Project ForgeStrength of Materials
Bending of Beams
GATE 2019
Medium
Consider an elastic straight beam of length L=10π m, with square cross-section of side a=5 mm, and Young's modulus E=200 GPa. This beam was bent so that its two ends meet, forming a circle of mean radius R. Assuming Euler-Bernoulli beam theory, the maximum tensile bending stress in the bent beam is ___ MPa.
100 MPa(± 1 accepted)
Explanation
The mean radius is R = L/(2π) = 10π/(2π) = 5 m. Maximum bending stress occurs at the outer fibre, c=a/2=2.5mm: σ = Ec/R = (200×10⁹ Pa × 0.0025 m)/5 m = 1×10⁸ Pa = 100 MPa.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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