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Constant Radius Beam Bending

  1. Oct 1, 2012 #1
    Hi All,
    I need to calculate how much force is required to bend a beam to a constant radius. The beam will be simply supported on both ends and the force will be applied much like a 3 point bend but with a curved face instead of a single point. For most of my application, the beams are small enough and the radius is large enough to only experience elastic bending. Any help on this is appreciated
  2. jcsd
  3. Oct 1, 2012 #2
    If you are bending beams elastically they will follow the elastic bending curve not one of constant radius.

    So in order to force the beam to follow a constant radius curve you have to arrange a loading that is the inverse of this.

    That is R = EI/M = a constant along the beam.

    For a homogenous beam of constant cross section that means that M must be constant.

    In other words you must load you beam with a pure couple only, not a force.
    I will have a think to see if you can arrange a force loading to 'cancel out' the distance effect on the moment.
    Last edited: Oct 1, 2012
  4. Oct 1, 2012 #3


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    You definitely can't make a simply-supported homegenous beam of constant-cross section bend in a constant radius using a point load. You have to either do as Studiot said apply a moment at the end of the beam, or a varying distributed load which is shaped to counteract the elastic bending curve.
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