Differentiating between elastically bent rectangular beams and plates

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Abstract
We report x-ray microdiffraction curvature measurements of a (100)-type Si single crystal loaded in four-point bending and provide experimental verification of a procedure for differentiating between anisotropic, elastically bent beams and plates. In general usage, beam and plate components are distinguished by dimensions alone. In mechanics, however, beams and plates are differentiated based on their flexural rigidity and stress state. Since current textbooks do not provide a quantitative technique for selecting the proper constitutive equations for these two types of structures, we suggest the extension of an analysis for isotropic materials originated by Searle [G. F. C. Searle, Experimental Elasticity (Cambridge University Press, Cambridge, 1908), pp. 40–58] and expanded on by Ashwell [D. G. Ashwell, J. R. Aeronaut. Soc. 54, 708 (1950)]. We demonstrate that, by varying the degree of bending of an anisotropic strip, a single specimen can behave as both a beam and a plate, as is predicted by this analysis.

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