Weight Distribution (RTU Corner Weights, Know Center of Gravity)

[bmartin32]

I have an RTU (roof top air conditioning unit) that has a total weight of 8444lbs. I know that the center of gravity is and the overall dimension. I need to figure out what the weight at each corner is. Could anyone tell me how to figure this out? I have attached a document showing the data. Let me know if there is anything else you need. Thanks Alot.

B.

 

[rb1957]

if i said the load at the corner is inversly proportional to the distance to the CG, does that help you ?

the closer the corner is to the CG, the more load it reacts.

P = k/L

P1+P2+P3+P4 = W
k/L1+k/L2+k/L3+k/L4 = W
k = W/(1/L1+1/L2+1/L3+1/L4)
P1 = k/L1, ...

 

[MintJulep]

I bet the manufacturer knows.

rb1957's solution assumes that the RTU is perfectly rigid, which it is not. The method might be "close enought" though.

 

[msquared48]

If the unit is mounted on steel or wood sleepers, you should be fine with the results, especially if you're a government worker.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[zekeman]

I've seen this indeterminate problem at least 5 times on this forum and rb1957 continues to write equations that are his "rule of thumb". I still haven't seen any proof of its validity.although in the absence of more information , I would buy the idea of CM proximity to mounting points having a relationship like the closer it comes to each mount the higher it gets. but, please, no equations.

The problem as rb well knows, is indeterminate and dependent on the flexibility of the mounting points and the understructure of the roof.

 

[rb1957]

the inversely proportional to distance "rule of thumb" is derived from the equations of equilibrium assuming the body is rigid; that the body is two sets of beams each reacting proportional load; it's easy to prove for yourself (i did when someone posted it here). it is a simple approach to a very complex problem, as we all know, statically indeterminate where the correct result is determined by the relative stiffness of alternate loadpaths.

how stiff is the roof structure under each corner ?

how stiff is the body, providing the loadpath from the CG to each corners) ?

how flat is the roof ?

how different is the correct answer from the rough one ?

how big is the safety factor ? (so is the difference significant ?)

 

[msquared48]

You are overthinking this and making it too complicated for the level of the loads seen. The sleepers, coupled with the stiffness of the unit should make the results very close to reality.

To be better though you really should consider line loads at the sleepers.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[bmartin32]

Thanks for your help, but I think we are overthinking my purpose of the information. I am not concerned about the strucure, I need to know the corner weights to I can size the springs to support the unit against vibration. I have a program that provides me with the correct springs and location of them if i supply the corner weights of the unit. I was also thinking that the weight would be inversley proportional to the location of center of gravity. The location of the center of gravity is slightly to the right and toward the top of the unit. I have come up with the top right corner 3394.48 lbs, bottom right 1342.5 lbs, lower left 1047.05 lbs, and top left 2659.86 lbs. Would you guys agree?

 

[zekeman]

No, if you are now talking of mounting springs,rb 1957 inverse equation does not apply.
You need a program that accounts for the mass distribution , the forcing frequencies and their locations.

If I did this , I would put springs at the designated mounting points, write the 3 dynamic equations. Then I would try to eliminate the rocking modes by judicious spring selection. A big problem but depends on the driving forces.
Elimination of the rocking modes would allow one to treat this as a single degree of freedom linear problem and an isolation damper could be found for a single frequency input.

 

[rb1957]

well, it depends on what the OP means by "correct spring".

if this means the sring stiffness is selected so that the basic rigid assumption (plane sections remain plane) still holds, then i'd've thought that the rigid assumption would still be pretty good.

dynamic response is a whole different problem. maybe people who mount these things for a living could help you better. how will the support springs react to imbalance loads ? to oscillating loads ??

since we've only just heard of springs being involved (maybe they were assumed from the description), maybe we'll also hear "well of course they're damped".

how did you derive your reactions ? is weight the critical load ??

 

[zekeman]

" Then I would try to eliminate the rocking modes by judicious spring selection. A big problem but depends on the driving forces.
Elimination of the rocking modes would allow one to treat this as a single degree of freedom linear problem and an isolation damper could be found for a single frequency input"

Disregard this statement; you can't eliminate the rocking mode since the forcing function is rotational at the motor/compressor.
It is fairly simple to write the linear and rocking equations.


.

 

[RossABQ]

I would have assumed the compressor and fan are already internally isolated on a spring base? If not they should be.

 

[jmcoope3]

I agree with Mint, call the manufacturer, they should know.

If you don't know, don't assume the risk.

 

[zekeman]

"I would have assumed the compressor and fan are already internally isolated on a spring base? If not they should be."


Then what do you think he's looking for?