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The recent postings concerning floor vibration analysis have been interesting. I am the first author of the AISC/CISC Design Guide 11, "Floor Vibrations due to Human Activity" and the author or co-author of a number of paper and articles in AISC publications. I admit that I never stated that the procedures in these publications apply only to rectangular or nearly rectangular bays but they do. It never occurred to me or my co-authors that someone would want to apply the procedures to triangular or trapezoidal bays. All of the examples are for rectangular bays, which I guess we thought would define the limits of the DG11 or earlier procedures. If they could be applied to other bay configurations, we would certainly have provided examples for such.

I have been involved with floor vibration evaluation for over 40 years. I get questions on a daily basis and reports of floor problems at least monthly. There has never been a report of a vibration problem that did not involve rectangular or nearly rectangular bays. Once I tried to measure the response of a triangular bay and was not able to excite it sufficiently to get a good measurement. Whenever anyone asks about the vibration of significantly non-rectangular framing, I tell them that I would not be concerned and that there is no need to do an analysis. Now if the bay is slightly non-rectangular, I recommend, as an approximation, to use the average span length in the DG11 procedures. What's slightly? Engineering judgment is required.

On the subject of using FE analysis for walking vibrations. We at Virginia Tech have been working on this problem for several years. If one "walks" a standard footstep pulse like the one shown in Figure 6.3 of DG11 at a sub-harmonic of the predicted floor frequency, a very high acceleration will be predicted by the FE model. Actual walking will not result in an acceleration nearly that high. The reason for the difference is that the FE "walking" will be at a precise sub-harmonic frequency whereas actual walking will rarely exactly match the sub-harmonic frequency. Further, I have yet to read a paper where FE analysis was successfully used to predict measured floor response due to walking. (Rhythmic excitation is a different matter.) There have been a few papers on footbridges, but none on floors to my knowledge. One other comment, I get questions periodically from someone who is trying to do a FE analysis for walking. The most common question is "what I do with all of the frequencies that I get?"

Concerning Figure 7.2, this floor was actually "fixed" by Dave Allen, one of the DG11 authors. Dave provided the following: "The two interior beams at 45degreesadjacent to the atrium support a busy walkway shared with an office. These beams supported a small mass and had a low natural frequency (about 4 Hz), hence the biggest walking acceleration (about 1%g) throughout the floor. The girders in the bay to the left were stiffened for the same reason as for many other bays. The whole floor was unacceptable based on Chapter 4 (about 0.8%g). However it was acceptable based on the CSA S16 Appendix. The girders at 45 degrees at the exterior walls were not a problem." Note that it was not any of the triangular bay framing that caused the problem. Certainly, DG11 procedures could be used to evaluate the interior 45 degrees beams, but not the triangular areas themselves.

Hope this helps.

Tom Murray

Thomas M. Murray, Ph.D., P.E.
Montague-Betts Professor of Structural Steel Design
Department of Civil Engineering
Virginia Tech
Blacksburg, VA 24061
540-231-7532 Fax

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