Graphical Modal Analysis and Earthquake Statics of Linear One-Way Asymmetric Single-Story Structure

Abstract eng:
Graphical Static methods were developed in 1800s by European engineers and were a fundamental practice for generations of structural designers. Today they remain generally a valuable tool for representing and visualizing problems of structural mechanics that are governed by linear equations and rigid body kinematics, i.e. beam section analysis, mechanics of rigid bodies, etc. In this work we explore an application of graphical methods to the static earthquake response and vibrations of a single story elastic structure with a rigidbody diaphragm and a one-way asymmetry. We show that, based on involutory relations with respect to the floor ellipse of elasticity it is possible to graphically determine the lateral deflection under bi-directional earthquake loads, and the vibrational mode shapes. The method proves effective to gain insight into parameters that govern the earthquake response, and may be further explored to study more complex and general structures.

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