Concept explainers
Calculate the two values of
Answer to Problem 76P
The values of
Explanation of Solution
Given information:
The components of stress
The maximum shear stress
Calculation:
Consider
Modify Equation (1) as shown below.
Calculate the average normal stress
Substitute
Calculate the value u as shown below.
Substitute
Case 1:
For
Calculate the value of
Substitute
Calculate the average normal stress
Substitute
Calculate the principal stresses
Substitute
Calculate the maximum shearing stress as shown below.
Substitute
For
Calculate the value of
Substitute
Calculate the average normal stress
Substitute
Calculate the principal stresses
Substitute
Hence, the principal stresses
Calculate the maximum shearing stress as shown below.
Substitute
Hence, the value of
Case 2:
Assume the maximum principal stress
Calculate the minimum principal stress as shown below.
Substitute
The minimum principal stress
Substitute
Substitute
Calculate the value of
Substitute
Calculate the value of R as shown below.
Substitute
Calculate the principal stress
Substitute
Hence, the principal stresses
Therefore, the value of
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Chapter 7 Solutions
Mechanics of Materials, 7th Edition
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