genealogy of performance-based seismic ......• the capacity spectrum method (csm) • a few design...

GENEALOGY OF PERFORMANCE-BASED SEISMIC DESIGN:IS THE PRESENT A RE-CRAFTED VERSION OF THE PAST?

M.A. Sözen1, P. Gülkan2 and A. İrfanoğlu1

1School of Civil Engineering, Purdue University, W. Lafayette, IN 479072Department of Civil Engineering, Çankaya University, Ankara 06790

Symposium on New Generation of Seismic Codes and New Technologies in Earthquake Engineering

February 26 and 27, 2015Ankara, Turkey

Disclaimer

This presentation uses a minimum number of equations. Only the most basic principles are employed.

SUMMARY

Earthquake structural engineering is undergoing a keen revision in its approach toward the fulfillment of seismic safety and utilitarian serviceability in design. Rather sticking to the established precepts of prescriptive design rules, design has turned toward the achievement of specific results through procedures that are tailored for different buildings and uses. These procedures represent notable research contributions, but they are complicated conceptually for implementation in structural engineering practice. With widely divergent results that are considered as acceptable there is a danger that the methodology could descend into confusion. The Achilles’ heel could prove to be the notion that the design basis earthquake lends itself to precise quantification.

Equivalent linearization of nonlinear systems to analyze complex forms through the use of an 80-year old instrument, the response spectrum, forms the backbone of many current approaches.

RecognitionWe gratefully acknowledge the contribution of W.D. Iwan, Caltech, for the account of the historic development of the response spectrum as the prime tool for linear or non-linear analysis. Some slides have been used with his permission.

5

1. From the Establishment of Learning– Knowledge (K) is Power (P): K = P

2. From Technology– Power (P) is Work (W)/Time (T): P = W/T

3. From Commerce and Common Sense– Time (T) is Money (M): T = M

Summary of First Principles in Mechanics and Other Topics of Public Discourse

6

Solving for Knowledge (K) (simple algebra):K = W/M

Interpretation:1. Greater work yields greater knowledge.2. The more you know, the less money you are

likely to make.

A Few Ideas Come to Mind forExtrapolations (I)

K(nowledge) = P(ower) P = W(ork)/T(ime), T = M

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Solving for Money:M = W/K

Interpretation:1. One way of making more money is to work harder.

We may call that the hard way to riches.2. But recall that money approaches infinity as

knowledge approaches zero, regardless of the work done. We may call that the easy way to becoming rich.

Further Derived ResultsK(nowledge) = P(ower)

P = W(ork)/T(ime), T = M

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The inverse of Knowledge, K, is Ignorance (I) which is of course equal to Bliss, B. Therefore, with

I = BI = 1/KB = M/W

which requires no interpretation.

Further Derived ResultsK(nowledge) = P(ower)

P = W(ork)/T(ime), T = M

It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits, and not to seek exactness where only an approximation is possible.

Aristotle: Nicomachean Ethics

Overview of Presentation• The nature of the problem• Reinforced concrete isn’t inherently ductile

and other sobering realities• Linearizing non-linear systems• Response spectrum concept• The Capacity Spectrum Method (CSM)• A few design and analysis procedures• Issues and prospects• Conclusions

Engineers must work with imperfect knowledge. More often than not, the demands on and the capabilities of a particular structure are not known with the precision required by exact analysis. So, experience drives design.

In reinforced concrete our methods fall in three categories.

1. Methods that explain as well as predict (e.g., flexural theory for reinforced concrete).

2. Methods that predict but do not explain (e.g., methods used for proportioning for shear or bond strength).

3. Methods that neither predict nor explain (e.g., maximum and minimum limits for shrinkage or temperature reinforcement specified in codes).

The Complexity of Structural Nonlinearity

The response of a structure can be sensed from three indices listed in order of importance:

1. The ratio of lateral drift capability to height. 2. The ratio of stiffness to mass. 3. The ratio of strength to weight.

max

4 and /w wy

p

f aDR a d

v d

Pujol (2002), from 15 reports on column tests:

DRp = Limiting Drift Ratio, defined as drift at which 20 percent loss ofstrength occurs

ρw = Ratio of cross-sectional area of hoops at spacing sfwy = Yield stress of transverse reinforcementvmax = Ratio of the maximum value of the shear force to the cross-

sectional area of reinforced concrete member defined as the product bd, where b is the width of the section and d is the effective depth

a = span length from maximum moment at face of joint to point of no moment

d = effective depth of the section

13 1 50 1 1400 10

s wy be

c g c

f d P LDR

f D A f D

Eberhard and Berry (2003), analyzing data from 62 tests:

DRe = Limiting Drift Ratio in percent, defined as drift when reinforcement buckles

ρs = Volumetric ratio of transverse reinforcement to confined core

fwy= Yield stress for transverse reinforcementdb = Diameter of longitudinal reinforcing barD = Depth of sectionP = Axial loadAg = Gross area of sectionf’c = Cylinder strength of concreteL = Clear height or span

0.005 0.006 0.007 0.008 0.009 0.010Transverse Reinforcement Ratio

0

1

2

3

4

5Li

miti

ng D

rift R

atio

, %Column Slenderness = 4

PujolEberhard_LowEberhard_Hi

0.005 0.006 0.007 0.008 0.009 0.010Transverse Reinforcement Ratio

0

1

2

3

4

5Li

miti

ng D

rift R

atio

, %

PujolEberhard_LowEberhard_Hi

Column Slenderness = 6

Frequency Spectrum Analysis Versus Time History Analysis

• Random-like signals are often better described in the frequency domain.

• Smoothed frequency spectra are useful for design and can be easily tied to probabilistic hazard descriptions.

• Strictly speaking, frequency domain analysis is only applicable to linear systems, so the nonlinear system must be linearized to use this approach.

Why linearize an inherently nonlinear problem?

• Linear analysis is well understood, easy to apply, and provides intuitive insights into the nature of the system, and range of possible outcomes.

• The response of many nonlinear systems appears similar to that of linear systems.

• Seismic excitation is often specified by a linear frequency domain representation such as the Response Spectrum.

History of the Response Spectrum

Concept of the Earthquake SpectrumBiot, 1932 (Caltech Thesis)

The Response SpectrumBenioff, 1934 Housner, 1941-59

Response Spectra for Recorded MotionsBiot, Housner, Hudson, Caughey, McCann, 1941-75

Procedures for Developing Design Response SpectraHousner, 1959 Newmark, 1965-81 Newmark and Hall, 1982

The Inelastic Response SpectrumNewmark and Hall, 1982

The Capacity Spectrum MethodFreeman, et al, 1975 SSC/ATC, 1996








NRC Regulatory Guide 1.60NRC Regulatory Guide 1.60







The Capacity Spectrum MethodFreeman, wt al, 1975 SSC/ATC, 1996

Demand SpectrumThe Acceleration Displacement Response Spectrum (ADRS)

Concept of the Earthquake SpectruBiot, 1932 (Caltech Thesis)





The Capacity Spectrum MethodFreeman, wt al, 1975 SSC/ATC, 1996

Evolution of the Capacity SpectrumStatic Pushover

F


F = MA

Appeal of the CSM Concept

• Uses readily available actual and design linear Response Spectra

• Based on “intuitive” concept of the equality of Earthquake Demand and Structural Capacity

• Readily adapted to Performance-Based Design

Capacity-Based Performance Criteria

Inelastic Spectrum or CSM?

• Inelastic Response Spectrum (IRS)Pro: Provides a direct solution (no iteration).Con: IRS is only available for a limited set of ground

motions and system behavior. Can not be easily adjusted.

• Capacity Spectrum Method (CSM)Con: A slightly more complex iterative solution

procedure is needed. Damping controversial.Pro: Uses readily available linear RS. Easily

adaptable to different system behavior. Relates to Performance-Based Engineering.

Crucial Question:

How can we best make an inherently nonlinear problem appear to be linear for purposes of analysis?

In principle, we need to find a set of “equivalent linear” stiffness and damping parameters that minimizes some measure of the difference between the response of the actual nonlinear inelastic system and the replacement equivalent linear system.

Equivalent Linear Parameters of the Conventional CSM

ADRS = Acceleration Displacement Response Spectrum

ATC-40

Equivalent Linear Damping

Equivalent Linear Stiffness (Period)

CAMUS Experiment

Performance in blind predictions:Closest: driftsNext: Moments, forcesWorst: Strains

Labbé and Altınyollar (2011)

CAMUS Experiment: Range of Calculated Floor Response SpectraLabbé and Altınyollar (2011)


• The equivalent linear damping factor is derived from the area within the hysteresis loop of the structural system. Loops vary in size during dynamic response.

• The equivalent linear stiffness (or period) is the “secant” stiffness (or period) associated with the Capacity Spectrum.


• The equivalent linear damping factor is derived from the area within the hysteresis loop of the structural system.

• The equivalent linear stiffness (or period) is the “secant” stiffness (or period) associated with the Capacity Spectrum.

Deficiencies of the Conventional CSM Approach

• There is inadequate theoretical or numerical basis for the conventional formulas for equivalent damping.

• The secant stiffness is known to be a poor estimate of the equivalent linear stiffness of most nonlinear systems.

• Equivalent linear parameters are inter-related, so modifying one parameter requires modifying several others.

• This presentation will discuss only one of many methods for improvement of the conventional CSM approach to determine the limiting displacement. There are manyother possible ways of calculating the performance point.

Example of CSM DeficienciesRatio of Actual to Conventional CSM Response

Near-field Ground Motion

Statement of the Problem

Find a new set of equivalent linear stiffness (or period) and damping parameters that gives better response predictions than the conventional CSM and, if possible, do this without further complicating the analysis.

An Early Approach to LinearizationTranslate the RS along a constant displacement axis to minimize

the mean square difference from a linear Response Spectrum

Iwan, 1980

Near-field Ground Motions

• Associated with high ground velocities• Characterized by strong pulse-like motion• Influenced by directivity effects• Fault perpendicular direction usually most demanding• Observed from earthquake records in China, US,

Europe, Japan, and Taiwan

Significant European Near-field Ground Motions

• MS=6.9 Erzincan, March 13, 1992• MW =7.4 Kocaeli, August 17,1999• MW=7.2 Düzce, November 12, 1999

Erzincan Earthquake Accelerogram

Resolving a Potential Difficulty

By not employing the Secant Stiffness (period), the Performance Point will not automatically lie on the Capacity Curve. This can lead to misinterpretation of the results and a more complicated solution procedure. But this potential problem can easily be solved by using a slightly modified response spectrum

The Modified ADRS (MADRS)

Construct Capacity Spectrum from pushover analysis.

S a

Capacity Spectrum

S a

Capacity Spectrum

S d

Determine To and dy from the Capacity Spectrum.

S a T 0

d y

Capacity Spectrum

S a T 0

d y

Capacity Spectrum

S d

Find maximum displacements for a set of discrete values of ductility.

S a T 0

d y d m=2 d m=3 dm=4 dm=5

Capacity Spectrum

S a T 0


Capacity Spectrum

S d

Construct Secant Stiffness for each ductility.

S a T 0T m=2

T m=3

T m=4

T m=5


Capacity Spectrum

S a T 0T m=2

T m=3

T m=4

T m=5


Capacity Spectrum

S d

Construct a family of site ADRS for damping coefficients consistent with the selected

ductilities.S a

ζ 0

m=5

Capacity Spectrum

S a

ζ 0

ζ

Capacity Spectrum

S d

ADRS Family

Compute MADRS from ADRS for chosen set of ductilities

S a

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

Capacity Spectrum

S a

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

Capacity Spectrum

S d

( )MADRS M xADRSm

Compute MADRS from ADRS for chosen set of ductilities

S a T 0T m=2

T m=3

T m=4

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

T m=5


Capacity Spectrum

MADRSFamily

S a T 0T m=2

T m=3

T m=4

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

T m=5


Capacity Spectrum

Family

S d

Identify intersections of MADRS and Secant Stiffness lines.

S a T 0T m=2

T m=3

T m=4

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

T m=5


Capacity Spectrum

MADRSFamily

S a T 0T m=2

T m=3

T m=4

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

T m=5


Capacity Spectrum

Family

S d

Connect points to obtain the Locus of Performance Points.

S a T 0T m=2

T m=3

T m=4

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

T m=5


Capacity Spectrum

MADRSFamily

S a T 0T m=2

T m=3

T m=4

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

T m=5


Capacity Spectrum

Locus of Performance Points

Family

S d

Locate intersection of Locus of Performance points and Capacity Spectrum. This is the

system Performance Point.S a T 0

T m=2

T m=3

T m=4

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

T m=5


dmax

amax

Capacity Spectrum

MADRSFamily

Performance Point

S a T 0T m=2

T m=3

T m=4

ζ 0

ζ m=2

ζ m=3

ζ m=4

ζ m=5

T m=5


dmax

amax

Capacity Spectrum

MADRSFamily

Performance Point

S d

Locus of Performance Points

Example of an Earthquake-Specific MADRS and Locus of Performance Points

El Centro Max Velocity Direction

An Interesting Possible Extension of the New Approach

The Locus of Performance Points could be used as a basis for determining the Seismic Margin of important

structures and systems.

Conclusions

1. Equivalent linearization can be an accurate and useful tool for seismic design and analysis if performed properly.

2. By using the a statistical approach for determining equivalent linear parameters, it is possible to obtain significantly improved accuracy over the conventional CSM approach.

Conclusions (continued)

3. Using the Modified Acceleration-Displacement Response Spectrum approach allows for simple and direct application of the improved equivalent linear parameters in design calculations.

4. This approach provides useful additional basic insight into the fundamental nature of nonlinear structural response through the Locus of Performance Points.

Conclusions (continued)

5. The Locus of Performance Points could be used to determine the Seismic Margin for critical systems.

6. The response deformation shape used in a single-mode linear analysis may not accurately predict local structural deformations in long-period MDOF system subjected to near-field ground motions.

Conclusions (continued)7. Gross measures of performance such as drift or

plastic rotation are better suited to judgment of performance.

genealogy of performance-based seismic ......• the capacity spectrum method (csm) • a few design...

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