Earthquake Engineering Research at UC Berkeley andRecent Developments atCSI Berkeley BYEd WilsonProfessor Emeritus of Civil EngineeringUniversity of California, Berkeley

October 24 - 25, 2008

Summary of PresentationUC Berkeley in the in the period of 1953 to 1991The FacultyThe SAP Series of Computer ProgramsDynamic Field Testing of StructuresThe Load-Dependent Ritz Vectors LDR Vectors - 1980The Fast Nonlinear Analysis Method FNA Method - 1990A New Efficient Algorithm for the Evaluation of AllStatic and Dynamic Eigenvalues of any Structure - 2002 Final Remarks and RecommendationsAll Slides can be copied from we site edwilson.org

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Early Finite Element Research at UC Berkeley by Ray Clough and Ed Wilson

The Development of Earthquake Engineering Software at Berkeleyby Ed Wilson - Slides

Early Finite Element Research at Berkeley by Ray Clough and Ed Wilson The Development of Earthquake Engineering Software at Berkeley by Ed Wilson - Slides

Early Finite Element Research at Berkeley by Ray Clough and Ed Wilson The Development of Earthquake Engineering Software at Berkeley by Ed Wilson - Slides

Dynamic Research at UC BerkeleyRetired Faculty Members by Date Hired1946Bob Wiegel Coastal Engineering - Tsunamis1949Ray Clough Computational and Experimental Dynamics1950Harry Seed Soil Mechanics - Liquefaction 1953 Joseph Penzien Random Vibrations Wind, Waves & Earthquake1957 Jack Bouwkamp Dynamic Field Testing of Real Structures1963Robert Taylor Computational Solid and Fluid Dynamics1965James Kelly Base Isolation and Energy Dissipation1965Ed Wilson Numerical Algorithms for Dynamic Analysis196?Beresford Parlett Mathematics - Numerical Methods196?Bruce Bolt Seismology Earthquake Ground Motions

Professor Ray W. Clough1942 BS University of Washington1943 - 1946 U. S. Army Air Force1946 - 1949 MIT - D. Science - Bisplinghoff 1949 - 1986 Professor of CE U.C Berkeley1952 and 1953 Summer Work at BoeingNational Academy of EngineeringNational Academy of SciencePresidential Medal of ScienceThe Franklin Institute Medal April 27, 2006

Doug, Shirley and Ray Clough The Franklin Institute Awards April 27, 2006

Joe Penzien

1945 BS University of Washington1945 US Army Corps of Engineers1946 Instructor - University of Washington1953 MIT - D. Science 1953 - 88 Professor UCB1990 - 2006International Civil Engineering Consultants Principal withDr. Wen Tseng

Professor Joe Penzien First Director of EERC at UC BerkeleyThe Franklin Institute Awards April 27, 2006

Berkeley, CA, February 26, 2004 Computers and Structures, Inc., is pleased to release the latest revision to Dynamics of Structures, 2nd Edition by Professors Clough and Penzien. A classic, this definitive textbook has been popular with educators worldwide for nearly 30 years. This release has been updated by the original authors to reflect the latest approaches and techniques in the field of structural dynamics for civil engineers. csiberkeley.comAsk for Educational DiscountNew Printing of the Clough and Penzien Book

Ed Wilson - edwilson.org

1955 BS University of California1955 - 57 US Army 15 months in Korea1958 MS UCB1957 - 59 Oroville Dam Experimental Project 1960First Automated Finite Element Program1963 D Eng UCB1963 - 1965Research Engineer, Aerojet - 10g Loading1965 - 1991 Professor UCB 29 PhD Students 1991 - 2008Senior Consultant To CSI Berkeley where 95% of my work is in Earthquake Engineering

My Book 23 Chapterscsiberkeley.comAsk for Educational Discount

NINETEEN SIXTIES IN BERKELEY1.Cold War - Blast Analysis2. Earthquake Engineering Research3.State And Federal Freeway System4.Manned Space Program5.Offshore Drilling 6.Nuclear Reactors And Cooling Towers

NINETEEN SIXTIES IN BERKELEY1.Period Of Very High Productivity2.No Formal Research Institute3.Free Exchange Of Information Gave programs to profession prior to publication4.Worked Closely With Mathematics Group5.Students Were Very Successful

UC Students Berkeley During The Late 1960s And Early 1970s Graduate Study Was Like Visiting An Intellectual Candy Store

Thomas HughesProfessor, University of Texas

S A P

STRUCTURAL ANALYSIS PROGRAMALSO A PERSON

Who Is Easily Deceived Or Fooled

Who Unquestioningly Serves Another

"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 1970From The Foreword Of The First SAP Manual

The SAP Series of Programs1969 - 70 SAP Used Static Loads to Generate Ritz Vectors1971 - 72Solid-Sap Rewritten by Ed Wilson1972 -73 SAP IV Subspace Iteration Dr. Jgen Bathe1973 74NON SAP New Program The Start of ADINALost All Research and Development Funding 1979 80SAP 80New Linear Program for Personal Computers1983 1987SAP 80 CSI added Pre and Post Processing1987 - 1990 SAP 90Significant Modification and Documentation1997 PresentSAP 2000 Nonlinear Elements More Options With Windows Interface

FIELD MEASUREMENTS REQUIRED TO VERIFY1.MODELING ASSUMPTIONS2.SOIL-STRUCTURE MODEL3.COMPUTER PROGRAM4.COMPUTER USER

MECHANICAL VIBRATION DEVICESCHECK OF RIGID DIAPHRAGM APPROXIMATION

FIELD MEASUREMENTS OF PERIODS AND MODE SHAPESMODETFIELDTANALYSIS Diff. - %11.77 Sec.1.78 Sec.0.521.691.680.631.68 1.680.040.600.610.950.600.610.960.590.590.870.320.320.2----110.230.322.3

15 th PeriodTFIELD = 0.16 Sec.FIRST DIAPHRAGM MODE SHAPE

Load-Dependent Ritz VectorsLDR Vectors - 1980

DYNAMIC EQUILIBRIUM EQUATIONS

M a + C v + K u = F(t)

a = Node Accelerationsv = Node Velocitiesu = Node DisplacementsM = Node Mass MatrixC= Damping MatrixK= Stiffness MatrixF(t)= Time-Dependent Forces

PROBLEM TO BE SOLVEDM a + C v + K u = fi g(t)i For 3D Earthquake LoadingTHE OBJECTIVE OF THE ANALYSISIS TO SOLVE FOR ACCURATE DISPLACEMENTS and MEMBER FORCES= - Mx ax - My ay - Mz az

METHODS OF DYNAMIC ANALYSISFor Both Linear and Nonlinear SystemsSTEP BY STEP INTEGRATION - 0, dt, 2 dt ... N dtUSE OF MODE SUPERPOSITION WITH EIGEN OR LOAD-DEPENDENT RITZ VECTORS FOR FNAFor Linear Systems Only TRANSFORMATION TO THE FREQUENCYDOMAIN and FFT METHODSRESPONSE SPECTRUM METHOD - CQC - SRSS

STEP BY STEP SOLUTION METHOD1.Form Effective Stiffness Matrix

2.Solve Set Of Dynamic Equilibrium Equations For Displacements At Each Time Step

3.For Non Linear ProblemsCalculate Member Forces For Each Time Step and Iterate for Equilibrium - Brute Force Method

MODE SUPERPOSITION METHOD1.Generate Orthogonal Dependent Vectors And Frequencies

2.Form Uncoupled Modal EquationsAnd Solve Using An Exact MethodFor Each Time Increment.

3. Recover Node DisplacementsAs a Function of Time

4. Calculate Member Forces As a Function of Time

GENERATION OF LOAD DEPENDENT RITZ VECTORS1.Approximately Three Times Faster Than The Calculation Of Exact Eigenvectors2.Results In Improved Accuracy Using A Smaller Number Of LDR Vectors3.Computer Storage Requirements Reduced 4.Can Be Used For Nonlinear Analysis To Capture Local Static Response

STEP 1. INITIAL CALCULATIONA.TRIANGULARIZE STIFFNESS MATRIXB.DUE TO A BLOCK OF STATIC LOAD VECTORS, f,SOLVE FOR A BLOCK OF DISPLACEMENTS, u,

K u = f

C.MAKE u STIFFNESS AND MASS ORTHOGONAL TO FORM FIRST BLOCK OF LDL VECTORS V 1 V1T M V1 = I

STEP 2. VECTOR GENERATION i = 2 . . . . N BlocksA.Solve for Block of Vectors, K Xi = M Vi-1

B.Make Vector Block, Xi , Stiffness and Mass Orthogonal - Yi

C.Use Modified Gram-Schmidt, Twice, toMake Block of Vectors, Yi , Orthogonalto all Previously Calculated Vectors - Vi

STEP 3. MAKE VECTORS STIFFNESS ORTHOGONALA.SOLVE Nb x Nb Eigenvalue Problem[ VT K V ] Z = [ w2 ] Z

B.CALCULATE MASS AND STIFFNESS ORTHOGONAL LDR VECTORS

VR = V Z =

10 AT 12" = 240"100 poundsFORCETIMEDYNAMIC RESPONSE OF BEAM

MAXIMUM DISPLACEMENTNumber of Vectors Eigen Vectors Load Dependent Vectors10.004572(-2.41)0.004726(+0.88)20.004572(-2.41)0.004591( -2.00)30.004664(-0.46)0.004689(+0.08)40.004664(-0.46)0.004685(+0.06)50.004681(-0.08)0.004685( 0.00)70.004683(-0.04)90.004685(0.00)( Error in Percent)

MAXIMUM MOMENTNumber of Vectors Eigen Vectors Load Dependent Vectors

14178( - 22.8 %)5907( + 9.2 )24178( - 22.8 )5563( + 2.8 )34946( - 8.5 )5603( + 3.5 )44946( - 8.5 )5507( + 1.8) 55188( - 4.1 )5411( 0.0 )75304( - .0 )95411( 0.0 )( Error in Percent )

LDR Vector SummaryAfter Over 20 Years Experience Using the LDR Vector Algorithm We Have Always Obtained More Accurate Displacements and Stresses Compared to Using the Same Number of Exact Dynamic Eigenvectors.SAP 2000 has Both Options

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

FAST NONLINEAR ANALYSIS2.SOLVE ALL MODAL EQUATIONS WITH NONLINEAR FORCES ON THE RIGHT HAND SIDEUSE EXACT INTEGRATION WITHIN EACH TIME STEP 4.FORCE AND ENERGY EQUILIBRIUM ARESTATISFIED AT EACH TIME STEP BY ITERATION3.

IsolatorsBASE ISOLATION

BUILDINGIMPACTANALYSIS

FRICTIONDEVICECONCENTRATEDDAMPERNONLINEARELEMENT

GAP ELEMENTTENSION ONLY ELEMENTBRIDGE DECK ABUTMENT

P L A S T I CH I N G E S2 ROTATIONAL DOFALSO DEGRADING STIFFNESS ARE Possible

Mechanical DamperMathematical ModelF = C vNF = kuF = f (u,v,umax )

LINEAR VISCOUS DAMPINGDOES NOT EXIST IN NORMAL STRUCTURESAND FOUNDATIONS5 OR 10 PERCENT MODAL DAMPING VALUES ARE OFTEN USED TO JUSTIFY ENERGY DISSIPATION DUE TO NONLINEAR EFFECTSIF ENERGY DISSIPATION DEVICES ARE USEDTHEN 1 PERCENT MODAL DAMPING SHOULD BE USED FOR THE ELASTIC PART OF THE STRUCTURE - CHECK ENERGY PLOTS

103 FEET DIAMETER - 100 FEET HEIGHT ELEVATED WATER STORAGE TANKNONLINEAR DIAGONALSBASEISOLATION

COMPUTER MODEL

COMPUTER TIME REQUIREMENTS PROGRAM( 4300 Minutes )ANSYSINTEL 4863 DaysANSYSCRAY3 Hours( 180 Minutes )SADSAPINTEL 4862 Minutes ( B Array was 56 x 20 )

Nonlinear Equilibrium Equations

Summary Of FNA Method

Calculate Load-Dependant Ritz Vectors for StructureWith Nonlinear Elements Removed.

These Vectors Satisfy the FollowingOrthogonality Properties

The Solution Is Assumed to Be a Linear Combination of the LDR Vectors. Or,

Which Is the Standard Mode Superposition EquationRemember the LDR Vectors Are a Linear Combination of the Exact Eigenvectors; Plus, the Static Displacement Vectors.No Additional Approximations Are Made.

A typical modal equation is uncoupled. However, the modes are coupled by theunknown nonlinear modal forces whichare of the following form:

The deformations in the nonlinear elementscan be calculated from the followingdisplacement transformation equation:

Since the deformations in the nonlinearelements can be expressed in terms of the modal response by

Where the size of the array is equal to the number of deformations times the number of LDR vectors.

The array is calculated only once prior to the start of mode integration.

THE ARRAY CAN BE STORED IN RAM

The nonlinear element forces are calculated, for iteration i , at the end of each time step t

FRAME WITH UPLIFTING ALLOWED

UPLIFTING ALLOWED

Four Static Load Conditions Are Used To Start TheGeneration of LDR Vectors EQ DL Left Right

TIME - SecondsDEAD LOADLATERAL LOADLOAD0 1.0 2.0 3.0 4.0 5.0NONLINEAR STATIC ANALYSIS50 STEPS AT dT = 0.10 SECONDS

Advantages Of The FNA Method1.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.

A COMPLETE EIGENVECTOR SUBSPACE FOR THE LINEAR AND NONLINEAR DYNAMIC ANALYSIS OF STRUCTURES

Definition Of Natural EigenvectorsThe total number of Natural Eigenvectors that exist is always equal to the total number of displacement degrees-of-freedom of the structural system. The following three types of Natural Eigenvectors are possible:Rigid Body VectorsDynamic VectorsStatic Vectors

EXAMPLE OF SIX DEGREE OF FREEDOM SYSTEM

How Do We Solve a System That Has Both Zero and Infinite Frequencies?

Solve Static and Dynamic Equilibrium Equations by Mode SuperpositionThe Modal Equations Can Now Be Written As

SOLUTION OF TYPICAL MODAL EQUATION

FOR DYNAMIC MODES, USE PIECE-WISE EXACT SOLUTIONFOR RIGID-BODY MODES, Direct INTEGRATION

FOR STATIC MODES, THE SOLUTION IS

Calculation of Frequencies from Natural Eigenvalues

Eigenvalues for Simple Beam

Mode Natural Eigenvalue Frequency Period1100 02100 030.826 0.9956.31400500600

CALCULATION OF NATURAL EIGENVECTORSUse Recurrence Equation Of Following FormThe First Load Block Must Be The Static Load Patterns Acting on The StructureSubsequent Load Blocks Are Calculated FromIteration Is Not Required

The Natural Eigenvector Algorithm (2)Must be made Stiffness Orthogonal to All Previously Calculated Vectors By the Modified Gram-Schmidt AlgorithmIf a Vector Is the Same As a Previously Calculated Vector It Must Be Rejected

The Natural Eigenvector Algorithm (3)A Static Vector Has A Zero Eigenvalue And An Infinite Frequency

A Truncated Set of Natural Eigenvalues Contains Linear Combinations of the Dynamic and Static Eigen Vectors That Are Excited by the LoadingTherefore, They Are a Set of Load Dependent Ritz Vectors

Error Estimation1. Dynamic Load Participation Ratio2. Static Load Participation Ratio

Therefore, this allows the LDR Algorithm to Automatic Terminate Generation when Error Limits are Satisfied

The dynamic load participation ratio for load case Fj is defined as the ratio of the kinetic energy captured by the truncated set of vectors to the total kinetic energy. Or For earthquake loading, this is identical to the mass participation factor in the three different directions A minimum of 90 percent is recommended

The static load participation ratio for load case Fj is defined as the ratio of the strain energy captured by the truncated set of vectors to the total strain energy due to the static load vectors. Or,Always equal to 1.0 for LDR vectors

FINAL REMARKS

Existing Dynamic Analysis Technology allows us to design earthquake resistant structures economically . However, many engineers are using Static PushoverAnalysis to approximate earthquake forces.

Advances in Computational Aero and Fluid Dynamics are not being used by the Civil Engineering Profession to Design Safe Structures for wind and wave loads.

Many engineers are still using approximate wind tunnel results to generate Static Wind Loads.

In a large earthquake the safest place to be is on the top of a high-rise buildingOver 25 Stories

COMPUTERS1958 TO 2008

IBM 701 - Multi-Processors

The Current Speed of a $1,000 Personal Computer is 1,500 Times Faster than the $10,000,000 Cray Computer of 1975

C = COST OF THE COMPUTER19571997timeS = MONTHLY SALARY OF ENGINEER C/S = 5,000C/S = 0.5A FACTOR OF 10,000 REDUCTION IN 40 YEARS $$1,500$7,500$4,000,000$800

Floating-Point Speeds of Computer SystemsDefinition of one Operation A = B + C*D 64 bits - REAL*8

YearComputer or CPUOperations Per SecondRelative Speed1963CDC-640050,00011967CDC-6600100,00021974CRAY-13,000,000601981IBM-309020,000,0004001981CRAY-XMP40,000,0008001990DEC-50003,500,000701994Pentium-903,500,000701995Pentium-1335,200,0001041995DEC-5000 upgrade14,000,0002801998Pentium II - 33337,500,0007501999Pentium III - 45069,000,0001,3802003Pentium IV 2,000220,000,0004,4002006AMD - Athlon440,000,0008,800

Cost of Personal Computer Systems

YEARCPUSpeed MHzOperations Per SecondRelative SpeedCOST1980808042001$6,000198480871013,00065$2,5001988803872093,000465$8,00019918048633605,0003,025$10,000199480486661,210,0006,050$5,0001996Pentium23310,300,00052,000$4,0001997Pentium II23311,500,00058,000$3,0001998Pentium II33337,500,000198,000$2,5001999Pentium III45069,000,000345,000$1,5002003Pentium IV2000220,000,0001.100,000$2.0002006AMD - Athlon2000440,000,0002,200,000$950

Ed Wilson atUCLA MeetApril 17, 1954

Ed set a 880 yard record of 1 Minute and 54 Seconds. PresidentRobert .SproulIn the last 50 years, Ed is getting Slower and Computer are getting Faster

The Future Of Personal ComputersMulti-Processors Will RequireNew Numerical MethodsandModification of Existing Programs

Speed and Accuracy are Important

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