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BESTARI CONSULTING ENGINEERS SDN BHD; 9-3-2011, Wednesday, 11:45:14

JABATAN BOMBA, KUANTAN - BANGUNAN UTAMA

FILE PATHNAME : \\Bariah\DATA\PROJECT AUTOCAD-DRAWING\74_JABATAN_BOMBA\ESTEEM

\D. BOMBA-BANGUNAN UTAMA_LATEST\Copy of D. BOMBA - BANGUNAN UTAMA\TNB,PJ,DW.gcd;

Pile Footing Detailed Design Calculation:

Code of Practice Used: BS8110:1997

The Design Parameters used:

Steel fy = 460 N/mm^2; Concrete fcu = 45 N/mm^2Concrete cover, cov = 50 mmRebar maximum spacing = 300 mm, Minimum spacing = 100 mmSteel maximum bar size = 25 mm, Minimum bar size = 16 mmShear capacity at stump face, 0.8*sqrt(fcu) = 5.37 N/mm^2

Rebar percentage used for Shear Design = 0.30Design Shear Stress, vc = 0.79*(100As/bd)^(1/3)*(400/d)^(1/4)/Ym

The Following Design Parameters are used for Bending Moment Design:Maximum Concrete strain, Ecc = 0.0035Average Concrete Stress Above Neutral Axis, k1 = 17.71 N/mm^2Concrete Lever Arm Factor, k2 = 0.4419Limiting Effective Depth Factor, cb = 0.50Limiting Concrete Moment Capacity Factor, kk1

= cb*k1*(1-cb*k2) = 0.50*17.71(1-0.50*0.4419) = 6.9004 N/mm^2k2/k1 Factor, kkk = 0.0249

COLUMN FOUNDATION DESIGN:

Location of Footing: 10--A

Dead Load, DL = 129.5; Live Load, LL = 57.9; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 142.5; Live Load, LL = 63.7

Total Unfactored Load = 142.5 + 63.7 + 0.0 = 206.2 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/271) = 1.474Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.474)^1/4*(1.600)^1/3 )/1.25 = 0.545 N/mm^2

Based on preliminary pile-cap size of 600 X 600 X 521 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(0.600X0.600X0.521)x24 = 5.0 kNTotal No of Piles required = 211.1/(60.0*9.81) = 1

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 860.1/(900*900) = 1.062 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

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Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/271) = 1.474Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.474)^1/4*(1.600)^1/3 )/1.25 = 0.545 N/mm^2

Stump Size, A & B Dimensions,mm = 230 mm x 230 mm

Design Shear stress based on d, 271 mm = 0.545 N/mm^2

Ratio of shear plane from stump face to effective depth, p = 0.496Distance of shear plane from stump face, a = 134 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*271*0.545/134 = 1.100 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*1.100*271*(4*0.496*271+230+230) = 595.8 kN

Load Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =1.062 *(2*0.496*271+230)*(2*0.496*271+230) = 264.3 kN

Ultimate Load = Total load,P - Pi = 860.1 - 264.3 = 595.8 kN O.K. !!

Required effective depth to satisfy punching shear, d = 271 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 860.1-1.062*230*230/1000 = 803.9 kN

Stump Face Shear Capacity, Pc = 2*5.367*163(230+230)/1000 = 803.9 kN

Effective Depth required at stump face = 163 mm

Summary: Effective depth for Punching Shear Stump Shear

271 163

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/271^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 25.6 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*25.6 = 454.04 kN

Steel area required, As = Fc/(fyy*fy) = 454.04/(0.95*460) = 1039 mm^2

Moment capacity = Fc(d-k2.x) = 454.04(271-0.4419*25.6)/1000 = 118.1 kNm

Steel area required, As = 1039 mm^2

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/271^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 25.6 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*25.6 = 454.04 kN

Steel area required, As = Fc/(fyy*fy) = 454.04/(0.95*460) = 1039 mm^2

Moment capacity = Fc(d-k2.x) = 454.04(271-0.4419*25.6)/1000 = 118.1 kNm

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Steel area required, As = 1039 mm^2

Location of Footing: 10-A

Dead Load, DL = 512.8; Live Load, LL = 106.6; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 564.1; Live Load, LL = 117.3

Total Unfactored Load = 564.1 + 117.3 + 0.0 = 681.4 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/328) = 1.221Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.221)^1/4*(1.600)^1/3 )/1.25 = 0.520 N/mm^2

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/490) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/144) = 2.785Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.785)^1/4*(1.600)^1/3 )/1.25 = 0.639 N/mm^2

Based on preliminary pile-cap size of 1500 X 600 X 869 to calculate Selfweight,SW:

Selfweight of PileCap,SW = 1.10 x(1.500X0.600X0.869)x24 = 20.6 kNTotal No of Piles required = 702.0/(60.0*9.81) = 2

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 1688.0/(1800*900) = 1.042 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/328) = 1.221Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.221)^1/4*(1.600)^1/3 )/1.25 = 0.520 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 328 mm = 0.520 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.546Distance of shear plane from stump face, a = 179 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*328*0.520/179 = 0.954 N/mm^2

Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =2*0.954*328*(4*0.546*328+450+450) = 1008.8 kN

Load Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =1.042 *(2*0.546*328+450)*(2*0.546*328+450) = 679.2 kN

Ultimate Load = Total load,P - Pi = 1688.0 - 679.2 = 1008.8 kN O.K.

!!

Required effective depth to satisfy punching shear, d = 328 mm

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Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 1688.0-1.042*450*450/1000 = 1477.0 kNStump Face Shear Capacity, Pc = 2*5.367*153(450+450)/1000 = 1477.0 kN

Effective Depth required at stump face = 153 mm

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/490) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,490 mm = 0.495 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.690Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.495/0.690 = 0.717 N/mm^2

Required effective depth to satisfy flexure shear, d = 490 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.717*490*900 = 632.2 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =1.042 *(2*0.690*490+450)*900 = 1055.8 kN

Ultimate Load = Total load - above = 1688.0 - 1055.8 = 632.2 kN

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/144) = 2.785Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.785)^1/4*(1.600)^1/3 )/1.25 = 0.639 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,144 mm = 0.639 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.780Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.639/0.780 = 0.820 N/mm^2

Required effective depth to satisfy flexure shear, d = 144 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.820*144*1800 = 423.8 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.042 *(2*0.780*144+450)*1800 = 1264.3 kN

Ultimate Load = Total load - above = 1688.0 - 1264.3 = 423.8 kN

Summary: Effective depth for Punching Shear Stump Shear Flexural Shear

328 153 490

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Total No of Piles used = 2

Total ultimate pile load = 1.5*2*60.0*9.81 = 1765.8 kN

Total ultimate X-pile load = 1.5*1.00*60.0*9.81 = 882.9 kN

Total ultimate Y-pile load = 1.5*0.00*60.0*9.81 = 0.0 kN

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total Moment about Y-axis = 844.0 kN *0.225 m = 189.9 kNm

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Moment about Y-axis = 189.9 kN/0.500 m = 379.8 kNm/m

Y-Distance from piles' centroid to column face = 225 - 450/2 = 0 mm

Total Moment about X-axis = -1.$ kN *0.000 m = 0.0 kNm

Moment about X-axis = 0.0 kN/1.400 m = 0.0 kNm/m

STUMP FACE SHEAR CAPACITY: Equivalent piles = 2.00 ; Thickness,d = 175 mm

Total ultimate pile load,Pu = 1.5*2.00*60.0*9.81 = 1688.0 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2

Total ultimate shear capacity,TVu = 2*5.37*175*(450+450)/1000 = 1688.0 kN

TVu = 1688.0 ; Pu = 1688.0 ; i.e. Minimum thickness required = 175 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 619 mm; Width

= 500 mm

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 844.0 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*619*0.49/225 = 2.72 N/mm^2

Total ultimate shear capacity,TVu = 2.72*619*500/1000 = 844.0 kN

TVu = 844.0 ; Pu = 844.0 ; i.e. Minimum thickness required = 619 !!!

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/619) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch2 1400 600 619 490 619 0 175 0

Design for Bending Moment: 379.8/1.00 = 379.8 kNm

Mu/bd^2 = 379.8*1000/619^2 = 0.990

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.990 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.990 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 51.4 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*51.4 = 910.48 kN

Steel area required, As = Fc/(fyy*fy) = 910.48/(0.95*460) = 2083 mm^2

Moment capacity = Fc(d-k2.x) = 910.48(617-0.4419*51.4)/1000 = 541.5 kNm

Steel area required, As = 2083 mm^2

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/619^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 51.4 mm

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Concrete Compression Force, Fc = k1.b.x = 17.71*51.4 = 910.48 kN

Steel area required, As = Fc/(fyy*fy) = 910.48/(0.95*460) = 2083 mm^2

Moment capacity = Fc(d-k2.x) = 910.48(617-0.4419*51.4)/1000 = 541.5 kNm

Steel area required, As = 2083 mm^2

Location of Footing: 10-B

Dead Load, DL = 1186.9; Live Load, LL = 207.9; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 1305.6; Live Load, LL = 228.7

Total Unfactored Load = 1305.6 + 228.7 + 0.0 = 1534.3 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/493) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Based on preliminary pile-cap size of 1500 X 1300 X 868 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(1.500X1.300X0.868)x24 = 44.7 kN

Total No of Piles required = 1579.0/(60.0*9.81) = 3

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 2523.9/(1800*1800) = 0.779 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/493) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 493 mm = 0.495 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.545Distance of shear plane from stump face, a = 268 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*493*0.495/268 = 0.908 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*0.908*493*(4*0.545*493+450+450) = 1765.3 kN

Load Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =0.779 *(2*0.545*493+450)*(2*0.545*493+450) = 758.6 kN

Ultimate Load = Total load,P - Pi = 2523.9 - 758.6 = 1765.3 kN O.K.!!

Required effective depth to satisfy punching shear, d = 493 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 2523.9-0.779*450*450/1000 = 2366.1 kNStump Face Shear Capacity, Pc = 2*5.367*245(450+450)/1000 = 2366.1 kN

Effective Depth required at stump face = 245 mm

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Summary: Effective depth for Punching Shear Stump Shear

493 245

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Total No of Piles used = 3

Total ultimate pile load = 1.5*3*60.0*9.81 = 2648.7 kN

Total ultimate X-pile load = 1.5*1.00*60.0*9.81 = 882.9 kN

Total ultimate Y-pile load = 1.5*0.50*60.0*9.81 = 441.5 kN

X-Distance from piles' centroid to column face = 450 - 450/4 = 338 mm

Total Moment about Y-axis = 2152.7 kN *0.338 m = 726.6 kNm

Moment about Y-axis = 726.6 kN/1.279 m = 567.9 kNm/m

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mm

Total Moment about X-axis = 1308.7 kN *0.295 m = 385.6 kNm

Moment about X-axis = 385.6 kN/1.400 m = 275.4 kNm/m

Y - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 500 mm; Width

= 1000 mm

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 841.3 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*500*0.49/295 = 1.68 N/mm^2

Total ultimate shear capacity,TVu = 1.68*500*1000/1000 = 841.3 kN

TVu = 841.3 ; Pu = 841.3 ; i.e. Minimum thickness required = 500 !!!

STUMP FACE SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 261 mm

Total ultimate pile load,Pu = 1.5*3.00*60.0*9.81 = 2523.9 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2

Total ultimate shear capacity,TVu = 2*5.37*261*(450+450)/1000 = 2523.9 kN

TVu = 2523.9 ; Pu = 2523.9 ; i.e. Minimum thickness required = 261 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 618 mm; Width

= 500 mm

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 841.3 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*618*0.49/225 = 2.72 N/mm^2

Total ultimate shear capacity,TVu = 2.72*618*500/1000 = 841.3 kN

TVu = 841.3 ; Pu = 841.3 ; i.e. Minimum thickness required = 618 !!!

PUNCHING SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 477 mm

Total ultimate pile load, Pu = 1.5*3.00*60.0*9.81 = 2523.9 kN

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Enhanced shear Vc1 = VcFac*d*vc/a = 2.0*477*0.49/225 = 2.10 N/mm^2

X-Ultimate shear capacity, TVc1 = 2*2.10*477*(450+295)/1000 = 1491.4 kN

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Y - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 477 mm; Width

= 1400 mm

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mm

Enhanced shear Vc2 = VcFac*d*vc/a = 2.0*477*0.49/295 = 1.60 N/mm^2

Y-Ultimate shear capacity, TVc2 = 2*1.60*477*(450+225)/1000 = 1032.5 kN

Total ultimate shear capacity,TVu = TVc1 + TVc2 = 1491.4+1032.5 = 2523.9 kN

TVu = 2523.9 ; Pu = 2523.9 ; i.e. Minimum thickness required = 477 !!!

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/618) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch3 1400 1300 618 493 618 500 261 477

Design for Bending Moment: 567.9/1.00 = 567.9 kNm

Mu/bd^2 = 567.9*1000/618^2 = 1.484

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.484 ; 0.5*kk1 = 3.450Mu/bd^2 = 1.484 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 53.9 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*53.9 = 954.93 kN

Steel area required, As = Fc/(fyy*fy) = 954.93/(0.95*460) = 2185 mm^2

Moment capacity = Fc(d-k2.x) = 954.93(616-0.4419*53.9)/1000 = 566.0 kNm

Steel area required, As = 2185 mm^2

Design for Bending Moment: 567.9/1.00 = 567.9 kNm

Mu/bd^2 = 567.9*1000/618^2 = 1.484

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.484 ; 0.5*kk1 = 3.450

Mu/bd^2 = 1.484 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 53.9 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*53.9 = 954.93 kN

Steel area required, As = Fc/(fyy*fy) = 954.93/(0.95*460) = 2185 mm^2

Moment capacity = Fc(d-k2.x) = 954.93(616-0.4419*53.9)/1000 = 566.0 kNm

Steel area required, As = 2185 mm^2

Location of Footing: 10-C

Dead Load, DL = 1507.9; Live Load, LL = 325.3; Wind Load, WL = 0.0

After additional 10 percent load allowance

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Dead Load, DL = 1658.7; Live Load, LL = 357.8

Total Unfactored Load = 1658.7 + 357.8 + 0.0 = 2016.5 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/570) = 1.000

Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Based on preliminary pile-cap size of 1500 X 1500 X 819 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(1.500X1.500X0.819)x24 = 48.6 kNTotal No of Piles required = 2065.2/(60.0*9.81) = 4

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 3378.6/(1800*1800) = 1.043 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/570) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 570 mm = 0.495 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.450Distance of shear plane from stump face, a = 256 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*570*0.495/256 = 1.100 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*1.100*570*(4*0.450*570+450+450) = 2412.2 kN

Load Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =1.043 *(2*0.450*570+450)*(2*0.450*570+450) = 966.4 kN

Ultimate Load = Total load,P - Pi = 3378.6 - 966.4 = 2412.2 kN O.K.

!!

Required effective depth to satisfy punching shear, d = 570 mm

At Ratio of p = 0.460, enhanced shear stress, v = 1.076 N/mm^2Shear Capacity = 2*1.076*570*(4*0.460*570+450+450) = 2387.6 kN

Load Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =1.043 *(2*0.460*570+450)*(2*0.460*570+450) = 989.4 kN

Ultimate Load = Total load,P - Pi = 3378.6 - 989.4 = 2389.1 > 2387.6 kN. Not O.K.!!!!

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 3378.6-1.043*450*450/1000 = 3167.4 kNStump Face Shear Capacity, Pc = 2*5.367*328(450+450)/1000 = 3167.4 kN

Effective Depth required at stump face = 328 mm

Summary: Effective depth for Punching Shear Stump Shear

570 328

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Total No of Piles used = 4

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TVu = 1689.3 ; Pu = 1689.3 ; i.e. Minimum thickness required = 524 !!!

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/533) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch4 1400 1400 570 570 524 524 350 533

Design for Bending Moment: 407.2/1.00 = 407.2 kNm

Mu/bd^2 = 407.2*1000/570^2 = 1.255

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.255 ; 0.5*kk1 = 3.450Mu/bd^2 = 1.255 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 47.7 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*47.7 = 845.14 kN

Steel area required, As = Fc/(fyy*fy) = 845.14/(0.95*460) = 1934 mm^2

Moment capacity = Fc(d-k2.x) = 845.14(570-0.4419*47.7)/1000 = 463.6 kNm

Steel area required, As = 1934 mm^2

Design for Bending Moment: 407.2/1.00 = 407.2 kNm

Mu/bd^2 = 407.2*1000/570^2 = 1.255

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.255 ; 0.5*kk1 = 3.450Mu/bd^2 = 1.255 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 47.7 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*47.7 = 845.14 kN

Steel area required, As = Fc/(fyy*fy) = 845.14/(0.95*460) = 1934 mm^2

Moment capacity = Fc(d-k2.x) = 845.14(570-0.4419*47.7)/1000 = 463.6 kNm

Steel area required, As = 1934 mm^2

Location of Footing: 10-D

Dead Load, DL = 1710.4; Live Load, LL = 351.9; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 1881.4; Live Load, LL = 387.1

Total Unfactored Load = 1881.4 + 387.1 + 0.0 = 2268.5 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/569) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

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vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Based on preliminary pile-cap size of 1500 X 1500 X 819 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(1.500X1.500X0.819)x24 = 48.6 kNTotal No of Piles required = 2317.1/(60.0*9.81) = 4

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 3375.3/(1800*1800) = 1.042 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/569) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 569 mm = 0.495 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.450Distance of shear plane from stump face, a = 256 mm

Enhanced shear stress,v = fVcFac*d*vc/a = 1.0*569*0.495/256 = 1.100 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*1.100*569*(4*0.450*569+450+450) = 2410.4 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

1.042 *(2*0.450*569+450)*(2*0.450*569+450) = 965.0 kN

Ultimate Load = Total load,P - Pi = 3375.3 - 965.0 = 2410.4 kN O.K.

!!

Required effective depth to satisfy punching shear, d = 569 mm

At Ratio of p = 0.460, enhanced shear stress, v = 1.076 N/mm^2Shear Capacity = 2*1.076*569*(4*0.460*569+450+450) = 2385.9 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

1.042 *(2*0.460*569+450)*(2*0.460*569+450) = 988.0 kNUltimate Load = Total load,P - Pi = 3375.3 - 988.0 = 2387.4 > 2385.9 kN. Not O.K.!!!!

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 3375.3-1.042*450*450/1000 = 3164.4 kN

Stump Face Shear Capacity, Pc = 2*5.367*328(450+450)/1000 = 3164.4 kN

Effective Depth required at stump face = 328 mm

Summary: Effective depth for Punching Shear Stump Shear

569 328

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Total No of Piles used = 4

Total ultimate pile load = 1.5*4*60.0*9.81 = 3531.6 kN

Total ultimate X-pile load = 1.5*2.00*60.0*9.81 = 1765.8 kN

Total ultimate Y-pile load = 1.5*2.00*60.0*9.81 = 1765.8 kN

X-Distance from piles' centroid to column face = 450 - 450/4 = 338 mm

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Total Moment about Y-axis = 1687.7 kN *0.338 m = 569.6 kNm

Moment about Y-axis = 569.6 kN/1.400 m = 406.8 kNm/m

Y-Distance from piles' centroid to column face = 450 - 450/4 = 338 mm

Total Moment about X-axis = 1687.7 kN *0.338 m = 569.6 kNm

Moment about X-axis = 569.6 kN/1.400 m = 406.8 kNm/m

STUMP FACE SHEAR CAPACITY: Equivalent piles = 4.00 ; Thickness,d = 349 mm

Total ultimate pile load,Pu = 1.5*4.00*60.0*9.81 = 3375.3 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2

Total ultimate shear capacity,TVu = 2*5.37*349*(450+450)/1000 = 3375.3 kN

TVu = 3375.3 ; Pu = 3375.3 ; i.e. Minimum thickness required = 349 !!!

PUNCHING SHEAR CAPACITY: Equivalent piles = 4.00 ; Thickness,d = 533 mm

Total ultimate pile load, Pu = 1.5*4.00*60.0*9.81 = 3375.3 kN

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Enhanced shear Vc1 = VcFac*d*vc/a = 2.0*533*0.49/225 = 2.34 N/mm^2

X-Ultimate shear capacity, TVc1 = 2*2.34*533*(450+225)/1000 = 1687.7 kN

Y - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 4.00 ; Thickness,d = 533 mm; Width

= 1400 mm

Y-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Enhanced shear Vc2 = VcFac*d*vc/a = 2.0*533*0.49/225 = 2.34 N/mm^2

Y-Ultimate shear capacity, TVc2 = 2*2.34*533*(450+225)/1000 = 1687.7 kN

Total ultimate shear capacity,TVu = TVc1 + TVc2 = 1687.7+1687.7 = 3375.3 kN

TVu = 3375.3 ; Pu = 3375.3 ; i.e. Minimum thickness required = 533 !!!

Y - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 2.00 ; Thickness,d = 524 mm; Width

= 1400 mm

Y-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total ultimate pile load,Pu = 1.5*2.00*60.0*9.81 = 1687.7 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*524*0.49/225 = 2.30 N/mm^2

Total ultimate shear capacity,TVu = 2.30*524*1400/1000 = 1687.7 kN

TVu = 1687.7 ; Pu = 1687.7 ; i.e. Minimum thickness required = 524 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 2.00 ; Thickness,d = 524 mm; Width

= 1400 mm

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mmTotal ultimate pile load,Pu = 1.5*2.00*60.0*9.81 = 1687.7 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*524*0.49/225 = 2.30 N/mm^2

Total ultimate shear capacity,TVu = 2.30*524*1400/1000 = 1687.7 kN

TVu = 1687.7 ; Pu = 1687.7 ; i.e. Minimum thickness required = 524 !!!

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/533) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

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vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch4 1400 1400 569 569 524 524 349 533

Design for Bending Moment: 406.8/1.00 = 406.8 kNm

Mu/bd^2 = 406.8*1000/569^2 = 1.255

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.255 ; 0.5*kk1 = 3.450

Mu/bd^2 = 1.255 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 47.7 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*47.7 = 844.78 kN

Steel area required, As = Fc/(fyy*fy) = 844.78/(0.95*460) = 1933 mm^2

Moment capacity = Fc(d-k2.x) = 844.78(569-0.4419*47.7)/1000 = 463.2 kNm

Steel area required, As = 1933 mm^2

Design for Bending Moment: 406.8/1.00 = 406.8 kNm

Mu/bd^2 = 406.8*1000/569^2 = 1.255

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.255 ; 0.5*kk1 = 3.450

Mu/bd^2 = 1.255 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 47.7 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*47.7 = 844.78 kN

Steel area required, As = Fc/(fyy*fy) = 844.78/(0.95*460) = 1933 mm^2

Moment capacity = Fc(d-k2.x) = 844.78(569-0.4419*47.7)/1000 = 463.2 kNm

Steel area required, As = 1933 mm^2

Location of Footing: 10-E

Dead Load, DL = 1106.3; Live Load, LL = 220.7; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 1216.9; Live Load, LL = 242.7

Total Unfactored Load = 1216.9 + 242.7 + 0.0 = 1459.6 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/493) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Based on preliminary pile-cap size of 1500 X 1300 X 869 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(1.500X1.300X0.869)x24 = 44.7 kNTotal No of Piles required = 1504.4/(60.0*9.81) = 3

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

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Ultimate soil pressure for design, Wu = 2530.0/(1800*1800) = 0.781 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/493) = 1.000

Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 493 mm = 0.495 N/mm^2

Ratio of shear plane from stump face to effective depth, p = 0.545Distance of shear plane from stump face, a = 269 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*493*0.495/269 = 0.908 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*0.908*493*(4*0.545*493+450+450) = 1768.5 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

0.781 *(2*0.545*493+450)*(2*0.545*493+450) = 761.5 kN

Ultimate Load = Total load,P - Pi = 2530.0 - 761.5 = 1768.5 kN O.K.

!!

Required effective depth to satisfy punching shear, d = 493 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 2530.0-0.781*450*450/1000 = 2371.9 kNStump Face Shear Capacity, Pc = 2*5.367*246(450+450)/1000 = 2371.9 kN

Effective Depth required at stump face = 246 mm

Summary: Effective depth for Punching Shear Stump Shear

493 246

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Total No of Piles used = 3

Total ultimate pile load = 1.5*3*60.0*9.81 = 2648.7 kN

Total ultimate X-pile load = 1.5*1.00*60.0*9.81 = 882.9 kN

Total ultimate Y-pile load = 1.5*0.50*60.0*9.81 = 441.5 kN

X-Distance from piles' centroid to column face = 450 - 450/4 = 338 mm

Total Moment about Y-axis = 2157.9 kN *0.338 m = 728.3 kNm

Moment about Y-axis = 728.3 kN/1.279 m = 569.2 kNm/m

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mm

Total Moment about X-axis = 1311.8 kN *0.295 m = 386.5 kNm

Moment about X-axis = 386.5 kN/1.400 m = 276.1 kNm/m

Y - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 501 mm; Width

= 1000 mm

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 843.3 kN

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Enhanced shear Vc = VcFac*d*vc/a = 2.0*501*0.49/295 = 1.68 N/mm^2

Total ultimate shear capacity,TVu = 1.68*501*1000/1000 = 843.3 kN

TVu = 843.3 ; Pu = 843.3 ; i.e. Minimum thickness required = 501 !!!

STUMP FACE SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 262 mm

Total ultimate pile load,Pu = 1.5*3.00*60.0*9.81 = 2530.0 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2

Total ultimate shear capacity,TVu = 2*5.37*262*(450+450)/1000 = 2530.0 kN

TVu = 2530.0 ; Pu = 2530.0 ; i.e. Minimum thickness required = 262 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 619 mm; Width

= 500 mm

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 843.3 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*619*0.49/225 = 2.72 N/mm^2

Total ultimate shear capacity,TVu = 2.72*619*500/1000 = 843.3 kN

TVu = 843.3 ; Pu = 843.3 ; i.e. Minimum thickness required = 619 !!!

PUNCHING SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 478 mm

Total ultimate pile load, Pu = 1.5*3.00*60.0*9.81 = 2530.0 kN

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Enhanced shear Vc1 = VcFac*d*vc/a = 2.0*478*0.49/225 = 2.10 N/mm^2

X-Ultimate shear capacity, TVc1 = 2*2.10*478*(450+295)/1000 = 1495.0 kN

Y - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 478 mm; Width

= 1400 mm

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mmEnhanced shear Vc2 = VcFac*d*vc/a = 2.0*478*0.49/295 = 1.60 N/mm^2

Y-Ultimate shear capacity, TVc2 = 2*1.60*478*(450+225)/1000 = 1035.0 kN

Total ultimate shear capacity,TVu = TVc1 + TVc2 = 1495.0+1035.0 = 2530.0 kN

TVu = 2530.0 ; Pu = 2530.0 ; i.e. Minimum thickness required = 478 !!!

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/619) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch3 1400 1300 619 493 619 501 262 478

Design for Bending Moment: 569.2/1.00 = 569.2 kNm

Mu/bd^2 = 569.2*1000/619^2 = 1.484

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.484 ; 0.5*kk1 = 3.450Mu/bd^2 = 1.484 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 54.0 mm

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Concrete Compression Force, Fc = k1.b.x = 17.71*54.0 = 956.08 kN

Steel area required, As = Fc/(fyy*fy) = 956.08/(0.95*460) = 2188 mm^2

Moment capacity = Fc(d-k2.x) = 956.08(617-0.4419*54.0)/1000 = 567.3 kNm

Steel area required, As = 2188 mm^2

Design for Bending Moment: 569.2/1.00 = 569.2 kNm

Mu/bd^2 = 569.2*1000/619^2 = 1.484

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.484 ; 0.5*kk1 = 3.450Mu/bd^2 = 1.484 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 54.0 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*54.0 = 956.08 kN

Steel area required, As = Fc/(fyy*fy) = 956.08/(0.95*460) = 2188 mm^2

Moment capacity = Fc(d-k2.x) = 956.08(617-0.4419*54.0)/1000 = 567.3 kNm

Steel area required, As = 2188 mm^2

Location of Footing: 10-F

Dead Load, DL = 588.4; Live Load, LL = 136.2; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 647.2; Live Load, LL = 149.8

Total Unfactored Load = 647.2 + 149.8 + 0.0 = 797.0 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/143) = 2.794Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.794)^1/4*(1.600)^1/3 )/1.25 = 0.640 N/mm^2

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/527) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/50) = 8.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(8.000)^1/4*(1.600)^1/3 )/1.25 = 0.832 N/mm^2

Based on preliminary pile-cap size of 600 X 1500 X 776 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(0.600X1.500X0.776)x24 = 18.4 kNTotal No of Piles required = 815.5/(60.0*9.81) = 2

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 1691.7/(1800*900) = 1.044 N/mm^2

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Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/143) = 2.794Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.794)^1/4*(1.600)^1/3 )/1.25 = 0.640 N/mm^2

Stump Size, A & B Dimensions,mm = 350 mm x 1650 mm

Design Shear stress based on d, 143 mm = 0.640 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.704Distance of shear plane from stump face, a = 101 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*143*0.640/101 = 0.909 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*0.909*143*(4*0.704*143+350+1650) = 625.3 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

1.044 *(2*0.704*143+350)*(2*0.704*143+1650) = 1066.5 kN

Ultimate Load = Total load,P - Pi = 1691.7 - 1066.5 = 625.3 kN O.K.!!

Required effective depth to satisfy punching shear, d = 143 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 1691.7-1.044*350*1650/1000 = 1088.7 kNStump Face Shear Capacity, Pc = 2*5.367*51(350+1650)/1000 = 1088.7 kN

Effective Depth required at stump face = 51 mm

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/527) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,527 mm = 0.495 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.690

Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.495/0.690 = 0.717 N/mm^2

Required effective depth to satisfy flexure shear, d = 527 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.717*527*900 = 679.8 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.044 *(2*0.690*527+350)*900 = 1012.0 kN

Ultimate Load = Total load - above = 1691.7 - 1012.0 = 679.8 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/50) = 8.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(8.000)^1/4*(1.600)^1/3 )/1.25 = 0.832 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,50 mm = 0.832 N/mm^2

Ratio of shear plane from stump face to effective depth, p = 0.500Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.832/0.500 = 1.664 N/mm^2

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Required effective depth to satisfy flexure shear, d = 50 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*1.664*50*1800 = 299.6 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.044 *(2*0.500*50+1650)*1800 = 3195.5 kN

Ultimate Load = Total load - above = 1691.7 - 3195.5 = -1503.8 kN

Summary: Effective depth for Punching Shear Stump Shear Flexural Shear

143 51 527

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 1650 mm x 350 mm

Total No of Piles used = 2

Total ultimate pile load = 1.5*2*60.0*9.81 = 1765.8 kN

Total ultimate X-pile load = 1.5*1.00*60.0*9.81 = 882.9 kN

Total ultimate Y-pile load = 1.5*0.00*60.0*9.81 = 0.0 kN

X-Distance from piles' centroid to column face = 450 - 1650/2 = -375 mm

Total Moment about Y-axis = 845.9 kN *-0.375 m = -317.2 kNmMoment about Y-axis = -317.2 kN/0.500 m = -634.4 kNm/m

Y-Distance from piles' centroid to column face = 175 - 350/2 = 0 mm

Total Moment about X-axis = -1.$ kN *0.000 m = 0.0 kNm

Moment about X-axis = 0.0 kN/1.400 m = 0.0 kNm/m

STUMP FACE SHEAR CAPACITY: Equivalent piles = 2.00 ; Thickness,d = 79 mm

Total ultimate pile load,Pu = 1.5*2.00*60.0*9.81 = 1691.7 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2

Total ultimate shear capacity,TVu = 2*5.37*79*(1650+350)/1000 = 1691.7 kN

TVu = 1691.7 ; Pu = 1691.7 ; i.e. Minimum thickness required = 79 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 0 mm; Width =

500 mm

X-Distance from piles' centroid to column face = 450 - 1650/2 = -375 mm= - VE --> NO

CHECKING NECESSARY !!!

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/79) = 5.076Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(5.076)^1/4*(1.600)^1/3 )/1.25 = 0.743 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch2 500 1800 527 527 0 0 79 0

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/527^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

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Concrete Neutral Axis, x = 44.5 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*44.5 = 788.71 kN

Steel area required, As = Fc/(fyy*fy) = 788.71/(0.95*460) = 1805 mm^2

Moment capacity = Fc(d-k2.x) = 788.71(527-0.4419*44.5)/1000 = 399.8 kNm

Steel area required, As = 1805 mm^2

Design for Bending Moment: -634.4/1.00 = -634.4 kNm

Mu/bd^2 = -634.4*1000/527^2 = -2.288

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = -2.288 ; 0.5*kk1 = 3.450Mu/bd^2 = -2.288 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 44.5 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*44.5 = 788.71 kN

Steel area required, As = Fc/(fyy*fy) = 788.71/(0.95*460) = 1805 mm^2

Moment capacity = Fc(d-k2.x) = 788.71(527-0.4419*44.5)/1000 = 399.8 kNm

Steel area required, As = 1805 mm^2

Location of Footing: 10-F2

Dead Load, DL = 466.6; Live Load, LL = 131.8; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 513.3; Live Load, LL = 145.0

Total Unfactored Load = 513.3 + 145.0 + 0.0 = 658.3 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/329) = 1.217Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.217)^1/4*(1.600)^1/3 )/1.25 = 0.520 N/mm^2

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/491) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/144) = 2.774Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.774)^1/4*(1.600)^1/3 )/1.25 = 0.639 N/mm^2

Based on preliminary pile-cap size of 1500 X 600 X 871 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(1.500X0.600X0.871)x24 = 20.7 kNTotal No of Piles required = 679.0/(60.0*9.81) = 2

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

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Ultimate soil pressure for design, Wu = 1699.4/(1800*900) = 1.049 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/329) = 1.217Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.217)^1/4*(1.600)^1/3 )/1.25 = 0.520 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 329 mm = 0.520 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.546Distance of shear plane from stump face, a = 179 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*329*0.520/179 = 0.953 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*0.953*329*(4*0.546*329+450+450) = 1013.3 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

1.049 *(2*0.546*329+450)*(2*0.546*329+450) = 686.1 kN

Ultimate Load = Total load,P - Pi = 1699.4 - 686.1 = 1013.3 kN O.K.!!

Required effective depth to satisfy punching shear, d = 329 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 1699.4-1.049*450*450/1000 = 1486.9 kNStump Face Shear Capacity, Pc = 2*5.367*154(450+450)/1000 = 1486.9 kN

Effective Depth required at stump face = 154 mm

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/491) = 1.000

Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,491 mm = 0.495 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.690Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.495/0.690 = 0.717 N/mm^2

Required effective depth to satisfy flexure shear, d = 491 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.717*491*900 = 634.3 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.049 *(2*0.690*491+450)*900 = 1065.0 kNUltimate Load = Total load - above = 1699.4 - 1065.0 = 634.3 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/144) = 2.774Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.774)^1/4*(1.600)^1/3 )/1.25 = 0.639 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,144 mm = 0.639 N/mm^2

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Ratio of shear plane from stump face to effective depth, p = 0.780Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.639/0.780 = 0.819 N/mm^2

Required effective depth to satisfy flexure shear, d = 144 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.819*144*1800 = 425.0 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.049 *(2*0.780*144+450)*1800 = 1274.4 kN

Ultimate Load = Total load - above = 1699.4 - 1274.4 = 425.0 kN

Summary: Effective depth for Punching Shear Stump Shear Flexural Shear

329 154 491

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Total No of Piles used = 2

Total ultimate pile load = 1.5*2*60.0*9.81 = 1765.8 kN

Total ultimate X-pile load = 1.5*1.00*60.0*9.81 = 882.9 kN

Total ultimate Y-pile load = 1.5*0.00*60.0*9.81 = 0.0 kN

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total Moment about Y-axis = 849.7 kN *0.225 m = 191.2 kNm

Moment about Y-axis = 191.2 kN/0.500 m = 382.4 kNm/m

Y-Distance from piles' centroid to column face = 225 - 450/2 = 0 mm

Total Moment about X-axis = -1.$ kN *0.000 m = 0.0 kNm

Moment about X-axis = 0.0 kN/1.400 m = 0.0 kNm/m

STUMP FACE SHEAR CAPACITY: Equivalent piles = 2.00 ; Thickness,d = 176 mm

Total ultimate pile load,Pu = 1.5*2.00*60.0*9.81 = 1699.4 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2Total ultimate shear capacity,TVu = 2*5.37*176*(450+450)/1000 = 1699.4 kN

TVu = 1699.4 ; Pu = 1699.4 ; i.e. Minimum thickness required = 176 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 622 mm; Width

= 500 mm

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 849.7 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*622*0.49/225 = 2.73 N/mm^2

Total ultimate shear capacity,TVu = 2.73*622*500/1000 = 849.7 kN

TVu = 849.7 ; Pu = 849.7 ; i.e. Minimum thickness required = 622 !!!

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/622) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch2 1400 600 622 491 622 0 176 0

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Design for Bending Moment: 382.4/1.00 = 382.4 kNm

Mu/bd^2 = 382.4*1000/622^2 = 0.990

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.990 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.990 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 51.6 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*51.6 = 913.21 kN

Steel area required, As = Fc/(fyy*fy) = 913.21/(0.95*460) = 2090 mm^2

Moment capacity = Fc(d-k2.x) = 913.21(620-0.4419*51.6)/1000 = 545.0 kNm

Steel area required, As = 2090 mm^2

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/622^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450

Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 51.6 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*51.6 = 913.21 kN

Steel area required, As = Fc/(fyy*fy) = 913.21/(0.95*460) = 2090 mm^2

Moment capacity = Fc(d-k2.x) = 913.21(620-0.4419*51.6)/1000 = 545.0 kNm

Steel area required, As = 2090 mm^2

Location of Footing: 10-G2

Dead Load, DL = 1142.7; Live Load, LL = 162.2; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 1256.9; Live Load, LL = 178.4

Total Unfactored Load = 1256.9 + 178.4 + 0.0 = 1435.3 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/492) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Based on preliminary pile-cap size of 1500 X 1300 X 867 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(1.500X1.300X0.867)x24 = 44.6 kN

Total No of Piles required = 1479.9/(60.0*9.81) = 3

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 2515.1/(1800*1800) = 0.776 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997

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Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/492) = 1.000

Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 492 mm = 0.495 N/mm^2

Ratio of shear plane from stump face to effective depth, p = 0.545

Distance of shear plane from stump face, a = 268 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*492*0.495/268 = 0.908 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*0.908*492*(4*0.545*492+450+450) = 1760.6 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

0.776 *(2*0.545*492+450)*(2*0.545*492+450) = 754.6 kN

Ultimate Load = Total load,P - Pi = 2515.1 - 754.6 = 1760.6 kN O.K.

!!

Required effective depth to satisfy punching shear, d = 492 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 2515.1-0.776*450*450/1000 = 2358.0 kN

Stump Face Shear Capacity, Pc = 2*5.367*244(450+450)/1000 = 2358.0 kN

Effective Depth required at stump face = 244 mm

Summary: Effective depth for Punching Shear Stump Shear492 244

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Total No of Piles used = 3

Total ultimate pile load = 1.5*3*60.0*9.81 = 2648.7 kN

Total ultimate X-pile load = 1.5*1.00*60.0*9.81 = 882.9 kN

Total ultimate Y-pile load = 1.5*0.50*60.0*9.81 = 441.5 kN

X-Distance from piles' centroid to column face = 450 - 450/4 = 338 mm

Total Moment about Y-axis = 2145.3 kN *0.338 m = 724.0 kNm

Moment about Y-axis = 724.0 kN/1.279 m = 565.9 kNm/m

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mm

Total Moment about X-axis = 1304.2 kN *0.295 m = 384.2 kNm

Moment about X-axis = 384.2 kN/1.400 m = 274.4 kNm/m

Y - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 500 mm; Width

= 1000 mm

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 838.4 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*500*0.49/295 = 1.68 N/mm^2

Total ultimate shear capacity,TVu = 1.68*500*1000/1000 = 838.4 kN

TVu = 838.4 ; Pu = 838.4 ; i.e. Minimum thickness required = 500 !!!

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STUMP FACE SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 260 mm

Total ultimate pile load,Pu = 1.5*3.00*60.0*9.81 = 2515.1 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2

Total ultimate shear capacity,TVu = 2*5.37*260*(450+450)/1000 = 2515.1 kN

TVu = 2515.1 ; Pu = 2515.1 ; i.e. Minimum thickness required = 260 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 617 mm; Width

= 500 mm

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 838.4 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*617*0.49/225 = 2.72 N/mm^2

Total ultimate shear capacity,TVu = 2.72*617*500/1000 = 838.4 kN

TVu = 838.4 ; Pu = 838.4 ; i.e. Minimum thickness required = 617 !!!

PUNCHING SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 476 mm

Total ultimate pile load, Pu = 1.5*3.00*60.0*9.81 = 2515.1 kN

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Enhanced shear Vc1 = VcFac*d*vc/a = 2.0*476*0.49/225 = 2.10 N/mm^2

X-Ultimate shear capacity, TVc1 = 2*2.10*476*(450+295)/1000 = 1486.2 kN

Y - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 3.00 ; Thickness,d = 476 mm; Width

= 1400 mm

Y-Distance from piles' centroid to column face = 520 - 450/2 = 295 mm

Enhanced shear Vc2 = VcFac*d*vc/a = 2.0*476*0.49/295 = 1.60 N/mm^2

Y-Ultimate shear capacity, TVc2 = 2*1.60*476*(450+225)/1000 = 1028.9 kN

Total ultimate shear capacity,TVu = TVc1 + TVc2 = 1486.2+1028.9 = 2515.1 kN

TVu = 2515.1 ; Pu = 2515.1 ; i.e. Minimum thickness required = 476 !!!

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/617) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch3 1400 1300 617 492 617 500 260 476

Design for Bending Moment: 565.9/1.00 = 565.9 kNm

Mu/bd^2 = 565.9*1000/617^2 = 1.484

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.484 ; 0.5*kk1 = 3.450Mu/bd^2 = 1.484 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 53.8 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*53.8 = 953.28 kN

Steel area required, As = Fc/(fyy*fy) = 953.28/(0.95*460) = 2181 mm^2

Moment capacity = Fc(d-k2.x) = 953.28(615-0.4419*53.8)/1000 = 564.0 kNm

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Steel area required, As = 2181 mm^2

Design for Bending Moment: 565.9/1.00 = 565.9 kNm

Mu/bd^2 = 565.9*1000/617^2 = 1.484

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 1.484 ; 0.5*kk1 = 3.450Mu/bd^2 = 1.484 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 53.8 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*53.8 = 953.28 kN

Steel area required, As = Fc/(fyy*fy) = 953.28/(0.95*460) = 2181 mm^2

Moment capacity = Fc(d-k2.x) = 953.28(615-0.4419*53.8)/1000 = 564.0 kNm

Steel area required, As = 2181 mm^2

Location of Footing: 10-I

Dead Load, DL = 231.7; Live Load, LL = 94.4; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 254.9; Live Load, LL = 103.8

Total Unfactored Load = 254.9 + 103.8 + 0.0 = 358.7 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/159) = 2.513Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(2.513)^1/4*(1.600)^1/3 )/1.25 = 0.623 N/mm^2

Based on preliminary pile-cap size of 600 X 600 X 500 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(0.600X0.600X0.500)x24 = 4.8 kNTotal No of Piles required = 363.4/(60.0*9.81) = 1

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 857.8/(900*900) = 1.059 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/159) = 2.513Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.513)^1/4*(1.600)^1/3 )/1.25 = 0.623 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 159 mm = 0.623 N/mm^2

Ratio of shear plane from stump face to effective depth, p = 0.646Distance of shear plane from stump face, a = 103 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*159*0.623/103 = 0.965 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*0.965*159*(4*0.646*159+450+450) = 402.8 kN

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Load Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =1.059 *(2*0.646*159+450)*(2*0.646*159+450) = 455.0 kN

Ultimate Load = Total load,P - Pi = 857.8 - 455.0 = 402.8 kN O.K. !!

Required effective depth to satisfy punching shear, d = 159 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 857.8-1.059*450*450/1000 = 643.4 kNStump Face Shear Capacity, Pc = 2*5.367*67(450+450)/1000 = 643.4 kN

Effective Depth required at stump face = 67 mm

Summary: Effective depth for Punching Shear Stump Shear159 67

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/250^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 24.1 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*24.1 = 426.07 kN

Steel area required, As = Fc/(fyy*fy) = 426.07/(0.95*460) = 975 mm^2

Moment capacity = Fc(d-k2.x) = 426.07(250-0.4419*24.1)/1000 = 102.0 kNm

Steel area required, As = 975 mm^2

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/250^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 24.1 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*24.1 = 426.07 kN

Steel area required, As = Fc/(fyy*fy) = 426.07/(0.95*460) = 975 mm^2

Moment capacity = Fc(d-k2.x) = 426.07(250-0.4419*24.1)/1000 = 102.0 kNm

Steel area required, As = 975 mm^2

Location of Footing: 10-J

Dead Load, DL = 170.0; Live Load, LL = 32.6; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 187.0; Live Load, LL = 35.9

Total Unfactored Load = 187.0 + 35.9 + 0.0 = 222.9 kN

Refer to Table 3.9 of BS8110:1997

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Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/158) = 2.539

Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.539)^1/4*(1.600)^1/3 )/1.25 = 0.625 N/mm^2

Based on preliminary pile-cap size of 600 X 600 X 500 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(0.600X0.600X0.500)x24 = 4.8 kNTotal No of Piles required = 227.7/(60.0*9.81) = 1

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 842.7/(900*900) = 1.040 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/158) = 2.539Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.539)^1/4*(1.600)^1/3 )/1.25 = 0.625 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 158 mm = 0.625 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.646Distance of shear plane from stump face, a = 102 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*158*0.625/102 = 0.967 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*0.967*158*(4*0.646*158+450+450) = 398.3 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

1.040 *(2*0.646*158+450)*(2*0.646*158+450) = 444.4 kN

Ultimate Load = Total load,P - Pi = 842.7 - 444.4 = 398.3 kN O.K. !!

Required effective depth to satisfy punching shear, d = 158 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 842.7-1.040*450*450/1000 = 632.0 kNStump Face Shear Capacity, Pc = 2*5.367*65(450+450)/1000 = 632.0 kN

Effective Depth required at stump face = 65 mm

Summary: Effective depth for Punching Shear Stump Shear

158 65

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/250^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 24.1 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*24.1 = 426.07 kN

Steel area required, As = Fc/(fyy*fy) = 426.07/(0.95*460) = 975 mm^2

Moment capacity = Fc(d-k2.x) = 426.07(250-0.4419*24.1)/1000 = 102.0 kNm

Steel area required, As = 975 mm^2

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Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/250^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 24.1 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*24.1 = 426.07 kN

Steel area required, As = Fc/(fyy*fy) = 426.07/(0.95*460) = 975 mm^2

Moment capacity = Fc(d-k2.x) = 426.07(250-0.4419*24.1)/1000 = 102.0 kNm

Steel area required, As = 975 mm^2

Location of Footing: 09-H

Dead Load, DL = 541.3; Live Load, LL = 164.4; Wind Load, WL = 0.0

After additional 10 percent load allowanceDead Load, DL = 595.5; Live Load, LL = 180.9

Total Unfactored Load = 595.5 + 180.9 + 0.0 = 776.3 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/329) = 1.215Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.215)^1/4*(1.600)^1/3 )/1.25 = 0.520 N/mm^2

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/492) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/144) = 2.772Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.772)^1/4*(1.600)^1/3 )/1.25 = 0.638 N/mm^2

Based on preliminary pile-cap size of 1500 X 600 X 872 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(1.500X0.600X0.872)x24 = 20.7 kN

Total No of Piles required = 797.0/(60.0*9.81) = 2

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 1702.3/(1800*900) = 1.051 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25

Effective depth ratio = max(1,400/d) = max(1,400/329) = 1.215Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600

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Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.215)^1/4*(1.600)^1/3 )/1.25 = 0.520 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 329 mm = 0.520 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.546Distance of shear plane from stump face, a = 180 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*329*0.520/180 = 0.952 N/mm^2

Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*0.952*329*(4*0.546*329+450+450) = 1014.5 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =1.051 *(2*0.546*329+450)*(2*0.546*329+450) = 687.9 kN

Ultimate Load = Total load,P - Pi = 1702.3 - 687.9 = 1014.5 kN O.K.

!!

Required effective depth to satisfy punching shear, d = 329 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 1702.3-1.051*450*450/1000 = 1489.6 kN

Stump Face Shear Capacity, Pc = 2*5.367*154(450+450)/1000 = 1489.6 kN

Effective Depth required at stump face = 154 mm

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/492) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,492 mm = 0.495 N/mm^2

Ratio of shear plane from stump face to effective depth, p = 0.690Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.495/0.690 = 0.717 N/mm^2

Required effective depth to satisfy flexure shear, d = 492 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.717*492*900 = 634.9 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.051 *(2*0.690*492+450)*900 = 1067.5 kN

Ultimate Load = Total load - above = 1702.3 - 1067.5 = 634.9 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/144) = 2.772Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(2.772)^1/4*(1.600)^1/3 )/1.25 = 0.638 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,144 mm = 0.638 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.780Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.638/0.780 = 0.819 N/mm^2

Required effective depth to satisfy flexure shear, d = 144 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.819*144*1800 = 425.3 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.051 *(2*0.780*144+450)*1800 = 1277.0 kN

Ultimate Load = Total load - above = 1702.3 - 1277.0 = 425.3 kN

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Summary: Effective depth for Punching Shear Stump Shear Flexural Shear

329 154 492

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Total No of Piles used = 2

Total ultimate pile load = 1.5*2*60.0*9.81 = 1765.8 kN

Total ultimate X-pile load = 1.5*1.00*60.0*9.81 = 882.9 kN

Total ultimate Y-pile load = 1.5*0.00*60.0*9.81 = 0.0 kN

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total Moment about Y-axis = 851.2 kN *0.225 m = 191.5 kNm

Moment about Y-axis = 191.5 kN/0.500 m = 383.0 kNm/m

Y-Distance from piles' centroid to column face = 225 - 450/2 = 0 mm

Total Moment about X-axis = -1.$ kN *0.000 m = 0.0 kNm

Moment about X-axis = 0.0 kN/1.400 m = 0.0 kNm/m

STUMP FACE SHEAR CAPACITY: Equivalent piles = 2.00 ; Thickness,d = 176 mm

Total ultimate pile load,Pu = 1.5*2.00*60.0*9.81 = 1702.3 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2

Total ultimate shear capacity,TVu = 2*5.37*176*(450+450)/1000 = 1702.3 kN

TVu = 1702.3 ; Pu = 1702.3 ; i.e. Minimum thickness required = 176 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 622 mm; Width

= 500 mm

X-Distance from piles' centroid to column face = 450 - 450/2 = 225 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 851.2 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*622*0.49/225 = 2.74 N/mm^2

Total ultimate shear capacity,TVu = 2.74*622*500/1000 = 851.2 kN

TVu = 851.2 ; Pu = 851.2 ; i.e. Minimum thickness required = 622 !!!

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/622) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch2 1400 600 622 492 622 0 176 0

Design for Bending Moment: 383.0/1.00 = 383.0 kNm

Mu/bd^2 = 383.0*1000/622^2 = 0.990

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.990 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.990 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 51.6 mm

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Concrete Compression Force, Fc = k1.b.x = 17.71*51.6 = 913.92 kN

Steel area required, As = Fc/(fyy*fy) = 913.92/(0.95*460) = 2091 mm^2

Moment capacity = Fc(d-k2.x) = 913.92(620-0.4419*51.6)/1000 = 545.9 kNm

Steel area required, As = 2091 mm^2

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/622^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 51.6 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*51.6 = 913.92 kN

Steel area required, As = Fc/(fyy*fy) = 913.92/(0.95*460) = 2091 mm^2

Moment capacity = Fc(d-k2.x) = 913.92(620-0.4419*51.6)/1000 = 545.9 kNm

Steel area required, As = 2091 mm^2

Location of Footing: 09-H1

Dead Load, DL = 440.4; Live Load, LL = 81.2; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 484.5; Live Load, LL = 89.3

Total Unfactored Load = 484.5 + 89.3 + 0.0 = 573.8 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/355) = 1.128Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.128)^1/4*(1.600)^1/3 )/1.25 = 0.510 N/mm^2

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/507) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/162) = 2.472Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.472)^1/4*(1.600)^1/3 )/1.25 = 0.620 N/mm^2

Based on preliminary pile-cap size of 1500 X 600 X 902 to calculate Selfweight,SW:Selfweight of PileCap,SW = 1.10 x(1.500X0.600X0.902)x24 = 21.4 kNTotal No of Piles required = 595.2/(60.0*9.81) = 2

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 1684.2/(1800*900) = 1.040 N/mm^2

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Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/355) = 1.128Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.128)^1/4*(1.600)^1/3 )/1.25 = 0.510 N/mm^2

Stump Size, A & B Dimensions,mm = 400 mm x 400 mm

Design Shear stress based on d, 355 mm = 0.510 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.504Distance of shear plane from stump face, a = 179 mmEnhanced shear stress,v = fVcFac*d*vc/a = 1.0*355*0.510/179 = 1.012 N/mm^2Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =

2*1.012*355*(4*0.504*355+400+400) = 1087.5 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

1.040 *(2*0.504*355+400)*(2*0.504*355+400) = 596.6 kN

Ultimate Load = Total load,P - Pi = 1684.2 - 596.6 = 1087.5 kN O.K.!!

Required effective depth to satisfy punching shear, d = 355 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 1684.2-1.040*400*400/1000 = 1517.8 kNStump Face Shear Capacity, Pc = 2*5.367*177(400+400)/1000 = 1517.8 kN

Effective Depth required at stump face = 177 mm

Refer to Table 3.9 of BS8110:1997

Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/507) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,507 mm = 0.495 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.690

Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.495/0.690 = 0.717 N/mm^2

Required effective depth to satisfy flexure shear, d = 507 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.717*507*900 = 654.9 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.040 *(2*0.690*507+400)*900 = 1029.3 kN

Ultimate Load = Total load - above = 1684.2 - 1029.3 = 654.9 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/162) = 2.472Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.472)^1/4*(1.600)^1/3 )/1.25 = 0.620 N/mm^2

Calculate Effective Depth, d to Satisfy Flexural Shear:

Design Shear stress based on d,162 mm = 0.620 N/mm^2

Ratio of shear plane from stump face to effective depth, p = 0.770Enhanced shear stress,v = fVcFac*vc/p = 1.0*0.620/0.770 = 0.806 N/mm^2

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Required effective depth to satisfy flexure shear, d = 162 mm

Ultimate Shear Capacity = 2v.d.'L'/1000 kN = 2*0.806*162*1800 = 469.4 kN

Load Within Shear Perimeter = Wu(2p.d+'A').'L'/1000 kN =

1.040 *(2*0.770*162+400)*1800 = 1214.8 kN

Ultimate Load = Total load - above = 1684.2 - 1214.8 = 469.4 kN

Summary: Effective depth for Punching Shear Stump Shear Flexural Shear

355 177 507

CONVENTIONAL DESIGN METHOD FOR PILE FOOTING:

Stump Size, A & B Dimensions,mm = 400 mm x 400 mm

Total No of Piles used = 2

Total ultimate pile load = 1.5*2*60.0*9.81 = 1765.8 kN

Total ultimate X-pile load = 1.5*1.00*60.0*9.81 = 882.9 kN

Total ultimate Y-pile load = 1.5*0.00*60.0*9.81 = 0.0 kN

X-Distance from piles' centroid to column face = 450 - 400/2 = 250 mm

Total Moment about Y-axis = 842.1 kN *0.250 m = 210.5 kNmMoment about Y-axis = 210.5 kN/0.500 m = 421.0 kNm/m

Y-Distance from piles' centroid to column face = 200 - 400/2 = 0 mm

Total Moment about X-axis = -1.$ kN *0.000 m = 0.0 kNm

Moment about X-axis = 0.0 kN/1.400 m = 0.0 kNm/m

STUMP FACE SHEAR CAPACITY: Equivalent piles = 2.00 ; Thickness,d = 196 mm

Total ultimate pile load,Pu = 1.5*2.00*60.0*9.81 = 1684.2 kN

Stump Face shear Vc = 0.8*sqrt(fcu) = 0.8*sqrt(45) = 5.37 N/mm^2

Total ultimate shear capacity,TVu = 2*5.37*196*(400+400)/1000 = 1684.2 kN

TVu = 1684.2 ; Pu = 1684.2 ; i.e. Minimum thickness required = 196 !!!

X - FLEXURAL BEAM SHEAR CAPACITY: Equivalent piles = 1.00 ; Thickness,d = 652 mm; Width

= 500 mm

X-Distance from piles' centroid to column face = 450 - 400/2 = 250 mm

Total ultimate pile load,Pu = 1.5*1.00*60.0*9.81 = 842.1 kN

Enhanced shear Vc = VcFac*d*vc/a = 2.0*652*0.49/250 = 2.58 N/mm^2

Total ultimate shear capacity,TVu = 2.58*652*500/1000 = 842.1 kN

TVu = 842.1 ; Pu = 842.1 ; i.e. Minimum thickness required = 652 !!!

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/652) = 1.000Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(1.000)^1/4*(1.600)^1/3 )/1.25 = 0.495 N/mm^2

Pile:No Footing: x y t ; tPad tBeamX tBeamY tFace tPunch2 1400 500 652 507 652 0 196 0

Design for Bending Moment: 421.0/1.00 = 421.0 kNm

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Mu/bd^2 = 421.0*1000/652^2 = 0.990

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.990 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.990 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 53.8 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*53.8 = 953.43 kN

Steel area required, As = Fc/(fyy*fy) = 953.43/(0.95*460) = 2182 mm^2

Moment capacity = Fc(d-k2.x) = 953.43(650-0.4419*53.8)/1000 = 597.3 kNm

Steel area required, As = 2182 mm^2

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/652^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 53.8 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*53.8 = 953.43 kN

Steel area required, As = Fc/(fyy*fy) = 953.43/(0.95*460) = 2182 mm^2

Moment capacity = Fc(d-k2.x) = 953.43(650-0.4419*53.8)/1000 = 597.3 kNm

Steel area required, As = 2182 mm^2

Location of Footing: 09-J

Dead Load, DL = 113.9; Live Load, LL = 103.6; Wind Load, WL = 0.0

After additional 10 percent load allowance

Dead Load, DL = 125.2; Live Load, LL = 113.9

Total Unfactored Load = 125.2 + 113.9 + 0.0 = 239.1 kN

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/161) = 2.478Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30vc = ( 0.79*(0.30)^1/3*(2.478)^1/4*(1.600)^1/3 )/1.25 = 0.621 N/mm^2

Based on preliminary pile-cap size of 600 X 600 X 500 to calculate Selfweight,SW:

Selfweight of PileCap,SW = 1.10 x(0.600X0.600X0.500)x24 = 4.8 kNTotal No of Piles required = 243.9/(60.0*9.81) = 1

ALTERNATIVE DESIGN METHOD FOR PILE FOOTING: USING EQUIVALENT ULTIMATE SOIL PRESSURE

Ultimate soil pressure for design, Wu = 879.8/(900*900) = 1.086 N/mm^2

Calculate Effective Depth, d to Satisfy Punching Shear:

Refer to Table 3.9 of BS8110:1997Shear Capacity,vc = 0.79*((100As/(bd))^1/3)*(400/d)^1/4)*((fcu/25)^1/3)/1.25Effective depth ratio = max(1,400/d) = max(1,400/161) = 2.478

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Concrete Grade ratio = min(40,fcu)/25 = min(40,45)/25 = 1.600Steel Percentage, 100As/(bd) = min(3,0.30) = 0.30

vc = ( 0.79*(0.30)^1/3*(2.478)^1/4*(1.600)^1/3 )/1.25 = 0.621 N/mm^2

Stump Size, A & B Dimensions,mm = 450 mm x 450 mm

Design Shear stress based on d, 161 mm = 0.621 N/mm^2Ratio of shear plane from stump face to effective depth, p = 0.646Distance of shear plane from stump face, a = 104 mm

Enhanced shear stress,v = fVcFac*d*vc/a = 1.0*161*0.621/104 = 0.962 N/mm^2

Ultimate Shear Capacity = 2v.d(4p.d+A+B)/1000 kN =2*0.962*161*(4*0.646*161+450+450) = 408.9 kNLoad Within Shear Perimeter, Pi = Wu(2p.d+A)*(2p.d+B)/1000 kN =

1.086 *(2*0.646*161+450)*(2*0.646*161+450) = 470.9 kN

Ultimate Load = Total load,P - Pi = 879.8 - 470.9 = 408.9 kN O.K. !!

Required effective depth to satisfy punching shear, d = 161 mm

Calculate Effective Depth, d to Satisfy Stump Face Shear:

Ultimate Load, Pu = 879.8-1.086*450*450/1000 = 659.9 kNStump Face Shear Capacity, Pc = 2*5.367*68(450+450)/1000 = 659.9 kN

Effective Depth required at stump face = 68 mm

Summary: Effective depth for Punching Shear Stump Shear

161 68

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/250^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 24.1 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*24.1 = 426.07 kN

Steel area required, As = Fc/(fyy*fy) = 426.07/(0.95*460) = 975 mm^2

Moment capacity = Fc(d-k2.x) = 426.07(250-0.4419*24.1)/1000 = 102.0 kNm

Steel area required, As = 975 mm^2

Design for Bending Moment: 0.0/1.00 = 0.0 kNm

Mu/bd^2 = 0.0*1000/250^2 = 0.000

For Footing Design, limit Mu/bd^2 < 0.5*kk1: Mu/bd^2 = 0.000 ; 0.5*kk1 = 3.450Mu/bd^2 = 0.000 < 3.450 -->O.K. !

Concrete Neutral Axis, x = 24.1 mm

Concrete Compression Force, Fc = k1.b.x = 17.71*24.1 = 426.07 kN

Steel area required, As = Fc/(fyy*fy) = 426.07/(0.95*460) = 975 mm^2

Moment capacity = Fc(d-k2.x) = 426.07(250-0.4419*24.1)/1000 = 102.0 kNm

Steel area required, As = 975 mm^2