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
Related questions
Question
![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 o, (o, > 2). 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
(o}+o}-2va, o2)
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,o, + 2(1+ v)r,]
2E
is identical with the expression given above.
[City U.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91cfa0cc-c22b-4fc1-83d1-038ad89f8e0e%2F7e462f1e-59b8-4cad-8467-c313170d9776%2Fuqtqajo_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 o, (o, > 2). 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
(o}+o}-2va, o2)
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,o, + 2(1+ v)r,]
2E
is identical with the expression given above.
[City U.]
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