Explicit Kinematic Solution for Tall Rigid-Jointed Frames

Abstract

A new set of equations for linear elastic analysis of tall rigid-jointed frames loaded at the joints is derived. These are simultaneous difference equations involving four local kinematic quantities, with story level as the single independent variable. They may be solved explicitly for certain classes of frames of practical interest. The solution is nontrivial and employs techniques that are of general interest in the kinematic and static analysis of periodic elastic structures. Application to an eight-bay, 40-story frame under lateral loading yields topmost story drift within 6% of the exact finite-element solution. The solution represents a vertex of the subspace of kinematically admissible states. Thus, it may be used in the hypercircle formulas of Prager and Synge to obtain bounds on displacement and stress, or as a stand-alone analysis and design tool for tall planar frames. The current solution may be implemented easily in commercial spreadsheet software, offering a significant advantage to the structural analyst.