Bending Moment at Supports in Simply Supported Beams

A simply supported beam is a common structural element supported at its ends. These supports typically allow rotation but prevent vertical displacement. Common examples include pin supports and roller supports.

Understanding Bending Moment

The bending moment at any point along a beam is a measure of the internal forces that cause the beam to bend. It's calculated based on the applied loads and the distance from a reference point.

Bending Moment at Supports

For a beam that is simply supported at its ends:

• The supports are designed to provide vertical reactions to counteract the applied loads.
• Crucially, these simple supports (like pins or rollers) do not offer any resistance to moments. They allow the beam end to rotate freely.
• Because the supports cannot resist or hold any moment, the bending moment at the exact point of the support (the ends of the beam) is always zero.

Consider a beam subjected to various loads. While there might be significant bending moments within the span of the beam, the physical constraints and design of the simple supports dictate that the bending moment directly at these support locations must be zero.

For instance, if you were to draw the bending moment diagram for a simply supported beam, the diagram would start at zero at one end, rise to a maximum value somewhere within the beam's span (depending on the loading), and then return to zero at the other end support.