A capped cast-iron pipe is compressed by a brass rod, as shown. The mil is turned until it is just snug, then add an additional quarter turn to pre-compress the cast-iron pipe. The pitch of the threads of the bolt ap = 52 mils (a mil is one-thousandth of an inch). Use the numerical properties provided.
(a) What stresses a and arwill be produced in the cast-iron pipe and brass rod. respectively, by the additional quarter turn of the nut?
(b) Find the bearing stress ahbeneath the washer and the shear stress t(in the steel cap.
(a)
The stress produced in pipe and bar.
Answer to Problem 2.5.25P
The stress produced in pipe is=
The stress produced in bar is =
Explanation of Solution
Given information:
The pitch of the bolt is
Write the expression for area of rod.
Here, area of rod is
Write the expression for area of pipe.
Here, area of pipe is
Write the expression for displacement between cut ends.
Here, displacement between cut ends of the rod is
Write the expression for relative displacement between cut ends.
Here, relative displacement between cut ends is
Write the compatibility Equation for displacement.
Write the expression for force on rod.
Here, force on rod is
Write the expression for force on pipe.
Here, force on pipe is
Write the expression for stress on cast iron pipe.
Here, stress on cast iron pipe is
Write the expression for stress in rod.
Here, stress on rod is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The stress produced in pipe is =
The stress produced in bar is =
(b)
The bearing stress in cap.
The shearing stress in the cap.
Answer to Problem 2.5.25P
The bearing stress in cap is =
The shearing stress in the cap is =
Explanation of Solution
Given information:
The pitch of the bolt is
Write the expression for area of cap.
Here, area of cap is
Write the expression for bearing stress on cap.
Here, bearing stress on cap is
Write the expression for shearing stress on the cap.
Here, shearing stress on the cap is
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The bearing stress in cap is =
The shearing stress in the cap is =
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Chapter 2 Solutions
Mechanics of Materials (MindTap Course List)
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