Consider an elastic straight beam of length $L = 10 π$ m , with square cross-section of side a = 5mm, 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.

100

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Solution

The correct option is A 100
Given : $L = 10 π m;$ a = 5mm; E =200 GPa

Perimeter of wire = Length of wire

$2 π R = 10 π$

R = 5 m

We know that,

$\frac{M}{I} = \frac{σ}{y} = \frac{E}{R}$

$N o w, \frac{σ}{y} = \frac{E}{R}$

$σ_{b} = \frac{200 \times 10^{3} \times 2.5 \times 10^{- 3}}{5}$

= 100 MPa

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The correct option is A 100Given : L=10πm; a = 5mm; E =200 GPa Perimeter of wire = Length of wire 2πR=10π R = 5 m We know that, MI=σy=ER Now, σy=ER σb=200×103×2.5×10−35 = 100 MPa