What is the required force to achieve constant radius beam bending?

[DeereAdam]

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

 

[Studiot]

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.

 

[Mech_Engineer]

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.