__Shear forces and Bending Moment__

What are shear forces?

*Shear
force*
is the force in the beam acting perpendicular to its longitudinal (x) axis. For
design purposes, the beam's ability to resist shear force is more important than
its ability to resist an axial force. *Axial
force* is the force in the beam acting parallel to the longitudinal
axis.

An example of a Shear force is given below

There are
two different types of shear:-

**Vertical**

**Horizontal**

This occurs when a beam is made up of layers and when a force acts down on the beam it deflects and causes the layers to slide over each other.

The following is a drawing of a simply-supported beam of length L under a uniform load, q:

This beam has the following support reactions:

where R_{l}
and R_{r} are the reactions at the left and right ends of the beam,
respectively.

The shear forces at the ends of the beam are equal to the vertical forces of the support reactions. The shear force F(x) at any other point x on the beam can be found by using the following equation.

where x is the distance from the left end of the beam.

Shear force diagrams are simply plots of the shear force (on the y-axis) versus the position of various points along the beam (on the x-axis). Thus, the following is the generalized shear force diagram for the beam shown above.

What is Bending
moment?

The definition is give
below

The* ** bending
moment* at any point along the beam is equal to the area under
the shear force diagram up to that point. (Note: For a simply-supported beam,
the bending moment at the ends will always be equal to zero.)

To calculate the bending moment the beam must be broken up into two sections:

(a) |
one
from x = 0 to x = L/2 and |

(b) |
the
other from x = L/2 to x = L. |

The bending moment M(x) at any point x along the beam can be found by using the following equations:

Bending moment diagrams are simply plots of the bending moment (on the y-axis) versus the position of various points along the beam (on the x-axis). Thus, the following is the generalized bending moment diagram for the beam shown above.