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PSAD Civil Engineering Licensure Examination (CELE) Practice Test

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Angle of twist for a shaft is θ = TL / (J G) in radians. Given T = 80 N·m, L = 0.8 m, J = 1.2×10^-5 m^4, and G = 30 GPa, compute θ in radians.
Correct Answer:
1.78e-4 rad
Explanation:
The quantity tested is how torsion relates torque, length, polar moment, and shear modulus. For a shaft under torsion, the angle of twist is θ = TL/(JG). Here JG combines the shaft’s geometry with its material stiffness, and the result must be dimensionless (radians). Compute step by step: T times L is 80 × 0.8 = 64 N·m^2. The product JG is (1.2×10^-5 m^4) × (30×10^9 N/m^2) = 3.6×10^5 N·m^2. The ratio gives θ = 64 / 3.6×10^5 ≈ 1.78×10^-4 radians. Thus the angle of twist is about 1.78×10^-4 radians, which matches the given correct value.

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