Calculating the exact material properties of diaphragms to include in your structural model can be a time consuming task. Often times, structures with semi-rigid diaphragms also take longer to analyze due to the additional degrees of freedom. Semi-rigid diaphragms can be more complex to analyze than their flexible or rigid counterparts. However, accurate analysis results may not be so hard to accomplish within a short amount of time.
In the May 2020 SE University session, Allen Adams, PE, SE, from Bentley Systems, Inc. / RAM, presented Practical Strategies for the Modeling and Analysis of Diaphragms. Allen explained the differences between flexible, semi-rigid, and rigid diaphragms and how these affect analytical results. He reviewed code requirements pertaining to diaphragms and shared how sensitive analytical models are to the various components of semi-rigid diaphragm models. Allen advised on balancing the necessary level of accuracy with business demands for speed and simplicity when modeling diaphragms.
Allen presented several case studies which examined varying diaphragm properties to see their influence on the structural analysis results. For example, Allen questioned how much influence does mesh size have on the analysis results? Allen used the same model with the diaphragm mesh varying from a 1 foot mesh to a 15 foot mesh. Assuming the 1 foot mesh is the most accurate, Allen examined the percent difference between using a smaller mesh versus a larger 15 foot mesh. The analysis results for the frame story shears, surprisingly showed a minimal difference between the smaller mesh and the larger mesh. However, the time required for the analysis to be complete was significantly higher for the smaller mesh. A more average mesh size on the order of 4 feet or 8 feet resulted in similar frame story shears while still completing the analysis in a shorter time frame similar to the larger mesh.
Allen also examined how material properties of the diaphragm affect the analysis results. Specifically, Allen examined how much influence does inaccuracy in the effective modulus of elasticity (E’) have on the results? Allen analyzed the same model while varying E’ from 500 ksi to 24000 ksi. Again, surprisingly, while the effective modulus of elasticity was varied by 48 times, the results only varied by 3.7 percent. While this is just one example, it shows that it is not necessary to spend hours nailing down the exact E’ of the diaphragm, especially in complex instances where it may vary throughout the same story. A close estimate will suffice to garner accurate results. There was some additional variability when examining the moment within the diaphragm as the E’ was varying, however, when a close estimate is assumed, the resulting moment remained accurate. Minimal variability was noted when examining the story drift at the frames, however there was significant differences noted in the drift away from the frames. Allen noted that it would be more appropriate to look at the drift at the frames rather than away from the frames for accurate drift results. Also, the drift results measured at points on the diaphragm away from the frames did not account for the stiffness added from the presence of gravity framing which would also limit those story drift results.
Overall, Allen’s case study examples proved to be enlightening for engineers that feel they must model the diaphragm down to the tiniest detail to get accurate analysis results. It is worth noting that having a general idea of the material properties will suffice and the model does not need to be so detailed that the analysis takes an extreme amount of time to complete.