Derivative Theorems of the Principle of Quasi Work

Derivative theorems of Principle of Quasi Work, a powerful pseudo energy principle, are derived. These theorems, viz. Applied Load Theorem, Deflection Theorem and Unit Load Theorem are applicable to a pair of topologically similar structural systems. One more theorem referred to as Relative Deflection Theorem along with its two corollaries are also derived from this principle for facilitating truss analysis. Using these theorems, a new methodology for calculating nodal deflections of a truss from its internal member forces and vice versa is presented in this paper. This methodology is amazingly simple, easy, and fast. These theorems form the basis of present methodology. Thirteen nodal deflections of a four bay truss included in this paper were calculated by hand in less than fifteen minutes.