Energy-Based Assessment of the Ultimate Limit State of a Physically Nonlinear Structure

The paper addresses issues of nonlinear analysis of load-bearing structural members. It highlights the main distinction from the traditional approach, which involves a two-step procedure where static and dynamic analyses are separated from the local reliability check of design sections. In contrast, the nonlinear analysis employs a single-step analysis and a global assessment of the structural behavior while simultaneously checking the performance of all sections. It is proposed to use the work done by external forces as a measure for determining the ultimate load. An incremental procedure is analyzed, through which the equilibrium state curve is constructed and this work is calculated. The paper highlights the issue of numerical instability in the computational process as it approaches the failure load. As a way to address this problem, it is suggested to consider a state of the structure as ultimate when it significantly loses its ability to resist the increasing load (loss of resistance). The paper proposes a method for finding design combinations of independent load cases, based on the energy approach, which offers sufficient applicability. It is noted that in the case of nonlinear (global) analysis, the selection of a design load combination should be based not on a local criterion but on a global one, which defines the composition of loads and actions constituting the design combination. The energy of deformation is suggested as such a criterion. The algorithm for searching for dangerous load combinations relies on a plausible hypothesis that the energy-based composition of load combinations leading the system to its ultimate state, due to the global nature of energy assessments, will be the same as in the case of linear analysis. This algorithm enables to solve the problem without resorting to an exhaustive evaluation of all possible load combinations.