We mostly assume that materials are 90% as strong as they say they are, that the building weighs 1.2 times as much as it really does, and that stuff in the building weighs 1.6 times as much as it really does. The total factor of safety is something like 1.5.
The reason that buildings don't vibrate (noticably under service loads) is that people would get queasy, so we design things for stiffness as well as strength. Aircraft are more space and weight limited, and no one is sitting on the end of the wing, so the engineers mostly just care that everything will stay attached.
Low FoS yes, but even if you doubled it to 3, you'd still see the wing tip moving - only half as much.
Truck trailers are also very soft in torsion. See an empty one go over a big bump and it'll visibly twist. Not close to failure, just not very stiff.
I'd be really worried if 1 was "A fully loaded plane of 180lbs adults with two checked bags of 50lbs each flying in clear blue skies with no wind."
For the FAA part 23 certified aircraft, the basics are here (for Federal laws, these are written in fairly plain English, but you need to hop around a bit at times): http://www.ecfr.gov/cgi-bin/retrieveECFR?n=pt14.1.23#se14.1....
For FAA part 25 certified aircraft (transport category aircraft): http://www.ecfr.gov/cgi-bin/text-idx?rgn=div5;node=14%3A1.0....
On the outset, there are different failures possible, tensile, warping, etc.
Under a load distribution, a structure would fail at some point depending on the intensity of the load. It could be tensile or due to bending moment. Call that L. Now, you would add flitches or increase say, the thickness of a plate to withstand upto 1.5L. That is a design with a 1.5 times factor of safety.
For example, a small bridge in a seldom used road in the countryside might have a few cars per hour. That's a load of a couple of tons per car. But cars density isn't randomly distributed. If one is slow, then there might be a lineup of 4 cars in a row, and that's more likely then a simple calculation based on 1-(1-p)^4 where p is the single car density.
Then twice a day there's the school bus. And there's the occasional cattle truck, and semi, and anhydrous tanker. So you might have a school bus with a couple of heavy vehicles behind it, as a possible maximum design load.
The odds of this can't be described with a simple Gaussian, so standard deviations make no sense.
Of course, there's no need to go crazy overboard and design all bridges to handle a convoy of M1 Abrams tanks. That's why rural bridge might have a posted weight limit of, say, 10 tons, with only 1 truck allowed at a time. Even then, some people will push the limits, which is why there's a safety factor.
For example http://blogs.mcall.com/roadwarrior/2014/08/wehrs-mill-bridge... describes a wooden bridge which had a 10 ton limit, until some dumbass fuel tanker weighing 38.2 tons went through. Now the rated limit is 4 tons because of the structural damage.
So it's not "the maximum that was ever recorded in the dataset of all rural bridges" but "the maximum expected for this bridge", along with efforts to restrict higher loads.
In reality, cyclic fatigue is also considered.
This seems like a nice discussion that shows the complexity:
http://www.coe.montana.edu/me/faculty/cairns/Introduction%20...
Blow on a stretched rubber band, and it'll vibrate, too.
A factor of safety is applied to a design after every load the structure will be subjected to is calculated, they multiply by 1.5 to be sure the structure will be safe. 1.5 may sound conservative but it is the smallest factor of safety someone normally encounters, spacecraft and fighter jets might use 1.2 while cars often use 3; buildings and bridges use 5. Airplanes are used much closer to the strength limit of their materials so we see them flexing.
Of course everything deflects under load - my strength of materials instructor illustrated this by analyzing how much an anvil compresses when a fly lands on it; answer: less than can be measured.