Calculate the minimum thickness

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Homework Statement



I have a large polymer plate of 45cm x 120cm, with Young Modulus 0.8 GPa and I want to calculate the safe thickness (before fracture) of that plate on a middle line force across the width of the plate with magnitude of 0.6 kN.

The middle line force distribution is shown here: http://img819.imageshack.us/img819/7450/49266917.jpg [Broken]

Homework Equations



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The Attempt at a Solution



I use flexural modulus formula but i just noticed that flexural modulus is not the same with young modulus.
 
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Answers and Replies

  • #2
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can anyone help please?
 
  • #3
PhanthomJay
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I don't do much work with polymers, but you should concern yourself more with the yield stress rather than the elastic modulus if you are looking for the thickness that provides a factor of safety against failure rather than against large deformations. So calculate the bending moment at the center of the plate, and adjust the thickness to calculate the section modulus bt^2/6 to provide an appropriate safety factor against yield stress ( you need to know the value of the yield stress in compression and tension for the particular polymer you are using.
 
  • #4
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I have the stress-strain curve and the load-extension curve for this material. I can get the yield stress for this material but I am not sure how the thickness will be determined using the bending formula. it is not a beam, it is a large plate with b,d and t. By using the moment formula, only b and t are used.

thank you for your help
 
  • #5
PhanthomJay
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I have the stress-strain curve and the load-extension curve for this material. I can get the yield stress for this material but I am not sure how the thickness will be determined using the bending formula. it is not a beam, it is a large plate with b,d and t. By using the moment formula, only b and t are used.

thank you for your help
yes, it is a plate, but it is simply supported at the ends and free at the edges, and subject to a line loading at its center, so you can treat it as a beam with a length of 120 cm and a cross sectional area of 45(t) cm^2, with a load of 0.6 kN applied as a concentrated load at its center.
 
  • #6
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i will try it and i will be back to you. thank you
 
  • #7
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am trying to calculate the moment:

So the force is in the middle:

M= (Force*distance)/length= [(0.6*10^3)*0.45]/(1.2).

Is that the moment?
 
  • #8
PhanthomJay
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am trying to calculate the moment:

So the force is in the middle:

M= (Force*distance)/length= [(0.6*10^3)*0.45]/(1.2).

Is that the moment?
Moment has units of force times length. For a simply supported beam with a load at the center, the moment varies from 0 at the supports to a maximum at the center (at L/2). Can you find the value of this max moment?
 

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