Bending Moment – definition, equation, units & diagram

If we apply a sufficient amount of force on a free object, it will move. We already have discussed this concept in an article on Newton’s second law of motion. Now if we want to rotate the free object, we need to apply two parallel forces in the opposite direction. This creates a Torque on the object. In structural engineering, engineers need to bend the structural elements to design a structure. Do we need to apply a Torque to bend those elements? No, to rotate or bend a body that is fixed with one of its ends, a single force on its free end is enough. This introduces the concept of Moment of force on the body. In this conceptual note, I’m going to explain the basic concepts of Bending Moment, its definition, equation and diagram.

Contents of this article:

  1. Definition of Bending Moment
  2. Bending Moment diagram
  3. Formula of Bending Moment
  4. Units of Bending Moment

What is Bending Moment of a beam?

When a force is applied at the free end of a body which is fixed at another end, a moment of force arises in the body that can bend it. This moment is called the Bending Moment. One can observe such bending in the cantilever beam. The external force must be applied perpendicular to the length of the beam or rod which is known as the moment arm.

Bending Moment diagram

The following diagram shows how to bend a cantilever beam by applying bending moments on it.

Bending of Beam by moments
Bending of Beam by moments

Here F is the applied force at the free end of the beam and L is the length of the beam.

Equation of Bending Moment

If an external force F is applied on a rod of length L perpendicularly, then the formula of the bending moment on the rod is, M = F×L ……..(1)

Here L gives the length of arm.

Structural engineers use this equation of moments to design structures by bending their elements.

Units of Bending moment

Bending moments = Force × Length.

Therefore, N.m is its SI unit and dyn.cm is its CGS unit. The most common unit of bending moment is kN.m.

This is all from this article on the moments of bending of a cantilever beam. If you still have any doubts on this topic you can ask me in the comment section.

Thank you!

Related posts:

  1. Rotation of an object by Torque
  2. Moment of Inertia