Abstract:
In parallel with the development of modern digital computers there is an increasing quest for a thorough understanding of the dynamic response characteristics of typical civil engineering structures. Of particular interest is the response of such structures to earthquake derived loadings. The current generation of computer programs favour the modelling of structures by equivalent two-dimensional components. This principle has been widely used in elastic analyses of symmetric buildings laid out in rectangular grids. In the absence of torsional ground motion components, the principle of superposition can be used to combine results obtained separately along each of the major axes of the building. The principle of superposition cannot be used however when the building is stressed beyond its elastic range. An initially symmetric building can develop significant eccentricities in the distribution of its effective lateral stiffness and, thereby, torsional action, because of biaxial yielding in columns. In this study a computer program is developed which predicts the time-history response of three dimensional frame structures to earthquake ground motion. The program is not restricted to a rectangular grid layout but can model a completely general structure geometry. Yielding 1s allowed for in both beams and columns with a library of yield surface options available depending on the principle structural action, or actions, of the component elements. For a typical beam element, the yield status may be a function of the principle bending moment only, whereas for an exterior column account can be taken of biaxial bending coupled with axial load. The principle of modal superposition is encountered commonly in elastic analyses, however the response of yielding structures is predicted almost universally by direct integration of the equations of motion. The study demonstrates that the principles of modal superposition can be extended, with some reconstitution of the coordinate transformations involved, into the post-elastic domain. One advantage of the transformation to a generalized coordinate system is a reduction in the number of dynamic degrees-of-freedom which need to be included in the response determination. A second, and perhaps more significant consequence, is the analyst now has access to the instantaneous dynamic properties of the structure. Yielding softens the structure and lengthens the effective modal periods and this shift in period can be related to the earthquake response spectrum giving a new insight into the structure's earthquake resistance mechanism. To demonstrate the implementation of the computer program, the response of two typical structures is investigated. The first is a two-span bridge with a steel truss superstructure and a central concrete pier. The second is a six-storey reinforced concrete ductile frame building. In both cases the response based on an equivalent planar frame assumption is shown to be modified significantly when account •is taken of concurrent earthquake effects.