Problem # p038

Shear force and Moment diagram

A beam is subject to a sinusoidally distributed load as shown in the top figure to the left :

w(x)= wo sin(pi*x/L)

acting downwards. wo is the weight per unit length at the center of the beam (x=L/2) and pi=3.1415....

Please determine in terms of wo and beam length L the following :
  1. The total weight of the continuous load.
  2. The support forces R1 and R2.(Think about where the center of mass of the continuous load might be).
  3. Use dV/dx = - w(x) to determine the shear forces V(x) as function of x and sketch it into the graph provided.
  4. Use dM/dx=V(x) to determine the moment M(x) as function of x and sketch it into the graph provided.
  5. What is equation for the maximum value of M(x) ?