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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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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

- 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

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

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

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

The Franklin Institute Awards – April 27, 2006

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

Professor Joe Penzien– First Director of EERC at UC Berkeley

The Franklin Institute Awards – April 27, 2006

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

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

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

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

“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

STRUCTURAL ANALYSIS PROGRAM

ALSO A PERSON

“ Who Is Easily Deceived Or Fooled”

“ Who Unquestioningly Serves Another”

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

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

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

LDR Vectors - 1980

- 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

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

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

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

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

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

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

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

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 =

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)

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 )

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

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

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

Isolators

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

103

ELASTIC FRAME ELEMENTS

56

NONLINEAR DIAGONAL ELEMENTS

600

TIME STEPS @ 0.02 Seconds

COMPUTER MODEL

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 )

Calculate Load-Dependant Ritz Vectors for Structure With Nonlinear Elements Removed.

These Vectors Satisfy the Following

Orthogonality Properties

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

Which Is the Standard

Mode Superposition Equation

Remember 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 the
- unknown nonlinear modal forces which
- are of the following form:
- The deformations in the nonlinear elements
- can be calculated from the following
- displacement transformation equation:

Since the deformations in the nonlinear elements 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

- 50 STEPS AT dT = 0.10 SECONDS

DEAD LOAD

LOAD

LATERAL LOAD

0 1.0 2.0 3.0 4.0 5.0

TIME - Seconds

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.

Definition Of Natural Eigenvectors

The 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 Vectors

Dynamic Vectors

Static Vectors

Solve Static and Dynamic Equilibrium Equations by Mode Superposition

The Modal Equations Can Now Be Written As

SOLUTION OF TYPICAL MODAL EQUATION

FOR DYNAMIC MODES, USE PIECE-WISE EXACT SOLUTION

FOR RIGID-BODY MODES, Direct INTEGRATION

FOR STATIC MODES, THE SOLUTION IS

- Mode Natural Eigenvalue Frequency Period
- 1 100 0
- 2 100 0
- 3 0.826 0.995 6.31
- 4 0 0
- 5 0 0
- 6 0 0

CALCULATION OF NATURAL EIGENVECTORS

Use Recurrence Equation Of Following Form

The First Load Block Must Be The Static Load Patterns Acting on The Structure

Subsequent Load Blocks Are Calculated From

Iteration Is Not Required

The Natural Eigenvector Algorithm (2)

Must be made Stiffness Orthogonal to All Previously Calculated Vectors By the Modified Gram-Schmidt Algorithm

If 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 Loading

Therefore, They Are a Set of

Load Dependent Ritz Vectors

1. Dynamic Load Participation Ratio

2. 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 caseFj 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

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

Analysis 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 building

Over 25 Stories

1958 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 COMPUTER

S = MONTHLY SALARY OF ENGINEER

$4,000,000

C/S = 5,000

C/S = 0.5

$7,500

$1,500

$800

time

1957

1997

A FACTOR OF 10,000 REDUCTION IN 40 YEARS

Floating-Point Speeds of Computer Systems

Definition of one Operation A = B + C*D 64 bits - REAL*8

UCLA Meet

April 17, 1954

Ed set a 880 yard record of 1 Minute and 54 Seconds.

President

Robert .

Sproul

In the last 50 years, Ed is getting Slower and

Computer are getting Faster

The Future Of Personal Computers

Multi-Processors Will Require

New Numerical Methods

and

Modification of Existing Programs

Speed and Accuracy are Important

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