PAST, PRESENT AND FUTURE

OF

EARTHQUAKE ANALYSIS OF STRUCTURES

By Ed Wilson Draft dated 8/15/14

September 22 and 24 2014

SEAONC Lectures

http://edwilson.org/History/Slides/Past%20Present%20Future%202014.ppt

1964 Gene’s Comment – a true story

. Ed developed a new program for the Analysis of Complex Rockets

Ed talks to Gene ------

Two weeks later Gene calls Ed ------

Ed goes to see Gene -----

The next day, Gene calls Ed and tells him

“Ed, why did you not tell me about this program.

It is the greatest program I ever used.”

Summary of Lecture Topics

1. Fundamental Principles of Mechanics and Nature

2. Example of the Present Problem – Caltrans Criteria

3. The Response Spectrum Method

4. Demand Capacity Calculations

5. Speed of Computers– The Last Fifty Years

6. Terms I do not Understand

7. The Load Dependant Ritz Vectors - LDR Vectors

8. The Fast Nonlinear Analysis Method – FNA Method

9. Recommendations edwilson.org

10. Questions ed-wilson1@juno.com

Fundamental Equations of Structural Analysis

1.Equilibrium - Including Inertia Forces - Must be Satisfied

2.Material Properties or Stress / Strain or Force / Deformation

3.Displacement Compatibility Or Equations or Geometry

Methods of Analysis

1.Force – Good for approximate hand methods

2.Displacement - 99 % of programs use this method

3.Mixed - Beam Ex. Plane Sections & V = dM/dz

Check Conservation of Energy

My First Earthquake Engineering Paper

October 1-5 1962

THE PRESENT

SAB Meeting on August 28, 2013

Comments on the

Response Spectrum Analysis Method

As Used in the CALTRANS SEISMIC DESIGN CRITERIA

Topics

1. Why do most Engineers have Trouble with Dynamics?

Taught by people who love math – No physical examples

2 Who invented the Response Spectrum Method?

Ray Clough and I did ? – by putting it into my computer program

3 Application by CalTrans to “Ordinary Standard Structures”

Why 30 ? Why reference to Transverse & Longitudinal directions

4 Physical behavior of Skew Bridges – Failure Mode

5 Equal Displacement Rule?

6 Quote from George W. Housner

Who Developed the Approximate Response Spectrum Method of Seismic Analysis of Bridges and other Structures?

1. Fifty years ago there were only digital acceleration records for 3 earthquakes.2. Building codes gave design spectra for a one degree of freedom systems

with no guidance of how to combine the response of of the higher modes.

3. At the suggestion of Ray Clough, I programmed the square root of the sum of the square of the modal values for displacements and member forces. However, I required the user to manually combine the results from the two orthogonal spectra. Users demanded that I modify my programs to automatically combine the two directions. I refused because there was no theoretical justification.

4. The user then modify my programs by using the 100%+30% or 100%+40% rules.

5. Starting in 1981 Der Kiureghian and I published papers showing that the CQC method should be used be used for combining modal responses for each spectrum and the two orthogonal spectra be combined by the SRSS method.

6. We now have Thousands or of 3D earthquake records from hundred of seismic events. Therefore, why not use Nonlinear Time-History Analyses that SATISFIES FORCE EQUILIBREUM.

Base Shear Mode 2

Base Shear Mode 1

X

Y

If Equal Spectra are applied to any Global X–Y-Z System

Member Forces are the same for all Global X–Y Systems, If Calculated from

iZiYiXi FFFF

Torsion or Mode 1, 2 or Mode 3

Nonlinear Failure Mode For Skew Bridges

u(t)

F(t)

Tensional Failure

Tensional Failure

u(t)

F(t)

F(t)Abutment Force

Acting on Bridge

Abutment Force

Acting on Bridge

Contact at Left Abutment

Contact at Right Abutment

Possible Torsional Failure Mode

Design Joint Connectors for Joint Shear Forces?

Figure 5.2.2-1 EDA Modeling Techniques

Use Global X-Y-Z System for all Models

+Y

-Y

+X-X

Use a Global Modal for all Analyses

Seismic Analysis Advice by Ed Wilson

1. All Bridges are Three-Dimensional and their Dynamic Behavior is governed by the Mass and Stiffness Properties of the structure. The Longitudinal and Transverse directions are geometric properties. All Structures have Torsional Modes of Vibrations.

2. The Response Spectrum Analysis Method is a very approximate method of seismic analysis which only produces positive values of displacements and member forces which are not in equilibrium. Demand / Capacity Ratios have Very Large Errors

3. A structural engineer may take several days to prepare and verify a linear SAP2000 model of an Ordinary Standard Bridge. It would take less than a day to add Nonlinear Gap Elements to model the joints. If a family of 3D earthquake motions are specified, the program will automatically summarize the maximum demand-capacity ratios and the time they occur in a few minutes of computer time.

Convince Yourself with a simple test problem

1. Select an existing Sap 2000 model of a Ordinary Standard Bridge with several different spans – both straight and curved.

2. Select one earthquake ground acceleration record to be used as the input loading which is approximately 20 seconds long.

3. Create a spectrum from the selected earthquake ground acceleration record.

4. Using a number of modes that captures a least 90 percent of the mass in all three directions.

5. At a 45 degree angle, Run a Linear Time History Analysis and a Response Spectrum Analysis.

6. Compare Demand Capacity Ratios for both SAP 2000 analysis for all members.

7. You decide if the Approximate RSA results are in good agreement with the Linear time History Results.

Educational Priorities of an Old Professor on Seismic Analysis of Structures

Convince Engineers that the Response Spectrum Method Produces very Poor Results

1. Method is only exact for single degree of freedom systems2. It produces only positive numbers for Displacements and Member

Forces. 3. Results are maximum probable values and occur at an “Unknown

Time”4. Short and Long Duration earthquakes are treated the same using

“Design Spectra”5. Demand/Capacity Ratios are always “Over Conservative” for most

Members. 6. The Engineer does not gain insight into the “Dynamic Behavior of

the Structure” Results are not in equilibrium. More modes and 3D analysis will cause more errors.

7. Nonlinear Spectra Analysis is “Smoke and Mirrors” – Forget it

Convince Engineers that it is easy to conduct “Linear Dynamic Response Analysis”

It is a simple extension of Static Analysis – just add mass and time dependent loads

1. Static and Dynamic Equilibrium is satisfied at all points in time if all modes are included

2. Errors in the results can be estimated automatically if modes are truncated

3. Time-dependent plots and animation are impressive and fun to produce

4. Capacity/Demand Ratios are accurate and a function of time – summarized by program.

5. Engineers can gain great insight into the dynamic response of the structure and may help in the redesign of the structural system.

Terminology commonly used in nonlinear analysis that do not have a unique definition

1.Equal Displacement Rule – can you prove it?

2.Pushover Analysis

3.Equivalent Linear Damping

4. Equivalent Static Analysis

5.Nonlinear Spectrum Analysis

6.Onerous Response History Analysis

Equal Displacement Rule

In 1960 Veletsos and Newmark proposed in a paper presented at the 2nd WCEE

For a one DOF System, subjected to the El Centro Earthquake, the Maximum Displacement was approximately the same for both linear and nonlinear analyses.

In 1965 Clough and Wilson, at the 3rd WCEE, proved the Equal Displacement Rule did not apply to multi DOF structures.

http://edwilson.org/History/Pushover.pdf

1965 Professor Clough’s Comment

. “If tall buildings are designed for elastic column behavior and restrict the nonlinear bending behavior to the girders, it appears the danger of total collapse of the building is reduced.”

This indicates the strong-column and week beam design is the one of the first statements on

Performance Based Design

The Response Spectrum MethodBasic Assumptions

I do not know who first called it a “response spectrum,” but unfortunate the term leads people to think that the characterize the building’s motion, rather than the ground’s motion.

George W. Housner

EERI Oral History, 1996

Typical Earthquake Ground Acceleration – percent of gravity

Integration will produce Earthquake Ground Displacement – inches

These real Eq. Displacement can be used as Computer Input

Relative Displacement Spectrum for a unit mass with different periods

1. These displacements Ymax are maximum (+ or -) values versus period for a structure or mode.

2. Note: we do not know the time these maximum took place.

Pseudo Acceleration SpectrumNote: S = w2 Ymax has the same

properties as the Displacement Spectrum. Therefore, how can anyone justify combining values, which occur at different times, and expect to obtain accurate results.

CASE CLOSED

General Horizontal Response Spectrum from ASCE 41- 06

go? hatthe didWhere

No -Structures NonLinear

Realistic not isShape

Neglected been has Duration

Calculatedbe to Constants

Data Defined UserSimple

s0

sx1xs

1

1x

xs

T2.0T

S/ST

)100ln(6.5[4B

periodsec0.1atvalueS

onacceleratibasepeakS

ratioviscouseffective

Where did the Hat go - on the Response Spectrum ? As I Recall -------

0.1

)P

)t(P1(M

C)t(M

)P

)t(P1(M

C)t(M

P

)t(P)t(R

3e3cb

33

2e2cb

22

crc

If the axial force and the two moments are a function of time, the Demand-Capacity ratio will be a function of time and a smart computer program will produce R(max) and the time it occurred.

A smart engineer will hand check several of these values.

Demand-Capacity RatiosThe Demand-Capacity ratio for a linear elastic, compression member is given by an equation of the following general form:

RSM Demand-Capacity RatiosIf the axial force and the two moments are produced by the Response Spectrum Method the Demand-Capacity ratio may be computed by an equation of the following general form:

0.1

)P

(max)P1(M

C(max)M

)P

(max)P1(M

C(max)M

P

(max)P(max)R

3e3cb

33

2e2cb

22

crc

A smart computer program can compute this Demand-Capacity Ratio. However, only an idiot would believe it.

SPEED and COST of COMPUTERS

1957 to 2014 to the Cloud

You can now buy a very powerful small computer for less than $1,000

However, it may cost you several thousand dollars of your time to learn

how to use all the new options.

If it has a new operating system

1957 My First Computer in Cory Hall

IBM 701 Vacuum Tube Digital Computer

Could solve 40 equations in 30 minutes

1981 My First Computer Assembled at Home

Paid $6000 for a 8 bit CPM Operating System with FORTRAN.

Used it to move programs from the CDC 6400 to the VAX on Campus.

Developed a new program called SAP 80 without using any Statements from previous versions of SAP.

After two years, system became obsolete when IBM released DOS with a floating point chip.

In 1984, CSI developed Graphics and Design Post-Processor and started distribution of the Professional Version of Sap 80

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

YearComputer

or CPUOperationsPer 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

1981 CRAY-XMP 40,000,000 800

1994 Pentium-90 3,500,000 70

1995 Pentium-133 5,200,000 104

1995 DEC-5000 upgrade 14,000,000 280

1998 Pentium II - 333 37,500,000 750

1999 Pentium III - 450 69,000,000 1,380

YEAR CPUSpeed MHz

Operations Per Second

Relative Speed

COST

1980 8080 4 200 1 $6,000

1984 8087 10 13,000 65 $2,500

1988 80387 20 93,000 465 $8,000

1991 80486 33 605,000 3,025 $10,000

1994 80486 66 1,210,000 6,050 $5,000

1996 Pentium 233 10,300,000 52,000 $4,000

1997 Pentium II 233 11,500,000 58,000 $3,000

1998 Pentium II 333 37,500,000 198,000 $2,500

1999 Pentium III 450 69,000,000 345,000 $1,500

2003 Pentium IV 2000 220,000,000 1.100,000 $2.000

2006 AMD - Athlon 2000 440,000,000 2,200,000 $950

Cost of Personal Computer Systems

YearComputer

or CPUCost Operations

Per SecondRelative Speed

1962 CDC-6400 $1,000,000 50,000 1

1974 CRAY-1 $4,000,000 3,000,000 60

1981 VAX or Prime $100,000 100,0002

1994 Pentium-90 $5,000 4,000,00070

1999 Intel Pentium III-450 $1,500 69,000,0001,380

2006 AMD 64 Laptop $2,000 400,000,0008,000

2009 Min Laptop $300 200,000,0004,000

2010 2.4 GHz Intel Core i3 64 bit Win 7 Laptop

$1,0001.35 Billion Intel Fortran

27,000

20132.80 GHz 2 Quad Core 64

bit Win 7$1,000

2.80 Billion Parallelized Fortran

56,000

The cost of one operation has been reduced by 56,000,000 in the last 50 years

1963 Time 2013

Computer Cost versus Engineer’s Monthly Salary

$1,000

$10,000

$1,000

$1,000,000c/s = 1,000 c/s = 0.10

Fast Nonlinear AnalysisWith Emphasis

On Earthquake EngineeringBY

Ed WilsonProfessor Emeritus of Civil Engineering

University of California, Berkeley

edwilson.org

May 25, 2006

Summary Of Presentation1. History of the Finite Element Method

2. History Of The Development of SAP 3. Computer Hardware Developments

4. Methods For Linear and Nonlinear Analysis

5. Generation And Use Of LDR Vectors and Fast Nonlinear Analysis - FNA Method

6. Example Of Parallel EngineeringAnalysis of the Richmond - San Rafael Bridge

"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

From The Foreword Of The First SAP Manual

The SAP Series of Programs1969 - 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 – 80 SAP 80 New Linear Program for Personal Computers

Lost All Research and Development Funding

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

Load-Dependent Ritz Vectors

LDR Vectors – 1980 - 2000

MOTAVATION – 3D Reactor on Soft Foundation

3 D Concrete Reactor

3 D Soft Soil Elements 360 degrees

Dynamic Analysis - 1979by Bechtel using SAP IV

200 Exact Eigenvalues were Calculated and all of the Modes were in the foundation – No Stresses in the Reactor.

The cost for the analysis on the CLAY Computer was

$10,000

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 SOLVED

M a + C v + K u = fi g(t)i

For 3D Earthquake Loading

THE OBJECTIVE OF THE ANALYSISIS TO SOLVE FOR ACCURATE

DISPLACEMENTS and MEMBER FORCES

= - Mx ax - My ay - Mz az

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 FREQUENCYDOMAIN and FFT METHODS

RESPONSE SPECTRUM METHOD - CQC - SRSS

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 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 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

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

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, toMake Block of Vectors, Yi , Orthogonalto all Previously Calculated Vectors - Vi

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 =

10 AT 12" = 120"

100 pounds

FORCE = Step Function

TIME

DYNAMIC RESPONSE OF BEAM

MAXIMUM DISPLACEMENTNumber of 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)

MAXIMUM MOMENTNumber 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 )

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 ANALYSIS

1.EVALUATE LDR VECTORS WITHNONLINEAR ELEMENTS REMOVED ANDDUMMY ELEMENTS ADDED FOR STABILITY

2.SOLVE ALL MODAL EQUATIONS WITH

NONLINEAR FORCES ON THE RIGHT HAND SIDE

USE EXACT INTEGRATION WITHIN EACH TIME STEP

4. FORCE AND ENERGY EQUILIBRIUM ARESTATISFIED AT EACH TIME STEP BY ITERATION

3.

Isolators

BASE ISOLATION

BUILDINGIMPACTANALYSIS

FRICTIONDEVICE

CONCENTRATEDDAMPER

NONLINEARELEMENT

GAP ELEMENT

TENSION ONLY ELEMENT

BRIDGE DECK ABUTMENT

P L A S T I CH I N G E S

2 ROTATIONAL DOF

DEGRADING STIFFNESS ?

Mechanical Damper

Mathematical Model

F = C vN

F = kuF = f (u,v,umax )

LINEAR VISCOUS DAMPINGDOES NOT EXIST IN NORMAL STRUCTURESAND FOUNDATIONS

5 OR 10 PERCENT MODAL DAMPING VALUES ARE OFTEN USED TO JUSTIFY ENERGY DISSIPATION DUE TO NONLINEAR EFFECTS

IF 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 TANK

NONLINEAR DIAGONALS

BASEISOLATION

COMPUTER MODEL

92 NODES

103 ELASTIC FRAME ELEMENTS

56 NONLINEAR DIAGONAL ELEMENTS

600 TIME STEPS @ 0.02 Seconds

COMPUTER TIME REQUIREMENTS

PROGRAM

( 4300 Minutes )ANSYS INTEL 486 3 Days

ANSYS CRAY 3 Hours ( 180 Minutes )

SADSAP INTEL 486 (2 Minutes )

( B Array was 56 x 20 )

Nonlinear Equilibrium Equations

Nonlinear Equilibrium Equations

Summary Of FNA Method

1. Calculate LDR Vectors for StructureWith the Nonlinear Elements Removed.

2. These Vectors Satisfy the FollowingOrthogonality Properties

T K 2 T M I

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

Which Is the Standard Mode Superposition Equation

n

nn tytYtu )()()(

Remember the LDR Vectors Are a Linear Combination of the Exact Eigenvectors; Plus, the Static Displacement Vectors.

No Additional Approximations Are Made.

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

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

f Fn n n

Au

6. 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

)()( tYtu

( ) ( ) ( )t A Y t B Y t

B

B

B

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

Equation Modal of SolutionNew

History Element of Function

Elements Nonlinear

in nsDeformatio

Loads Modal Nonlinear

)(

)(t

T)(N

)(

)(t

Y

YBf

P

BY

1it

ii

it

i)i(t

t

8. Calculate error for iteration i , at the end of each time step, for the NNonlinear elements – given Tol

tttwithsteptimenexttogoTolErrIf

1iiwithiteratetoContinueTolErrIf

|)(tf|

|)(tf| - |)(tf|

= Errin

N

=1n

1-in

N

=1n

in

N

=1n

FRAME WITH UPLIFTING ALLOWED

UPLIFTING ALLOWED

Four Static Load Conditions Are Used To Start The

Generation of LDR Vectors

EQ DL Left Right

TIME - Seconds

DEAD LOAD

LATERAL LOAD

LOAD

0 1.0 2.0 3.0 4.0 5.0

NONLINEAR STATIC ANALYSIS50 STEPS AT dT = 0.10 SECONDS

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.

PARALLEL ENGINEERING

AND

PARALLEL COMPUTERS

ONE PROCESSOR ASSIGNED TO EACH JOINT

ONE PROCESSOR ASSIGNEDTO EACH MEMBER

1

2

3

1 23

PARALLEL STRUCTURAL ANALYSIS

DIVIDE STRUCTURE INTO "N" DOMAINS

FORM AND SOLVE EQUILIBRIUM EQ.

FORM ELEMENT STIFFNESS

IN PARALLEL FOR

"N" SUBSTRUCTURES

EVALUATE ELEMENT

FORCES IN PARALLEL

IN "N" SUBSTRUCTURES

NONLINEAR LOOP

TYPICALCOMPUTER

FIRST PRACTICAL APPLICTION OF

THE FNA METHOD

Retrofit of the

RICHMOND - SAN RAFAEL BRIDGE

1997 to 2000

Using SADSAP

S T A T I C

A N D

D Y N A M I C

S T R U C T U R A L

A N A L Y S I S

P R O G R A M

TYPICAL ANCHOR PIER

MULTISUPPORT ANALYSIS

( Displacements )

ANCHOR PIERS

RITZ VECTORLOAD PATTERNS

SUBSTRUCTURE PHYSICS

JOINT REACTIONS( Retained DOF )

MASS POINTS and

MASSLESS JOINT( Eliminated DOF )

Stiffness Matrix Size = 3 x 16 = 48

"a"

"b"

SUBSTRUCTURE STIFFNESS

k k

k kaa ab

ba bb

REDUCE IN SIZE BY LUMPING MASSES

OR BY ADDING INTERNAL MODES

ADVANTAGES IN THEUSE OF SUBSTRUCTURES

1. FORM OF MESH GENERATION

2. LOGICAL SUBDIVISION OF WORK

3. MANY SHORT COMPUTER RUNS

4. RERUN ONLY SUBSTRUCTURES WHICH WERE REDESIGNED

5. PARALLEL POST PROCESSINGUSING NETWORKING

ECCENTRICALLY BRACED FRAME

FIELD MEASUREMENTS REQUIRED TO VERIFY

1. MODELING ASSUMPTIONS

2. SOIL-STRUCTURE MODEL

3. COMPUTER PROGRAM

4. COMPUTER USER

MECHANICAL VIBRATION DEVICES

CHECK OF RIGID DIAPHRAGM APPROXIMATION

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

15 th Period

TFIELD = 0.16 Sec.

FIRST DIAPHRAGM MODE SHAPE

At the Present Time

Most Laptop Computers

Can be directly connected to a

3D Acceleration Seismic Box

Therefore, Every Earthquake Engineer

C an verify Computed Frequencies

If software has been developed

Final RemarkGeotechnical Engineers must

produce realistic Earthquake records

for use by Structural Engineers

Errors Associated with the use of

Relative Displacements

Compared with the use of real

Physical Earthquake Displacements

Classical Viscous Damping does not exist

In the Real Physical World

20@

15’=300

’

Properties:Thickness = 2.0 ft

Width =20.0 ft

I = 27,648,000 in4

E = 4,000 ksi

W = 20 kips /story

Mx = 20/g

= 0.05176 kip-sec2 /in

Myy = 517.6 kip-sec2 -in

Total Mass = 400 /g

Typical Story Height

h = 15 ft = 180 in.

A. 20 Story Shear Wall With Story Mass

B. Base Acceleration Loads Relative Formulation

)(tubC. Displacement Loads Absolute Formulation

Typical Story Load

)(tubM

First Story Load

)(12

3tu

h

EIb

First Story Moment

)(6

2tu

h

EIb

x

zComparison of Relative and Absolute Displacement Seismic Analysis

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00TIME - Seconds

SH

EA

R -

Kip

s

Linear Acceleration Loads, or Cubic Displacement Loads - Zero Damping - 40 Modes

Linear Displacement Loads - Zero Damping - 40 Modes

Shear at Second Level Vs. Time With Zero Damping Time Step = 0.01

R E L A T I V E D I S P L A C E M E N T F O R M U L A T I O N A B S O L U T E D I S P L A C E M E N T F O R M U L A T I O N

ru su

xu

rxs uuu

xum

0IC xss xu 0IC xss xu

Illustration of Mass-Proportional Component in Classical Damping.