Question

Relationship between radius of curvature R, bending moment M and flexural rigidity EI

Answer 1

From the bending equations of beams, we get, 
$\frac{M}{I}= \frac{E}{R}$, therefore, 
$M=EI/R$

Answer 2

The relation between the radius of curvature R, bending moment M, and flexural rigidity E I is R = E I / M.

• The mathematical expression for the relationship between R, M, and E I :

             R = E I / M

         here, R is the radius of curvature of the beam

         E is the Young's modulus

         I is the area moment of inertia

         E I, collectively called flexural rigidity

         M is the bending moment

• The above equation can also be written as:

         Radius of curvature of beam = flexural rigidity/bending moment

• From the equation we can conclude that:

         flexural rigidity ∝  bending moment

         flexural rigidity ∝  radius of curvature of the beam