Shear Forces and Bending Moment

Members with support loadings applied perpendicular to their longitudinal axis are called beams. Beams classified according to the way they are supported.

Types of Beam

• Simply supported beam

If the ends of a beam are made to rest freely on supports, it is called simply supported beam.

Simply supported beam

• Fixed Beam

If both ends of a beam are fixed, it is called fixed beam.

Fixed Beam

• Cantilever Beam

If beam is fixed at one end and another end is free, it is called cantilever beam.

Cantilever Beam

• Continuous Beam

It more than two supports are provided to a beam, it is called continuous beam.

Continuous Beam

Shear Force And Bending Moment

It is an internal force acting tangentially to the section which is normal to longitudinal direction. Bending moment at any section is internal reaction due to all the transverse force either from left side or right.

where w = load per unit length (N/m), V = shear force, M = bending moment

Note:

• At a hinge bending moment will be zero.
• Bending moment will be maximum or minimum where shear force is zero.
• A point of contraflexture / point of inflexion is a point where the curvature of beam changes sign. It occurs points on the beam where bending moment changes sign i.e. BM is zero.

Shear force and Bending Moment diagram for an applied moment(Fd)