Frame Interaction in Nonorthogonal Grids

A method, based on the theorem of minimum total potential, is proposed for the analysis of nonorthogonal grids subjected to a set of static, horizontal forces arbitrary in magnitude and direction. Effects of interaction resulting from unsymmetrical bending of columns common to nonorthogonal intersecting frames are duly taken into account. Shear walls may be included in the analysis. Stiffness matrices of the individual stiffness elements and a matrix comprising the force set are utilized as basic input information. The method ultimately results in a system of linear algebraic equations from which translational (u, v), and rotational (φ) displacements of the rigid floor plates are determined. Subsequently, translational and flexural deformations of the stiffness elements are computed, from which stress resultants may be determined. Part one covers the formulation of the method of analysis through the development of equilibrium, compatibility, and force (moment) deformation relationships for subsequent utilization according to the minimum total potential theorem. In part two, a numerical application is presented.