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. TheophilouEmail author
  • Marios K. Chryssanthopoulos
  • Andreas J. Kappos
Original Research Paper


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.


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



Engineering demand parameter


Intensity measure


Moment magnitude


Sample size


Normalized hysteretic energy


Distance from fault


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


Significant duration


Natural period of system


Elongated period of system


Equivalent natural period


Normalizing constant


Shear wave velocity in the top 30 m of the ground


Yield strength


Maximum elastic force


Elastic stiffness


Secant stiffness


Strain-hardening stiffness




Response displacement

\( \dot{u} \)

Response velocity

\( {\ddot{u}} \)

Response acceleration

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

Ground acceleration


Maximum displacement demand


Yield displacement


Maximum elastic displacement


Strain hardening coefficient


Significance level



\( \zeta \)

Viscous damping ratio

\( \zeta_{eq} \)

Equivalent damping ratio

\( \mu_{d} \)

Displacement ductility factor

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

Mean annual frequency of exceeding variable x


Correlation coefficient


Natural circular frequency


Mean spectral displacement


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Aris-Artemis I. Theophilou
    • 1
    Email author
  • 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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