Example

Determine the reactions for the beam shown in Figure 2.28 and draw its shear force and bending moment diagrams.

It can be seen from the figure that there are three reactions, namely, MA, RA, and Rc, one more than that required for a stable structure. The reaction Rc can be removed to make the structure determinate. We know that the deflection at support C of the beam is zero. One can determine the deflection dCP at C due to the applied load on the cantilever in Figure 2.28b. In the same way the deflection dCR at C due to the redundant reaction on the cantilever (Figure 2.28c) can be determined. The compatibility equation gives dcp - dcR = 0

By moment area method,

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