Calculate ultimate and gross allowable bearing capacity for shallow footings using supplied Terzaghi factors, footing shape, and factor of safety.
Direct solving is free and needs no account. Have a word problem instead? Submit it as text.
Worked examples
These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.
Example 1
square footing in dense sand (the motivating exam problem)
Given
footing shape
square
width
2 m
depth
1.5 m
unit weight
18 kN/m^3
nc
57.8
nq
41.4
ngamma
42.4
factor of safety
3
Assumptions
Terzaghi general shear failure; homogeneous soil; vertical centric load; water table deep (use effective unit weights otherwise); N-factors as provided by the problem.
Solution steps
Assemble the three capacity terms
Cohesion, surcharge from the founding depth, and soil self-weight below the footing each contribute.
q_ult = sc·c·Nc + γ·Df·Nq + sγ·0.5·γ·B·Nγ
cohesion term = 0 kPa; surcharge term = 1118 kPa; width term = 610.6 kPa
Ultimate capacity
Sum the three contributions.
q_ult = sum of the terms
q_ult = 1728.4 kPa
= 1728.4 kPa
Gross allowable capacity
Divide the ultimate capacity by the factor of safety. (Some texts subtract the surcharge first for a NET allowable — check which your course uses.)
Terzaghi general shear failure; homogeneous soil; vertical centric load; water table deep (use effective unit weights otherwise); N-factors as provided by the problem.
Solution steps
Assemble the three capacity terms
Cohesion, surcharge from the founding depth, and soil self-weight below the footing each contribute.
q_ult = sc·c·Nc + γ·Df·Nq + sγ·0.5·γ·B·Nγ
cohesion term = 442.5 kPa; surcharge term = 125.8 kPa; width term = 63.75 kPa
Ultimate capacity
Sum the three contributions.
q_ult = sum of the terms
q_ult = 632.05 kPa
= 632.05 kPa
Results
Ultimate bearing capacity q_ult
632.05kPa
Where this answer was checked
source
Terzaghi with cohesion, strip shape factors 1.0 — B = 1.5, Df = 1, γ = 17, c = 25; Nc = 17.7, Nq = 7.4, Nγ = 5.0
Terzaghi general shear failure; homogeneous soil; vertical centric load; water table deep (use effective unit weights otherwise); N-factors as provided by the problem.
Solution steps
Assemble the three capacity terms
Cohesion, surcharge from the founding depth, and soil self-weight below the footing each contribute.
q_ult = sc·c·Nc + γ·Df·Nq + sγ·0.5·γ·B·Nγ
cohesion term = 483.6 kPa; surcharge term = 416.3 kPa; width term = 218.7 kPa