Accuracy of Deflection Calcs (and Eee)
Deflections and Average Modulus of Elasticity
(c) Jeff R. Filler, 2022
A word on the accuracy of deflection calculations … wood beams, joists, etc.
In the example above (link) we calculated a deflection of 0.599 in. How accurate is this number? (I showed it to three significant figures … accurate to half a percent?) Leaving out, for now, the accuracy/precision of the other input, and the deflection equation itself, let’s look at Modulus of Elasticity, E. Take a look at Appendix F of the NDS (National Design Specification® for Wood Construction). It points out that the Modulus of Elasticity values in the NDS Supplement (which we used to calculate the deflection above) are average values. Yeah. I get that. Note that it goes on to say that individual pieces will have values higher and lower than the average. (Of course! … the age old panic that half the students in the class are performing `below average’!) And then the Appendix goes on to say how we might calculate the (lower) values. Let’s take a look!
Equation F-1, for example, can be used to calculate the E value at one standard deviation less than the mean, E 16, whereby we would get an E value for which we would expect 16 percent of the pieces (in that species and grade) to have a value less than that calculated. Let’s do it.
E 16 = E (1 – 1.0 COVE)
For sawn lumber (from Appendix F), COVE = 0.25, for glued laminated timber COVE = 0.10, and so on.
So, for the (sawn lumber) example where E = 1,800,000 psi, E 16 = 1,800,000 psi [1 – 1.0 (0.25) ] = 1,400,000 psi (0.75) = 1,350,000 psi. Whoa, 1 out of 6 pieces of lumber might very well have an E value of 25 percent of the average value, or even less … or … 1 out of 6 pieces of lumber might very well give us 25 percent more deflection than we calculated.
Note: the example linked above is that of a plank loaded (only) with a concentrated load at mid-span. It’s a real life scenario, but not one that would be a permanent part of a building. In an actual building we would not accept a deflection of 0.599 inches for an 8 foot span. We would come up with a different spanning member, or different framing system.