A Modified Response Spectrum Analysis Procedure (MRSA) to Determine the Nonlinear Seismic Demands of Tall Buildings

Transcription

1 Fawad A. Najam Pennung Warnitchai Asian Institute of Technology (AIT), Thailand A Modified Response Spectrum Analysis Procedure (MRSA) to Determine the Nonlinear Seismic Demands of Tall Buildings

2 The Earthquake Problem Building Linear/Nonlinear Analysis Model Characterization of Seismic Ground Motions Rock Fault Future ground shaking Site Soil Site Response Ground motion can be amplified by soil Attenuation Seismic waves lengthen and diminish in strength as they travel away from the ruptured fault. Estimation of Linear/Nonlinear Seismic Demands Global-level Responses Inter-story Responses Component-level Responses 2

3 Simplified Structural Models Triangular Simplified Seismic Analysis Procedures Simplified Estimation of Seismic Demands Simplified Loading Any combination of simplified approaches Modal Expansion

4 Dynamic Response of Structures The Concept of Vibration Mode Shapes 4

5 Structural Models The World of Linear Elastic Seismic Analysis of Structures Detailed 3D Linear Model The Linear Response History Analysis (LRHA) Procedure (Direct Integration) Linear Elastic MDF Model Modal Analysis, Spectral Analysis, Standard Response Spectrum Analysis (RSA) Procedure Relative Uncertainty Low The Equivalent Lateral Force Procedure (LSPs) Linear Elastic SDF Model or High Static Single Lateral Load Vector Static Multiple Lateral Load Vectors Ground Motions Seismic Loading

6 Structural Models The World of Nonlinear Seismic Analysis of Structures Detailed 3D Nonlinear Model The Detailed Nonlinear Response History Analysis (NLRHA) Procedure Relative Uncertainty Low Equivalent Nonlinear MDF Model The Multi-mode Pushover Analysis Procedures The NLRHA Procedure using Simplified MDF Model High The Nonlinear Static Procedures (NSPs) Equivalent Nonlinear SDF Model The NLRHA Procedure using Simplified SDF Model Static Single Lateral Load Vector Static Multiple Lateral Load Vectors Ground Acceleration Records Seismic Loading

7 Spectral Acceleration (SA) Force The Standard RSA Procedure (ASCE 7-, IBS 12, EC 8) Linear Elastic Model Eigen-value Analysis K ω 2 M Φ = O N Stories Determine Spectral Acceleration for each Significant Mode Determine Modal Properties T 1 T i, φ i, Γ Time Period (sec) i SA 3 T 3 T 2 SA 2 For Initial Viscous Damping SA 1 Determine Elastic Base Shears φ 1 φ 2 φ 3 V b1 V b2 V b3 N V bn = Γ n. m i. φ i,n. SA n i=1 V el = (V b1 ) 2 + (V b2 ) 2 + (V b3 ) 2 + Reduce Elastic Base Shear to account for inelasticity F in F el R = Response Modification Factor, ASCE 7 (or Behavior Factor, EC 8) V in = V el R el = in Displacement Problem Different modes undergoes different levels of nonlinearity. Reducing elastic responses of every mode by the same R factor is not correct. Several modified RSA procedures have been proposed using different R factor for different mode. V Design = M Design = = C d (V b1 ) 2 + (V b2 ) 2 + (V b3 ) 2 + R (M b1 ) 2 + (M b2 ) 2 + (M b3 ) 2 + R ( el1 ) 2 + ( el2 ) 2 + ( el3 ) 2 + R 7

8 Story Level The Original Intent of R Basic Idea: A structure can be economically designed for a fraction of the estimated elastic seismic design forces, while maintaining the basic life safety performance objective. The elastic forces obtained from the standard RSA procedure The RSA elastic forces reduced by R The intent of R is to simplify the structural design forces such that only linearly elastic static analysis is needed for most building design. The inelastic forces obtained from the NLRHA procedure The underestimation causing a false sense of safety due to directly reducing the RSA elastic forces by R factor R factor can be traced back to a K factor which appeared in the first edition of the Blue Book (SEAOC Recommended Lateral Force Requirements and Commentary) in The reward of making a nonlinear model Story Shear (x 6 N) 8

9 What R to use? Structural Type and Material US West Coast Japan New Zealand** Europe Concrete Frame Concrete Structural Wall Steel Frame Steel Eccentrically Braced Frame Masonry Walls Timber Structural Walls Pre-stressed Wall Dual Wall/Frame Bridges **S p factor of.67 incorporated Source: Direct Displacement-based Design by Priestley MJN et al., 7 9

10 What R to use? Is it justified to equally modify the response of each vibration mode? R??? Our Approach Lets separate them and check one-by-one What actually happens to the structure during the time history analysis?

11 The Concept of Modal Decomposition 11

12 Modal Decomposition of Nonlinear Seismic Responses Classical Modal Analysis Mode 1 Mode 2 Mode A Detailed 3D Elastic Structural Model The Uncoupled Modal Response History Analysis (UMRHA) Mode 1 F D NL Mode 2 Mode 3 F F + D NL + NL D + A Detailed 3D Inelastic Structural Model 12

13 The Uncoupled Modal Response History Analysis (UMRHA) Procedure

14 The Equivalent Single-degree-of-freedom (SDF) System Full 3D Nonlinear MDF Model Monotonic Pushover Analysis Determination of Pushover Curve Idealization of Pushover Curve Equivalent SDF System F n... x 1 r V b1 F 1 F 1 x 1 r D 1 V b1 14

15 Monotonic Pushover Analysis A 44-story Case Study Building No Crack Cracked Base Shear vs. Roof Drift Ratio Pushover Curve (Strong Direction) 3D View Elevation View

16 Δ Cyclic Pushover Analysis Base Shear (V) Roof Drift (Δ) V

17 Normalized Base Shear ( ) Mapping the Cyclic Response to an Equivalent SDF System Roof Drift ( ) -.3 Reversed-cyclic Pushover Analysis (Solid Line) Response of an equivalent SDF system under a ground motion -. 17

18 The CONCLUSION Each Mode is Different Normalized Base Shear (V b1 /W) V b2 /W V b3 /W Mode Mode Mode Roof Drift (x 1 r /H) Roof Drift (x 2 r /H) Roof Drift (x 3 r /H) Cyclic pushover curve Idealized SDF system 18

19 The CONCLUSION Each Lollipop is Different

20 From UMRHA to The Modified Response Spectrum Analysis (MRSA)

21 What Happens when a System Starts Experiencing Nonlinearity? Natural Period Elongation k Additional Hysteretic Damping 21

22 Natural Period Elongation

23 The Basic Concept of Modified Response Spectrum Analysis (MRSA) Mode 1 Mode 2 Mode 3 F D NL F F D + NL + NL D + Nonlinear Structure Detailed 3D Nonlinear Response History Analysis (NLRHA) Uncoupled Modal Response History Analysis (UMRHA) NLRHA Mode 1 Mode 2 Mode 3 UMRHA F D EL F F D EL + + EL + D MRSA T eq1, ξ eq1 T eq2, ξ eq2 T eq3, ξ eq3 Modified Response Spectrum Analysis (MRSA)

24 Spectral Acceleration (SA) Spectral Acceleration (SA) Spectral Acceleration (SA) Spectral Acceleration (SA) The Basic Concept of Modified Response Spectrum Analysis (MRSA) Mode 1 Mode 2 Mode 3 Linear Elastic Structure F F F D D D SA 3 For Initial Viscous Damping SA 2 SA 1 Time Period (sec) T 1 Time Period (sec) T 2 Time Period (sec) T 3 Time Period (sec) 24

25 Conversion of a Nonlinear System in to an Equivalent Linear System Force Force Equal-Energy Assumption Energy dissipated by total damping in a Nonlinear System = K i Hysteretic Damping (ξ h ) E D (x) K eq Equivalent Viscous Damping (ξ eq ) K eq Energy dissipated by equivalent viscous damping in an equivalent linear system E so (x) x o x o Displacement Displacement ξ h = 1 4π E D (x) E so (x) = E D (x) 2π K e x 2 o Total ξ eq = Sum of Equivalent Inherent Damping and Equivalent Hysteretic Damping A Nonlinear System Converted to An Equivalent Linear System with Elongated Period and Additional Damping

26 Evaluation of the MRSA Procedure - 3 Case study Buildings Located in Bangkok, Thailand Heights vary from to 44 stories RC slab-column frames carry gravity loads RC walls & cores resist lateral loads Masonry infill walls extensively used Designed for wind loads, but not for seismic effects 44 Story B1 33 Story B2 Story B3 Possess configuration irregular features commonly found in typical tall buildings, such as podium and non-symmetrical arrangement of RC walls, etc.

27 Spectral Acceleration (g) Ground Motions..3. Short-Period Target Spectrum and Matched Ground Motions Set 2 UHS Target Spectrum and Matched Ground Motions Set 1.2. Long-Period Target Spectrum and Matched Ground Motions Set 3.1. Target Mean of Matched Individual Ground Motions Time Period (sec) 27

28 Spectral Acceleration (g) Spectral Acceleration (g) Spectral Acceleration (g) Set 1 7.%-damped Mean Spectrum 2.%-damped Mean Spectrum %-damped Mean Spectrum Period (sec) %-damped Mean Spectrum 2.%-damped Mean Spectrum %-damped Mean Spectrum Set Period (sec) Target Mean of Matched GMs Individual Ground Motions %-damped Mean Spectrum %-damped Mean Spectrum Set %-damped Mean Spectrum Period (sec)

29 Spectral Acceleration (g) Ground Motions ξ = 2.% ξ = % ξ = % Set 4 Typical Code Target Spectrum and Matched Ground Motions Set 4 %-damped Target Response Spectrum Mean of Matched Ground Motions Individual Ground Motions Period (sec) 29

30 Nonlinear Modeling of Case Study Buildings Rigid Link Fiber section element (concrete and steel fibers) Linear-elastic frame element (shear deformation excluded) Linear shear spring Level m Linear shear spring Concrete and Steel fibers Level m-1 Masonry Infill Wall Model (FEMA 6) Lumped Fibers for RC Columns MVLEM for RC Walls

31 Normalized Base Shear (V b1 /W) Strong (x) Direction Columns begin to Crack Shear wall s steel bars begin to yield in compression Brick walls begin to crack Column s steel bars begin to yield in tension Concrete crushing in shear wall Shear wall s steel reinforcement bars begin to yield in tension Shear walls begin to crack Column s bars begin to yield in compression Roof Drift (x r i /H) Cyclic Pushover Monotonic Pushover in Positive Direction Monotonic Pushover in Negative Direction

32 Cyclic Pushover Analysis Strong Direction Normalized Base Shear (V b /W) V b /W V b /W story Building 33-story Building Mode 1 Mode story Building Mode Roof Drift ( /H) Roof Drift ( /H) Roof Drift ( /H) -story 33-story 44-story 32

33 No. of Stories UMRHA vs. NLRHA Displacement Envelope Inter-story Drift Ratio Story Shear Envelope Overturning Moment UMRHA(Combined 3 Modes) (Combined 3 Modes) NLRHA 6 Displacement (mm) IDR (%) Story Shear (x 6 N) Moment (x 6 KN m) 44-story case study building in Strong Direction 33

34 Level No. Modal Decomposition of Nonlinear Response Mode 3 Mode 1 Mode 3 Mode 2 Mode 1 Envelope of Combined History Mode 2 Envelope of Combined History 6 Peak Displacement (mm) Peak Inter-story Drift Ratio (%) 44-story case study building in Strong Direction 34

35 Modal Decomposition of Nonlinear Response Mode 3 Mode 2 Envelope of Combined History Mode 1 Mode 2 Envelope of Combined History Mode 1 Mode 3 Peak Story Shear (x 6 N) Peak Moment (x 6 KN m) 44-story case study building in Strong Direction

36 Shear Wall Cracking % of Cracking Strain % of Cracking Strain 8% of Cracking Strain Already Cracked UHS-Matched Ground Motion.2 sec CMS-Matched Ground Motion 3 sec CMS-Matched Ground Motion Set 1 Set 2 Set 3

37 Equivalent Linear Properties T sec,i /T i 4. Secant Periods from Envelope of Cyclic Pushover Curves Story (Mode 3) Story (Mode 3) 44 Story (Mode 3) 44 Story (Mode 2) Story (Mode 2) 33 Story (Mode 2) -story (Mode 1) story (Mode 1) 33-story (Mode 1) Roof Drift ratio, x r i /H (%) (a) T sec,i /T i vs. Roof Drift Ratio (x i r /H) 37

38 Equivalent Linear Properties ξ h,i (%) Hysteretic Damping from Area Enclosed by Cyclic Pushover Curves -story (Mode 1) -story (Mode 1) - Each loop start from initial unloaded condition 33-story (Mode 1) 44-story (Mode 1) (b) ξ h,i vs. Roof Drift Ratio (x i r /H) Roof Drift ratio, x i r /H (%) 38

39 No. of Stories Performance of MRSA at Individual Mode Level EQ 1 Mode 1 UMRHA MRSA Standard RSA (R = 4.) Mode 2 Mode 3 Story Shear (x 6 N) Story Shear (x 6 N) Story Shear (x 6 N) Modal Story Shears of a 44-story case study building in Strong Direction 39

40 No. of Stories Performance of MRSA at Individual Mode Level EQ 2 Mode 1 UMRHA Mode 2 Mode 3 MRSA Standard RSA (R = 4.) Story Shear (x 6 N) Story Shear (x 6 N) Story Shear (x 6 N) Modal Story Shears of a 44-story case study building in Strong Direction

41 No. of Stories Performance of MRSA at Individual Mode Level EQ 3 Mode 1 UMRHA Mode 2 Mode 3 MRSA Standard RSA (R = 4.) Story Shear (x 6 N) Story Shear (x 6 N) Story Shear (x 6 N) Modal Story Shears of a 44-story case study building in Strong Direction 41

42 No. of Stories Overall Performance of MRSA EQ Set 1 Displacement Envelope Inter-story Drift Ratio Story Shear Envelope Overturning Moment NLRHA MRSA Standard RSA (C d = 4, R = 4.) 6 8 Displacement (mm) IDR (%) Story Shear (x 6 N) Moment (x 6 KN m) 44-story case study building in Strong Direction 42

43 No. of Stories Overall Performance of MRSA EQ Set 2 Displacement Envelope Inter-story Drift Ratio Story Shear Envelope Overturning Moment NLRHA MRSA Standard RSA (C d = 4, R = 4.) Displacement (mm) IDR (%) Story Shear (x 6 KN) Moment (x 6 KN m) 44-story case study building in Strong Direction 43

44 No. of Stories Overall Performance of MRSA EQ Set 3 Displacement Envelope Inter-story Drift Ratio Story Shear Envelope Overturning Moment NLRHA MRSA Standard RSA (C d = 4, R = 4.) 7 Displacement (mm) IDR (%) Story Shear (x 6 KN) Moment (x 6 KN m) 44-story case study building in Strong Direction 44

45 No. of Stories Local Response - Bending Moment in Columns (EQ Set 4) M M NLRHA Mean MRSA Standard RSA Standard RSA Ω Moment (x 6 N mm) Moment (x 6 N mm) 44-story case study building (Strong Direction)

46 No. of Stories Local Response Shear Walls (EQ Set 4) V M NLRHA Mean MRSA Standard RSA Standard RSA Ω Shear (x 6 N) - - Moment (x 6 N mm) 44-story case study building (Strong Direction) 46

47 No. of Stories Local Response Axial Strain in Shear Walls (EQ Set 4) NLRHA Mean MRSA Standard RSA Standard RSA Ω Tensile Cracking Tensile Cracking Axial Strain (x 6 mm/mm) Axial Strain (x 6 mm/mm) 44-story case study building (Strong Direction) 47

48 Seismic Analysis Practice for Structural Design - The Case of Pakistan 48

49 Source: Zaman and Warnitchai (16)

50 How Safe are Our Buildings Against Earthquakes?

51

52 Peak Ground Acceleration (g)

53 Abbottabad, 8 th October Source: Durrani et al.,

54 How much we understand? Abbottabad, 8 th October Elastic Spectrum of EW Component S D S C S B S A Period (sec) 4

55 Peak Ground Acceleration Source: Zaman and Warnitchai (16)

56 Spectral Acceleration at.2 sec Source: Zaman and Warnitchai (16)

57 Spectral Acceleration at 1 sec Source: Zaman and Warnitchai (16)

58

59 Thank you for your attention 9