Two theorems on statical indeterminacy of structures

Classical structural theorems are concerned with extremum conditions of energy as a function of displacement degrees of freedom or that of the complementary energy as a function of member forces. In this brief note the extremum conditions of energy and complementary energy are viewed from the perspective of degrees of indeterminacy in the system. Specifically, it is shown that the complementary energy in a system, under prescribed displacements, is reduced as the statical indeterminacy of the systems is lowered by removal of some redundant members. Further, it is shown that the loss in the complementary energy of the system is greater than the complementary energy in the removed redundant members