I'm trying to calculate how much simply-supported round beams of several materials and diameters deflect under their own weight plus an additional weight in the middle.
I know the material densities so I can calculate weight of the entire beam, and I know the material Young's Modulus so I can calculate Moment of Inertia.
I've got the deflection due to an added weight calculated correctly, but I'm stuck on deflection due to the shaft's own weight.
Several places have given the formula:
$$\delta C = \frac {5 q L^4} {384 E I}$$
eg: https://en.wikipedia.org/wiki/Deflection_(engineering)#Uniformly-loaded_simple_beams
But I am not sure what q
represents.
Wikipedia describes that as "Uniform load on the beam (force per unit length)" and I see other sites mention it in Newtons.
Is that gravity's acceleration (9.80665 m/sec^2
) times the beam's own weight in kilograms to get Newtons of downward force?
eg: https://en.wikipedia.org/wiki/Newton_(unit)#Examples
For example, a 102g beam would exert 1N of downward force, so q
would be 1
?