Reciprocity of Work, Principle of

(also called Betti’s Theorem), one of the most important energy properties of a body that is being linearly deformed; it consists in the fact that upon the action on the body of two indepen-dent force systems (the states i and k), the work W_ik of the external or internal forces of the state / on the virtual displacements that are caused by the action of the forces of the state k is equal to the work Wki of the forces of state k on the displacements caused by the action of the forces of state /—that is, Wik = Wki. The principle of reciprocity of work was first formulated by E. Betti (1823-92). The principles of reciprocity of displacements and reactions, which are used in strength of materials and structural mechanics in calculating elastic systems, are consequences of the principle of reciprocity of work.