Question

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 straight beam was bent in such a way that the two ends meet, to form a circle of mean radius R. Assuming that Euler-Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is _________ MPa.

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Answer :

100



L = 10 π m

a = 5 mm

E = 200 GPa

Perimeter of wire = Length of wire

2πR = 10π

R = 5 m

We know that,

M / I = σ/y = E/R

Now,

σ/y = E /R

σb = (200•103•2.5•10-3)/5  = 100 MPa

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