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Homework - Creep Calculation

  1. Jun 2, 2009 #1
    Hi all,

    I'm trying to crack what is admittedly a homework question. I don't necessarily want you to just spit out the right answer for me, but if you could point me in the right direction it would be appreciated.

    A shelf for a hot air dryer is to be made from acrylic sheet. The shelf is simply
    supported as shown in Figure 1, and has width w = 500mm, thickness t = 8mm and
    depth b = 200mm. It must carry a distributed load of 50N at 60oC with a design life of 8000 hours of continuous use. How much will the shelf sag in that time?

    Essentially Figure 1 simply show's that the force is evenly distributed across the entire shelf, it's not a point load.

    We also have a graph of Creep Modulus (GPa) vs Time (s).

    8000 hours * 60 seconds/hour = 480000s

    Reading the graph of 4.8x10^5 seconds, we have a Ec of ~2.5 GPa.

    Can anyone give me some pointers of a direction to go in from here?

    Thanks.
     
  2. jcsd
  3. Jun 2, 2009 #2

    Mapes

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    Here's where I would start:

    1. Find the definition of "creep modulus."

    2. Find the relevant state of stress in the beam (hint: shelf problems are often bending problems).

    3. Connect the creep modulus to the stress to get strain.

    4. Relate strain to the amount of sag.
     
  4. Jun 2, 2009 #3
    Any chance you can help me out with finding the stress in the shelf?

    I'm using

    defl = Force * Length^3 / Second moment of Area * Creep Modulus * Loading constant.

    I don't think this is right, because I'm getting a deflection of 6.1m (obviously wrong) and I don't think this method takes into account the fact the creep modulus is changing.

    Any chance of giving a bit more of a hint for which formula to use?

    Thanks.
     
  5. Jun 2, 2009 #4

    Mapes

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    It's likely there's a calculation or units problem somewhere. Recheck your calculations carefully.
     
  6. Jun 2, 2009 #5
    I = 0.5m * 0.008m^3 / 12

    I = 2.13333x10^-8 m^4



    defl = 50 N * 0.5m / (384/5) * 2.5x10^6 Pa * 2.13333x10-8 m^4


    Pascals cancels a m^2 down the bottom and N up the top leaving m / m^2

    This gives m^-1 which I suppose can't be right, any idea where I've gone wrong though?
     
  7. Jun 2, 2009 #6

    Mapes

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    Your equations in #3 and #5 seem to be different, and neither looks quite right. I suggest checking a textbook or reference book for the exact equation, and check what a GPa is again.
     
  8. Jun 2, 2009 #7
    Thanks for spotting the mistake. Stupid me.

    The equation is definitely right in the following sense.

    Stiffness = C1 * E * I / L^3

    Stiffness = force / deflection.

    So force / deflection = C1 * E * I / L^3

    Therefore, deflection = L^3 * F / C1 * E * I

    I changed 2.5 GPa to MPa in my outline of the data, labelling it as 2500 MPa, But stupid me only said 2.5x10^6 (MPa) instead of 2.5x10^8 (GPa) in the working.

    That gives a deflection now of 6.1cm, much more reasonable.
     
  9. Jun 2, 2009 #8

    Mapes

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    OK, cool. (And I was wrong about your #3 equation being wrong; I was thinking that the distributed load was in N/m, but it wasn't.)
     
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