How is an object's weight distributed among the fours legs of a table?

[Anie Nancu]

When I place an object in a table, how is the weight distributed in the four legs? Is there an mathematical calculations for that?

 

[anorlunda]

Welcome to PF Anie. We're glad to have you.

We don't answer questions in the "new member introduction" forum, so I moved this to Mechanical Engineering.

 

[Anie Nancu]

Oh. Thank you so much Ms Anorlunda. It would be so nice of you if you guide me to find the answer to my question as it would be useful to proceed my research.

 

[fresh_42]

You could draw a vector diagram. There is only one weight vector from the mass pointing straight down. This vector has to split into four vectors across the table and four vectors along the legs, resulting in four diagonal vectors. The sum of all four diagonal vectors equals the weight vector. As this is not uniquely solvable but nature would uniquely solve it, you then have to find what the minimal solution is.

 

[Anie Nancu]

Thank you so much Fresh. Herewith I have attached word file just for you to visualize my question. In this case I would like to get a like to know from which point I need to draw the vector diagram. Thereby how do I get the individual vectors.

 

[sophiecentaur]

IF you could post your figures as pdf, then everyone can see them. Propriatory software is not available to everyone.

You could draw a vector diagram.

If you assume the table is rigid then you only need consider vertical forces and you can apply the principle of Moments in the simplest way. Whilst problems involving Moments are often only restricted to a two dimensional situation, it's easily applied to a three dimensional object like a loaded table.
Just take moments about an axis along the table top and then about an axis across the top.

 

[Anie Nancu]

Okay Mr. Fresh. So kind of you to help me. I will try the steps and get back to you in case of doubts.

 

[PeroK]

Thank you so much Fresh. Herewith I have attached word file just for you to visualize my question. In this case I would like to get a like to know from which point I need to draw the vector diagram. Thereby how do I get the individual vectors.

If you are really not sure about this, then you need to get hold of some material on statics. AS others have said, you need to learn about force vectors and moments.

A simpler scenario would be a one-dimensional beam on two legs, with a weight supported a variable distance along the beam. The table would be the 2D version of this. Perhaps it's better to start with a 1D problem.

 

[Anie Nancu]

Thanks Ms.Sophie and Mr. Pero. I calculated the reactive forces as per the method in the paper. I experimented with books and other objects. I assumed the center point of the book as the reference. By assuming the centre point I was able to calculate the other parameters. Thereby I was able to calculate the individual reactive forces. The interesting thing is that the theoretical values of the total weight of the book matched with the total practical weight of the object. But the individual theoretical reactive forces did not match with the practical reactive forces. I found the individual reactive forces (practical) by placing separate weighing machine under the four legs of the table.

 

[sophiecentaur]

@Anie Nancu pdf =
That paper seems to say it all. It may be a bit overkill for the problem but which bit are you finding problematical?
The practical differences could be in the measurements of the actual placing of the Force meters.(?) If you are assuming that the effective force from each leg is at the corner - or at the centre of the table / leg joint then either of those assumptions could be affecting your results. But how far out are your measurements?

 

[Anie Nancu]

SET 1	PRACTICAL VALUES	W	B	H	h	b	THEORETICAL VALUES (T)
R1	1.2​	4.8​	0.615​	0.415​	0.33​	0.25​	R1T	0.58348516​
R2	1​	4.8​	0.615​	0.415​	0.33​	0.25​	R2T	0.39964737​
R3	1.5​	4.8​	0.615​	0.415​	0.33​	0.25​	R3T	1.551572142​
R4	0.8​	4.8​	0.615​	0.415​	0.33​	0.25​	R4T	2.265295328​
TOTAL WEIGHT	4.5​							4.8​

'W' represents the actual weight of the object.
The Practical and the theoretical values of the reactive forces tabulated. The total seems to match somewhat but the individual values are not coinciding. That is my actual doubt. Think of it Ms Sophie. Do you think that I am proceeding in the correct method? If there is any other better choice kindly let me know. It is already 12.25 am. I am very tired thinking about it all day long. I need to sleep. I don't know what time it is now at your place. Tomorrow morning I will be eagerly waiting for your reply. Take care.

 

[sophiecentaur]

@Anie Nancu It seems to me you may not have a lot of experience in mechanical measurements involving ' heavy' loads. Seemingly simple measurements can often involve more skill and experience than you might think. Believe nothing that your instruments tell you until they have been checked.
You should first query the measurements you have been getting (the theory is pretty easy and we can assume you can handle the numbers accurately). One thing you could try would be to calibrate the force meters and check they are consistent. Then swap them round around and see if you get the same error. I don't know what quality of equipment you are using but, if they are 'bathroom scales', you may have had experience of using a home weighing machine and you may have found that you can alter readings by tilting your feet etc.. Try tapping / hitting the table and see if that changes the four readings when they re- settle.

 

[Anie Nancu]

I am back to my work place Ms. Sophie. Thank you so much. I have got the clarification. I will work on it and get back to you.

 

[PeroK]

SET 1	PRACTICAL VALUES	W	B	H	h	b	THEORETICAL VALUES (T)
R1	1.2​	4.8​	0.615​	0.415​	0.33​	0.25​	R1T	0.58348516​
R2	1​	4.8​	0.615​	0.415​	0.33​	0.25​	R2T	0.39964737​
R3	1.5​	4.8​	0.615​	0.415​	0.33​	0.25​	R3T	1.551572142​
R4	0.8​	4.8​	0.615​	0.415​	0.33​	0.25​	R4T	2.265295328​
TOTAL WEIGHT	4.5​							4.8​

'W' represents the actual weight of the object.
The Practical and the theoretical values of the reactive forces tabulated. The total seems to match somewhat but the individual values are not coinciding. That is my actual doubt. Think of it Ms Sophie. Do you think that I am proceeding in the correct method? If there is any other better choice kindly let me know. It is already 12.25 am. I am very tired thinking about it all day long. I need to sleep. I don't know what time it is now at your place. Tomorrow morning I will be eagerly waiting for your reply. Take care.

Clearly those figures don't match at all. What is the weight of the book and the weight of the table?

 

[Anie Nancu]

Yes. I had this doubt. The weight of the table is around 3.5 and the weight of book is 1.5. These are rounded off values.

 

[Anie Nancu]

Sorry the weight of the book is around 1 kg

 

[PeroK]

Sorry the weight of the book is around 1 kg

Those theoretical values don't look right to me, unless you have the book very near the edge. And then there may be a larger error due to the thickness of the table legs.

I'd say something heavier (and smaller cross sectional area than a book) and not too close to the edge of the table would be better.

 

[PeroK]

PS I'd also suggest you initially test the weight on a line down the centre of the table to check the 1D case. This will be a simpler way to test your measurements and calculations.

 

[Anie Nancu]

S I'd also suggest you initially test the weight on a line down the centre of the table to check the 1D case. This will be a simpler way to test your measurements and calculations.

This will be a simpler way to test your measurements and calculations.

 

[Anie Nancu]

Okay sir. Thank you.

 

[sophiecentaur]

PS I'd also suggest you initially test the weight on a line down the centre of the table to check the 1D case. This will be a simpler way to test your measurements and calculations.

Yes. The table may just not be uniform in the first place. With no book, are the four readings all the same?
This is the sort of checking that 'we' do as a matter of course, if we are used to experimenting and measurements. Fault finding is just not something that's taught in Schools but we learn it, once we get used to the business. How to teach that approach is such a challenge. It's something that gets taught on Mechanical Apprenticeship Courses but not on academic courses.
Perhaps when they start to teach 'coding' seriously to all Schoolkids, things will change.

 

[Anie Nancu]

True.

 

[sophiecentaur]

True.

Note - it is not your fault if you have been set an exercise to do which demands extra skills that may be new to you. Look upon it as an excuse to learn an approach which your teachers may have not helped you with. PF is a good source of practical advice for people who have taken the trouble to come here.
Do you have time to repeat your measurements or is your lab time too short to allow it? If you cannot repeat then your write-up should include these ideas in the conclusions - "possible experimental improvements".