show work thanks A rigid block (neglect its weight) is to be supported by three equally spaced rods (spaced by adistance a), each of which has Young's modulus E, cross section area A and length L. The rodsare to be pinned to the block, but during assembly it is found that one of the bars is slightly toolong; before it is attached its pin-hole extends a small distance s beneath the corresponding hole inthe block. To finish the assembly, the 'over-sized bar' is compressed and attached to the block,and then the assembly is released.(1) Find the force that is induced in each of the three bars in terms of parameters E, A, L, sand a (note that you may not need all of them).(2) After the assembly, we increase the temperature of the first and the third rod (temperature ofthe second rod is kept the same). The thermal expansion coefficient is a. Is it possible to achievezero forces in the first and third rod (F, = F3 = 0) during the heating process? If yes, find therequired temperature increase AT, in terms of E, A, L, s, a and a (note that you may not need allof them). If no, explain the reason.Note: please draw clear free body diagrams.1232JAB*ka -t a

Answered: A rigid block (neglect its weight) is…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A rigid block (neglect its weight) is to be supported by three equally spaced rods (spaced by a
distance a), each of which has Young's modulus E, cross section area A and length L. The rods
are to be pinned to the block, but during assembly it is found that one of the bars is slightly too
long; before it is attached its pin-hole extends a small distance s beneath the corresponding hole in
the block. To finish the assembly, the 'over-sized bar' is compressed and attached to the block,
and then the assembly is released.
(1) Find the force that is induced in each of the three bars in terms of parameters E, A, L, s
and a (note that you may not need all of them).
(2) After the assembly, we increase the temperature of the first and the third rod (temperature of
the second rod is kept the same). The thermal expansion coefficient is a. Is it possible to achieve
zero forces in the first and third rod (F, = F3 = 0) during the heating process? If yes, find the
required temperature increase AT, in terms of E, A, L, s, a and a (note that you may not need all
of them). If no, explain the reason.
Note: please draw clear free body diagrams.
1
2
3
2
JA
B*
ka -t a

Expert Solution

Introduction

Elongation or compression in any body depends upon many factors acting to cause change in them. Force acting on a body and temperature are one of those factors.

Change in length due to tensile/compressive force

$∆ L = \frac{P L}{A E}$

Change in length due to rise or fall in temperature

$∆ L = L . α . ∆ T$

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