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Two Dimensional Loading - Determining Dimensional Chanage

  1. Aug 29, 2015 #1
    Hi all,

    I have hit what seems to be a mental mind / stumbling block on the question below. I am looking for some guidance wherever possible.


    1. The problem statement, all variables and given/known data

    c) The column exerts a lateral force on the base plate of 50kN due to wind loading. If Poisson's ratio = 0.34 determine the change in the base plate dimensions under this two dimensional loading. Assume a value of Young's Modulus of E = 2 x 1011 N/m2 for steel.


    Info relating to the question -
    Base plate = 300 x 300 x 15mm
    Force in the X direction = 300kN
    Force in the Y Direction = 50kN
    E = 2 x 10^11
    V = 0.34

    Here is my attempt at a solution -

    Direct Stress

    σX = F/A
    (300 x 10^3) / (0.3 x 0.3) = 3.33 x 10^6

    σY = F/A
    (50 x 10^3) / (0.3 x 0.015) = 1.11 x 10^7

    Direct Strain

    X = (1/E)(σx -Vσy)

    (1 / (2 x 10^11))(3.33x10^6 -0.34(1.11x10^7)) = 2.22 x 10^-6

    Y = (1/E)(σy -Vσx)
    (1 / (2 x 10^11))(1.11x10^7 -0.34(3.33x10^6)) = 4.98 x 10^-5

    I am pretty confident with the above, its the dimensional changes i am not so.... here's my attempt -

    Dimension Change


    ΔL = Direct Strain(x) x X
    (2.22 x 10^-6) x 0.3 = 6.66 x 10^-7

    ΔL = Direct Strain(y) x Y

    (4.98 x 10^-5) x 0.015 = 7.47 x 10^-7

    Thanks in advance to your help and responses.

    Scott


     
  2. jcsd
  3. Aug 29, 2015 #2

    OldEngr63

    User Avatar
    Gold Member

    You really need a figure to make your problem clear.
     
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