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Young's modulus of the material

  1. Oct 8, 2004 #1
    Hello again,
    I dont understand how to derive equations.
    C = YI / r

    Y = Young's modulus of the material
    r = radius of curvature of the neutral surface
    I = geometrical moment of inertia of the cross section of the beam
    C = bending moment

    I = wt^3 / 12

    I = moment of inertia
    w = width of rectangular beam
    t = thickness of rectangular beam

    Koenig's Apparatus
    theta = h / 2(d+2D)

    theta =angle of deflection
    d = distance between mirrors on rectangular beam
    D = distance between mirror(mirror which is closer to telescope) to scale
    h = difference between the reading of scale

    Thank you :D
    i'm not good wif deriving equations :(

    oh, and one more
    have a question asking me to arrange three beams in the order of their radius of curvature when Y, C and A are equal, the three beams are Round beam, Square beam, H-shaped beam.
    i just need to find equations for moment of inertia for these shapes?
  2. jcsd
  3. Oct 9, 2004 #2
    for arranging the order for three beams
    Round beam, i have I = A^2 / 12
    Square beam, i have I = A^2 / 12

    with equation C = YI / r
    Round beam will have r = YI / C = [Y*(A^2 / 12)] / C
    Square beam will have r = YI / C = [Y*(A^2 / 12)] / C

    but i dont know how to convert the H-shaped beam
    i found out, for H-shaped beam
    A = HB + hb
    I = (BH^3 + bh^3) / 12


    Attached Files:

    Last edited: Oct 9, 2004
  4. Oct 9, 2004 #3
    i've derived the other formulae
    but i'm still stuck on this one, Koenig's Aparatus formula
    here's a picture of it with the formula need to derive into

    theta = h / [2(d+2D)]

    Attached Files:

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