Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 10.3, Problem 10.8P
Use the strain transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. In each case specify the orientation of the element and show how the strains deform the element within the x–y plane.
Prob. 10−8
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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
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dy
Yxy
FExdx
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dx
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 at the point on the gear tooth has
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650(106). Use the strain-transformation equations to
determine (a) the in-plane principal strains and (b) the
maximum in-plane shear strain and average normal strain.
In each case specify the orientation of the element and
show how the strains deform the element within the
x-y plane.
Chapter 10 Solutions
Mechanics of Materials (10th Edition)
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