## Monday, 23 September 2013

### Three Basic Principles

There are three basic principles every civil engineer must understand.

F = ma
The simple explanation:
Force is equal to mass times acceleration. Newton said so.
The real explanation:
The equation is just a mathematical expression of Newton's Second Law. It applies to everything in civil engineering. Beams, columns, cranes, entire bridges, flowing water, you name it. All of the forces acting on a non-accelerating system must sum to zero. If a = 0 then F = 0. That's where we get the equations of statics, which are so important that every engineer (not just the CivEs) learns them in their 1st year engineering mechanics class. Because if you don't satisfy statics, the structure will do it for you:
 This crane had to tip over in order to satisfy the equations of statics.

You can't push a rope
The simple explanation:
If you try, you get this:
 Ropes have a habit of offering no resistance to compression.
The real explanation:
Obviously this doesn't mean that you can't push a rope in the sense that a coil of rope can't be pushed up a hill. But a rope can't be utilized to resist forces in compression, because ropes are made of a bunch of very slender fibers all woven together. To resist tension, the only important geometric parameter is the total cross-sectional area. So when it comes to tension, it doesn't matter if you have one 100 mm² rod or twenty 5 mm² wires. Compression is different. Cross-sectional area is only important when the thing you're squashing is short compared to its thickness. Otherwise, you get buckling and the important geometric parameter becomes the second moment of area (civil engineers call it "moment of inertia"). Providing the same total cross-sectional area with many smaller parts gives you a much smaller moment of inertia. For example, the 100 mm² rod has a moment of inertia of about 796 mm, but the twenty 5 mm² wires have a combined moment of inertia of only about 40 mm. That's a 95% reduction in buckling capacity. Ropes are usually pretty slender to begin with, and then when you go and divide the cross-section up into dozens of fibers, you end up with negligible capacity to resist compression.

Water flows downhill
The simple explanation:
Because of gravity.
 It's how rivers work. All of them.

The real explanation:
Again, this doesn't mean water can't be forced to go uphill. How else would everyone get hot showers and flushing toilets in high-rise buildings? But to do so, you have to apply a force large enough to beat gravity. Otherwise, water flows downhill. It's the reason rivers flow from tributaries in the mountains down to lakes or seas below. It's the reason sewage lines are downward sloping wherever possible. Pumping waste uphill costs money, and if there's a problem, the local people are quick to complain about it. It's also the reason flat roofs aren't supposed to actually be flat. They're supposed to be gently sloped towards drains so that the roof doesn't become a swimming pool. If your yard slopes toward your house, you're much more likely to have a wet basement after a heavy rain. Water's everywhere. If not properly controlled, it causes a significant amount of property damage. Putting "water flows downhill" into practice is the best way to manage water and prevent damage.
 This roof slopes to the corner instead of the drain. Stagnant water provides a mosquito breeding ground and can eventually leak through flaws in the roof as it ages.

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