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):

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:

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