Concept explainers
The block shown is made of a magnesium alloy for which E = 45 GPa and ν = 0.35, Knowing that ϭx = -180 MPa, determine (a) the magnitude of ϭy for which the change in the height of the block will be zero, (b) the corresponding change in the area of the face ABCD, (c) the corresponding change in the volume of the block.
Fig. P2.70
(a)
Find the magnitude of
Answer to Problem 70P
The magnitude of
Explanation of Solution
Given information:
The poison’ ratio
The young’s modulus (E) is
The normal stress,
Calculation:
Consider that the change in height of the block is zero.
Find the normal stress
Substitute 0.35 for
Thus, the magnitude of
(b)
Find the corresponding change in the area of the face ABCD.
Answer to Problem 70P
The corresponding change in the area of the face ABCD is
Explanation of Solution
Calculation:
Consider the stress strain relationship for homogeneous, isotropic material.
Find the strain along z direction as follows:
Strain in z direction.
Here,
Substitute 0.35 for
Find the strain along x direction as follows:
Substitute 0.35 for
Write the expression of area
Write the expression of A as shown follows:
Determine the change in area face ABCD as follows:
Substitute
Substitute
Thus, the corresponding change in the area of the face ABCD is
(c)
Find the corresponding change in the volume of block.
Answer to Problem 70P
The corresponding change in the volume of block is
Explanation of Solution
Calculation:
Write the expression of area
Write the expression of V as shown follows:
Determine the change volume block as follows:
Substitute
Substitute
Thus, the corresponding change in the volume of block is
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Chapter 2 Solutions
Mechanics of Materials, 7th Edition
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