3-pile Cap Design u5f25
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CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
References: 1 - ACI 318M-05, Building Code requirements for Structural Concrete, 2005 2 - ASCE 7-10, Minimum Design loads for Buildings & Other Structures, 2010 3 - Preliminary Geotechnical report, Trintoplan Consultants Limited, October 2013 4 - STAAD output 5 - ASTM A615-04, Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement Summary of calculation checks Soil bearing capacity Two-way (punching) shear x-axis: One-way (wide beam) shear Flexural Min. Flexural reinforcement Shrinkage reinforcement z-axis: One-way (wide beam) shear Flexural Min. Flexural reinforcement Shrinkage reinforcement
Utilisation ratio (actual vs capacity) 0.97 OK bearing capacity 0.37 OK two-way shear
Starter bar reinforcement Starter bar embedment Starter bar development length
**this condition governs**
0.42 0.44 0.88 0.46
OK one-way shear (x-axis) OK in flexure (x-axis) OK min. rfct flexure (x-axis) OK min. rfct shrinkage (x-axis)
0.50 0.46 0.84 0.46
OK one-way shear (z-axis) OK in flexure (z-axis) OK min. rfct flexure (z-axis) OK min. rfct shrinkage (z-axis)
OK starter bar min. rfct OK embed. depth 0.13 OK dev't dev t length
Note for and reader: Bordered cells denote -input, all other cells are calculated via this spreadsheet using the relevant base data, material and guidance from the noted References FOOTING GEOMTERY & MATERIAL PROPERTIES Foundation geometry pedestal width (in X-direction), px = pedestal breadth (in Z-direction), pz = pedestal height (in Y-direction), H Footing thickness, h Founding depth below GL Length of footing, L (in X-direction) Breadth of footing, B (in Z-direction) Footing shape:
580 760 500 500 1300 6000 6000 Square
Concrete density (kN/m3) Pedestal volume Pedestal weight Footing volume Footing weight 3
Soil weight above pad (assumes =20kN/m ) = ∴ Total footing & soil weight Ff =
23.1 0.2 5.1 18.0 415.2 928.9 1349.2
6000 6000 500
Calculation of footing & soil surcharge weight Ref 4: Tbl C3-2
580 760 500 500
mm mm mm mm mm mm mm
kN/m3 m3 kN 3 m kN kN kN
500
580
760
6000
6000
Material properties 28-day concrete comp. strength, f'c Ref 1: 7.7.1 Ref 5
Ref 3
30 N/mm2 Cover to reinforcement 75 mm Main reinforcement to be used A615 Gr 60 2 Reinforcement yield strength, fy = 420 N/mm Effective depth, d (for x-axis checks) 415 mm Effective depth, dz (for z-axis checks) 395 mm 2 Allowable soil bearing capacity, qa 55.0 kN/m
f'c=30MPa
208
LOADING DATA Note; Use Serviceability Limit state values when checking for soil bearing pressures. There is already a Factor of Safety built in to the allowable bearing pressure parameter as outlined in the geotehcnical report. Use Ultimate Limit State results for all other design checks.
Ref 4
Ref 4
Serviceability Limit State results From STAAD output, using Serviceability Limit state analysis: Fx (kN) Fy (kN) Maximum FY occurrence (SLS) 4.5 565.1
Fz (kN) 70.7
Mx (kNm) My (kNm) 14.3 0.6
Mz (kNm) 1.7
Node 4005
Ultimate Limit State results From STAAD output, using Ultimate Limit state analysis: Fx (kN) Fy (kN) Maximum FY occurrence (ULS) 7.9 936.3
Fz (kN) 312.2
Mx (kNm) My (kNm) 90.0 2.6
Mz (kNm) 2.8
Node 4005
Page 1 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
CHECK ON SOIL BEARING PRESSURES 1914.4 Bearing pressure along x-axis Pressure distr. under base: qmax,min = Ref 4
Use Fy (serviceability) = Load FV on underside of footing = Fy+Ft = FV/LB = 2
MZ+FXH/BL = qmax= qmin= Bearing pressure along z-axis Pressure distr. under base: qmax,min =
FV M Z FX H LB BL 2 565.1 1914.4 53.2 0.0 53.2 53.2
4.5
kN kN
6000
kN/m2 2 kN/m kN/m2 2 kN/m
FV Mx FzH LB LB 2
1914.4 70.7
Ref 4
Use Fy (serviceability) = Load FV on underside of footing = Fy+Ft = FV/LB = MX+FZH/LB2 = qmax= qmin=
Ref 3
∴ Use max bearing pressure as pa = Allowable soil bearing capacity, qa Ratio of pa to qa =
565.1 1914.4 53.2 0.3 53.5 52.8
kN kN kN/m2 2 kN/m kN/m2 kN/m2
Ref 1: 9.3.2.4
53.5 kN/m2 55.0 kN/m2 0.973
Ref 1: 10.17.1
Ref 4
Nominal pedestal or bearing load capacity, Pn Pn(0.85f'cA1)*[√A2/A1] A1 = A2 = (px+4d)*(pz+4d) = √A2/A1 (but max. 2.0)= f'c = ∴ Pn Fy = Ratio of Fy to Pn
0.6
6000
OK bearing capacity
936.3
CHECK FOR pedestal BEARING (transfer of load from pedestal into footing)
Ref 1: 10.17.1
1.7
0.65 0.441 0 441 5.421 2.00 30.0 14,613 936.3 0.06
[unitless]
415
m2 m2 [unitless] N/mm2 kN kN OK col bearing resistance
SHEAR CHECKS Check for Two-way (punching) shear capacity Vn Ref 1: 9.3.2.3 Ref 1: 11.1.1 Ref 1: 11.12.1.2
0.75 Where VnV c Assuming g that no shear reinforcement is used in the footing g Shear perimeter is located at a distance of 1.0d outside of the pedestal/pedestal face Shear perimeter length, bo is given by bo = 2(px+d)+(2(pz+d) px = 580 mm pz = 760 mm d= ∴ bo = Factored net soil pressure qu = Fy = Pu = ∴ qu =
415 mm 4340 mm Pu/BL 936.3 kN 26.0 kN/m2
Find the total shear force for two-way shear, VU2 where VU2 = Pu-qu(px+d)(py+d) ∴ VU2 = 905.9 kN
Page 2 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
Calculate the nominal shear strength, VC of the footing Vc (kN) = min of
Ref 1: 11.12.2.1
(a) (b) (c)
0.17(1+2/)√f'cbod 0.083([sd/bo]+2)√f'cbod 0.33√f'cbod 6000
Condition (a) Ratio of long side to short side of col, = f'c = bo = d= Vc-condition (a) =
1.00 [unitless] 30.0 N/mm2 4,340 mm 415 mm 5,031.2 kN
208
Condition (b) Ref 1: 11.12.2.1
pedestal location for determining as = s = Vc-condition (b) =
Edge 30 3,986.4 kN
760
Condition (c) Vc-condition (c) =
Vc = min of
∴ Use Vc = Vc = VU2 = Ratio of VU2/Vc =
(a) (b) (c)
580 5,031.2 kN 3,986.4 kN 3,255.5 kN
208
415
3,255.5 kN 2 441 6 kN 2,441.6 905.9 kN 0.37
OK two-way shear
Check for one-way (wide beam) shear: The critical section for one-way (wide beam) shear extends across the width of the footing at a distance d from the face of the loaded area. 6000
One-way shear parallel to x-axis Vc = 0.17√f'cBd
Ref 1: 11.3.1.1
B= Vc = ∴ Vc =
6000 mm 2,318.5 kN 1,738.9 kN
Find the projection noted as L' Footing shape: Square L' = 2295 mm Shear force on shear plane, Vu1 = BL'qu = 732.5 kN Ratio of Vu1/Vc = 0.42
6000
Ref 1: 11.12.1.1
3,255.5 kN
OK one-way shear (x-axis)
415
One-way shear parallel to z-axis Vc = 0.17√f'cLdz L= Vc = ∴ Vc =
6000 mm 2,206.8 kN 1,655.1 kN
2295
Find the projection noted as L' Footing shape: Square L' = 2585 mm Shear force on shear plane, Vu1 = BL'qu = 829.9 kN Ratio of Vu1/Vc = 0.50 [unitless]
415
Note: sketch also holds for one-way shear in the z-axis
OK one-way shear (z-axis)
Page 3 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
MOMENT AND REINFORCEMENT CHECKS Bending parallel to x-axis Find the projection noted as Lm Lm = moment on the bending plane, Mux = qu =
2710 mm 2 quBL m/2
26.0 kN/m2 ∴ Mux = 573.0 kNm Required steel ratio, = 0 . 85 f ' c
fy
2 Ru 1 1 0 .85 f c'
6000 2
Coefficient of resistance Ru = Mux / (Øbd ) = ∴ Ru = 0.85f'c / fy = 2RU/((0.85f'c) = ∴ = Area of steel required As req = ∴ As req =
R f 1: Ref 1 10 10.5.1 51
Ref 1: 7.12.2.1
0.9 0.6162 0.061 0.054 0.0017 Bd 4,115 mm2
6000
Ref 1: 9.3.2.1
Check for minimum reinforcement required for flexure 0 25Bd√f'c / fy 0.25Bd√f As min (flexure) max of 1.4Bd/ fy 0.25Bd√f'c / fy = 8,118 mm2 1.4Bd/ fy = 8,300 mm2 ∴ Use As min (flexure) = 8,300 mm2
2710
Check for minimum reinforcement required for shrinkage As, min (shrinkage) = 0.0018 (times gross sectional area) 2 0.0018Bh = 5,400 mm Reinforcement selection Select bar diameter (mm) Select number of bars Provide bar spacing (to nearest 25mm) As prov As total = Ratio of As (flexure) / As prov = Ratio of As min (flexure) / As prov = Ratio of As min (shrinkage) / As prov =
Bottom 20 30 200 9,425 11,781 0.44 0.88 0.46
Top 10 30 200 mm 2 2,356 mm 2
mm [unitless] [unitless] [unitless]
OK in flexure (x-axis) OK min. rfct flexure (x-axis) OK min. rfct shrinkage (x-axis
Page 4 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
Bending parallel to z-axis Find the projection noted as Lm Lm = moment on the bending plane, Muz = qu = ∴ Muz = Required steel ratio, =
2710 mm quLL2m/2 26.0 kN/m2 573.0 kNm
0 .85 f c' 2 Ru 1 1 fy 0 .85 f c'
2 Coefficient of resistance Ru = Muz / (ØLdz )
∴ = Area of steel required As req = ∴ As req =
Ref 1: 10.5.1
Ref 1: 7.12.2.1
0.9 0.6801 0.061 0.059
6000
0.0018 Ldz 4,329 mm2
Check for minimum reinforcement required for flexure 0.25Bdz√f'c / fy As min (flexure) max of 1.4Bdz/ fy 0.25Ldz√f'c / fy = 7,727 mm2 1 4Ldz/ fy = 1.4Ld 7 900 mm2 7,900 ∴ Use As min (flexure) = 7,900 mm2
6000
= ∴ Ru = 0.85f'c / fy = 2RU/((0.85f'c) =
Ref 1: 9.3.2.1
2710
Check for minimum reinforcement required for shrinkage As, min (shrinkage) = 0.0018 (times gross sectional area) 2 0.0018Lh = 5,400 mm Reinforcement selection ∴ Governing area of steel required = Select bar diameter (mm) Select number of bars Provide bar spacing (to nearest 25mm) As prov As prov (total) = Ratio of As (flexure) / As prov = Ratio of As min (flexure) / As prov = Ratio of As min (shrinkage) / As prov =
7,900 Bottom 20 30 200 9,425 11,781 0.46 0.84 0.46
mm2 Top 10 30 200 mm 2,356 mm2 mm2 [unitless] [unitless] [unitless]
OK in flexure (z-axis) OK min. rfct flexure (z-axis) OK min. rfct shrinkage (z-axis
REINFORCEMENT SUMMARY Along x-axis, bottom mat Along x-axis, top mat Along g z-axis,, bottom mat Along z-axis, top mat Ref 1: 7.12.2.1
Check on distribution of steel parallel to the x-axis: Centre band zone, s =
31-T20-200 B 31-T10-200 T 31-T20-200 B 31-T10-200 T
2/(+1)
= s =
1.00 1.00 ∴ No special reinforcement distribution needed over the length of the footing
Page 5 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
CHECK ON STARTER BARS Check on minimum % reinforcement to starter bars diameter of starter bar, db =
20 mm 8 Nr 2,513 mm2
Number of starter bars = Cross sectional area of bars = Minimum As-starter = 0.005Ag
Ref 1: 15.8.2.1
(note: minimum 4)
440,800 mm2 0.006
pedestal cross-section area Ag=(px*pz) = As-starter / Ag =
OK starter bar min. rfct
Check on starter bar embedment into footing Min of
Ref 1: 12.3.2
length of embedment ldc =
larger of
fy = 420 db = 20 f'c = 30 (0.24fy/√f'c)db = 368 0.043fydb = 361 ∴ Use ldc as = 368 Check on ldc versus depth of footing, h, and effective depth, d d= h=
200 mm (0.24fy/√f'c)db 0.043fydb N/mm2 mm N/mm2 mm mm mm
Say
370 mm (rounded up)
415 mm 500 mm
OK embed. b d d depth th
Check on development length of starter bars Critical sections for the development length (ld) of the starter bars occur at the pedestal/footing interface ld =
Ref 1: 12.2.2
f y t 2 .1
For Ψt Ref 1: 12.2.4 (a) Ref 1: 12.2.4 (b)
depth of freshly cast concrete below ld ∴ Ψt = Ψe = Ψt Ψe =
Ref 1: 12.2.4 (d)
λ = fy = fc = ∴ ld =
e
f c'
db
<300mm 1.00 1.00 (assuming uncoated reinforcement) 1.00 (not to exceed 1 1.7) 7) 1.00 420 N/mm2 30 N/mm2 735 mm
(rounded up)
Dimensional check on ld ld must be less than ∴ Use ld as
5,470 mm 735 mm 8-T20
OK dev't length
Page 6 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
SUMMARY OUTPUT
8-T20
580
31-T10-200 T 31-T10-200 T
500
370
500
735
6000
6000
760
31-T20-200 B
580
f'c=30MPa
31-T20-200 B
Page 7 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
APPENDIX STAAD ANALYSIS OUTPUT Ref 4
The is to carry out the analysis in STAAD and use the post-processing results to obtain the values shown in these tables. Note that two limit state Envelopes are used, Serviceability Limit State and Ultimate Limit State.
Max Fx Min Fx Max Fy Min Fy Max Fz Min Fz Max Mx Min Mx Max My Min My Max Mz Min Mz Maximum values Corresponding values at Fy max
Max Fx Min Fx Max Fy Min Fy Max Fz Min Fz Max Mx Min Mx Max My Min My Max Mz Min Mz Maximum values Corresponding values at Fy max
Node 4005 1005 4005 1005 1005 4005 1005 4005 4005 1005 4005 1005
SERVICEABILITY LIMIT STATE (1.0DL+1.0LL) Horizontal Vertical Horizontal L/C Fx kN Fy kN Fz kN 1 1.0DL+1.0 4.51 565.14 -70.74 534.17 56.90 1 1.0DL+1.0 4.38 1 1.0DL+1.0 4.51 565.14 -70.74 1 1.0DL+1.0 4.38 534.17 56.90 1 1.0DL+1.0 4.38 534.17 56.90 565.14 -70.74 1 1.0DL+1.0 4.51 534.17 56.90 1 1.0DL+1.0 4.38 1 1.0DL+1.0 4.51 565.14 -70.74 1 1.0DL+1.0 4.51 565.14 -70.74 1 1.0DL+1.0 4.38 534.17 56.90 565.14 -70.74 1 1.0DL+1.0 4.51 534.17 56.90 1 1.0DL+1.0 4.38
4005
4.51 4 51 4.51
565.14 565 14 565.14
56.90 70 74 70.74
ULTIMATE LIMIT STATE (All Load Combs) Horizontal Vertical Horizontal Node L/C Fx kN Fy kN Fz kN 647.54 -80.34 4005 DL+1.0EQ(-X 53.59 4005 0.9DL+1.0EQ -45.51 364.81 -42.81 936.32 -312.19 4005 1.0WL(+Z)+1 7.88 1005 0.9DL+1.0W 0.04 52.79 -196.10 1.0WL(-Z)+1 7.84 904.98 298.53 1005 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 1005 1.0WL( Z)+1 7.84 904.98 298.53 1 0WL(-Z)+1 7 84 904 98 298 53 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 1.0WL(-Z)+1 7.84 904.98 298.53 1005 4005 DL+1.0EQ(+X -43.27 645.37 -80.19 366.98 -42.97 4005 0.9DL+1.0EQ 51.35 4005
53.59 7.88
936.32 936.32
298.53 312.19
Moment Mx kNm -14.29 9.67 -14.29 9.67 9.67 -14.29 9.67 -14.29 -14.29 9.67 -14.29 9.67
My kNm 0.57 -0.47 0.57 -0.47 -0.47 0.57 -0.47 0.57 0.57 -0.47 0.57 -0.47
Mz kNm 1.73 1.56 1.73 1.56 1.56 1.73 1.56 1.73 1.73 1.56 1.73 1.56
9.67 14.29 14 29
0.57 0 57 0.57
1.73 1 73 1.73
Moment Mx kNm -16.17 -8.38 -89.96 -67.27 85.42 -89.96 85.42 85 42 -89.96 -89.96 85.42 -16.14 -8.40
My kNm 0.93 0.06 2.64 1.69 -2.54 2.64 2.54 -2 54 2.64 2.64 -2.54 0.36 0.63
Mz kNm -12.57 15.67 2.77 0.25 2.56 2.77 2.56 2 56 2.77 2.77 2.56 16.52 -13.43
85.42 89.96
2.64 2.64
16.52 2.77
This is achieved with Load Combination: 106 1.2DL+1.0WL(+Z)+1.0LL+0.5LR Ref 2
Listing of Load combinations used: 100: 1.0DL 101: 1.0DL+1.0LL 102: 1.4DL 103: 1.2DL+1.6LL+0.5LR 104: 1.2DL+1.6LR+1.0LL 105: 1.2DL+1.0WL(+X)+1.0LL+0.5LR 106: 1.2DL+1.0WL(+Z)+1.0LL+0.5LR 107: 1.2DL+1.0WL(-X)+1.0LL+0.5LR 108: 1.2DL+1.0WL(-Z)+1.0LL+0.5LR 109: 1.2DL+1.0EQ(+X)+1.0LL 110: 1.2DL+1.0EQ(+Z)+1.0LL 111: 1.2DL+1.0EQ(-X)+1.0LL 112: 1.2DL+1.0EQ(-Z)+1.0LL 113: 0.9DL+1.0WL(+X) 114: 0.9DL+1.0WL(+Z) 115: 0.9DL+1.0WL(-X) 116: 0.9DL+1.0WL(-Z) 117: 0.9DL+1.0EQ(+X) 118: 0.9DL+1.0EQ(+Z) 119: 0.9DL+1.0EQ(-X) 120: 0.9DL+1.0EQ(-Z)
Page 8 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
SUMMARY OF MAIN QUANTITIES 3 46.80 m
Excavation Concrete Pedestal Footing Total concrete
10.2.7.3
3 0.22 m 3 18.00 m 3 18.22 m
Reinforcement Bottom mat (x-axis) Top mat (x-axis) Bottom mat (z-axis) Top mat (z-axis) Total reinforcement
484.6 121.1 484.6 121.1 1211.5
kg kg kg kg kg
Formwork Pedestal (x-axis) Pedestal (z-axis) Length Breadth Total formwork
0.58 0.76 6.00 6.00 13.34
m m2 m2 m2 m2
2
Section analysis (x-axis) /0 85f cB Depth of stress block, block a = Asfy/0.85f 1 (stress block depth to neutral axis depth) = 0.84 [unitless] ∴a= c= ∴c= ∴ c/d ratio =
25.9 mm a/1 31.0 mm 0.075 <0.375 ∴ Strains are in the tension-controlled zone, OK for ductile conditions
x-axis= 0.851[c/d] f'c/fy x-axis= 0.0038 Flexural resistance factor, R = fy(1-(fy/1.7fc)) Flexural resistance factor factor, R = Nominal moment capacity (x-axis), Mn = Nominal moment capacity (x-axis), Mn = Actual moment along x-axis, Mux = Ratio of Mux/Mn =
10.2.7.3
1.51 1 51 Rbd2 1555.7 kNm 573.0 kNm 0.37
OK for bending along x-axis
Section analysis (z-axis) Depth of stress block, a = Asfy/0.85f cL 1 (stress block depth to neutral axis depth) = 0.84 [unitless] ∴a= c=
25.9 mm a/1
∴c= ∴ c/dz ratio =
31.0 mm 0.078 <0.375 ∴ Strains are in the tension-controlled zone, OK for ductile conditions
z-axis= 0.851[c/dz] f'c/fy z-axis= 0.0040 Flexural resistance factor, R = fy(1-(fy/1.7fc)) Flexural resistance factor, R = Nominal moment capacity (z-axis), Mn = Nominal moment capacity (z-axis), Mn = Actual moment along z-axis, Muz = Ratio of Muz/Mn =
1.58 Rbdz2 1476.5 kN 573.0 kNm 0.39
OK for bending along z-axis
Page 9 of 9
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
References: 1 - ACI 318M-05, Building Code requirements for Structural Concrete, 2005 2 - ASCE 7-10, Minimum Design loads for Buildings & Other Structures, 2010 3 - Preliminary Geotechnical report, Trintoplan Consultants Limited, October 2013 4 - STAAD output 5 - ASTM A615-04, Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement Summary of calculation checks Soil bearing capacity Two-way (punching) shear x-axis: One-way (wide beam) shear Flexural Min. Flexural reinforcement Shrinkage reinforcement z-axis: One-way (wide beam) shear Flexural Min. Flexural reinforcement Shrinkage reinforcement
Utilisation ratio (actual vs capacity) 0.97 OK bearing capacity 0.37 OK two-way shear
Starter bar reinforcement Starter bar embedment Starter bar development length
**this condition governs**
0.42 0.44 0.88 0.46
OK one-way shear (x-axis) OK in flexure (x-axis) OK min. rfct flexure (x-axis) OK min. rfct shrinkage (x-axis)
0.50 0.46 0.84 0.46
OK one-way shear (z-axis) OK in flexure (z-axis) OK min. rfct flexure (z-axis) OK min. rfct shrinkage (z-axis)
OK starter bar min. rfct OK embed. depth 0.13 OK dev't dev t length
Note for and reader: Bordered cells denote -input, all other cells are calculated via this spreadsheet using the relevant base data, material and guidance from the noted References FOOTING GEOMTERY & MATERIAL PROPERTIES Foundation geometry pedestal width (in X-direction), px = pedestal breadth (in Z-direction), pz = pedestal height (in Y-direction), H Footing thickness, h Founding depth below GL Length of footing, L (in X-direction) Breadth of footing, B (in Z-direction) Footing shape:
580 760 500 500 1300 6000 6000 Square
Concrete density (kN/m3) Pedestal volume Pedestal weight Footing volume Footing weight 3
Soil weight above pad (assumes =20kN/m ) = ∴ Total footing & soil weight Ff =
23.1 0.2 5.1 18.0 415.2 928.9 1349.2
6000 6000 500
Calculation of footing & soil surcharge weight Ref 4: Tbl C3-2
580 760 500 500
mm mm mm mm mm mm mm
kN/m3 m3 kN 3 m kN kN kN
500
580
760
6000
6000
Material properties 28-day concrete comp. strength, f'c Ref 1: 7.7.1 Ref 5
Ref 3
30 N/mm2 Cover to reinforcement 75 mm Main reinforcement to be used A615 Gr 60 2 Reinforcement yield strength, fy = 420 N/mm Effective depth, d (for x-axis checks) 415 mm Effective depth, dz (for z-axis checks) 395 mm 2 Allowable soil bearing capacity, qa 55.0 kN/m
f'c=30MPa
208
LOADING DATA Note; Use Serviceability Limit state values when checking for soil bearing pressures. There is already a Factor of Safety built in to the allowable bearing pressure parameter as outlined in the geotehcnical report. Use Ultimate Limit State results for all other design checks.
Ref 4
Ref 4
Serviceability Limit State results From STAAD output, using Serviceability Limit state analysis: Fx (kN) Fy (kN) Maximum FY occurrence (SLS) 4.5 565.1
Fz (kN) 70.7
Mx (kNm) My (kNm) 14.3 0.6
Mz (kNm) 1.7
Node 4005
Ultimate Limit State results From STAAD output, using Ultimate Limit state analysis: Fx (kN) Fy (kN) Maximum FY occurrence (ULS) 7.9 936.3
Fz (kN) 312.2
Mx (kNm) My (kNm) 90.0 2.6
Mz (kNm) 2.8
Node 4005
Page 1 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
CHECK ON SOIL BEARING PRESSURES 1914.4 Bearing pressure along x-axis Pressure distr. under base: qmax,min = Ref 4
Use Fy (serviceability) = Load FV on underside of footing = Fy+Ft = FV/LB = 2
MZ+FXH/BL = qmax= qmin= Bearing pressure along z-axis Pressure distr. under base: qmax,min =
FV M Z FX H LB BL 2 565.1 1914.4 53.2 0.0 53.2 53.2
4.5
kN kN
6000
kN/m2 2 kN/m kN/m2 2 kN/m
FV Mx FzH LB LB 2
1914.4 70.7
Ref 4
Use Fy (serviceability) = Load FV on underside of footing = Fy+Ft = FV/LB = MX+FZH/LB2 = qmax= qmin=
Ref 3
∴ Use max bearing pressure as pa = Allowable soil bearing capacity, qa Ratio of pa to qa =
565.1 1914.4 53.2 0.3 53.5 52.8
kN kN kN/m2 2 kN/m kN/m2 kN/m2
Ref 1: 9.3.2.4
53.5 kN/m2 55.0 kN/m2 0.973
Ref 1: 10.17.1
Ref 4
Nominal pedestal or bearing load capacity, Pn Pn(0.85f'cA1)*[√A2/A1] A1 = A2 = (px+4d)*(pz+4d) = √A2/A1 (but max. 2.0)= f'c = ∴ Pn Fy = Ratio of Fy to Pn
0.6
6000
OK bearing capacity
936.3
CHECK FOR pedestal BEARING (transfer of load from pedestal into footing)
Ref 1: 10.17.1
1.7
0.65 0.441 0 441 5.421 2.00 30.0 14,613 936.3 0.06
[unitless]
415
m2 m2 [unitless] N/mm2 kN kN OK col bearing resistance
SHEAR CHECKS Check for Two-way (punching) shear capacity Vn Ref 1: 9.3.2.3 Ref 1: 11.1.1 Ref 1: 11.12.1.2
0.75 Where VnV c Assuming g that no shear reinforcement is used in the footing g Shear perimeter is located at a distance of 1.0d outside of the pedestal/pedestal face Shear perimeter length, bo is given by bo = 2(px+d)+(2(pz+d) px = 580 mm pz = 760 mm d= ∴ bo = Factored net soil pressure qu = Fy = Pu = ∴ qu =
415 mm 4340 mm Pu/BL 936.3 kN 26.0 kN/m2
Find the total shear force for two-way shear, VU2 where VU2 = Pu-qu(px+d)(py+d) ∴ VU2 = 905.9 kN
Page 2 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
Calculate the nominal shear strength, VC of the footing Vc (kN) = min of
Ref 1: 11.12.2.1
(a) (b) (c)
0.17(1+2/)√f'cbod 0.083([sd/bo]+2)√f'cbod 0.33√f'cbod 6000
Condition (a) Ratio of long side to short side of col, = f'c = bo = d= Vc-condition (a) =
1.00 [unitless] 30.0 N/mm2 4,340 mm 415 mm 5,031.2 kN
208
Condition (b) Ref 1: 11.12.2.1
pedestal location for determining as = s = Vc-condition (b) =
Edge 30 3,986.4 kN
760
Condition (c) Vc-condition (c) =
Vc = min of
∴ Use Vc = Vc = VU2 = Ratio of VU2/Vc =
(a) (b) (c)
580 5,031.2 kN 3,986.4 kN 3,255.5 kN
208
415
3,255.5 kN 2 441 6 kN 2,441.6 905.9 kN 0.37
OK two-way shear
Check for one-way (wide beam) shear: The critical section for one-way (wide beam) shear extends across the width of the footing at a distance d from the face of the loaded area. 6000
One-way shear parallel to x-axis Vc = 0.17√f'cBd
Ref 1: 11.3.1.1
B= Vc = ∴ Vc =
6000 mm 2,318.5 kN 1,738.9 kN
Find the projection noted as L' Footing shape: Square L' = 2295 mm Shear force on shear plane, Vu1 = BL'qu = 732.5 kN Ratio of Vu1/Vc = 0.42
6000
Ref 1: 11.12.1.1
3,255.5 kN
OK one-way shear (x-axis)
415
One-way shear parallel to z-axis Vc = 0.17√f'cLdz L= Vc = ∴ Vc =
6000 mm 2,206.8 kN 1,655.1 kN
2295
Find the projection noted as L' Footing shape: Square L' = 2585 mm Shear force on shear plane, Vu1 = BL'qu = 829.9 kN Ratio of Vu1/Vc = 0.50 [unitless]
415
Note: sketch also holds for one-way shear in the z-axis
OK one-way shear (z-axis)
Page 3 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
MOMENT AND REINFORCEMENT CHECKS Bending parallel to x-axis Find the projection noted as Lm Lm = moment on the bending plane, Mux = qu =
2710 mm 2 quBL m/2
26.0 kN/m2 ∴ Mux = 573.0 kNm Required steel ratio, = 0 . 85 f ' c
fy
2 Ru 1 1 0 .85 f c'
6000 2
Coefficient of resistance Ru = Mux / (Øbd ) = ∴ Ru = 0.85f'c / fy = 2RU/((0.85f'c) = ∴ = Area of steel required As req = ∴ As req =
R f 1: Ref 1 10 10.5.1 51
Ref 1: 7.12.2.1
0.9 0.6162 0.061 0.054 0.0017 Bd 4,115 mm2
6000
Ref 1: 9.3.2.1
Check for minimum reinforcement required for flexure 0 25Bd√f'c / fy 0.25Bd√f As min (flexure) max of 1.4Bd/ fy 0.25Bd√f'c / fy = 8,118 mm2 1.4Bd/ fy = 8,300 mm2 ∴ Use As min (flexure) = 8,300 mm2
2710
Check for minimum reinforcement required for shrinkage As, min (shrinkage) = 0.0018 (times gross sectional area) 2 0.0018Bh = 5,400 mm Reinforcement selection Select bar diameter (mm) Select number of bars Provide bar spacing (to nearest 25mm) As prov As total = Ratio of As (flexure) / As prov = Ratio of As min (flexure) / As prov = Ratio of As min (shrinkage) / As prov =
Bottom 20 30 200 9,425 11,781 0.44 0.88 0.46
Top 10 30 200 mm 2 2,356 mm 2
mm [unitless] [unitless] [unitless]
OK in flexure (x-axis) OK min. rfct flexure (x-axis) OK min. rfct shrinkage (x-axis
Page 4 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
Bending parallel to z-axis Find the projection noted as Lm Lm = moment on the bending plane, Muz = qu = ∴ Muz = Required steel ratio, =
2710 mm quLL2m/2 26.0 kN/m2 573.0 kNm
0 .85 f c' 2 Ru 1 1 fy 0 .85 f c'
2 Coefficient of resistance Ru = Muz / (ØLdz )
∴ = Area of steel required As req = ∴ As req =
Ref 1: 10.5.1
Ref 1: 7.12.2.1
0.9 0.6801 0.061 0.059
6000
0.0018 Ldz 4,329 mm2
Check for minimum reinforcement required for flexure 0.25Bdz√f'c / fy As min (flexure) max of 1.4Bdz/ fy 0.25Ldz√f'c / fy = 7,727 mm2 1 4Ldz/ fy = 1.4Ld 7 900 mm2 7,900 ∴ Use As min (flexure) = 7,900 mm2
6000
= ∴ Ru = 0.85f'c / fy = 2RU/((0.85f'c) =
Ref 1: 9.3.2.1
2710
Check for minimum reinforcement required for shrinkage As, min (shrinkage) = 0.0018 (times gross sectional area) 2 0.0018Lh = 5,400 mm Reinforcement selection ∴ Governing area of steel required = Select bar diameter (mm) Select number of bars Provide bar spacing (to nearest 25mm) As prov As prov (total) = Ratio of As (flexure) / As prov = Ratio of As min (flexure) / As prov = Ratio of As min (shrinkage) / As prov =
7,900 Bottom 20 30 200 9,425 11,781 0.46 0.84 0.46
mm2 Top 10 30 200 mm 2,356 mm2 mm2 [unitless] [unitless] [unitless]
OK in flexure (z-axis) OK min. rfct flexure (z-axis) OK min. rfct shrinkage (z-axis
REINFORCEMENT SUMMARY Along x-axis, bottom mat Along x-axis, top mat Along g z-axis,, bottom mat Along z-axis, top mat Ref 1: 7.12.2.1
Check on distribution of steel parallel to the x-axis: Centre band zone, s =
31-T20-200 B 31-T10-200 T 31-T20-200 B 31-T10-200 T
2/(+1)
= s =
1.00 1.00 ∴ No special reinforcement distribution needed over the length of the footing
Page 5 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
CHECK ON STARTER BARS Check on minimum % reinforcement to starter bars diameter of starter bar, db =
20 mm 8 Nr 2,513 mm2
Number of starter bars = Cross sectional area of bars = Minimum As-starter = 0.005Ag
Ref 1: 15.8.2.1
(note: minimum 4)
440,800 mm2 0.006
pedestal cross-section area Ag=(px*pz) = As-starter / Ag =
OK starter bar min. rfct
Check on starter bar embedment into footing Min of
Ref 1: 12.3.2
length of embedment ldc =
larger of
fy = 420 db = 20 f'c = 30 (0.24fy/√f'c)db = 368 0.043fydb = 361 ∴ Use ldc as = 368 Check on ldc versus depth of footing, h, and effective depth, d d= h=
200 mm (0.24fy/√f'c)db 0.043fydb N/mm2 mm N/mm2 mm mm mm
Say
370 mm (rounded up)
415 mm 500 mm
OK embed. b d d depth th
Check on development length of starter bars Critical sections for the development length (ld) of the starter bars occur at the pedestal/footing interface ld =
Ref 1: 12.2.2
f y t 2 .1
For Ψt Ref 1: 12.2.4 (a) Ref 1: 12.2.4 (b)
depth of freshly cast concrete below ld ∴ Ψt = Ψe = Ψt Ψe =
Ref 1: 12.2.4 (d)
λ = fy = fc = ∴ ld =
e
f c'
db
<300mm 1.00 1.00 (assuming uncoated reinforcement) 1.00 (not to exceed 1 1.7) 7) 1.00 420 N/mm2 30 N/mm2 735 mm
(rounded up)
Dimensional check on ld ld must be less than ∴ Use ld as
5,470 mm 735 mm 8-T20
OK dev't length
Page 6 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
SUMMARY OUTPUT
8-T20
580
31-T10-200 T 31-T10-200 T
500
370
500
735
6000
6000
760
31-T20-200 B
580
f'c=30MPa
31-T20-200 B
Page 7 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
APPENDIX STAAD ANALYSIS OUTPUT Ref 4
The is to carry out the analysis in STAAD and use the post-processing results to obtain the values shown in these tables. Note that two limit state Envelopes are used, Serviceability Limit State and Ultimate Limit State.
Max Fx Min Fx Max Fy Min Fy Max Fz Min Fz Max Mx Min Mx Max My Min My Max Mz Min Mz Maximum values Corresponding values at Fy max
Max Fx Min Fx Max Fy Min Fy Max Fz Min Fz Max Mx Min Mx Max My Min My Max Mz Min Mz Maximum values Corresponding values at Fy max
Node 4005 1005 4005 1005 1005 4005 1005 4005 4005 1005 4005 1005
SERVICEABILITY LIMIT STATE (1.0DL+1.0LL) Horizontal Vertical Horizontal L/C Fx kN Fy kN Fz kN 1 1.0DL+1.0 4.51 565.14 -70.74 534.17 56.90 1 1.0DL+1.0 4.38 1 1.0DL+1.0 4.51 565.14 -70.74 1 1.0DL+1.0 4.38 534.17 56.90 1 1.0DL+1.0 4.38 534.17 56.90 565.14 -70.74 1 1.0DL+1.0 4.51 534.17 56.90 1 1.0DL+1.0 4.38 1 1.0DL+1.0 4.51 565.14 -70.74 1 1.0DL+1.0 4.51 565.14 -70.74 1 1.0DL+1.0 4.38 534.17 56.90 565.14 -70.74 1 1.0DL+1.0 4.51 534.17 56.90 1 1.0DL+1.0 4.38
4005
4.51 4 51 4.51
565.14 565 14 565.14
56.90 70 74 70.74
ULTIMATE LIMIT STATE (All Load Combs) Horizontal Vertical Horizontal Node L/C Fx kN Fy kN Fz kN 647.54 -80.34 4005 DL+1.0EQ(-X 53.59 4005 0.9DL+1.0EQ -45.51 364.81 -42.81 936.32 -312.19 4005 1.0WL(+Z)+1 7.88 1005 0.9DL+1.0W 0.04 52.79 -196.10 1.0WL(-Z)+1 7.84 904.98 298.53 1005 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 1005 1.0WL( Z)+1 7.84 904.98 298.53 1 0WL(-Z)+1 7 84 904 98 298 53 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 4005 1.0WL(+Z)+1 7.88 936.32 -312.19 1.0WL(-Z)+1 7.84 904.98 298.53 1005 4005 DL+1.0EQ(+X -43.27 645.37 -80.19 366.98 -42.97 4005 0.9DL+1.0EQ 51.35 4005
53.59 7.88
936.32 936.32
298.53 312.19
Moment Mx kNm -14.29 9.67 -14.29 9.67 9.67 -14.29 9.67 -14.29 -14.29 9.67 -14.29 9.67
My kNm 0.57 -0.47 0.57 -0.47 -0.47 0.57 -0.47 0.57 0.57 -0.47 0.57 -0.47
Mz kNm 1.73 1.56 1.73 1.56 1.56 1.73 1.56 1.73 1.73 1.56 1.73 1.56
9.67 14.29 14 29
0.57 0 57 0.57
1.73 1 73 1.73
Moment Mx kNm -16.17 -8.38 -89.96 -67.27 85.42 -89.96 85.42 85 42 -89.96 -89.96 85.42 -16.14 -8.40
My kNm 0.93 0.06 2.64 1.69 -2.54 2.64 2.54 -2 54 2.64 2.64 -2.54 0.36 0.63
Mz kNm -12.57 15.67 2.77 0.25 2.56 2.77 2.56 2 56 2.77 2.77 2.56 16.52 -13.43
85.42 89.96
2.64 2.64
16.52 2.77
This is achieved with Load Combination: 106 1.2DL+1.0WL(+Z)+1.0LL+0.5LR Ref 2
Listing of Load combinations used: 100: 1.0DL 101: 1.0DL+1.0LL 102: 1.4DL 103: 1.2DL+1.6LL+0.5LR 104: 1.2DL+1.6LR+1.0LL 105: 1.2DL+1.0WL(+X)+1.0LL+0.5LR 106: 1.2DL+1.0WL(+Z)+1.0LL+0.5LR 107: 1.2DL+1.0WL(-X)+1.0LL+0.5LR 108: 1.2DL+1.0WL(-Z)+1.0LL+0.5LR 109: 1.2DL+1.0EQ(+X)+1.0LL 110: 1.2DL+1.0EQ(+Z)+1.0LL 111: 1.2DL+1.0EQ(-X)+1.0LL 112: 1.2DL+1.0EQ(-Z)+1.0LL 113: 0.9DL+1.0WL(+X) 114: 0.9DL+1.0WL(+Z) 115: 0.9DL+1.0WL(-X) 116: 0.9DL+1.0WL(-Z) 117: 0.9DL+1.0EQ(+X) 118: 0.9DL+1.0EQ(+Z) 119: 0.9DL+1.0EQ(-X) 120: 0.9DL+1.0EQ(-Z)
Page 8 of 9
CLIENT PROJECT Location Sub-Location
RAINBOW CONSTRUCTION LIMITED EDEN GARDENS APARTMENTS 2-BEDROOM APARTMENT MODEL Pad footing -F1, F4,
Date By Project:
Reference
10-Jun-15 M V Rampersad 135-006
Calculation
Output
SUMMARY OF MAIN QUANTITIES 3 46.80 m
Excavation Concrete Pedestal Footing Total concrete
10.2.7.3
3 0.22 m 3 18.00 m 3 18.22 m
Reinforcement Bottom mat (x-axis) Top mat (x-axis) Bottom mat (z-axis) Top mat (z-axis) Total reinforcement
484.6 121.1 484.6 121.1 1211.5
kg kg kg kg kg
Formwork Pedestal (x-axis) Pedestal (z-axis) Length Breadth Total formwork
0.58 0.76 6.00 6.00 13.34
m m2 m2 m2 m2
2
Section analysis (x-axis) /0 85f cB Depth of stress block, block a = Asfy/0.85f 1 (stress block depth to neutral axis depth) = 0.84 [unitless] ∴a= c= ∴c= ∴ c/d ratio =
25.9 mm a/1 31.0 mm 0.075 <0.375 ∴ Strains are in the tension-controlled zone, OK for ductile conditions
x-axis= 0.851[c/d] f'c/fy x-axis= 0.0038 Flexural resistance factor, R = fy(1-(fy/1.7fc)) Flexural resistance factor factor, R = Nominal moment capacity (x-axis), Mn = Nominal moment capacity (x-axis), Mn = Actual moment along x-axis, Mux = Ratio of Mux/Mn =
10.2.7.3
1.51 1 51 Rbd2 1555.7 kNm 573.0 kNm 0.37
OK for bending along x-axis
Section analysis (z-axis) Depth of stress block, a = Asfy/0.85f cL 1 (stress block depth to neutral axis depth) = 0.84 [unitless] ∴a= c=
25.9 mm a/1
∴c= ∴ c/dz ratio =
31.0 mm 0.078 <0.375 ∴ Strains are in the tension-controlled zone, OK for ductile conditions
z-axis= 0.851[c/dz] f'c/fy z-axis= 0.0040 Flexural resistance factor, R = fy(1-(fy/1.7fc)) Flexural resistance factor, R = Nominal moment capacity (z-axis), Mn = Nominal moment capacity (z-axis), Mn = Actual moment along z-axis, Muz = Ratio of Muz/Mn =
1.58 Rbdz2 1476.5 kN 573.0 kNm 0.39
OK for bending along z-axis
Page 9 of 9
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