Keywords: shear, torsion, B-region, D-region, strut-and-tie, coupled response, concrete, nonlinear modelling, constructability.

Non-linear analysis represents a crucial tool for assessing constructed structures and predicting the actual response of new designs, especially under severe conditions and also under service loading. The most extended form of a non-linear model consists of frame elements with one-dimensional fibre cross-section models, which is limited to axial force and bending moments. This makes this type of model insufficient for correctly estimating the structural performance [1], i.e. with the presence of high shear forces and torsion, discontinuity regions, etc. Improving the capacity of frame element analysis is possible by means of new sectional analysis techniques capable of considering three-dimensional effects.

This enables a modelling possibility in which different cross-section models can be used along B-regions of a structure according to the type of loading and behaviour expected. In this sense, traditional uniaxial fiber sectional models can be used in regions governed by normal forces, while higher order sectional models are included in regions where shear and torsion are likely to influence the response. Substructures of special three or two-dimensional finite elements are required for modelling D-regions. The elements needed for this type of modelling are therefore: traditional cross-section models, special cross-section models capable of considering tangential forces, traditional frame elements, and D-regions elements. Possibilities for the new elements needed are presented and analysed in this paper.

In particular, a total interaction nonlinear sectional analysis (TINSA) is presented in this paper as a local sectional model capable of considering most three-dimensional phenomena governing B-regions under the combination of the six internal forces. By means of adding warping and distortion to the Navier-Bernoulli cross-section kinematics, the theory is capable of reproducing three-dimensional stress and strains states distributions that satisfy three-dimensional internal equilibrium [2]. This is achieved by means of a special function equation that is internally solved. Two alternative internal solvers are possible: planar finite element model sof the cross-section and by means of generalized coordinate's methods. By means of different case studies, the capabilities for considering confinement effects and tangential forces and their effects in the global structural response are shown.

On the other hand, a model for the design and analysis of D-regions is also presented. The design methodology is based on topological optimization and is capable of considering constructability aspects in the proposed reinforcement arrangement. Response of this type of region is assessed by means of a finite element non-linear analysis.

1

J.M. Bairán, A.R. Marí, "Shear-Bending-Torsion Interaction in Structural Concrete Members: A Nonlinear Coupled Sectional Approach", Arch. Comput. Methods. Eng., 14, 249-278, 2007. doi:10.1007/s11831-007-9007-5

2

J.M. Bairán, A.R. Marí, "Coupled model for the nonlinear analysis of anisotropic sections subjected to general 3D loading. Part 1: Theoretical formulation", Computers & Structures, 84(31-32), 2254-2263, 2006. doi:10.1016/j.compstruc.2006.08.036

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