Terzaghi bearing capacity (strip footing): Terzaghi’s general equation for ultimate bearing capacity of a continuous (strip) footing is (Nc, Nq, Nγ are bearing capacity factors, γ is unit weight, D is foundation depth, B is footing width):
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Aq_u = cNc + γDNq + 0.5γBNγ
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Bq_u = cNc − γDNq + 0.5γBNγ
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Cq_u = cNc + γDNq − 0.5γBNγ
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Dq_u = cNc − γDNq − 0.5γBNγ
Answer
Correct Answer: q_u = cNc + γDNq + 0.5γBNγ
Explanation
Introduction / Context:Terzaghi’s classical bearing capacity theory provides closed-form expressions for the ultimate pressure a footing can impose on soil before shear failure. For strip footings, the equation uses dimensionless bearing capacity factors that depend on the friction angle of the soil.
Given Data / Assumptions:
- Continuous (strip) footing on homogeneous soil.
- General shear failure assumed.
- Symbols: c, φ, γ, B, D, Nc, Nq, Nγ.
Concept / Approach:The ultimate bearing pressure is composed of three parts: cohesion term (cNc), surcharge term (γDNq), and unit weight term (0.5γBNγ). The N-factors are functions of φ; the width term is halved for strip footings in Terzaghi’s formulation.
Step-by-Step Solution:
Write the general form q_u = cNc + qNq + 0.5γBNγ where q = γD.Substitute q = γD to obtain q_u = cNc + γDNq + 0.5γBNγ.Confirm signs: all additive contributions to capacity.Verification / Alternative check:For c = 0, equation reduces to granular soil case q_u = γDNq + 0.5γBNγ, matching standard charts.
Why Other Options Are Wrong:
- Options B–D use incorrect negative signs, contradicting the physical contributions.
Common Pitfalls:Confusing ultimate and net ultimate; omitting shape/depth factors for non-strip footings; misusing surcharge q.
Final Answer:q_u = cNc + γDNq + 0.5γBNγ