Weight Distributed at Three Points

[dmw08001]

Homework Statement

Total Weight of System = 3301 kg
Length, Width of Sytem = (4670mm, 1931mm)
Calculated Center of Mass = (2261mm, 1065mm)

Find weight at the following points:

Point I (104, 1046)
Point II (3182, 1867)
Point III (3182, 225)

Homework Equations

Center of Gravity equation already used

The Attempt at a Solution

3182-2261=921
921/2261=.4075
40.75% of 3301kg = 1345
Weight at B+C = 1345*2=2690

3301-2690=610kg <--weight at Point I

I really am lost...

 

[SteamKing]

Without knowing more about your 'system', it is hard to follow your calculations.

From simple statics, having more than two points of support introduces the possibility of a statically indeterminate situation, where one needs more information than just the total weight and the locations of the c.g. and the points of support to resolve the reactions.

 

[dmw08001]

Sorry SteamKing,

This isn't actually a formal homework problem so I understand more info may be needed. What additional information can I provide that will help determine a solution?

My train of thought is as follows:

(Point 2 X Value) - (Center of Gravity X) = Distance from CG

Distance from CG in X Coordinate / CG in X coordinate = Percentage of Weight in X Direction

Weight in X Direction * 2 (because point II and III are along the same plane) = Weight at II + Weight III

Total Weight - Weight II + III = Weight I

 

[SteamKing]

Well, you need to provide more information about this 'system' and its construction. Don't be bashful about telling what it is (unless it's secret or something.)

(Hint: it's against the rules at PF to post the same or similar threads in multiple forums. All you do is cause confusion.)

 

[dmw08001]

It is just a big rectangular piece of machinery that we manufacture in china and we need to determine weights at each of the three feet so that we can give the customer and operations guys estimates for installation.

Static solution is all that is needed.

 

[PhanthomJay]

You can sum moments in 2 directions, and sum forces in the vertical direction, to solve. We can do the math, but essentially your support forces in each leg are close to equal, about 1100 kg force in each leg. I didn't do the exact math, so this number is approximate, I'd use it for estimating only, and the value needs to be checked! Do not use it for design!