The objective of the present work is that of making a contribution to the performance-based seismic design of RC buildings with U-shaped walls. Since U-shaped walls are often placed at the perimeter of a building and are typically stiffer and stronger than other lateral strength providing structural elements, many of these buildings possess in-plan strength and stiffness eccentricities and are therefore prone to damage due to twist-induced displacements. The work focuses therefore on two aspects of the design of such buildings for which the knowledge state was judged unsatisfactory. These are: (i) the inelastic behaviour of U-shaped walls under different directions of seismic loading and (ii) the estimation of displacement demands on structural elements in torsionally eccentric buildings. Within the scope of this endeavour two U-shaped walls were tested under a quasi-static cyclic, bi-directional loading regime. The two test units were analysed using plastic hinge models and wide-column models. From the comparison with the experimental results, modelling guidelines for U-shaped walls were developed. In the second part of the report the torsional response of inelastic structural wall buildings was studied and a semi-empirical method for estimating the twist-induced displacements was developed. The method can be used to extend the application of the direct displacement-based design approach to the class of torsionally restrained structures that are asymmetric in-plan but regular over the height.