For a cantilever beam of circular cross section, loaded at the end, how does the deflection of the free end vary as a function of beam length and diameter?
I expect the answer will be something like:
$$\dfrac{L^2}{D^3}$$
Engineering Stack Exchange is a question and answer site for professionals and students of engineering. It only takes a minute to sign up.
Sign up to join this communityFor a cantilever beam of circular cross section, loaded at the end, how does the deflection of the free end vary as a function of beam length and diameter?
I expect the answer will be something like:
$$\dfrac{L^2}{D^3}$$
For a cantilever with a point load at the free end, the deflection at that free end is:
$$\dfrac{WL^3}{3EI}$$
Handbook of Structural Steelwork - 3rd edition
where
The Young's modulus depends on the material, see Wikipedia for various examples.
The second moment of area for a circle is:
$$\dfrac{\pi r^4}{4} = \dfrac{\pi d^4}{64}$$
So your overall equation is:
$$\dfrac{64WL^3}{3\pi Ed^4}$$