Engineering Fundamentals: Equilibrium
What do Civil Engineers and Zen Buddhists have in common? They both believe in, and constantly strive for, equilibrium (nothing to do with Christian Bale).
Before Newton invented equilibrium in 1686, the world remained in check because of Aristotle‘s assertion that everything has its natural place.
A few weeks ago I had to do a test. Amongst other things it was on the fundamental principles behind classical engineering. Considering I have a degree in the subject, I did pretty badly. My excuse is this: In design we mostly use applied principles. In my eight pages of Eurocode calculations, or my report about the impact of loading on arches, I very rarely have to derive the more advanced theories and practices I’m applying. So intermittently, throughout this year, I thought I’d do a series on the fundamentals- as much for my own sake, than anyone else’s!
“Thou shalt always have static equilibrium”
The principle is easy: the sum of all the actions acting on a structure should come to zero.
Before Newton invented equilibrium in 1686, the world remained in check because of Aristotle‘s assertion that everything has its natural place. That is: rocks like to be on the ground, and therefore they fall, unless propelled by an external agent. About 1800 years later Gallilio chipped-in; removing the sense of belonging that came from a ‘natural place’ and instead suggesting that things move at a constant speed (which includes ‘at-rest’, unless you’re at the gym) until they are forced to change.
With his best seller: the Philosophiæ Naturalis Principia Mathematica Newton refined these theories with over 200 experiements (which seems overkill to me) and derived the infamous laws of motion. As far as Civil Engineers are concerned this was when it all began; hence the BN/AN (Before-/After- Netwon) calander we use amongst ourselves. The logic goes as such:
- Structures neither move, nor do they accelerate (this is an axiom that the public insists on…)
- Therefore the ‘velocity’ of the structure, and all of the components that make it, is always zero.
- That means that the net force on the structure is zero (Newton’s first law)
- All forces applied to a structure are due to accelerating masses (e.g. cake-mob loading; Newton’s second law)
- At a global level these actions on the structure are resisted by the reactions of its supports (Newton’s third law)
Like all good articles of faith, however, this doesn’t quite stand up to scrutiny; that is- Newton took the assumption that everything is a single point of mass. 50 years later, however, Euler wrote a second testament: “Laws of Motion 2: Motion Harder“, which bridges the gap. In practice, however, the distinction is rarely made by Civil Engineers.
So the next time you pick-up some engineering calculations (as I’m sure you do everyday), look-out for the incantation ΣF = 0. By invoking this statement, engineers call the structure into equilibrium; and once you know that a body is in equilibrium, working out the forces at any point within the structure is as simple as balancing the equation.