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DESIGN GUIDE FOR FLOOR VIBRATIONS
Article · January 2008
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EUROSTEEL 2008, 3-5 September 2008, Graz, Austria
DESIGN GUIDE FOR FLOOR VIBRATIONS
Oliver Hechler a, Markus Feldmann b, Christoph Heinemeyer b, Flavio Galanti c
a
b
ArcelorMittal, Commercial Sections, Technical Advisory, Luxembourg
Lehrstuhl für Stahlbau und Leichtmetallbau, RWTH Aachen, Germany
c
TNO Built Environment and Geosciences, Delft, The Netherlands
INTRODUCTION
In the past, the demand for flexible use of commercial and administrative buildings was leading to a
request for floors with long spans. These expectations have been met by the development of
innovative construction techniques, e.g. composite floor systems as well as pre-stressed hollow core
slabs. This trend has been supported further by the use of modern, high strength materials. Hence
serviceability criteria, such as deflection limits and the vibration behaviour, define in the first
instance the design of these new, slender constructions.
While deflection limits are regulated in the relevant standards, the vibration comfort of slabs is not
clearly defined. A directed design with regard to floor vibrations is presently not possible. In
addition, a generally accepted method for the reliable prediction of the action effects for vibrations,
in general expressed in accelerations or velocities, are not available.
This paper presents a design guide comprehending a simple design method for floors in reference to
human induced vibrations [1]. Comfort criteria for vibrations are defined in relation to the use of the
floor. Further a simple design method for prediction of vibration intensity of floors due to human
induced vibrations to check these criteria is introduced. The content of this work has been
developed and validated in the scope of the RFCS-project “Vibrations of Floors” [2].
1
COMFORT CRITERIA FOR FLOOR VIBRATIONS
The perception of vibrations by persons and the individual feeling of annoyance depend on several
aspects. Although the perception of vibrations is a very individual sensation a number of parameters
influencing this reaction could be identified:
•
•
•
•
•
The current activity of the considered person is of relevance for its perception of vibrations persons working in the production hall in a factory have a different perception of vibrations
from those working in an office or surgery;
Age and health of affected people may affect the annoyance level of vibrations;
Posture of the people such as standing, laying or sitting;
The relation of the person to the source of excitation (are the vibrations expected or
unforeseen);
Frequency and amplitude of the vibration.
These parameters have been reviewed and assigned to perception classes recommended for different
utilization of floors, see Table 1. These perception classes represent the targeted design
recommendations with regard to floor vibrations and thus the comfort criteria. The design values for
classification are based on the ISO 10137 [5] however they have been adapted according to the
European partners’ experiences drafted in the project “Vibrations of Floors” [2].
Table 1. Classification of floor utilizations in respect to perception classes
A
B
C
D
E
F
2
Sports
Industrial use
Hotel
Retail
Meeting
Office
Residential
Education
Health
Critical workspace
Class
Utilization of floor
Recommended
Critical
Not recommended
DYNAMIC SLAB PROPERTIES
2.1 General
The dynamic behaviour of floors depends basically on the mass, stiffness and damping of the floor.
The ratio between stiffness and mass determines the natural frequency of the floor. Natural
frequencies in a range of step frequencies induced by pedestrians walking on the floor can become
critical. In Fig. 1 the frequency distribution of the step frequency of 200 persons passing the
entrance hall of the TNO-administration building in Delft is shown.
25
40
acceleration sensor 1
35
acceleration sensor 2
30
25
20
15
10
percentage of Dutch adults
Frequency distribution
45
20
women
men
15
10
5
5
0
0
1,6 1,7 1,8 1,9 2,0 2,1 2,2 2,3 2,4 2,5
Step frequency [Hz]
Fig. 1. Frequency distribution of the step
frequencies [2]
45 50 55 60 65 70 75 80 85 90 95 100 105 110
mass (kg)
Fig. 2. Frequency distribution of the exciter mass
(pedestrians)
The harmonic excitation of a floor depends further on the size of the floor, as several foot steps are
required until the floor starts vibrating. The guideline presented in this paper assumes that the
length of the floor is reasonably large for harmonic excitation to occur.
While the influence of the stiffness of the floor is confined to the natural frequency, the mass of the
floor affects additionally the dynamic behaviour of the floor. The ratio between the mass of the
exciter to the mass of the excited floor is a significant parameter for the dynamic response of the
floor. The sensitivity to floor vibrations increases with increasing ratio of exciter mass and floor
mass. The exciter mass is a pedestrian whose representative weight distribution is given in Fig. 2.
The excited mass is defined as modal mass of the floor. Each frequency of the floor corresponds to
a modal mass. Simplified modal mass can be described as the mass participating in the vibration
mode considered.
Modern floors with large spans are light-weight constructions with a low stiffness. The low stiffness
leads to low natural frequencies while the low weight to an increase in the ratio of the exciter mass
to the excited mass. Therefore the assessment of the vibration of floors may become essential.
Furthermore damping has an important influence on the vibration behaviour of the floor. The
damping properties are not only dependent on the structure, but also on the finishes and use of the
premises. Thus separation walls, ceilings under the floor, free floating floors or swimming screeds
affect the damping properties significantly.
Appropriate damping values can be taken from Table 2. The system damping D is obtained by
summing up the appropriate values. In the evaluation of the dynamic floor characteristics also a
realistic fraction of imposed load should be considered in the mass of the floor. Experienced values
for residential and office building are 10% to 20% of the imposed load.
Table 2. Estimation of the floors’ damping
Type
Structural damping D1
Wood
Concrete
Steel
Composite (Steel-Concrete)
Damping due to furniture D2
Traditional office for 1 to 3 persons with separation walls
Paperless office
Open plan office
Library
Residential
Schools
Gymnastic rooms
Damping due to finishes D3
Ceiling under the floor
Free floating floor
Swimming screed
Total damping D = D1 + D2 + D3
Damping (% of critical damping)
6%
2%
1%
1%
2%
0%
1%
1%
1%
0%
0%
1%
0%
1%
2.2 Determination of the Relevant Floor Properties
The determination of the dynamic floor properties specified above is an unusual task for designers
of buildings in their daily practice. Therefore design guidance has been elaborated for the
determination of the natural frequency and corresponding modal mass of floors. In this design guide
[1], straightforward aids for the manual calculation applied to simple, regular static systems as well
as guidance for the evaluation using FEA calculations is given.
In Table 3 a selection of manual formulas for the determination of the first natural frequency (acc.
to [4]) and the modal mass of isotropic plates for different supporting conditions are presented.
For the application of the given equations it is assumed that no lateral deflection at any edges of the
plate occurs.
Further manual formulas for orthotropic plates (e.g. composite slabs) as well as general rules and
approximation methods for the determination of the dynamic properties are included.
Table 3. Simple determination of the natural frequency and modal mass of isotropic plates
Support condition
clamped
Frequency; Modal mass
f =
hinged
α
L2
E t3
; M mod = β ⋅ M tot
12 ⋅ m (1 − υ 2 )
α
10
α = 1.57 ⋅ ( 1 + λ2 )
8
6
B
4
2
L
0
0,5
1,0
1,5
2,0
Ratio λ = L/B
β ≈ 0,25 for all λ
B
L
α
16
14
12
10
8
6
4
2
0
α = 1 . 57
0,5
1 + 2 . 5 λ 2 + 5 . 14 λ 4
1,0
1,5
2,0
Ratio λ = L/B
β ≈ 0,20 for all λ
B
L
α
18
16
14
12
10
8
6
4
2
0
α = 1 . 57
0,5
5 . 14 + 3 . 13 λ 2 + 5 . 14 λ 4
1,0
1,5
2,0
Ratio λ = L/B
β ≈ 0,17 for all λ
E
t
m
υ
Mtot
Young Modulus in N/m²
Plate thickness in m
Specific mass of the floor including finishes and a fraction of the imposed load in kg/m²
Poisson ratio
Total mass of floor including finishes and a representative fraction of the imposed load in kg
3
ASSESSMENT OF COMFORT
A design value used to calculate a response of the floor is OS-RMS90. This value covers the
response velocity of the floor for a significant step with the intensity of 90% of people’s steps
walking normally – called the "one step root mean square 90", see Fig. 3. It is a root mean square of
the velocity determined as follows:
T
v
1
v RMS =
v(t ) 2 dt ≈ Peak
∫
T 0
2
where T
is the investigated period of time.
one step RMS
1
4
3
3
2.5
2
2
1
1.5
0
1
100
2.5
80
0.5
90%
0.8
Probability
RMS
3.5
0.6
0.4
0.2
2
60
mass of
person walking
(1)
40 1.5
pace
frequency
0
0
1
2
One-step RMS
3
4
Fig. 3. The OS-RMS90
For the comfort assessment of floors the classification introduced in chapter 1 has been included
into diagrams, see Fig. 4. Consequently the perception classes A to F from Table 1 can be read
directly from these design diagrams. Thus input parameters for the determination of the perception
class of the floor are following:
•
•
•
Damping (taking into account finishes and furniture),
Natural frequency,
Corresponding modal mass of floor.
After the designation of these dynamic properties the designer chooses a relevant design diagram in
reference to the damping of the floor.
The diagram is applied by introducing modal mass on the x-axis and corresponding frequency on
the y-axis. On the intersection of the both entered values the OS-RMS90 and the acceptance class
can be read, see Fig. 4. Design diagrams have been elaborated for 1% up to 9% damping.
This method leads in general to conservative results when applied as single bay method using the
mode related to the fundamental frequency. However, in special cases in which the modal mass for
a higher mode is significantly low, also higher modes need to be considered.
Classification based on a damping ratio of 3%
Frequency [Hz]
20 10
19
11
18
9
8
5
7
3
6
17
12
13
16
10
15
9
11
17
14
13 25
8
29
10
45
49 41
0.1
0.4
0.2
0.3
0.7 0.6
1.2
1
8
3.2 2.6
2.8
4
7
33
21
25
0.2
0.3
1.6
1.4
0.7 0.6
B
0.4
1.2 1
1.8
2.2
2.4
0.5
0.2
0.8
0.3
13
6
10
37
29
96
56
76
45
41
49
11
17
4
5
9
156 136
8
2.8
2
7
1.8
D
3
0.4
236
256 176
0.2
1 0.8
1.61.4 1.2
E
12
F
3.2
2.8
4
2.2
5
3
7
29
0.7
0.5 0.4
0.3
0.6
0.8 0.7 0.50.4
1
0.6
0.8
2.6 21.8
1.2
1.4
1
2.8 2.2
1.6
3.2
2.4
1.2
1.8
1.4
2
3
4
2.6 2.2 1.6
6
5
136
96
1
100
200
12
33
21
56
49
500
10
98
13
45
41
6
7
4
3.2
2.2 1.8
1.6
1.4
3 2.6
25
1.8
2
1.6
1.4
3
2.2
2.6
1.8
1.2
2.4 2 1.6
1
1.4
0.8
1.2
1
0.80.7 0.6
0.5
0.4
0.6
0.5
2
1
2.4
2000
5000
2.8
1.2
5
1000
2.8
2.4
3.2
156
76
0.2
1.41.2
1.6
11 8
17
116
256236
0.3
0.50.4
0.3
0.8 0.6
1
9
2
0.4
2.4
37
796
696 576
856
536 476
836
616
676
876
776
756
416336296
816
736
596 496
636
716
396
656
436
556
516 376
0.3
0.5
0.7
2
1.8
3
196
216
0.4 0.3
0.6
2.6
13
10
276
316
356
456
0.3
0.70.6 0.5
25
276
0.2
0.8
6
196
216
4
0.1
0.2
0.3
0.4
0.5
2.2
2.4
21
0.7 0.6
1
1.2
1.6 1.4
3.2 2.6
33
5
0.1
C
12
8
116
A
0.1
0.4
0.5
0.8
2
3
6
7
Eigenfrequency of the floor (Hz)
5
9
11
17
0.5
0.1
10
11 37
2 1.8
2.2
2.4
3
6
12
13
0.70.6
0.8
1.6 1.4
3.2 2.6
2.8
5 4
7
21
12
9
1.61.4
1.2 1
2 1.8
2.2
2.4
3.2 2.6
2.8
4
10000
0.8
20000
0.7
0.4
50000
0.3
100000
Modal mass of the floor (kg)
Modal Mass [kg]
Fig. 4. Read-off of the perception class from the design diagrams (here for 3% damping)
4
SUMMARY AND ACKNOWLEDGMENT
The design guide presented in this paper [1] is a simple tool addressed to designers who do not have
deep knowledge about dynamic behaviour of structures. It enables them to assess floors for human
induced vibrations. The method is semi-probabilistic and the results lead to a determination of the
vibration response of sensitive floors with a reliable accuracy.
The authors wish to express their deep gratitude to the RFCS (Research Fund for Coal and Steel of
the European Community) for its financial support ([2] and [3]) and to the representatives of the
partner SCI, Ascot, UK, for their inspiring cooperation.
REFERENCES
[1] Feldmann, M., Heinemeyer, Ch., Völling, B., Design guide for floor vibrations, ArcelorMittal,
Commercial Sections, http://www.arcelormittal.com/sections/, 2007
[2] European Commission, Generalisation of criteria for floor vibrations for industrial, office,
residential and public building and gymnastic halls - Vibration of floor (VoF), ECSC 7210CR04040, Report EUR 21972 EN, ISBN 92 76 01705 05, 2006
[3] European Commission, Human induced vibration of steel structures (HiVoSS), RFS2-CT2007-00033, to be published 2009
[4] Bachmann, H., Ammann W.. Vibration of structures induced by Man and Machines, IABSEAIPC-IVBH, Zürich. ISBN 3-85748-052-X, 1987
[5] ISO 10137:2007-11, Bases for design of structures - Serviceability of buildings and walkways
against vibrations
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