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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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