Computational Errors in Estimating Concrete Member Deflection

Science is oftentimes not an “exact science”.  We all do our best to understand the physical world as precisely as possible, but there will always be limitations: those that are simply unavoidable (part of nature and consequences of our limited scientific vocabulary), and others that can be attributed to the simple fact that we are human beings.  We make errors, not always due to negligence or incompetence, and we can be stubborn.  As we study and attempt to understand things of science, it is important to deal honestly with the tools of the trade.  When consulting research, it is important to understand the basic conclusions and how they apply to the question being answered.  When reviewing the results of testing, it is important to understand the constraints set in place that allow the testing to be possible (and reliable), and to understand the application of the results and conclusions.  When performing calculations, it is important to know when more advanced forms of analysis are necessary (or preferred), what effect variability and uncertainty have on the input (how “real” is the assumed dead load), and what factors can lead to inaccurate or incomplete conclusions.  Part of the process of managing calculations involves knowing potential avenues for error and avoiding or compensating for them in some way.

 As I assembled a PowerPoint presentation on the serviceability of concrete slabs, I came across a great article written by Russell S. Fling entitled Practical Considerations in Computing Deflection of Reinforced Concrete, part of a collection of papers published by the American Concrete Institute, “SP-133: Designing Concrete Structures for Serviceability and Safety” (1992).  In his paper, Fling identifies some of the computational errors that can create a discrepancy between calculated and actual deflections of concrete members, which I’d like to summarize here.

  1. There are 10 steps in calculating deflection and error can creep into any of these steps, so an engineer needs to be cautious and attentive.  These steps include (1) load, (2) moment, (3) location of center of gravity of the gross section, (4) uncracked moment of inertia, (5) section modulus of the gross section, (6) cracking moment, (7) cracked moment of inertia, (8) effective moment of inertia, (9) instantaneous deflection, and (10) long-term deflection.

  2. Live load might be incorrectly assessed.

  3. Redundancy might not be considered.

  4. Factored loads might be inadvertently used instead of service loads.

  5. Maximum moments from pattern loading might be used instead of actual moments.

  6. Complexities of dealing with T-beams might be ignored.

  7. Using average values of the moment of inertia instead of specific values.

  8. Rotation of the support for cantilevered beams might not be correctly accounted for.

Problems in serviceability of concrete members can be revealed by unanticipated or extensive cracking, movement or damage to nonbearing partitions, sticking of doors or windows, or noticeable vibration.  It might not be enough to just rely on the standard ACI 318 formulas for calculating minimum slab thicknesses, and you should be ready to determine expected deflections when needed to evaluate the usability of your design.  When doing so, use appropriate care in your work and be aware of the possible pitfalls discussed above.