Question

Consider an elastic straight beam of length $L=10\pi$ 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 for mean radius R. Assuming that Euler - Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress developed in the bent beam is MPa

• A. 100

Answer 1

The correct option is A 100

$L=10\pi m$
a = 5 mm
E = 200 GPa
Perimeter of bent up beam = Length of straight beam
$\Rightarrow 2\pi R=10\pi$
$\Rightarrow R=5m$
We know that,
$\frac{M}{I}=\frac{\sigma }{y}=\frac{E}{R}$
$\Rightarrow \frac{\sigma }{y}=\frac{E}{R}$
$\therefore {\sigma }_{max}=\frac{E}{R}{y}_{max}=\frac{200\times {10}^3\times 2.5\times {10}^{-3}}{5}=100MPa$