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

Reactions of Propped Beam with Triangular Load by Area Moment Method | Theory of Structures

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

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


Problem 713 | Fully restrained beam with symmetrically placed concentrated loads

Problem 713
Determine the end moment and midspan value of EIδ for the restrained beam shown in Fig. PB-010. (Hint: Because of symmetry, the end shears are equal and the slope is zero at midspan. Let the redundant be the moment at midspan.)



Problem 704 | Solution of Propped Beam

Reactions of Propped Beam by Double Integration Method | Theory of Structures

Problem 704
Find the reactions at the supports and draw the shear and moment diagrams of the propped beam shown in Fig. P-704.



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