The regular prismatic bar under torsion: A new approach based on caustics

Theocaris, PS

dc.contributor.author	Theocaris, PS	en
dc.date.accessioned	2014-03-01T11:44:23Z
dc.date.available	2014-03-01T11:44:23Z
dc.date.issued	1989	en
dc.identifier.issn	0001-5970	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/36917
dc.subject.classification	Mechanics	en
dc.subject.other	Elasticity--Mathematical Models	en
dc.subject.other	Structural Design--Stresses	en
dc.subject.other	Longitudinal Warping	en
dc.subject.other	Triangular Bars	en
dc.subject.other	Twisted Bars	en
dc.subject.other	Bars	en
dc.title	The regular prismatic bar under torsion: A new approach based on caustics	en
heal.type	other	en
heal.identifier.primary	10.1007/BF01178178	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF01178178	en
heal.language	English	en
heal.publicationDate	1989	en
heal.abstract	A new approach to the general torsion problem of the regular prismatic bar was introduced, based on extensive and meticulous experimental evidence, indicating that the twisted prismatic bars, except the cylindrical ones, present, a longitudinal warping, following a sinusoidal type of curves for the warping displacements with their extrema displaced towards the corners. As a guide for the establishment of the method the solutions of the elliptical and the equiangular triangular bars were used. It was found that the regions inside the inscribed circles tangent to the sides of their undeformed cross-sections constituted regions whose warped surfaces constitute undulated forms following sinusoidal surfaces. This property was proved exact for the exact solutions for the elliptic and triangular cross-sections and it is assumed by induction valid for any regular cross-section. Comparing the warping displacements along the inscribed circle to a square or regular polygon cross section with the classical Timoshenko solution for the square bar it was found an exact coincidence in these displacements. It was further shown that these circles and all concentric full circles constitute the initial curves of the caustics formed from reflections of the warped cross-sections of the twisted bars. The differences between the stresses and displacements between the existing approximate solutions and the new approach appear in the partly curved triangles lying outside the inscribed circles. For the square cross-section it was shown that the w-displacements between Timoshenko's solution and the present one were less than 5 percent. Experimental evidence with the Moiré method and comparison with the exact solution for the equiangular triangular cross section proved that the present approach is closer to reality and therefore presents higher accuracy than any approximate method. Furthermore, it presents the advantage that the full circles inscribed inside the cross-section constitute the initial curves forming caustics in space when a parallel light beam is reflected on the warped cross-section of the twisted bars. interesting properties of caustics, proved in this paper, help down-rightly for a thorough study of the form and properties of the twisted bars. © 1989 Springer-Verlag.	en
heal.publisher	Springer-Verlag	en
heal.journalName	Acta Mechanica	en
dc.identifier.doi	10.1007/BF01178178	en
dc.identifier.isi	ISI:A1989CE51500001	en
dc.identifier.volume	80	en
dc.identifier.issue	1-2	en
dc.identifier.spage	1	en
dc.identifier.epage	38	en