Very thin and short members in bending (flexure)

[gray8317]

I am working with .005" thick spring steel. I have a 1-inch wide piece clamped at both ends so only .015" are exposed to bending. I am interested in stresses due to bending. A standard beam bending analysis approach wont work due to large deflections and short length. Anyone have any input.

 

[EnglishMuffin]

It depends on how the bending loads are applied. The fact that the beam is short may or may not matter. If you just have a pure bending moment all along your beam, the standard beam equation will work fine. If the material behaves linearly, there is no reason why the "large deflections" should matter. If it's spring steel, the strain will be small. If you are applying a transverse load, however, you will develop shear stresses, and you must obviously consider these in addition to the direct stresses produced by bending. The deflection will then also not be the same as the standard beam deflection equation. The shorter the beam, the more the additional shear deflection will dominate the bending deflection. See Timoshenko - strength of Materials Vol 1. I can't tell how you are loading the spring from your description, so its not clear which of Timoshenko's various cases will apply, if any. If I had to guess, I would say it looks as though you are using the spring steel as a frictionless pivot, with a long lever arm, and so the shear stress may be very low, in which case you could just use the standard bending equation.