Finding Average Shear Strain in a flexible connection of rubber and steel

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Discussion Overview

The discussion revolves around calculating the average shear strain in a flexible connection involving rubber and steel, as presented in a homework problem. Participants are attempting to derive the shear strain (γ) and horizontal displacement based on given parameters such as thickness, load, and shear modulus (G). The conversation includes attempts at applying relevant equations and clarifying the use of provided data.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in calculating shear strain (γ) and horizontal displacement, mentioning confusion about how thickness is utilized in the problem.
  • Another participant clarifies that τ represents shear stress and suggests calculating the area over which the load is applied to determine shear stress accurately.
  • A participant proposes a specific area calculation (150 x 10) but later questions its correctness after calculating stress and strain, indicating a potential misunderstanding of the area involved.
  • Further clarification is provided regarding the correct dimensions for the area of applied force, emphasizing the need to consider both dimensions for accurate calculations.
  • One participant suggests using average values for force or stress in the calculations, indicating uncertainty about the correct approach to finding average strain.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to calculating shear strain, with multiple competing views on how to interpret the problem and apply the relevant equations. The discussion remains unresolved as participants continue to refine their calculations and understanding.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the area of force application and the interpretation of the problem statement. Participants express uncertainty about the correct use of thickness and the average values needed for calculations.

dabest1
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Homework Statement



[See Attachment]

Given: Thickness, load, G

Find:γ and horizontal displacement.

Homework Equations


τ=γG
Angle change should be the shear strain.

The Attempt at a Solution



I tried plugging 800 into tau and the given value of G to get γ, but that isn't working. I also tried to draw a deformation, but I don't know how to deduce how much it will deform from the question. I also don't know where thickness is used in this problem.
 

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Why are you 'plugging' 800 into Tau? Isn't tau the denoted symbol for shear stress? Look carefully at the diagram given to you. Figure (b) is a section view of figure (a), therefore you can deduce the area over which P is applied using that. You can then calculate the shear stress, and since you are given the shear modulus of rubber, you can finally move on to calculate the shear strain of the rubber.
 
Will the area be 150 x 10?

So I calculated the stress = (15000)/(1500 x 10^-3) = 10000

Then did 15000/800000 for y.

It is wrong.
 
Last edited:
No, it won't. The area of the applied force is 200mm x 150mm right? 10mm is the thickness of the steel plates. Now, try recalulating the shear stress on area where the force P is applied. Remember, the question asks for the average shear stress, so a bit more work is involved after.
 
Alright, so I did that.

stress = force/area = 15000/(200x150x10^-3) = 500

tau = yG

500 = y*800000

y = 6.25 x 10^-4..

Which is still wrong...
 
Bare with me as I havn't done this in class yet, just read over it whilst looking through a book. It's looking for the average strain, yes? So I'm assuming you have to use the average force that is applied or the average stress you calculate (again, bare with me). Try it with both, and see what answer you get.

Oh, and when converting you units of area, do it for both dimensions, not just the one. :)
 

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