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rdx
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Suppose I have a table with 4 legs and on this table I have a concentrated weight at an arbitrary location. How do I work out the distribution of weights on the legs?
olgranpappy said:put a scale under each leg and then read the scales.
cyrusabdollahi said:Sum the forces and moments.
cyrusabdollahi said:You have 4 unknown forces.
(1)- Force Balance
(2-4) - moment balance
I don't see why it would be statically indeterminate as of yet. You should show some work so I can see if it is indeterminate or not.
cyrusabdollahi said:Do another moment equation about a line that goes through two legs.
cyrusabdollahi said:I don't get it. Take the moments about a line that passes through two of the legs. Its one equation with two unknowns in it.
cyrusabdollahi said:You know how to take the sum of moments, right? Sum the moments about a line that has an axis through two of the legs, any two. I expect you to come up with the eqn.
rdx said:LOL, did you mean piss or bliss? Y R U trying to insult me?
olgranpappy said:calm down. lance armstrong is wrong. you are correct. the problem in textbook, though.
This problem does not involve deformations.olgranpappy said:yes. with four legs you do not have enough equations, you need one more involving stresses or strains. or something, I can look up how to do it later, but I think this problem should be solved in most intro textbooks. look up stress or stain or young modulus in the index...
olgranpappy said:How about a library? I looked up "Young's modulus" in my old intro textbook (Halliday Resnick and Walker, "Fundementals of physics") and within a few pages I found a section on "Indeterminate Structures." There is a picture of a pink elephant sitting on a four legged table... it's exactly the problem you are interested in...
to find webpages maybe just google "Elasticity" or "Indeterminate Structures" or "Pink Elephants." Maybe not that last one.
russ_watters said:Most tables are symmetrical, so assuming this one is, you could just split it into two one-dimensional center of mass problems. That's probably functionally equivalent to what cyrus said, but maybe makes it easier to understand how it could work.
I don't see anything particularly difficult about this problem either - it is just slightly more involved than the most basic one-dimensional problem.
russ_watters said:This problem does not involve deformations.
rdx said:I find it fascinating that an apparently simple problem like a table is so hard/impossible to solve.
AlephZero said:The problem is not "hard" to solve at all. You just need to make a CORRECT model of the situation, which involves the flexibilility of complete table (flexible legs and a flexible top, in general).
If you assume the table is a rigid body, there is no unique solution. Consider vertical forces of +1 on the two legs on one diagonal, and forces of -1 on the other two legs. The resultant forces and moments about any point are zero.
If you make some simplifying assumptions (e.g. the legs all have the same flexibility and the top is rigid), it's easy enough to find a closed form solution using energy methods. See any textbook on solid mechanics for the details of how to do it.
Some special cases are easy to solve by symmetry (e.g. if the mass is at the center of the table).
Statically determinate structures, where you CAN calculate reaction forces without considering the deflections of the structure, are a special situation that hardly ever occurs in reality. They are very common in exercises in elementary mechanics textbooks though, because you can practise working with forces and moments without worrying about anything else.