The state of plane stress shown occurs in a machine component made of a steel with σy = 30 ksi. Using the maximum- distortion-energy criterion, determine whether yield will occur when (a) τXV = 6 ksi, (b) τXV = 12 ksi, (c) τXV = 14 ksi. If yield does not occur, determine the corresponding factor of safety.
Fig. P7.164
(a)
Check the yield will occur for the given condition or not?.
Find the corresponding factor of safety for not occurring the yield.
Answer to Problem 164RP
The yielding will
Explanation of Solution
Given information:
The normal stress in x-axis is
The normal stress in y-axis is
The shearing stress in xy-plane is
The allowable yield strength of the steel is
Use maximum distortion-energy theory.
Calculation:
Consider the normal stress in z-axis is
The minimum principal stress is
Find the average normal stress
Substitute 24 ksi for
Find the radius of the Mohr circle (R) using the equation.
Substitute 24 ksi for
Find the maximum principal stress
Substitute 19 ksi for
Find the minimum principal stress
Substitute 19 ksi for
Check the yielding condition using the Maximum-distortion-energy criteria as follows;
Substitute 26.81 ksi for
The yielding will not occur.
Find the factor of safety (FOS) using the relation.
Substitute 30 ksi for
Therefore, the yielding will
(b)
Check the yield will occur for the given condition or not?.
Find the corresponding factor of safety for not occurring the yield.
Answer to Problem 164RP
The yielding will
Explanation of Solution
Given information:
The normal stress in x-axis is
The normal stress in y-axis is
The shearing stress in xy-plane is
The allowable yield strength of the steel is
Use maximum distortion-energy theory.
Calculation:
Consider the normal stress in z-axis is
The minimum principal stress is
Find the average normal stress
Substitute 24 ksi for
Find the radius of the Mohr circle (R) using the equation.
Substitute 24 ksi for
Find the maximum principal stress
Substitute 19 ksi for
Find the minimum principal stress
Substitute 19 ksi for
Check the yielding condition using the Maximum-distortion-energy criteria as follows;
Substitute 32 ksi for
The yielding will not occur.
Find the factor of safety (FOS) using the relation.
Substitute 30 ksi for
Therefore, the yielding will
(c)
Check the yield will occur for the given condition or not?.
Find the corresponding factor of safety for not occurring the yield.
Answer to Problem 164RP
The yielding will occur.
Explanation of Solution
Given information:
The normal stress in x-axis is
The normal stress in y-axis is
The shearing stress in xy-plane is
The allowable yield strength of the steel is
Use maximum distortion-energy theory.
Calculation:
Consider the normal stress in z-axis is
The minimum principal stress is
Find the average normal stress
Substitute 24 ksi for
Find the radius of the Mohr circle (R) using the equation.
Substitute 24 ksi for
Find the maximum principal stress
Substitute 19 ksi for
Find the minimum principal stress
Substitute 19 ksi for
Check the yielding condition using the Maximum-distortion-energy criteria as follows;
Substitute 33.866 ksi for
The yielding will occur.
Therefore, the yielding will occur.
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