Stability and Influence Vectors of Trusses

The necessary and sufficient conditions for geometrical stability of plane truss constructions, either statically determinate, or indeterminate, are presented. The procedure of testing stability involves only the velocity analysis of rigid bodies. After removing the redundants (if any) and an additional reaction component, the structure becomes a mechanism having a single degree of freedom. Assign an arbitrary permissible velocity to a link of the mechanism. The velocities of a few points can be used as the criteria for stability. The coliaries of the criteria are given in terms of the instantaneous centers of the mechanism. Furthermore, the force systems that can be sustained by an unstable structure in its own original form are asserted. The concept of influence vectors is introduced. The dot product of a force vector and the appropriate influence vector of a quantity is equal to that amount of the quantity produced by the force. The procedure of testing stability can be used to establish influence vectors or influence-vectors diagrams for statically determinable quantities.