Q for engineers & others: Will the volume of a steel box change when deformed?

[RootSkier]

This might be plane on a treadmill adjacent, but it is a serious question for engineers, know-it-alls, and other dorks:

Consider a steel dumpster that is ostensibly 3 cubic yards in size. As it is loaded, lifted, dumped, and set back down, it obviously gets dents and other types of deformations.

Question: Is it more likely that these deformations increase or decrease the internal volume of the dumpster?

The background of this involves a real-world scenario where I have a purported expert opining that deformed dumpsters generally increase in volume. This seems insane to me. I have read the abstracts of mathematical studies (which I don't understand) that basically assume that solids undergoing plastic deformation maintain the same volume, but we are obviously not dealing with a solid object here.

Moreover, I can't get past the fact that if you have an empty aluminum can, fill it to the brim, and try to deform it it any way, that it is going to lose volume and force water out of the can.

But I can also see why a three dimensional box-type shape with angled sides could theoretically increase in volume depending on the elasticity of the steel or other facts (e.g. can the middle of the top front edge of a dumpster be forced "outwards" in a way that doesn't also deform the sides, which could potentially lead to an increase in volume?).

One more data point is that this expert literally wrote in his report that "the floor deflection that occurred due to the undersigned's weight of 290 pounds was approximately 1/4 inch." I find this hilarious, because these dumpsters are used for residential/business purposes, rather than industrial, and I have a hard time believing (a) that fatboy would put this in his report and (b) that these dumpsters frequently see 290 pound point loads.

Regardless, he went on to conclude that "While it would be difficult to measure and calculate the exact amount of volume created from wall and floor outward bending of each container, this outward bending creates more unloaded container volume, which will be unique to each container from its unique outward bending."

What say you all?

[carlh]

Dumpsters are rectangular not cylindrical like a can. Any dents pushing walls out will increase volume. Any dents pushing walls in will decrease volume.
When you throw heavy shit in the dumpster and it hits and dents that wall that pushes it out increasing volume. I would expect that happens all the time.
To push a wall in you would have to hit it from outside which I would expect happens less frequently.

[californiagrown]

i read the first sentence of your post.

depends. If you cram shit into it that deforms the sides out (think punching out a toe box in a ski boot) then the volume increases. If your frontend loading garbage truck keeps missing the side slots and slams its forklift arms into the front, then you are decreasing the volume.

My guess, is that your guy is talking about how overtime, the floor of the dumpster is slightly deformed downwards by the years of heavy garbage and so the volume is increased. It would be easy to measure by simply filling it with water at the beginning, and then filling with water at the end and measuring/metering the volume of water used.



Why do you care?

[warthog]

Pretty simple. Take the same amount of metal required to make a rectangle, and make it into cylinders and spheres- do those hold more? Probably- they have rounded corners. There must be some shape that holds more volume than others, but maybe it is finite. Maybe if you have enough metal to hold 3 cu yards, that is all that that amount of metal will hold, no matter the shape used, but I doubt it. I am sure there is an easy equation for this, but you aren't increasing the amount of material it is made of, just changing the shape. I guess if the side dents out 1 inch, the object may shrink by 1 inch somewhere else?
Also, we have to account for the material stretching- a dent tends to thin the metal out a bit, so 12 gauge may become 13 gauge, giving it a little more volume.

From messing with body work, I can tell you that the metal surely thins when worked. That has to figure into the equation.

[RootSkier]

Why do you care?

Because I am fighting with a company that lied about the size of its dumpsters for a very long time.

[RootSkier]

Dumpsters are rectangular not cylindrical like a can. Any dents pushing walls out will increase volume. Any dents pushing walls in will decrease volume.
When you throw heavy shit in the dumpster and it hits and dents that wall that pushes it out increasing volume. I would expect that happens all the time.
To push a wall in you would have to hit it from outside which I would expect happens less frequently.

Ok, but consider a top rail. If you bend a straight piece of metal, the straightline distance between the two ends gets shorter, right? Does that not happen with the sides of a dumpster if the front or back rail is bent?

[californiagrown]

Because I am fighting with a company that lied about the size of its dumpsters for a very long time.

The amount of volume that it would increase/decrease is negligible...as long as the dumpster is still in decent shape. If these guys had dumpsters whose sizes were out of compliance, it would be by half a yard or more... not by a couple dents here or there.

[toast2266]

Pretty simple. Take the same amount of metal required to make a rectangle, and make it into cylinders and spheres- do those hold more?

A sphere will always have the highest volume for a given surface area. And I'm sure a heavy handed trash truck operator could turn a dumpster into a sphere given the time and inclination. Presumably they would do so at around 4 a.m.

[californiagrown]

Ok, but consider a top rail. If you bend a straight piece of metal, the straightline distance between the two ends gets shorter, right? Does that not happen with the sides of a dumpster if the front or back rail is bent?

No it doesnt get shorter... necessarily. The distance can stay about the same and the top rail just lengthens/deforms.

You are also forgetting that the dumpsters arent holding water. The amount of trash and shit that they hold is approximate, doesnt fill up every nook and cranny, and certainly isnt bounded by the top edge.


We obviously dont know the story, but it seems like you are majoring in the minors here and arguing about +3yard dumpsters being out of compliance by a few cubic inches which is laughable to anyone inolved in trash or construction.

[toast2266]

Because I am fighting with a company that lied about the size of its dumpsters for a very long time.

They're trying to say the dumpsters aren't undersized because they have dents and deflection that increase the volume?

[RootSkier]

The amount of volume that it would increase/decrease is negligible...as long as the dumpster is still in decent shape. If these guys had dumpsters whose sizes were out of compliance, it would be by half a yard or more... not by a couple dents here or there.

So if someone was providing "3 YD" dumpster service but the dumpsters measure exactly 2.5 cubic yards, by their expert's own admission, you'd think it was "out of compliance"?

[warthog]

Ok, but consider a top rail. If you bend a straight piece of metal, the straightline distance between the two ends gets shorter, right? Does that not happen with the sides of a dumpster if the front or back rail is bent?

All depends on the elasticity of the metal. Dumpsters tend to be made out of metal that dents easily, probably so they do less damage to the shit hitting them.

[californiagrown]

So if someone was providing "3 YD" dumpster service but the dumpsters measure exactly 2.5 cubic yards, by their expert's own admission, you'd think it was "out of compliance"?

Whats the tolerance for "in compliance"? is 2.99cy in compliance? is 2.84CY in compliance?

Does the supplier mean a 3 yard dumpster can hold ~3 yards of crap, or its volume is dead-nuts on 3 yards? Are you being charged based on the size-type of the dumpster, or on the volume of the dumpster, or on the weight/volume of crap you put in the dumpster?


When you order 10yards of dirt to be delivered, are you going to whine and moan about it only being 9.5 yards? and it being even less than that once you have it compacted to spec?

[toast2266]

So if someone was providing "3 YD" dumpster service but the dumpsters measure exactly 2.5 cubic yards, by their expert's own admission, you'd think it was "out of compliance"?

Are the lids completely flat with the top, or do they kinda curve a bit providing some volume above the rim of the metal box? So is it supposed to be 3 yards within the metal box, or 3 yards with the lids closed (which, depending on the lids, might be exactly the same)?

[Dhelihiker]

I think a basic understating of geometry gets you there. You dont have to drag engineers into this.

The answer is yes