fully restrained beam

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

 

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
$\delta_A = 0$

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

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

 

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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