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Problem 11.114

While the load at C is 7.5 kips, it must be replaced by an unknown F temporarily, since it would otherwise be impossible to take the partial derivative of the energy with respect to F.

The energy of the truss is

where P is the axial force in each member of the truss (the members are two-force members). These axial forces will have to expressed in terms of the (temporarily) unknown load F. Clearly, member BC must be in compression. Taking a free body about joint B:

Next, I take a free body about joint C: The deflection at C, according to Castigliano's Theorem, is

The partial derivatives are:

Lengths will be needed:

Substituting these into the equation above...

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