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December 2012

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

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Problem 719 | Propped beam with concentrated load at midspan by moment-area method

Problem 719
For the propped beam shown in Fig. P-719, determine the propped reaction R and the midspan value of EIδ.
 

719-propped-beam-concentrated-load-midspan.gif

 

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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

 

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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.

 

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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

 

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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

 

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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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Problem 715 | Distributed loads placed symmetrically over fully restrained beam

Problem 12
Determine the moment and maximum EIδ for the restrained beam shown in Fig. RB-012. (Hint: Let the redundants be the shear and moment at the midspan. Also note that the midspan shear is zero.)
 

715-restrained-beam-symmetrical-uniform-loads.gif

 

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Problem 714 | Triangular load over the entire span of fully restrained beam

Problem 714
Determine the end moments of the restrained beam shown in Fig. P-714.
 

714-restrained-beam-triangular-load.gif

 

Solution
$\delta_A = 0$

$\delta_{triangular\,\,load} - \delta_{fixed\,\,end\,\,moment} - \delta_{reaction\,\,at\,\,A} = 0$
 

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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.)
 

713-fully-restrained-beams-symmetrical-point-loads.gif

 

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