Statics Problem - I've been out of school too long.

[Michael Wakefield]

Any help will be greatly appreciated.

Simple representation of the problem is the analysis of the forces and reactions of a table with a non-centered weight on it. I am seeking the reaction forces at the four legs.

Specifics...
Table width - 48"
Table length - 72"
Table height - 36"
Total weight of table and load is 250 lbs.
C.O.G. of all weight is...
x=32" (width)
y=26" (length)
z=28" (height)

I need to determine, from this loading, how much force each of the four legs exerts on the floor.

I have summed forces, summed moments, and come up with 3 equations and four unknowns. How can I get to the answer?

Thanks in advance for any efforts to show me how to do this. I have an ME degree but please make no assumptions of prerequisite knowledge. I'm afraid it has been long forgotten. Please spell it out for me if you can.
MW

 

[NoTime]

How do you know where the C.O.G. is if you can't figure out the rest of the problem?
Are the legs at the corners or inset?

Why not just scrounge up some bathroom scales.
Put one under each leg.

 

[PhanthomJay]

Any help will be greatly appreciated.

Simple representation of the problem is the analysis of the forces and reactions of a table with a non-centered weight on it. I am seeking the reaction forces at the four legs.

Specifics...
Table width - 48"
Table length - 72"
Table height - 36"
Total weight of table and load is 250 lbs.
C.O.G. of all weight is...
x=32" (width)
y=26" (length)
z=28" (height)

I need to determine, from this loading, how much force each of the four legs exerts on the floor.

I have summed forces, summed moments, and come up with 3 equations and four unknowns. How can I get to the answer?

Thanks in advance for any efforts to show me how to do this. I have an ME degree but please make no assumptions of prerequisite knowledge. I'm afraid it has been long forgotten. Please spell it out for me if you can.
MW

The table, asumed bolted to the floor, is stable with just three legs. With 4 unknowns, you need to do a deflection analysyis and superposition, just as you would have to do if you had a beam in 2D supported on 3 supports. Best to get out the bathroom scales.

 

[civil_dude]

Interesting problem. You need another equation. There are many ways to sum up the moments. You can sum the moments about the diagonals also if you haven't already.

 

[PhanthomJay]

Interesting problem. You need another equation. There are many ways to sum up the moments. You can sum the moments about the diagonals also if you haven't already.

Yeah, but you can sum the moments about any axis till thy kingdom come and it won't buy you the 4th equation. The problem is indeterminate using only the equilibrium equations. Only by removing one of the supports and calculating the deflection at that removed support, then placing an unknown load R at that removed support and calculating the deflection at that same point, and reactions in terms of R, then summing the 2 deflections to zero, can you sove this problem. Not too bad in 2D, but a bear in 3. Of course, a computer would help. Or a good handbook that calculates Reactions from a concentrated load at any point acting on a flat plate supported on 4 pinned supports will work (Roarke's "Stress and Strain" comes to mind).

 

[Michael Wakefield]

Thanks guys. Appreciate the advice. I drastically simplified the assembly with my "table" analogy. Actual assembly is a structual steel welded base, fan, motor, and housings all mounted on four springs. Because of this complexity the bathroom scale idea, while it would give me exactly what I need, is not workable.

I am glad to know I recalled statics correctly. 3 equations and 4 unknowns just doesn't cut it. As opposed to getting into the superposition logic I think I will try to get the computer to solve it for me. I have an FEA software, COSMOS, that I think will tell me the reactions if I can place the proper force at the center of gravity.

Thanks again for your suggestions and confirmation that it is not a straight forward problem to solve.
MW

 

[PhanthomJay]

Thanks guys. Appreciate the advice. I drastically simplified the assembly with my "table" analogy. Actual assembly is a structual steel welded base, fan, motor, and housings all mounted on four springs. Because of this complexity the bathroom scale idea, while it would give me exactly what I need, is not workable.

I am glad to know I recalled statics correctly. 3 equations and 4 unknowns just doesn't cut it. As opposed to getting into the superposition logic I think I will try to get the computer to solve it for me. I have an FEA software, COSMOS, that I think will tell me the reactions if I can place the proper force at the center of gravity.

Thanks again for your suggestions and confirmation that it is not a straight forward problem to solve.
MW

Ok, if it's on springs, be sure to model in the spring constants and plate rigidity correctly. When the supports deflect, results could be far different than analysis using rigid supports would show. Good luck!

 

[ragul]

you have summed forces, summed moments, and come up with 3 equations and four unknowns... try using the joint method... it will increase the no. of your equation by involving the internal reaction of the joint or bolt (assuming that the table is hold by a bolt, joint or nail)... You can have a reference on Engineering Mechanics by Singer...