Historic Structural Detail: Load Sharing

by Don Friedman on February 4, 2016

Good design ideas can show up anywhere, even on a fire-escape stair:

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What’s the purpose of those little straps at the center of stair, connecting tread to tread? If we analyze the stair in the usual manner, with a uniform load over each tread, the straps don’t make it any stronger or any stiffer. The straps do not change the fact that the treads have to be strong enough to span laterally between the stringers by themselves, carrying the code live load of 100 psf.

What if we look at real-life loading? This is a fire egress, and its worst-case loading is carrying hundreds of people out of the building. When people walk, there is a repeated moment when all of their weight is one foot, and the average American adult weighs approximately 180 pounds. Each tread is approximately 11 inches deep and three feet high, and is meant to accommodate two people walking side-by-side, so the real-life load I expect on a tread is two people, each balancing one foot, for a total of 360 pounds. That averages to a little over 130 psf. So far, so bad: I seem to have proven that the code-mandated load is too low.

But, what about occupancy geometry? People can pack together pretty tightly when standing on a flat surface but walking, and particularly descending a stair, takes more room. Even the most crowded stair has some space between people or they literally cannot move. So if a stair tread has two people with their full weight on it, the treads immediately above and below will be unloaded; during the other half of the step cycle, when their weight is split between both of their feet, there may be some overlap between people on individual treads, but their load is more evenly distributed.

What about loading geometry? If two people are on one three-foot-wide tread, they have to be pretty close to the edges of it. Three feet is actually not enough room for two average adults to stand side-by-side with their shoulders squared, so walking in that space will require them to keep as far apart as possible and to twist their torsos a bit. So the loading from individual feet will not be at the center of the tread width, but rather pushed towards the outer ends.

Back to that mysterious strap: it allows load sharing by hanging the center of the tread from the tread above, and posting down to the center of the tread below. In the case where a tread is occupied by two people, each with their full weight on one foot, a portion of the load will go to the tread above and a portion to the tread below, effectively halving the load. The loaded treads shed one-quarter of their load to the treads above and one-quarter to the treads below, reducing their load by half. The “unloaded” treads gather one-quarter of a loaded-tread load from the treads above and one-quarter from the treads below. The loaded and unloaded treads will share load so that they are loaded, roughly, equally.

Even better, because the load on the loaded treads is not centered, the bending moment in those treads is lower than a uniform load would suggest. Since the mechanism for load sharing is the deflection of the tread mid-point pulling and pushing on the straps, the entire system is stiffer than shown by the uniform load model.

What does all this mean in a practical sense? The treads had to be designed to meet the code uniform load, which they do, barely, But their performance is better than that bare-bones design because of real-life loading and geometry, and the clever use of those straps to share load.

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