Stress path adapting Strut-and-Tie models in cracked and uncracked R.C. elements

In this paper, a general method for the automatic search for Strut-and-Tie (S&T) models<br />representative of possible resistant mechanisms in reinforced concrete elements is proposed. The<br />representativeness criterion here adopted is inspired to the principle of minimum strain energy and<br />requires the consistency of the model with a reference stress field. In particular, a highly indeterminate<br />pin-jointed framework of a given layout is generated within the assigned geometry of the concrete<br />element and an optimum truss is found by the minimisation of a suitable objective function. Such a<br />function allows us to search the optimum truss according to a reference stress field deduced through a<br />F.E.A. and assumed as representative of the given continuum. The theoretical principles and the<br />mathematical formulation of the method are firstly explained; the search for a S&T model suitable for the<br />design of a deep beam shows the method capability in handling the reference stress path. Finally, since<br />the analysis may consider the structure as linear-elastic or cracked and non-linear in both the component<br />materials, it is shown how the proposed procedure allows us to verify the possibilities of activation of the<br />design model, oriented to the serviceability condition and deduced in the linear elastic field, by following<br />the evolution of the resistant mechanisms in the cracked non-linear field up to the structural failure.