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PI’s: J. W. Wallace, E. Taciroglu , J.P. Stewart Staff: D.H. Whang, Y. Lei, S. Keown, S. Kang

Forced Vibration Testing & Analytical Modeling of a Four-story Reinforced Concrete Frame Building. PI’s: J. W. Wallace, E. Taciroglu , J.P. Stewart Staff: D.H. Whang, Y. Lei, S. Keown, S. Kang Students: E. Yu, D. Skolnik, W. Elmer. OUTLINE. Forced Vibration Tests Modal Identification

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PI’s: J. W. Wallace, E. Taciroglu , J.P. Stewart Staff: D.H. Whang, Y. Lei, S. Keown, S. Kang

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  1. Forced Vibration Testing & Analytical Modeling of a Four-story Reinforced Concrete Frame Building PI’s: J. W. Wallace, E. Taciroglu, J.P. Stewart Staff: D.H. Whang, Y. Lei, S. Keown, S. Kang Students: E. Yu, D. Skolnik, W. Elmer

  2. OUTLINE • Forced Vibration Tests • Modal Identification • Finite Element Model Updating • Conclusions & Outlook

  3. Forced Vibration Tests

  4. BACKGROUND • Goals of forced vibration tests/studies • Extract dynamic properties of the structure experimentally • Validate the assumptions of analyticalmodel used to predict structural response • Evaluate predictive capability of analyticalmodels • Until now, forced vibration tests have been performed at low-level response amplitudes • Two kinds of shakers were used as vibration sources • Eccentric mass shaker • Linear shaker

  5. BACKGROUND • Eccentric Mass Shaker • Generate harmonic forces through rotation of mass • Steady state response -> frequency-response curve • Generally, larger maximum load capacity • Laborious tests; one frequency at a time • Linear Shaker • Arbitrary forcing function (Broadband excitation) • Transient response : reduce test time / more computation • Effective in System Identification • Simulation of earthquake vibration

  6. OBJECTIVE &OVERVIEW • Produce a high-quality dataset - Low noise 155 dB accelerometer, 24-bit AD converter - High spatial density Acceleration + Story Displacement + Strain - Low / high amplitude excitation ~max 200 kip force Test Building : 4-story RC frame building • Damage survey • nees@UCLA equipment • Instrumentation scheme • Test procedure

  7. THE BUILDING • “Four Seasons Building” • 4-Story RC Building with penthouse • Constructed in 1977 • Damaged by the 1994 Northridge earthquake • Yellow Tagged (unoccupied, will be demolished) Western Exterior of the Building

  8. LOCATION • Located near the intersection of 101 & 405 Freeway, in Sherman Oaks, California (16 km from UCLA) UCLA

  9. STRUCTURAL SYSTEM • Lateral Load: Special Moment Frame (Beams+Columns) around perimeter • Gravity Load: Post-tensioned flab slab with drop panels + Interior columns • Foundation: Belled Caissons + Grade beams • No shear walls Section along Lone B Typical Floor Plan

  10. STRUCTURAL MEMBERS • Beam : 24”x30” (Typical), 24”x36” (2nd Floor) • Column : 24”x24” • Slab : 8-1/2” with 7-1/2” drop panel (typical) ; Lightweight Concrete (3000 psi) Normal weight concrete (4000 psi) Slab-Column connection Interior Columns Exterior Columns

  11. PREVIOUS STUDIES • Damage report (Sabol, 1994) • Previous analytical studies • Dovitch and Wight, 1994 • Ascheim and Moehle, 1996 • Hueste and Wight, 1998 • Analytical results were not able to identify the amount of damage observed in the building • Effects of torsion / vertical response were significant, or • Ground motions were more severe

  12. OBSERVED DAMAGE • Interior frame • Punching shear failure at slab-column connections around the perimeter of drop panel Column B6 (3rd Floor) Column B2 (2nd Floor) Slab dropped 0.5 ~ 0.75 in. downwards

  13. OBSERVED DAMAGE • Perimeter Frame • Beam-Column joint crack with concrete spalling • Spalling of cover concrete at beam end • Flexural cracks Spalling at beam end (Column A7 at 3F level) Diagonal joint crack (column A4 at 3F level) Flexural cracks (column B2 at 4th story)

  14. OBSERVED DAMAGE • Non-structural Members • Separated from adjacent structural members • No structural contribution during the test was expected, except possibly at the penthouse level Partition wall at 2nd story Penthouse drywall Masonry wall at ground floor

  15. 1 1 2 2 3 3 4 4 5 6 7 A (T) Slight (T) Slight (T) N.A. (T) N.A. B (T) N.A. (T) N.A. (T) N.A. (T) N.A. (T) N.A. (B) Slight (B) Moderate (B) Slight (B) Slight (T) Slight (T) N.A. (T) N.A. (T) N.A. (T) N.A. C (B) Moderate (B) Slight (B) Slight (B) Slight D (T) N.A. (T) Severe (T) Severe (T) N.A. (T) Moderate (T) Severe (B) Slight (B) Slight (T) N. A. (B) Moderate (B) Moderate (B) Moderate (B) Moderate (B) Severe (B) Severe (B) Moderate (B) N. A. (B) Slight (B) Slight (T) Severe (T) Slight (T) N.E. (T) Severe (T) N. A. (T) N. A. (T) N. A. (B) Severe (B) Moderate (B) Moderate (B) Moderate (B) Severe (B) Slight (B) Slight (B) Slight INTERIOR DAMAGE Roof 4th Floor N T : Top face B : Bottom face N.A. : Not Accessible (blank) : No Damage 3rd Floor 2nd Floor Severe : Big chunk crushed out, Floor level dropped or Reinforcements exposed Moderate : Large and developed cracks, small chunk crushed out, or aggregate exposed Slight : long crack around drop panel

  16. EXTERIOR DAMAGE N E 2 A B C D 1 3 4 5 6 7 South Perimeter Frame (Line 1 & 2) West Perimeter Frame (Line A) North Perimeter Frame (Line 7) East Perimeter Frame (Line D) Diagonal joint crack Diagonal joint crack with concrete spalling N Severe concrete crushing (at beam end) /Shear crack • Building experienced more deformation in N-S direction than E-W direction

  17. TESTING EQUIPMENT – nees@UCLA • Two 100-kip capacity eccentric mass shakers • 15-kip capacity linear shaker • Force-Balanced Accelerometers (FBA) • LVDTs (DC-DC Type) • Concrete strain gauges • 24-bit AD converters • Wireless data-logging (Antelope) & Networking system • National Instrument signal conditioning units (LabView) • Mobile Command Center (MCC) • Power generators

  18. ECCENTRIC MASS SHAKER • Two 100-kip capacity shakers • Generate harmonic forces through rotation of mass nees@UCLA Eccentric Mass Shaker, MK-15

  19. ECCENTRIC MASS SHAKER • Adjustable basket Pulse Marker 69 Steel bricks Hydrostone Leveling • Basket configurations for this study

  20. LINEAR SHAKER • Produce force through linear motion of a moving mass • Moving mass (5 kip/g) + Dynamic Actuator (15 kip, ±15”) + Hydraulic system (90 gpm servo-valve, 30 gpm pump, 4 accumulators) + Controller • Digital control : PD, LQG, adaptive ; displacement, acceleration • Broadband excitation ; white-noise, sine-sweep, earthquake-type Linear Shaker Example sine-sweep forcing function

  21. 37.2 m (122 ft) Eccentric Mass Shaker (South) 45° Eccentric Mass Shaker (North) Linear Shaker 9.3 m (30.5 ft) Reference Point N SHAKER LOCATIONS

  22. SENSORS & DATALOGGERS High performance 24-bit Datalogger (Kinemetrics, Q330) Force-balance Accelerometer Synchronization using GPS time National Instrument Signal Conditioning Module used for concrete strain gauges (32 ch X 3 units) DCDT (DC-DC type LVDT) Strain Gauge

  23. WIRELESS DATA ACQUISITION DC : Data Concentration Point WAP : Wireless Access Point Data Concentration Point (DC) Yagi Antenna Wireless Communication Wireless Access Point (WAP) DC Sensors Wired WAP Q330 Wireless Antelope server WAP Mobile Command Center

  24. POWER GENERATORS Power for the shakers Power for DAQ Battery box/portable power

  25. INSTRUMENTATION • Acceleration • Force-balance type Accelerometer • Strain • Strain gauges placed at top and bottom of floor slabs and 3 faces of columns • Interstory • Displacement • DCDTs measure displacement from bottom of one column to top of the consecutive column • 197 Total channels • 16 tri-axial + 27 uniaxial accelerometers • 26 DCDT’s • 96 Strain gauges

  26. NS Accelerometer EW Accelerometer Vertical Accelerometer Column with strain gauge 1 2 3 4 5 6 7 Rv4 3v1 LVDT-NS1 3v4 Rv1 Ru4 3u1 3w1 Ru1 A Rw4 Rw1 A 3w4 3u4 Pu1 LVDT-EW Pv1 Pv2 3v2 3v3 Rv2 Rv3 N LVDT-NS2 3u3 3u2 Ru2 3w2 3w3 Ru3 Rw3 Rw2 3rd floor level Roof / Penthouse 1v2 1v1 LVDT-NS1 1 2 3 4 5 6 7 1u1 1u2 1w2 1w1 Roof Level 1w5 1w6 3F Level 1w7 Ground 1v4 1v3 LVDT-EW N LVDT LVDT-NS2 1w4 1w3 1w8 Ground floor Elevation (A-A) INSTRUMENTATION PLAN

  27. INSTRUMENTATION PLAN • Column Strain Gauges • 3 faces for curvature calculation in both directions • Along A2 & B2 column from ground floor to roof floor • Below and above the floor slab level Curtain Wall 12" 8" 8" 12" 4" 8" 24" 1 2 3 • Floor Slab Strain Gauges • Top and bottom faces of 3rd & 4th floor slab A 0.25L S8 S10 0.25L S5 42" L =30'-6" 0.25L S4 S7 S9 S3 0.25L S2 B S6 S1 60" 60"

  28. TESTING SEQUENCE

  29. VIDEO CLIPS Eccentric Mass Shaker Test

  30. Modal Identification

  31. TESTING & DATA ACQUISITION • Identification and updating performed with data from the linear shaker white noise excitation • Data recorded with four tri-axial accelerometers used derive three story responses

  32. SYSTEM IDENTIFICATION • N4SID (Numerical Algorithm for Subspace State Space System Identification) • Discrete time domain method uses measured data directly • Makes projections of certain subspaces generated from the input/output observations to estimate state sequence using linear algebra tools such as QRD and SVD. • Identifies system matrices from estimated states based on a linear least squares solution • Can be applied to systems subjected to known or unknown excitation • Well implemented in MATLAB’s System Identification Toolbox u: input force applied with linear shaker y: output measured floor responses

  33. SYSTEM IDENTIFICATION Stability Plot • Stability Tolerances • Df ≤ 1.5% • Dz ≤ 5% • MAC ≥ 98% EWNS Tor

  34. For Amb SYSTEM IDENTIFICATION Frequencies and Damping Ratios EWNS Tor

  35. DISCUSSION • Ambient vibration > linear shaker test > EMS test => Stiffness degradation of structural member (contribution of nonstructural elements is negligible ; damage survey) • 3 ~ 4% frequency drop in ambient vibration after EMS test due to the high amplitude vibrations during Half-full basket testing => degradation of (cladding / Foundation & soil / structural member) ?? • Larger frequency drop in N-S direction => effect of damage

  36. Finite Element Model Updating

  37. N FINITE ELEMENT MODELING • Modeling Assumptions • Lumped Mass • Rigid Diaphragms • Classical Damping • From Core Tests • rn =140pcf, rl = 115pcf • Ecn = 4028ksi, Ecl = 2517ksi • Effective Stiffness (FEMA 356 , Paulay&Priestley, “Effective Beam Method”) • Columns: 0.5EcnIg • Beams: 0.42EcnIg • Slabs: 0.4EclIg

  38. FINITE ELEMENT MODELING Natural Frequencies (Hz) EWNS Tor

  39. FINITE ELEMENT MODELING FRF - NS direction

  40. MODEL UPDATING Sensitivity-Based Updating Procedure using Frequency Response Function (FRF) and Modal Frequencies

  41. MODEL UPDATING Parameter Vector Error residuals Non-linear functions of p Linearize with a first-order Taylor series expansion

  42. MODEL UPDATING Objective Function such that and

  43. MODEL UPDATING • Dimensionless Parameters • 10 Mass • 52 Stiffness • 9 Damping

  44. MODEL UPDATING

  45. MODEL UPDATING

  46. MODEL UPDATING Natural Frequencies (Hz) EWNS Tor

  47. MODEL UPDATING FRF - NS direction

  48. Penthouse Roof 4th Floor 3rd Floor 2nd Floor MODEL UPDATING Predicted and Measured NS response to 0.5 - 5 Hz linear shaker sine sweep

  49. Conclusions & Outlook

  50. CONCLUSIONS • Identified modal properties of the first seven modes using N4SID • Frequencies identified from ambient vibrations represent a stiffer structure than that identified from white noise excitation • FE model is updated using a modal- FRF-sensitivity based method • Frequencies, mode shapes, and FRF of the updated model compare well with those identified • Predicted acceleration response of the updated model compares quite well with the measured data

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