Concept explainers
The factor of safety for yielding from distortion-energy theory.
The factor of safety for yielding from maximum-shear-stress theory.
Answer to Problem 42P
The factor of safety for yielding from distortion-energy theory is
The factor of safety for yielding from maximum-shear-stress theory is
Explanation of Solution
The given assumption is that the belt tension on the loose side at
Write the relationship between tension 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.
Substitute
Calculate the tension on the loose side.
Here, the tension on the tight side of pulley
Write the magnitude of bearing reaction force at
Here, the tension on tight side of pulley
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
The calculations for shear force and bending moment diagram in
Calculate the shear force at
Here, the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the moment at
The moment at the supports of the simply supported beam is zero.
Calculate the moment at
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 shear force at
Here, the shear force at
Calculate the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the moment at
The moment at the supports of the simply supported beam is zero.
Calculate the moment at
Here, the moment at
Calculate the moment at
Here, the moment at
It is clear from the bending moment diagrams, that the critical location is 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
Calculate the maximum principal stress.
Here, the maximum principal stress is
Calculate the minimum principal stress.
Here, the minimum principal stress is
Calculate the maximum shear stress.
Here, maximum shear stress is
Calculate the factor of safety from maximum-shear-stress theory.
Here, the maximum yield stress for
Calculate the factor of safety from distortion-energy theory.
Here, the Von Mises stress is
Write the expression for von Mises stress.
Substitute
Conclusion:
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Thus, the shear force diagram and bending moment diagram for the shaft in
Figure (1)
Substitute
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Thus, the shear force diagram and bending moment diagram for the shaft in
Figure (2)
Substitute
Substitute
Convert diameter of shaft into
Substitute
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Refer to the Table A-20 “Deterministic ASTM Minimum Tensile and Yield Strengths for Some Hot-Rolled (HR) and Cold-Drawn (CD) Steels” and obtain
Substitute
Thus, the factor of safety for yielding from maximum-shear-stress theory is
Substitute
Thus, the factor of safety for yielding from distortion-energy theory is
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Chapter 5 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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