Question

Radius of curvature of a stressed beam and modulus of elasticity

Answer 1

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Answer 2

The radius of curvature R is directly proportional to the modulus of elasticity E.

Given,

radius of curvature

modulus of elasticity

To find,

relation between radius of curvature and modulus of elasticity

Formula to be used,

We can take by the bending equation that,

$\(\frac{M}{I} = \frac{\sigma }{y} = \frac{E}{R}\)$

Here,

I = The moment of inertia of the beam (tendency of any body resisting angular acceleration)

σ = The bending stress induced in the beam (large stress experienced at a particular point)

E = The modulus of elasticity of the beam (basically E is the measure of stiffness of any body)

R = The radius of curvature

R = $\frac{{Ey}}{\sigma }\)$

Therefore, the radius of curvature is directly proportional to the modulus of elasticity.