How to calculate radius of curvature of beam?

Main Question or Discussion Point

If I start out with a flat beam of length a and then I fix one side and then bend the other side up to form an arc with height h, is that enough information to determine the radius of curvature of the bent beam? If so, how would I do it?

Thanks!

rcurv.jpg

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Answers and Replies

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If I start out with a flat beam of length a and then I fix one side and then bend the other side up to form an arc with height h, is that enough information to determine the radius of curvature of the bent beam? If so, how would I do it?
Don't you mean fix one end?
And doesn't this belong in an engineering or physics forum?

The radius of curvature at any point on a prismatic beam is equal to EI/M,

Where E is the modulus of elasticity, I is the moment of inertia of the cross section and M is the applied moment at that point. M depends upon the loading regime, E and I are characteristic properties of the beam itself.

Alternatively, if your 'beam' was thin and flexible enough you could use a spline curve. A cubic spline would be usual. These are the curves taken up by old fashioned draftsmen's splines used for drawing such curves.
 

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