Formulation of a similarity law for static and low-velocity collision experiments for beam in gravitational field

Abstract

Scaled testing offers a financially viable and pragmatic methodology for ascertaining the performance attributes of full-scale civil engineering structures. While the necessity for a similarity law to guide scaled experiments is well-understood, few studies has been directed toward formulating a similarity law that comprehensively addresses both geometrical and mechanical equivalences in experiments where material properties and gravitational factors remain constant between the scaled and full-scale tests. Our prior work has introduced a similarity law tailored for scaled experiments conducted within gravitational fields, utilising materials that bear a resemblance to those used in full-scale structures; however, the scope of applicability was restricted to elastic responses. This study introduces a method for approximating the elasto-plastic displacement in full-scale beams based on data gathered from scaled tests, utilising an integrated approach that combines the principles of similarity and equal-energy laws as formulated by Veletsos et al. Validation of this innovative method was achieved through static three-point bending tests using circular cross-sectional steel beams, with tests conducted at six varying similarity ratios, ranging from 0.26 to 1.00. The empirical results demonstrated that the estimated displacement for the full-scale structure exhibited an error margin of approximately 10 %. When an impact analysis involving a steel ball was carried out on a steel cantilever beam, the residual displacement estimates were found to be significantly imprecise when plastic deformations occurred at multiple locations within the structure. In conclusion, this research contributes to foundational advancements in the field of structural modelling through the introduction of a new methodological approach.