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FOUNDATION ANALYSIS & DESIGN (ACI318) In accordance with ACI318-11 incorporating Errata as of August 8, 2014 Tedds calculation version 3.0.00
FOUNDATION ANALYSIS Length of foundation; foundation;
Lx = 10 ft 10 ft
Width of foundation; foundation;
Ly = 5 ft
Foundation area; area;
A = Lx × Ly = 50 ft 50 ft2
Depth of foundation; foundation;
h = 12 in 12 in
Depth of soil over foundation; foundation;
hsoil = 18 in 18 in
Density of concrete; concrete;
γ conc 150.0 lb/ft3 conc = 150.0 lb/ft
y
x
1
2.279 ksf
2.279 ksf
Column no.1 details Length of column; column;
lx1 = 18.00 in 18.00 in
Width of column; column;
ly1 = 24.00 in 24.00 in
position in x-axis; x-axis ;
x1 = 60.00 in 60.00 in
position in y-axis; y-axis;
y1 = 12.00 in 12.00 in
Soil properties Gross allowable bearing pressure; pressure ;
qallow_Gross = 2.5 ksf 2.5 ksf
Density of soil; soil;
Coefficient of base friction; friction;
γ soil 120.0 lb/ft3 soil = 120.0 lb/ft φb = 30.0 deg 30.0 deg δbb = 30.0 deg 30.0 deg tan(δbb) = 0.577
Dead surcharge load; load;
FDsur = 50 psf 50 psf
Self weight; weight;
Fswt = h × γ conc 150 psf conc = 150 psf
Soil weight; weight;
Fsoil = hsoil × γ soil 180 psf soil = 180 psf
Angle of internal friction; friction; Design base friction angle; angle;
Column no.1 loads Dead load in z; z;
FDz1 = 16.7 kips 16.7 kips
Live load in z; z;
FLz1 = 18.5 kips 18.5 kips
Live roof load in z; z;
FLrz1 = 4.2 kips 4.2 kips
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Foundation analysis for soil and stability Load combinations per ASCE 7-10 1.0D (0.526) 1.0D + 1.0Lr (0.619) 1.0D + 1.0S (0.526) 1.0D + 1.0R (0.526) 1.0D + 0.75L + 0.75Lr (0.911) 1.0D + 0.75L + 0.75S (0.839) 1.0D + 0.75L + 0.75R (0.839) (1.0 + 0.14 × SDS)D + 0.7E (0.542) (1.0 + 0.10 × SDS)D + 0.75L + 0.75S + 0.525E (0.850) (0.6 - 0.14 × SDS)D + 0.7E (0.299) Combination 6 results: 1.0D + 0.75L + 0.75Lr Forces on foundation Force in z-axis;
Fdz = γ D × A × (Fswt + Fsoil + FDsur) + γ D × FDz1 + γ L × FLz1 + γ Lr × FLrz1 = 52.7 kips
Moments on foundation Moment in x-axis, about x is 0;
Mdx = γ D × (A × (Fswt + Fsoil + FDsur) × Lx / 2) + γ D × (FDz1 × x1) + γ L × (FLz1 × x1) + γ Lr × (FLrz1 × x1) = 263.4 kip_ft
Moment in y-axis, about y is 0;
Mdy = γ D × (A × (Fswt + Fsoil + FDsur) × Ly / 2) + γ D × (FDz1 × y1) + γ L × (FLz1 × y1) + γ Lr × (FLrz1 × y1) = 81.2 kip_ft
Uplift verification Vertical force;
Fdz = 52.675 kips PASS - Foundation is not subject to uplift
Bearing resistance Eccentricity of base reaction Eccentricity of base reaction in x-axis;
edx = Mdx / Fdz - Lx / 2 = 0 in
Eccentricity of base reaction in y-axis;
edy = Mdy / Fdz - Ly / 2 = -11.507 in
Length of bearing in y-axis;
L'yd = min(Ly,3 × (Ly / 2 - abs(edy))) = 55.478 in
Pad base pressures q1 = 2 × Fdz / (3 × Lx × (Ly / 2 + edy)) = 2.279 ksf q2 = 0 ksf q3 = 2 × Fdz / (3 × Lx × (Ly / 2 + edy)) = 2.279 ksf q4 = 0 ksf Minimum base pressure;
qmin = min(q1,q2,q3,q4) = 0 ksf
Maximum base pressure;
qmax = max(q1,q2,q3,q4) = 2.279 ksf
Allowable bearing capacity Allowable bearing capacity;
qallow = qallow_Gross = 2.5 ksf qmax / qallow = 0.911 PASS - Allowable bearing capacity exceeds design base pressure
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FOUNDATION DESIGN (ACI318) In accordance with ACI318-11 incorporating Errata as of August 8, 2014 Material details Compressive strength of concrete;
f’c = 3500 psi
Yield strength of reinforcement;
fy = 60000 psi
Cover to reinforcement;
cnom = 3 in
Concrete type;
Normal weight
Concrete modification factor;
λ = 1.00
Column type;
Concrete
Analysis and design of concrete footing Load combinations per ASCE 7-10 1.4D (0.359) 1.2D + 1.6L + 0.5Lr (0.957) 1.2D + 1.6L + 0.5S (0.909) 1.2D + 1.6L + 0.5R (0.909) 1.2D + 1.0L + 1.6Lr (0.808) 1.2D + 1.0L + 1.6S (0.657) 1.2D + 1.0L + 1.6R (0.657) (1.2 + 0.2 × SDS)D + 1.0L + 0.2S + 1.0E (0.666) (0.9 - 0.2 × SDS)D + 1.0E (0.220) Combination 2 results: 1.2D + 1.6L + 0.5Lr Forces on foundation Ultimate force in z-axis;
Fuz = γ D × A × (Fswt + Fsoil + FDsur) + γ D × FDz1 + γ L × FLz1 + γ Lr × FLrz1 = 74.5 kips
Moments on foundation Ultimate moment in x-axis, about x is 0;
Mux = γ D × (A × (Fswt + Fsoil + FDsur) × Lx / 2) + γ D × (FDz1 × x1) + γ L × (FLz1 × x1) + γ Lr × (FLrz1 × x1) = 372.4 kip_ft
Ultimate moment in y-axis, about y is 0;
Muy = γ D × (A × (Fswt + Fsoil + FDsur) × Ly / 2) + γ D × (FDz1 × y1) + γ L × (FLz1 × y1) + γ Lr × (FLrz1 × y1) = 108.7 kip_ft
Eccentricity of base reaction Eccentricity of base reaction in x-axis;
eux = Mux / Fuz - Lx / 2 = 0 in
Eccentricity of base reaction in y-axis;
euy = Muy / Fuz - Ly / 2 = -12.489 in
Length of bearing in y-axis;
L'yu = min(Ly,3 × (Ly / 2 - abs(euy))) = 52.532 in
Pad base pressures qu1 = 2 × Fuz / (3 × Lx × (Ly / 2 + euy)) = 3.402 ksf qu2 = 0 ksf qu3 = 2 × Fuz / (3 × Lx × (Ly / 2 + euy)) = 3.402 ksf qu4 = 0 ksf Minimum ultimate base pressure;
qumin = min(qu1,qu2,qu3,qu4) = 0 ksf
Maximum ultimate base pressure;
qumax = max(qu1,qu2,qu3,qu4) = 3.402 ksf
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Shear diagram, x axis
Shear (kips)
22.3
31.1
0 0
1
2 -22.3
-31.1
Moment diagram, x axis Moment (kip_ft)
0
0 1
2
56.2
77.8
Shear diagram, y axis
Shear (kips)
25.6 4.2 4.2
-0.7 0
1
2
-26.1
Moment diagram, y axis Moment (kip_ft)
-6 0 0.0 1
2
13.4
Moment design, x direction, positive moment Ultimate bending moment;
Mu.x.max = 56.238 kip_ft
Tension reinforcement provided;
5 No.5 bottom bars (13.3 in c/c)
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Area of tension reinforcement provided;
Asx.bot.prov = 1.55 in2
Minimum area of reinforcement (10.5.4);
As.min = 0.0018 × Ly × h = 1.296 in2
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PASS - Area of reinforcement provided exceeds minimum smax = min(3 × h, 18 in) = 18 in
Maximum spacing of reinforcement (10.5.4);
PASS - Maximum permissible reinforcement spacing exceeds actual spacing Depth to tension reinforcement;
d = h - cnom - φx.bot / 2 = 8.688 in
Depth of compression block;
a = Asx.bot.prov × fy / (0.85 × f'c × Ly) = 0.521 in
Neutral axis factor;
β1 = 0.85 c = a / β1 = 0.613 in εt = 0.003 × d / c - 0.003 = 0.03952
Depth to neutral axis; Strain in tensile reinforcement (10.3.5);
PASS - Tensile strain exceeds minimum required, 0.004 Nominal moment capacity;
Mn = Asx.bot.prov × fy × (d - a / 2) = 65.309 kip_ft
Flexural strength reduction factor;
φf = min(max(0.65 + (εt - 0.002) × (250 / 3), 0.65), 0.9) = 0.900 φMn = φf × Mn = 58.778 kip_ft Mu.x.max / φMn = 0.957
Design moment capacity;
PASS - Design moment capacity exceeds ultimate moment load One-way shear design, x direction Ultimate shear force;
Vu.x = 22.28 kips
Depth to reinforcement;
dv = h - cnom - φy.bot - φx.bot / 2 = 8.062 in
Shear strength reduction factor;
φv = 0.75 Vn = 2 × λ × √(f'c × 1 psi) × Ly × dv = 57.238 kips φVn = φv × Vn = 42.929 kips Vu.x / φVn = 0.519
Nominal shear capacity (Eq. 11-3); Design shear capacity;
PASS - Design shear capacity exceeds ultimate shear load Footing geometry factor (15.4.4.2); Area of reinf. req. for uniform distribution (CRSI);
βf = Lx / Ly = 2.000 Asreq = (Mu.y.max / (φf × fy × (d - a / 2))) × 2 × βf / (βf + 1) = 0.000 in2 PASS - Reinforcement can be distributed uniformly
Moment design, y direction, negative moment Ultimate bending moment;
Mu.y.min = -5.957 kip_ft
Tension reinforcement provided;
9 No.5 top bars (14.1 in c/c)
Area of tension reinforcement provided;
Asy.top.prov = 2.79 in2
Minimum area of reinforcement (10.5.4);
As.min = 0.0018 × Lx × h = 2.592 in2 PASS - Area of reinforcement provided exceeds minimum
Maximum spacing of reinforcement (10.5.4);
smax = min(3 × h, 18 in) = 18 in PASS - Maximum permissible reinforcement spacing exceeds actual spacing
Depth to tension reinforcement;
d = h - cnom - φy.top / 2 = 8.688 in
Depth of compression block;
a = Asy.top.prov × fy / (0.85 × f'c × Lx) = 0.469 in
Neutral axis factor;
β1 = 0.85 c = a / β1 = 0.552 in εt = 0.003 × d / c - 0.003 = 0.04424
Depth to neutral axis; Strain in tensile reinforcement (10.3.5);
PASS - Tensile strain exceeds minimum required, 0.004 Nominal moment capacity;
Mn = Asy.top.prov × fy × (d - a / 2) = 117.92 kip_ft
Flexural strength reduction factor;
φf = min(max(0.65 + (εt - 0.002) × (250 / 3), 0.65), 0.9) = 0.900
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φMn = φf × Mn = 106.128 kip_ft abs(Mu.y.min) / φMn = 0.056
Design moment capacity;
PASS - Design moment capacity exceeds ultimate moment load One-way shear design, y direction Ultimate shear force;
Vu.y = 4.176 kips
Depth to reinforcement;
dv = min(h - c nom - φy.bot / 2,h - cnom - φy.top / 2) = 8.688 in
Shear strength reduction factor;
φv = 0.75 Vn = 2 × λ × √(f'c × 1 psi) × Lx × dv = 123.35 kips φVn = φv × Vn = 92.513 kips Vu.y / φVn = 0.045
Nominal shear capacity (Eq. 11-3); Design shear capacity;
PASS - Design shear capacity exceeds ultimate shear load Two-way shear design at column 1 Depth to reinforcement;
dv2 = 8.375 in
Shear perimeter length (11.11.1.2);
lxp = 26.375 in
Shear perimeter width (11.11.1.2);
lyp = 28.188 in
Shear perimeter (11.11.1.2);
bo = 2 × lyp + lxp = 82.750 in
Shear area;
Ap = lxp × lyp = 743.445 in2
Surcharge loaded area;
Asur = Ap - lx1 × ly1 = 311.445 in2
Ultimate bearing pressure at center of shear area;
qup.avg = 2.490 ksf
Ultimate shear load;
Fup = γ D × FDz1 + γ L × FLz1 + γ Lr × FLrz1 + γ D × Ap × Fswt + γ D × Asur × Fsoil + γ D × Asur × FDsur - qup.avg × Ap = 40.347 kips
Ultimate shear stress from vertical load;
vug = max(Fup / (bo × d),0 psi) = 56.124 psi
Column geometry factor (11.11.2.1);
β = ly1 / lx1 = 1.33 αs =30 vcpa = (2 + 4 / β) × λ × √(f'c × 1 psi) = 295.804 psi vcpb = (αs × dv2 / bo + 2) × λ × √(f'c × 1 psi) = 297.949 psi vcpc = 4 × λ × √(f'c × 1 psi) = 236.643 psi
Column location factor (11.11.2.1); Concrete shear strength (11.11.2.1);
vcp = min(vcpa,vcpb,vcpc) = 236.643 psi Shear strength reduction factor;
φv = 0.75
Nominal shear stress capacity (Eq. 11-2);
vn = vcp = 236.643 psi
Design shear stress capacity (Eq. 11-1);
φvn = φv × vn = 177.482 psi vug / φvn = 0.316 PASS - Design shear stress capacity exceeds ultimate shear stress load
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Sheet no./rev.
7 Calc. by
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6 No.5 bottom bars (22.6 in c/c) 9 No.5 top bars (14.1 in c/c)
1 5 No.5 bottom bars (13.3 in c/c)
Date
