Pipe 2 has been inserted snugly into Pipe I. but the holes Tor a connecting pin do not line up; there is a gap s. The user decides to apply either force P:lo Pipe I or force P-, to Pipe 2, whichever is smaller. Determine the following using the numerical properties in the box.
(a) If only P{is applied, find Pt{tips} required to close gap s; if a pin is then inserted and Ptremoved, what are reaction forces RAand RBfor this load case?
(b) If only P2is applied, find P2{kips) required to close gap a; if a pin is inserted and P2removed, what are reaction forces R^ and RBfor this load case?
(c) What is the maximum shear stress in the pipes, for the loads in parts (a) and (b)?
(d) If a temperature increase IT is to be applied to the entire structure to close gaps{instead of applying forces Ptand P2), find the AT required to close the gap. If a pin is inserted after the gaphas closed, what are reaction forces .''.', and RBfor this case? (e) Finally, if the structure (with pin inserted) then cools to the original ambient temperature, what are reaction forces Rtand P
(a)
The reactions at A and B.
Answer to Problem 2.5.21P
The reaction at A is =
The reaction at B is =
Explanation of Solution
Given information:
The gap between the pipes is
Write the expression for elongation in pipe 1.
Here, length of pipe 1 is
Write the expression for elongation at point B.
Here, elongation at point B is
Write the expression for net elongation at B.
Here, elongation at point 1 is
Substitute
Write the reaction at point A.
Here, reaction at A is
Calculation:
Substitute
The force required to close the gap is
Substitute
Substitute
Conclusion:
The reaction at A is
The reaction at B is
(b)
The reaction at A is
The reaction at B is
Answer to Problem 2.5.21P
The reaction at A is
The reaction at B is
Explanation of Solution
Given information:
The gap between the pipes is
Write the expression for force applied at pipe 2.
Here, force applied at pipe 2 is
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The reaction at A is
The reaction at B is
(b)
The maximum shear stress in pipe 1 and pipe 2.
.
Answer to Problem 2.5.21P
The maximum shear stress in pipe 1 is
The maximum shear stress in pipe 2 is
Explanation of Solution
Given information:
The gap between the pipes is
Write the expression for maximum shear stress in pipe 1.
Here, maximum shear stress in pipe 1 is
Write the expression for maximum shear stress in pipe.
Here, maximum shear stress in pipe 2 is
Calculation:
Substitute
The maximum shear stress in pipe 1 is =
Substitute
Conclusion:
The maximum shear stress in pipe 1 is =
The maximum shear stress in pipe 2 is =
(d)
The rise in temperature required to close the gap.
The reactions.
Answer to Problem 2.5.21P
The rise in temperature required to close the gap is
The reactions are
Explanation of Solution
Given information:
The gap between the pipes is
Write the expression for temperature raise.
Here, raise in temperature is
Calculation:
Substitute
Since the temperature remains constant, so the reactions are zero.
Conclusion:
The temperature raise required to close the gap is
The reactions are
(e)
The reaction at A.
The reaction at B.
Answer to Problem 2.5.21P
The reaction at A is
The reaction at B is
Explanation of Solution
Given information:
The gap between the pipes is
Calculation:
Substitute
Substitute
Conclusion:
The reaction at A is =
The reaction at B is =
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