Simultaneous static and kinematic indeterminacy of space trusses with cyclic symmetry

Abstract

This paper examines the structural rigidity of pin-jointed space trusses with cyclic symmetry. Although the necessary condition of static and kinematic determinacy, the so-called Maxwell's rule, is satisfied, the structures are both statically and kinematically indeterminate. The physical meaning of the static and kinematic indeterminacy is presented. In the case of both statically and kinematically indeterminate cylindrical trusses having planes of mirror symmetry, it is proved that although the cylindrical truss consists of individually both unstable and redundant “rings”, the degree of static and kinematic indeterminacy is independent of the number of the “rings”.