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Thin Plate Deflection

  1. Oct 29, 2013 #1
    1. The problem statement, all variables and given/known data

    Will the following thin steel plate plasticly deform due to its own weight, what is the maximum deflection of the plate? Plate dimensions 0.25 cm thickness, 3.0 m length, 3.0 m width. The plate is supported on two ends, by a wall (welded).

    2. Relevant equations

    σ = (pb^2)/[(2t^2)((0.623{b/a)^6)+1)]

    y = (0.0284pb^4)/[(Et^3)((1.056[b/a]^5)+1)]



    3. The attempt at a solution

    density = 8050 kg/m^3
    area = (3m)(3m) = 9m^2
    volume = (3m)(3m)(0.0025m) = 0.0225m^3
    weight = (8050kg/m^3)(0.0225m^3)(9.81m/s^2) = 1776.83N

    p = 1776.83N/9m^2 = 197Pa

    σmax = ((197)(3^2))/{(2[0.0025^2])((0.623([3/3])^6)+1))} = 87.3937MPa
    Therefore, no plastic deformation.

    ymax = (0.0284(197)(3^4))/[((200x10^9)(0.0025^3))((1.056[3/3]^5)+1)] = 0.07053m
    Therefore, the deflection is 0.07053m.

    ------

    Well, that's my attempt at this problem. Not 100% sure if it's right though. :(
     
  2. jcsd
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