Unslender Skyscrapers

The picture above is a 1900 Detroit Publishing portrait of the Ellicott Square Building in Buffalo, an 1896 building with a full steel skeleton frame, designed by D. H. Burnham & Co. of Chicago. It’s still there, and it shows up in The Structure of Skyscrapers. Of course, to modern eyes, it doesn’t really look much like a skyscraper. Partially, that’s its height (ten floors, 144 feet) but really it’s the stockiness. It has a slenderness ratio of 0.7, which seems squat no matter how tall it is.

This issue affects structural design, too. The difficulty in designing tall buildings is not really in dealing with gravity load. Yes, those loads can be quite high, but they are linear (double the height of the building and you double the load at its base) and their effects are linear (double the compressive stress in a column and you double the amount that the column gets shorter under load). You might end up with more or bigger columns than you want, but you can deal with the problem.

The difficult lies in lateral load. For the sake of simplicity – keeping this blog post under 5000 words – I’m going to simplify the problem a bit. I’ll assume that the building, like Ellicott Square, is rectangular in plan and elevation, with only typical floors at the same vertical spacing, and I’ll only look at wind load, not seismic. The general discussion below applies in broad terms to seismic loading, and by looking at wind only I can talk about the original design of buildings built before seismic loads were first put into codes. The last simplifying assumption: let’s say that the overall wind pressure used for frame design (what is in the current code referred to as the wind on the Main Wind Force Resisting System) is the same for the full height of the building. That may not even be an assumption: for a building this height, it’s possible that a minimum wind load might apply to the full height.

If we treat the building as an undifferentiated block (what engineering students are introduced to as a “free body diagram”) then the building is effectively a cantilever beam sticking up out of the ground and loaded with a uniform pressure. I used this diagram not long ago and here’s that beam, turned on its side:

Treating the building as a block doesn’t get us very far. One thing we can definitely say is that linearity is well behind us. Doubling the height of the building will increase the bending moment M by a factor of 4 (W is the uniform load per foot, usually represented as lower-case w, times the length, so the moment M here is wL²/2) and increases the maximum deflection at the tip D (sideway at the top of the building) by a factor of 16.

Ellicott Square has a moment frame: a jungle gym of steel beams and columns rigidly connected at the joints. The lateral push of the wind is converted into bending, shear, and longitudinal forces in each beam and column. But it’s a very stocky building, with many bays of columns of beams in the plane of the wind force. A lot of slender older buildings, and some new ones, are only one bay wide, so the forces and moments in the frame have to be resolved in a limited number of members that are, relative to the height, closely spaced. It’s hard to directly com[are the frame stiffness with the simple stiffness (EI) of the beam model above. The moment of inertia for a beam (I) is proportional to the cube of the beam depth, so increasing beam depth is one of the most effective ways of controlling deflection. In very very rough terms, the stiffness of the frame also increases disproportionally fast as the frame width increases, reducing the sideway.

So it’s not just visually that a building like this differs from most modern skyscrapers. It’s also easier to design for the stresses and sway of lateral loads.

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