Abstract
Unique strain gage based methods are developed to identify magnitudes and locations of multiple loads and the resultant of a distributed load on a slender beam. Four uniaxial strain gages mounted to the bottom surface of the beam create a force transducer capable of identifying the magnitude and location of a load inside the weight area, where the load can be a concentrated or distributed load. 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. However, this creates an ill-posed problem for loads separated by only one strain gage location. A new 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 are experimentally validated on a prismatic beam with rest boundary conditions.
Similar content being viewed by others
References
1. Asnachinda, P., Pinkaew, T., and Laman, J.A., “Multiple Vehicle Axle Load Identification from Continuous Bridge Bending Moment Response,” Engineering Structures 30: 2800–2817 (2008).
Adams, R., and Doyle, J.F., “Multiple Force Identification for Complex Structures,” Experimental Mechanics 42: 25–36 (2002).
Yuan, X.R., Cheng, E.L., and Chan, T.H., “Identification of Moving Loads from the Response of Simply Supported Beam,” Proceedings of the International Conference on Structural Dynamics, Vibration, Noise and Control, Hong Kong; December 1995, pp. 924–929.
Hillary, B., and Ewins, D.J., “The Use of Strain Gauges in Force Determination and Frequency Response Function Measurements,” Proceedings of the 2nd International Modal Analysis Conference and Exhibit, Orlando, FL; February 1984, pp. 627–634.
Fred Moses, M., “Weigh-in-Motion System Using Instrumented Bridges,” Transportation Engineering Journal 105: 233–249 (1979).
Peters, R.J., “AXWAY—a system to obtain vehicle axle weights,” The 12th ARRB Conference, Hobart, Tasmania; August 1984, pp. 10–18.
Skelton, S.B., and Richardson, J.A., “A Transducer for Measuring Tensile Strains in Concrete Bridge Girders,” Experimental Mechanics 46: 325–332 (2006).
Bednarz III, E.T., Zhu, W.D., and Smith, S.A., “Identifying the Magnitude and Location of a Load on a Slender Beam Using a Strain Gage Based Force Transducer,” Strain, in press.
Law, S.S., Bu, J.Q., Zhu, X.Q., and Chan, S.L., “Moving Load Identification on a Simply Supported Orthotropic Plate,” International Journal of Mechanical Sciences 49: 1262–1275 (2007).
Moller, P.W., “Load Identification Through Structural Modification,” Journal of Applied Mechanics 66(1): 236–241 (1999).
Zhu, X.Q., and Law, S.S., “Practical Aspects in Moving Load Identification,” Journal of Sound and Vibration 258: 123–146 (2002).
Bu, J.Q., Law, S.S., and Zhu, X.Q., “Innovative Bridge Condition Assessment from Dynamic Response of a Passing Vehicle,” Journal of Engineering Mechanics 132: 1372–1379 (2006).
Rowley, C.W., O’Brien, E.J., Gonzalez, A., and Znidaric, A., “Experimental Testing of a Moving Force Identification Bridge Weigh-in-Motion Algorithm,” Experimental Mechanics 49: 743–746 (2009).
Jiu, J., Ma, C., Kung, I., and Lin, D., “Input Force Estimation of a Cantilever Plate by Using a System Identification Technique,” Computer Methods in Applied Mechanics and Engineering 190: 1309–1322 (2000).
Masroor, S.A., and Zachary, L.W., “Designing an All-Purpose Force Transducer,” Experimental Mechanics 31(1): 33–35 (1991).
Andrae, J., and Sawla, A., “Time Synchronized Measurement of Multi-Bridge Force Transducers,” Measurement 29: 105–111 (2001).
Blakeborough, A., Clement, D., Williams, M.S., and Woodward, N., “Novel Load Cell for Measuring Axial Force, Shear Force and Bending Moment in Large-Scale Structural Experiments,” Experimental Mechanics 42: 115–122 (2002).
Dorsey, J., “Homegrown Strain-Gage Transducers,” Experimental Mechanics 17: 255–260 (1977).
Frederiksen, P.S., and Petersen, T., “On Calibration of Adjustable Strain Transducers,” Experimental Mechanics 36: 218–223 (1996).
Vishay Measurements Group, Inc., Strain Gage Thermal Output and Gage Factor Variation with Temperature, Tech Note TN-504-1 (2010), pp. 35–47.
Craig, R.R., Jr., Mechanics of Materials, John Wiley & Sons Inc., New York (1996).
Nash, W.A., Schaum’s Outlines: Statics and Mechanics of Materials, McGraw-Hill, New York (1992).
The Technical Staff of Measurements Group, Inc., Strain Gage Based Transducers: Their Design and Construction (1988), pp. 1–79.
Vishay Measurements Group, Inc., “SC-300 Strain Measuring Systems Workshop,” 2003.
Vishay Measurements Group, Inc., Plane-Shear Measurement with Strain Gages, Tech Note TN-512-1 (2010), pp. 113–118.
Muvdi, B.B., and McNabb, J.W., Engineering Mechanics of Materials, Macmillan, New York (1980).
Vishay Measurements Group, Inc., Measurement of Force, Torque, and Other Mechanical Variables with Strain Gages, Technical Publication (2011), pp. 1–26.
Bednarz III, E.T., and Zhu, W.D., “Identifying Magnitudes and Locations of Loads on Slender Beams with Welded and Bolted Joints Using Strain Gage Based Force Transducers with Application to a Portable Army Bridge,” Journal of Bridge Engineering, in press.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bednarz, E.T., Zhu, W.D. & Smith, S.A. Identifying Magnitudes and Locations of Multiple Loads and the Resultant of a Distributed Load on a Slender Beam Using Strain Gage Based Methods. Exp Tech 40, 15–25 (2016). https://doi.org/10.1007/s40799-015-0003-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40799-015-0003-7