Bearing Capacity Factor Nc
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
Nc is not an independent result but a consequence: Prandtl's plasticity solution ties the cohesion term to the surcharge term through N_c = (N_q − 1) cot φ. With Nq = 18.40 at φ = 30°, Nc = 17.40 ÷ tan 30° = 30.14 — again the tabulated value. At φ = 35°, Nq = 33.30 gives Nc = 46.12.
The interesting case is φ = 0, where cot φ blows up and the formula is useless — but the limit is finite and famous: Nc → π + 2 = 5.14. That is the undrained bearing capacity of saturated clay, q_u = 5.14 c_u for a strip footing and about 6.2 c_u for a square or circular one, and it is the single most-used number in shallow foundation design on clay. The trap is applying the φ = 0 analysis with a drained strength, or vice versa: undrained (total stress, c_u, φ = 0) governs immediately after construction, drained (effective stress, c′, φ′) governs decades later, and a clay foundation must be checked for both. Skempton's 1951 paper set out that two-case discipline and it has not been improved on.
- = Cohesion bearing capacity factor
- = Surcharge bearing capacity factor
- = Angle of internal friction
- Cohesion bearing capacity factor — Bearing Capacity Factor Nq, Terzaghi Ultimate Bearing Capacity (Strip Footing)
- Surcharge bearing capacity factor — Bearing Capacity Factor Nq, Terzaghi Ultimate Bearing Capacity (Strip Footing)
- Angle of internal friction — Rankine Active Earth Pressure Coefficient, Rankine Passive Earth Pressure Coefficient