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 ed-wilson1@juno.com

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