Calculating modulus of elasticity?

  1. I'm trying to figure out how to calculate the modulus of elasticity for a board clamped to a surface plate at one end and free-floating on the other. I've measured the deflection with a 1k weight at the free end of the board. So I've got that data as well as the dimensions of the free-hanging portion of the board.

    I've done this test with numerous boards of different thicknesses and dimensions and want to compare them in terms of stiffness.
  2. jcsd
  3. Mapes

    Mapes 2,532
    Science Advisor
    Homework Helper
    Gold Member

    Hi tobyrzepka, welcome to PF. Try a search for "beam bending equations" to find the deflection vs. Young's modulus for a number of different boundary conditions. For the case of a cantilevered beam (clamped at one end, transverse load on the other), the deflection is [itex]\delta=PL^3/3EI[/itex], where [itex]I=wt^3/12[/itex] is the second moment of area. Does this answer your question?
  4. Like Mapes stated correctly, δ=F*L^3 / 3E*I

    Since you measured deflection you can solve as E (elasticity modulus) and you'll have it.

    E=I*F*L^3 / 3δ

    F = Force applied (1kg as you mentioned)
    L = Length (Length of each board)
    E = Elasticity modulus (You will do the math)
    I = Inertia moment (b*h^3)/12 where h=width of board and h=height (thickness)
    δ= Deflection (As you measured)

    I hope that helped
  5. So you said :
    I = Inertia moment (b*h^3)/12 where h=width of board and h=height (thickness)

    I assume you meant b = width of the board, and h = height... is that right?

  6. b=width, h=depth/height

    for a rectangular section I =(b.h^3)/12
    mohamed hassan likes this.
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