Originally Posted by
AndrewLewis
Deflection of a bar is generally governed by the following equation:
Deflection = (FL^3)/("Some Constant"*E*I) where I is the second area moment of inertia. In the case of a rod, I = Pi*(r^4)/4, so we can see that the equation becomes
Deflection = (FL^3)/("Some Constant"*E*r^4).
E (elastic modulus or Young's modulus) is essentially the same for all steels.
Therefore, the only factors you can controls are:
1) F, Force - which we are not going to modify for the sake of reduced deflection
2) L, Length - which is the distance from the center of mass of the plates (sort of) to the center of the bar.
3) r, Bar radius
Let's examine the Ohio Power Bar.
You can buy the Ohio Power Bar at 29 mm bar instead of a 28.5mm bar which is a 1.8% difference. A 7ft bar with collar to collar length of about 54 inches will have a length from collar-to-center of 26". If you can go from 5 rubber plates to 5 cast iron plates, you reduce the distance between the plate center of mass and center of bar from about 34.1in to 29.3 (a 4.8in difference or 14% change).
When we account for the power factors, it is shown that increasing the radius will decrease the deflection by 6.7% and going from rubber plates to cast iron plates will decrease the defection by 57.6%.
The conclusion being that the biggest realistic factor in affecting the whip of the bar is going to be the distance from center of bar to center of mass of plates.
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