+( ):=

Check_qsjif Pmax.netj

qs "OK, q max < q allowable", "N.G. Redesign",( ):=

Pmax.netj

138.27

113.47

101.18

125.96

117.17

65.33

52.79

kPa

= Check_qsj

"OK, q max < q allowable"







= Pmax.netj


24/38

Calculation Sheet

CALCULATE ULTIMATE LOADS

E.2 TOTAL FACTORED VERTICAL LOAD AND ECCENTRICITIES Use Load Factor LF 1.4:=

FOUNDATION, SOIL AND SURCHARGE:

WuTotal WTotal LF:= WuTotal 443.5kN=

TOTAL VERTICAL LOAD:

Applied load + Excess pier weight PutynPu

n ExcessPier_wtn

LF+:=

PutyT

32.1( ) kN= Puty 32.1kN=

PuTotal WuTotal Puty+:= PuTotal 475.6kN=

ECCENTRICITY ALONG Z-AXIS:

Moment due to Py: Muexn

Putyn

Zpn

:=

MuexT

16.1( ) kN m= Muex 16.1 kN m=

Due to Fz and Mx: MuoxnVuz

n h

nT+( ) Muxn+:=

MuoxT

3.2( ) kN m= Muox 3.2kN m=

Eccentricity: euz

Muex Muox+PuTotal

:= euz 0.027m=

ECCENTRICITY ALONG X-AXIS:

Moment due to Py:Muezn Putyn Xpn:=

MuezT

0.0( ) kN m= Muez 0.0kN m=

Due to Fx and Mz: MuoznVux

nhn

T+( ) Muzn+:=

MuozT

6.4( ) kN m= Muoz 6.4kN m=

Eccentricity: eux

Muez Muoz+PuTotal

:= eux 0.014m=

CALCULATE ULTIMATE LOADS

CALCULATE ULTIMATE SOIL BEARING

TOTAL RESULTANT ULTIMATE LOAD AND ECCENTRICITIES:

Total Vertical Load PuTotal 475.6kN=

Eccentricity along X-axis eux 0.014m=

Eccentricity along Z-axis euz 0.027m=



25/38

Calculation Sheet

ULTIMATE SOIL BEARING CORNER PRESSURES:

Pu138.31kPa=

Pu242.57kPa=

Pu340.96kPa=

Pu436.70kPa=

F. CHECK SHEAR

F.1 FOOTING ANALYSIS ALONG X-DIRECTIONS

L 4m=

quL

Pu3Pu4

+

2:= quR

Pu1Pu2

+

2:=

quL 38.8kPa= quR 40.4kPa=

qx CALCULATIONS

q at critical sections:

q d1n( )39.9 kPa

= q d6n( )39.4 kPa

= q d2n( )39.8 kPa

= q d5n( )39.5 kPa

= q d3n( )39.7 kPa

= q d4n( )39.5 kPa

=



26/38

Calculation Sheet

Diagrams

Soil Bearing Pressure Diagram

L (mm)

qu(kPa)

0.25m1

0.25 m1

max B L,( )

mm

0


L (mm)

qu(kPa)

0.25m1

0.25 m1

max B L,( )

mm

0




27/38

Calculation Sheet

Shear Diagram

L (mm)

Vu

(kN)

0.25m1

0.25 m1

max B L,( )

mm

0

Shear Diagram

L (mm)

Vu

(kN)

0.25m1

0.25 m1

max B L,( )

mm

0



28/38

Calculation Sheet

Moment Diagram

L (mm)

Mu(

kN-m)

0.25m1

0.25 m1

max B L,( )

mm

0

Moment Diagram

L (mm)

Mu(

kN-m)

0.25m1

0.25 m1

max B L,( )

mm

0



29/38

Calculation Sheet

Max Beam Shear & Bending Moment

Wide-beam shear along Z direction Max negative moment at face of support Muneg.z 14.9kN m=

VuLz 8.6kN= VuRz 12.9kN= Max positive moment: Mupos.z kN m=Mupos.z

F.2 FOOTING ANALYSIS ALONG Z-DIRECTIONS

B 3m=

quL

Pu1Pu4

+

2:= quR

Pu3Pu2

+

2:=


qz CALCULATIONS

q at critical sections:

q d1n( )41.3 kPa

= q d6n( )39.4 kPa

= q d2n( )41.0 kPa

= q d5n( )39.7 kPa

= q d3n( )40.7 kPa

= q d4n( )40.0 kPa

=



30/38

Calculation Sheet

Diagrams


B (mm)

qu(kPa)

0.25m1

0.25 m1

max B L,( )

mm

0


B (mm)

qu(kPa)

0.25m1

0.25 m1

max B L,( )

mm

0




31/38

Calculation Sheet

Shear Diagram

B (mm)

Vu(kN)

0.25m1

0.25 m1

max B L,( )

mm

0

Shear Diagram

B (mm)

Vu(kN)

0.25m1

0.25 m1

max B L,( )

mm

0



32/38

Calculation Sheet

Moment Diagram

B (mm)

Mu(

kN-m)

0.25m1

0.25 m1

max B L,( )

mm

0

Moment Diagram

B (mm)

Mu(

kN-m)

0.25m1

0.25 m1

max B L,( )

mm

0



33/38

Calculation Sheet

Max Beam Shear & Bending Moment

Wide-beam shear along X direction Max negative moment at face of support Muneg.x 8.4kN m=

VuLx 8.0kN=

VuRx 6.1kN= Max positive moment:

Mupos.x kN m=

Mupos.x

F.4 PUNCHING SHEAR

Capacity reduction factor v 0.85:=

Shear strength provided

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

VcT

1167( ) kN=

Punching Shear

Perimeter around column/pier:

Along x-direction boxT

0.915( ) m=

Along z-direction bozT

0.915( ) m=

Area of Punching Shear:

Apnboxn

bozn:= Ap

T0.837( ) m

2=

Total force from column/pier:

PuynPutyn

LF ApnT c D s+ Q+( )+:=

Puy

T

63.0( ) kN=q at d/2 distance from supports:

Along x-directionqx.2

T39.8( ) kPa=

qx.5T

39.5( ) kPa=

Along z-directionqz.2

T41.0( ) kPa=

qz.5T

39.7( ) kPa=

Total force acting on punched area

Rqn

1

2max qx.5n

qx.2n+ qz.5n

qz.2n+,( ) Apn:=

RqT

33.8( ) kN=

Net punching shear:

VupnPuyn

Rqn:=

VupT

29.3( ) kN=



34/38

Calculation Sheet

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 8.6kN= VuRz 12.9kN=

Shear strength provided Vnb v 0.17 f c MPa B de( ):= Vnb 985.4kN=


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 8.0kN= VuRx 6.1kN=

Shear strength provided Vnb v 0.17 f c MPa L de( ):= Vnb 1313.8kN=


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 14.9kN m=

Moment at face of pedestal Z-direction Muneg.x 8.4kN 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 ds1

2

As fy

0.85 f c b

=

Mr max Muneg.z 0.001 kN m,( ):= Mr 14.9kN m= b B:=

Reinforcement provided

Size of bar barx 6 Bar diameter diabarx20mm=



35/38

Calculation Sheet

Proposed bar spacing Sx.bot 200mm:= Bar area Asbarx314mm

2=

Area of steel provided As

Asbarx

b

Sx.bot:= As 4710mm

2=

Distance from extreme compressive fiberto centroid of reinforcing steel

d T cov 0.5 diabarx:= d 415mm=

Solve the quadratic equation for the areaof steel required

Given Mr f As fy d1

2

As fy

0.85 f c b

=

As.reqd Find As( ):= As.reqd 96mm2

=

Minimum reinforcement As.min min min b d4

3As.reqd,

:= As.min 129mm2

=

Temperature reinforcement As.temp temp bT

2:= As.temp 1350mm

2=

Reinforcing steel required As.reqd max A s.reqdAs.min, As.temp,( ):= As.reqd 1350mm2

=

Check As provided As >=? As.reqd "YES!.. SATISFACTORY"=

Bars in Z-direction


2

As fy

0.85 f c b

=

Mr max Muneg.x 0.001 kN m,( ):= Mr 8.4kN m= b L:=


Size of bar barz 6 Bar diameter diabarz20mm=

Proposed bar spacing Sz.bot 200mm:= Bar area Asbarz314mm

2=

Area of steel provided AsAsbarz b

Sz.bot:= As 6280mm

2=


d T cov diabarx

0.5 diabarz

:= d 395mm=


Given Mr f As fy d1

2

As fy

0.85 f c b

=

As.reqd Find As( ):= As.reqd 57mm2

=


3As.reqd,

:= As.min 76mm2

=


2:= As.temp 1800mm

2=

Reinforcing steel required As.reqd max A s.reqdAs.min, As.temp,( ):= As.reqd 1800mm2=

Check As provided As >=? As.reqd "YES!.. SATISFACTORY"=

G.3 TOP REINFORCEMENTS

Bars in X-direction


2

As fy

0.85 f c b

=

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



36/38

Calculation Sheet


Size of bar barx.top 6:= Bar diameter diabarx.top20mm=

Proposed bar spacing Sx.top 200mm:= Bar area Asbarx.top314mm

2=


Asbarx.top

b

Sx.top:= As 4710mm

2=


d T cov 0.5 diabarx.top

:= d 415mm=


Given Mr f As fy d1

2

As fy

0.85 f c b

=

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

=As.reqd


3As.reqd,

:= As.reqd As.min mm2

=As.min

Temperature reinforcement As.temp

temp

bT

2:= A

s.temp1350mm

2=

Reinforcing steel required As.reqd max A s.reqdAs.min, As.temp,( ):= As.reqd As.reqd mm2

=As.reqd

Check As provided As >=? As.reqd=As.reqd

Bars in Z-direction


2

As fy

0.85 f c b

=

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


Size of bar barz.top 6:= Bar diameter diabarz.top20mm=

Proposed bar spacing Sz.top 200mm:= Bar area Asbarz.top314mm2=


Asbarz.top

b

Sz.top:= As 6280mm

2=


d T cov diabarx.top

0.5 diabarz.top

:= d 395mm=


Given Mr f As fy d1

2

As fy

0.85 f c b

=

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

=As.reqd

Minimum reinforcement As.min min min b d 43

As.reqd, :=As.reqd As.min mm2=As.min


2:= As.temp 1800mm

2=

Reinforcing steel required As.reqd max A s.reqdAs.min, As.temp,( ):= As.reqd As.reqd mm2

=As.reqd

Check As provided As >=? As.reqd=As.reqd



37/38

Calculation Sheet

H. SUMMARY/DETAILS

PLAN REINFORCEMENTS

cL Z-Axis

cLX-Axis

L 4.000m=

BARS PARALLEL TO 'L'

B 3.000m=

BARS PARALLEL TO 'B'



38/38

Calculation Sheet

SUMMARY OF REINFORCEMENTS:

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

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

FOOTING DIMENSIONS: L 4.000m= B 3.000m= T 0.500m=

ELEVATION ALONG X-AXIS

BARS PARALLEL TO

T 0.500m=

BARS PARALLEL TO

L 4.000m=

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Mathcad - Footing F-2