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Beam Bending - Cranked Beam

  1. Sep 9, 2009 #1
    Hello all

    I have a beam bending problem I need some help on.

    I need to calcuate the deflections at the load (and in the plane of the load) for a simply supported beam with equal point loads overhanging the supports. However my beam is cranked as shown in the attached diagram of the problem geometry.

    I know that for a straight beam the formula for the deflection (y) at the loads is

    y = Fc2(2c +3b) / 6 EI

    where

    F = the force applied at each overhang
    c = the distance of the overhang
    b = the distance between the support
    E = the modulus of elasticity of the beam
    I = the second area of moment of the beam

    (A diagram of the straight beam case is also attached).

    Can anyone help me get started on solving this problem?

    Thanks

    Tony
     

    Attached Files:

  2. jcsd
  3. Sep 9, 2009 #2
    I see there are many posts asking to calculate deflections. The problem is it is very hard to explain these calculation theories, algorithms and the calculations take a long time. I recommend to find some building mechanic book to learn or to try search names:
    1) Enrico Betti theorem
    2) Clapeyron theorem
    3) Vereschagin's rule
    4) Simpsons rule
     
  4. Sep 12, 2009 #3
    Anytime i see something start to get complicated i just use Castiglianos's Method. http://www.roymech.co.uk/Useful_Tables/Beams/Beam_energy_methods.html
    If you were using this method you would differentiate with respect to the force to get the displacement in that direction (say the y direction). For the x direction you just put a force in there so that you can differentiate w.r.t. that force and once you have the equation you set that imaginary force = 0.
     
    Last edited: Sep 12, 2009
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