well you asked for it!
just taking some numbers out of fresh air: diameter 10mm, overhang 100mm, tip load 1 N, use property values for steel
Twisting
Shear modulus = 79.6 N/mm^2
tool tip to centre of bar = 6 mm
Torque = 1 N * 6 mm = 6 N.mm
angular deflection = 32 * 100 * 6 / (79.6 * pi * 10^4) = 0.0077 rads **LINK**
This gives rise to a tangential deflection of 0.0064 * 5 = 0.032 mm
Bending Modulus = 207 N/mm^2
Second moment of area = pi * 10^4 / 64 = 490 mm^4
end deflection = 1 * 100^3 / (3 * 207 * 490 ) = 3.29 mm
With a much shorter bar the difference would be smaller, if the length was about 10mm they would be the same, but I don't think we'd care. If anyone wants this sum in SMath studio send me a pm, I'll not hold my breath
Edited By duncan webster on 09/09/2020 22:19:46