Deflections in Simply Supported Beams | Area-Moment Method

The deflection δ at some point B of a simply supported beam can be obtained by the following steps:

Area-moment method of finding deflections in simply supported beam

1. Compute $t_{C/A} = \dfrac{1}{EI}(Area_{AC}) \, \bar{X}_C$

2. Compute $t_{B/A} = \dfrac{1}{EI}(Area_{AB}) \, \bar{X}_B$

3. Solve δ by ratio and proportion (see figure above).

$\dfrac{\delta + t_{B/A}}{x} = \dfrac{t_{C/A}}{L}$