Vulnerability Of Frame Structures Based On Energy Flow Network

Vulnerability of structures reflects the structures'action of vulnerability in unexpected events. For structures with high level of vulnerability, although probability of structural collapse may be quite small, the consequences of the collapse are very serious. How to evaluate the structural vulnerability quantitatively is one of the most challenging problems in structural engineering. Based on the network of energy flow in frame structures, the quantitative methods to evaluate the index of member importance and the index of vulnerability of a structure are presented. The main contents are as follows:(1) The quantitative method to evaluate the index of member importance is constructed. Based on the network of energy flow in frame structures, three matrixes of energy change are constructed due to reduction of member stiffness: matrix of change of energy flow, matrix of change of stored energy and matrix of change of structural energy. By calculating the matrix of change of structural energy, the effects both on the structure when a member is damaged and on the member itself when other portion of the structure is damaged, are considered. Then the index of member importance is determined.(2) The quantitative method to evaluate the index of vulnerability of a structure is put forward. By analogy to the chain law in calculus, the index of member importance and the index of vulnerability of a structure are combined. The index of vulnerability of a structure is defined on the importance indexes of a series of the most important members. (3) The reasonability and feasibility of the presented method is demonstrated by several exampled. Vulnerabilities of continuous beam of different spans are analyzed. The differences of vulnerabilities among continuous beams with different spans are also discussed. Member importance of a two-span continuous beam is analyzed and compared with other methods. Finally, member importance and vulnerability of a three-hinged frame are analyzed as an example to show its feasibility to statically determinate structures.(4) The presented method is applied to determine reasonable arrangements of main members in engineering practice, as well as structural health monitoring to show its preliminary application.