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Earthquake Engineering Research at UC Berkeley and Recent Developments at CSI Berkeley BY Ed Wilson Professor Emerit

Earthquake Engineering Research at UC Berkeley and Recent Developments at CSI Berkeley BY Ed Wilson Professor Emeritus of Civil Engineering University of California, Berkeley October 24 - 25, 2008. Summary of Presentation UC Berkeley in the in the period of 1953 to 1991 The Faculty

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Earthquake Engineering Research at UC Berkeley and Recent Developments at CSI Berkeley BY Ed Wilson Professor Emerit

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  1. Earthquake Engineering Research at UC Berkeley and Recent Developments at CSI Berkeley BY Ed Wilson Professor Emeritus of Civil Engineering University of California, Berkeley October 24 - 25, 2008

  2. Summary of Presentation • UC Berkeley in the in the period of 1953 to 1991 • The Faculty • The SAP Series of Computer Programs • Dynamic Field Testing of Structures • The Load-Dependent Ritz Vectors – LDR Vectors - 1980 • The Fast Nonlinear Analysis Method – FNA Method - 1990 • A New Efficient Algorithm for the Evaluation of All • Static and Dynamic Eigenvalues of any Structure - 2002 • Final Remarks and Recommendations • All Slides can be copied from we site edwilson.org

  3. “edwilson.org” Copy Papers and Slides Early Finite Element Research at UC Berkeley by Ray Clough and Ed Wilson The Development of Earthquake Engineering Software at Berkeley by Ed Wilson - Slides

  4. Dynamic Research at UC Berkeley Retired Faculty Members by Date Hired 1946 Bob Wiegel – Coastal Engineering - Tsunamis 1949 Ray Clough – Computational and Experimental Dynamics 1950 Harry Seed – Soil Mechanics - Liquefaction 1953 Joseph Penzien – Random Vibrations – Wind, Waves & Earthquake 1957 Jack Bouwkamp – Dynamic Field Testing of Real Structures 1963 Robert Taylor – Computational Solid and Fluid Dynamics 1965 James Kelly – Base Isolation and Energy Dissipation 1965 Ed Wilson – Numerical Algorithms for Dynamic Analysis 196? Beresford Parlett – Mathematics - Numerical Methods 196? Bruce Bolt – Seismology – Earthquake Ground Motions

  5. Professor Ray W. Clough 1942 BS University of Washington 1943 - 1946 U. S. Army Air Force 1946 - 1949 MIT - D. Science - Bisplinghoff 1949 - 1986 Professor of CE U.C Berkeley 1952 and 1953 Summer Work at Boeing National Academy of Engineering National Academy of Science Presidential Medal of Science The Franklin Institute Medal – April 27, 2006

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

  7. Joe Penzien 1945 BS University of Washington 1945 US Army Corps of Engineers 1946 Instructor - University of Washington 1953 MIT - D. Science 1953 - 88 Professor UCB 1990 - 2006 International Civil Engineering Consultants – Principal with Dr. Wen Tseng

  8. Professor Joe Penzien– First Director of EERC at UC Berkeley The Franklin Institute Awards – April 27, 2006

  9. New Printing of the Clough and Penzien Book 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.com Ask for Educational Discount

  10. Ed Wilson - edwilson.org 1955 BS University of California 1955 - 57 US Army – 15 months in Korea 1958 MS UCB 1957 - 59 Oroville Dam Experimental Project 1960 First Automated Finite Element Program 1963 D Eng UCB 1963 - 1965 Research Engineer, Aerojet - 10g Loading 1965 - 1991 Professor UCB – 29 PhD Students 1991 - 2008 Senior Consultant To CSI Berkeley – where 95% of my work is in Earthquake Engineering

  11. My Book – 23 Chapters csiberkeley.com Ask for Educational Discount

  12. 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

  13. 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

  14. UC Students “Berkeley During The Late 1960’s And Early 1970’s Graduate Study Was Like Visiting An Intellectual Candy Store” Thomas Hughes Professor, University of Texas

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

  16. 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

  17. 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 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

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

  19. CHECK OF RIGID DIAPHRAGM APPROXIMATION MECHANICAL VIBRATION DEVICES

  20. 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

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

  22. Load-Dependent Ritz Vectors LDR Vectors - 1980

  23. DYNAMIC EQUILIBRIUM EQUATIONS • M a + C v + K u = F(t) • a = Node Accelerations • v = Node Velocities • u = Node Displacements • M = Node Mass Matrix • C = Damping Matrix • K = Stiffness Matrix • F(t) = Time-Dependent Forces

  24. PROBLEM TO BE SOLVED M a + C v + K u = fi g(t)i = - Mx ax - My ay - Mz az For 3D Earthquake Loading THE OBJECTIVE OF THE ANALYSIS IS TO SOLVE FOR ACCURATE DISPLACEMENTS and MEMBER FORCES

  25. METHODS OF DYNAMIC ANALYSIS For Both Linear and Nonlinear Systems ÷ STEP BY STEP INTEGRATION - 0, dt, 2 dt ... N dt USE OF MODE SUPERPOSITION WITH EIGEN OR LOAD-DEPENDENT RITZ VECTORS FOR FNA For Linear Systems Only TRANSFORMATION TO THE FREQUENCY DOMAIN and FFT METHODS ÷ RESPONSE SPECTRUM METHOD - CQC - SRSS

  26. STEP BY STEP SOLUTION METHOD 1. Form Effective Stiffness Matrix 2. Solve Set Of Dynamic Equilibrium Equations For Displacements At Each Time Step 3. For Non Linear Problems Calculate Member Forces For Each Time Step and Iterate for Equilibrium - Brute Force Method

  27. MODE SUPERPOSITION METHOD 1. Generate Orthogonal Dependent Vectors And Frequencies 2. Form Uncoupled Modal Equations And Solve Using An Exact Method For Each Time Increment. 3. Recover Node Displacements As a Function of Time 4. Calculate Member Forces As a Function of Time

  28. GENERATION OF LOAD DEPENDENT RITZ VECTORS 1. Approximately Three Times Faster Than The Calculation Of Exact Eigenvectors 2. Results In Improved Accuracy Using A Smaller Number Of LDR Vectors 3. Computer Storage Requirements Reduced 4. Can Be Used For Nonlinear Analysis To Capture Local Static Response

  29. STEP 1. INITIAL CALCULATION A. TRIANGULARIZE STIFFNESS MATRIX B. 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

  30. STEP 2. VECTOR GENERATION i = 2 . . . . N Blocks A. 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, to Make Block of Vectors, Yi, Orthogonal to all Previously Calculated Vectors - Vi

  31. STEP 3. MAKE VECTORS STIFFNESS ORTHOGONAL A. SOLVE Nb x Nb Eigenvalue Problem [ VT K V ] Z = [ w2 ] Z B. CALCULATE MASS AND STIFFNESS ORTHOGONAL LDR VECTORS VR = V Z =

  32. DYNAMIC RESPONSE OF BEAM 100 pounds 10 AT 12" = 240" • FORCE TIME

  33. MAXIMUM DISPLACEMENT Numberof Vectors Eigen Vectors Load Dependent Vectors 1 0.004572 (-2.41) 0.004726 (+0.88) 2 0.004572 (-2.41) 0.004591 ( -2.00) 3 0.004664 (-0.46) 0.004689 (+0.08) 4 0.004664 (-0.46) 0.004685 (+0.06) 5 0.004681 (-0.08) 0.004685 ( 0.00) 7 0.004683 (-0.04) 9 0.004685 (0.00) ( Error in Percent)

  34. MAXIMUM MOMENT Number of Vectors Eigen Vectors Load Dependent Vectors 1 4178 ( - 22.8 %) 5907 ( + 9.2 ) 2 4178 ( - 22.8 ) 5563 ( + 2.8 ) 3 4946 ( - 8.5 ) 5603 ( + 3.5 ) 4 4946 ( - 8.5 ) 5507 ( + 1.8) 5 5188 ( - 4.1 ) 5411 ( 0.0 ) 7 5304 ( - .0 ) 9 5411 ( 0.0 ) ( Error in Percent )

  35. LDR Vector Summary After 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

  36. 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

  37. EVALUATE LDR 1. VECTORS WITH NONLINEAR ELEMENTS REMOVED AND DUMMY ELEMENTS ADDED FOR STABILITY FAST NONLINEARANALYSIS 2. SOLVE ALL MODAL EQUATIONS WITH NONLINEAR FORCES ON THE RIGHT HAND SIDE 3. USE EXACT INTEGRATION WITHIN EACH TIME STEP 4. FORCE AND ENERGY EQUILIBRIUM ARE STATISFIED AT EACH TIME STEP BY ITERATION

  38. BASE ISOLATION Isolators

  39. BUILDING IMPACT ANALYSIS

  40. FRICTION DEVICE CONCENTRATED DAMPER NONLINEAR ELEMENT

  41. GAP ELEMENT BRIDGE DECK ABUTMENT TENSION ONLY ELEMENT

  42. P L A S T I C H I N G E S 2 ROTATIONAL DOF ALSO DEGRADING STIFFNESS ARE Possible

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

  44. LINEAR VISCOUS DAMPING DOES NOT EXIST IN NORMAL STRUCTURES AND FOUNDATIONS 5 OR 10 PERCENT MODAL DAMPING VALUES ARE OFTEN USED TO JUSTIFY ENERGY DISSIPATION DUE TO NONLINEAR EFFECTS IF ENERGY DISSIPATION DEVICES ARE USED THEN 1 PERCENT MODAL DAMPING SHOULD BE USED FOR THE ELASTIC PART OF THE STRUCTURE - CHECK ENERGY PLOTS

  45. 103 FEET DIAMETER - 100 FEET HEIGHT NONLINEAR DIAGONALS BASE ISOLATION ELEVATED WATER STORAGE TANK

  46. 92 NODES 103 ELASTIC FRAME ELEMENTS 56 NONLINEAR DIAGONAL ELEMENTS 600 TIME STEPS @ 0.02 Seconds COMPUTER MODEL

  47. COMPUTER TIME REQUIREMENTS PROGRAM ( 4300 Minutes ) ANSYS INTEL 486 3 Days ANSYS CRAY 3 Hours ( 180 Minutes ) 2 Minutes SADSAP INTEL 486 ( B Array was 56 x 20 )

  48. Nonlinear Equilibrium Equations

  49. Summary Of FNA Method Calculate Load-Dependant Ritz Vectors for Structure With Nonlinear Elements Removed. These Vectors Satisfy the Following Orthogonality Properties

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