Concept explainers
7.13 through 7.16 For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) 25° clockwise, (b) 10° counterclockwise.
Fig. P7.14
(a)
The normal and shearing stresses after the element has been rotated through
Answer to Problem 14P
The normal stresses are
The shear stress is
Explanation of Solution
Given information:
The stress component along x direction as
The stress component along y direction as
The shear stress component as
The orientation of the principal plane as
Calculation:
Calculate the normal stress along x direction
Substitute
Hence, the normal stress as
Calculate the normal stress along y direction
Substitute
Hence, the normal stress as
Calculate the shear stress
Substitute
Therefore, the shear stress as
(b)
The normal and shearing stresses after the element has been rotated through
Answer to Problem 14P
The normal stresses are
The shear stress is
Explanation of Solution
Given information:
The stress component along x direction as
The stress component along y direction as
The shear stress component as
The orientation of the principal plane as
Calculation:
Calculate the normal stress along x direction
Substitute
Hence, the normal stress
Calculate the normal stress along y direction
Substitute
Hence, the normal stress as
Calculate the shear stress
Substitute
Therefore, the shear stress as
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Chapter 7 Solutions
Mechanics of Materials, 7th Edition