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Strain in cantilever beam 
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#1
Aug1114, 09:44 AM

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Hi everyone. I feel there should be a simple answer to this but I can't seem to find anything on this.
So I have a simple cantilever beam, supported at one side and loaded at the free end. I have the force displacement data and can easily calculate the stress. However, for the strain I do not want to use Hookes Law, but instead calculate the strain from the force displacement data. Any hints? Thanks! 


#2
Aug1114, 10:27 AM

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Chet 


#3
Aug1114, 10:57 AM

P: 4

Apologies, I should have stated I am looking for the maximum strain.
I have got the full forcedisplacement data of a bend experiment. I know the geometry of the beam (triangular cross section) so can calculate the maximum stress at any time as (M*y)/I, which for the triangular crosssection is equal to (24*Force*Length)/(width*thickness^2). In a code I have access to it states that the maximum strain at any time would be equal to (2*displacement*thickness)/(Length^2), but I can't figure out why this would be the case. 


#4
Aug1114, 11:29 AM

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Strain in cantilever beam
Chet 


#5
Aug1114, 11:34 AM

P: 4

Thanks for your reply. Maximum curvature is at the fixed end. However, I can't measure the curvature to any degree of accuracy, as such for the sake of this problem it is not available.



#6
Aug1114, 11:52 AM

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What I meant was, analytically , what is the curvature in terms of the displacement ?



#7
Aug1114, 12:01 PM

P: 4

I'm not sure how I could describe the curvature in terms of the parameters I have.
If I was to reverse engineer the equation for strain I have 


#8
Aug1114, 02:36 PM

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P: 7,288

If you know the maximum stress, you can get the maximum strain using Young's modulus and Hooke's law.
The stresses and strains in the beam are statically determinate. They only depend on the applied loads, not on the displacement of the beam. 


#9
Aug1114, 03:16 PM

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Step 2: What is your equation for the displacement in terms of the load F. Step 3: Combine these relationships to get the bending moment in terms of the displacement. Step 4: Determine the curvature from the bending moment Step 5: Determine the curvature as a function of the displacement Step 6: Determine the strain from the curvature chet 


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