Collapse Considerations and Electrical Analogies for Statically Indeterminate Structures

Abstract

It is a commonly held belief that increased levels of statical indeterminacy equip structures with enhanced factors of safety against collapse. This belief is loosely predicated on the idea that statically indeterminate structures can, after localized failure, activate alternative force paths and so can significantly delay overall collapse while continuing to support load. The first part of this paper is in the nature of a review of research into two forms of highly statically indeterminate structure, namely the steel space truss and the reinforced concrete frame, which challenges this received wisdom. This review shows that research published subsequent to the failure of a real space truss has identified factors which render such trusses prone to “premature” collapse, in spite of the inherently high degrees of statical indeterminacy of these structures. Indeed, a key idea identified from this work is that the presence or absence of collapse mechanisms in a truss is not influenced exclusively by the degree of statical indeterminacy of the truss. This idea is shown to lead to the important result that a truss can be statically indeterminate and also a mechanism. Another key result of this work is shown to be that states of self-stress due to this very indeterminacy can actively assist in precipitating (rather than inhibiting) collapse of trusses and frames. The role of member postbuckling behavior in triggering progressive collapse of trusses is also discussed. Anti-collapse schemes, including selective member removal (normally held to be detrimental to structural integrity), are then presented. In the second part of the paper, analogies are drawn between trusses and electrical circuits. It is shown that truss material stiffness is analogous to conductivity, not resistivity, in the circuit. Further, the electrical analogy of a truss inextensional mechanism is shown to exist when parallel capacitor–inductor arrangements satisfying a unique mathematical relationship are present in the circuit. Potential uses of these analogies are stated. It is concluded that care must be exercised in relying on statical indeterminacy to provide fail-safe characteristics, and that future research should focus on optimizing the balance between indeterminacy and stability in structures.