# Problem 707 | Propped beam with moment load at simple support by moment-area method

**Problem 707**

For the propped beam shown in Fig. P-707, solved for vertical reaction R at the simple support.

**Solution**

Taking the fixed support to be the moment center, the moment diagram by parts is shown to the right.

$EI \, t_{A/B} = (Area_{AB})\, \bar{X}_A = 0$

$ML(\frac{1}{2}L) – \frac{1}{2}L(RL)(\frac{2}{3}L) = 0$

$\frac{1}{2}ML^2 – \frac{1}{3}RL^3 = 0$

$R = \dfrac{3M}{2L}$ *answer*

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