Determining Effective Centroid Position in Biomechanical Testing: A Technique for Simplifying Whole Bone Analysis

[+] Author and Article Information
Gabrielle Whan

School of Engineering, University of Guelph, Guelph, ON, Canada N1G 2W1

R. John Runciman1

School of Engineering, University of Guelph, Guelph, ON, Canada N1G 2W1jruncima@uoguelph.ca

Mark Hurtig

Ontario Veterinary College, University of Guelph, Guelph, ON, Canada N1G 2W1


To whom correspondence should be addressed.

J Biomech Eng 127(5), 736-741 (May 04, 2005) (6 pages) doi:10.1115/1.1993663 History: Received September 17, 2004; Revised May 04, 2005

Background: Whole bone in vitro biomechanical compressive testing can be complicated by three factors: sample asymmetry, heterogeneous material properties, and unknown effective centroid location. Method of approach: The technique presented here facilitates the calculation of effective centroid position, modulus of elasticity and equivalent uniform strain magnitude for a cross section of bone from a simple whole bone compressive test. Simplification of section response to load is achieved through a combination of linear beam and simple planer geometry theory. The technique requires three longitudinal strain gauges be affixed around the test specimen cross section of interest, gauge position need not be determined. Sample loading is then accomplished using a simple four point loading jig. Results: Results of the technique are presented on an object with known elasticity and geometry, an aluminium tube, and seven pairs of equine third metacarpal whole bones. Conclusions: Average cross section modulus of elasticity, equivalent uniform cross section strain, and effective centroid locations were all predicted to within the range of published values. Employing the testing setup and analysis technique presented in this paper resulted in a significant savings in both implementation complexity and cost over previously available techniques.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

(a) Top: A symmetrical two-dimensional homogenous vertical column with two strain measurement sites, 1 and 2, and three independently applied loads, FA, FB, and FC. All three loads generate uniform compressive strain at the cross section passing through the two measurement sites, but, FA and FB also generate strains due to bending. (b) Middle: Corresponding cross section strains. FA and FB produce opposite strain reactions. Measuring strain at sites 1 and 2 allows strain response of the column to be constructed, lines ϵA and ϵB, respectively. The intersection of lines ϵA and ϵB is coincident with the location of the neutral surface. Equivalent uniform strain, ϵC, would occur in the section if the column were loaded in pure compression by load, FC, located over the neutral surface. (c) Bottom: Rearranging the strain values from Fig. 1, and plotting them with respect to load position produces strain lines ϵ1 and ϵ2. The intersection of these lines is also coincident with the neutral surface and facilitates calculation of equivalent uniform strain, ϵC and neutral surface location with respect to load positions.

Grahic Jump Location
Figure 2

Whole bone biomechanical testing setup. Only mid level gauges were used for this study.



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