double integration method

Problem 707 | Propped Beam with Moment Load

Problem 707
A couple M is applied at the propped end of the beam shown in Fig. P-707. Compute R at the propped end and also the wall restraining moment.
 

707-propped-beam-moment-load.gif

 

Problem 706 | Solution of Propped Beam with Decreasing Load

Example 03
The propped beam shown in Fig. P -706 is loaded by decreasing triangular load varying from wo from the simple end to zero at the fixed end. Find the support reactions and sketch the shear and moment diagrams
 

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

 

Problem 705 | Solution of Propped Beam with Increasing Load

Problem 705
Find the reaction at the simple support of the propped beam shown in Fig. P-705 and sketch the shear and moment diagrams.
 

Propped beam loaded with triangular or uniformly varying load

 

Problem 704 | Solution of Propped Beam

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

704-propped-beam-uniform-load.gif

 

Application of Double Integration and Superposition Methods to Restrained Beams

Superposition Method

There are 12 cases listed in the method of superposition for beam deflection.

  • Cantilever beam with...
    1. concentrated load at the free end.
    2. concentrated load anywhere on the beam.
    3. uniform load over the entire span.
    4. triangular load with zero at the free end
    5. moment load at the free end.
  • Simply supported beam with...
    1. concentrated load at the midspan.
    2. concentrated load anywhere on the beam span.
    3. uniform load over the entire span.
    4. triangular load which is zero at one end and full at the other end.
    5. triangular load with zero at both ends and full at the midspan.
    6. moment load at the right support.
    7. moment load at the left support.

See beam deflection by superposition method for details.
 

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