Rationalizing The Minimum Higher

by Don Friedman on June 20, 2016

It’s something of a cliché to note that engineers go through an apprenticeship, where we learn to apply the analysis and sign techniques we learned in college to real-life situations. Many of the differences between theory and practice are subtle, but I want to discuss an example that was as unsubtle as it gets.

In 1987, about a week after I started my first job as an engineer, I was asked to design a concrete slab to span between two masonry walls. In technical terms, this was a one-way, simply-supported slab, which is about as simple as concrete design can get. I sat at my desk for an hour or so with my copy of ACI 318 (the concrete code), a pad of graph paper, a few pencils, and my calculator. By the end, I had a page of calculations and a section through the slab, carefully calling out all the components. Specially, I had calculated the required rebar in the direction of the span to be #3 bars at 10 inches on center, and the rebar at right angles to the span (which would not be stressed by loading) as #3 bars at 12 inches on center. The rebar perpendicular to the span is usually called “temperature and shrinkage reinforcing,” often abbreviated “temperature bars” because its main function is to minimize cracking from those two sources of movement, and the amount of bar is based simply on a percentage of the gross area of the slab cross-section.

Attribution: Mcapdevila A similar slab during construction. Attribution: Mcapdevila

I rather proudly sat down with my boss’s boss, who had given me the assignment, and walked him though my shear, moment, and deflection calculations. He ticked off each correct item on my calculations with a brown Sharpie, which was certainly going to outlast my pencil marks. I got all checkmarks until we reached the cross-section and I mentioned the differing spacing of the bars in the two directions. Then suddenly I had a large brown slash through the page, obliterating the #3@12″o.c. note.

He asked me three questions: how much rebar was I saving by using the bigger spacing on the temperature? How much was that saved bar worth? And, how likely was it that the lathers (the laborers who install rebar in the concrete forms) would get the spacings reversed and give me too little rebar in the important spanning direction? My answers were “I don’t know,” “I don’t know,” and “Probably not very likely.”

Over the course of the next day I figured out that I had saved exactly thirty feet of #3 bar, that the cost of that bar was less than $20, and that every single project manager I asked about this topic had at least one experience of rebar being installed “backwards” with the spacing reversed between the two directions. It was a rare event, but if you work on enough projects it was almost inevitable; and it was most likely to happen when the bar sizes and spacing were similar in the two directions. The solution was, of course, to spend the extra twenty dollars and have the same spacing in both direction.

Theory said that I could use a bit less rebar. Practice said that the potential consequences of a silly mistake on site far outweighed the very small savings I could get. The absolute minimum was a mistake in practice, which is a lesson the could be illustrated with a dozen different examples from everyday structural design. I ended up with a higher minimum that was a rational response to actual conditions. That logic is as clear an example as I could give of why engineering is design and not applied science.

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