Vibration of Timber and Hybrid Floors: A Review of Methods of Measurement, Analysis, and Design
Abstract
:1. Introduction
1.1. Industry Challenge
1.2. Long Span Timber Floor Systems
2. Systems View of Vibration: Evaluation, Perceptibility, and Comfort
2.1. Vibration Evaluation According to ISO 2631-1 (AS 2670.1)
Criterion | Position | Wd | Kx | Wd | Ky | Wk | Kz |
---|---|---|---|---|---|---|---|
Comfort | Seated (translational vibration) | ✓ | 1.0 | ✓ | 1.0 | ✓ | 1.0 |
Seated (rotary vibration) | ✓ | 0.4 | ✓ | 0.5 | ✓ | 0.4 | |
Standing | ✓ | 1.0 | ✓ | 1.0 | ✓ | 1.0 | |
Recumbent | ✓ | 1.0 | ✓ | 1.0 | ✓ | 1.0 | |
Perception | All | ✓ | 1.0 | ✓ | 1.0 | ✓ | 1.0 |
2.2. Vibration Criteria in ISO 10137
Multiplying Factors to Base Curves in Figure 4 | |||
---|---|---|---|
Building Usage | Time | Continuous and Intermittent Vibration | Impulsive Vibration |
Residential | Day | 2–4 | 30–90 |
Night | 1.4 | 1.4–20 | |
Office and School | Day | 4 * | 60–128 |
Night | 4 * | 60–128 | |
Vibration Dose Values (m/s1.75) in Equation (4) from BS 6472 [36] | |||
Building usage | Adverse comment unlikely | Adverse comment possible | Adverse comment probable |
Residential 16 h day | 0.2–0.4 | 0.4–0.8 | 0.8–1.6 |
Residential 8 h night | 0.13 | 0.26 | 0.51 |
3. Dynamic Actions Applied to the Floor
ISO 10137 [31] | CCIP-016 [22] | SCI-P354 [21] | AISC DG 11 [23] | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Harmonic Number n | Forcing Frequency fw (Hz) | Fourier Coefficient αn | Harmonic Number n | Forcing Frequency fw (Hz) | Fourier Coefficient αn | Harmonic Number n | Forcing Frequency fw (Hz) | Fourier Coefficient αn | Harmonic Number n | Forcing Frequency fw (Hz) | Fourier Coefficient αn |
1 | 1.2 to 2.4 | 0.37f − 0.37 | 1 | 1–2.8 | 0.41f − 0.3895 < 0.56 | 1 | 1.8–2.2 | 0.436f − 0.4142 | 1 | 1.6–2.2 | 0.5 |
2 | 2.4 to 4.8 | 0.1 | 2 | 2–5.6 | 0.069 + 0.0056f | 2 | 3.6–4.4 | 0.0738 + 0.012f | 2 | 3.2–4.4 | 0.2 |
3 | 3.6 to 7.2 | 0.06 | 3 | 3–8.4 | 0.033 + 0.0064f | 3 | 5.4–6.6 | 0.0364 + 0.021f | 3 | 4.8–6.6 | 0.1 |
4 | 4.8 to 9.6 | 0.06 | 4 | 4–11.2 | 0.013 + 0.0065f | 4 | 7.2–8.8 | 0.014 + 0.028f | 4 | 6.4–8.8 | 0.05 |
5 | 6.0 to 12.0 | 0.06 | >4 | >11.2 | 0 | >4 | >8.8 | 0 |
4. Floor Dynamics
Standard/Guideline | Low-Frequency Floor | High-Frequency Floor |
---|---|---|
ISO 10137 [31] | 8 Hz < fn < 10 Hz or smaller | 10 Hz < fn |
SCI-P354 [21] | fn < 10 Hz | 10 Hz < fn |
CCIP-016 [22] | fn < 10.5 Hz | 10.5 Hz < fn |
AISC DG11 [23] | fn < 9 Hz | 9 Hz < fn |
Toratti and Talja [40] | fn < 10 Hz | 10 Hz < fn |
BS 6472-1:2008 [34] | 7 Hz < fn < 10 Hz or smaller | 10 Hz < fn |
Allen and Murray [43] | fn < 9 Hz | 9 Hz < fn |
Wyatt and Dier [44] | fn < 7 Hz | 7 Hz < fn |
Ohlsson [45] | fn < 8 Hz | 8 Hz < fn |
4.1. Frequency, Mode Shape, and Modal Mass in One-Way and Two-Way Spanning Floor Systems
4.2. Modal Damping
5. Vibration Design Methods
5.1. Rules of Thumb
5.2. Empirical and Simplified Analytical Methods
5.2.1. Empirical Method in ISO/TR21136
5.2.2. Hamm et al.
5.2.3. Combined Frequency, Deflection, and Impulse Velocity Method in EN 5:2004
5.2.4. Vibration-Controlled Span Method in CSA 086:19
5.2.5. One Step Root Mean Square Method in HIVOSS:2007
5.2.6. Floor Performance vs. Floor Usage in prEN 1995-1-1: 2025 (Final Draft)
Floor Performance Levels | ||||||
---|---|---|---|---|---|---|
Criteria | Level I | Level II | Level III | Level IV | Level V | Level VI |
d1kN (mm) ≤ | 0.25 | 0.25 | 0.5 | 0.8 | 1.2 | 1.6 |
Response factor (R) | 4 | 8 | 12 | 20 | 30 | 40 |
Floor Usage | Quality Choice | Base Choice | Economy Choice | |||
Multi-family residential | Levels I, II, III | Level IV | Level V | |||
Single-family residential | Levels I, II, III, IV | Level V | Level VI | |||
Office | Levels I, II, III | Level IV | Level V |
5.3. Modal Superposition Methods
CCIP-016 [22] | ||||
---|---|---|---|---|
Low-Frequency Floor | High-Frequency Floor | |||
Floor Use | Peak Acceleration | Response Factor, R | VRMS (m/s) | Response Factor, R |
Commercial (offices, retail, restaurants, and airports) | 0.57% g | 8 | 8 × 10−4 | 8 |
Residential (day) | 0.28–0.57% g | 4 to 8 | 4–8 × 10−4 | 4 to 8 |
Premium quality office, open office with busy corridors near midspan, heavily trafficked public areas with seating | 0.28% g | 4 | 4 × 10−4 | 4 |
Residential (night) | 0.2% g | 2.8 | - | - |
Hospitals and critical work areas | 0.071% g | 1 | - | - |
AISC DG 11 [23] | ||||
Low-Frequency Floor | High-Frequency Floor | |||
Floor Use | Peak Acceleration | Response Factor, R | VRMS (m/s) | Response Factor, R |
Outdoor pedestrian bridges | 5% g | 70 | - | - |
Indoor pedestrian bridges, shopping malls | 1.5% g | 21 | - | - |
Offices, residences, quiet areas | 0.5% g | 7 | - | - |
Ordinary workshops | - | - | 8 × 10−4 | 8 |
Offices | - | - | 4 × 10−4 | 4 |
Residences | - | - | 2 × 10−4 | 2 |
Hospital patient rooms | - | - | 1.5 × 10−4 | 1.5 |
5.3.1. CCIP-016
- Find the frequency, fn, modal mass, m*n, and modal damping, ζm, of each mode. The mode shape values at the excitation, μen, and response, μrn, locations in each mode on the floor are also needed. While this is normally conducted through FEA, it can also be calculated using simple equations such as those provided in Equations (17) and (18).
- Calculate the harmonic forcing frequency, fh = h fw, for harmonic numbers, h, from 1 to 4, and the harmonic force, Fh, from coefficients in Table 3 and using Equation (8) at each harmonic.
- Find the real and imaginary parts of the acceleration from Equation (36).
- Sum the real and imaginary responses in all modes and find the magnitude of the acceleration at the harmonic, ah, by summing the square root of the real and imaginary accelerations at this harmonic.
- Convert ah to a response factor, Rh, for this harmonic by dividing ah by the base acceleration, aR = 1,h (m/s2), given in Equation (37) for the corresponding fh.
- Find the total response factor, R, which is the “square root sum of the squares” combination of the response factor for each of the four harmonics.
- The impulsive footfall force, FI, in Ns is calculated from Equation (9) [22] for all modes with frequencies up to twice the fundamental frequency of the floor.
- Find the peak velocity of each mode, vn, and the time history of the velocity response, vn(t), over the period of one footfall, Tw, from Equation (38).
- Add the velocity response in each mode, vn(t), in the time domain to find the total response, v(t) (m/s).
- Calculate the RMS velocity (VRMS) and divide it by the baseline RMS velocity, VR = 1 (m/s), at the fundamental frequency, f1, to determine the response factor, R, and compare it against the target values in Table 7 for the desired floor use (see Equation (38)).
5.3.2. SCI-P354
5.3.3. American Institute of Steel Construction AISC/CISC DG 11
5.3.4. Harmonized Peak Acceleration and VDV Approach
5.4. Time History Analysis Method
6. Hybrid Floor Systems
7. Case Study I: EMA and NMA of a CLT Floor
Rank | Mode Shape (i,j) | EMA Frequency f EMA (Hz) | NMA Frequency f NMA (Hz) | Difference |
---|---|---|---|---|
1 | 1,1 | 11.7 | 10.0 | 15% |
2 | 0,2 | 16.5 | 15.4 | 7% |
3 | 1,2 | 27.9 | 25.1 | 10% |
4 | 2,0 | 34.2 | 28.8 | 16% |
5 | 2,1 | 40.6 | 34.7 | 15% |
6 | 0,3 | 44.7 | 42.3 | 5% |
7 | 2,2 | 55.3 | 50.7 | 8% |
8 | 1,3 | 58.4 | 51.0 | 13% |
9 | 3,0 | 85.6 | 75.1 | 12% |
10 | 2,3 | 88.3 | 76.2 | 14% |
11 | 3,1 | 94.0 | 79.9 | 15% |
12 | 0,4 | 112.8 | 82.2 | 27% |
8. Case Study II: EMA and NMA of a 6 m × 6 m Cassette Floor
8.1. The Floor System and FEA Model
Property | MGP 12 | MGP 10 | Particle Board |
---|---|---|---|
Density (kg/m3) | 594 | 550 | 748 |
EL (MPa) | 12,700 | 10,000 | 3000 |
ER (MPa) | 1435 | 1130 | 3000 |
ET (MPa) | 991 | 780 | 3000 |
GLR (MPa) | 1029 | 810 | 1360 |
GLT (MPa) | 165 | 130 | 1360 |
GRT (MPa) | 1041 | 820 | 1360 |
μLR | 0.292 | 0.292 | 0.103 |
μLT | 0.382 | 0.382 | 0.103 |
μRT | 0.328 | 0.328 | 0.103 |
8.2. Dynamic Properties
Accelerometer A | Accelerometer B | Accelerometer C | Damping | |||||
---|---|---|---|---|---|---|---|---|
favg (Hz) | CoV | favg (Hz) | CoV | favg (Hz) | CoV | ζ | CoV | |
1 | 9.08 | 0.59% | 9.08 | 0.01% | 9.08 | 0.01% | 0.90% | 0.14% |
2 | 17.05 | 3.77% | 16.68 | 2.81% | 16.77 | 0.50% | 1.08% | 0.66% |
3 | 17.84 | 0.01% | 17.45 | 2.65% | 17.98 | 0.31% | 1.03% | 0.17% |
4 | 19.41 | 0.01% | 19.49 | 0.19% | 19.40 | 0.34% | 0.84% | 0.55% |
5 | 20.98 | 0.01% | 21.03 | 0.20% | 21.04 | 0.24% | 0.91% | 0.14% |
6 | 22.01 | 0.26% | 22.31 | 0.33% | 22.23 | 0.37% | 0.89% | 0.14% |
7 | 24.86 | 0.01% | 23.69 | 2.41% | 23.55 | 0.40% | 0.95% | 0.21% |
8.3. Walking Tests and Evaluation to ISO 2631.2 and BS 6472-1
Walking Configuration | ||||||
---|---|---|---|---|---|---|
fw (Hz) | Walker 1 (80 kg) | Walker 2 (75 kg) | Single Walker W1 @ St. 1 | Double Walkers W1 Start @ St.1 W2 Start @ St. 2 | Double Walkers W1 Start @ St.1 W2 Start @ St. 3 | |
T1 | 1.80 | ✓ | - | ✓ | - | - |
T2 | 2.25 | ✓ | - | ✓ | - | - |
T3 | 1.80 | ✓ | ✓ | - | ✓ | - |
T4 | 2.25 | ✓ | ✓ | - | ✓ | - |
T5 | 1.80 | ✓ | ✓ | - | - | ✓ |
T6 | 2.25 | ✓ | ✓ | - | - | ✓ |
Vibration Response Parameters | ||||||
aw (m/s2) Equation (2) | aw,max (m/s2) | MTVV (m/s2) Equation (3) | VDV (m/s1.75) Equation (4) | Equation (5) | Max number of events, ne Equation (43) | |
T1 | 0.75 | 1.75 | 0.75 | 0.92 | No | 11 |
T2 | 0.91 | 2.05 | 0.91 | 1.10 | No | 10 |
T3 | 1.17 | 2.66 | 1.17 | 1.39 | No | 10 |
T4 | 1.54 | 3.72 | 1.54 | 1.89 | No | 11 |
T5 | 0.78 | 1.79 | 0.78 | 0.92 | No | 9 |
T6 | 1.29 | 2.66 | 1.29 | 1.52 | No | 9 |
8.4. Vibration Design to AS 1170.0 and IRC
8.5. Vibration Design Based on Empirical and Simplified Analytical Methods
8.5.1. Simplified Method in ISO/TR 21136
8.5.2. Empirical Method of Hamm et al.
8.5.3. Combined Frequency, Deflection, and Impulse Velocity in EN 1995-1-1:2004
8.5.4. Vibration-Controlled Span in CSA 086:19
8.5.5. One Step Root Mean Square Method (HIVOSS)
8.5.6. Floor Performance vs. Floor Usage in prEN 1995-1-1: 2025 (Final Draft)
8.6. Vibration Design Based on the Modal Superposition Methods
8.6.1. AISC/CISC DG 11
8.6.2. CCIP-016
8.6.3. SCI-P354
8.6.4. Harmonized Peak Acceleration and VDV Approach
9. Conclusions and Suggestions for Future Work
- Measure and formulate load functions of continuous and impulsive excitations as well as rhythmic activities, tailored for long-span timber floors. The existing dynamic vertical forces are based on measurement of footfall forces using force plates and on stiff grounds. Furthermore, these force models do not account for the human-induced response between the walker and the floor, such as the feed-back phenomenon observed between the user and the structure with the Millennium Bridge in [98]. These models can be improved by using more accurate measurement equipment such as digital pressure mats. In laboratory testing, the walker can be placed in a virtual reality (VR) environment using VR goggles to achieve more realistic walking dynamics.
- Characterize the dynamic properties (frequencies, modal mass, mode shape, and damping) and response to vibration of long-span floor panels (i) in the laboratory environment, and (ii) floor systems in selected constructed or completed buildings. This will help in understanding the difference between a slab design analogy and the actual performance of the floor within the mass timber or light-frame structural system.
- Develop experimentally validated analytical models that can reliably predict the dynamic properties and vibration response of the floor systems.
- Assess occupant comfort with different floor usages and identify acceptance criteria for the investigated floor systems. Selected completed buildings with long-span timber floors, an office floor for instance, can be instrumented and monitored during working hours, and the occupants’ experiences can be collected from surveys. There will be vast benefit in gathering the data from field tests and occupant surveys to establish an international database for researchers and practitioners worldwide for vibration design of long-span timber floor systems.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Karampour, H.; Piran, F.; Faircloth, A.; Talebian, N.; Miller, D. Vibration of Timber and Hybrid Floors: A Review of Methods of Measurement, Analysis, and Design. Buildings 2023, 13, 1756. https://doi.org/10.3390/buildings13071756
Karampour H, Piran F, Faircloth A, Talebian N, Miller D. Vibration of Timber and Hybrid Floors: A Review of Methods of Measurement, Analysis, and Design. Buildings. 2023; 13(7):1756. https://doi.org/10.3390/buildings13071756
Chicago/Turabian StyleKarampour, Hassan, Farid Piran, Adam Faircloth, Nima Talebian, and Dane Miller. 2023. "Vibration of Timber and Hybrid Floors: A Review of Methods of Measurement, Analysis, and Design" Buildings 13, no. 7: 1756. https://doi.org/10.3390/buildings13071756