Example 1 - Virtual Work

Strategy:

1. Determine the (DOF) degrees of freedom of the structure and identify the variable (or variables) that determine the position of the structure.

2. Pick coordinate axes with a fixed origin to locate the external forces and moments that do virtual work during a virtual displacement of the structure.

3. Calculate the coordinates and take the derivative to obtain the virtual displacements. The virtual displacements must be consistent with the

kinematic constraints.

4. Calculate the dot product of the external forces with the virtual displacements to establish the virtual work performed during a virtual displacement.

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

A weightless beam has an applied load P acting at end C of the beam and is supported by a frictionless pivot at B shown below. Use the method of virtual work to find the external force Q acting at A to maintain equilibrium of the beam.

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).

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