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Seismic Analysis and Design Using Response Spectra
Of Structures Using Response Spectra Or Time History Motions BY Ed Wilson Professor Emeritus of Civil Engineering University of California, Berkeley February 24, 2010 1
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On Advanced Numerical Modeling and Analytical Techniques
SUMMARY OF PRESENTATION On Advanced Numerical Modeling and Analytical Techniques Personal Remarks – 50 years experience of dynamic analysis Seismic Analysis Using Response Spectra – CQC3 Comparison with Direct Time History Dynamic Analysis Retrofit of the San Mateo Bridge _- The Fast Non-Linear Analysis Method – FNA Method Retrofit of the Richmond San Rafael Bridge Near Fault Seismic Analysis Concluding Remarks
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edwilson.org and ed-wilson1@juno.com
1882 Father Born In San Francisco – Carpenter and Walked Guard in S.F. after 1906 Earthquake 1931 Ed born in Ferndale CA – Earthquake Capitol of USA 1950 Graduated - Christian Brothers HS in SAC. Sacramento Jr. College BS in Civil Eng. – UC Berkeley DOT CA Bridge Dept. – Ten Mile River Bridge US Army – Korea – Radio Repairman M.S. and D. Eng. With Prof. Ray Clough 1960 With Ray, Conducted the first Time-Histories Earthquake Response of Buildings Bridges & Dams. - Fifty Years Ago Worked on the Apollo Program at Aerojet in Sacramento - Designed Structures for 10 g Loads Professor at UC Berkeley
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NINETEEN SIXTIES IN BERKELEY
1. Cold War - Blast Analysis 2. Earthquake Engineering Research 3. State And Federal Freeway System 4. Manned Space Program 5. Offshore Drilling 6. Nuclear Reactors And Cooling Towers
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NINETEEN SIXTIES IN BERKELEY
1. Period Of Very High Productivity 2. No Formal Research Institute 3. Free Exchange Of Information – Gave programs to profession prior to publication 4. Worked Closely With Mathematics Group 5. Students Were Very Successful
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DYNAMIC ANALYSIS USING RESPONSE SPECTRUM SEISMIC LOADING
Before the Existence of Inexpensive Personal Computers, the Response Spectrum Method was the Standard Approach for Linear Seismic Analysis
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Figure 15.1a Typical Earthquake Ground Acceleration - Percent of Gravity
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Figure 15.1b Absolute Earthquake Ground Displacements - Inches
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Figure 15.2b Pseudo-Acceleration Spectrum,
- Percent of Gravity Figure 15.2a Relative Displacement Spectrum y (T)MAX Inches
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Figure 15.2b Pseudo-Acceleration Spectrum Percent of Gravity
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Major Approximation The loads are applied directly to the structure; whereas, the real earthquake displacements are applied at the foundation of the real structure.
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Development of the Three Spectrum
In Addition, All Spectrum Values Are Maximum Peak Values The Time History Details of the Duration of the Earthquake Have Been Lost
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Examples of Three-Dimensional Spectra Analyses
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Definition of Earthquake Spectra Input
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Three-Dimensional Spectra Analyses
Equal Spectrum from any direction – CQC3 Method Maximum Peak Column Moments - Symmetrical All Values are Positive
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Three-Dimensional Spectra Analyses 100/30 Spectrum Method
Maximum Peak Column Moments - Not Symmetrical All Values are Positive
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Summary of Multi-Component Combination Rules
The 100/30 and 100/40 percent rules have no theoretical basis. The SRSS combination rule, applied to equal spectra, produces identical results for all reference systems and requires only one analysis to produce all design forces and displacements.
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The CQC3 method should be used where the horizontal orthogonal components of the seismic input are not equal. In case of the seismic analysis of structures near a fault, the fault normal and parallel motions are not equal.
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In 1996 The CQC3 was Proposed by Professor Armen Der Kiureghian
As a Replacement for the 30%, 40% & SRSS Rules For Multi-Component Seismic Analysis
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Design Checks of Three-Dimensional Frame Members for Seismic Forces
In order to stratify various building codes, every one-dimensional compression member within a structure must satisfy the following Demand/Capacity Ratio at all points in time: t = 0 = Static Loads Only
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Where the forces acting on the frame element cross-section at time “t” are including the static forces prior to the application of the dynamic loads. The empirical constants are code and material dependent and are normally defined as .
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Design Checks of Three-Dimensional Frame Members for Spectra Forces
For the case maximum peak spectra forces, compression members within a structure must satisfy the following Demand/Capacity Ratio Where P(max), M2(max) and M3(max) have been Calculated by the CQC Method
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The Retrofit of the San Mateo Bridge
Demand/Capacity Ratios were calculated using COC forces using spectrum calculated from several three-dimensional sets of earthquake motions. Time-dependent Demand/Capacity Ratios were calculated directly from the same set of earthquake motions. In general, the time-dependent Demand/Capacity Ratios were approximately 50 percent of the ratios using the CQC forces.
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Limitations of Response Spectrum Analysis
All forces and displacements obtained from a Response Spectrum Analysis are Maximum Peak Values and are all positive numbers. The specific time the Maximum Peak Values occur is different for every period. Nonlinear Behavior CANNOT be considered in a Response Spectrum Analysis. Except for a single degree of freedom, a Response Spectrum Analysis is an APPROXIMATE METHOD This is not Performance Based Design
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STRUCTURAL ANALYSIS PROGRAM
S A P STRUCTURAL ANALYSIS PROGRAM ALSO A PERSON “ Who Is Easily Deceived Or Fooled” “ Who Unquestioningly Serves Another” 5
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From The Foreword Of The First SAP Manual
"The slang name S A P was selected to remind the user that this program, like all programs, lacks intelligence. It is the responsibility of the engineer to idealize the structure correctly and assume responsibility for the results.” Ed Wilson 1970 6
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The SAP Series of Programs
SAP Used Static Loads to Generate Ritz Vectors Solid-Sap Rewritten by Ed Wilson SAP IV Subspace Iteration – Dr. Jűgen Bathe 1973 – 74 NON SAP New Program – The Start of ADINA 1979 Lost All Research and Development Funding 1979 – 80 SAP 80 New Linear Program for Personal Computers 1983 – 1987 SAP 80 CSI added Pre and Post Processing SAP 90 Significant Modification and Documentation 1997 – Present SAP Nonlinear Elements – More Options – With Windows Interface
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FIELD MEASUREMENTS REQUIRED TO VERIFY
1. MODELING ASSUMPTIONS 2. SOIL-STRUCTURE MODEL 3. COMPUTER PROGRAM 4. COMPUTER USER
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CHECK OF RIGID DIAPHRAGM APPROXIMATION
MECHANICAL VIBRATION DEVICES
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FIELD MEASUREMENTS OF PERIODS AND MODE SHAPES
MODE TFIELD TANALYSIS Diff. - % Sec Sec. 0.5
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FIRST DIAPHRAGM MODE SHAPE
15 th Period TFIELD = 0.16 Sec.
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The Fast Nonlinear Analysis Method
The FNA Method was Named in 1996 Designed for the Dynamic Analysis of Structures with a Limited Number of Predefined Nonlinear Elements
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BASE ISOLATION Isolators 25
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BUILDING IMPACT ANALYSIS 26
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FRICTION DEVICE CONCENTRATED DAMPER NONLINEAR ELEMENT 27
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GAP ELEMENT BRIDGE DECK ABUTMENT TENSION ONLY ELEMENT 28
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Degrading Stiffness Elements are in SAP 2000
P L A S T I C H I N G E S 2 ROTATIONAL DOF Degrading Stiffness Elements are in SAP 2000 29
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Mechanical Damper F = f (u,v,umax ) F = ku F = C vN Mathematical Model
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First Application of the FNA Method - 1994
103 FEET DIAMETER FEET HEIGHT NONLINEAR DIAGONALS BASE ISOLATION Nonlinear Seismic Analysis of ELEVATED WATER STORAGE TANK 30
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COMPUTER MODEL 92 NODES 103 ELASTIC FRAME ELEMENTS 56
NONLINEAR DIAGONAL ELEMENTS 600 TIME Seconds 31
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COMPUTER TIME REQUIREMENTS PROGRAM ANSYS INTEL 486 3 Days
( 4300 Minutes ) ANSYS CRAY 3 Hours ( 180 Minutes ) SADSAP INTEL 486 2 Minutes ( B Array was 56 x 20 ) 32
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EXAMPLE OF FRAME WITH UPLIFTING ALLOWED
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Four Static Load Conditions Generation of LDR Vectors
Are Used To Start The Generation of LDR Vectors EQ DL Left Right 41
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Column Axial Forces
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Confirmed by Shaking Table Tests
Summary of Results for Building Uplifting Example from Two Times the Loma Prieta Earthquake Uplift Computer Time Max. Displace-ment (inches) Max. Column Force (kips) Max. Base Shear (kips) Max. Base Moment (k-in) Max. Strain Energy (k-in) Max. Uplift (inches) Without 14.6 Sec 7.76 924 494 424,000 1,547 0.0 With 15.0 Sec 5.88 620 255 197,000 489 1.16 Percent Diff. -24% -33% -40% -53% -68% Confirmed by Shaking Table Tests By Ray Clough on Three Story Frame
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Advantages Of The FNA Method
1. The Method Can Be Used For Both Static And Dynamic Nonlinear Analyses 2. The Method Is Very Efficient And Requires A Small Amount Of Additional Computer Time As Compared To Linear Analysis 2. The Method Can Easily Be Incorporated Into Existing Computer Programs For LINEAR DYNAMIC ANALYSIS. 47
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MULTISUPPORT SEISMIC ANALYSIS (Earthquake Displacements Input )
ANCHOR PIERS Hayward Fault San Andreas Fault East West 54
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Eccentrically Braced Towers
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Analysis and Design of Structures for Near Fault Earthquake Motions
On the UC Berkeley Campus Fault Normal and Parallel Foundation Displacements are Significantly Different Used six different Time-History Earthquake Motions for Nonlinear Dynamic Analyses
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Base Isolated in 2004 Hearst Mining Building – Built in 1905 to 07
50 Yards from the Hayward Fault Base Isolated in 2004
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Near Fault Analysis and Design - SRC
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Concluding Remarks The 100/30 percent Rule should replaced by the SRSS Rule - Until the CQC3 is implemented in SAP 2000. Response Spectra Seismic Analysis is an Approximate Method and is restricted to linear structural behavior and may satisfy a design code. However, it may not produce a Performance Based Design In general, Nonlinear Time-History Analyses produce more realistic results and can produce Performance Based Design
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Nonlinear Seismic Analyses are possible due to:
Performance Based Design is using all the information about the seismic displacement loading on the structure and to the accurately predict the nonlinear behavior and damage to the structure. All Code Based Designed Structures appear to be based on Linear Analysis. Nonlinear Seismic Analyses are possible due to: New Methods of nonlinear analysis have been developed. New Nonlinear Energy Dissipation and Simple Isolation Device can be used. The new inexpensive personal computer can easily conduct the required calculations.
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Floating-Point Speeds of Computer Systems
Definition of one Operation A = B + C*D 64 bits - REAL*8 Year Computer or CPU Operations Per Second Relative Speed 1962 CDC-6400 50,000 1 1964 CDC-6600 100,000 2 1974 CRAY-1 3,000,000 60 1981 IBM-3090 20,000,000 400 CRAY-XMP 40,000,000 800 1994 Pentium-90 3,500,000 70 1995 Pentium-133 5,200,000 104 DEC-5000 upgrade 14,000,000 280 1998 Pentium II - 333 37,500,000 750 1999 Pentium III - 450 69,000,000 1,380 2003 Pentium IV – 2,000 220,000,000 4,400 2006 AMD - Athlon 440,000,000 8,800 2009 Intel – Core 2 Duo 1,200,000,000 25,000
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