Need help on figuring out weight distribution when adding a third axle

[rlpjr]

We have a truck that weighs 20,000 lbs, 8,100 on the front and 11,900 on the rear. The wheel base from the front axle to the rear axle is 272". The center of gravity is 161.84" which we found by taking 272" * 11,900 / 20,000 = 161.84".

What would the load be on each axle if we add a third axle that weighs nothing (for the sake of keeping it simple) at 220" that is an 'independent non-load sharing axle'? Meaning its just like the original rear axle and not like a normal tandem setup that shares (splits) a load evenly between the two.

Any insight into this is much appreciated,

Thanks.



p.s.

To get more into it what would the loads be on each axle when we add a payload of 26,000 lbs at 200"?

 

[jack action]

Even if it is an independent axle, you still need to find an «average» wheelbase between the front and the rear axles and split the rear load evenly between the two rear axles.

So the «average» wheelbase would be 246", the rear load would 13 158 lb (so 6579 lb on each rear axle) and 6842 lb on the front axle.

Although, the split between the two rear axles will be affected if one of the rear axle has a much stiffer suspension than the other, or if the springs of one rear axle are more preloaded than the ones from the other rear axle. The stiffer or more preloaded axle will support more weight.

So the rear load (F_r) is related to the initial preload of the springs (F_pl), the stiffness of the springs (K) and the displacement of the springs (x) on the two rear axles (1 & 2):

F_r = (F_{pl 1} + K₁x) + (F_{pl 2} + K₂x)

or:

x = [F_r - (F_{pl 1} + F_{pl 2})] / (K₁ + K₂)

The displacement x is the same for both axles. You can then find the load on each axle by adding its preload and the force created by the displacement.