Suppose an unstable structure admits no rigid motions-only mechanisms. Let f be an external force on the structure that maintains equilibrium. Suppose that you stabilize the structure by adding in the minimal number of reinforcing bars. Prove that the given force f induces the same stresses in the original bars, while the reinforcing bars experience no stress. Are the displacements necessarily the same? Does the result continue to hold when more reinforcing bars are added to the structure?