A combined loading transducer for calculating the bending moment and torque in a slender circular beam using the minimum numbers of strain gauges, strain grids, and measurement channels

Abstract

The purpose of this work is to develop a new methodology that uses the minimum numbers of strain gauges, strain grids, and measurement channels to calculate the bending moment and torque in a slender circular beam under combined loading from measured strains in it. In general, each independent variable requires a minimum of one independent measurement. Two grids of a single-rosette strain gauge located at 45° and −45° from the longitudinal axis of the beam are used in conjunction with two measurement channels to gather all measurements and form a combined loading transducer. A theoretical set of equations of the new methodology is developed to minimize numbers of strain grids and measurement channels, and an experimental configuration was tested in a variety of scenarios. Calibration factors were independently developed for the bending moment and torque of the beam by separately loading it in their respective directions. These calibration factors were applied to different combined loading scenarios, where errors were found to be on average 1.6% for moment comparison and 6.7% for torque comparison.