Precision and Variance in Engineering Calcs

concrete pour
These guys don’t care about tolerances.

In the course of trying to determine the load capacities of some 50 year-old concrete slabs, I came across this little tidbit of engineering wisdom, published in the 1956 CRSI Design Handbook:

Precision of Computations for Reinforced Concrete

If the somewhat involved mathematical methods used in rigid frame analysis lead one to believe that the design of reinforced concrete structures requires a high degree of precision, such is not the case. Concrete is a job-made material. Tests or control cylinders that do not vary more than ten per cent are remarkably good. Reinforcing bars may vary in strength from three to five per cent; weights can vary 3 1/2 per cent. Formwork also has its variations; frequently a 2×8 or 2×10 (measuring, respectively, 7 5/8 and 9 1/2) is used to form the soffit of an 8 or 10 in. beam. Bars that are held in place to an accuracy of between 1/8 and 1/4 in. are extremely well placed. Two figure accuracy is sufficient for almost all problems in reinforced concrete design.

Concrete is weak in tension; reinforcing steel is supplied to make up that deficiency; the time and effort of the designer is best spent in recognizing and providing for such tensions wherever they may exist, not in striving for a high degree of mathematical precision by carrying figures to an excessive number of places.

This is still good advice today. Sitting in an office with a calculator that will happily spit out numbers past the decimal all day long, it’s easy to forget that construction, and concrete especially, is a game of tolerances and imprecision. It’s mixed by the yard and the pound. Everything is assembled by hand. And it’s all done by someone who only wants to finish as fast as possible without the inspector chewing him out, correct spacing and clearance be damned.

With modern software packages, it’s always possible for an engineer to spend an asymptotically increasing amount of time making more and more exact calculations, refining your designs more and more. But the precision they give is a false precision, when your f’c might actually only be 3900 instead of 4000, and your bar clearance might be 1 1/2″ instead of 1″. Instead of worrying that, say, a member’s capacity is a fraction of a percent under the calculated load, an engineer is better served by taking a step back and understanding the behavior of what he’s designing.

Of course, this also goes to the point that modern complaints about engineers who use software with no understanding of the numbers it spits out aren’t exactly new.

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