Tipping Over a Table: How Much Overhang?

In summary: W = \frac{L}{2}$$The equation is quadratic in L, so the overhang can be any positive value as long as it's not greater than the width of the table.
  • #1
kevelev
12
2
TL;DR Summary
Designing a table and need to know how much overhang for certain weight, or how much weight for certain overhang.
I'm designing a table and need to know how much overhang I can have. Assuming the table is completely rigid, is symmetric, and has weight W acting on the CG, how much overhang x can I have? For instance, I know that zero overhang could have L = ∞ (if completely rigid) as the load wouldn't be outside (i.e. to the right of) the tipping point TP. I also know that as L increases, the CG will shift to the right, meaning the distance a will decrease. So the tipping point will be when a = 0. Is there an equation that incorporates the changing tipping point?
 
Engineering news on Phys.org
  • #2
Welcome to PF.

Why do you want an overhang on this table? Is it for artistic content, or some practical reason? Can you show us some sketches of your work so far?
 
  • #3
Screenshot_20220210-133542_Adobe Acrobat.jpg
 
  • Like
Likes berkeman
  • #4
Couldn't get the image to work at first. Overhang is for artistic reasons yes.
 
  • #5
Well, it also leaves room for chairs and such when people are sitting at the table. Can you show us your FBD for the table to get the equations involved in the Tipping Point calculation?
 
  • #6
I posted the image with the known forces.
 
  • #7
Well, can you post the equation for the sum of Moments, and say what it takes to avoid tipping it over with the extra downward edge force?
 
  • #8
The equation where it doesn't tip is given by $$Wa\gt Lx $$ Or if you prefer $$L \lt W\frac a x$$. These both say that the "lefty" torque in the picture must be bigger than the "righty" torque about the obvious tipping point. That make sense?
EDIT: Sorry I stepped on @berkeman and gave it away...
 
  • Informative
Likes berkeman
  • #9
hutchphd said:
The equation where it doesn't tip is given by $$Wa\gt Lx $$ Or if you prefer $$L \lt W\frac a x$$. These both say that the "lefty" torque in the picture must be bigger than the "righty" torque about the obvious tipping point. That make sense?
EDIT: Sorry I stepped on @berkeman and gave it away...
Seems there was an issue with the formatting of the equation...I'm not sure what it's saying.
 
  • #10
  • Wow
Likes berkeman
  • #11
No, no, you are doing fine. :smile:
 
  • #12
If we assume the table was massless and only forces W and L were acting on it (as well as a reaction force at the tipping point), then we could say Wa = Lx and then solving, then max overhang x = Wa/L. The problem is that the table isn't massless so if a 200 lb person sits on the end, then the new CG of the table + the person will shift to the right.
 
  • #13
kevelev said:
Seems there was an issue with the formatting of the equation...I'm not sure what it's saying.
It's the sum of Moments equation that I was alluding to. It doesn't make sense?
 
  • #14
No I got the sum of the moments. It was just hard to read with all the dollar signs and strange formatting.
 
  • #15
kevelev said:
If we assume the table was massless and only forces W and L were acting on it (as well as a reaction force at the tipping point), then we could say Wa = Lx and then solving, then max overhang x = Wa/L. The problem is that the table isn't massless so if a 200 lb person sits on the end, then the new CG of the table + the person will shift to the right.
Well, the drawing makes it look like the table has plenty of mass. And yes, whatever situation you envision (distributions of loads), that will modify your FBD and sum of Moments.
 
  • #16
kevelev said:
No I got the sum of the moments. It was just hard to read with all the dollar signs and strange formatting.
Oh, got it. Yeah, the PF software uses something called "lazy LaTeX" rendering, which doesn't render it until you refresh your browser once. After that it should be rendered correctly (at least for that particular thread).
 
  • #17
(BTW, there is a useful "LaTeX Guide" in the lower left of the Edit window in case you would like to learn how to post math at discussion forums) :smile:
 
  • #18
I have a CAD model of the table. With a known density, it calculates the weight of the table and center of mass. I also created a CAD model of a large lead weight and placed that on the edge of the table. That made a new CG and I was making sure that the point of the new CG was still within the edges of the base of the table. This is one way of doing it, but I wanted to have a formulaic approach rather than one by trial and error of varying lead weights and overhangs.
 
  • #19
Long story short, the table width is 48", the base is 36". That's a 6" overhang on each side. The table weight is about 350 lbs. My trial and error approach shows that with my design I can have about 1200 lbs. at the edge before it tips.
 
  • #20
kevelev said:
This is one way of doing it, but I wanted to have a formulaic approach rather than one by trial and error of varying lead weights and overhangs.

Yeah, the formulaic approach is just to use the sum of Moments equation.
 
  • #21
So the size and weight of the table are a factor for it's stability in this case.
 
  • Like
Likes berkeman
  • #22
Yes, absolutely!
 
  • #23
*huge factor...
 
  • #24
I thought you meant that TP was the "edge" of base of the table. You want that (call it the "base edge" to be right of the "balance point" of the force moments (torques). I am assuming W is the weight of the table and L is the Load (person's weight). Thats what the equations say.
 
  • #25
*huge factor...
 

1. What is the maximum overhang for a table before it tips over?

The maximum overhang for a table before it tips over depends on several factors such as the weight and distribution of objects on the table, the height and width of the table, and the stability of the table legs. Generally, it is recommended to keep the overhang less than 1/3 of the total table length to prevent tipping over.

2. Can a table with a larger base support more overhang?

Yes, a table with a larger base and wider legs can typically support more overhang compared to a table with a smaller base. This is because a larger base provides more stability and a wider surface area for the weight to be distributed.

3. How does the shape of the table affect its tipping over?

The shape of the table can affect its tipping over as it can impact the distribution of weight and the center of gravity. For example, a round table with a centered base may be more stable compared to a rectangular table with legs on the corners.

4. Is there a difference in tipping over between a solid wood table and a hollow table?

Generally, a solid wood table will have more stability and be less likely to tip over compared to a hollow table. This is because the solid wood provides more weight and support, while a hollow table may have less weight and be more prone to tipping over.

5. Can adding weight to the base of the table prevent it from tipping over?

Adding weight to the base of the table can help prevent it from tipping over, but it may not completely eliminate the risk. It is important to consider the overall weight and distribution of objects on the table in addition to the weight added to the base.

Similar threads

Calculating the load required to tip a table?
    • Mechanical Engineering
Replies
15
Views
1K
Why are table legs placed at the corners?
    • Mechanical Engineering
Replies
25
Views
3K
How much force to tip over an umbrella stand?
    • Mechanical Engineering
Replies
27
Views
4K
Tipping of a cabinet and determining velocity at a given point?
    • Mechanical Engineering
Replies
2
Views
973
What is the weight of my table using only one scale?
    • Mechanical Engineering
Replies
4
Views
1K
Raising a farm windmill tower
    • Mechanical Engineering
Replies
5
Views
88
Calculate dimensions of floating laptop stand
    • Mechanical Engineering
Replies
4
Views
887
How to design hydraulic system and size cooler
    • Mechanical Engineering
Replies
6
Views
1K
How far can the remote control extend without tipping over?
    • Introductory Physics Homework Help
Replies
5
Views
2K
Calculating force to tip over a cabinet (static equilibrium)
    • Introductory Physics Homework Help
Replies
11
Views
4K

Hot Threads

Recent Insights

Back
Top