Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Textbook Question
Chapter 10.3, Problem 13P
Determine the equivalent state of strain which represents (a) the principal strains, and (b) the maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original element.
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1. Find the relationships between strain components in the polar coordinate and
strain components in the rectangular coordinate.
The state of strain in a plane element is ex =-200 x 10-6, Ey = 0, and yxy = 75 × 10-6 , as
shown below. Determine the equivalent state of strain which represents
(a) the principal strains
(b) the maximum in-plane shear strain and the associated average normal strain. Specify
the orientation of the corresponding elements for these states of strain with respect to the
original element.
y
Yxy
2
dy
Yxy
FExdx
dx
The state of strain in a plane element is €x = -200 x 10-6 , Ey = 100 × 10-6 , and
Yxy = 75 x 10-6 , as shown below. Determine the equivalent state of strain
which represents
(a) the principal strains
(b) the maximum in-plane shear strain and the associated average normal
strain. Specify the orientation of the corresponding elements for these states
of strain with respect to the original element.
y
Eydy
Yxy
2
dy
Yxy
FExdx
2
dx
Chapter 10 Solutions
Mechanics of Materials
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