25/01/2013. Agenda. Advanced Approaches to Modeling and Assessment of Floors for Control of Human Activity. Ultra-Low Vibration Environments

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1 // Advanced Approaches to Modeling and Assessment of Floors for Control of Human Activity Brad Pridham, Ph.D., P.Eng. February, Finite Element Modeling Application Example Air Quality Wind & Climate Sound, Vibration & EMI/RFI Sustainable Water Novus Environmental Inc. Research Lane, Suite, Guelph, Ontario, Canada NG T info@novusenv.com tel.7.88 fax.7.88 Learning Objectives Provide an understanding of: fundamental concepts in structural dynamics the characteristics of footfall forces floor vibration criteria benefits of using advanced methods Ultra-Low Vibration Environments Vibration effects on image quality Provide tips on: structural modeling for dynamic response analysis assessment of as-built floors Medical imaging Microscopy Micro-surgery Occupant Comfort Executive Office Footfall measurements measurement

2 // Crowd Loading - Walking Crowd Loading Jumping/Jouncing Video clip downloaded from Youtube URL: XWZ8 Video clip downloaded from Youtube URL: Scope of the Seminar Walking activity on floor structures Discussion limited to a single walker Ultra-low to moderate vibration level environments Science & Technology Health care facilities Higher Ed Office Environments Finite Element Modelling Application Example The Simple Oscillator - SDOF Applied Force Frequency Mass Amplitude - cycle per second = Hz Reduced mass and/or increased stiffness Stiffness Damping Amplitude cycles per second = Hz -

3 // Damping Resonance: Amplitude Amplitude increased damping Acceleration F(t) F(t) By(t ) - - Damping and Resonance Dynamic Amplification Factor - D % damping ) Acceleration By(t Acceleration By(t) - - % damping.% damping Dynamic Bymax(t)=(F=k) / Static.% damping % damping.. Frequency Frequency Rat io (r Ratio = f p=f n) Steady State Response Dynamic Amplification Factor Transient (Impulse) Response Unit impulse at t =. sec Newton s st Law Sinusoid Acceleration By(t) F(t) FI (t) - x -

4 // Transient Response Damped frequency Multi-Degree-of-Freedom (MDOF) Systems Mass, stiffness, force and response are distributed spatially o Matrix formulation Newton s st Law Exponentially Decaying Sinusoid # of DOFs determines the number of modes of vibration Possible DOFs at node i r u u m i r u r Lumped mass After some math. Generalized Coordinates ( Modal Space ) Generalized Force Mode Mode Mode n Generalized Mass System is decoupled in to n SDOFs or n modes of vibration Mode n Modal frequency and damping, Mode Shape Vector of spatial distribution of motion for mode n Response,,, Steady Response SDOF input,,, Transient Response mass,, response Results are summed for all modes to arrive at total response

5 // Footfall Forces Primary concern for floors are the vertical components of force Finite Element Modelling Application Example Left foot Right foot Footfall Forces Effect of Cadence Footfall Forces Time Domain Left foot Right foot Force / Weight.7.9 Slow cadence Natural cadence Fast cadence Force / Weight T = t - t f = / T *data normalized to max force for Slow cadence % of Stride t t t Force Frequency Range Footfall Forces Frequency Domain There are physical limits to our capability to walk comfortably Reported range: Practical range: Average for the population:. Hz. Hz 7 spm spm. Hz Hz 9 spm spm.87 Hz, spm Dynamic Load Factor (F/W)..... f f f f

6 // Dynamic Load Factor vs. Pacing Frequency Perfect Footfall Force Model... Low-frequency /Resonant component: sin F / / W... F F=W / W. -. f f f f.. What about floors/modes with? For floors/modes having frequencies above ~ Hz the force is modeled as an effective impulse High-frequency / Transient Force Model.. 7 Acceleration By(t) F FI I (t) (t) - x - F FI I.. f n (Hz). f f (Hz). Perfect Force Models in the Literature Perfect Force Model AISC DG Ungar s Model ISO 7 SCI P F/W Similarity: assume perfect periodicity.... Differences: number of DLFs magnitude of DLFs excitation ranges treatment of high frequency modes DLF

7 // Probabilistic Force Model Probabilistic Force Model F/W Probability distributions are assigned to: o Dynamic Load Factors o Pacing rate: f DLF o walker s stride length o Pulse amplitude Benefits Limitations PDF of the pacing frequency FEM Loads & Materials Finite Element Modelling Field assessment Permanent loads are applied as area mass Magnitudes should represent actual loads Typically apply % of LL for modeling Distribution is VERY important as it effects the mode shapes. Concrete dynamic modulus: 8 Gpa/ ksi for NWC Gpa/ ksi for LWC FEM Profiled Slabs t s E C FEM Profiled Slabs t s E C Beams, girders inserted at correct elevations y NA I Y Slab modeled as equivalent uniform shell y NA I Y t s E C Orthotropic shell properties E C and E CX t s E CX, I Y I Y 7

8 // FEM Connections & Boundary Conditions Rigid connections on primary framework, but free to move in all DOFs Perimeter cladding -> pinned Core walls -> fully restrained Columns -> pinned at inflection points Partitions -> added mass and damping what about stiffness? FEM Dynamic Analysis Eigenvalue analysis of the FEM produces: o Mode frequencies o Mode shapes o Lumped masses For response analysis retain modes up to at least twice the fundamental frequency More modes may be required depending on criteria for specific equipment etc. (i.e., high frequency sensitivities) Finite Element Modelling Generic Criteria Human Comfort RMS Acceleration (%g)... Application Example 8 8 Generic Criteria Human Comfort Generic Criteria Response Factors x, ISO-Op Steps: Operating theathers x, ISO-Res Residences x, ISO-Office Offices RMS Acceleration (%g)... 8 ) filter time series ) calculate sliding -sec RMS ) divide RMS by.%g Weighting Factor 8x, ISO-Workshop Workshops 8 8,.%g. 8

9 // Response Factors - Example f = Hz; f n = Hz; β =.% Response Factors - Example f = Hz; f n = Hz; β =.% un-weighted Acceleration By(t) (g) x Acceleration Bywt(t) (g) Running s RMS weighted Acceleration Bywt(t) (g) x R R RMS Acceleration (%g) Generic Criteria Equipment & Procedures Conversion to RMS velocity RMS Velocity ( in/s) 8 8 Generic Criteria Equipment & Procedures /x, Class A Low res microscopy /x, Class B CT scanners /8x, Class C High res microscopy RMS Velocity ( in/s) /x /x, Class D/E MRI, SEM, NMR ISO-Op A B C 8 D E 8 8 Additional Comments Manufacturer s criteria should always be used when available Data processing should be consistent with criteria End User requirements are very important in Sci- Tech and Health Care facilities Finite Element Modelling Application Example 9

10 // Numerical Assessment Methodology. Construct FEM. Extract the modal parameters (frequencies, lumped masses, mode shapes). Select damping ratio, input & response locations. Compute floor responses. Compare against criteria. Establish mitigation, if required Selecting the Damping Ratio ISO 7, SCI P Floor Condition β design Steel joist/concrete slab, bare floor.% Composite steel beam with shear connectors, bare floor.% Prestressed concrete, precast, bare floor.% Reinforced concrete, monolithic, bare floor.% Fully fit-out and furnished floors % Floors where partitions interrupt relevant modes % Single Point Method Single Point Method Select worst-case locations on the floor Force location Response location Typically maximum mode shape locations or locations of sensitive equipment Fit-Out Floor,,, Steady Response,,,,, Transient Response,, FEM Mode Shape Single Point Method Benefits: Easy to implement in a spreadsheet Fast calculations Conservative walking on-the-spot to steady state Limitations: Moving loads are not considered Difficult to visualize response of entire floor Results cannot easily be processed into specific formats Full Time Domain Simulation In reality, the forces are varying in both time and space! Benefits: Full walking paths are considered All force models can be used Results can be processed in any format Visualization Drawbacks: Complex implementation and computationally intensive

11 // Example: Response Contours Example: MRI Criteria Evaluation. x - Path B Acceleration (m/s ) Acceleration (m/s ) Finite Element Modelling Application Example Building Re-Use: Bare Floor L Office Suite Full-height partition Final Fit-Out: Executive Office Suite L Servery

12 // Modal Testing of Bare Floor Modal Testing and Model Correlation Impact point Measurement point x = 8 point test grid Mode, 7.8 Hz Mode, 7. Hz Measured =.9% =.7% A A A A Footfall Testing of Bare Floor Path A B B FEM Mode, 7. Hz Mode, 7. Hz Path B A A B A A B Test pacing rates: Measurement point.,.,.8,. Hz 87, 9, 9, spm Maximum Response Force Model Validation Probabilistic Model spm, Path A Walking Path A, 9 spm Measured Walking Path B, 9 spm Measured Model Model Acceleration (m/s ).. -. Running s RMS Response Factor - R ISO Office Criterion Response Factor - R 9 Room - Measurement/Prediction Location Response Factor - R 9 Room - Measurement/Prediction Location -. 8 Time 8 Time

13 // Force Model Validation Probabilistic Model Force Model Comparisons Walking Path A, 9 spm Measured Walking Path B, 9 spm Measured Model Model Response Factor - R Response Factor - R 9 Room - Measurement/Prediction Location 9 Room - Measurement/Prediction Location R Factor Predicted vs. Measured 8 Max Measured Predicted 7 Summary Key Takeaways. MDOF systems de-couple in to SDOF modes of vibration. Two components of footfall force i. Low-frequency, resonant ii. High-frequency, transient. Forces contain harmonics that are multiples of the pacing frequency Room - Measurement/Prediction Location. Probabilistic force model best-reflects reality Summary Key Takeaways. Most connections can be modeled as rigid for FEM (small strains). Magnitude and distribution of mass in FEM is important due to the effect on mode shapes 7. Generic vibration criteria are derived from the ISO Base Curve for perceptibility 8. Full time domain simulations of response provide the most comprehensive assessment of response