Monumental, aesthetically pleasing staircases are getting incorporated more and more in the architectural design of institutional and commercial buildings. Monumental staircases frequently cause vibration serviceability issues. This is due to their complex shapes, and long spans, slenderness, and lack of columns. Such staircases vibrates when people climb up and/or down the stairs. Moreover, the transmission of that vibration to other parts of the building, can cause discomfort to the occupants.

DEICON measured the staircase’s fundamental frequency (6.1 Hz) and damping ratio (2%). Subsequently, DEICON designed and fabricated a 500 lb tuned mass damper targeting the first mode of vibration. The dimensions of the TMD were selected such that it could fit in the cavity underneath the landing, and be out of sight.

Subjective evaluations as well as comparison of the measured staircase vibration without and with the TMD pointed to the effectiveness of the tuned mass damper in dampening its target mode, increasing it from 2% to 10%, abating the vibration of the staircase.
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Based on extensive numerical modeling and measurements the acoustics consultant of the project recommended the stiffening of the frames along with tuned damping of 5 bays of the floor system of a Pharmaceutical laboratory. The floor vibration criterion used was VC-A (50 μm/s RMS in one-third octave bands). The VC criteria take the form of a set of one-third octave band velocity spectra labeled vibration criterion curves VC-A through VC-G, currently published in an IEST (Institute of Environmental Sciences and Technology) Recommended Practice.

Following the applications of supplemental stiffening steel to the existing beams and girders of the target bays, the natural frequencies of the bays were measured and used in tuning 10 tuned mass dampers targeting the first modes of the 5 bays. The TMDs were installed underneath the 5 bays (2 TMDs/bay) by the steel contractor of the project and commissioned/fine-tuned by DEICON.

Following the commissioning, the acoustic consultant conducted the final measurement of the floor system. The measurement revealed that the vibration amplitudes in the bays where the TMDs were installed were reduced significantly from the untreated floor. The bays with TMDs installed all meet the VC-A criterion (50 μm/s RMS) due to typical walkers in the lab area.
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The floor system of a large room at the 3rd floor administration building of a large university with the square footage of around 1760 ft^2s consists of 3 bays exhibited excessive walking-induced floor vibration. This composite floor system is made up of 3 ½” regular weight concrete on 1 1/2” metal deck, supported by 9 wide flange beams.

Numerical analysis as well as vibration measurement revealed that the floor system vibrates at 3 different frequencies, corresponding to the natural frequencies of the first 3 modes of the structure, depending on where and at what pace the floor is walked on (perturbed). In modes 1 and 2 the three bays vibrate collectively, but in mode 3, each bay vibrates individually, although at the same frequency.

Reactive damping, provided by appending tuned mass dampers (TMDs) to the floor system, was decided on and implemented for abating the vibration. Six tuned mass dampers (TMDs) targeting 3 modes of vibration were designed, fabricated, and installed underneath the floor system. The couple most effectively with the floor system, the TMDs were installed at the locations where their target modes have the highest vibration level.

Following the installation of the TMDs, floor vibration at the target bays, without and with the tuned mass dampers operational, were measured. Comparison of the two sets of measurements, pointed to the effectiveness of the tuned mass dampers in adding substantial amount of damping to their three target modes, quieting the vibration of the floor system.
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In recent years companies with medical imaging equipment have been leasing space in medical office buildings on the upper floors. This is problematic as medical imaging equipment can be very sensitive to vibration velocity. CT, CAT and PET scanners typically are sensitive to vibrations larger than 2,000 micro-in/s and MRI machines are affected by vibrations as little as 500 micro-in/s. Compare this to a typical office building which has a sensitivity of 16,000 micro-in/s (Murray 2016). Therefore, CT, CAT and PET scanners are 8 times more sensitive and an MRI machine is 32 times more sensitive than an office floor. Someone simply walking down the hall may induce vibrations in these machines that blur the images that they create. Since many office building floors may not even meet the office vibration criteria, meeting the criteria for such scanners is well beyond normal performance of an office floor system.

It was desired to place an MRI machine on an elevated floor of an existing office building with 50-foot spans. The floor was constructed of steel open-web trusses with concrete fill over metal deck. As discussed previously MRI machines are highly sensitive to vibrations; this particular unit required a maximum velocity of 0.07 micro-meters per second (micro-m/s) or 25,000 micro-in/s.
When the existing floor was modeled the velocity was predicted at 2.1 micro-m/s in the location of the MRI, thirty times what was allowed. To mitigate such a drastic difference, multiple strategies were implemented.

First the trusses were strengthened to three times (3x) their original stiffness. This stiffening only reduced the velocity to 0.62 micro-m/s, still far from what was required. Note that the velocity has decreased as well as the fundamental frequency increased to ~7.5 Hz. Stiffening the floor has a significant effect on vibration reduction, but even stiffening by a factor of 3 was not nearly enough for this situation.
Next a bridging member (a truss similar to the original trusses in this case) was added to the model. The natural frequency remained at ~7.5 Hz but the resonant velocity further decreased from 0.62 micro-m/s (with stiffening only) to 0.22 micro-m/s (with stiffening plus bridging). The reason for the natural frequency remaining unchanged is that bridging increases not only the stiffness of the structure but it also increases the portion of the floor mass participating in vibration. As noted earlier the maximum velocity at the unit location is reduced but still not enough.
Finally, TMDs were added to the model in addition to the stiffening and the bridging member. TMDs were included in the bay with the unit and the adjacent bay (perpendicular to the direction of the bridging truss). Placing TMDs in the adjacent bay was nearly as effective as placing it in the main bay as the two bays behaved as a continuous beam in the main modes. With 2 TMDs in each bay the velocity was reduced to 0.043 micro-m/s.

Following the installation of the TMDs, floor vibration at the target bays, without and with the tuned mass dampers operational, were measured. With two TMDs in place in each bay, the actual measured velocity in the floor system was approximately 0.07 micro-m/s which was the maximum allowed.
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Dancing, as in other rhythmic activities, subjects the floor to repetitive loadings. The frequency of dancing load depends on the tempo of the music (normally between 1.5-3.5 Hz and even as high as 4 Hz). Depending on the type of dance, the dancers are either always in contact with the floor or the they are jumping in which the contact with the floor is not maintained. In the first type, the floor is subject to the dancing load at the fundamental (dancing) frequency and a very few of higher order harmonics (multiples of dancing frequency). The second type of dancing load is potentially more severe than the first type; this is mainly because in addition to the fundamental (dancing frequency) the floor is subject to many of its higher order harmonics. These high order harmonics can potentially resonate even the rather stiff floor systems with higher natural frequencies.

Following the measurement of vibration and finite element analyses of the floor system, five bays of a dance floor were identified as having objectionable floor vibration. As the outcome of the measurement and analyses, the natural frequencies and the shapes of the first vibration mode of these bays were identified. Subsequently, ten tuned mass dampers (TMDs) with the active mass sizes of 700 and 750 Kg were designed and built to mitigate the tonal vibration of these bays. Two TMDs were installed underneath each of the 5 target bays. Three sets of coils springs in conjunction with the above-mentioned active mass sizes were used for individually tuning the TMDs to the natural frequencies of the first vibration mode of the bays they were designed for.

Following the installation of the TMDs, floor vibration at the 5 target bays, without and with the tuned mass dampers operational, were measured. Comparison of the measured floor vibration without and with the TMDs clearly showed the effectiveness of the TMDs in adding a substantial amount of damping to the first mode of vibration of their corresponding bays. The tuned mass dampers successfully dampened their target modes, quieting the vibration of the floor system.
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