# Understanding Shear Force and Bending Moment Diagrams

**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. These diagrams can be used to easily determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure. Another application of shear and moment diagrams is that the deflection of a beam can be easily determined using either the moment area method or the conjugate beam method.

#### What are Shear Forces and Bending Moments?

Shear forces and bending moments are resultants which are used to conveniently represent the internal forces that develop within a beam when external loads are acting on it.

The internal forces that exist within the beam will depend on how the beam is loaded, and how it is supported. Beams are typically loaded by concentrated forces, distributed forces, and concentrated moments. Typical beam supports include pinned supports, roller supports, and fully fixed supports.

#### How Do We Draw the Shear Force and Bending Moment Diagrams?

Determining shear forces and bending moments along the length of a beam typically involves three steps:

– First we draw the free body diagram of our beam.

– Next we use the equilibrium equations to calculate the reaction forces and moments.

– Finally, we cut our beam at a single location and use the equilibrium equations to determine the shear force and bending moment at that location. We repeat this process for each location along the beam, and draw the result on our shear force and bending moment diagrams.

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