For a simply supported beam of length L, the bending moment M is described as M = a(x - x³/L²), 0 ≤ x < L; where a is a constant. The shear force will be zero at

Explanation:

a) In a bending beam, a point of contra flexure is a location where the bending moment is zero (changes its sign). In a bending moment diagram, it is the point at which the bending moment curve intersects with the zero lines.

• At the point of contra flexure, the bending moment is zero.

​b) The rate of change of bending moment at any section is equal to the shear force at that section.

• \(\frac{{dM}}{{dx}} = F \Rightarrow dM = Fdx \Rightarrow M = \smallint Fdx\)

c) The rate of change of shear force at any section is equal to load intensity at that section.

• \(\frac{{dF}}{{dx}} = \omega \Rightarrow dF = \omega dx \Rightarrow F = \smallint \omega dx\)

d) For bending moment to be maximum or minimum, shear force should change its sign.

\({d {\ [a (x - {x^3 \over L^2}) } ]\over dx } = V\)

\({ {\ a (1 - {3x^2 \over L^2}) } } = 0\)

x = L/√3