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Seismic Analysis and Design Of Structures Using Response Spectra Or Time History Motions BY Ed Wilson Professor Emeritus of Civil Engineering University of California, Berkeley February 24, 2010. SUMMARY OF PRESENTATION On Advanced Numerical Modeling and Analytical Techniques

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slide1

Seismic Analysis and Design

Of Structures

Using Response Spectra

Or

Time History Motions

BY

Ed Wilson

Professor Emeritus of Civil Engineering

University of California, Berkeley

February 24, 2010

slide2

SUMMARY OF PRESENTATION

  • On Advanced Numerical Modeling and Analytical Techniques
  • Personal Remarks – 50 years experience of dynamic analysis
  • Seismic Analysis Using Response Spectra – CQC3
  • Comparison with Direct Time History Dynamic Analysis
  • Retrofit of the San Mateo Bridge_-
  • The Fast Non-Linear Analysis Method – FNA Method
  • Retrofit of the Richmond San Rafael Bridge
  • Near Fault Seismic Analysis
  • Concluding Remarks
slide4

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

slide5

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

slide6

DYNAMIC ANALYSIS USING RESPONSE

SPECTRUM SEISMICLOADING

Before the Existence of Inexpensive Personal Computers, the Response Spectrum Method was the Standard Approach for Linear Seismic Analysis

slide9

Figure 15.2b Pseudo-Acceleration Spectrum,

- Percent of Gravity

Figure 15.2a Relative Displacement Spectrum y (T)MAX Inches

slide11

Major Approximation

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

slide12

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

slide15

Three-Dimensional Spectra Analyses

Equal Spectrum from any direction – CQC3 Method

Maximum Peak Column Moments - Symmetrical All Values are Positive

slide16

Three-Dimensional Spectra Analyses

100/30 Spectrum Method

Maximum Peak Column Moments - Not Symmetrical

All Values are Positive

slide17

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.
slide18

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.
slide19

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

slide21

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

slide22

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

.

slide23

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

Where P(max), M2(max) and M3(max)have been

Calculated by the CQC Method

slide24

The Retrofit of the San Mateo Bridge

Demand/Capacity Ratios were calculated using COC forces using spectrum calculated from several three-dimensional sets of earthquake motions.

Time-dependent Demand/Capacity Ratioswere calculated directly from the same set of earthquake motions.

In general, the time-dependent Demand/Capacity Ratioswere approximately 50 percentof the ratios using the CQC forces.

slide25

Limitations of Response Spectrum Analysis

  • 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 METHOD
  • This is not Performance Based Design
slide26

S A P

STRUCTURAL ANALYSIS PROGRAM

ALSO A PERSON

“ Who Is Easily Deceived Or Fooled”

“ Who Unquestioningly Serves Another”

slide27

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

slide28

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 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

slide29

FIELD MEASUREMENTS REQUIRED TO VERIFY

1. MODELING ASSUMPTIONS

2. SOIL-STRUCTURE MODEL

3. COMPUTER PROGRAM

4. COMPUTER USER

slide31

CHECK OF RIGID DIAPHRAGM APPROXIMATION

MECHANICAL VIBRATION DEVICES

slide32

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

slide33

FIRST DIAPHRAGM MODE SHAPE

15 th Period

TFIELD = 0.16 Sec.

slide34

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

slide36

BUILDING

IMPACT

ANALYSIS

slide37

FRICTION

DEVICE

CONCENTRATED

DAMPER

NONLINEAR

ELEMENT

slide38

GAP ELEMENT

BRIDGE DECK ABUTMENT

TENSION ONLY ELEMENT

slide39

P L A S T I C

H I N G E S

2 ROTATIONAL DOF

Degrading Stiffness Elements are in SAP 2000

slide40

Mechanical Damper

F = ku

F = f (u,v,umax )

F = C vN

Mathematical Model

slide41

First Application of the FNA Method - 1994

103 FEET DIAMETER - 100 FEET HEIGHT

NONLINEAR

DIAGONALS

BASE

ISOLATION

Nonlinear Seismic Analysis of

ELEVATED WATER STORAGE TANK

slide42

92 NODES

103

ELASTIC FRAME ELEMENTS

56

NONLINEAR DIAGONAL ELEMENTS

600

TIME STEPS @ 0.02 Seconds

COMPUTER MODEL

slide43

COMPUTER TIME

REQUIREMENTS

PROGRAM

( 4300 Minutes )

ANSYS

INTEL 486

3 Days

ANSYS

CRAY

3 Hours

( 180 Minutes )

2 Minutes

SADSAP

INTEL 486

( B Array was 56 x 20 )

slide44

EXAMPLE OF

FRAME WITH

UPLIFTING ALLOWED

UPLIFTING ALLOWED

slide45

Four Static Load Conditions

Are Used To Start The

Generation of LDR Vectors

EQ DL Left Right

slide48

Confirmed by Shaking Table Tests

By Ray Clough on Three Story Frame

slide49

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.

slide52

MULTISUPPORT SEISMIC ANALYSIS

(Earthquake Displacements Input )

ANCHOR PIERS

Hayward Fault San Andreas Fault

East West

slide55

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

slide56

Hearst Mining Building – Built in 1905 to 07

50 Yards from the Hayward Fault

Base Isolated in 2004

slide58

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 Design
  • In general, Nonlinear Time-History Analyses produce more realistic results and can produce Performance Based Design
slide59

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.
slide60

Floating-Point Speeds of Computer Systems

Definition of one Operation A = B + C*D64 bits - REAL*8