The Role & Interpretation of Damping in the Prediction of Human Induced Floor Vibration Response Levels

Transcription

1 The Role & Interpretation of Damping in the Prediction of Human Induced Floor Vibration Response Levels Jack Carson, Scott Hilliard Research Scholars, FSET, Swinburne University of Technology **Prof Nicholas Haritos CPEng; FIEAust; NER (Civ, Struct, Man) FSET, SUT **

2 Background Overview of Floor Vibration Measurements, Instrumentation/Analysis Methodology Investigation of Walking Response Records Modal Properties from HEMA Method Concluding Remarks Questions

3 Test results reported for the dynamic characteristics of the floor system of the 9 th Storey of a Multi-storey Commercial building under construction in downtown Melbourne deemed dubious by structural consultant for this building (f o ~ 5.4 Hz; damping ~15% critical WOW! Larger than damping value for response under earthquake loading with several plastic hinges!) Strucomp P/L was commissioned to perform an independent investigation that would more realistically estimate the first mode natural frequency & damping (needed for the design of the building floor system for acceptable human induced floor vibration levels)

4 0.29 kn Modal Frequency < (Acceptability Criterion for Office Floors) Modal Damping Modal Weight Murray s Prediction of Peak Floor Acceleration relative to g.

5 Structural Consultant had limited budget; (what s new!) Building already constructed to 15 th Storey (over 1/3 of its total height) so any unfavourable floor vibration results would affect the design of the remaining floors and possibly require retrofitting of already built floors; Testing to be done on the Saturday of upcoming long - weekend when no construction work going on (as this could interfere with measurements) Re-test of Floor 9 specified, but opportunity to also test and compare results for Floors 10, 11 and 14 Final Year Project.

6 Two men, identified as NH, (weight 85kg), & DG, (weight 110kg) of different stature & walking style, performed walking and heel-drop tests on the following test floors: Floors 9 & 10: two nominally identical, fully fitted-out floors, (which included desks, computers, chairs etc). Floor 11: a partially fitted-out floor (which included desks but no computers or chairs), and Floor 14: a floor which consisted of only the bare structure, (no floor coverings or on-floor fittings).

7 Floor 9 DG Walking Test

8 Floor 14 DG Walking Test

9 Background Overview of Floor Vibration Measurements, Instrumentation/Analysis Methodology Investigation of Walking Response Records Modal Properties from HEMA Method Concluding Remarks Questions

10 The two men, NH and DG, took turns performing walking & heel-drop tests on all four test floors to allow: Three four repeat test records of the acceleration response of the floor slab measured at 1m to NW of centre of the NE corner span of the building for 8192 data points/record sampled at 128Hz 64 s time length each Accelerometer used was a GCDC X2-1 with a resolution of 60 micro-g logging data into separate sequential data files 64 secs long in.csv format suitable for EXCEL processing

11 GCDC X2-1 The X2-1 includes a high-sensitivity low noise (to 60 µg), 3-axis +/-2g accelerometer sensor Selectable sample rates: 8, 16,, 512 Hz This logger is ideal for low amplitude vibration monitoring. The X2-1 operates for 10 hours using a 500mAh rechargeable lithium-polymer battery Accurate (5 PPM) time stamped data

12 Accelerometer adhered to Primary Steel Beam. Walking strategy was to pace back & forth inside the NE corner span taking a mixed route with near steady, natural pace passing by location of accelerometer (marked by builder s tape).

13 Acceleration (m/s 2 ) Acceleration (m/s 2 ) Acceleration Response Walking Records for Floor 9 - NH & DG NH DG Peak values in typical records close to, or slightly exceed 0.5%g (0.05m/s 2 ) acceptability criterion for Office Floors (both NH&DG) (Criterion based on 72kg person, so when apply 72/85 & 72/110 reduction factors to peaks, response levels become acceptable)

14 Background Overview of Floor Vibration Measurements, Instrumentation/Analysis Methodology Investigation of Walking Response Records Modal Properties from HEMA Method Concluding Remarks Questions

15 Spectral Density S a (f) (mm 2 /s 3 ) Spectral Density S a (f) (mm 2 /s 3 ) Spectral Density S a (f) (mm 2 /s 3 ) DG NH f (Hz) NH f (Hz) step frequency Two dominant participating modes Acceleration Response Spectra of Time Domain Records Floor twice step frequency Possible minor participating modes f (Hz)

16 f o f R Haritos Equal Area Method (Solver in Excel f o, ζ, A) Area of Bounded Experimental Spectrum f L = Acceleration Spectral Density assumed equivalent to scaled Accelerance Function only true if forcing near constant energy between f L and f R HEAM: Select f L & f R ; Initial f o, ζ, A Solver optimises values

17 Acceleration Spectrum S a (f) (mm 4 /s 3 ) Modal Extraction Averaged Acceleration Spectra Floor 9:NH & DG Walking frequency Mode Hz f (Hz) x Walking frequency Mode Hz Mode Hz Mode Hz Mode Hz Mode Hz NH DG HEAM: Applied to 6 ranges of f L & f R ; Initial A, f o, ζ Solver optimised values

18 Acceleration Response Spectrum S a (f) (mm 4 /s 3 ) NO mode Acceleration Response Spectrum S a (f) (mm 4 /s 3 ) Acceleration Response Spectrum S a (f) (mm 4 /s 3 ) mode Acceleration Response Spectrum S a (f) (mm 4 /s 3 ) NO mode 1000 Floor 9 Spectrum Mode Floor 11 Spectrum Mode Mode Mode 2 Walking frequency Mode 3 Mode 4 Walking frequency Mode 3 Mode 4 10 Mode 5 10 Mode 5 1 f (Hz) f (Hz) Floor 10 Walking frequency Spectrum Mode 1 Mode 2 Mode 3 Mode 4 Mode Floor 14 Walking frequency Dominant Spectrum Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 1 f (Hz) f (Hz) mode HEAM: Applied to observed modal f L f R to four floors NH data, Solver A, f o, ζ

19 Acceleration Response Spectrum S a (f) (mm 4 /s 3 ) Acceleration Response Spectrum S a (f) (mm 4 /s 3 ) Acceleration Response Spectrum S a (f) (mm 4 /s 3 ) Acceleration Response Spectrum S a (f) (mm 4 /s 3 ) Floor 9 Walking frequency Spectrum Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 f (Hz) Floor 11 Walking frequency Spectrum Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 f (Hz) Floor 10 Walking frequency Spectrum Mode 1 Mode 2 Mode 3 Mode Floor 14 Walking frequency Spectrum Mode 1 Mode 2 Mode Mode 5 f (Hz) Fairly 10 1 Similar Mode 4 f (Hz) HEAM: Applied to observed modal f L f R to four floors DG data, Solver A, f o, ζ

20 Background Overview of Floor Vibration Measurements, Instrumentation/Analysis Methodology Investigation of Walking Response Records Modal Properties from HEMA Method Concluding Remarks Questions

21 Modal results for natural frequency in Hz NH DG First Mode of 5.40 Hz for Floor 9 (Average of NH & DG) NH did not generate Mode 2 for Floors 9-14 nor Mode 3 for Floors 9-11 Floor 14 single mode dominant response: NH 7.14Hz & DG 6.37Hz

22 Modal results for damping - ratio to critical NH DG Floor Fitout Status Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9 Mode10 Floor 9 Complete Fitout 0.80% % 1.50% % % 3.40% Floor 10 Complete Fitout 2.40% 2.49% % % 2.67% Floor 11 Part Fitout 1.16% 2.31% % 1.37% 1.29% % 2.20% Floor 14 Bare structure % % % 2.08% First Mode damping ~ 1.0 % Hz for Floor 9 (Average of NH & DG) HEAM conservative Some significant differences for NH & DG in corresponding modes Floors 11 lower damping than 9 & 10 (NH) Floor 14 single mode damping < 1%

23 Background Overview of Floor Vibration Measurements, Instrumentation/Analysis Methodology Investigation of Walking Response Records Modal Properties from HEMA Method Concluding Remarks Questions

24 Concluding Remarks Acceleration response levels on the two fitted floors and the partially fitted floor all exhibited peak accelerations of less than 0.5%g Only on floor 14 (the bare floor) were levels higher than 0.5%g Different walkers (different weight, pacing frequency, footwear, walking path adopted, walking style, etc), can excite different modes in a floor plate with different levels of modal participation in the resultant acceleration response records Some modes in a floor plate can be closely spaced in modal frequency unlike for the case of one-way slab construction where modes are more beam-like so that successively higher modes show greater separation in modal frequency Damping levels of strongly participating modes of floors with open plan fit-out (such as call centres) appear to have quite low damping levels (vicinity of 1% to 1.5% critical) whereas completely bare floors may exhibit damping levels slightly under 1% critical.

25 Background Overview of Floor Vibration Measurements, Instrumentation/Analysis Methodology Investigation of Walking Response Records Modal Properties from HEMA Method Concluding Remarks Questions

26 Role & Interpretation of Damping in Floor Vibration Studies

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