The strut-and-tie models in reinforced concrete structures analysed by a numerical technique

the strut-and-tie models are appropriate to design and to detail certain types of structural elements in reinforced concrete and in regions of stress concentrations, called "d" regions. this is a good model representation of the structural behavior and mechanism. the numerical techniques presented herein are used to identify stress regions which represent the strut-and-tie elements and to quantify their respective efforts. elastic linear plane problems are analyzed using strut-and-tie models by coupling the classical evolutionary structural optimization, eso, and a new variant called seso - smoothing eso, for finite element formulation. the seso method is based on the procedure of gradual reduction of stiffness contribution of the inefficient elements at lower stress until it no longer has any influence. optimal topologies of strut-and-tie models are presented in several instances with good settings comparing with other pioneer works allowing the design of reinforcement for structural elements.