Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Shear strength
Question Statement:
A shear annulus with inner and outer diameters of 240 mm and 300 mm, respectively is used to measure shear strength of soil in the field. When it is inserted into the soil and rotated, the torque measured at the soil failure is 50 N·m. Shear strength of the soil in kPa is (Take π = 3.14)
Options:
(A) 14.49
(B) 18.94
(C) 21.54
(D) 28.98
Official Answer Key:
A
Step-by-Step Solution & Explanation
For a shear vane/annulus with inner radius rᵢ and outer radius r₀, integrating uniform shear stress τ over the annular ring gives T = (2πτ/3)(r₀³ − rᵢ³), so τ = 3T/[2π(r₀³ − rᵢ³)]. r₀ = 0.15 m, rᵢ = 0.12 m: r₀³ = 0.003375, rᵢ³ = 0.001728, difference = 0.001647 m³. τ = 3×50/(2×3.14×0.001647) = 150/0.010343 = 14,502 Pa ≈ 14.49 kPa, matching (A).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.