Example 3 – Virtual Work

 

 

A weightless beam of length L has an external moment, MA  acting at end A of the beam.  It is restrained by a frictionless pivot at A and a spring with spring constant, K, at  end B as shown below.  The spring is unstretched when the beam is horizontal.  Use the method of virtual work to find the angle, θ, for equilibrium of the beam.

 

 

                                      

 

 

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

 

 

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

 

 

                           

 

                                   

3:  Calculate y-coordinate of B.         yB  =  L sin θ

 

     and take the derivative to find the virtual displacement.

 

                                                     δyB =  L cos θ δθ

 

 

Click here to continue with this example.

 

                                   

 


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