A beam of cross section area A is made of a material of Young modulus Y. The beam is bent into the arc of a circle of radius R. The bending moment is proportional to

\frac{Y}{R}

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\frac{Y}{R A}

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\frac{R}{Y}

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Y R

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Solution

The correct option is A $\frac{Y}{R}$
Bending moment $C = \frac{Y I_{G}}{R}$
Therefore, $C$ is proportional to $\frac{Y}{R}$

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Q. 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.

Consider an elastic straight beam of length $L = 10 π$ 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