The warping functions of regular prismatic bars under torsion evaluated by caustics

Theocaris, PS

dc.contributor.author	Theocaris, PS	en
dc.date.accessioned	2014-03-01T01:07:43Z
dc.date.available	2014-03-01T01:07:43Z
dc.date.issued	1989	en
dc.identifier.issn	0014-4851	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10129
dc.subject	Approximate Solution	en
dc.subject	Closed Form Solution	en
dc.subject	Cross Section	en
dc.subject	Exact Solution	en
dc.subject	General Solution	en
dc.subject	Shear Stress	en
dc.subject.classification	Materials Science, Multidisciplinary	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Materials Science, Characterization & Testing	en
dc.subject.other	Light--Reflection	en
dc.subject.other	Materials Testing--Torsion Tests	en
dc.subject.other	Photoelasticity	en
dc.subject.other	Strain	en
dc.subject.other	Stresses--Torsional	en
dc.subject.other	Caustics	en
dc.subject.other	Elasticity	en
dc.subject.other	Regular Prismatic Bars	en
dc.subject.other	Warping Functions	en
dc.subject.other	Bars	en
dc.title	The warping functions of regular prismatic bars under torsion evaluated by caustics	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF02321409	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF02321409	en
heal.language	English	en
heal.publicationDate	1989	en
heal.abstract	Reflection of a bundle of coherent light on the warped cross section of a prismatic bar submitted to torsion forms a caustic on a receiver plane. From the mathematical expression of this curve and the theory of reflected caustics, it is possible to evaluate accurately the warping function of the cross section. Using this idea, it was possible to study the torsion problem in prismatic bars with sections which were equilateral triangles and squares. It was observed that the shape of the caustic is an hypocycloid curve with three or four cusps respectively. By evaluating the warping function by using elements from the respective caustics it was possible to find out that, for the triangular cross section, the expression for the warping function coincided exactly with the expression given by the exact solution of the problem. For the square cross section, a closed-form solution for its warping function was readily derived, to which the series approximation solution differed only by a few percent at maximum for the shear stresses. Since the method can be readily extended to any canonical polygonic cross section, it constitutes a general solution for the torsion of prismatic bars, which approximates their exact deformations better than the solutions based on the Saint-Vénant assumptions. © 1989 Society for Experimental Mechanics, Inc.	en
heal.publisher	Kluwer Academic Publishers	en
heal.journalName	Experimental Mechanics	en
dc.identifier.doi	10.1007/BF02321409	en
dc.identifier.isi	ISI:A1989AZ36600009	en
dc.identifier.volume	29	en
dc.identifier.issue	3	en
dc.identifier.spage	285	en
dc.identifier.epage	290	en