PSI - Issue 44

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ScienceDirect

Procedia Structural Integrity 44 (2023) 528–535 Structural Integrity Procedia 00 (2022) 000–000 Structural Integrity Procedia 00 ( 022) 000–000

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© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy. Abstract Pushover analysis is an incremental quasi-static procedure for evaluating the seismic behavior of buildings accounting for their non-linear behaviour. The simplest and classical version of this method is based on the following assumptions: (i) the structure has a vertical plane of symmetry; (ii) there is a single horizontal earthquake component, parallel to the plane of symmetry; (iii) the structural dynamic behavior in this plane is governed by a dominant mode of vibration. These assumptions prevent asymmetric buildings to be accurately analyzed accounting for torsion e ff ects. Moreover, even for symmetric structures and single component earthquakes, the e ff ect of higher modes is not taken into account. In order to overcome these limitations, several multi-modal generalizations of the basic pushover analysis method have been proposed in the past years. In this paper, a new multi-modal approach is presented. Inspired by the Direct Vectorial Addition (DVA) method, the load pattern for the pushover analysis is defined as a linear combination of modal load patterns. The novel approach improves the original DVA by introducing an operative procedure for the calculation of modal combination factors (called “ α -factors”). This Enhanced DVA (E-DVA) method is based on the notion of elliptical response envelopes and allows several earthquake components to be taken into account simultaneously. In addition, an approach is proposed for the identification of dominant modes and for their use into the definition of the pushover load pattern. Furthermore, this paper describes a method to obtain the equivalent Single-Degree-of-Freedom (SDoF) oscillator properties in the general multi-modal case under multi-component earthquake, with the corresponding factors for the capacity curve normalization. The definition of response spectrum for multi-component earthquakes is also given. For illustrative purposes, the E-DVA method is applied to a non-symmetric structure (SPEAR building), and the main results are presented and discussed. 2022 The Authors. Published by Elsevier B.V. T is is an open access article under the CC BY- C-ND license (http: // cr ativec mmons.org / licenses / by-nc-nd / 4.0 / ) P r re ie unde responsibility of the scientific committee of the X X ANIDIS Conf rence, Se smic Engineering in Italy. Keywords: Multi-modal pushover analysis; Direct Vectorial Addition (DVA); Multi-component earthquake; Non-symmetric structure; Dominant modes XIX ANIDIS Conference, Seismic Engineering in Italy The E-DVA method for multi-modal pushover analysis and dominant modes Olivier LHERMINIER a, , Silvano ERLICHER a , Miquel HUGUET a , Maxime BARAKAT b a EGIS, 4 rue Dolores Ibarruri, 93188 Montreuil, France b Ecole des Ponts ParisTech - Universite´ Paris-Est, 6-8 Av Pascal, Cite´ Descartes, 77455 Marne-la-Valle´e - Cedex 2, France Abstract Pushover analysis is an incremental quasi-static procedure for evaluating the seismic behavior of buildings accounting for their non-linear behaviour. The simplest and classical version of this method is based on the following assumptions: (i) the structure has a vertical plane of symmetry; (ii) there is a single horizontal earthquake component, parallel to the plane of symmetry; (iii) the structural dynamic behavior in this plane is governed by a dominant mode of vibration. These assumptions prevent asymmetric buildings to be accurately analyzed accounting for torsion e ff ects. Moreover, even for symmetric structures and single component earthquakes, the e ff ect of higher modes is not taken into account. In order to overcome these limitations, several multi-modal generalizations of the basic pushover analysis method have been proposed in the past years. In this paper, a new multi-modal approach is presented. Inspired by the Direct Vectorial Addition (DVA) method, the load pattern for the pushover analysis is defined as a linear combination of modal load patterns. The novel approach improves the original DVA by introducing an operative procedure for the calculation of modal combination factors (called “ α -factors”). This Enhanced DVA (E-DVA) method is based on the notion of elliptical response envelopes and allows several earthquake components to be taken into account simultaneously. In addition, an approach is proposed for the identification of dominant modes and for their use into the definition of the pushover load pattern. Furthermore, this paper describes a method to obtain the equivalent Single-Degree-of-Freedom (SDoF) oscillator properties in the general multi-modal case under multi-component earthquake, with the corresponding factors for the capacity curve normalization. The definition of response spectrum for multi-component earthquakes is also given. For illustrative purposes, the E-DVA method is applied to a non-symmetric structure (SPEAR building), and the main results are presented and discussed. © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy. Keywords: Multi-modal pushover analysis; Direct Vectorial Addition (DVA); Multi-component earthquake; Non-symmetric structure; Dominant modes XIX ANIDIS Conference, Seismic Engineering in Italy The E-DVA method for multi-modal pushover analysis and dominant modes Olivier LHERMINIER a, , Silvano ERLICHER a , Miquel HUGUET a , Maxime BARAKAT b a EGIS, 4 rue Dolores Ibarruri, 93188 Montreuil, France b Ecole des Ponts ParisTech - Universite´ Paris-Est, 6-8 Av Pascal, Cite´ Descartes, 77455 Marne-la-Valle´e - Cedex 2, France

∗ Corresponding author. Tel.: + 3-362-783-5140 E-mail address: olivier.lherminier@egis.fr ∗ Corresponding author. Tel.: + 3-362-783-5140 E-mail address: olivier.lherminier@egis.fr

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy. 10.1016/j.prostr.2023.01.069 2210-7843 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy. 2210-7843 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of the XIX ANIDIS Conference, Seismic Engineering in Italy.