Evolutive and Kinematic Limit Analysis Algorithms for Large-Scale 3D Truss-Frame Structures: Comparison Application to Historic Iron Bridge Arch

Abstract

Two new computational algorithms for the Limit Analysis (LA) of large-scale 3D truss-frame structures recently proposed by the authors are reconsidered and adapted for a comparison prediction of the elastoplastic response of a strategic beautiful historic infrastructure, namely the Paderno d’Adda bridge (or San Michele bridge), a riveted wrought iron railway viaduct that was built in northern Italy in 1889. The first LA algorithm traces a fully exact evolutive piece-wise linear elastoplastic response of the structure, up to plastic collapse, by reconstructing the true sequence of activation of made-available plastic joints (as a generalization of plastic hinges), in the true spirit of LA. The second LA algorithm develops an independent kinematic iterative approach apt to directly determine the plastic collapse state, in terms of collapse load multiplier and plastic mechanism, based on the upper-bound theorem of LA. Specifically, the marvelous doubly built-in parabolic arch of the bridge is analyzed, under a static loading configuration at try-out stage, and its elastoplastic response is investigated, in terms of evolutive load-displacement curve, collapse load multiplier and plastic collapse mechanism. The two LA algorithms are found to much effectively run and perform, despite the rather large size of the computational model, with a number of dofs in the order of four thousands, by achieving good corresponding matches in terms of the estimate of the load-bearing capacity and of the collapse characteristics of the arch substructure, showing this to constitute a well-set structural element. Moreover, the direct kinematic method displays a rather dramatic performance, in truly precipitating from above onto the collapse load multiplier and rapidly adjusting to the collapse mode, in very few iterations, by a considerable saving of computational time, with respect to the complete evolutive elastoplastic analysis. This shall open up the way for further adoption of such advanced LA tools, with LA regaining a new momentum within the modern optimization analysis of structural design and form-finding problems.