Ultimate Bearing Capacity on Sand

Equation: Terzaghi strip footing, q_ult = c·Nc + q·Nq + 0.5·γ·B·Nγ, where q = γ·Df is the overburden pressure at the footing base. Values: c = 0 for clean sand, so the cohesion term drops out. γ = 18 kN/m³ is the soil unit weight. Df = 1 m is the depth from the ground surface to the footing base. B = 2 m is the footing width. Nq = 18.4 and Nγ = 15.7 are the bearing capacity factors given. Step 1: q = γ·Df = 18 × 1 = 18 kPa. Step 2: overburden term, q·Nq = 18 × 18.4 = 331.2 kPa. Step 3: width term, 0.5 × 18 × 2 × 15.7 = 282.6 kPa. Step 4: q_ult = 0 + 331.2 + 282.6 = 614 kPa. Dropping the width term gives 331 kPa; forgetting the 0.5 gives 896 kPa.