# Shear force – Definition diagram and calculation

In structural engineering, for design purpose of members, analysis of shear force and bending moment induced are of the at most importance. The interesting thing is that you can draw shear force and bending moment distribution along any beam, by understanding what exactly is the shear force and bending moment.

In this article, we discuss beams, loads and shear force and their diagram and its calculations.

## Beam

A beam is a member; whose cross-sectional dimensions is small as compared to its length. The members are essential to resist forces that are applied laterally or transversely to their axis.

A Beam is a structural member subjected to a system of external forces which act perpendicular to the longitudinal axis of the beam.

The beams are made from several usable engineering materials like Metal, Wood, Concrete, Plastic etc. Beams are most commonly used in buildings, bridges, automobiles or in mechanical systems. Structural Designers would be interested to know, that at what load it will fail? How much deflection occurs under the applied loads? while dealing with beams.

**If you are already aware of basics, and looking for the deeper information about the diagram, analysis or design things you might want to see a cool spreadsheet that can do a lot of stuff with huge beams follow this link. – http://ccivilengineer.com/the-beam/**

**Classification of Beams**

- Classification based on the basis of geometry normally includes features such as the shape of the X-section and whether the beam is straight or curved.
- Beams are classified into several groups, depending firstly on the kind of supports used.

**Statically Determinate or Statically Indeterminate Beams:**

When all the external forces and moments acting on the beam can be determined from the equilibrium conditions alone then it is termed as a statically determinate beam, whereas in the statically indeterminate beams.

**Based on the supports:**

1.Simply supported beam

2.Cantilever beam

3.Overhanging beam

4.Continuous beam

5.Fixed beam

On the basis of the support, the beams may be classified as follows:

Simply Supported beam which is pinned at one end and roller at the other end. Sometimes the beam is made freely rest on supports the beam.

Cantilever beam which is fixed or built in at one end whereas its other end is free, is termed as a cantilever beam.

The overhanging beam which has one or both end portions extending beyond its any number of supports.

The continuous beam which is provided more than two supports.

The fixed beam which is fixed at its both ends.

## Support and Reaction

An object that bears the load of the beam or any object and keeps it at the right position. Supports are used to provide suitable reactions to beams or any member.

A reaction is an external force exerted by a support on the beam or any object.

### Types of supports and reaction:

- Fixed end support
- Simple support
- Roller support
- Pin support

## Load

In structural engineering, loads are playing a very important role. Loads cause stresses and deformations and displacements in structures. By excess or over load may cause structure failure.

Load is a force, deformation and displacement which are applied to a structures.

**Types of loads**

Beams may be subjected to various types of loads:

- Concentrated load
- Distributed load
- Varying load

The concentrated load which is applied over a very small area and is regarded as a single load. This load is also called point load.

Distributed load which is formed to spread over an entire span of the beam or over a particular portion of the beam in some aspect.

The varying load is an intensity that varies according to some rules along the length of the beam.

## Defination of Shear force

Shear stress is the force applied on per unit area of the member whereas the Shear force is the resultant force acting on any one of the parts of the beam normal to the axis.

Shear force is the force in the beam acting perpendicular to its longitudinal axis.

**Sign Convention for Shear **

Positive shear force: The resultant force normal to the axis of the beam member on the right side of the section which is in the downwards direction and the left side of the section is upwards direction.

Negative shear force: The resultant force normal to the axis of the beam member on the right side of the section which is in a downwards direction and the left side of the section is upwards direction.

## Shear Force diagram

A shear force diagram for a structural member. This is a diagram shows the values of shear forces at various cross-sections of the member.

**How to construct?**

When we can be constructing the shear force diagram than use the point that the shear force, is constant over the unloaded bays of the beam, varies linearly where the loading is uniformly distributed and changes negatively as a vertical downward concentrated load is crossed in the positive x-direction by the value of the load.

## Shear force formula

The formula is to calculate average shear stress is force per unit area. Its S.I. unit is Pascal.

*τ = F/A *

where, *τ *= the shear stress, *F *= the force applied and *A *= the cross-sectional area of material with area parallel to the applied force vector.

## The Shear force Calculation

Now we can easily calculate the distribution of shear force along the length of the beam. We will see few examples.

**Cantilever Beam with concentrated load**

The cantilever of length L carrying a concentrated load W at the free end. A cantilever AB fixed at end A and free at end B and W load carrying at free end B.

Consider a section X at distance of x from the free end.

S.F. at X = Sx = +W

Hence, we find that the S.F. is constant at all sections of the member between A and B.

**Simply supported beam with uniformly distributed load**

Simply supported beam AB simply supported at the ends A and B. Let the span of the beam L and carrying a concentrated load W at mid span.

**Simply supported beam with varying load**

A simply supported beam AB of span L carrying a load whose intensity varies uniformly from zero at each end to w per unit run at mid span.

Dive in into more basic to read about Stress Strain Hooke’s Law and Poisson Ratio HERE

If you want to really learn by basic and prefer it old school I would recommend the following Book. Or you can search for one for yourself HERE

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