Borhanul hasan Tapu
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Bangladesh Bangladesh Institute of Technology Khulna Bangladesh
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PILE CAP DESIGN (ACI318-11) TEDDS calculation version 1.1.07
tcap
eemb
w2
L
g i a d _ e d s i
Ly
P1 s
s
hcol w1
0.866s
0.288s 0.288s
bcol s P3
dpile e
P2 e Lx
Pile details Number of piles; piles;
N=3
Pile diameter ;
dpile = 20.0 in 20.0 in
Pile capacity (service); (service) ;
Pcap = 120.0 kips 120.0 kips
Pile spacing provided; provided;
s = 60.0 in 60.0 in
Minimum pile spacing required; required;
smin = max (36 in, (d pile + 24 in)) = 44.0 in 44.0 in PASS - Provided spacing is not less than minimum required
Edge distance of pile from pile cap edge; edge ;
e = 11.0 in 11.0 in
Minimum edge distance required; required;
emin = 11 in 11 in PASS - Provided edge distance is not less than minimum required
Pile cap details Concrete cover ;
cc = 3.0 in 3.0 in
Length of pile cap along X axis; axis;
Lx = s + d pile + 2 e = 8.5 ft 8.5 ft
Length of pile cap along Y axis; axis;
Ly = sin(60) s + dpile + 2 e = 7.8 ft 7.8 ft
Overall pile cap thickness; thickness ;
tcap = 40.0 in 40.0 in w1 = dpile + 2 e = 3.50 ft 3.50 ft w2 = dpile + 2 e = 3.50 ft 3.50 ft
Diagonal length of sides; sides;
Lside_diag = ((Ly - w1)2 + ((Lx - w2) / 2)2) = 5.000 ft 5.000 ft
Pile embedment distance; distance;
eemb = 6.0 in 6.0 in
Minimum pile embedment distance; distance;
ec_min = 6 in PASS - Provided embedment distance is not less than minimum required
Column details Column width along X axis; axis;
bcol = 24.0 in 24.0 in
Column width along Y axis; axis;
hcol = 18.0 in 18.0 in
Borhanul hasan Tapu
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Bangladesh Institute of Technology Khulna
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Yield strength of tension reinforcement;
f y = 60 ksi
Concrete strength;
f’c = 4 ksi
Concrete density;
c = 150 lb/ft3
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Material properties
Reinforcement details (ACI 318, cl. 7.12, cl. 10.5) Diameter number of steel bar along X axis;
Dx_bar_num = 6
Diameter of steel bar along X axis;
Dx_bar = 0.75 in
Depth of cap above bottom reinforcement (X axis); dx = tcap – eemb -cc - Dx_bar / 2 = 30.6 in Total number of steel bars along X axis;
Nx_bar = 22
Spacing of steel bars along X axis;
sx_bar = (Ly – 2 cc - Dx_bar ) / (Nx_bar - 1) = 4.2 in Ast_x = Nx_bar 0.25 Dx_bar 2 = 9.7 in2
Area of steel provided along X axis; Gross cross sectional area of cap along Y axis;
Ag_y = Ly tcap = 3758.5 in2
C/S area of cap above bottom reinf. along Y axis;
Ab_y = Ly d = 2842.3 in2
Minimum area of steel required along X axis;
Ast_min_x = max (0.0018 Ag_y, 200 Ab_y1psi /f y, 3(f’c1psi) Ab_y/f y) Ast_min_x = 9.5 in2 PASS - Provided area of steel along X axis is greater than minimum required
Loading details
Strength reduction factor (tied-arch);
f = 0.90 v = 0.75 t = 0.75
Column axial dead load;
Pdl = 150.0 kips
Strength reduction factor (flexure); Strength reduction factor (shear);
Area of pile cap;
Acap = Lx Ly - sin(60) Lside_diag2/2 = 55.731 ft2
Weight of pile cap;
Pwt = (Acap tcap - 3 dpile eemb / 4) c = 27.4 kips
Surcharge pressure on pile cap; Surcharge load;
sur = 3.000 ksf Psur = sur (Acap - hcol bcol) = 158.2 kips
Column axial live load;
Pll = 20.0 kips
Total column load (unfactored);
Pn = Pdl + Pll = 170.0 kips
The service load per pile is;
Pn_pile = (Pn + Pwt + Psur ) / 3 = 118.5 kips PASS - Pile capacity is sufficient
Total column load (factored);
Pu = 1.2 Pdl + 1.6 Pll = 212.0 kips
The ultimate load per pile is;
Pu_pile = (Pu + 1.2 (Pwt + Psur )) / 3 = 144.9 kips
Pile cap forces – tied arch method Distance between centroid of column and pi le;
dcl_pl = ((s / 2)2 + (0.288 s)2) = 34.621 in xcl_pl = (dcl_pl2 + d2) = 45.975 in
Compression within pile cap; Tension within pile cap;
= atan(dcl_pl / d) = 48.855 deg = acos(((d2 + (0.288 s)2)) / xcl_pl) = 40.733 deg Cmax = Pu_pile / cos( ) = 220.212 kips T = Cmax sin() / 2 = 71.848 kips
Compression checks for pile cap Strength reduction factor (struct plain concrete); Strength reduction factor (bearing on concrete);
u = 0.55 b = 0.65
Check diagonal comp. as an unreinforced column, using a core equivalent to 2 pile diameters (ACI 318-05, cl. 22.5.2) Bearing capacity of core equivalent to 2 pile dia;
Pc = u 0.60 f’c ((2 dpile)2) / 4 = 1451.4 kips
Borhanul hasan Tapu
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Bangladesh Institute of Technology Khulna Bangladesh
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PASS - Compression within cap is less than diagonal compression Check bearing capacity of pile cap over piles (ACI 318, cl. 22.5.5) Area of pile cap; Cross sectional area of pile; Bearing capacity of cap above pile ;
Acap = 8025.230 in2 Apile = dpile2 / 4 = 314.16 in2 Pbrg_pile = u 0.85 f’c Apile min (2, (Acap / Apile)) = 1028.1 kips PASS - Bearing capacity pile cap over pile is sufficient
Check bearing capacity of pile cap under column; (ACI 318, cl. 10.14) Cross sectional area of column; Bearing capacity of cap below column;
Acol = bcol hcol = 432.00 in2 Pbrg_col = b 0.85 f’c Acol min (2, (Acap / Acol)) = 1670.8 kips PASS - Bearing capacity pile cap under column is sufficient
Area of steel check for moment resistance Distance from pile to face of column;
xface = max (0.577 s – min (b col , hcol) / 2, 0 in) = 25.6 in
Pressure due to weight and surcharge;
qu = 1.2 (sur + Pwt / Acap) = 4.2 ksf
Width at column face;
bw = 71.6 in
Ultimate moment at column face;
Muy = Pu_pilexface - quw2xface2/2+20.577 xface3/3) = 260.2 kip_ft
Net moment at column face;
Mny = Muy / v = 347.0 kip_ft Rreq_y = Mny / (f’c d2) / Lx = 0.012746
Lever arm factor ; Area of steel required to resist moment;
Jy = (0.25 - Rreq_y / (0.85 2)) + 0.5 = 0.9924 Ast_req_Mx = Mny / (f y Jy d) = 2.3 in2 Ast_req_T = T / ( t f y) = 1.6 in2
Area of tension steel required for tied-arch behavior ; Area of steel required along X axis;
Ast_req_x = max (A st_req_Mx, Ast_req_T) = 2.3 in2 PASS - Provided area of steel along X axis is sufficient
Each set of bar should be placed in the direction of axis connecting centers of piles (tringular pattern) Stress block depth factor ; Depth of equivalent rectangular stress block; Balanced neutral axis depth(X axis); Strain in steel (X axis);
= 0.85 a = Ast_x f y / (0.85 f’c Lx) = 1.92 in c = a / 1 = 2.261 in ty = 0.003 ((d – c) / c) = 0.03714 Pass - Ductility is sufficient at ultimate strength
Necessary shear checks Beam action at distance 'd' in t he section parallel to X axis is not applicable Beam action at column face in the section parallel to X axis must be checked Beam action at distance 'd' in t he section parallel to Y axis is not applicable Beam action at column face in the section parallel to Y axis must be checked Punching of single pile is not applicable Punching of pile at corner must be check ed Punching of overlapping piles is not applicable Punching shear at d / 2 from column face is not applicable Punching shear at column face must be checked Beam action at face of column Distance from face of column to edge of cap;
xo = max ((Ly - e - d pile / 2 - 0.288 s - hcol / 2), 0 in) = 46.7 in bx = min ((w2 + 2 (e + dpile / 2) tan(30)), (2 w12)) = 59.40 in
Shear at face of column parallel to X axis;
Vact_face = Pu_pile = 144.9 kips VMrat1 = Muy / (Vact_face d) = 0.7
Borhanul hasan Tapu
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Bangladesh Institute of Technology Khulna Bangladesh
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4/11/2016
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w = Ast_x / (Ly d) = 0.003419 f 1 = (d / xface) (3.5 - 2.5 VMrat1) = 2.0 f 2 = 1.9 1 psi (f’c / (1 psi)) = 0.1 ksi f 3 = 2500 w 1 psi / VMrat1 = 0.0 ksi Vc1 = f 1 (f 2 + f 3) Lx d = 779.0 kips Vc2 = min (Vc1, 10 1 psi (f’c / (1 psi)) Lx d) = 779.0 kips Vc = max (Vc2, 2 1 psi (f’c / (1 psi)) Lx d) = 779.0 kips Vs = 0 kips Shear resist. at face of column parallel to X axis;
Vr_face = v (Vc + Vs) = 584.2 kips PASS - Pile cap is safe in beam action at face of column
Punching of single pile at corner check Perimeter of area at ‘d / 2’ from pile at corner ;
bo = (dpile + d) / 4 + 2 (e + d pile / 2) = 81.47 in
Shear resistance of concrete;
Vc = 4 1 psi (f’c / 1 psi) bo d = 583.173 kips
Shear resistance of steel;
Vs = 0 kips
Ultimate shear resistance;
Vr_corner = v (Vc + Vs) = 437.379 kips
Shear acting;
Vact_ corner = Pu_pile = 144.9 kips PASS - Resistance to pile punching at corner is sufficient
Punching shear check at face of column Length of shear perimeter d / 2 from column face;
bo = 2 (bcol + d + h col + d) = 205.000 in
Length of shear perimeter at column face;
bs = 2 (bcol + hcol) = 84.000 in w = 22.620 in Vact_pun_face = Pu + (Psur + Pwt) (s min (Ly, s)) / L x2 = 276.210 kips Vc1 = (d / w) (bo / bs) 2 1 psi (f’c / 1 psi) bs d = 981.242 kips Vc2 = min (Vc1, 32 1 psi (f’c / 1 psi) bs d) = 981.242 kips Vc = max (Vc2, 4 1 psi (f’c / 1 psi) bo d) = 1467.484 kips Vs = 0 kips Vr_ pun_face = v (Vc + Vs) = 1100.613 kips PASS - Pile cap is safe in punching shear at face of column
Development length of tension steel (ACI 318, cl. 12.5) All bars must be provided with standard 180 end hooks. ldh_1 = (0.02 e f y 1 psi-1 dev (f’c / 1 psi))) Dx_bar = 15.213 in Modification factor ;
mod1 = 0.7
Required development length of hook;
ldh_req = max (ldh_1 mod1, 6 in, 8 Dx_bar ) = 10.649 in
Provided development length;
ldh_prov = e – c c + dpile / 2 = 18.00 in PASS - Hook development length is sufficient
