They are solid objects, not plastic yet they behave like they are plastic or have moving parts.
When they sway, one side is flexed, the opposite side is compressed, and the other two are being twisted. What is happening to the steel or reinforced concrete frame?
The other two are twisted? Sure, potentially they are, but not necessarily. They could be in pure (or almost pure) bending without torsion.
I’m not sure what you’re asking about the frame. They’re bending. Some of the deformation is in the joints, some is in the physical members themselves. There is no such thing as a rigid object so I don’t think we should expect anything to not sway when subject to a lateral force.
Solid materials (plastic is also solid) can also be elastic. For example, the Young’s modulus of steel might be something like 200 GPa.
Added: see this page for some simple examples of bending calculations. The thing to notice is how the amount of bending depends on the forces applied, the length and cross section of the beam, and the elastic modulus.
Everything flexes, to some degree. The bigger you build something, the more noticeable the flex.
Flex is designed into the braces and support structures. Taller buildings will try to minimize the sway of the building using a damper
I know nothing about architecture or engineering, but I remember when the Sears Tower was under construction, there were newspaper articles about how the building was designed to sway in the wind. I couldn’t recall how so had to look it up. Here’s the explanation:
I don’t know if that’s detailed enough to help.
It also helps them survive earthquakes; they flex with the shockwaves, instead of rigidly resisting and shattering like concrete.
Because I’m a Chicago tour guide, I talk some about this subject and so I’ve chatted a bit with structural engineers about what they call structural drift. There’s a formula for how much is acceptable; without looking it up I want to say 0.4% of the height. For Willis Tower, 443m high, that would be 1.7 meters. Though you hear stories of the water in the toilets showing ripples during high winds, I’ve never seen proof. I think the period of such sway should be on the order of 90 seconds or more.
One of the reasons residential highrises are almost always concrete is that they sway less than steel. People apparently get more uncomfortable living in swaying buildings than working.
As for why nothing breaks, the movement is distributed over dozens of neoprene window gaskets or similarly forgiving exterior (and interior) details. In extreme cases—notably Boston’s former John Hancock Building—the window glass does pop out and fall to the street.
That’s right. Robert Hooke was the first to say that everything deforms, and the degree of deformation is proportional to the force applied.
In simple terms: all the world’s a spring.
(Shakespeare died 19 years before Hooke was born. They were nearly contemporaries).
Yes, but don’t some sway more than others? From the article I linked to above:
That seems like quite a difference. I wonder if the difference is solely due to the tube design mentioned above or if there are other factors.
The basic reason the Empire State does not move a lot is because it’s much more over-designed with regard to strength than later similarly tall steel frame buildings.
Strength basically means how much stress, force per unit area, the material can take without being permanently bent or broken and not springing back, and/or without eventually cracking though it does spring back on the first X (100’s or 1000’s) cycles ie ‘fatigue’. Stiffness is how far the material will deflect for a given force per unit area. Considering a single material strength and stiffness are directly related, so a steel structure might be designed* for strength, or for stiffness. But considering differing materials strength is not directly related to stiffness. Steel is much less stiff than steel reinforced concrete for a given strength.
Newer very tall buildings typically have a lot of steel reinforced concrete in their structures to give low movement in wind without grossly over-designing for strength. Super-tall buildings (like the 828m Burj Khalifa or 1km Jeddah Tower now under construction, v 442m Willis Tower and 381m Empire State) probably would not be practical without steel reinforced concrete construction.
*the ESB wasn’t necessarily consciously designed to be stiff as opposed to being very conservatively designed wrt strength given structural design knowledge at the time. But in some cases structures are explicitly designed to a stiffness not a strength requirement. For example the portions of structure under a large merchant ship’s 100’s to few 1000 tonne diesel engine are fabricated from very thick plates of ‘mild’ (relatively low strength) steel for stiffness, to keep engine and shaft aligned. There is no point in using high strength steel in such a case. The two types of steel will deflect almost exactly as much under a given stress, it’s just that the high strength steel can deflect further without being permanently bent. That’s useful in some cases but not others.
The Hancock building’s tendency to shed glass (until it was fixed) was due to negative pressure caused by strong winds, not the building swaying.
Yup. If an object didn’t deform, the speed of sound in that object would be infinite (and FTL communication would be possible by mechanical linkage)
Not a direct answer to OP, but those participating in the thread may be interested in a fascinating podcast I listened to a while back about a design flaw in the Citicorp building which prevented it from swaying properly under some conditions. Lots of good story elements as well.
Steel is actually a very elastic material, and withstands a huge amount of elastic deformation. That’s why springs are almost always made of steel.
And plastics aren’t very good for it. Plastics tend to deform and stay deformed, rather than springing back to its original shape. In fact that’s what “plastic” means.
They are flexing over a very LONG distance. Each bit is only under a small amount tension or compression relative to it’s neighbors. But there are a lot of bits, so that small amount multiplied a hundred or a thousand times equals quite a large amount. overall. Your house can probably flex an inch or two without causing problems or even being noticeable. So, a building 100x the height of your house could easily flex 8 feet (100 x 1 inch=100 inches, 100 inches = 8 feet 4 inches).
Here are buildings in Tokyo swaying after the 2011 Tohoku earthquake. One of the two featured buildings is the Shinjuku Center Building, 54 stories (223 m) tall. As the video shows, the period for these buildings is much shorter, about four seconds. Not sure what the period for the twice-as-tall Willis tower would be, but I gotta believe it’s far less than 90 seconds.
As for how much distortion of material is required for the top of a tall building to sway by a given amount…I just did a quick drawing in Solidworks for a skyscraper 443 meters tall, 40 meters wide (the Willis tower varies in width, but 40 m is a decent average). I assumed a constant radius of curvature from base to top. If you sway the top 1.7m from its neutral position, the compressive strain on the leeward side of the building (and tensile strain on the windward side) is just 0.035 percent. Depending on the alloy involved, this can be a modest fraction of the amount of strain steel will tolerate before there’s concern about damage.
As noted upthread, windows usually don’t break or fall out because they’re mounted in soft materials that absorb the deformation instead of passing it on to the glass itself. Not much give is required: for a ten-foot tall window, 0.035% strain amounts to a squeeze of just 0.003 inches.
:smack:
Math error: 0.035% strain over a distance of ten feet is more like 0.04 inches. Still easily absorbed by soft mounts.
If solid rock can bend into folds, synclines, and anticlines (look at the geology of central Pennsylvania!), it isn’t much of a trick for metals to do so.