Terzaghi Bearing Capacity (Strip Footing)
Terzaghi Bearing Capacity (Strip Footing)
Terzaghi's bearing capacity equation was the first rigorous general method for predicting how much pressure a shallow footing can carry before the soil beneath it fails in shear, and it remains the conceptual basis (with refinements) for nearly every modern bearing capacity method used in practice today. The equation sums three independent contributions — soil cohesion, surcharge from the overburden beside the footing, and the footing's own weight/width effect — each carrying its own bearing capacity factor (Nc, Nq, Ngamma) that depends only on the soil friction angle; using bearing capacity factors for the wrong footing shape or depth condition is a common source of over-optimistic foundation designs.
Terzaghi's ultimate bearing capacity for a strip footing is qu = c*Nc + q*Nq + 0.5*gamma*B*Ngamma. where c_bear is soil cohesion, N_c, N_q, and N_gamma are Terzaghi's dimensionless bearing capacity factors, q_over is the surcharge pressure from soil beside the footing, gamma_b is soil unit weight, and B_foot is the footing width.
Inputs
c_bear := 10 kPa=10000 Pa
N_c := 30=30
q_over := 18 kPa=18000 Pa
N_q := 18=18
gamma_b := 18 kN/m^3=18000 kg/m^2/s^2
B_foot := 1.5 m=1.5 m
N_gamma := 15=15
Each of the three terms represents an independent physical contribution to capacity — cohesive shear strength, confinement from the surrounding soil, and the footing's own width effect — and superposition lets them simply be added together.
q_u := c_bear·N_c + q_over·N_q + 0.5·gamma_b·B_foot·N_gamma=826500 Pa
Results
An ultimate bearing capacity in the range of several hundred to around a thousand kPa is typical for this footing on a moderately strong soil, and dividing this value by a safety factor of 2.5-3 gives the allowable bearing pressure used for design. Note that the surcharge term (Nq) usually dominates for wider or deeper footings while the gamma-B term grows with footing width, so widening a footing helps capacity but with diminishing proportional benefit compared to increasing embedment depth.
Assumptions & limitations
- Strip (long, continuous) footing — not valid directly for square or circular footings.
- General shear failure assumed (dense/stiff soil); loose soils may fail in local or punching shear instead.
- Homogeneous soil properties above and below the footing base.
- Ultimate capacity only — a safety factor must still be applied for allowable bearing pressure.