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

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

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. 1950 - 52 Sacramento Jr. College 1953 - 54 BS in Civil Eng. – UC Berkeley DOT CA Bridge Dept. – Ten Mile River Bridge 1955 - 57 US Army – Korea – Radio Repairman 1957 - 63 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 1963- 65 Worked on the Apollo Program at Aerojet in Sacramento - Designed Structures for 10 g Loads 1965 -91 Professor at UC Berkeley

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

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

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

Figure 15.1a Typical Earthquake Ground Acceleration - Percent of Gravity

Figure 15.1b Absolute Earthquake Ground Displacements - Inches

Figure 15.2b Pseudo-Acceleration Spectrum, - Percent of Gravity Figure 15.2a Relative Displacement Spectrum y (T)MAX Inches

Figure 15.2b Pseudo-Acceleration Spectrum Percent of Gravity

Major Approximation The loads are applied directly to the structure; whereas, the real earthquake displacements are applied at the foundation of the real structure.

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

Examples of Three-Dimensional Spectra Analyses

Definition of Earthquake Spectra Input

Three-Dimensional Spectra Analyses Equal Spectrum from any direction – CQC3 Method Maximum Peak Column Moments - Symmetrical All Values are Positive

Three-Dimensional Spectra Analyses 100/30 Spectrum Method Maximum Peak Column Moments - Not Symmetrical All Values are Positive

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.

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.

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

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

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 .

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

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.

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

STRUCTURAL ANALYSIS PROGRAM S A P STRUCTURAL ANALYSIS PROGRAM ALSO A PERSON “ Who Is Easily Deceived Or Fooled” “ Who Unquestioningly Serves Another” 5

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

The SAP Series of Programs 1969 - 70 SAP Used Static Loads to Generate Ritz Vectors 1971 - 72 Solid-Sap Rewritten by Ed Wilson 1972 -73 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 1987 - 1990 SAP 90 Significant Modification and Documentation 1997 – Present SAP 2000 Nonlinear Elements – More Options – With Windows Interface

FIELD MEASUREMENTS REQUIRED TO VERIFY 1. MODELING ASSUMPTIONS 2. SOIL-STRUCTURE MODEL 3. COMPUTER PROGRAM 4. COMPUTER USER

CHECK OF RIGID DIAPHRAGM APPROXIMATION MECHANICAL VIBRATION DEVICES

FIELD MEASUREMENTS OF PERIODS AND MODE SHAPES MODE TFIELD TANALYSIS Diff. - % 1 1.77 Sec. 1.78 Sec. 0.5 2 1.69 1.68 0.6 3 1.68 1.68 0.0 4 0.60 0.61 0.9 5 0.60 0.61 0.9 6 0.59 0.59 0.8 7 0.32 0.32 0.2 - - - - 11 0.23 0.32 2.3

FIRST DIAPHRAGM MODE SHAPE 15 th Period TFIELD = 0.16 Sec.

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

BASE ISOLATION Isolators 25

BUILDING IMPACT ANALYSIS 26

FRICTION DEVICE CONCENTRATED DAMPER NONLINEAR ELEMENT 27

GAP ELEMENT BRIDGE DECK ABUTMENT TENSION ONLY ELEMENT 28

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

Mechanical Damper F = f (u,v,umax ) F = ku F = C vN Mathematical Model

First Application of the FNA Method - 1994 103 FEET DIAMETER - 100 FEET HEIGHT NONLINEAR DIAGONALS BASE ISOLATION Nonlinear Seismic Analysis of ELEVATED WATER STORAGE TANK 30

COMPUTER MODEL 92 NODES 103 ELASTIC FRAME ELEMENTS 56 NONLINEAR DIAGONAL ELEMENTS 600 TIME STEPS @ 0.02 Seconds 31

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

EXAMPLE OF FRAME WITH UPLIFTING ALLOWED 40

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

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

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 66

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

Base Isolated in 2004 Hearst Mining Building – Built in 1905 to 07 50 Yards from the Hayward Fault Base Isolated in 2004

Near Fault Analysis and Design - SRC

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

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.

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