Identifying the Magnitude and Location of a Load on a Slender Beam Using a Strain Gage Based Force Transducer

2012 ◽  
Author(s):  
Edward T. Bednarz ◽  
W. D. Zhu ◽  
Scott A. Smith
Keyword(s):  
Boundary Conditions ◽  
Strain Gage ◽  
Cross Sections ◽  
Bending Moment ◽  
Force Transducer ◽  
Bottom Surface ◽  
Homogeneous Material ◽  
Variable Cross ◽  
Fixed Boundary ◽  
Unique Strain

A unique strain gage based method is developed to identify the magnitude and location of a load on a slender beam with non-homogeneous material, variable cross sections, and pinned, firm rest, soft rest, pinned-fixed, and fixed boundary conditions. Four uniaxial strain gages are mounted to the bottom surface of the beam, and the bending moment diagram of the beam can be constructed using measured strains on the beam. By combining individually scaled strain gage outputs, the magnitude and location of the load can be accurately identified. The strain gage based force transducer methodology is experimentally validated on prismatic beams with firm rest, soft rest, firm rest-fixed, and fixed boundary conditions, and a continuously tapered beam with rest boundary conditions. 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.

Identifying Magnitudes and Locations of Multiple Loads on a Slender Beam Using Strain Gage Based Methods

2012 ◽  
Author(s):  
Edward T. Bednarz ◽  
W. D. Zhu ◽  
Scott A. Smith
Keyword(s):  
Strain Gage ◽  
Force Transducer ◽  
Uniaxial Strain ◽  
Bottom Surface ◽  
Strain Gages ◽  
Multiple Loads ◽  
Force Transducers ◽  
Prismatic Beam ◽  
Ill Posed ◽  
Unique Strain

Unique strain gage based methods are developed to identify magnitudes and locations of multiple loads 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. 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.

Identifying Magnitudes and Locations of Loads on Slender Beams With Welded and Bolted Joints Using a Strain Gage Based Force Transducer With Application to a Portable Army Bridge

2013 ◽  
Author(s):  
E. T. Bednarz ◽  
W. D. Zhu
Keyword(s):  
Strain Gage ◽  
Calibration Method ◽  
Force Transducer ◽  
Bolted Joints ◽  
Bottom Surface ◽  
Strain Gages ◽  
Bolted Joint ◽  
Stress Concentrations ◽  
Slender Beams ◽  
Aluminum Beam

A strain gage based force transducer has been developed to identify magnitudes and locations of loads on non-continuous slender beams with welded and bolted joints. The slopes of the bending moment curves on the two sides of a load are calculated from measured strains on a beam. Four uniaxial strain gages are mounted to the bottom surface of the beam, with two strain gages on each side of the load. A calibration method developed earlier can be used 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 force transducer methodology is experimentally validated on a continuously tapered aluminum beam with a series of welded joints, an aluminum beam with a constant cross section and a bolted joint, a half aluminum and half steel beam with two different cross sections and a bolted joint, and a full scale portable army bridge at the US Army Aberdeen Test Center.

scholarly journals Influence of Boundary Conditions on Cracking of Sanxingdui Moon Bay City Wall

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jin Qu ◽  
Jianlin Ma ◽  
Bai Yang
Keyword(s):  
Stress Distribution ◽  
Free Boundary ◽  
Tensile Stress ◽  
Boundary Conditions ◽  
Crack Spacing ◽  
Water Evaporation ◽  
Bottom Surface ◽  
City Wall ◽  
Fixed Boundary ◽  
Boundary Length

The Sanxingdui Moon Bay City Wall, in China, is built of pale-yellow sand and yellow-brown clay, and the yellow-brown layers are suffering severely. In order to discuss the desiccation cracks in a section of this wall, this paper conducts evaporation tests in laboratory and observes the variations in the characteristics of the boundary conditions of the bottom surface of the sample. The results show that the boundary conditions of the bottom surface of the sample consist of two free boundaries, two sliding boundaries, and one fixed boundary from the outside to the inside. During the drying process, the free boundary extends, but the fixed boundary shrinks; the sliding boundary also remains basically stable. We obtain the surface tensile stress distribution under different boundary conditions through stress analysis and deduce that the tensile stress distribution has a trapezoidal pattern. Moreover, we calculate the lower limit on the crack spacing of the sample using the energy method, and the double of the sum of the maximum sliding boundary length and the free boundary length is the upper limit to the crack spacing. Maintaining the stability of the soil moisture content of the site is the main factor in the protection of the earthen archaeological site under the humid conditions of the museum above the site. In order to reduce the water evaporation rate of the soil, the surface of the site should be coated by a protectant, the main determining features of which are permeability, tensile strength, and compatibility with the earthen site.

scholarly journals Analytical Modeling of the Mechanical Behavior of MEMS/NEMS-Multilayered Resonators with Variable Cross-Sections for Sensors and Energy Harvesters

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Eustaquio Martinez-Cisneros ◽  
Luis A. Velosa-Moncada ◽  
Ernesto A. Elvira-Hernandez ◽  
Omar I. Nava-Galindo ◽  
Luz Antonio Aguilera-Cortes ◽  
...  
Keyword(s):  
Mechanical Behavior ◽  
Cross Sections ◽  
Analytical Modeling ◽  
Variable Cross ◽  
Energy Harvesters

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

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