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The paper develops a novel and general methodology to characterize thenonlinearity of structural systems and to provide a mathematically proven basisfor applying partial safety factors to nonlinear structural systems. Itestablishes, for the first time since the development of limit-state theory,the necessary key relationship between the partial safety factor concept andthe reliability theory of nonlinear structural systems. The degree ofhomogeneity has been introduced as a nonlinearity measure at the design point,allowing an efficient mathematical decoupling of the reliability index intononlinearity-invariant partial reliability indexes. With this formulation,critical safety situations in extreme cases of nonlinearities have beenidentified in complex nonlinear structural systems. The theory resulted in twomain outcomes based on the asymptotic behaviour of the reliability index.First, the reliability index of any nonlinear structural system remains alwaysbounded between an upper and lower bound, which can be determined by theconcept of nonlinearity-invariant partial reliability indexes. The second isnonlinearity-invariant critical partial safety factors, a concept that assuresa reliability index greater than the target reliability index in any nonlinearstructural system. Homogeneity analysis has been suggested to assess the safetyof complex nonlinear structural systems. While it can be coupled with advancedcomputational methods available in structural mechanics, it is not specificallydesigned for engineering practice. The proposed theory is designed primarily toprovide code writers with the necessary procedure for calibrating partialsafety factors for nonlinear structural systems, and to identify the over-safeor under-safe cases in the codes of practice.

The theory of homogeneity of nonlinear structural systems -- A general basis for structural safety assessment