seismic analysis and design of structures using response spectra or time history motions by ed...
TRANSCRIPT
Seismic Analysis and DesignOf Structures
Using Response Spectra Or
Time History Motions BY
Ed WilsonProfessor Emeritus of Civil Engineering
University of California, Berkeley
February 24, 2010
SUMMARY OF PRESENTATION
On Advanced Numerical Modeling and Analytical Techniques
1. Personal Remarks – 50 years experience of dynamic analysis
2. Seismic Analysis Using Response Spectra – CQC3
3. Comparison with Direct Time History Dynamic Analysis4. Retrofit of the San Mateo Bridge
_-
5. The Fast Non-Linear Analysis Method – FNA Method
6. Retrofit of the Richmond San Rafael Bridge
7. Near Fault Seismic Analysis
8. Concluding Remarks
1882 Father Born In San Francisco – Carpenter and Walked Guard in S.F. after 1906 Earthquake
1931 Ed born in Ferndale CA – Earthquake Capitol of USA
1950 Graduated - Christian Brothers HS in SAC.
1950 - 52 Sacramento Jr. College
1953 - 54 BS in Civil Eng. – UC Berkeley
1953 - 54 DOT CA Bridge Dept. – Ten Mile River Bridge
1955 - 57 US Army – Korea – Radio Repairman
1957 - 63 M.S. and D. Eng. With Prof. Ray Clough
1960 With Ray, Conducted the first Time-HistoriesEarthquake Response of Buildings Bridges &
Dams. - Fifty Years Ago1963- 65 Worked on the Apollo Program at Aerojet in
Sacramento - Designed Structures for 10 g Loads
1965 -91 Professor at UC Berkeley
edwilson.org and [email protected]
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
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
DYNAMIC ANALYSIS USING RESPONSE
SPECTRUM SEISMIC LOADING
Before the Existence of Inexpensive Personal Computers, the Response Spectrum Method was the Standard Approach for
Linear Seismic Analysis
TIME - seconds
0 1 2 3 4 5 6 7 8 9 10-25
-20
-15
-10
-5
0
5
10
15
20
25
Figure 15.1a Typical Earthquake Ground Acceleration - Percent of Gravity
0 1 2 3 4 5 6 7 8 9 10
TIME - seconds
- 12
- 10
- 8
- 6
- 4
- 2
0
2
Figure 15.1b Absolute Earthquake Ground Displacements - Inches
0 1 2 3 4 5
PERIOD - Seconds
0
2
4
6
8
10
12
14
16
18
20
1.0 Percent Damping 5.0 Percent Damping
Figure 15.2b Pseudo-Acceleration Spectrum,
- Percent of Gravity
Figure 15.2a Relative Displacement Spectrum y (T)MAX Inches
MAXy )(
0 1 2 3 4 5
PERIOD - Seconds
0
10
20
30
40
50
60
70
80
90
100
1.0 Percent Damping 5.0 Percent Damping
Figure 15.2b Pseudo-Acceleration Spectrum Percent of Gravity
MAXa yS )(2
)()()( tutyty gT )()()( tutyty gT
Major Approximation
Structure theof Base At the
ntsDisplaceme Ground Earthquake The
Motion Ground Earthquake
the toRalativent Displaceme The
nt Displaceme Total The)(
(t) u
y(t)
ty
Where
g
T
The loads are applied directly to the structure; whereas, the real earthquake displacements are applied at the foundation of the real structure.
structure the of properties the of function a not are Spectrum 3The
ve numbersAll positiS(t)up = y(t) + (t)y 2+ (t)y
numbers positive AllS(t)up = y(t) + (t)y 2+ (t)y
number positive AllS (t)up= y(t) + (t)y 2+ (t)y
ionhree equatollowing tn of the fby solutioproduced are spectrum Or, the
(t)up + (t)up + (t)up = y(t) + (t)y 2+ (t)y
zgznzn2nnnnn
gnn2nnnnn
gnn2nnnnn
gznzgngnn2nnnnn
)(
)(
s )(
: 3
222
111
2211
Development of the Three Spectrum
In Addition, All Spectrum Values Are Maximum Peak Values
The Time History Details of the Duration of the Earthquake Have Been Lost
Examples of Three-Dimensional Spectra Analyses
P l a n V i e w
9 0
0
9 0
S 1
S 2
Definition of Earthquake Spectra Input
Three-Dimensional Spectra AnalysesEqual Spectrum from any direction – CQC3 Method
Maximum Peak Column Moments - Symmetrical All Values are Positive
Three-Dimensional Spectra Analyses100/30 Spectrum Method
Maximum Peak Column Moments - Not Symmetrical
All Values are Positive
Summary of Multi-Component Combination Rules
1. The 100/30 and 100/40 percent rules have no theoretical basis.
2. The SRSS combination rule, applied to equal spectra, produces identical results for all reference systems and requires only one analysis to produce all design forces and displacements.
3. The CQC3 method should be used where the horizontal orthogonal components of the seismic input are not equal.
4. In case of the seismic analysis of structures near a fault, the fault normal and parallel motions are not equal.
In 1996 The CQC3 was Proposed
by
Professor Armen Der Kiureghian
As a Replacement for the
30%, 40% & SRSS Rules
For Multi-Component Seismic Analysis
rule SRSS the toreduces method CQC3 The 1.0 a If
spectrum horizontalother thedefine toused
constant alproportion theis "" Where
]cossin)1(2
sin)()1([
12
21
2900
2
2290
20
2290
220
SaS
a
FFa
FFaFaFF
z
peak
Design Checks of Three-Dimensional Frame Members for Seismic Forces
In order to stratify various building codes, every
one-dimensional compression member within a structure must satisfy the following Demand/Capacity Ratio at all points in time:
t = 0 = Static Loads Only
0.1
))(
1(
)(
))(
1(
)()()(
33
33
22
22
ecb
ecb
crc
P
tPM
CtM
P
tPM
CtM
P
tPtR
Where the forces acting on the frame element cross-section at time “t” are including the static forces prior to the application of the dynamic loads. The empirical constants are code and material dependent and are normally defined as
.
)(and)(),( 32 tMtMtP
ed.approximat lengths effective with
axis an3 2 about the capacities load buckingEuler and
capacity load Axial
capacitiesMoment and
factors reductionMoment and
factors Resistance and
32
32
32
ee
cr
cc
bc
PP
P
MM
CC
φ
Design Checks of Three-Dimensional Frame Members for Spectra Forces
For the case maximum peak spectra forces,
compression members within a structure must satisfy the following Demand/Capacity Ratio
0.1
)(max)
1(
(max)
)(max)
1(
(max)(max))(
33
33
22
22
ecb
ecb
crc
P
PM
CM
P
PM
CM
P
PtR
Where P(max), M2(max) and M3(max) have been
Calculated by the CQC Method
The Retrofit of the San Mateo BridgeDemand/Capacity Ratios were calculated using COC forces using spectrum calculated from several three-dimensional sets of earthquake motions.
Time-dependent Demand/Capacity Ratios were
calculated directly from the same set of earthquake motions.
In general, the time-dependent Demand/Capacity Ratios
were approximately 50 percent of the ratios using the CQC forces.
1. All forces and displacements obtained from a Response Spectrum Analysis are Maximum Peak Values and are all positive numbers.
2. The specific time the Maximum Peak Values occur is different for every period.
3. Nonlinear Behavior CANNOT be considered in a Response Spectrum Analysis.
4. Except for a single degree of freedom, a Response Spectrum Analysis is an APPROXIMATE METHOD
5. This is not Performance Based Design
Limitations of Response Spectrum Analysis
S A P
STRUCTURAL ANALYSIS
PROGRAM
ALSO A PERSON
“ Who Is Easily Deceived Or Fooled”
“ Who Unquestioningly Serves Another”
"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 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
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
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
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 Elements are in SAP 2000
Mechanical Damper
Mathematical Model
F = C vN
F = kuF = f (u,v,umax )
103 FEET DIAMETER - 100 FEET HEIGHT
Nonlinear Seismic Analysis ofELEVATED WATER STORAGE TANK
NONLINEAR DIAGONALS
BASEISOLATION
First Application of the FNA Method - 1994
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 )
EXAMPLE OFFRAME WITH
UPLIFTING ALLOWED
UPLIFTING ALLOWED
Four Static Load Conditions Are Used To Start The
Generation of LDR Vectors
EQ DL Left Right
0 1 2 3 4 5 6 7 8 9 10
TIME - seconds
-600
-400
-200
0
200
400
600
LEFTRIGHT
Column Axial Forces
0 05.
Summary of Results for Building Uplifting Example
from Two Times the Loma Prieta Earthquake
UpliftComputer
Time
Max. Displace-
ment(inches)
Max. Column Force (kips)
Max. Base Shear(kips)
Max. Base
Moment(k-in)
Max. Strain
Energy(k-in) Max. Uplift
(inches)
Without14.6 Sec
7.76 924 494 424,000 1,547 0.0
With15.0 Sec 5.88 620 255 197,000 489 1.16
PercentDiff. -24% -33% -40% -53% -68%
Confirmed by Shaking Table TestsBy Ray Clough on Three Story Frame
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.
MULTISUPPORT SEISMIC ANALYSIS(Earthquake Displacements Input )
ANCHOR PIERS
Hayward Fault San Andreas Fault
East West
Eccentrically Braced Towers
Analysis and Design of Structures for
Near Fault Earthquake Motions
On the UC Berkeley Campus
Fault Normal and Parallel Foundation Displacements are
Significantly Different
Used six different Time-History Earthquake Motions for Nonlinear Dynamic Analyses
Hearst Mining Building – Built in 1905 to 07
50 Yards from the Hayward Fault
Base Isolated in 2004
Near Fault Analysis and Design - SRC
Concluding Remarks
1. The 100/30 percent Rule should replaced by the SRSS Rule - Until the CQC3 is implemented in SAP 2000.
2. Response Spectra Seismic Analysis is an Approximate Method and is restricted to linear structural behavior and may satisfy a design code. However, it may not produce a Performance Based Design
3. In general, Nonlinear Time-History Analyses produce more realistic results and can produce Performance Based Design
4. Performance Based Design is using all the information about the seismic displacement loading on the structure and to the accurately predict the nonlinear behavior and damage to the structure.
5. All Code Based Designed Structures appear to be based on Linear Analysis.
6. Nonlinear Seismic Analyses are possible due to:
• New Methods of nonlinear analysis have been developed.
• New Nonlinear Energy Dissipation and Simple Isolation Device can be used.
• The new inexpensive personal computer can easily conduct the required calculations.
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
2003 Pentium IV – 2,000 220,000,000 4,400
2006 AMD - Athlon 440,000,000 8,800
2009 Intel – Core 2 Duo 1,200,000,000 25,000