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

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?

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.

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?

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.

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Originally Posted by californiagrown

Why do you care?

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

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Originally Posted by 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.

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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?

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Originally Posted by RootSkier

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

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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.

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Originally Posted by 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?

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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.

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Originally Posted by RootSkier

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?

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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.

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Originally Posted by RootSkier

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

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

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Originally Posted by californiagrown

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.

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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"?

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Originally Posted by RootSkier

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?

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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.

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Originally Posted by RootSkier

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"?

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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?

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Originally Posted by RootSkier

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"?

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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)?

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

The answer is yes

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Originally Posted by toast2266

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)?

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The lids add volume. There are several different "3 YD" models. The smaller ones are 2.44 cubic yards measured in a flat plane across the top. The addition of a lid gets them to 2.52 yards.

The company charges an "overage" if there is too much garbage in there. What constitutes an overage is disputed, but the company now says it requires a full extra yard of garbage. Not sure how that helps when that means you are paying for 4 yards of service but it is only providing 3.

FWIW, your choices are 1.5 yards, 2 yards, or 3 yards. The 1.5- and 2-yard dumpsters are the "full" stated yardage, and some of the 3-yard dumpsters are too. But the vast majority of the "3 YD" dumpsters are undersized.

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Originally Posted by RootSkier

The lids add volume. There are several different "3 YD" models. The smaller ones are 2.44 cubic yards measured in a flat plane across the top. The addition of a lid gets them to 2.52 yards.

The company charges an "overage" if there is too much garbage in there. What constitutes an overage is disputed, but the company now says it requires a full extra yard of garbage. Not sure how that helps when that means you are paying for 4 yards of service but it is only providing 3.

FWIW, your choices are 1.5 yards, 2 yards, or 3 yards. The 1.5- and 2-yard dumpsters are the "full" stated yardage, and some of the 3-yard dumpsters are too. But the vast majority of the "3 YD" dumpsters are undersized.

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Yeah, but if it's got a bunch of dents, it's probably at least 2.53 yards.

As a sitting member of the TGR jury, you've convinced me. Fuck those guys. Take them to the cleaners.

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Originally Posted by RootSkier

The lids add volume. There are several different "3 YD" models. The smaller ones are 2.44 cubic yards measured in a flat plane across the top. The addition of a lid gets them to 2.52 yards.

The company charges an "overage" if there is too much garbage in there. What constitutes an overage is disputed, but the company now says it requires a full extra yard of garbage. Not sure how that helps when that means you are paying for 4 yards of service but it is only providing 3.

FWIW, your choices are 1.5 yards, 2 yards, or 3 yards. The 1.5- and 2-yard dumpsters are the "full" stated yardage, and some of the 3-yard dumpsters are too. But the vast majority of the "3 YD" dumpsters are undersized.

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1) switch services
2) if that service is the only service in town, demand to pick from the available 3yard dumpsters. and or request new dumpsters be delivered until you get one close-enough to 3yards.
3) be careful picking this battle. There are likely all sorts of conservative specs regarding their service that they typically ignore, but now might start enforcing on you because you decided to pick this fight. (E.g. path of travel for their truck and clear area, they might skip you guys every so often, etc). Make sure the juice is worth the squeeze.

Also, there is a very good argument that their volumes are approximate, and no different than stating they have Small, medium, large and XL dumpsters for you to use, which correspond generally to certain volumes.

Thanks. That is pretty much the universal response to the easiest elevator pitch case of all time.

A class is already certified and, separately, a False Claims Act complaint has been unsealed and served. I was just re-reading the defendants' own expert report and laughing.

I wondered if volume had something to do with the widget in a can of guinness but its about the nitrogen

I think dents in a dumpster will lower the volume, I mean thats why people crush beer cans

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Originally Posted by californiagrown

Also, there is a very good argument that their volumes are approximate, and no different than stating they have Small, medium, large and XL dumpsters for you to use, which correspond generally to certain volumes.

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You sound like a defense attorney who plays fast and loose with discovery. They keep changing their defense, from "wE diDn'+ r3pR3s3n+ nE sp3cifik siz3s" even though it's right there on the invoice to "derp some of them are full size derp so it will be too derping hard to figure out who had derp dumpsters at specific derp times."

Fuckin' thieves. And they were a monopoly until a new company came to town and this all came out in a Public Service Commission contested case. Whoops!

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Originally Posted by RootSkier

You sound like a defense attorney who plays fast and loose with discovery. They keep changing their defense, from "wE diDn'+ r3pR3s3n+ nE sp3cifik siz3s" even though it's right there on the invoice to "derp some of them are full size derp so it will be too derping hard to figure out who had derp dumpsters at specific derp times."

Fuckin' thieves. And they were a monopoly until a new company came to town and this all came out in a Public Service Commission contested case. Whoops!

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Eh, i work on the private side of engineering so im used to making "common sense" arguments when we cant exactly meet code. Also, my wife is running 4 or 5 false claims class actions right now, so i practice arguing devils advocate on these kind of things at home.


Their experts claim of dumpsters enlarging over time is legit, but its a neglible amount if we are saying these dumpsters were undersized by 20% from the start. Overfill charges on small dumpsters might be easy enough to recover, but you arent paying by the volume, you are paying by the size category and nailing down what is an acceptable tolerance to qualify as being the correct size will be important. That last part is subjective, and id have to assume they have some fine-print somewhere saying the actual volumes advertised are approximate. But didnt you say that they also allowed you to overfill by 1CY before penalty?... wouldnt that mean they were providing 0.5-1CY additional volume than they advertised?

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Originally Posted by californiagrown

you arent paying by the volume, you are paying by the size category and nailing down what is an acceptable tolerance to qualify as being the correct size will be important. That last part is subjective, and id have to assume they have some fine-print somewhere saying the actual volumes advertised are approximate. But didnt you say that they also allowed you to overfill by 1CY before penalty?... wouldnt that mean they were providing 0.5-1CY additional volume than they advertised?

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I disagree with your first premise. If your choices are 1.5, 2, or 3 yards, and the smaller sizes measure true to size, but the 3-yard ones do not, isn't that problematic? It sure seems like it to me. Additionally, these were kind of a one-off that was ordered for a single market, and they were not the fabricator's standard 3-yard dumpster. Moreover, they switched a few years ago and all of the newer 3-yard dumpsters measure true to size. If providing dumpsters that were significantly smaller than advertised was within the bounds of commercial reasonableness, why wouldn't they do it everywhere all the time? If you were one of the largest solid waste handlers in the country, think of how much money you could return to your shareholders if you simply provided less than customers paid for all the time!

Further, there is definitely not any small print anywhere, and the entity keeps changing its position about whether 3 yards means the true size of the dumpster or the amount of service provided.

"If you were one of the largest solid waste handlers in the country, think of how much money you could return to your shareholders if you simply provided less than customers paid for all the time!"

Pretty sure that's the general plan.

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Originally Posted by Cisco Kid

"If you were one of the largest solid waste handlers in the country, think of how much money you could return to your shareholders if you simply provided less than customers paid for all the time!"

Pretty sure that's the general plan.

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If it was, all of their newer dumpsters would be undersized as well... but theyre not. All of their new dumpsters are apparently accurately sized.


to me this reads as a company growing really quickly and using whatever they had on-hand to fit into the marketing, instead of spending the money to upgrade their older product. Or it reads as a regional operator trying to boost profit by cutting expenses (upgrading/buying new dumpsters to replace the weird ones on-hand or that they bought used from someone).

they probably thought that the smaller dumpsters were "close enough", and if they gave customers 1CY overfill for free that it was all good.



Was the 1CY of overfill for free advertised, or not? If it wasnt advertised, then werent they actually providing 3.5-4CY of dumpster service, but only charging for 3?


Also (and this is related), my complete inability to only consider arguments presented by the attorneys, and not consider arguments i makeup in my own head is why i will never be selected to a jury.