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Predicting collapse loads for buildings subjected to seismic shock

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Abstract

In this paper an analytical expression that estimates the collapse load of a generic class of multi-storey, uniform, moment-resisting steel frames is presented. This expression is validated and calibrated with nonlinear pushover analyses (NPA) and incremental dynamic analyses for a set of buildings, of differing heights, that are designed according to the Eurocodes. The efficacy of different seismically induced load profiles in NPA is discussed with a preferred profile suggested for this class of structural system. The relationship between the actual seismic force reduction factor and code specified behavior factors is underlined.

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Abbreviations

\(C\) :

Generalised damping coefficient for low order building model \([\hbox {F}][\hbox {T}][\hbox {L}]^{-1}\)

\(F_i\) :

Estimated inertial forces applied at \(i\hbox {th}\) floor [F]

\(F_b \left( x \right) \) :

Generalised base shear for low order building model [F]

\(F_b\) :

Design base shear, EC8 [F]

\(F_{bE}\) :

Elastic base shear demanded by seismic event, EC8 [F]

\(F_{bI}\) :

Inelastic collapse base shear of structural system [F]

\(F_y\) :

Base shear at which structural system exhibits first plastic hinge [F]

\(F_s \left( x \right) \) :

Generalised stiffness force-deflection function for low order building model [F]

\(g\) :

Gravitational acceleration constant \([\hbox {L}][\hbox {T}]^{-2}\)

\(h\) :

Height of building [L]

\(k\) :

Index used in seismic force profile up the building []

\(L_b\) :

Beam spans [L]

\(L_{ci}\) :

Column heights, from floor \(i-1\) to floor \(i\) [L]

\(m_i\) :

Moment capacity of beam sections on \(i\hbox {th}\) floor [F][L]

\(M\) :

Generalised mass of low order building model \([\hbox {F}][\hbox {T}]^{2}[\hbox {L}]^{-1}\)

\(\bar{{M}}\) :

Total (actual) building mass of building \([\hbox {F}][\hbox {T}]^{2}[\hbox {L}]^{-1}\)

\(n_b\) :

Number of bays in framework []

\(n_s\) :

Number of storeys in framework []

\(n_p\) :

Number of plastic-damaged storeys in framework []

\(N\) :

Generalised excitation factor for low order building model \([\hbox {F}][\hbox {T}]^{2}[\hbox {L}]^{-1}\)

\(q\) :

EC8 behaviour faction []

\(u\left( {z,t} \right) \) :

Horizontal, time varying, displacement up elevation of building [L]

\(S_e \left( T \right) \) :

EC8 specified elastic response spectrum (total acc.) for period \(T [\hbox {F}][\hbox {T}]^{2}[\hbox {L}]^{-1}\)

\(S_d \left( T \right) \) :

EC8 specified design response spectrum (total acc.) for period \(T [\hbox {F}][\hbox {T}]^{2}[\hbox {L}]^{-1}\)

\(V_i\) :

Shear forcing in exterior columns in \(i\hbox {th}\) storey [F]

\(w_i\) :

Total weight of \(i\hbox {th}\) floor [F]

\(W_E\) :

External work in plastic analysis of building [F][L]

\(W_I\) :

Internal work in plastic analysis of building [F][L]

\(x\) :

Generalised coordinate for low order building model [L]

\(\ddot{x}_g\) :

Seismic ground acceleration \([\hbox {L}][\hbox {T}]^{-2}\)

\(z\) :

Vertical coordinate up height of building [L]

\(\alpha \) :

Ratio of beam to column spans []

\(\phi (\varsigma )\) :

Lateral displacement shape function of building []

\(\nu \) :

Parameter used in estimation of beam moment capacity []

\(\rho \) :

Generalised participation factor of low order building model []

\(\lambda \) :

Ratio of EC8 specified effective modal building mass to actual building mass []

\(\tau _1\) :

Ratio of generalised mass to actual mass of building []

\(\tau _2\) :

Ratio of generalised excitation factor to actual mass of building []

\(\tau _3\) :

Non-dimensional external work in plastic analysis of building []

\(\tau _4\) :

Non-dimensional internal work in plastic analysis of building []

\(\tau \) :

Ratio of non-dimensional internal/external work in plastic analysis of building []

\(\chi \) :

Building damage index, ratio of number of damaged storeys to total []

\(\varsigma \) :

Non-dimensional vertical coordinate up height of building []

\(\varsigma _i\) :

Non-dimensional vertical coordinate of \(i\hbox {th}\) floor []

Dimensional analysis of all terms above uses Force [F], Length [L] and time [T]

Nondimensional terms are signified by []

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Acknowledgments

This research was supported by Universiti Sains Malaysia under Research University (Individual) Grant (814223). Some parts of the material in this article have been accepted by Penerbit USM for publication 2015 in book.

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Authors and Affiliations

  1. Disaster Research Nexus, School of Civil Engineering, Engineering Campus, Universiti Sains Malaysia, 14300, Nibong Tebal, Penang, Malaysia

    Fadzli Mohamed Nazri

  2. Department of Civil Engineering, University of Bristol, Bristol, UK

    Nicholas A. Alexander

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  1. Fadzli Mohamed Nazri
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Correspondence to Fadzli Mohamed Nazri.

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Nazri, F.M., Alexander, N.A. Predicting collapse loads for buildings subjected to seismic shock. Bull Earthquake Eng 13, 2073–2093 (2015). https://doi.org/10.1007/s10518-014-9707-9

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