Concept explainers
6–37* to
6–46* For the problem specified in the table, build upon the results of the original problem to determine the minimum factor of safety for fatigue based on infinite life, using the modified Goodman criterion. The shaft rotates at a constant speed, has a constant diameter, and is made from cold-drawn AISI 1018 steel.
Problem Number | Original Problem, Page Number |
6–37* | 3–68, 151 |
6–38* | 3–69, 151 |
6–39* | 3–70, 151 |
6–40* | 3–71, 151 |
6–41* | 3–72, 152 |
6–42* | 3–73, 152 |
6–43* | 3–74, 152 |
6–44* | 3–76, 153 |
6–45* | 3–77, 153 |
6–46* | 3–79, 153 |
Problem 3–70*
Dimensions in inches.
The minimum factor of safety for fatigue on infinite life, using the modified Goodman criterion.
Answer to Problem 39P
The minimum factor of safety for fatigue on infinite life is
Explanation of Solution
The Free body diagram of pulley
Figure-(1)
The free body diagram of pulley
Figure-(2)
The given assumption is that the belt tension on the loose side at
Write the relationship between tensions on the loose side with respect to tension on the tight side.
Here, the tension on the tight side is
Write the equation to balance the tension on the counter shaft.
Here, the tension on the tight side of pulley
Substitute
Calculate the tension on the loose side.
Write the magnitude of bearing reaction force at
Here, the magnitude of the bearing force at
Write the magnitude of bearing reaction force at
Write the magnitude of bearing reaction force at
Here, the magnitude of bearing force at
Write the magnitude of bearing force at
Here, the magnitude of bearing reaction force at
Calculate the bearing reaction force at
Here, the bearing reaction force at
Calculate the bearing reaction force at
Here, the bearing reaction force at
Calculate the shear force at in
Here, the shear force at
Calculate the moment at
Here, the moment at
Calculate the moment at in
Here, the moment at
The calculations for shear force and bending moment diagram in
Calculate the shear force at
Here, the shear force at
Calculate the moment at
Here, the moment at
Calculate the moment at
Here, the moment at
Write the net moment at
Here, the net moment at
Write the net moment at
Here, the net moment at
Write the torque transmitted by shaft from
Here, the torque transmitted by shaft from
Calculate the bending stress.
Here, the bending stress is
Calculate the shear stress.
Here, the shear stress is
Write the expression for von Mises stress for alternating
Here, alternating stress due to completely reversed is
Write the expression for von Mises stress for mid-range.
Here, mean stress due to completely reversed is
Write the expression for von Mises for maximum stress.
Write the expression for yielding by using distortion energy theory.
Here the
Write the expression for endurance limit of rotary test specimen.
Write the expression for surface condition modification factor.
Write the expression for size modification factor.
Write the expression for modified endurance limit.
Write the expression to find out factor of safety by using modified Goodman.
Here modified endurance limit is
Conclusion:
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Since
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Thus the minimum factor of safety by using modified Goodman criterion is
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Chapter 6 Solutions
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