In my previous post I discussed the impact of the semirigid diaphragm mesh size on the analysis results, and presented the results of an informal study of a structure using a range of mesh sizes. Two of the sizes included a 1-foot mesh and a 30-foot mesh. The results were that a small refined mesh is not necessary, and that a larger mesh in the range of 4ft to 8ft is probably acceptable, with the benefit of substantially faster analysis times.
In a previous article I mentioned the difficulty in determining the proper semirigid diaphragm material properties, such as the elastic modulus, moment of inertia, poisson’s ratio, etc. The problem is made more difficult when the effective properties are a function of span or the patterns of connection to the framing; these will vary over the floor plan, potentially necessitating a tedious definition of the properties in different areas. This is especially true for untopped metal deck and wood-framed flooring systems.
To determine the sensitivity on the analysis results of the accuracy of the diaphragm material properties I once again created a model and performed a series of analyses, this time using varying values of effective modulus of elasticity, E’, ranging from 500 ksi to 24000 ksi. For comparison the model was also analyzed with a rigid diaphragm.
The correct value of E’ for this model is probably around 2000 ksi, but the purpose of this study was not to prove any particular value, but rather to see how much the results vary when there are large changes in diaphragm properties. So using 500 ksi as the baseline, the following results were compiled for the frame story shears at each level:
Surprisingly, if the diaphragm stiffness is varied by a factor of 48 times, the distribution of the story shears to the frames varied at worst by less than 4%. It is also noteworthy that if 2000 ksi is approximately the correct value to use in this model, incorrectly specifying a value that is one-fourth that value (500 ksi) or four times that value (8000 ksi) would have virtually no impact on the results. It indicates that in the distribution of the forces to the frames, the results are not sensitive to the diaphragm properties; even a large error will have negligible impact on the results.
Note the large error in the frame story shears when the diaphragm was modeled as Rigid; as much as 67%. Again, this shows that the Rigid diaphragm assumption is not appropriate for some conditions, in this example a narrow diaphragm and untopped roof deck.
In addition to the frame story force comparison discussed above, the results for several other structural responses were similarly tabulated and compared. Space doesn’t allow for an exhaustive presentation of those results here, but a few things are noteworthy. The impact of varying diaphragm stiffness properties on the diaphragm shear across the narrow segment of diaphragm was considerably more pronounced: there was a 23% difference between the value given with an effective E’ of 500 ksi and that given with an effective E’ of 24000. That difference dropped to 8% for an effective E’ of 8000 ksi and was 2% for an effective E’ of 2000 ksi. The differences in story drift at the most critical end of the structure, measured at a point on the diaphragm corresponding to the location of a frame column was minimal between an effective E’ of 500 ksi and that given with an effective E’ of 24000: less than 5%. However, the differences in story drift measured at a point on the diaphragm that was 30 ft from the nearest frame column was highly impacted by the values of E’; small values of E’ resulted in large values of drift, and the drift decreased roughly proportionally to the increase E’. These results are probably not realistic however, because the analysis did not include the drag beams or the gravity beams which would have provide significant stiffening of the diaphragm in those areas that were not near the lateral frames; investigating the drifts at the frame column locations provides more realistic drift design values, and as indicated above those were only nominally impacted by the value of E’ used in the analysis.
I suggest that it is sufficient to make a best effort at determining and defining the diaphragm properties, recognizing that even if they are somewhat off the analysis won’t be significantly impacted. Make a reasonable but practical effort. Don’t spend undue time trying to define the slightly different properties in every different region of the diaphragm.
Again, you need to recognize that this is just one small example, and the study was certainly not exhaustive. As I stated last time, you should take advantage of the analytical tools that are now available to you to create your own models and do your own studies. You need to decide for yourself what you are comfortable with.
This concludes the discussion of each of the diaphragm types – Flexible, Rigid, and Semirigid – individually. In the next article I will discuss the differences in how the lateral loads are determined and applied for each different type of diaphragm. The next article in this series is Loads on Rigid, Semirigid, and Flexible Diaphragms.
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