Concept explainers
For the state of stress shown, determine two values of σy for which the maximum shearing stress is 10 ksi.
Fig. P7.77
The two values of
Answer to Problem 77P
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
Hence, the principal stresses are
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 are
Calculate the maximum shearing stress as shown below.
Substitute
Hence, the value of
Case 2:
Assume the minimum principal stress
Calculate the maximum principal stress as shown below.
Substitute
The maximum principal stress
Substitute
Substitute
Calculate the value of
Substitute
Calculate the value of R as shown below.
Substitute
Calculate the average normal stress
Substitute
Calculate the principal stress
Substitute
Hence, the principal stresses
Therefore, the value of
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Chapter 7 Solutions
Mechanics Of Materials - Si Version
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