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This should be a straight one for most of you. Given a cantilevered beam that has a force F applied across it (or at one end), causing a displacement d and deflection [tex]\theta[/tex] , what is the relationship between the torsional spring constant k[tex]_{theta}[/tex] and the linear spring constant k?

What I do know is that the linear spring constant can be expressed in terms of the moment of inertia and modulus of elasticity as follows:

k = [tex]\frac{3EI}{l^{3}}[/tex]

I would like to know how to derive the relation between the two spring constants. In my problem, the parameters that I have are E, I, length, and [tex]\theta[/tex] .

If you could point to some website that derives this, that would be good too.