Theorems for the Synthesis of Simply-Stiff Frameworks

Extract

Systematic knowledge of the theorems available for building statically determinate frameworks appears to be restricted in this country to a very small circle. Many engineers are content with the knowledge that a simply-stiff plane framework can be produced by attaching a joint O by bars OA, OB. to joints A and B of a simply-stiff plane framework; and that a simply-stiff space framework can be produced by attaching a joint O by bars OA, OB, OC to joints A, B and C of a simply-stiff space framework. By these simple means, two- and threedimensional simply-stiff frameworks can be built up respectively from the basic triangle and basic tetrahedron.

Most textbooks give no other rules of synthesis, and are content to give as “ proofs ” of the relationships existing between the number of joints j and the number of bars m of a simply-stiff framework (m = 2j—3 in the two-dimensional case and m=3j—6 in the three-dimensional case) the obvious inferences of these relationships from the system of synthesis just described.