How Reliable Are Deflection Calculations?

It is naive to believe that just because a concrete is expertly designed using an allowable deflection ratio of 1/360, that the resulting beam will deflect in accordance with the design. However, most people are surprised at how inaccurate these calculations can be. Consider this extended quote from a standard engineering text authored by an MIT Ph.D.:

A study of deflections of reinforced concrete beams must account for instantaneous elastic deflections as loads are first applied, as well as for the long-term deflections that develop due to creep and shrinkage and continue to increase over a period of several years. Under a constant value of load, by the time long-term deflections reach their maximum size they are generally of the order of twice the magnitude of the initial elastic deflections.

Kenneth Leet. Reinforced Concrete Design, 2nd edition McGraw-Hill, Inc. 1991, New York

Notice that deflection is broken into two parts: immediate deflection and a deflection (called creep) that develops over time. The maximum creep deflection may be of the order of twice the magnitude of the initial deflection, so creep deflection has to be taken into account. The standard design procedures do consider creep deflection.      

Although the research engineer in the laboratory is able to carry out carefully controlled loading 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 predicted and measured deflections, constructed under actual field conditions. Deflections are minimized when beams are carefully constructed out of high-strength low slump concretes that are well compacted and effectively cured. In the field the  engineer has a certain limited control over construction methods and procedures by means of the plans and specifications covering the design of concrete mix and details of placing steel and concrete; however what the designer specifies what the construction crews produce can differ widely. Water content may be increased at the job site, incomplete compaction may leave voids and honeycombing, and reinforcing bars may be improperly positioned. By reducing the quality of the concrete, these and other construction procedures can produce members that will undergo larger than expected deflections.

Here is a quote on this same issue lifted from An ACI publication: 

It should be emphasized that the magnitude of actual deflection in concrete structural elements, particularly 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 constituent materials of these elements and the quality control exercised in their construction. Therefore, for practical considerations, the computed deflection values… ought to be interpreted within this variability. 

ACI 435R-95 Control of Deflection in Concrete Structures. Reported by ACI Committee 435. American Concrete Institute Box 19150 Redford Station, Detroit Michigan 48219  

Why are these calculations such poor predictors of performance

There are several things to keep in mind. The purpose of any design method is to produce a design that has resulted in a satisfactory product. There is no question in my mind that the published design methods result in structurally adequate reinforced concrete structural elements. I am not criticizing the current practice.    

There are a number of reasons why making reliable estimates of deflection. Concrete is very difficult to model realistically.

For instance, we assume that concrete is homogeneous.  This is a significant simplification, but it is necessary for a quantitative design procedure. It is normally assumed that after 5 years the total deflection will be three times the initial deflection. That calculation is just an estimate. It is based, in part, on the calculated initial deflection which could be off by as much as 40% according to the ACI.

Other causes of poor deflection estimates include sand pockets, voids, and honeycombing in the stiffening beams. Sand pockets I have watched many concrete slab pours. Not once have I seen a vibrator used in the interior stiffening beams. In fact, it is my experience that even the perimeter grade beams are not vibrated. Instead, a worker will pound the perimeter form boards with a sledgehammer. This can do an adequate job, but a vibrator will produce a better and more consistent job.




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