The bending moment of a beam is defined as the algebraic sum of all the moments to the neutral axis of any cross-section of a beam. A beam only supports the load by bending. A bending moment is simply the bend that occurs in a beam due to a moment.
In engineering mechanics, the term ‘beam’ has a very specific meaning. It can be defined as a component that is designed to support transverse loads; that is, external load applied perpendicularly to a longitudinal axis of the element. The bending moment at any point along the beam is equal to the area under the shear-force diagram up to that point. For a simply-supported beam, the bending moment at the end is always equal to zero.
To calculate the bending moment, the beam must be broken up into two sections:
(a) one from x = 0 to x = L/2, and
(b) the other from x = L/2 to x = L.
Now, the bending moment M(x) at any point x along the beam can be found by using the following equations:
For 0 < x < L/2, use M(x) = x/2 (R1 + F(x)) = qx/2 (L-x).
For L/2 < x < L, use M(x) = M (L/2) + (x – (L/2)) F(x) = qx/2 (L-x).
In these equations, L denotes length and q denotes under a uniform load.