The problem with concrete deflection calculations
Most people would think that when a concrete beam is designed and constructed that if you took that beam and applied the design load the actual deflection would closely match the computed deflection. They would be mistaken. The actual deflection would be as much as 20% lower and 40% more than the calculations indicate.
For those who think I am making this up, consider this quote from a standard text on reinforced concrete design:
Although the research engineer in the laboratory is able to carry out carefully controlled load tests in which measured instantaneous elastic deflections are within 20 or 30 percent of those predicted by empirical equations for deflection, the practicing engineer must expect deviations greater than 30 percent between and measured deflections of beams constructed under actual field conditions.
From Reinforced Concrete Design, 2nd edition by Kenneth Leet, PhD (MIT)
Leet uses 30% on the high side, but remember that number is for a reinforced concrete beam created in an engineering laboratory by research engineers.
For field conditions, it gets worse
The ACI (American Concrete Institute) publication Control of Deflections in Concrete Structures, 1995 puts the upper bound at 40%. Consider the following quote:
It should be emphaszied that the magnitude of avtual deflection in concrete structural elements, particularity in buildings, which are the emphasis and the intent of this Report can only be estimated within a range of 20-40 percent accuracy. This is because of the large variability in the properties of the constitiuent materials of these elements and the quality control exercised in their construction. Therefore, for practical considerationse, …computed deflection values …ought to be interpreteted within this variability.
Control of Deflection in Concrete Structures, ACI 435R-95, 1995, page 3.
The bottom line
The evidence is clear: practicing engineers do not know how much a concrete reinforced beam will deflect for a given load. They only know that it may deflect less than calculations suggest and it may deflect significantly more.
To make matters worse, the calculated deflection is for live loads only while our measurements are made on a