deviation from tangent

Problem 735 | Fixed-ended beam with one end not fully restrained

Problem 735
The beam shown in Fig. P-735 is perfectly restrained at A but only partially restrained at B, where the slope is woL3/48EI directed up to the right. Solve for the end moments.
 

735-fixed-ended-beam-one-end-not-fully-restrained.gif

 

Problem 733 | Cantilever beam with moment load at the free end and supported by a rod at midspan

Problem 733
The load P in Prob. 732 is replaced by a counterclockwise couple M. Determine the maximum value of M if the stress in the vertical rod is not to exceed 150 MPa.
 

Problem 722 | Propped beam with moment load on the span by area-moment method

Problem 722
For the beam shown in Fig. P-722, compute the reaction R at the propped end and the moment at the wall. Check your results by letting b = L and comparing with the results in Problem 707.
 

722-propped-beam-moment-load.gif

 

Solution

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.
 

707-propped-beam-moment-load.gif

 

Problem 721 | Propped beam with decreasing load by moment-area method

Problem 721
By the use of moment-are method, determine the magnitude of the reaction force at the left support of the propped beam in Fig. P-706.
 

Propped with decreasing load from w at simple support to zero at the fixed end.

 

Problem 720 | Propped beam with increasing load by moment-area method

Problem 720
Find the reaction at the simple support of the propped beam shown in Fig. P-705 by using moment-area method.
 

Propped beam loaded with triangular or uniformly varying load

 

Problem 704 | Propped beam with some uniform load by moment-area method

Problem 704
Find the reaction at the simple support of the propped beam shown in Figure PB-001 by using moment-area method.
 

704-propped-beam-uniform-load.gif

 

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

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

 

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