## Definition of Shear Force and Bending Moment

### Shear Force

Shear force is the **unbalanced vertical force which is acting on to the right or left of the section.**It’s also termed as aligned forces pushing **one part of the body in the specific direction,** and the** other part** of the** body is another direction.**

Sometimes, a** crack is developed in a body from the parallel shear force acting** in a different direction at another point of the body.Â Colinear forces are also **termed as compressive forces.**

### Bending Moment

Bending moment is the **algebraic sum of all the moment of forces, according to the right or left of the section. **It’s the reaction which is induced in a** structural element due to external force or moment is applied.**

In the** equilibrium position**, the moment which is created by **external forces is balanced by the couple** induced by the internal load; this internal couple is** called a bending moment.**

## What Is Shear Force : Sign Convention of Shear Force:

Shear force is an unbalanced vertical force, so it tends to **slide one portion of the beam upward or downward with respect to the other. **Shear force at a section is considered as **positive when the left-hand portion tends to slide upward, or the right-hand portion tends to slide downward.**

Same as a shear force at a section is **negative when the left-hand portion tends to slide downward, or the right-hand portion tends to slide upward.**

## What Is Bending Moment : Sign Convention for Bending Moment:

We considered bending moment at a section is positive when it tends to bend the beam at a point to a curvature having a **concavity at the top **or when the moments are acting **clockwise direction to the left or anti-clockwise direction to the right.**

On the other hand, we considered bending moment at a section is negative when it tends to bend the beam at a point to a curvature having **convexity at the top** or moments are taken **anti-clockwise direction to the left or clockwise direction to the right. **Sometimes the positive bending moment is termed as **sagging moment,** and the negative bending moment is termed as a **hogging moment.**

## Relation Between Loading, Shear Force & Bending Moment:

The following relations are essential for loading, shear force and bending moment relation- If there is a point load at a section on the beam, then the shear force suddenly changes**(i.e. the shear force line is vertical).** But the bending moment remains the same.

If there is no load between two points, then the **shear force does not change** (I.e. shear force line is horizontal) but the **bending moment changes linearly** (I.e. bending moment line is an inclined straight line).

If there is a uniformly distributed load between two points, then the **shear force changes linearly** (I.e. shear line is an inclined straight line). But the bending moment changes according to the **parabolic law**(i.e. bending moment line will be parabola).

If there us a uniformly varying load between two points then the shear force changes according to the **parabolic law**(i.e. shear force line will be parabola) but the bending moment changes according to the **cubic law. **Where **shear force changes, it’s sign there bending moment is maximum. **Where bending moment changes, it’s a sign that point is known as **the point of contra flexure or inflation point.**