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For footings that support inclined loads.
Meyerhof (1951, 1963) proposed a bearing-capacity equation similar to that of Terzaghi
but included a shape factor s-q with the depth term Nq. He also included depth factors and inclination factors.
The spreadsheet is based on Chapter 4-3 of Foundation Analysis and Design, Ed. 5 by Joseph E. Bowles (permission granted).
The equations are:
vertical q-ult = c*Nc*d-c*s-c + q-bar*Nq*d-q*s-q + 0.5*gamma*B*Ngam*d-gam*s-gam
inclined q-ult = c*Nc*d-c*i-c + q-bar*Nq*d-q*i-q + 0.5*gamma*B*Ngam*d-gam*i-gam
where:
c = soil cohesion in kPa
Nc = cohesion multiplier = (Nq - 1)*cot(PHI)
d-c = depth factor for cohesion = 1 + 0.2*sqrt(Kp)*D/B
s-c = length factor for cohesion = 1 + 0.2*Kp*B/L
i-c = inclination factor for cohesion = (1 - theta/90)^2
where Kp = passive earth pressure coefficient = tan(PI/4+PHI/2)^2
PHI = angle of internal friction in radians (entered in degrees)
theta = angle of load from vertical, in degrees
B = least lateral base dimension in m
L = the other base dimension in m
D = depth to base in m
q-bar = overburden pressure in kPa = gamma*D
gamma = unit weight of soil in kN/m3
Nq = overburden multiplier = e^(PI*tan(PHI))*Kp
d-q = 1 + 0.1*sqrt(Kp)*D/B for PHI >= 10, or 1.0 otherwise
s-q = 1 + 0.1*Kp*B/L for PHI >= 10, or 1.0 otherwise
i-q = i-c = (1 - theta/90)^2
Ngam = wedge weight multiplier = (Nq - 1)*tan(1.4*PHI)
d-gam = d-q = 1 + 0.1*sqrt(Kp)*D/B for PHI >= 10, or 1.0 otherwise
s-gam = s-q = 1 + 0.1*Kp*B/L for PHI >= 10, or 1.0 otherwise
i-gam = (1 - theta/PHI)^2 where PHI is in degrees
or i-gam = 0 if PHI = 0 or theta > PHI
Input values are obtained from tests of soil samples.
You should do at least one calculation manually, for two reasons:
1. to check the spreadsheet so you can have confidence in its results; and
2. to appreciate how much time the spreadsheet saves.
Please support the ongoing maintenance of this site.
Donate $7 and I shall send you the Excel spreadsheet
so you can satisfy yourself that the program uses the equations correctly.
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