Example 1 (continued) - Virtual Work

 

 

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

 

In vector form     δyA  = ( - 2L/3) cos θ δθ  j  and      δyC = (L/3) cos θ δθ j

 

And the external forces that do virtual work are   Q  =  - Q j   and  P  =  - P j

 

 

Step 4.  Calculate the dot product of the external forces with the virtual displacements

to establish the virtual work performed during the virtual displacement.

 

       δW  =  Q · δyA  +  P ·δyC   =   ( 2L/3) Q cos θ δθ  - (L/3) P cos θ δθ

 

 

Step 5.  Set the virtual work equal to zero and solve for the desired unknown (or unknowns).

 

                                               δW  =   0

 

                              [ ( 2L/3) Q cos θ - (L/3) P cos θ ] δθ   =   0

 

Since the virtual displacement, δθ, is arbitrary

 

                          ( 2L/3) Q cos θ - (L/3) P cos θ  =  0    or

 

                         [ ( 2L/3) Q  - (L/3) P ] cos θ  =  0

 

                              Q = (P/2) cos θ ,   since  θ = 0    Q = P/2 (result)

 

 

Click here for example 2.       Click here for example 3.

 

 

 

  


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