Singularity Functional Method In Structural Analysis Of High-Rise Buildings

The historical development and characteristics of structural analysis methods in high-rise building have been reviewed. The previous assumptions about inflection point at beam's mid-span, rigid floor plane and constant sectional coefficients are discussed. Author explicitly suggests that a) structural variable is of overall and partial behavior. b) A vertical member restrained by horizontal members may be substituted for multi-column elements or shear wall to form new structural analyzing model by singularity functions. And c) forces and displacements are selected as basic analyzing variables simultaneously in structural analysis by mixed method. In view of the above, combining singularity functions and matrix algebra, author presents a singularity function method in the analysis of high-rise building structures for the first time.At beginning, foundation conceptions, operation rules and theorems about singularity functions are introduced. Then, singularity functions are employed to describe the concentrated forces or abrupt change parameters of cross-section, by which the discontinuous variables are expressed in a continuous functional formal. Integrating the differential equation directly, author derives functional relations and a matrix equation between concentrated forces and deformations of a vertical member element.Abandoning the continuum assumption in shear wall structures, every shear wall is considered as an independent member element, and the lateral displacements, rotation angles and abrupt change parameters of structure are described directly by singularity functions. By the compatible relation of relative deflections at the mid-span of beams, the structure's equation is obtained and solved with the unknown quantities of beam's shear forces.Furthermore, abandoning the assumption of inflection point at mid-span of a beam, an analysis process is researched on two hands. First one, Base on the element equation of vertical member, an overall equation and a partial equation...