Step 1: Recall what makes a frame redundant.
A redundant frame has more unknown reactions or internal forces than the equations of equilibrium can solve for, so extra compatibility conditions involving deformation are needed.
Step 2: Recall what Castigliano's second theorem gives us.
This theorem says the partial derivative of the total strain energy with respect to a force gives the displacement in the direction of that force: \[ \delta = \frac{\partial U}{\partial P}. \] Setting this displacement to a known value, often zero at a redundant support, gives one equation per redundant force.
Step 3: Apply this to a redundant frame.
By writing one such energy equation for each redundant reaction, we get exactly enough equations to solve the whole frame.
\[ \boxed{\text{Castigliano's second theorem}} \]