Concept explainers
(a)
The normal stress
(a)
Answer to Problem 97P
The normal stress
Explanation of Solution
Given information:
The state of plane stress components are
The uniaxial tension for the aluminum alloy is
The uniaxial compression for the aluminum alloy is
Calculation:
Calculate the average normal stress
Substitute
Calculate the value of
Substitute
Calculate principal stresses
Substitute
Hence, stress point lies in the first quadrant.
Sketch the Mohr’s criterion for the machine component as shown in Figure 1.
Refer to Figure 1.
The principal stresses for (a) in the first quadrant of boundary.
Calculate the value of
Substitute
Therefore, the normal stress
(b)
The normal stress
(b)
Answer to Problem 97P
The normal stress
Explanation of Solution
Given information:
The state of plane stress components are
The uniaxial tension for the aluminum alloy is
The uniaxial compression for the aluminum alloy is
Calculation:
Calculate the average normal stress
Substitute
Calculate the value of
Substitute
Calculate principal stresses
Substitute
Hence, stress point lies in the forth quadrant.
Refer to Figure 1.
The principal stresses for (b) in the forth quadrant of boundary.
Calculate the value of
Substitute
Therefore, the normal stress
(c)
The normal stress
(c)
Answer to Problem 97P
The normal stress
Explanation of Solution
Given information:
The state of plane stress components are
The uniaxial tension for the aluminum alloy is
The uniaxial compression for the aluminum alloy is
Calculation:
Calculate the average normal stress
Substitute
Calculate the value of
Substitute
Calculate principal stresses
Substitute
Hence, stress point lies in the forth quadrant.
Refer to Figure 1.
The principal stresses for (b) in the forth quadrant of boundary.
Calculate the value of
Substitute
Therefore, the normal stress
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Chapter 7 Solutions
Mechanics of Materials, 7th Edition
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