Identification of magnitudes and locations of loads on slender beams using strain gage based methods with application to portable army bridges

Unique strain gage based methods were developed to identify magnitudes and locations of loads on a non-continuous, non-homogenous, slender beam with variable cross sections, welded and bolted joints, and pinned, firm rest, soft rest, pinned-fixed, and fixed boundary conditions. Four uniaxial strain gages mounted to the bottom surface of the beam created a force transducer capable of identifying the magnitude and location of a load inside the weight area. By combining individually scaled strain gage outputs, the bending moment diagram was constructed. For the case of multiple loads separated by two or more strain gage locations, uniaxial strain gages forming multiple force transducers can still identify the magnitudes and locations of all the loads. A calibration method was developed to account for the discrepancies between the theoretical and actual scaling factors arising from stress concentrations and unpredictable stress patterns in the beams due to the presence of the joints. The strain gage based force transducer methodology was experimentally validated on prismatic beams with firm rest, soft rest, firm rest-fixed, and fixed boundary conditions; an aluminum beam with a bolted joint; and a half aluminum and half steel beam with two different cross sections and a bolted joint. It was also experimentally validated on a continuous aluminum beam with a linearly varying cross section and rest boundary conditions, a tapered aluminum beam with a series of welded joints, and a full scale portable army bridge at the US Army Aberdeen Test Center. The force transducer methodology is independent of the boundary conditions of the beam and the error from strain gage drift due to uniform thermal expansion on a prismatic beam can cancel out.;When there are multiple loads separated by only one strain gage location, the problem is ill posed for the force transducer methodology. Another method has been developed using two shear gages mounted on the neutral axis of the beam, one on each side of a load, to identify the magnitude of the load in this case. A combination of two uniaxial strain gages and two shear gages, with one uniaxial strain gage and one shear gage at the same location on each side of a load, can be used to identify the location of the load. The strain gage based methods were experimentally validated on a prismatic beam with rest boundary conditions.