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 ʻover-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 (F1 = 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.

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 ʻover-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 (F1 = 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.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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