CONSULTING Engineering Calculation Sheet. Reference Sheets - Pile Cap Capacity (Generic) Tables XX

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Whitney Turner
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460N/mm 2 Yield strength of shear link steel, f yv 460N/mm 2 Type of concrete and density, ρ c 24kN/m 3 Cover to all (bottom) reinforcement, cover 1 (usually 100) Cover to all (top) reinforcement,

with 8 x φ link anchorage, top steel of either {T20EW@p b, T20EW@S l, none}, noting that the T20 top steel will be changed to a smaller bar size if base steel φ b is less than T20; Base steel

5 to 1.5).(2.5 to 3.0).T cap /(1.5 to 2.5) (0.5 to 1.5).(1.0 to 2.0).T cap ; (0.5 to 1.0).T cap first shear perimeter, (1.5 to 3.0).T cap second shear perimeter; Note a v 0.5d [EC2 cl.6.2.3(8)], note a v is the distance from 20% D inside face of pile to the column base face based on cl.

1 Job No. Sheet No. E N G I N E E R S Consulting Engineers jxxx 1 Pile Cap Capacity (Generic) Input Characteristic strength of concrete, f cu ( 60N/mm 2 ; HSC N/A) 40N/mm 2 OK Yield strength of longitudinal steel, f y 460N/mm 2 Yield strength of shear link steel, f yv 460N/mm 2 Type of concrete and density, ρ c 24kN/m 3 Cover to all (bottom) reinforcement, cover 1 (usually 100) Cover to all (top) reinforcement, cover 3 (usually 45 integrated base slab and Spacer for base steel, s r,base ( MAX (φ b, 25mm)) 75mm 75mm 75mm Inclusion of top steel in estimated steel reinforcement quantity Base steel, shear links with 8 x φ link anchorage, top steel of either {T20EW@p b, T20EW@S l, none}, noting that the T20 top steel will be changed to a smaller bar size if base steel φ b is less than T20; Base steel anchorage, top steel anchorage, binders excluded; Shear span, a v Note a v (0.5 to 1.5).S, where 0.5 and 1.5 refer to first and second shear perimeters, respectively (0.5 to 1.5).(2.5 to 3.0).D (0.5 to 1.5).(2.5 to 3.0).T cap /(1.5 to 2.5) (0.5 to 1.5).(1.0 to 2.0).T cap ; (0.5 to 1.0).T cap first shear perimeter, (1.5 to 3.0).T cap second shear perimeter; Note a v 0.5d [EC2 cl.6.2.3(8)], note a v is the distance from 20% D inside face of pile to the column base face based on cl and cl BS8110; Note a large value of a v would be critical for longitudinal shear, whilst a small value would be critical for deep beam bending and shear; Note a large value of a v would ensure no shear enhancement, i.e. 2d/a v = 1.00 as may be appropriate for rafts without piles; Pile cap design theory (shallow beam bending theory) Pile cap design theory (deep beam bending and shear theory) Note although deep beam theory may not apply for the extreme piles in certain pile caps due to their large width and / or length, it may be prudent to include deep beam theory in circumstances where there exist a significant number of piles which are also close to the column; Ultimate shear force theory (deep beam theory) Factor, k s Check longitudinal shear within section Roughness coefficient, c Roughness coefficient, µ Normal stress across longitudinal shear interface, σ n 0.00N/mm 2

2 E N G I N E E R S Consulting Engineers Job No. Sheet No. jxxx 2 Pile Cap Capacity (Generic) Equations Moment capacity per metre, M cap = (0.67.f cu /1.5 ).( x).(d-0.45x) Effective depth, d = T cap - cover 1 - φ link - [ φ b +(n layers,base -1)( φ b +s r,base )]/2 - φ b Base steel area provided per metre, A s,prov,b = ( π.φ b 2 /4). n layers,base / p b Base steel area %, ρ w = 100A s,prov,b /(1000.d) Neutral axis, x = (f y /1.05).(A s,prov,b )/[( ).(0.67f cu /1.5)] < 0.5d Moment capacity per metre (deep beam), M cap,db = A s,prov,b.f y.t cap / 1.75 [Reynolds T.148] Ultimate shear capacity per metre, V cap,ult = (1000.d).min(0.8f cu 0.5, 5N/mm 2 ) Design shear capacity per metre for design links, V cap,d = V cap,c A sv,prov /S l.(0.95f yv ).d Concrete shear capacity per metre for no nominal / design links, V cap,c = (2d/a v ).v c.(1000.d) Shear enhancement, 2d/a v 1.00 Area provided by all links per metre, A sv,prov = (1/S l ). π.φ link 2 /4 Effective area provided by all links per metre, 0.75A sv,prov [EC2 cl.6.2.3(8), BS8110 cl ] Effective shear area per square metre, 0.75A sv,prov / S l Nominal shear area per square metre, (0.4N/mm 2 ).1000/(0.95f yv ) Shear coefficient limit, (400/d) 1/4 >0.67 no links, (400/d) 1/4 >1.00 with links Shear strength, v c = (0.79/1.25)( ρ w f cu /25) 1/3 (400/d) 1/4 ; ρ w <3; f cu <40; (400/d) 1/4 >(0.67 or 1 Ultimate shear capacity per metre for no nominal / design links (deep beam), V cap,ult,db Note V cap,ult,db = 1000.T cap.f c '/10 γ m [cl Reynolds] Note f c ' is the cylinder compressive strength; Note V cap,ult,db = min{1000.t cap. ν u, T cap 2 ν c k s /a} [cl CIRIA Guide 2] Note ν u ultimate concrete shear strength from CP 110 T.6 and T.26 replaced by min{0.8f cu 0.5, 5.0}N/mm 2 }, ν c design concrete shear strength from CP 110 T.5 and T.25 replaced by v c and factor, k s = {0.6, 1.0}; Concrete shear capacity per metre for no nominal / design links (deep beam), V cap,c,db Note V cap,c,db = max{0, k 1.(T cap -0.35a).f t.1000}+k 2.A s,prov,b.d.sin 2 θ/t cap Distance to face of pile from column base face, a = MAX (0, a v - 0.2D) MAX (0, a v ) Empirical coefficient, k 1 = {0.70 NWC, 0.50 LWC} Empirical coefficient, k 2 = {100 plain round bars, 225 deformed bars} Cylinder splitting tensile strength, f t = 0.5(f cu ) 0.5 Angle between horizontal bar and critical diagonal crack, θ = tan -1 (T cap /a)

3 Job No. Sheet No. E N G I N E E R S Consulting Engineers jxxx 3 Longitudinal shear capacity per metre, V Rdi = (z.b i ).v Rdi / β Bending stress ratio per metre, K = [M cap,adopt /1000d 2 ] / f cu <= EC2 cl Lever arm, z = d.[0.5 + (0.25-K/0.9) 0.5 ] <= 0.95d Ratio, β = EC2 Width of the interface, b i = 1000mm 1000 mm cl Longitudinal shear stress limit, v Rdi Note c.f ctd = 0.00 if σ n is negative (tension); EC2 cl cl Roughness coefficient, c cl Roughness coefficient, µ 0.9 cl ) Design tensile strength, f ctd 1.40 N/mm 2 EC2 with α ct =1.0, γ C =1.5 cl N/mm 2 T N/mm 2 T N/mm 2 T.3.1 Characteristic cylinder strength of concrete, f ck 32 N/mm 2 T.3.1 Characteristic cube strength of concrete, f cu 40 N/mm 2 T.3.1 Normal stress across longitudinal shear interface, σ n 0.00 N/mm 2 EC2 Reinforcement ratio, ρ = A s / A i Area of reinforcement, A s = A sv,prov / S l Note that the area of reinforcement crossing the shear interface may include ordinary shear reinforcement with adequate anchorage at both cl EC2 cl sides of the interface; Area of the joint, A i = 1000.b i mm 2 /m/m EC2 Design yield strength of reinforcement, f yd = f yv / γ S, γ S = N/mm 2 cl Angle of reinforcement, α = degrees cl Design compressive strength, f cd 21 N/mm 2 EC2 with α cc =1.0, γ C =1.5 cl Strength reduction factor for concrete cracked in shear, ν EC2 cl.6.2.2

4 Job No. Sheet No. E N G I N E E R S Consulting Engineers jxxx 4 Practical Considerations in Choice of Pile Cap Reinforcement 1 Pile cap dimensions and reinforcement optimally chosen such that estimated steel reinforcement quantity is between kg/m 3. 2 Pile cap reinforcement chosen based upon: - (a) base steel diameter T12 when 300mm T cap 500mm base steel diameter T16 when 600mm T cap 1100mm base steel diameter T20 when 1200mm T cap 1800mm base steel diameter T20 when 1900mm T cap 2500mm base steel diameter T20 when 2600mm T cap 3100mm base steel diameter T20 when 3200mm T cap 3800mm base steel diameter T20 when 3900mm T cap 4500mm base steel diameter T20 when 4600mm T cap 5100mm base steel diameter T20 when 5200mm T cap 5800mm base steel diameter T20 when 5900mm T cap 6000mm (b) base steel pitch at 150mm (c) base steel layers 1 when 300mm T cap 1100mm base steel layers 2 when 1200mm T cap 1800mm base steel layers 3 when 1900mm T cap 2500mm base steel layers 4 when 2600mm T cap 3100mm base steel layers 5 when 3200mm T cap 3800mm base steel layers 6 when 3900mm T cap 4500mm base steel layers 7 when 4600mm T cap 5100mm base steel layers 8 when 5200mm T cap 5800mm base steel layers 9 when 5900mm T cap 6000mm (d) shear link diameter MIN {base steel diameter, 25mm} (e) shear link diameter 12mm when 300mm T cap 1100mm shear link diameter 16mm when 1200mm T cap 1800mm shear link diameter 16mm when 1900mm T cap 2500mm shear link diameter 16mm when 2600mm T cap 3100mm shear link diameter 20mm when 3200mm T cap 3800mm shear link diameter 20mm when 3900mm T cap 4500mm shear link diameter 20mm when 4600mm T cap 5100mm shear link diameter 20mm when 5200mm T cap 5800mm shear link diameter 20mm when 5900mm T cap 6000mm (f) shear link pitch at multiples of 150mm (g) shear link pitch 150mm when 300mm T cap 1100mm shear link pitch 300mm when 1200mm T cap 1800mm shear link pitch 300mm when 1900mm T cap 2500mm shear link pitch 300mm when 2600mm T cap 3100mm shear link pitch 450mm when 3200mm T cap 3800mm shear link pitch 450mm when 3900mm T cap 4500mm shear link pitch 450mm when 4600mm T cap 5100mm shear link pitch 450mm when 5200mm T cap 5800mm shear link pitch 450mm when 5900mm T cap 6000mm

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