A Diagnostic Method Based on Deflection Analysis for Monitoring Post-elastic Response of Beams

Abstract

A non-destructive diagnostic method based on deflection analysis for monitoring the post-elastic response of beams was developed, and a diagnostic indicator was proposed. The indicator was defined as the second moment of the normalised curvature function about the mid-span, where the curvature was computed from the normalised deflection function. Elastic reference values of the indicator were computed for simply supported beams under uniformly distributed load, three-point, and four-point bending. Development of the indicator under progressive loading was examined with the help of finite element analyses. The indicator value monotonically decreased with increasing deformation provided that maximum bending moment was located between 0.41L and 0.59L, where L is the span of the beam. In this interval, the value of the indicator was unique and enabled the direct monitoring of the post-elastic stress level in the cross-section. The method was validated with the help of available experiments on simply supported beams. For beams working in the elastic range, a mean error of $${2.1}{\%}$$ 2.1 % was obtained between the measured and theoretical indicator values. For quasi-brittle material in the post-elastic stage, the decreasing value of the indicator signified the development of damage in accordance with experimental results.