Stacking an object

[harrytos23]

Good Day,

I am just wondering if there's a direct way to calculate how high we can stack an object on top of another before it becomes unstable (wobbly) where it can fall into someone?

Let's use the book analogy, the object will be rectangular shape and let's assume they aligned properly. Any inputs would be appreciated because the only thing I can think of is if the bottom object(book) can handle the weight of the objects will be on top of it. Like when the bottom object starts to deform then there's the limit right? Please enlighten me.

 

[rb1957]

how rigid/flexible (particularly to lateral loads) are the books ? I expect the mass is stabilizing, but increasing height makes the tower more susceptible to lateral loads ...

 

[harrytos23]

how rigid/flexible (particularly to lateral loads) are the books ? I expect the mass is stabilizing, but increasing height makes the tower more susceptible to lateral loads ...

when you say rigid what do you mean? The object I'm referring is a rectangular shape like books but 750 lbs each and 12" is the height per item. I did FEA and it can handle 10 of them without any deformation but the question I have now is, what is the amount of this object can be stacked on top of one another before it becomes unstable.


But if you're asking how rigid each one is, it's made of ASTM A36.

 

[lucky-guesser]

If they are infinitely rigid, or made of something that effectively doesn't compress like concrete blocks, they will be much easier to stack.

You get a stack of boxes that weigh 50lb each, you get 6 high and all is well, then someone comes by and bumps the bottom one putting a dent in it and causing it to buckle, that's when the 300lb crumbles.

Then when you are folding towels, you can only go a few high, because they are so flexible that as you stack them they essentially (and quickly) just become one big cloth noodle that can't balance under its own weight.

Say you think your bottom "book" will compress unevenly under the weight, with worst case scenario having your top and bottom surfaces 5deg out of parallel. You could use that angle and the height of your stack to locate your CoG and find how tall you can go before your CoG is no longer within your base. If you get tall enough, deflection and eventually wind loads also become an issue.

This is just off the top of my head thinking, estimations at best I'm sure. Perhaps some structural guys will have an idea as I'm sure this is at least somewhat analogous to skyscrapers.

 

[Ron247]

I assume you are only looking at the tower being unstable due to the vertical weight of the materials, not falling over due to a gust of wind from the side or someone shaking the item the tower is on.

The main parameters to start with are density of the materials, plan view dimensions, thickness of each layer/level and how easily one level can slide across its adjacent level. I have never learned any current method of solving this puzzle. The instability is not just from compression of the materials, it is also because any item in compression is inherently unstable. As you compress the materials, they begin to move perpendicular to the load seeking relief from the vertical compression. They tend to buckle.

Before undertaking your current "column of books", why don't you look into a solid column made of steel or wood. A single tower. See what controls the buckling of it and then expand to your situation. Your problem is harder because the layers are not secured to each other.

 

[GregLocock]

Each book will have a torsional rigidity (about the axis into the screen in your picture). As you stack them up there is a compressive load due to the weight of the books, and at some point you will get Euler elastic buckling, which for self weight was first correctly solved in 1912. This is only one possible failure mode.

 

[MintJulep]

Stacks become unstable when the weight vector at the CG moves father than the center of pressure at the base, in response to small perturbations.

It's mostly about stiffness and geometry.