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## Homework Statement

Derive an expression geometrically for the radius of curvature of the following beam. This is part of a lab assignment for the bending of a simply supported beam with overhangs.

** I did this crappy diagram with AutoCAD, so I couldn't ( or didn't know how to ) include greek letters. Let's let r= [tex]\rho[/tex], and d= [tex]\delta[/tex] for my derivation.

## Homework Equations

a

^{2}+b

^{2}=c

^{2}

## The Attempt at a Solution

I just used the pythagorean theorem to solve for [tex]\rho[/tex].

Starting with: [tex]\rho[/tex]

^{2}= ([tex]\rho[/tex]-[tex]\delta[/tex])

^{2}+(L/2)

^{2}.

Factoring out ([tex]\rho[/tex]-[tex]\delta[/tex])

^{2}, solving for [tex]\rho[/tex] and simplifying , I end up with the following expression:

[tex]\rho[/tex]=([tex]\delta[/tex]/2)+(L

^{2}/8[tex]\delta[/tex])

I guess I have this question...is this the proper way to derive the radius of curvature geometrically? Is it ok to do it this way?

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