Dual Analysis of Rigidity for Structural Analysis Course

Source: Journal of Engineering Technology, Fall 2022, Volume 39 Issue 2, pg. 8-24

Abstract

This paper establishes comprehensible and practicable expressions using matrix for the equilibrium and geometry methods for structural rigidity analysis. A rigorous definition of structural rigidity is presented using the concept of differential for the geometric method. The dual relationship is proved between the equilibrium and geometry methods, which provides a theoretical base for the option of choosing an easier approach in different scenarios. Duality of equilibrium and geometric approaches is further investigated for the three-rigid-disc systems with fictitious hinges, which demonstrates the advantages of the two methods varying in different cases. In addition, Hennebergs method, which was originally developed to solve complex trusses, is introduced for rigidity analysis when the system is too complex for the triangular rule to be applied. Theoretical proof using notations of matrix is presented, and an example of truss is given to show the effectiveness of Hennebergs method for rigidity analysis. Two examples in practice, one of which is a special damper for structural vibration control and the other about displacement sensing for large-scale testing, are provided to show applications of rigidity analysis. Finally, suggestions are provided for teaching rigidity analysis with the duality of the equilibrium and geometry approaches in structural analysis course.

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