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Lecturer: E. Spacone

Nonlinear Response Analysis a.y. 2021/22


The main goal of the course is to provide students with skills that can be applied to both research and practice for analysing structures under earthquake loads. The class will focus on the theory of linear and nonlinear structural analysis, with particular emphasis on available computational models, their characteristics and limitations. Modelling alternatives and their effect on the model output will
be discussed. The course will present linear and nonlinear methods of analysis prescribed by the seismic design codes and available in the published literature
The final goal is to leave attendees with a firm idea of the importance of the modelling assumptions and the methods of analyses that are used to analyse a structure mainly with respect to the actual behaviours of structures under seismic loads.

1. Direct Integration of equations of motion (Linear Seismic Analysis of MDOF)
2. Response Spectrum Analysis: solution of MDOF systems
3. Computer software for linear structural analysis
4. Review of basic structural analysis formulations (Beam Theory – Strong Form) (review)
5. Formulation of linear elements (review)
6. Review of basic Energy theorems
7. Seismic response of structures: linear vs. nonlinear behavior. Sources and types of nonlinearities
8. Material Nonlinearities: Lumped vs. Distributed inelasticity a) Section models and Hinge element formulations b) Frame element formulations (Weak form) c) Section models d) Material modeling
9. Structure solution strategies: event-to-event, Newton type solution strategies. Advanced procedures
10. Modeling for computer analysis: use of computer programs.
11. Nonlinear methods of analysis: static vs dynamic
12. Geometric nonlinearities: P- theory and applications. Structural stability. Large displacement theory.



  • No textbook is required for the class. Handouts and selected papers will be distributed during the class.
  • Earthquake Engineering – From Engineering Seismology to Performance-Based Engineering, edited by Yousef Bozorgnia and Vitelmo V. Bertero, 2004
  • Bathe, K.-J. (1996). Finite Element Procedures. Prentice-Hall, Englewood Cliffs, New Jersey.
  • Crisfield, M.A. (1991). Non-linear Finite Element Analysis of Solids and Structures. John Wiley & Sons, Chichester, England.
  • Yang, Y.-B., and Kuo, S.-R. (1994). Theory and Analysis of Nonlinear Framed Structures. Prentice Hall, Englewood Cliffs, New Jersey.
  • Zienkiewicz, O.C. and Taylor, R.L (1989). The Finite Element Method. Volume 1. Basic Formulation and Linear Problems. Fourth Edition. McGraw Hill, London.
  • Zienkiewicz, O. C., and Taylor, R. L. (1991). The Finite Element Method. Volume 2. Solid and Fluid Mechanics, Dynamics and Non-Linearity. Fourth Edition. McGraw Hill, London.


There will be a three-hour final written examination June 9,2022 - 9 to 12.


Tipologia corso : Caratterizzante

Curriculum : Ingegneria Sismica e Sismologia

Periodo: Semestre II

Anno accademico: 2021-2022

Luogo : Eucentre classroom tbd