Simple supported round shaft deflection

[AQUAPOP]

Hello.
I'm looking for the deflections of a 1.938" dia. steel shaft at different lengths.
Supported in bearings at both ends.
150lbs. per foot of length, with all of the weight in the center of the rod.
I.E. how much does the rod deflect of there is 450lbs. pushing down between 36"...
I'm looking for 300 lbs. for 24", 450 for 36", and 600 for 48".

Thanks in advance,
Frank

 

[SteamKing]

Hello.
I'm looking for the deflections of a 1.938" dia. steel shaft at different lengths.
Supported in bearings at both ends.
150lbs. per foot of length, with all of the weight in the center of the rod.
I.E. how much does the rod deflect of there is 450lbs. pushing down between 36"...
I'm looking for 300 lbs. for 24", 450 for 36", and 600 for 48".

Thanks in advance,
Frank

For a simply supported beam, the max deflection for an evenly distributed load is

δ = 5wL$^{4}$/(384EI)

where:
L - distance between supports, in inches
w - distributed load, in pounds / inch
E - Young's modulus for the shaft material
(for example, for steel, E = 29*10$^{6}$ lbs/in$^{2}$)
I - second moment of area for the shaft, in inches$^{4}$

I for a circular shaft is πD$^{4}$/64, D - diameter in inches
δ - shaft deflection, in inches
π - constant = 3.14159

Make sure you use the correct units and you are good to go.