PSI - Issue 44

Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 44 (2023) 456–463 Structural Integrity Procedia 00 (2022) 000–000 Structural Integrity Procedia 00 (2022) 000–000

www.elsevier.com / locate / procedia www.elsevier.com / locate / procedia

© 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 This research investigates the formulation of a reduced modal space for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame buildings. Starting from a full finite element model, the modal shapes of the reduced model for the kinematics are selected as the relevant linear elastic modes of the generalized sti ff ness / mass linear eigenvalue problem in terms of participation factor plus collapse mechanisms associated to appropriate static lateral loads. The internal forces are evaluated on the full model to guaranty an accurate description of the constitutive laws. The equations of motion are then projected in the modal space for the step-by step solution by a Newmark average acceleration scheme. The advantage is that the Newton iteration of the implicit method are carried out by inverting only the reduced tangent matrix. The proposed reduction method is tested for a reinforced concrete building varying frequency content, direction and amplitude of the ground motion. Accuracy and robustness are demonstrated employing a few tens of modes, including elastic modes and plastic collapse mechanisms. The need for plastic modes for describing the structural dynamics in case of seismic actions leading to significant plastic excursions is highlighted, together with the limits of simplified approaches, as the pushover analysis, based on the hypothesis of shape conservation in the inelastic range regardless of the building regularity. 2022 The Authors. Published by Elsevier B.V. is is an open access article under the CC BY-NC-ND license (http: // cr ativec mmons.org / licenses / by-nc-nd / 4.0 / ) r-review unde responsibility of the scientific committee of the XIX ANIDIS Conf rence, Se smic Engineering in Italy. Keywords: 3D frame structures; plasticity; reduced order modeling, nonlinear time history analysis, nonlinear structural dynamics, earthquake engineering. Abstract This research investigates the formulation of a reduced modal space for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame buildings. Starting from a full finite element model, the modal shapes of the reduced model for the kinematics are selected as the relevant linear elastic modes of the generalized sti ff ness / mass linear eigenvalue problem in terms of participation factor plus collapse mechanisms associated to appropriate static lateral loads. The internal forces are evaluated on the full model to guaranty an accurate description of the constitutive laws. The equations of motion are then projected in the modal space for the step-by step solution by a Newmark average acceleration scheme. The advantage is that the Newton iteration of the implicit method are carried out by inverting only the reduced tangent matrix. The proposed reduction method is tested for a reinforced concrete building varying frequency content, direction and amplitude of the ground motion. Accuracy and robustness are demonstrated employing a few tens of modes, including elastic modes and plastic collapse mechanisms. The need for plastic modes for describing the structural dynamics in case of seismic actions leading to significant plastic excursions is highlighted, together with the limits of simplified approaches, as the pushover analysis, based on the hypothesis of shape conservation in the inelastic range regardless of the building regularity. © 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: 3D frame structures; plasticity; reduced order modeling, nonlinear time history analysis, nonlinear structural dynamics, earthquake engineering. XIX ANIDIS Conference, Seismic Engineering in Italy Nonlinear time history seismic analysis of inelastic 3D frame buildings in a reduced modal space Domenico Magisano a , Antonella Corrado ∗ a , Antonio Madeo a , Giovanni Garcea a a Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Universita` della Calabria, 87030 Rende (Cosenza), Italy XIX ANIDIS Conference, Seismic Engineering in Italy Nonlinear time history seismic analysis of inelastic 3D frame buildings in a reduced modal space Domenico Magisano a , Antonella Corrado ∗ a , Antonio Madeo a , Giovanni Garcea a a Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Universita` della Calabria, 87030 Rende (Cosenza), Italy

1. Introduction 1. Introduction

We can classify the seismic analysis into four fundamental types (Fragiadakis and Papadrakakis (2008)): linear static, nonlinear static, linear dynamic, nonlinear dynamic. In the nonlinear static analysis or Pushover analysis the material nonlinearity is directly considered in the calculation. A lateral static load, representative of the dynamic We can classify the seismic analysis into four fundamental types (Fragiadakis and Papadrakakis (2008)): linear static, nonlinear static, linear dynamic, nonlinear dynamic. In the nonlinear static analysis or Pushover analysis the material nonlinearity is directly considered in the calculation. A lateral static load, representative of the dynamic

∗ Corresponding author E-mail address: antonella.corrado@unical.it ∗ Corresponding author E-mail address: antonella.corrado@unical.it

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.2023.01.060 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.