Modal eccentricities of asymmetric structures

Modal eccentricities of monosymmetric structures are given by a simple hand method, which is based on the concept of the continuum medium. The method is applicable to structures consisting of any combination of walls, rigid frames and coupled wall bents that are uniform over the height of the structure. These structures do not belong to the special class of proportionate buildings for which the dynamic properties can be obtained approximately from the properties of an equivalent single-storey torsionally coupled building, in combination with those of a torsionally uncoupled multistorey structure. In the proposed method the equation of motion of each bent of the structure is approximated by that of an incompressible wall-frame system (model) of equal flexural rigidity, but of an equivalent modal shear rigidity, which accounts for axial deformations in the vertical members of the bent. With this model any uniform structure composed of different types of bents may be analysed by standard methods and dynamic properties may be determined by simple and rapid means. Modal eccentricities are given in respect to the centre of flexural rigidities, which is easily determined in uniform structures, and as the method is based on the continuous approach, a deep insight into the structural behaviour is possible by consideration of parameter variations. Approximate expressions are also given for frequencies and modal base shears, as these properties play a key role in the response spectrum analysis. In order to illustrate the accuracy of the proposed method comparisons are made with accurate results obtained by 3D computer dynamic analyses on discrete member models. Copyright © 2006 John Wiley & Sons, Ltd.