Failing the Factor of Safety
Inspired by XKCD’s scientific ‘what-ifs’ I thought I’d give this engineering hypothetical a shot:
“How much needs go wrong before the factor of safety runs out, and a structure collapses?”
Before we start, however, let me draw your attention to the disclaimer at the bottom of the page, and apologise for the drawing- it’s my first time using a tablet.
To make my life easier, let’s call our structure a 5m long cantilevering balcony office, with a reinforced concrete floor slab. For all you hard core engineers we’re talking 200mm effective depth with H20s a 150 centres.
Office blocks designed to current standards expect that floors will be loaded with a maximum of 250 kg/m2, and allow for an additional ‘over-weight’ of 270 kg at the worst possible place. Frankly, even managing to reach this design load is a bit of an achievement. Without filling the office with filling cabinets; the only time I can see our slab reaching design loading is if a mob forms around one hell of a cake.
As it turns out, to break our floor slab we have double our loads to 540 kg/m2, with a sizeable over-weight of 580 kg. This means that even in the light of a new company policy for all employees to drive motorbikes across the office– you’d probably still be safe. Curiously, however, at an average weight of 35 kg and potential density of 21 no./m2, a hoard of penguins would just tip our office floor over the edge. So consider yourself warned.
Length is a different matter altogether. The square relationship between length and moment means that our office slab begins to crack-up at about 6m. Although only one meter, this would be a fairly monumental cock-up for someone not to notice; but worse has been done before. If you do, however, notice a little extra space in the office, or see someone tacking an extension on; it’s probably best to starting making for the exit.
Interestingly, our slab cannot be too deep; the dead load simply doesn’t increase as fast as the capacity. It should be noted, however, that at a certain depth our cantilevered office will simply tip the rest of the building over.
Probably the most variable thing in a reinforced concrete structure is the concrete itself. Prone to variation, and heavily mix dependent, the safety factors applied to concrete represent a significant portion of the total.
There’s no need to evacuate the office block just yet, however, as even the most cowboy of contractors is unlikely not to notice they’re using concrete at the 50% strength required to cause our slab to fail.
Missing the Bar
The only other real construction issue for our ill-fated office slab is missing reinforcement. Once again, however, our cowboy contractor would really have to gunning it: Even if they forget to put in 2 bars for every meter width, our office will still be standing, just.
It’s hard to imagine that someone finding a spare quantity of reinforcement that size wouldn’t begin to suspect problems. Of course it could also have been designed by an architect… (true story).
Some Closing Notes
Before you go converting your office to the motorcycle standard, or adding a cheeky meter to get that dream desk space, it’s worth noting that a real structure will be subject to any combinations of these imperfections and over-loads.
For anyone who wants to check my workings, these were my fundamental assumptions:
- Slab fails in shear or bending only
- Design live load factor as 1.5
- Design steel factor as 1.15
- Design concrete factor as 1.5
- Concrete works at mean strength (+8 N/mm2 from characteristic)