Concept explainers
(a)
The fatigue factor of safety for the bolts using Goodman criteria.
(a)
Answer to Problem 52P
The fatigue factor of safety for the bolts using Goodman criteria is
Explanation of Solution
Write the expression of the length of the material squeeze between the bolt face and washer face.
Here, the length of the material squeeze between the bolt face and washer face is
Write the expression for the length of the bolt.
Here the length of bolt is
Write the expression of the threaded length for hexagonal bolt.
Here, the threaded length is
Write the expression of the length of the unthreaded portion in grip.
Here, the length of the unthreaded portion in the grip is
Write the expression of the length of the threaded portion in grip.
Here, the length of threaded portion in the grip is
Write the expression of the major area diameter.
Here, the nominal diameter of the bolt is
Write the expression of the stiffness for the bolt.
Here, the bolt stiffness is
Write the expression of stiffness for the steel cylinder.
Here, the stiffness of the steel cylinder is
Write the expression for the midpoint of the complete joint.
Here, the midpoint of the joint is
Write the expression of the thickness of the upper frustum.
Here, the thickness of upper frustum of the gasket is
Write the expression for the effective sealing diameter of the gasket sealing in upper frustum.
Here, the effective sealing diameter of upper frustum of the gasket sealing is
Write the expression for the stiffness of the upper frustum of cast iron vessel.
Here, the stiffness of the cast-iron pressure vessel in the upper frustum is
Write the expression for the stiffness of the lower frustum of the cast iron vessel.
Here, the stiffness of the cast-iron pressure vessel in the lower frustum is
Write the expression for the stiffness of the member or assembly.
Here, the stiffness of the member is
Write the expression of joint constant.
Here, the joint constant is
Write the expression of initial tension in the bolt.
Here, the tensile stress area is
Write the expression of the effective area of the cylinder.
Here, the effective area of the cylinder is
Write the expression for the total force acting on the assembly.
Here, the total load acting on the assembly is
Write the expression for the load acting on each bolt.
Here, the number of bolt is
Write the expression for the initial stress in the bolt.
Write the expression for the average stress.
Write the expression for the mean stress.
Write the expression for factor of safety by Goodman criteria.
Here, the ultimate strength is
Conclusion:
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Refer to Table
Refer to Table 8.9 “Metric Mechanical-Property Classes for Steel Bolts, Screws, and Studs” to obtain
Substitute
Thus, the fatigue factor of safety for the bolts using Goodman criteria is
(b)
The fatigue factor of safety for the bolts using Gerber criteria.
(b)
Answer to Problem 52P
The fatigue factor of safety for the bolts using Gerber criteria is
Explanation of Solution
Write the expression for the factor of safety using Gerber criteria.
Conclusion:
Substitute
Thus, the fatigue factor of safety for the bolts using Gerber criteria is
(c)
The fatigue factor of safety for the bolts using ASME-elliptic criteria.
(c)
Answer to Problem 52P
The fatigue factor of safety for the bolts using ASME-elliptic criteria is
Explanation of Solution
Write the expression for the factor of safety using ASME-elliptic criteria.
Conclusion:
Substitute
Thus, the fatigue factor of safety for the bolts using ASME-elliptic criteria is
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Chapter 8 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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