Research Team: Dr. Christian Málaga-Chuquitaype (Imperial College London, UK), Professor Ahmed Elghazouli (Imperial College London, UK)


Fig 1: Application of equivalent linearization to the estimation of peak displacements in a 6-storey CB frame. Pushover curve (left) and Demand and Capacity diagrams (right)
Fig 1: Application of equivalent linearization to the estimation of peak displacements in a 6-storey CB frame. Pushover curve (left) and Demand and Capacity diagrams (right)

Current earthquake performance-based design and assessment methodologies pay special attention to the reliable determination of structural displacements.

Although such seismic demands can be calculated through sophisticated nonlinear response history analyses, their application in practical assessment is still hampered by the considerable time, costs and expertise they require.

Therefore, there is a need for simplified yet reliable methods for the estimation of structural seismic demands. To this end, this research project deals with the estimation of peak inelastic displacements of structural systems representative of typical steel structures, under constant relative strength scenarios.

Mean inelastic deformation demands on bilinear systems (simulating moment resisting frames) are considered as the basis for comparative purposes.

Additional models representing partially-restrained and concentrically-braced (CB) frames are employed to assess the influence of different force-displacement relationships on peak inelastic displacement ratios.


The studies carried out to date have illustrated that the ratio between the overall yield strength and the strength during pinching intervals is the main factor governing the inelastic deformations of partially-restrained structures and leading to significant differences when compared with predictions based on bilinear structures, especially in the short-period range.

It has also been shown that the response of concentrically-braced (CB) systems can differ significantly from other pinching models when subjected to low or moderate levels of seismic demand, highlighting the necessity of employing dedicated models for studying the response of CB structures. Particular attention has also been given to the influence of a number of scalar parameters that characterise the frequency content of the ground motion on the estimated peak displacement ratios.

The relative merits of using the average spectral period Taver, mean period Tm, predominant period Tg, characteristic period Tc and smoothed spectral predominant period To of the earthquake ground motion, have been assessed. Our investigations have demonstrated that the predominant period, defined as the period at which the input energy is maximum throughout the period range, is the most suitable frequency content scalar parameter for reducing the variability in displacement estimations.

Finally, non-iterative equivalent linearization expressions based on the secant period and equivalent damping ratios are presented and verified for the prediction of peak deformation demands in steel structures.


  • Malaga-Chuquitaype C, Elghazouli AY, 2012, Inelastic displacement demands in steel structures and their relationship with earthquake frequency content parameters, Earthquake Engineering & Structural Dynamics, Vol:41, ISSN:0098-8847, Pages:831-852
  • Malaga-Chuquitaype C, Elghazouli AY, 2011, Consideration of seismic demand in the design of braced frames, Vol:4, Pages:65-72
  • Malaga-Chuquitaype C, Elghazouli AY 2012, Evaluation of Fatigue Damage and Park and Ang indexes in steel structures, 15th World Conference on Earthquake Engineering, Lisbon, Portugal
  • Malaga-Chuquitaype C, Elghazouli AY 2012, Influence of scalar frequency content parameters on the inelastic seismic demands of steel structures, 7th International Conference on Behaviour of Steel Structures in Seismic Areas (STESSA), CRC PRESS-TAYLOR & FRANCIS GROUP, Pages:833-839