Effects and Multi Directional Seismic Ground Motion

Transcription

1 SEAOSC Seismology Committee Webinar 14 April 2011 Analysis and Design for Orthogonal Effects and Multi Directional Seismic Ground Motion Considering Recent Code Changes PhD PE Arup, Los Angeles [currently at Arup, Hong Kong for a long term assignment]

2 Outline Introduction, ti Problem Dfiiti Definition Response Spectrum (RS) Representations Response Spectrum Analysis Modal Combination Procedures Directional Combination Procedures Compatibility of RS Representaions and Modal/Directional Combination Procedures Review of Some other Issues Suggestions for Analysis and Design 2

3 Introduction: Analysis and Design for Seismic Events STRUCTURAL 1 TIME HISTORIES ANALYSIS AND DESIGN GEOTECHNICAL & SEISMOLOGICAL 2 RESPONSE SPECTRUM CURVE 3

4 Problem Definition: Approximations There are many approximations done on both Geotech/Seism. and Structural Engineering sides of an RS derivation and analysis. GEOTECH/SEISMOLOGICAL All possible earthquakes are represented by a single Response Spectrum (RS) Curve. Horizontal ground motion at a given site is represented by a single RS Curve, which is a 2 D motion. STRUCTURAL ENGINEERING RS ANALYSIS requires modal combination rules RS ANALYSIS requires directional combination rules Peak resultant design member stresses (thedirection cannot be known) are estimated from peak displacements for the structures t FEM axis directions. COMPATIBILITYREQUIRED BETWEEN THE TWO FIELDS 4

5 Objectives To literature t review of the procedures used in Derivation of a Response Spectrum curve (Geotech) Response Spectrum Analysis (Structural) Review compatibility between Geotechnical and Structural Procedures To provide simple guidelines for Conservative analysis and design for multidirectional earthquake and orthogonal effects. 5

6 Response Spectrum Representations Data: a large set of recorded historical ground motion accelerations are used. EQ 1 EQ 2 EQ n (Acceleration) (Acceleration) (Acceleration) TIME X Dir Y Dir TIME X Dir Y Dir Some of the Representations. TIME X Dir Y Dir X Component Y Component Larger of the two horizontal component Geometric mean of the two horizontal component Arbitrary Horizontal Component Strike Normal, Strike Parallel Component MOST COMMON Maximum Rotated IN STR. ENG. 6

7 Response Spectrum Representations Geomean (in very simple terms): N S Directio onresponse: RN S NRESPONSE: RE WE W Period, T Damping, ξ RESPONSE SPECTRUM IS GM RS: R E W R E W E W Direction SOME KIND OF AVERAGE OF TWO COMPONENTS 7

8 Response Spectrum Representations Geomean Example: Consider a very approximate back of the envelope type engineering estimation: N S, 0.3g BUILDING PLAN GEOMEAN N S, GM RS = BUILDING PLAN E W, 0.4g GM RS = SQRT(0.3 x 0.4) = E W, GM RS = Geomean represents only one component of the seismic effects on the structure; it does not represent the complete seismic effects on the structure. The complete seismic effects on the structure can be achieved by applying two Geomean RS curves simultaneously. Geomean has been used in ASCE 7 05 and original NGA. 8

9 Response Spectrum Representations Maximum Rotated (in very simple terms): 2 D Response N S Direction Period, T Damping, ξ 2 D Analysis E W Direction RESPONSE SPECTRUM IS MAXIMUM RESULTANT: MR RS 9

10 Response Spectrum Representations Maximum Rotated Example: Consider a very approximate back of the envelope type engineering estimation: N S, g BUILDING PLAN MAX. ROTATED E W, 0.4g MR RS = RESULTANT(0304)= RESULTANT(0.3,0.4) Maximum Rotated represents the complete effect of both components of a seismic event on the structure. Therefore, application of one Maximum Rotated RS curve is adequate for structural analysis. Maximum Rotated has been used in ASCE 7 10 and amended to NGA. BUILDING PLAN 10

11 Response Spectrum Representations Comparison: Geomean RS vs Maximum Rotated RS GEOMEAN ASCE 7 05 MAX. ROTATED ASCE 7 10 RATIOS OF MAX. ROTATED RS TO GEOMEAN RS ARE PLOTTED (NGA) MAX.ROTATED GEOMEAN 1.3 (Campbell and Bozorgnia, 2007) 11

12 Response Spectrum Representations: Codes ASCE 7 05: GEOMEAN ASCE 7 10: MAX. ROTATED + NGA REMEMBER: HOW IS ASCE 7 05 RELATED TO ASCE 7 10? MAX.ROTATED GEOMEAN 1.3 HOWEVER, NGA resulted smaller RS values (for some locations) NGA MAX.ROTATED APPROXIMATELY: 1.0 GEOMEAN REMEMBER: ASCE 7 10 RS THEREFORE: ASCE 7 10: MAX ROTATED 1.0 ASCE 7 05 RS ASCE 7 05: GEOMEAN 12

13 Response Spectrum Represent.: California ORIGINAL NGA DATABASE NEAR FIELD FAR FIELD EARTHQUAKES EARTHQUAKES (STRONG) (WEAK) ORIGINAL NGA & GEOMEAN RESPONSE SPECTRUM NEW NGA DB., Huang et al. (2008) NEAR FIELD EARTHQUAKES (STRONG) (FOR REGIONS WITH STRONG SEISMIC ACTIVITY) E.G.: CALIFORNIA NGA NEAR FIELD & MAX. ROTATED RESPONSE SPECTRUM REQUIRED BY OSHPD, DSA 13

14 Structural Response Spectrum Analysis RESPONSE SPECTRUM ANALYSIS MODAL COMBINATION SRSS CQC + DIRECTIONAL COMBINATION SRSS 100%+30% CQC3 14

15 Modal Combination Procedures ONLY FOR 1 D (single dimension) seismic input applied to building X axis or Y axis Y X Mode 1: Peak Modal Response Mode 2: Peak kmodal lresponse. Mode n: Peak Modal Response MODAL COMBINATION PROCEDURES MAXIMUM STRUCTURAL AXIAL FORCE SRSS, CQC 15

16 Modal Combination Procedures: SRSS Square Root of Sum of Squares (SRSS) Let R n = Response value for the n th mode R structure = SQRT( R 12 + R R n2 ) Mostly proven to be OK for structures with well separated modes May have many other drawbacks for a general 3 D structure: Cannot address closely spaced modes (interacting modes) Ignores the signs of modal responses (in/out of phase) 16

17 Modal Combination Procedures: CQC Complete Quadratic Combination (CQC) Considersrelation relation between the modes using cross correlation coefficients, which can address Closely spaced modes Signs (+ or ) of the modal responses Mostly used in practice: Der Kiureghian (1981) equations CLOSELY SPACED MODES Chopra s boo ok. Der Kiur reghian (1981) printed from 17

18 Modal Combination Procedures: CQC Der Kiureghian CQC uses many assumptions (frequently used). Engineers should understand these assumptions in case they do not apply to structure they are analyzing. May not be accurate lightly damped ( < 0.5%) structures (e.g.: space truss type structures) May not be accurate for impulsive, short duration earthquakes. The structure should have classical mode shapes. The structure should not have sudden and significant changes in its mass, stiffness and damping characteristics. If possible, use CQC and avoid SRSS to be on the safe side 18

19 Directional Combination Procedures 2 D Seismic Input (two different RS curves) are applied simultaneously to building global axes DIFFERENT RS CURVES Y MODAL COMB. EG: CQC MODAL COMB. EG: CQC X MAX. STRUCTURAL RESPONSE (Curve 2 ONLY) DIRECTIONAL COMBINATION PROCEDURE MAX. STRUCTURAL RESPONSE (Curve 1 ONLY) MAX. STRUCTURAL RESPONSE SRSS, , CQC3 19

20 Directional Combination Procedures: SRSS BUILDING AND RS CURVE BASE SHEAR EG: MEMBER SHEAR FORCES EG: SRSS SHEAR FORCE RS APPL LIED IN THE X DIR a b SRSS a c 2 2 RS APPLIE ED IN THE Y D DIR c d SRSS b d

21 Directional Combination Procedures: CONSIDER A PERFECTSTRUCTURE STRUCTURE: ORTHOGONAL EFFECTS RS APPLIED IN THE X DIR BUILDING AND RS CURVE BASE SHEAR EG: 100% MEMBER SHEAR FORCE EG: 30% MEMBER SHEAR FORCE + = EG: 100%+30% M. SHEAR FORCE LOAD CASE 1 RS APPLIED IN THE Y DIR 30% + = LOAD CASE 2 21

22 Directional Combination Procedures: CONSIDER IRREGULAR STRUCTURE: ORTHOGONAL EFFECTS BUILDING AND RS CURVE BASE SHEAR EG: EG: EG: 100% MEMBER 30% MEMBER 100%+30% SHEAR FORCE SHEAR FORCE M. SHEAR FORCE IN THE RS APPLIED X DIR + = LOAD CASE 1 RS APPLIED IN THE Y DIR + 30% = LOAD CASE 2 22

23 Directional Combination Procedures: CQC3 Assume that the two dimensional earthquake is as follows: In the 1 st direction, 1 D RS curve is given as: CURVE A In the 2 nd direction, RS curve is assumed to be: CURVE B = a x CURVE A (0 < a < 1) In theory, 0< a < 1. In practice, 0.5 < a < 0.85 To be able to apply CQC3, the value of a has to be provided, which is generally not available. Therefore, CQC3 had limited use in practice. However, it has another use.. 23

24 Directional Combination Procedures: CQC3 CQC3 has an interesting ti property: (1) If a = 1, the Response Spectrum analysis results becomes independent d of the angle that t the RS is applied to the building (Wilson, et al., 1981): ROTATE ANGLE, α α BUILDING PLAN = α BUILDING PLAN 24

25 Directional Combination Procedures: CQC3 CQC3 has an interesting ti property (cont d): (2) If a = 1, the most critical response value IS achieved. (3) If a = 1, CQC3 is equivalent to CQC + SRSS CQC3 = PROCEDURE DIRECTIONS w/ a = 1 THE MOST CRITICAL RESPONSE VALUE THAT IS INDEPENDENT FROM ANGLE IS OBTAINED CQC PROCEDURE for MODAL COMBINATION FOR BOTH DIRECTIONS w/ SAME + RS SRSS for DIRECTIONAL COMBINATION 25

26 Compatibility: CQC3 Question: What type of RS representation is suitable for CQC3, when a = 1? Remember the Geomean RS example shown in the previous slides: N S, GM RS = BUILDING PLAN SINCE THE SAME GEOMEAN RS IS USED IN BOTH DIRECTIONS FOR GEOMEAN RS, a = 1 E W, GM RS = GEOMEAN IS COMPATIBLE WITH CQC3 when a =1 (or CQC+SRSS) 26

27 Compatibility: Perfect Structure w/ ASCE 7 10: 30% THE 100% COMPONENT REPRESENTS 100% MAX. ROTATED RESPONSE In Theory: 30% 100% THE RESULTANT REPRESENTS MAX. ROTATED RESPONSE THE 100% COMPONENT REPRESENTS GEOMEAN RESPONSE (???) However: Since RESULTANT 100% Component, Code is OK. 27

28 Compatibility: Irregular Struct. w/ ASCE 7 10: THE 100% COMPONENT REPRESENTS MAX. ROTATED RESPONSE In Theory: THE RESULTANT REPRESENTS MAX. ROTATED RESPONSE THE 100% COMPONENTREPRESENTS GEOMEAN RESPONSE (???) However: RESULTANT 100% Component t Code is not CLEAR 28

29 Analysis and Design: Suggestions Definition of Major and Minor Principal directions: MAJOR PRINCIPAL DIRECTION IS IN THE DIRECTION OF THE BASE SHEAR OF THE FUNDAMENTAL MODE 90 MINOR PRINCIPAL DIRECTION IS PERPENDICULAR TO Y MAJOR PRINCIPAL DIRECTION X Principal directions are obvious for regular structures. For irregular structures, principal directions are not obvious. bi 29

30 Analysis and Design: Suggestions Static If the structure t is regular, follow rule as usual. If the structure is irregular, may be conservative for max rotated RS. Depending on the level of irregularities, a RS analysis may be mandated by the code. Engineering judgment. Code, by nature, cannot address all types of irregularities. 30

31 Analysis and Design: Suggestions RS FOR GEOMEAN BASED RS (both regular and irregular): MAJOR PRINCIPAL DIRECTION 90 Y SAME RS CURVES SIMULTANEOUSLY APPLIED MINOR PRINCIPAL DIRECTION X Use CQC (Modal Comb.) SRSS (Directional Comb.) Scale: Find base shear for both Major and Minor principal directions. V Major & V Minor Scale both RS curves by the ratio STATIC BASE SHEAR MIN(V,V ) Major Minor NOTE: ASCE 7 05 has a factor or 0.85 in scaling 31

32 Analysis and Design: Suggestions FOR MAXIMUM ROTATED RS (For Regular Structures): MAJOR PRINCIPAL DIRECTION 90 Y MINOR PRINCIPAL DIRECTION X Use CQC (Modal Comb.) Scale: Find base shear for both Major and Minor principal directions. ONLY ONE RS CURVE IS APPLIED IN ANY OF THE PRINCIPAL DIRECTIONS, NOT BOTH V Major & V Minor Scale both RS curves by the ratio STATIC BASE SHEAR V OR V Major Minor NOTE: ASCE 7 05 has a factor or 085in 0.85 scaling 32

33 Analysis and Design: Suggestions FOR MAXIMUM ROTATED RS (For Irregular Structures): For irregular structures: Create many load cases for various angles of rotation ti of structure t (NOT RS angle). l) Scaling is an issue. Perhaps scale to ratio: STATIC BASE SHEAR MIN(V ) BUILDING PLAN Θ = 10 Θ = 5 Θ = 0 Θ =

34 Analysis and Design: Suggestions FOR MAXIMUM ROTATED RS(For Irregular Str): Alternative Suggestion (requires further study): RS 2 = RS 2 THIS FORM OF THE RS IS SUITABLE FOR CQC + SRSS, BUT SCALING SHOULD BE DONE WRT TO MAX ROTATED SPECTRA 34

35 Unclear points in Structural Codes Manyliterature agree/emphasize that current structural codes are not clear on some of the procedures and they are left to engineer s judgment. Example: Scaling RS base shear to static ti base shear. RESPONSE SPECTRUM IN SINGLE DIRECTION (X) REGULAR STRUCTURE V y ~ 0 CALCULATED BASE SHEAR V x V y 0 RESULTANT RESPONSE SPECTRUM IN SINGLE DIRECTION (X) IRREGULAR STRUCTURE CALCULATED BASE SHEAR V x HOW ARE THESE EFFECTED BY GEOMEAN, MAX ROTATED IS UNCLEAR. 35

36 Other Issues: RS analysis, etc Procedure May be unconservative for regular structures,. Is almost guaranteed to be unconservative for: Irregular structures, un orthogonal lateral systems, members have irregular x sections, and etc The code cannot address these types of structures as it is too structure specific. Engineer has to make a judgment on the level of accuracy. As structure gets complicated, RS analysis, by nature, have limitations Engineer has to make a judgment EXAMPLE: PMM Curve P My Mx x y y x y A I I x WHICH LOCAL ANGLE IS MORE CRITICAL? x y 36

37 Case Study: RC GRAVITY COLUMNS FLAT PLATE RC SLAB RC CORES SUMMARY: 11 Story Office Building Located in a no seismicity area RC Building Extreme torsional irregularity Gravity columns are not part of lateral system Gravity columns will be highly affected from the lateral lloads. CRITICAL GRAVITY COLUMN A Response Spectrum Analysis resulted about max. 30% larger lateral displacements of gravity columns compared to code defined static analysis. 37

38 Conclusions Therehas has been significantdevelopments on both geotechnical and structural aspects of analysis and design for multidirectional seismic motions and orthogonal effects. Structural codes are not clear and specific on how recent changes in the RS representations affects structural analysis and design. If you ask 10 different engineers, you will get 10 different answers. This is an heads up to inform SEsabout tthe procedures and the recent changes; not an attempt to propose new procedure or re invent the wheel(s). 38

39 Conclusions The topics on the RS derivation and analysis that t are crucial for the estimation of the most critical load affects are explained li din a very simple manner from a structural engineer s perspective. Simple guidelines are provided to assure the RS analysis yield conservative results based on an extensive literature survey. The presenter is very keen to share comments and receive suggestions. Baris.Erkus@arup.com 39

40 Future Research We are currently evaluating numerically some of these procedures for various types of structures with various levels l of irregularities. iti We hope to have an understanding of which method is accurate enough for which type of structure. 40

41 CODES? ENGINEERING JUDGMENT? HOW? SAMITOUR TOWER, CULVER CITY, CA 41

42 THANK YOU FOR YOUR ATTENTION 42

43 Problem Definition: Analysis and Design for Seismic Events ONE (1) EQ DATA TIME HISTORY ANALYSIS ACCURATE ESTIMATION OF STRUCTURAL RESPONSES (DISPLACEMENTS, MEMBER FORCES, MEMBER STRESSES) FOR A GIVEN SEISMIC ACCELERATION DATA RESPONSE SPECTRUM ANALYSIS PEAK VALUE OF A SPECIFIED STRUCTURAL RESPONSE IS OBTAINED FOR THE GIVEN RS CURVE. RS CURVE REPRESENTS MANY EQ DATA EQUIVALENT LATERAL FORCE PROCEDURE STATIC ANALYSIS 43

44 Modal Combination Procedures A Response Spectrum (RS) analysis Is an approximation of a more accurate time history (TH) analysis. Attempt to address a wider range of seismic events. TH ANALYSIS LESS ACCURATE, MORE GENERAL, ENVELOPE, PRESCRIPTIVE DESIGN MORE ACCURATE, LESS GENERAL, SPECIFIC, DESIGN FOR ACTUAL BEHAVIOR RS ANALYSIS Efficiency and applicability of RS analysis is mainly determined by the modal combination and directional combination procedures used. 44

45 Response Spectrum Representations Larger of the two horizontal components Example: Joyner and Boore (1982) Direction N S RESPONSE: R N S RESPONSE: R E W Period, T Damping, ξ RESPONSE SPECTRUM ISLARGER OF RS 1: (R E W, R N S ) E W Direction 45

46 Response Spectrum Representations N S S, RS = 3 E W, RS = 4 BUILDING PLAN GM = SQRT(3x4) = 3.46 GEOMEAN RS = 3.46 N S, E W, RS = 3.46 ASCE 7 05 BUILDING PLAN MAX. ROTATED 1 3 MAX. ROTATED 2 2 ASCE BUILDING PLAN NOTE: 5 / 3.46 = GM = 3.46 GM = 2.60 GM = 3.50 BUILDING PLAN 46

47 Response Spectrum Representations Assumptions used in the original ii ldevelopment of CQC3 procedure: Clough and Penzien (1993), Section 25 3: design spectra previously described single component horizontal motion can be used for both components; consistent with the strong ground motion data, the design intensity levels of one component should be reduced about 15 percent below the corresponding intensity level of the other component. The component of larger intensity should be directed along the critical axis of the structure. BUILDING PLAN CRITICAL AXIS However, many other research shows that this ratio is period dependent d and can vary significantly.??? 47

48 Modal Combination Procedures: CQC The following assumptions areimplemented in the derivation (Der Kiureghian, 1981): The structure has classical modes Input excitation ti is a stationary tti Gaussian excitation ti The excitation is a wide band process, i.e., have a smoothly varying power spectral density over a range of frequencies covering the significantmodes of vibration of structures In the original derivation, a Kanai Tajimi filter, with the following parameters is used ω g = 5π, ζ g = 06(60% 0.6 damping) There are several other assumptions in the stochastic dynamics portion of the derivation (e.g., peak factors, zero crossings and etc ) Excellent results for most of building type of structures, as long as assumptions are not significantly violated. 48

49 Directional Combination Procedures: Clough and Penzien (1993) interpretation of 100%+30% rule: Absolute sum of the responses. They compared the results with the multi component earthquakeresults results with SRSS combination of 100% RS in critical direction and 85% RS in the orthogonal direction. (NOTE: This is questionable. See the previous slides.) They conclude that t 100% + 30% summation of responses are max. 5% conservative than the SRSS combination. They conclude that RESPONSE [SRSS(100% RS, 85% RS) ~ 1.12 x RESPONSE [100% RS] This interpretation of the 100%+30% procedure seem to be compatible with the Geomean definition of RS. Does 100%+30% come from The seismic demand in orthogonal directions Orthe structural responses? 49

50 Notes: Thetopics discussed in this presentation are considerably complicated and are subject of current research in both seismology and structural engineering. g The intention in this presentation is to use a very simple language to communicate this complicated technical information for structural engineering community. The information provided herein is mostly a summary and compilation i of current literature. The author is keen to receive any feedback on his interpretation of the literature. The list of references is currently prepared. Will be available soon. 50