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.
If Equal Spectra are applied to any Global X–Y-Z System
Y
Base Shear Mode 2
X
Torsion or Mode 1, 2 or Mode 3
Base Shear Mode 1
Member Forces are the same for all Global X–Y Systems,
If Calculated from Fi  FiX  FiY  FiZ
Nonlinear Failure Mode For Skew Bridges
F(t)
Abutment Force
Acting on Bridge
Tensional Failure
u(t)
Contact at Right Abutment
u(t)
Tensional Failure
F(t)
Abutment Force
Acting on Bridge
Contact at Left Abutment
Possible Torsional Failure Mode
Design Joint Connectors for Joint Shear Forces?
Use a Global Modal for all Analyses
+Y
-X
+X
-Y
Figure 5.2.2-1 EDA Modeling Techniques
Use Global X-Y-Z System for all Models
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 systems
2. 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 Method
Basic 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 Spectrum

Note: 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
Simple User Defined Data
  effective viscous ratio
S xs  peak base acceleration
S x1  valueat 1.0 sec period
Constants to be Calculated
B1  4 [ 5.6  ln( 100 )
Ts  S x1 / S sx
T 0 0.2Ts
Duration has been Neglected
Shape is not Realistic
NonLinear Structures - No
Where did the hat go?
Where did the Hat go - on the Response Spectrum ?
As I Recall -------
Demand-Capacity Ratios
The Demand-Capacity ratio for a linear elastic,
compression member is given by an equation of the
following general form:
P( t )
M 2 ( t ) C2
M 3 ( t ) C3
R( t ) 


 1.0
P( t )
P( t )
c Pcr
b M c 2 ( 1 
) b M c 3 ( 1 
)
Pe 2
Pe 3
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.
RSM Demand-Capacity Ratios
If 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:
P(max)
R(max) 

c Pcr
M 2 (max)C2
M 3 (max)C3

 1.0
P(max)
P(max)
b M c 2 ( 1 
) b M c 3 ( 1 
)
Pe 2
Pe 3
A smart computer program can compute this DemandCapacity 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 Systems
Definition of one Operation A = B + C*D
Operations
Per Second
64 bits - REAL*8
Year
Computer
or CPU
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
Cost of Personal Computer Systems
YEAR
CPU
Speed
MHz
Operations
Per Second
Relative
Speed
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
Year
Cost
Computer
or CPU
Operations
Per Second
Relative
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
100,000
1994
Pentium-90
$5,000
4,000,000
1999
Intel Pentium III-450
$1,500
69,000,000
2006
AMD 64 Laptop
$2,000
400,000,000
2009
Min Laptop
$300
200,000,000
2.4 GHz Intel Core i3 64 bit
Win 7 Laptop
$1,000
1.35 Billion
Intel Fortran
27,000
2.80 GHz 2 Quad Core 64
bit Win 7
$1,000
2.80 Billion
Parallelized Fortran
56,000
2010
2013
2
70
1,380
8,000
4,000
The cost of one operation has been reduced by 56,000,000 in the last 50 years
Computer Cost versus Engineer’s Monthly Salary
$1,000,000
c/s = 1,000
c/s = 0.10
$10,000
$1,000
$1,000
1963
Time
2013
Fast Nonlinear Analysis
With Emphasis
On Earthquake Engineering
BY
Ed Wilson
Professor Emeritus of Civil Engineering
University of California, Berkeley
edwilson.org
May 25, 2006
Summary Of Presentation
1.
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 Engineering
Analysis of the Richmond - San Rafael Bridge
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
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
1973 – 74
NON SAP
New Program – The Start of ADINA
1979 – 80
SAP 80
New Linear Program for Personal Computers
Bathe
Lost All Research and Development Funding
1983 – 1987 SAP 80
CSI added Pre and Post Processing
1987 - 1990
Significant Modification and Documentation
SAP 90
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
Dynamic Analysis - 1979
by 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
3 D Concrete Reactor
3 D Soft Soil Elements
360 degrees
DYNAMIC EQUILIBRIUM
EQUATIONS
M a + C v + K u = F(t)
a
v
u
M
C
K
F(t)
=
=
=
=
=
=
=
Node Accelerations
Node Velocities
Node Displacements
Node Mass Matrix
Damping Matrix
Stiffness Matrix
Time-Dependent Forces
PROBLEM TO BE SOLVED
Ma + Cv+ Ku =
 f g(t)
i
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
METHODS OF DYNAMIC ANALYSIS
For Both Linear and Nonlinear Systems
÷ BY STEP INTEGRATION - 0, dt, 2 dt ... N dt
STEP
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
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
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
GENERATION
DEPENDENT
LOAD
VECTORS
OF
RITZ
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
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,
Ku=f
C.
MAKE
FORM
u STIFFNESS AND MASS ORTHOGONAL TO
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, to
Make Block of Vectors, Yi , Orthogonal
to all Previously Calculated Vectors - Vi
STEP 3. MAKE VECTORS
STIFFNESS ORTHOGONAL
A.
SOLVE Nb x Nb Eigenvalue Problem
[ V T K V ] Z = [ w2 ] Z
B.
CALCULATE MASS AND STIFFNESS
ORTHOGONAL LDR VECTORS
VR = V Z =

DYNAMIC RESPONSE OF BEAM
100 pounds
10 AT 12" = 120"
FORCE = Step Function
TIME
MAXIMUM DISPLACEMENT
Number 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 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 )
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
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 WITH
NONLINEAR ELEMENTS REMOVED AND
DUMMY ELEMENTS ADDED FOR STABILITY
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
BASE ISOLATION
Isolators
BUILDING
IMPACT
ANALYSIS
FRICTION
DEVICE
CONCENTRATED
DAMPER
NONLINEAR
ELEMENT
GAP ELEMENT
BRIDGE DECK
ABUTMENT
TENSION ONLY ELEMENT
PLASTIC
HINGES
2 ROTATIONAL DOF
DEGRADING STIFFNESS ?
Mechanical Damper
F = f (u,v,umax )
F = ku
F = C vN
Mathematical Model
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
103 FEET DIAMETER - 100 FEET HEIGHT
NONLINEAR
DIAGONALS
BASE
ISOLATION
ELEVATED WATER STORAGE TANK
COMPUTER MODEL
92 NODES
103 ELASTIC FRAME ELEMENTS
56 NONLINEAR DIAGONAL ELEMENTS
600 TIME STEPS @ 0.02 Seconds
COMPUTER TIME
REQUIREMENTS
PROGRAM
ANSYS
INTEL 486
3 Days
ANSYS
CRAY
3 Hours
SADSAP
INTEL 486
( B Array was 56 x 20 )
( 4300 Minutes )
( 180 Minutes )
(2 Minutes )
Nonlinear Equilibrium Equations
Nonlinear Equilibrium Equations
Summary Of FNA Method
1.
Calculate LDR Vectors for Structure
With the Nonlinear Elements Removed.
2.
These Vectors Satisfy the Following
Orthogonality Properties
 K     M  I
T
2
T
3. The Solution Is Assumed to Be a Linear
Combination of the LDR Vectors. Or,
u (t )  Y (t )    n y (t ) n
n
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.
4.
A typical modal equation is uncoupled.
However, the modes are coupled by the
unknown nonlinear modal forces which
are of the following form:
fn  
5.
n
Fn
The deformations in the nonlinear elements
can be calculated from the following
displacement transformation equation:
  Au
6.
Since u (t )  Y (t ) the deformations in
the nonlinear elements can be expressed
in terms of the modal response by
 (t )  A  Y(t )  B Y(t )
B
Where the size of the
array is equal to
the number of deformations times the
number of LDR vectors.
The B array is calculated only once prior
to the start of mode integration.
THE
B
ARRAY CAN BE STORED IN RAM
7. 7. The nonlinear element forces
are calculated, for iteration i , at the
end of each time step

(i )
t 
(i )
BYt
 Deformations in
Nonlinear Elements
(i )
Pt 
(i )
f Nt
Function of Element History
B
( i  1)
Yt 
T
(i )
Yt
 Nonlinear Modal Loads
New Solution of Modal Equation
8. Calculate error for iteration i , at the end
of each time step, for the N
Nonlinear elements – given Tol
N
 | f (t
Err =
N
i
)n | -
n=1
 | f (t
i -1
)n |
n=1
N
 | f (t
i
)n |
n=1
If
If
Err  Tol Continueto iterate with i  i  1
Err  Tol go to next time step with t  t  t
FRAME WITH
UPLIFTING
ALLOWED
UPLIFTING ALLOWED
Four Static Load Conditions
Are Used To Start The
Generation of LDR Vectors
EQ
DL
Left
Right
NONLINEAR STATIC ANALYSIS
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
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
3
2
1
3
1
2
ONE PROCESSOR ASSIGNEDTO EACH MEMBER
PARALLEL STRUCTURAL
ANALYSIS
DIVIDE STRUCTURE INTO "N" DOMAINS
FORM ELEMENT STIFFNESS
IN PARALLEL FOR
"N" SUBSTRUCTURES
FORM AND SOLVE EQUILIBRIUM EQ.
EVALUATE ELEMENT
FORCES IN PARALLEL
IN "N" SUBSTRUCTURES
NONLINEAR LOOP
TYPICAL
COMPUTER
FIRST PRACTICAL APPLICTION
OF
THE FNA METHOD
Retrofit of the
RICHMOND - SAN RAFAEL BRIDGE
1997 to 2000
Using SADSAP
S
A
D
S
A
P
TATIC
ND
YNAMIC
TRUCTURAL
NALYSIS
ROGRAM
TYPICAL ANCHOR
PIER
MULTISUPPORT
ANALYSIS
( Displacements )
ANCHOR PIERS
RITZ VECTOR
LOAD
PATTERNS
SUBSTRUCTURE PHYSICS
Stiffness Matrix
Size = 3 x 16 = 48
"a"
MASSLESS JOINT
( Eliminated DOF )
"b"
MASS POINTS and
JOINT REACTIONS
( Retained DOF )
SUBSTRUCTURE STIFFNESS
 k aa
k
 ba
k ab 

k bb 
REDUCE IN SIZE BY LUMPING MASSES
OR BY ADDING INTERNAL MODES
ADVANTAGES IN THE
USE 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 PROCESSING
USING NETWORKING
ECCENTRICALLY BRACED FRAME
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
FIRST DIAPHRAGM
MODE SHAPE
15 th Period
TFIELD = 0.16 Sec.
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 Remark
Geotechnical 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
Comparison of Relative and Absolute Displacement Seismic Analysis
z
Properties:
20@15’=300’
Thickness = 2.0 ft
Width =20.0 ft
I = 27,648,000 in4
E = 4,000 ksi
W = 20 kips /story
Mx = 20/g
Typical Story Load
Mub (t )
= 0.05176 kip-sec2 /in
Myy = 517.6 kip-sec2 -in
Total Mass = 400 /g
Typical Story Height
h = 15 ft = 180 in.
First Story Load
12 EI
ub (t )
3
h
x
A. 20 Story Shear Wall
With Story Mass
ub (t )
B. Base Acceleration Loads
Relative Formulation
First Story Moment
6EI
u (t)
2 b
h
C. Displacement Loads
Absolute Formulation
Shear at Second Level Vs. Time With Zero Damping
Time Step = 0.01
140
120
Linear Acceleration Loads, or Cubic Displacement Loads - Zero Damping - 40 Modes
100
Linear Displacement Loads - Zero Damping - 40 Modes
80
SHEAR - Kips
60
40
20
0
-20
-40
-60
-80
-100
0.00
0.20
0.40
0.60
0.80
1.00
1.20
TIME - Seconds
1.40
1.60
1.80
2.00
Illustration of Mass-Proportional Component in Classical Damping.
us
ur
m ux
C ss I x u x  0
C ss I x u x  0
ux
us  ux  ur
RELATIVE DISPLACEMENT FORMULATION
ABSOLUTE DISPLACEMENT FORMULATION