 | Main design parameters affecting floor vibration
Our first article on floor vibration, “Floor Vibration: From a joist fabricator’s point of view”, appeared in the March 2006 edition of Canam Info-Tech. That article was intended to clarify the responsibilities of building designers concerning floor vibration problems and to emphasize the importance of evaluating floor vibrations early in the design process.
This time, we will discuss the main design parameters that influence vibrations. Tables showing the results of our calculations are meant to guide building designers in selecting these parameters, but are for reference purposes only. The tables were developed according to the assumptions and calculations discussed in Floor Vibrations Due to Human Activity (Steel Design Guide Series 11) by David E. Allen and Thomas M. Murray.
The calculations were done for office floors where the peak acceleration (a0) annoyance threshold is 0.50% of gravity acceleration (g).
Concrete Slab
The thickness of the concrete slab is an important element in reducing floor vibrations. As the thickness of the slab increases, the floor becomes stiffer and decreases its natural frequency. A slight increase in slab thickness can reduce floor vibrations considerably.
Joists
Joist spans that cause the most vibration problems are those between 6 m and 9 m (20 ft. and 30 ft.). Floors comprised of mid-span joists have higher frequencies than those with longer spans.
a) Increasing joist inertia may be the solution to reducing vibrations in cases where peak acceleration is low (a0/g < 0.65%).
b) In more critical cases (a0/g > 0.65% and a0/g < 0.80%), it will be necessary to increase joist inertia considerably, often by a factor of 2 or 3, in order to achieve satisfactory results without increasing the joist depth. The result is a significant increase in weight and correspondingly higher costs. These costs will decrease if the joist depth can be increased to an economical value.
c) In very critical cases where a0/g > 0.80%, increasing joist inertia must not be considered as the only solution.
d) Increasing joist inertia will only have a more significant effect if the frequency of the joist panel mode (fj) is higher than the frequency of the girder panel mode (fg).
In the cases described in c) and d), increasing joist inertia must be combined with other solutions in order to resolve the problem.
Girders
Girder spans that cause the most vibration problems are between 7.6 m and 10.6 m (25 ft. and 35 ft.). Increasing girder inertia will generally reduce floor vibrations appreciably. Higher girder inertia will have a positive effect especially if the frequency of the girder panel mode (fg) is higher than the frequency of the joist panel mode (fj). This is an excellent solution when a beam is used on the free edge of a floor, such as in a mezzanine area.
Damping Ratio
Damping is one of the most important design parameters in reducing floor vibrations. It is not associated with such structural elements as joists, beams or slabs, but rather with the architectural elements of a floor, including floor finishes, partitions, furnishings and mechanical ducts. Three types of damping are illustrated in Table 4.1 on page 18 of the Steel Design Guide Series 11. For a given floor system with the same design parameters, the initial peak acceleration will vary considerably depending on the type of damping. A building having bays with the same structural members may have areas with different peak accelerations according to the use of the floor. Building owners often complain about floor vibrations in a specific area. The tables indicate the results of peak accelerations and frequencies according to the type of damping where β = 0.02 (open areas with little damping), β = 0.03 (average damping level) and β = 0.05 (a lot of damping). In Tables 1 to 6 where the type of damping is β = 0.02, floor vibrations caused by walking in open offices almost always exceed the annoyance threshold when the structural steel components are designed for gravity loads only.
Composite action between the slab and the girder
The composite action referred to here is the hypothetical resistance calculated to counter the vibrations produced by the impact of walking on the floor (as opposed to the composite action to resist flexion from gravity loads using shear studs on girders). No composite action is considered (Cg = 1.6) when the joist shoes have a depth that exceeds 100 mm (4 in.), such as 125 mm or 150 mm (5 or 6 in.). Only partial action is considered (Cg = 1.7) when the joist shoes are 100-mm (4-in.) deep, while composite action is assumed (Cg = 1.8) when the joist shoes are 63-mm (2½-in.) deep or when using Hambro joists. Composite action for joist shoes with a depth of 100 mm (4 in.) or more can be achieved by using stiffeners installed between the joist shoes. The stiffeners are welded to the girder and at the bottom of the deck flutes (Steel Design Guide Series 11, page 56). This relatively inexpensive practice helps reduce floor vibrations. Composite action can be achieved for secondary girders connected into the web of main girders. Tables 2, 4 and 6 give analysis results with composite action for vibration purposes using shear stubs welded to girders and deck.
An effective solution
The most efficient and cost-effective solution to minimize floor vibrations is to modify all the parameters, mentioned previously, at the design stage. Increasing the thickness of the concrete slab will increase the dimensions of the other load-bearing members, resulting in an overall positive effect. If the slab thickness cannot be increased, the most expedient solution is to increase girder and/or joist inertia according to the highest panel mode frequency.
Analysis results
Tables 1 to 6 indicate the results of vibration calculations using the following parameters.
Specified Gravity Loads
• Tables 1 and 2: concrete slab depth of 100 mm (4 in.) including deck profile
- dead load 3.6 kN/m2 (75 psf)
- live load 2.4 kN/m2 (50 psf)
• Tables 3 and 4: concrete slab depth of 125 mm (5 in.) including deck profile
- dead load 4.2 kN/m2 (87.5 psf)
- live load 2.4 kN/m2 (50 psf).
• Tables 5 and 6: concrete slab depth of 140 mm (5-1/2 in.) including deck profile
- dead load 4.5 kN/m2 (94 psf)
- live load 2.4 kN/m2 (50 psf).
Assumptions
- Building dimensions: 4 x girder spans by 4 x joist spans.
- Composite steel deck: Canam profile P-3606 or P-3615, Type 22.
- Joists and girders designed for the specified gravity loads only.
- Joist shoe depth of 100 mm (4 in.) considered to form with the concrete slab a partially composite girder for Tables 1, 3, and 5 and a fully composite girder for Tables 2, 4, and 6 using stubs to attach the beam and concrete slab for vibration purposes.
- Joist spacing varies between 1090 mm (3 ft. 6-7/8 in.) and 1220 mm (4 ft.) to fit the girder span.
- Actual superimposed loads considered for vibration analysis are:
• dead load 0.53 kN/m2 (11 psf)
• live load 0.20 kN/m2 (4 psf).
Note: The calculations in the following tables were done using the Imperial System of Measurement.
Table 1
 To download a PDF version of Table 1
Table 2
To download a PDF version of Table 2
Table 3
To download a PDF version of Table 3
Table 4
To download a PDF version of Table 4
Table 5
To download a PDF version of Table 5
Table 6
To download a PDF version of Table 6
Conclusion
All analysis results in the above tables give the building designer the main design parameters that influence floor vibration problems for certain loads. The purpose of this article was to present efficient solutions to the building designer when vibration problems are evident.
Note
Any comments that refer to structural and architectural parameters are based on calculations that do not cover every conceivable situation, so that additional calculations are required for different parameters. Canam does not warrant the accuracy of the analysis results and does not assume any liability arising from their use.
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