The photo above is from the HABS survey of an abandoned Armour & Company plant in Providence, Rhode Island. The building was a warehouse and factory for meat products, and had some mildly interesting Moderne architectural touches. It was abandoned, vandalized, and then demolished. I chose the picture for the nice view of the big smokestack.
As we head towards a future without fossil fuels, it occurs to me that someday smokestacks will look weird to people. We deliberately built structures to push polluting smoke high into the air so that it would be either diluted or someone else’s problem downstream. The latter scenario is exemplified by acid rain. Meanwhile, in the era of buildings that I most frequently work on – the last third of the nineteenth century and the first third of the twentieth – chimneys often seemed to be a form of bragging. The more chimneys a factory had, the more important it must be, or something like that.
In order to avoid the design fallacy, chimneys have to be completely hollow. That means the only way for forces to move from one side to another is around the perimeter, so a structural model of a chimney resembles, more than anything else, a cantilever beam made up of a hollow tube. The reason I’m focussing on the bending in the chimney is that chimneys rarely fail because their gravity load – their self-weight – is larger than their capacity. They fail because of lateral load – wind or seismic forces. While it is in theory possible to build a free-standing metal chimney, the old ones fall into two main categories: free-standing masonry chimneys, like Armour’s, and guyed steel chimneys. The guyed chimneys are a little boring from the analysis perspective: you resolve the lateral force into tension in the guy wires and then size the wires and whatever they’re attached to. The chimney just has to span between the bracing points created by the guys, and you can make those spans as small as you want.
The big masonry chimneys are a more interesting juggling act. You need to keep the masonry in compression, since no one would trust the brittle nature of unreinforced masonry in tension for a tall and slender structure with zero redundancy. The compression in the masonry from gravity load goes up linearly (double the height of the chimney and you double the compression at its base) while the wind load goes up a bit faster than by the square of the height. If the wind pressure and chimney cross-section are constant, then the wind pressure goes up exactly by the square; chimneys often taper a bit but more importantly the wind pressure is greater at higher altitudes. Roughly, doubling the height of the chimney quadruples the bending stress from wind at its base, creating tension on the windward side and compression on the leeward side. So we have to worry about the combined gravity and wind compression exceeding the capacity of the masonry and we have to worry about the wind tension exceeding the gravity compression. The height of the chimney is typically set by mechanical concerns (i.e., what height provides the draw necessary and gets the smoke far enough away) and can’t be changed by the structural engineer. Making the chimney wider increases the wind load linearly but increases the section modulus of the “hollow beam” section by the square, so it’s a net benefit. It’s easy with a computer to iterate the calculations but must have been quite annoying when doing this by hand.