Elastic no tensile resistant-plastic analysis of masonry arch bridges as an extension of Castigliano's method

On the grounds of the classical Castigliano’s theory, a step-wise procedure for the non-linear analysis of multi-span masonry arch bridges is developed and implemented by standard programming of a commercial F.E. code. The mechanical model for masonry is assumed perfectly elasto-plastic in compression and no tensile resistant (NTR). The iterative procedure is set following the standard scheme of an elastic prevision and subsequent non-linear correction of the nodal forces. Tensile stresses are not allowed to develop on the mortar joint by means of an adequate re-meshing of the arch, while the plastic response is taken into account via additional fictitious external forces. The procedure is applied to a flat arch with different models: a No Tensile Resistant (NTR) model that accounts for the original Castigliano’s method, models with different compressive strength. The structural response is estimated for different loading positions, pointing out the change of the collapse mechanism as a function of the geometric and mechanical parameters. The flexibility of the procedure allows the analysis of twin-span and three-span models, so that the effect of abutment compliance and material crushing in complete bridge models is taken into account and quantified