Analysis For Investigation 2

After yesterday’s long and somewhat esoteric discussion, a much more straightforward topic: what material is a beam? The piece of a photo above shows a metal frame being enclosed in masonry, where it will be hidden from view. How can you take an educated guess at the material (wrought iron or steel?; if steel, which strength?) without testing?

To keep this from getting too bizarre, I’m going to make two assumptions. First, we know what general type of material we’re guessing at. In other words, we know it’s a wood joist, or a heavy-timber beam, or a ductile metal beam, or a reinforced-concrete beam. The earliest stages of an investigation should get us that far. Second, the beam was designed as simply supported (if wood or ductile metal) or continuous at both ends (if concrete). This is usually, despite my somewhat twisted example yesterday, something we can get a sense of through early investigation.

The approach is to set up the basic calculations for bending stress and deflection in the beam and run through a bunch of scenarios. (This is where computers come in handy: cut & paste for equations is something that would have interested me intensely in 1988.) You can usually get an estimate of the dead load plus or minus 20 percent; of the code live load more exact than that; of the beam span and tributary width of load within 5 or 10 percent. You may have exact beam sizes or maybe only depths, or maybe only estimates of geometry. If it’s concrete, you will probably have the beam geometry but not the rebar sizes. In other words this is a calculation where one significant figure is the best you will do. All this inaccuracy is okay, for the reasons described below.

The first check on accuracy is to look at the current actual live load, which should make the demand side of your equation pretty accurate. For example, if it’s in an apartment house and the load above is ordinary apartment use, the code live load is 40 psf and the actual is around 10 or 12. Add that to your dead load estimate, multiply by the tributary width, plug that into the beam formulas and behold: you have a moment estimate. You can get a deflection estimate as well, if you take a guess at the stiffness. For metal beams, that’s a useful starting point, since you can measure the actual deflection and work from both ends, estimating the beam properties and looking at the known results. Because wood creeps, using defection is less helpful there.

This is where the different scenarios come in. Engineers, now and in the past, tend to design beams to have bending stress fairly close to that allowed by code. The biggest exception is when the designs are controlled by deflection, but that was rarer in the past because of the shorter spans used and the lower allowable stresses. In any case, looking at common beam sizes (that fit the known geometry) in the possible materials (different species and grades of wood, different strengths of wrought iron, steel, and concrete) will give you a spread of bending stresses and expected deflections. There is often a cluster of sensible results near one of the expected allowable maximum stresses. Checking multiple beams the should have different loading or are known to be of different sizes helps, too. Estimating tends to scatter, and the odds of multiple analyses having the same scatter – all being off in exactly the same way – is low.

This is neither ordinary analysis and design nor ordinary reverse engineering. It’s a guessing game where the results are fit into a pattern through logic…it’s twenty questions.

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