# Relation between shear force and bending moment

## Bending Moment

The algebraic sum of moment of external loads acting to either side of the section about the section is known as bending moment.

Here you can read some points which show the relation between shear force and bending moment.

1. Clockwise moments to the left and counterclockwise to the right are positive. It is also known as sagging bending moment and vise versa are called negative.
2. The rate of change of Bending moment is called shear force.
3. The couple does not change the shape of the shear force diagram.
4. The bending moment is zero at the internal hinge connection.
5. Bending moment due to moment is always a rectangle.
6. A point where bending moment changes sign is called point of contra flexure. It is also called the point of inflection.
7. Point where maximum bending moment has lowest shear force.

## Shear Force

The shear force acts tangential to the cross-section of the member. Shear force at a section is defined as the algebraic sum of transverse force acting to either side of the section.

Here are some points which show the relationship with bending moment.

1. Force upward to the left of a section or down to the right of the section are positive and vise versa are negative.
2. The rate of change of shear force is called the intensity of load.
3. Point of lowest shear force have maximum bending moment and vise versa.

## Diagram of shear force and bending moment due to different types of load

For point load shear force have a constant diagram but the bending moment has a linear diagram.

For Uniformly distributed load shear force has a linear diagram and bending moment have a parabolic diagram.

For constantly varying load parabolic diagram and bending moment have a curve diagram.

Happy Learning – Civil Concept 