# Bending moment Definition diagram calculation

In structural engineering, for design purpose of members, shear force and bending moment plays a very important role in the analysis of any member.

In this article, we will discuss Bending moment Definition diagram and calculation.

The bending moment (BM) is the algebraic sum of the moments of the forces and reactions acting on one side of the section about the section.

It can also be visualized as torque as it is also force multiplied by the distance from point of its application. First and the most important thing for BM is its sign convention.

**Hogging BM**: The tendency of the BM at section when beam bend so as to produce convexity above the center line. The sign considers as negative. It results that the bottom face of the beam in compression and top face in tension.

**Sagging BM**: The tendency of the BM at section when beam bend so as to produce concavity above the center line. The sign considers as positive. It results that the bottom face of the beam in tension and top face in compression.

## Bending moment formula

The bending moment formula is simply BM = Reaction * moment arm or in other word it is the product of force and distance of the point of application of force from the point at which moment is calculated.

## Bending moment diagram

Drawing bending moment can be very useful at most of the places it is most required things and it is useful in designing as well as analysis of members. A BM diagram for a member is a diagram which shows the values of the BM at various sections of the member. The BM varies linearly over unloaded bays of the beam and parabolically over lengths of the beam carrying a uniformly distributed load.

## Bending moment calculations

The procedure to find the BM at any section of the beam

- Consider the left or right part of the section.
- Remove all restraints and all forces on the part selected.
- Now introduce each force or reacting element one at a time and find its effect at the section that the moment produces a hogging or sagging at the section.

## Bending Moment Calculation

A very simple example for BMD is as below.

Here are some formulas and BM values that might come in handy while doing quick calculations.

For calculating BM. One must be aware well about shear force. Explore more about Shear forces HERE

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Special thanks to Baljinder Kaur for her contribution in this article.

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