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Excess Capacity From Unexpected Action

“Excess capacity” is a fancy way of saying that something is stronger than it needs to be. One way of looking at excess capacity is that it’s inefficiency. I prefer to think of it as a resource to be tapped. If a structure is stronger than it needs to be, then it can accept an overload or some damage without becoming unsafe. Old steel-frame buildings often have a great deal of excess capacity in their beams because of changes in code: we now allow bending stresses that are a higher percentage of the yield stress of the steel than were allowed in 1920 or 1930.

The picture above shows a soon-to-be-repaired column in a 1920 steel-frame building downtown. I like the way the material loss to rust makes it look like someone took a bite out of the column’s flange, but capacity calculations don’t like it. The obvious question: how scary is this? More specifically, was the column near (or past) overload because of the damage?

Column capacity is a funny thing to analyze. The two extreme cases – a very slender column and a very stocky column – are easy to analyze, but the in-between levels of slenderness are not. Very slender columns fail by buckling: their middle suddenly moves sideways and they lose nearly all capacity. (Steel columns, which typically have a cross-section composed of multiple thin pieces, flanges and webs, can have overall buckling triggered by local buckling of those constituent pieces, but that detail isn’t very important for this discussion.) Very stocky columns fail by crushing at the compressive limit of the material. We’ve got equations that do a pretty good job of describing the performance of columns of in-between slenderness, but they’re not based on theory, they’re based on curve-fitting. They’re engineering at its finest, taking lots of empirical data and turning it into a usable guide for design.

That column, like just about all columns in steel-frame buildings, was designed with the assumption that it’s unbraced between floors. That length – one floor-to-floor height – is half of the information you need to calculate the slenderness. The other half is the radius of gyration, a geometric property of the cross-section, in the weak-axis direction. The length of the column is generally unchanging, although I guess we could add bracing at the mid-floor height if we wanted to amuse ourselves by watching building occupants walk into steel. The radius of gyration got smaller in the damaged portion of the column, and in some damaged columns we’ve seen, it’s been reduced for an entire length of column, floor to floor. But is the column actually unbraced?

The column, before we started work, was encased in a continuous masonry pier, built as fire protection for the steel. The pier wasn’t intended to be particularly strong, but it takes a surprisingly small counter-push to prevent buckling. For the years leading up to now, with the masonry intact and the steel damaged, it’s quite likely that the column has been at least partly braced by the masonry. Such accidental bracing doesn’t reduce the actual stress in the steel, but it can raise the allowable stress significantly higher than the design value, thus creating excess capacity so that the bite out of the steel doesn’t cause a failure.

It’s still going to fixed.