11.29 (B/C). A state of two-dimensional plane stress on an element of material can be represented by theprincipal stresses o, and o, (o, > 2). The strain energy can be expressed in terms of the strain energy per unitvolume. Then:(a) working from first principles show that the strain energy per unit volume is given by the expression1(o}+o}-2va, o2)2Efor a material which follows Hooke's law where E denotes Young's modulus and v denotes Poisson's ratio,and(b) by considering the relations between each of o,,o,Ty respectively and the principal stresses, where x and y aretwo other mutually perpendicular axes in the same plane, show that the expression1[o+o-2vo,o, + 2(1+ v)r,]2Eis identical with the expression given above.[City U.]

Answered: Image /qna-images/answer/7e462f1e-59b8-4cad-8467-c313170d9776.jpg

rincipal stresses o, and o, (o, > 02). The strain energy can be expressed in terms of the strain energy per unit rolume. Then: (a) working from first principles show that the strain energy per unit volume is given by the expression 1 (o}+o}-2va, 2E for a material which follows Hooke's law where E denotes Young's modulus and v denotes Poisson's ratio, and (b) by considering the relations between each of o,, o, Ty respectively and the principal stresses, where x and y are two other mutually perpendicular axes in the same plane, show that the expression 1 [o+o;-2vo,0, + 2(1+ v)r,] 2E

rincipal stresses o, and o, (o, > 02). The strain energy can be expressed in terms of the strain energy per unit rolume. Then: (a) working from first principles show that the strain energy per unit volume is given by the expression 1 (o}+o}-2va, 2E for a material which follows Hooke's law where E denotes Young's modulus and v denotes Poisson's ratio, and (b) by considering the relations between each of o,, o, Ty respectively and the principal stresses, where x and y are two other mutually perpendicular axes in the same plane, show that the expression 1 [o+o;-2vo,0, + 2(1+ v)r,] 2E

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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