hw1sol - Materials Science and Engineering 765 mechanical...

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P.M. Anderson: Tel.: (614) 292-0176 FAX: (614) 292-1537 E-mail: anderson.1@osu.edu Materials Science and Engineering 765 mechanical behavior of materials Spring 2005 Homework 1- SOLUTIONS Due: At the start of class on Tuesday, April 12, 2005. Please show all work necessary to arrive at your answers. 1. Consider a differential element of dimensions dr, d θ , dz that is centered on the coordinate (r, θ , z) in a cylindrical coordinate system. (a) draw the differential element and label it with all components of stress which contribute a force in the θ -direction to the element. (b) derive the statement of equilibrium of the element in the θ -direction.
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2 Anderson G4:Users:peterand:Central files:Courses:MSE 765:2005:hw1sol.doc (c) Why is it necessary to assume that the differential element dimensions are small? The dimensions of the elements are small so that only the first two terms of a Taylor's series are necessary to represent the (+) and (-) values of stress, and so that sin θ ~ θ and cos θ ~ 1. 2.
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This note was uploaded on 07/17/2008 for the course MSE 765 taught by Professor Anderson during the Spring '05 term at Ohio State.

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hw1sol - Materials Science and Engineering 765 mechanical...

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