Terzaghi Bearing Capacity (strip)

q_{u l t} = c N_{c} + γ D_{f} N_{q} + 0.5 γ B N_{γ}

Ultimate bearing pressure of a shallow strip footing. Shape, depth, and inclination factors modify the three N terms in later Hansen/Vesic forms (Handbook). Allowable q_all = q_ult / FS, often FS = 3. Overburden at foundation level is q = γ D_f.

$B$ (m): Footing width
$D_{f}$ (m): Embedment depth
$N_{c}, N_{q}, N_{γ}$: Bearing capacity factors (φ)

Step-by-step solved example

Strip footing B = 2 m, Df = 1 m, sand c = 0, φ = 30° (Nc=30.1, Nq=18.4, Nγ=15.1), γ = 18 kN/m³. q_ult?

Terzaghi: q_ult = c Nc + γ D Nq + 0.5 γ B Nγ.

1. Terms
c term = 0. q term = 18×1×18.4 = 331 kPa. γ term = 0.5×18×2×15.1 = 272 kPa.
2. Sum
q_ult = 603 kPa. With FS = 3, q_all ≈ 201 kPa.
$q_{u l t} = 603 kPa$

Answer: 603 kPa (q_all ≈ 200 kPa for FS = 3)

10 practice questions

0/10 correct

1.For φ = 0 (undrained clay), Nq and Nγ are

2.Increasing Df generally

3.A square footing vs strip (same B, sand) typically has

4.FS on bearing is applied to

5.Water table at the base of a footing in sand mainly reduces

6.Settlement of sand is often estimated with

7.1-D consolidation settlement ss =

8.Time factor Tv =

9.A wider footing on sand (same q) generally settles

10.Punching shear failure is associated with