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.
 

Double Integration Method

Moment at any exploratory section

$EIy'' = M$

 

Slope of the beam at any point

$\displaystyle EIy' = \int M + C_1$

 

Deflection of beam at any point

$\displaystyle EIy = \int \int M + C_1x + C_2$

 

See the deflection of beam by double integration method for details.
 

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