Engr Help

Example 2 – (continued) Virtual Work

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

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

Next calculate the force in the spring noting that the value remains constant during a virtual displacement

F_s = K (extension) = K (2L/3) sin θ so F_s = - K (2L/3) sin θ j

and the external forces that do virtual work are F_s = ˗ K (2L/3) sin θ 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 = F_s · δy_A + P ·δy_C = K (2L/3) sin θ ( 2L/3) 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 or [ ( 4KL²/9) sin θ cos θ - (L/3) P cos θ ] δθ = 0

Since the virtual displacement, δθ, is arbitrary

[ {( 4KL²/9) sin θ ˗ PL/3} cos θ ] δθ = 0 implies that ( 4KL²/9) sin θ ˗ PL/3 = 0

sin θ = 3 P / 4KL (final result; what are limitations on P, K, and L ?)

Click here to return to example 1. Click here for example 3.

Return to Notes on Statics