Today we will be talking about Gravity! The force that causes things to fall down!
Every building ever built has an implacable and immortal foe in the Force of Gravity.
Every part of every building that isn't resting directly on the ground is experiencing a force (GRAVITY) that wants nothing more than to convert the potential energy of that part - at the moment temporarily suspended above the surface of the earth (Gravity will ALWAYS win in the long haul) - into kinetic energy (motion through space) leading to the satisfying SPLAT! of said part impacting the surface of the planet at an acceleration of 1 G, at which point electromagnetism takes over abruptly halting the parts voyage towards the earths center of mass, and thereby converting the parts kinetic energy, (née potential energy), into a crater, a lot of heat, and a net increase in the entropy of the universe as a whole.
This is not to say that the part that IS resting on the ground isn't experiencing an acceleration of 1 G, it is, it's just that the part has nowhere to go since there's a planet in the way, and it is currently in the lowest energy state it can attain, (all else being equal). If you could turn up the gravity below the object, at a certain point/level/volume ("Our Amps go up to 11!"), which would vary depending on the density of the foundation, the object would sink into the surface and continue it's journey towards the earths center of mass.
So the trick is building things in such a way that the force of gravity is counterbalanced by the strength of the electromagnetic repulsion between the buildings load bearing members and its foundation.
In the early days of construction there were serious limitations in what could be built due to the materials available.
Stone and Concrete are great materials under compressive loads, unfortunately stone and concrete have, well, pretty much no strength at all under tension. And not a hell of a lot of strength under shear loads. So to build with stone you can only pile things on top of other things. And once you reach the compressive limit, the base of the building will announce that fact by sudden and catastrophic failure. i.e. exploding. (There may be some cracking prior to failure, but then again there may not be.)
Wood has good resistance to compression along the grain, but is not quite as resistant to compression across the grain, wood is fairly resistant to shear loads applied across the grain, while shear loads applied along the grain tend to split it (see Axe, Wedge, Splitting Maul) and is remarkably strong under tension. So Wood is in many respects a wonder material! But, like kryptonite for Superman, wood has a weakness, Fire!
Another limitation (prior to the invention of Glulam™) was trees only grow so big, so wooden beams came in limited lengths therefore carpenters had to join pieces together for long spans. Unfortunately every joint is a place where stresses concentrate and the structure is weakened.
All these problems were discovered quite some time ago, still, the builders of the Great Cathedrals took stone as a structural material, (combined with the ARCH), to it's absolute limit. As is evidenced by the number of Cathedrals which collapsed while under construction and those which failed later. Cathedrals were not engineered as we understand the term, and there isn't a functioning country or government on the planet which would allow a single one of them to be built (as is) today.
Then came STEEL!
Steel is amazing stuff. Incredibly strong under tension, compression, and shear loads, it's fire resistant, can be welded, rolled, bolted, riveted, and be made pretty much any size you want.
Below is a simple diagram of a steel frame building.
The horizontal members carry the floor loads and transfer them to the vertical posts where they are transferred vertically to the foundation. In three dimensions, a steel frame is just a bunch of interconnected boxes with all the horizontal members transferring their loads to the vertical members at their connection points.
So long as the vertical posts have more load carrying capacity than the total loads transferred to them from the horizontal beams, the building will stand, all else being equal. But, (and this is a BIG but), this applies only so long as the load path and local gravity are in perfect alignment!
I. E. Only so long as NO SIDE LOADS (aka wind loads....) are applied to the structure.
The builders of the Great Cathedrals were the first to "discover" the power of gently (a warm summer zephyr), or not so gently (a gust front or autumn storm system), moving air .
Once you get up above the roofs of the town and the surrounding trees, there's almost ALWAYS a breeze blowing. And the higher you go, the faster the air is moving. A breeze may not sound like much, but a 20mph wind is applying a force of 1.2 lb ft^2, or 120 lbs per every 100'^2.
30 mph = 270 lbs per 100'^2
40 mph = 480 " " "
So what happens when you have thousands of ft^2 of wall?
At Chartres the walls are approx 15,730'^2
@ 20 mph, 15,730 x 1.2 = 18,876 lbs of side load.
(the above is grossly simplified, but you get the idea)
Solution? The Flying Buttress!!!! (A clever and beautiful way to convert side loads and roof loads into vertical loads.)
But you begin, I hope, to see the problem.
So what happens when a side load is applied to an unbraced square frame of any sort?
Have you ever opened a box, and then stepped on it?
Squashes right flat don't it?
Well a steel frame will behave in exactly the same way. The joints where the horizontal members attach to the vertical members will, under a side load, begin to act more like hinges than load transfer connections.
Notice that the gravity load (which is always vertical) and the load carrying path no longer line up? As the building drifts from the perpendicular, more and more of the load is shifted away from the posts vertical load path and onto a cross section of the post. The post acts less and less as a vertical load carrying structure, (because it isn't any more), and more and more like an arm (lever) applying a multiplied load to fixed end of the post.
"Give me lever and a place to stand and I can move the World."
In fact all high rise buildings are levers, but since one end is fixed, and (one hopes), immovable, while the other is free to dance about, they're a special form of lever called a cantilever.
So excessive flex is not a good thing, loads end up not over their supports, i.e. unsupported, members which should be under compression end up under tension and vice versa, more and more of the load is supported by AIR... not, and eventually the building falls over.
The P Delta is the point at which gravity wins and the building falls over. Tall buildings need to flex a bit. But not too much. You want to keep your flex below the P Delta.* Since the WTC towers never exceeded their P Delta there was absolutely no reason for them to fall over.
But there were a lot of reasons for them to fall down.
So we have a problem with our interlocked squares/boxes.
A square is not a strong structure.
A triangle, on the other hand, is an incredibly strong structure. (They have Infinitesimal Flex!)
Unfortunately, isosceles triangles suck at transferring vertical loads at all, and right triangles can only transfer vertical loads along one leg.
What to do... What to do....
Hey! You got chocolate on my peanut butter!
Hey! You got peanut butter on my chocolate!
Enter diagonal bracing! Aka making a
square from
two right triangles!!!
Or you can build a Shear Wall.
With a shear wall you fill in certain squares with vertical walls of reinforced concrete or other strong material and that, like a diagonal, prevents the building from flexing excessively
(My house has an open floor plan so the few walls I do have in my house are shear walls since where I live tends to rock and roll on a regular basis. The Castle Mountain Fault is a mere 20 or so mile from my house and is expected to produce a 7+ shaker sometime in the next hundred years or so. Be prepared! That's my motto! )
So if you combine triangles and squares you can build REALLY strong structures! The problem, from a rental point of view, is that lots of vertical posts (pillars) eat up rentable space, and result in lower rental income. Plus they use a LOT of material. And material costs money.
(The K bracing and Eccentric bracing above are used in seismic areas where you want a certain amount of ductility in the structure. The Eccentric and K braces have more flex and so help dissipate seismic energy. Seismic bracing is another whole kettle of fish, and type and placement will vary greatly depending on building height, resonant frequency - Every building has a resonant frequency - and the type of ground underlying the building. They have absolutely nothing to do with the WTC towers. I just live in a very active seismic zone, and I think they're interesting.)
One solution to the excessive loss of rental space is the Tube Frame of which the WTC towers were early examples.
*Actually the structure should never ever even get anywhere remotely close to P Delta because people have to live and work in these buildings, and the last thing you want is people getting motion sickness, or being flung around, every time the wind blows.
