Propped Beam

Problem 723 | Propped beam with uniform load over half the span

Problem 723
Find the reaction R and the moment at the wall for the propped beam shown in Fig. P-723.
 

723-propped-beam-uniform-load.gif

 

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 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

 

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

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

 

Problem 712 | Propped beam with initial clearance at the roller support

Problem 712
There is a small initial clearance D between the left end of the beam shown in Fig. P-712 and the roller support. Determine the reaction at the roller support after the uniformly distributed load is applied.
 

712-propped-beam-with-clearance.gif

 

Problem 709 | Propped Beam with Spring Support

Example 06
The beam in Figure PB-006 is supported at the left by a spring that deflects 1 inch for each 300 lb. For the beam E = 1.5 × 106 psi and I = 144 in4. Compute the deflection of the spring.
 

Beam with spring support

 

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