CalTrans-2010.ppt

Seismic Analysis and DesignOf Structures

Using Response Spectra Or Time History Motions BYEd WilsonProfessor Emeritus of Civil EngineeringUniversity of California, Berkeley

February 24, 2010

SUMMARY OF PRESENTATION On Advanced Numerical Modeling and Analytical TechniquesPersonal Remarks 50 years experience of dynamic analysis Seismic Analysis Using Response Spectra CQC3Comparison with Direct Time History Dynamic AnalysisRetrofit of the San Mateo Bridge _-The Fast Non-Linear Analysis Method FNA MethodRetrofit of the Richmond San Rafael BridgeNear Fault Seismic Analysis Concluding Remarks

edwilson.org and [email protected]

1882Father Born In San Francisco Carpenter and Walked Guard in S.F. after 1906 Earthquake1931Ed born in Ferndale CA Earthquake Capitol of USA1950Graduated - Christian Brothers HS in SAC.1950 - 52Sacramento Jr. College1953 - 54BS in Civil Eng. UC Berkeley1953 - 54DOT CA Bridge Dept. Ten Mile River Bridge1955 - 57 US Army Korea Radio Repairman1957 - 63 M.S. and D. Eng. With Prof. Ray Clough1960With Ray, Conducted the first Time-HistoriesEarthquake Response of Buildings Bridges & Dams. - Fifty Years Ago1963- 65Worked on the Apollo Program at Aerojet in Sacramento - Designed Structures for 10 g Loads1965 -91Professor at UC Berkeley

NINETEEN SIXTIES IN BERKELEY1.Cold War - Blast Analysis2. Earthquake Engineering Research3.State And Federal Freeway System4.Manned Space Program5.Offshore Drilling 6.Nuclear Reactors And Cooling Towers

NINETEEN SIXTIES IN BERKELEY1.Period Of Very High Productivity2.No Formal Research Institute3.Free Exchange Of Information Gave programs to profession prior to publication4.Worked Closely With Mathematics Group5.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

Figure 15.1a Typical Earthquake Ground Acceleration - Percent of Gravity

Figure 15.1b Absolute Earthquake Ground Displacements - Inches

Figure 15.2b Pseudo-Acceleration Spectrum, - Percent of GravityFigure 15.2a Relative Displacement Spectrum y (T)MAX Inches

Figure 15.2b Pseudo-Acceleration Spectrum Percent of Gravity

Major Approximation The loads are applied directly to the structure; whereas, the real earthquake displacements are applied at the foundation of the real structure.

Development of the Three SpectrumIn 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

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m

y

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2

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_909076709.unknown

_909076929.unknown

_909077065.unknown

_909077205.unknown

_909076812.unknown

_909076563.unknown

Definition of Earthquake Spectra Input

2

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1

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9

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w

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Three-Dimensional Spectra AnalysesEqual Spectrum from any direction CQC3 MethodMaximum Peak Column Moments - Symmetrical All Values are Positive

2.705

1.901

2.705

2.703

2.705

1.901

2.705

4

3

2

1

2.703

X

Y

0

Three-Dimensional Spectra Analyses100/30 Spectrum MethodMaximum Peak Column Moments - Not Symmetrical All Values are Positive

2.794

2.743

1.934

2.493

2.797

1.97301

2.743

4

3

2

1

-7.8 % Error

X

Y

0

Summary of Multi-Component Combination Rules The 100/30 and 100/40 percent rules have no theoretical basis. 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.

The CQC3 method should be used where the horizontal orthogonal components of the seismic input are not equal. 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 KiureghianAs a Replacement for the 30%, 40% & SRSS Rules For Multi-Component Seismic Analysis

Design Checks of Three-Dimensional Frame Members for Seismic ForcesIn 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

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.

Design Checks of Three-Dimensional Frame Members for Spectra ForcesFor the case maximum peak spectra forces, compression members within a structure must satisfy the following Demand/Capacity Ratio Where P(max), M2(max) and M3(max) have beenCalculated 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.

All forces and displacements obtained from a Response Spectrum Analysis are Maximum Peak Values and are all positive numbers. The specific time the Maximum Peak Values occur is different for every period.Nonlinear Behavior CANNOT be considered in a Response Spectrum Analysis. Except for a single degree of freedom, a Response Spectrum Analysis is an APPROXIMATE METHODThis is not Performance Based Design Limitations of Response Spectrum Analysis

S A P

STRUCTURAL ANALYSIS PROGRAMALSO 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 1970From The Foreword Of The First SAP Manual

The SAP Series of Programs1969 - 70 SAP Used Static Loads to Generate Ritz Vectors1971 - 72Solid-Sap Rewritten by Ed Wilson1972 -73 SAP IV Subspace Iteration Dr. Jgen Bathe1973 74NON SAP New Program The Start of ADINA1979 Lost All Research and Development Funding 1979 80SAP 80New Linear Program for Personal Computers1983 1987SAP 80 CSI added Pre and Post Processing1987 - 1990 SAP 90Significant Modification and Documentation1997 PresentSAP 2000 Nonlinear Elements More Options With Windows Interface

FIELD MEASUREMENTS REQUIRED TO VERIFY1.MODELING ASSUMPTIONS2.SOIL-STRUCTURE MODEL3.COMPUTER PROGRAM4.COMPUTER USER

MECHANICAL VIBRATION DEVICESCHECK OF RIGID DIAPHRAGM APPROXIMATION

FIELD MEASUREMENTS OF PERIODS AND MODE SHAPESMODETFIELDTANALYSIS Diff. - %11.77 Sec.1.78 Sec.0.521.691.680.631.68 1.680.040.600.610.950.600.610.960.590.590.870.320.320.2----110.230.322.3

15 th PeriodTFIELD = 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

IsolatorsBASE ISOLATION

BUILDINGIMPACTANALYSIS

FRICTIONDEVICECONCENTRATEDDAMPERNONLINEARELEMENT

GAP ELEMENTTENSION ONLY ELEMENTBRIDGE DECK ABUTMENT

P L A S T I CH I N G E S2 ROTATIONAL DOFDegrading Stiffness Elements are in SAP 2000

Mechanical DamperMathematical ModelF = C vNF = kuF = f (u,v,umax )

103 FEET DIAMETER - 100 FEET HEIGHT Nonlinear Seismic Analysis ofELEVATED WATER STORAGE TANKNONLINEAR DIAGONALSBASEISOLATIONFirst Application of the FNA Method - 1994

COMPUTER MODEL

COMPUTER TIME REQUIREMENTS PROGRAM( 4300 Minutes )ANSYSINTEL 4863 DaysANSYSCRAY3 Hours( 180 Minutes )SADSAPINTEL 4862 Minutes ( B Array was 56 x 20 )

EXAMPLE OFFRAME WITH UPLIFTING ALLOWED

UPLIFTING ALLOWED

Four Static Load Conditions Are Used To Start TheGeneration of LDR Vectors EQ DL Left Right

Column Axial Forces

Confirmed by Shaking Table TestsBy Ray Clough on Three Story Frame

Summary of Results for Building Uplifting Example from Two Times the Loma Prieta Earthquake

Uplift

Computer TimeMax. 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 Sec7.76924494424,0001,5470.0With15.0 Sec5.88620255197,000489 1.16Percent Diff.-24%-33%-40%-53%-68%

Advantages Of The FNA Method1.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 PIERSHayward Fault San Andreas Fault East West

Eccentrically Braced Towers

Analysis and Design of Structures forNear Fault Earthquake MotionsOn the UC Berkeley CampusFault 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 0750 Yards from the Hayward FaultBase Isolated in 2004

Near Fault Analysis and Design - SRC

Concluding Remarks

The 100/30 percent Rule should replaced by the SRSS Rule - Until the CQC3 is implemented in SAP 2000.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 DesignIn general, Nonlinear Time-History Analyses produce more realistic results and can produce Performance Based Design

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. All Code Based Designed Structures appear to be based on Linear Analysis.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 CPUOperations Per SecondRelative Speed1962CDC-640050,00011964CDC-6600100,00021974CRAY-13,000,000601981IBM-309020,000,0004001981CRAY-XMP40,000,0008001994Pentium-903,500,000701995Pentium-1335,200,0001041995DEC-5000 upgrade14,000,0002801998Pentium II - 33337,500,0007501999Pentium III - 45069,000,0001,3802003Pentium IV 2,000220,000,0004,4002006AMD - Athlon440,000,0008,8002009Intel Core 2 Duo1,200,000,00025,000

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