Tall Frame Analysis by Reduced Generalized Coordinates

The displacements and rotations of joints on the exterior (corner) columns are independently expressed in terms of a set of functions with undetermined coefficients (generalized coordinates). Floors are assumed to be rigid in plane. Interior joints on different levels are constrained to displace vertically and rotate in the same manner relative to the exterior joints at the corresponding levels. Transformation matrix connecting the actual joint displacements to the generalized coordinates are then derived from the joint compatibility conditions. The obtained generalized structure stiffness matrix has order significantly lower than that in standard frame analysis. A 26-story, 3-bay frame was analyzed using 24 generalized coordinates and the errors are generally less than 5% and 10%, respectively, for the displacements and internal forces.