Friday, May 18, 2007

My Beer Bed

My basement apartment is prone to flooding, a problem I shall have to correct with my landlord, hopefully before the next time it rains heavily here. In addition, the frame for my bed broke several months ago, so my box-spring has just been sitting on the floor. When water streams through / around a window in my bedroom, the resulting mini-flood tends to wet the box-spring, which takes a day or two at least to dry out. Having my bed elevated above the floor would be a big advantage.

The solution to this problem was discovered by my sister, who, while helping me clean up from the most recent flood, suggested a use for the cases of empty beer bottles I posses.

Et voila!


The other side.

I know at least one of my readers is a structural engineer - can someone please tell me exactly how stupid I am for placing my bed on 36 empty beer bottles in cardboard cases? Only the glass is bearing any weight, and all of that weight is vertical (I hope). What's the crush force for a beer bottle? I'm planning on increasing the number of supporting bottles, primarily by drinking more beer. So now I can claim any beer I buy as "for structural purposes".

The comedy part, besides the fact that I appear to be regressing in my university education, comes from the clinking noises every time I roll over in bed.

12 comments:

TR Gregory said...

Somebody get that man some milk crates!

Carlo said...

It's even better than recycling! It's like those families that make craft-art out of everything rather than throw it away... Circle-Square ranch... ungh...

King Aardvark said...

Hmm, I'm working on the calcs right now (seriously, I am). In the meantime, my official structural engineering opinion is to use one beer bottle on each corner just to see what happens. If still standing, start jumping up and down on the bed.

After you clean up the broken glass, proceed with your current plan of buying beer for structural purposes.

Anonymous said...

Martin-- its you other sister here. What about the soggyness factor? Won't the boxes suffer next time it floods? Steal yourself some milk crates...

Mike said...

Hammock!

Necator said...

I concur with gregory....milk crates...any self respecting student knows this.

King Aardvark said...

My official structural engineering opinion is to use one beer bottle on each corner just to see what happens. After you clean up the broken glass, proceed with your current plan of buying beer for structural purposes.

You are quite right to hope that all the weight is vertical. Glass is fairly good in straight compression but it’s brittle and not great in bending, tension, or shear. As you surmise, you can improve your lateral resistance by bundling your bottles in the cardboard boxes; however, these boxes are not the most stable method of ensuring all the bottles work together. For instance, if your apartment floods again the boxes may disintegrate. Perhaps wrapping each bundle of bottles with duct tape would be an improvement.

Now lets look at the actual forces and resistances:

Resistances
Reduction Factor for Glass
g = 0.4; assumed, note concrete is 0.6
Strength of Glass
Fr = 5 ksi = 34.474 MPa; reference
Thickness of Glass
t = 1.8 mm; reference
Least Diameter of Bottle
D = 16 mm
Least Circumference of Bottle
C = 3.1416 * D = 50.266 mm
Cross-Sectional Area of Bottle
A = t * C = 90.478 mm2
Strength of a Single Bottle
Crbottle = A * Fr = 3.119 kN
Number of bottles
n = 36
Total Factored Resistance
Cr = g * Crbottle * n = 44.915 kN

Loading
Assume Average Person Weight of
Pperson = 180 lbs = 0.801 kN
Assumed worst case Number of People
np = 4; friends/family crashing or you get EXTREMELY lucky
Dynamic Load Allowance
DLA = 1.25; assumed
Live Load Factor
LF = 1.5
Weight of Mattress and Box Spring
Pbed = 240 lbs; assumed
Dead Load Factor
DF = 1.25
Total Factored Weight
Cf = LF * Pperson * np * DLA + DF * Pbed = 7.340 kN

Notes; Crbottle = 701.207 lbs; Cr = 10097.374 lbs; Cf = 1650.000 lbs

As we can see, four bottles ought to be able to handle all the weight pretty easily assuming forces are fully vertical and no overturning takes place. Big if. Also note that my estimates of the compression resistance of bottles is probably high because I’m neglecting the effects of local stress concentrations (eg. Where the wide part meets the long skinny neck, also scratches in the glass). Glass in its ideal state is actually about 2.5 times as strong in compression as steel, but in practice is much weaker than that due to stress concentrations caused by small imperfections. Testing would have to be done on actual beer bottle samples to determine what the real individual bottle strength is.

In general, the brittleness of glass is bad because all looks well right up until the moment everything comes crashing down. In structural engineering, we try to ensure that any structure will fail in a ductile way before it will ever fail in a brittle way since it will give time to evacuate the failing building. Of course, it would be good if you had some ductility with your bed. Another problem with glass is that it is very susceptible to fatigue. Our assumed glass strength here is 35 MPa but it might decrease to half that if you use the bottles to hold the bed for a long time, say a year.

I also say you should not use milk crates. That would be too easy.

TheBrummell said...

Assumed worst case Number of People
np = 4; friends/family crashing or you get EXTREMELY lucky


I'd call that a BEST case number of people, not worst.

Thanks KA, that's exactly what I was hoping for.

Hmm, I'm working on the calcs right now (seriously, I am). In the meantime, my official structural engineering opinion is to use one beer bottle on each corner just to see what happens. If still standing, start jumping up and down on the bed.

After you clean up the broken glass, proceed with your current plan of buying beer for structural purposes.


Thanks for the professional advice. I like the experimentalist approach, very empirical!

Also, just out of curiosity, how much would such an opinion normally cost?

I'm guessing the strength of plastic milk crates is probably not as high as perfect-quality glass, but would fail in a ductile way rather than the rather unpleasant brittle way. Milk crates are a controlled substance in my area, whereas beer bottles are available for retail purchase (usually filled with a nutritious beverage as a bonus).

Another factor to consider is height. I am quite fond of the headboard I have, given it provides extra bed length for my pillow, important for someone of my height. This extra space only fits properly if the top surface of the mattress is the same distance above the floor. Beer bottles in (soggy) cases are about 1.5 cm too short - close enough I can use them, but a little sub-optimal.

I like the idea of bundling the bottles using duct tape or similar, that would also allow me to position each bottle under the box-spring's frame more exactly and ensure a more even distribution of weight.

Anybody have any suggestions for how I might add, say, 2 cm to the height of a load-bearing beer bottle?

King Aardvark said...

I spent about 1.5 hours on it yesterday (much of which would be billed to a steel company in Toronto that I was supposed to be doing work for, so you're off the hook for the bill). Much of the work was just searching for a decent approximate glass strength.

Since I'm not a P.Eng. yet, my opinion isn't really worth that much at the moment, so my part of the bill would probably end up being only $100-200. If you want a document stamped by a PEng you could easily double that.

We call it worst case because it's the produces the highest load, but yes, best case there. Note though that the average person weight is 180 lbs. I don't know how much you weigh, but if you have 4 people and they average more than that, then you're probably in worst case territory. Unless you're into that kind of thing.

Suzanne said...

Martin, you make me laugh!! Suzanne

TheBrummell said...

Note though that the average person weight is 180 lbs. I don't know how much you weigh, but if you have 4 people and they average more than that, then you're probably in worst case territory. Unless you're into that kind of thing.

Good point. Your estimate of my rest mass is pretty good - the last time I checked (months ago) I massed 78 kg on the balance at the gym. This seems a little low; for months at SFU I was checking every week and I was pretty stable at about 185 lbs.

I hope to avoid 4-somes in which the mean mass of the people involved is so high.

daedalus2u said...

The problem isn't so much the strength of the bottles, it is the distribution of load between them. To do that, you need a deformable material at the interface.

I also agree with your sister that the soggyness factor is more important than the strength factor.

What you need to do is:
1. lose the cardboard. It provides no structure and will wick water up to your bed.
2. make the structure "fail-safe". I suggest getting a roll of tape. Duct tape would be best, but expensive. Shipping tape would be ok, depending on how well it stretches and can contain breakage. Wrap each bottle with a layer of tape to confine the shards of glass when (not if) they break. Ideally you will remove the lable because the lable can wick water up too. Covering the lable with hydrophobic tape will help.
3. Back to the deformable interface. I suggest sand. Although another material to consider would be concrete. Concrete has the advantage of becoming permanant (but heavy). What you do is after you wrap each bottle whith tape, you fill it with dry ready-mix concrete powder which you can obtain from a store such as Home Depot. You could make it light weight by first filling the bottle with styrofoam peanuts (until it is full), then filling the voids with the concrete powder. When you have a whole case, cut the cardboard box such that there is about 2 inches deep. Put about 1.5 inches of concrete powder in the box, then invert the bottles and nestle them into it. You want to get the tops of all the bottles into the concrete powder, and have all the bottoms (now pointing up) in a plane. This plane is what you rest your bed on. Use the remainder of the cardboard to make a deformable interface between your bed and the bottoms of the bottles.

Once the bottles have "settled in" somewhat, and the load is distributed among them, you can wet the concrete powder, turing it into solid concrete. Once the water wicks up into the bottle and sets the concrete powder there, the system is now fail safe. Even if the glass does break, the inner concrete structure will support it. It would be a good idea to use the carboard dividers temporarilly to keep the bottles apart until the concrete sets. The bottles will be much stronger if they are not scratched, the tape will prevent that too, but a small gap is always a good idea. The cardboard should be removed to prevent wicking.