The yielding factor of safety.
The load factor.
The joint separation factor.
Answer to Problem 40P
The yielding factor of safety is
The load factor is
The joint separation factor is
Explanation of Solution
Write the expression tensile load per bolt.
Here, tensile load per bolt is
Write the expression for cross section area of sealing.
Here, area is
Write the expression for grip.
Here, total thickness of plate and washer is
Write the expression for length of bolt.
Write the expression for threaded length.
Here threaded length is
Write the expression for area of unthreaded portion.
Here, the area of unthreaded portion is
Write the expression for length of unthreaded portion in grip.
Here, the length of unthreaded portion in grip is
Write the expression for length of threaded portion in grip
Here, length of threaded portion in grip is
Write the expression for bolt stiffness.
Here, bolt stiffness is
Write the expression for stiffness of top frusta.
Here, the stiffness of top frusta is
Write the expression for total spring rate of the member.
Here, the total spring rate of the member is
Write the expression for joint stiffness constant.
Here, joint stiffness constant is
Write the expression for preload.
Here, preload is
Write the expression for load factor
Here, load factor is
Write the expression for yielding factor of safety.
Here, yielding factor of safety is
Write the expression for load factor guarding against joint separation.
Here, load factor guarding against joint is
Write the expression for total external load.
Here, the total load is
Write the expression for load on the bolt.
Here, the load on the bolt is
Write the expression for cross section area of the cylinder.
Here, area of cylinder is
Conclusion:
Substitute
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Substitute
Substitute
Refer to table 8-1 “Diameter and areas of unified screw threads UNC and UNF”, obtain tensile stress area for nominal diameter of
Refer to table 8-9 “SAE specification for steel”, to obtain the minimum proof strength as
Substitute
Figure (1) shows the frustum of the cone for compressive load on the joint.
Figure-(1)
Write the expression for thickness of frusta.
Write the expression for diameter of the top frusta.
Substitute
Write the expression for thickness of middle frusta.
Write the expression for diameter of the middle frusta.
Substitute
Write the expression for thickness of lower frusta.
Write the expression for diameter of the lower frusta.
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus the load factor is
Substitute
Thus the yielding factor of safety is
Substitute
Thus the load factor against joint separation is
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Chapter 8 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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