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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


    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?



    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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