11.29 (B/C). A state of two-dimensional plane stress on an element of material can be represented by theprincipal stresses o, and o2 (o, > 02). 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 expression(o}+o-2vo, o)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, tyy respectively and the principal stresses, where x and yaretwo 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.]

Write the expression for principle stress as follows.

11.29 (B/C). A state of two-dimensional plane stress on an element of material can be represented by the principal stresses o, and o2 (o, >). The strain energy can be expressed in terms of the strain energy per unit volume. Then: (a) working from first principles show that the strain energy per unit volume is given by the expression 1 2E

11.29 (B/C). A state of two-dimensional plane stress on an element of material can be represented by the principal stresses o, and o2 (o, >). The strain energy can be expressed in terms of the strain energy per unit volume. Then: (a) working from first principles show that the strain energy per unit volume is given by the expression 1 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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