A distribution factor method with cubic interpolating correction for analysis of building frames

Abstract

A more accurate approximating method for the analysis of building frames than the original distribution factor method described in Reference [7] is presented. The relative magnitudes of the joint displacements (w, α, β) on a particular floor are rather insensitive to the lateral load and are dependent largely on the local stiffness of the beams and columns of the floor of interest. These relative magnitudes are called distribution factors. The distribution factors corresponding to unit u, v, and θ displacements, respectively, can be determined floor by floor. The absolute magnitudes are then obtained by linear combination of the distribution factors. The coefficients of the linear combination are called the mixing factors. There are nine mixing factors per floor, three for each displacement (w, α, β) corresponding to unit u, v, and θ, respectively. The mixing factors are found after the lateral loads are imposed. This paper makes corrections on the displacements for very tall buildings where uneven elongations of columns along the height are important. A new distribution pattern in terms of cubic polynomials with an additional ten unknowns per floor is added to the original sets of distribution factors. The total number of unknowns per floor for a three-dimensional building is 22 (9 mixing factors + 10 coefficients of the cubic polynomial + 3 horizontal displacements u, v, θ) irrespective of the complexity. Less than 5% errors in the computed nodal displacements are achieved. The method is particularly suitable for microcomputers.