Beam moment and shear force calculations using digital-camera experiments

Shen Haw Ju,Hsin Hsiang Hsu

doi:10.1177/1687814019860675

Abstract

This article presents an image-based method to find the beam moment and shear force using the measured beam displacements. A least-squares method is first developed to find the rotations and lateral displacements at beam ends using the measured displacements along the beam. Then, the moments and shear forces of this beam segment are obtained using the matrix formulation including shear deformation and large displacement effects. Two experimental schemes, image symbol dot and image-correlation methods, were used to validate the accuracy of the proposed scheme. The comparison of the results between the finite element analysis and the two methods shows acceptable accuracy. Although this method is mainly applied to the elastic region, one can still find the moment and shear force at the inelastic region using the equilibrium equation.

Highlights

In detailed inspections of structural safety, the moments and shear forces of bridge girders or building beams are often the important objects that should be measured
Results for static displacements, natural frequencies, mode shapes, and damping of the model bridge were presented in their experiments and finite element analyses, and a comparison of the results showed that good correlation was obtained
In the charge-coupled device (CCD) experiment, 23 displacements were used in the leastsquares method to find moments and shear forces

Summary

Introduction

In detailed inspections of structural safety, the moments and shear forces of bridge girders or building beams are often the important objects that should be measured. Yoneyama et al.[13] applied the digital image-correlation method into deflection measurement of real bridge during the bridge load testing, but beam shear force and moment were not determined in their paper. In the finite element and experimental methods, both rotations and displacements of beams are obtained first in order to find their moments and shear forces. This article evaluates beam moments and shear forces using the measured lateral displacements, which can be obtained using any experimental method, such as digital-imagecorrelation or direct measurement methods. This kind of pattern could be obtained by first painting white paint and over-spraying with a mist of black paint

Experimental procedures

Experimental results and comparisons

Conclusion