Important Point

## 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. 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.**

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## 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.**

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## 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.**

## What Is Shear Force and Bending Moment

**Shear** and **bending moment** diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of **shear force and bending moment** at a given point of a structural element such as a beam.

## Definition of Shear Force and Bending Moment

**Shear force** is taken +ve if it produces a clockwise **moment** and it is taken -ve when it produces an anticlockwise **moment**. **Bending moment** at any point along a loaded beam may be **defined** as the sum of the **moments** due to all vertical **forces** acting on either side of the point on the beam.

## What Is Meant by Shear Force

**Shearing force** is **defined** as the **force** transverse to the beam at a given section tending to cause it to **shear** at that section.

## Shear Force

A **shear force** is a **force** applied perpendicular to a surface, in opposition to an offset **force** acting in the opposite direction. This results in a **shear** **strain**. In simple terms, one part of the surface is pushed in one direction, while another part of the surface is **pushed in the opposite direction**.

## Bending moment

In solid mechanics, a **bending moment** is the reaction induced in a structural element when an external force or **moment** is applied to the element, causing the element to bend. The most common or simplest structural element subjected to **bending moments** is the beam.

## Shear Force and Bending Moment:

Its baseline is equal to the span of the beam, drawn on a suitable scale. For point loads S.F. diagram has a straight horizontal line, for UDL( Uniformly Distributed Load), It has straight inclined lines, and for uniformly varying loads it has a parabolic curve.

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