Project ForgeStrength of Materials
Stress & Strain
GATE 2018
Medium
A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is __________ (correct to two decimal places).
35.34 kN-m/rad(± 0.1 accepted)
Explanation
J = (π/32)(do⁴−di⁴) = (π/32)(40⁴−20⁴) = (π/32)(2,560,000−160,000) ≈ 235,619.5 mm⁴. Torsional stiffness k = GJ/L = (150,000 N/mm²)×235,619.5 mm⁴ / 1000 mm ≈ 35,342,925 N·mm/rad ≈ 35.34 kN·m/rad.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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