Redundancy theory and evaluation index of cable–strut system

Redundancy theory of cable–strut system is developed for evaluation of structural design. This redundancy theory extends system-level redundancy to member-level redundancy and takes pre-force into account by introducing the second-order deformation of cable and strut. The linear and nonlinear redundancy matrices are derived through potential energy equations in the form of linear and nonlinear deformations, respectively. The characteristics of structural geometry, topology, and material property are included in both linear and nonlinear redundancy matrices. Nonlinear redundancy matrix is also related to pre-force. Two sets of redundancy-based indexes are proposed for evaluation of cable–strut system. The system-level index set is used to evaluate structural redundancy and the strengthening effect of the pre-force on the structural redundancy. The member-level index set is used to evaluate the distribution of redundancy and structural uniformity. Finally, three groups of 3-bar prisms and two groups of cable domes are designed and analyzed to verify the effectiveness of the proposed redundancy-based indexes. The results show that the two sets of redundancy-based indexes are able to reflect pre-force level and evenness of distribution of strain energy and thus can be used as structural evaluation indexes.