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Bulletin of Earthquake Engineering

, Volume 15, Issue 1, pp 249–270 | Cite as

A vector-valued ground motion intensity measure incorporating normalized spectral area

  • Aris-Artemis I. Theophilou
  • Marios K. Chryssanthopoulos
  • Andreas J. Kappos
Original Research Paper

Abstract

A vector-valued intensity measure is presented, which incorporates a relative measure represented by the normalized spectral area. The proposed intensity measure is intended to have high correlation with specific relative engineering demand parameters, which collectively can provide information regarding the damage state and collapse potential of the structure. Extensive dynamic analyses are carried out on a single-degree-of-freedom system with a modified Clough–Johnston hysteresis model, using a dataset of 40 ground motions, in order to investigate the proposed intensity measure characteristics. Response is expressed using the displacement ductility, and the normalized hysteretic energy, both of which are relative engineering demand parameters. Through regression analysis the correlation between the proposed intensity measure and the engineering demand parameters is evaluated. Its domain of applicability is investigated through parametric analysis, by varying the period and the strain-hardening stiffness. Desirable characteristics such as efficiency, sufficiency, and statistical independence are examined. The proposed intensity measure is contrasted to another one, with respect to its correlation to the engineering demand parameters. An approximate procedure for estimating the optimum normalized spectral area is also presented. It is demonstrated that the proposed intensity measure can be used in intensity-based assessments, and, with proper selection of ground motions, in scenario-based assessments.

Keywords

Intensity measure Normalized spectral area Nonlinear response Probabilistic seismic demand assessment Ground motion selection 

Abbreviations

EDP

Engineering demand parameter

IM

Intensity measure

M

Moment magnitude

N

Sample size

NHE

Normalized hysteretic energy

R

Distance from fault

Ry

Yield reduction factor

\( S_{a} \left( {T_{1} } \right) \)

Spectral acceleration at period T 1

\( S_{d} \left( {T_{1} } \right) \)

Spectral displacement at period T 1

\( S_{dN} \left( {T_{1} ,T_{2} } \right) \)

Normalized spectral area

SD

Significant duration

T1

Natural period of system

T2

Elongated period of system

Teq

Equivalent natural period

TN

Normalizing constant

VS30

Shear wave velocity in the top 30 m of the ground

fy

Yield strength

f0

Maximum elastic force

ke

Elastic stiffness

keq

Secant stiffness

ks

Strain-hardening stiffness

m

Mass

u

Response displacement

\( \dot{u} \)

Response velocity

\( {\ddot{u}} \)

Response acceleration

\( {\ddot{u}}_{g} \left( t \right) \)

Ground acceleration

um

Maximum displacement demand

uy

Yield displacement

u0

Maximum elastic displacement

α

Strain hardening coefficient

αs

Significance level

ε

Epsilon

\( \zeta \)

Viscous damping ratio

\( \zeta_{eq} \)

Equivalent damping ratio

\( \mu_{d} \)

Displacement ductility factor

\( \lambda \left( x \right) \)

Mean annual frequency of exceeding variable x

ρ

Correlation coefficient

ωn

Natural circular frequency

Δmean

Mean spectral displacement

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Aris-Artemis I. Theophilou
    • 1
  • Marios K. Chryssanthopoulos
    • 1
  • Andreas J. Kappos
    • 2
  1. 1.Department of Civil and Environmental Engineering, Faculty of Engineering and Physical SciencesUniversity of SurreyGuildfordUK
  2. 2.Department of Civil Engineering, School of Mathematics, Computer Science and EngineeringCity University LondonLondonUK

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