Thermal Expansion of Joined Plates - Finding Tension in Copper Plate

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Homework Help Overview

The problem involves a copper plate riveted to two steel plates, examining the tension generated in the copper plate due to thermal expansion when heated from 0°C to 20°C. The context includes material properties such as Young's modulus and coefficients of thermal expansion.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the configuration of the plates and the implications of thermal expansion on tension. There are attempts to clarify the mechanics involved, including the effects of rivets and the nature of expansions in different directions.

Discussion Status

The discussion has seen participants questioning the assumptions about the lengths and expansions of the plates. Some have provided insights into the mechanics of the system, while others have expressed confusion regarding lateral versus longitudinal expansion. There is a recognition of the need to clarify these concepts further.

Contextual Notes

Participants note the importance of understanding the relationship between the different expansions of the materials involved and how they affect the overall tension in the copper plate. There is an acknowledgment of the constraints imposed by the riveted connection between the plates.

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Homework Statement


A copper plate of length 1 m is riveted to two steel plates of same length and same cross-section area at 0°C. The tension (in kilo Newton) generated in copper plate when heated to 20°C is 56n. Find the value of n. (Given Ys,Yc,αs,αc,A)


The Attempt at a Solution



I googled 'rivet' and found that 2 plates are joined with a rivet. We have 3 plates here. Can someone draw a diagram of the situation above?
 
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Hi Abdul! :smile:
Abdul Quadeer said:
I googled 'rivet' and found that 2 plates are joined with a rivet. We have 3 plates here. Can someone draw a diagram of the situation above?

I think the idea is that, if the copper was riveted to only one steel plate and heated, then the two plates would bend :redface:

so they make a sandwich of it, between two steel plates, so that everything stays straight! :wink:
 
ok I can picture it in my mind now.
Lets solve the problem.
The copper plate is under mechanical stress.
Let the tension developed in it be F
Net expansion of the copper plate = lαcΔT - Fl/AYc
Net expansion of one of the steel plates = lasΔT + Fl/AYs

What is the next step?
 
ok, they can't be those lengths, because they are forced to be the same length as each other …

so what are the forces involved? :smile:
 
attachment.php?attachmentid=33505&stc=1&d=1301051523.jpg


Is the above diagram right? The plates expand along the horizontal direction. There can be a difference in their expansions which can lead to different 'l' values for each.
 

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the diagram looks ok (but what are those letters in the middle?)
Abdul Quadeer said:
There can be a difference in their expansions …

There cannot be a difference in their expansions …

they are riveted together, and so they must have the same expansion
 
S-Steel
C-Copper
S-Steel

They can have different expansions along horizontal direction. In simple words, there is a lateral as well as longitudinal expansion of the system. If they are riveted together, which expansion will be same?
 
oh i see … yes, their lateral expansions won't be the same, so the lateral compressions will be different

but the question is asking about the longitudinal expansion, and the tension which that creates in the copper :wink:
 
I got the answer. The only confusion was in lateral/longitudinal expansion.
Thank you!
 

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