beam rotation

Problem 725 | Propped beam with partially restrained wall and settling simple support

Problem 725
If the support under the propped beam in Problem 724 settles an amount $\delta$, show that the propped reaction decreases by $3EI\delta / L^3$.

Problem 724 | Propped beam with partially restrained wall support

Problem 724
The beam shown in Fig. P-724 is only partially restrained at the wall so that, after the uniformly distributed load is applied, the slope at the wall is $w_oL^3 / 48EI$ upward to the right. If the supports remain at the same level, determine $R$.



Application of Area-Moment Method to Restrained Beams

See deflection of beam by moment-area method for details.

Rotation of beam from A to B

$\theta_{AB} = \dfrac{1}{EI}(\text{Area}_{AB})$


Deviation of B from a tangent line through A

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