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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.