Example 2 – Virtual Work

 

 

A weightless beam has an applied load  P acting at end C of the beam and is restrained by a frictionless pivot at B and a spring with spring constant, K, at  A as shown below.  The spring is unstretched when the beam is horizontal.  Use the method of virtual work to find the angle, θ, once the beam is in equilibrium.

 

 

                          

 

                                   

Step 1:  There is one degree of freedom.  Pick  θ  the angle of rotation of the beam (CCW positive).

 

 

Step 2:  Pick coordinate axes, x and y with origin at B (a fixed point).

 

 

              

 

                                    

                                   

Step 3:  Calculate y-coordinates of A and of C.        yA  = ( - 2L/3) sin θ ,  yC  = (L/3) sin θ

               and take derivatives to find virtual displacements.

 

                             δyA  = ( - 2L/3) cos θ δθ    and      δyC = (L/3) cos θ δθ

 

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