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.
Solution to Problem 422 | Shear and Moment Equations Jhun Vert Tue, 04/21/2020 - 06:45 pm

Problem 422
Write the shear and moment equations for the semicircular arch as shown in Fig. P-422 if (a) the load P is vertical as shown, and (b) the load is applied horizontally to the left at the top of the arch.
 

Simply supported circular arc member

 

Solution to Problem 421 | Shear and Moment Equations Jhun Vert Tue, 04/21/2020 - 06:43 pm

Problem 421
Write the shear and moment equations as functions of the angle θ for the built-in arch shown in Fig. P-421.
 

Circular arc beam with fixed end support and free at one end

 

Shear and Moment Diagrams Jhun Vert Tue, 04/21/2020 - 11:01 am

Shear and Moment Diagrams
Consider a simple beam shown of length L that carries a uniform load of w (N/m) throughout its length and is held in equilibrium by reactions R1 and R2. Assume that the beam is cut at point C a distance of x from he left support and the portion of the beam to the right of C be removed. The portion removed must then be replaced by vertical shearing force V together with a couple M to hold the left portion of the bar in equilibrium under the action of R1 and wx.
 

Shear and moment diagrams by shear and moment equations