Biyernes, Abril 01, 2011

Deflection in Simply Supported Beams

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} $
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