8.4: Shear and Bending Moment Diagrams

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Beams are structural elements primarily designed to support vertical loads. When designing a beam it is important to locate the points of maximum shear and maximum moment and their magnitudes because that’s where the beam is most likely to fail. To find these weak points, we need to check the internal loading at every point along the beam’s full length.

The previous section presented a method to find the shear and bending moment at a single point, which is useful; but in order to find the shear and moment at every point in the object you will need a more powerful approach. This can be done by creating a shear and bending moment diagram. This section will discuss three related but different methods to produce shear and bending moment diagrams, and conclude with a comparison of the advantages and disadvantages of each approach.

Shear and Bending Moment Diagrams

Shear and moment diagrams are graphs which show the internal shear and bending moment plotted along the length of the beam. They allow us to see where the maximum loads occur so that we can optimize the design to prevent failures and reduce the overall weight and cost of the structure.

Since beams primarily support vertical loads the axial forces are usually small, so they will not be considered in this section.

Beams can be supported in a variety of ways as shown in Figure 8.4.1. The common support methods are

Simply Supported Supported by a pin on one end and a roller at the other.
Cantilevered Fixed at one end, and unsupported at the other.
Overhanging One or both ends overhang the supports.

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(a) Simply Supported (b) Cantilevered (c) Overhanging

Figure 8.4.1. Beam Supports