Seismic structural analysis and design

Expected Learning Outcomes

Knowledge and Understanding

At the end of the course, students will possess a thorough understanding of the fundamental principles of structural dynamics and earthquake engineering, with particular emphasis on the dynamic modelling of single-degree-of-freedom (SDOF) and multiple-degree-of-freedom (MDOF) systems, the seismic response of structures, and the main seismic design criteria.

Students will also acquire knowledge of innovative seismic protection systems, including base isolation, supplemental energy dissipation devices, vibration control systems, and traditional strengthening techniques. They will understand their physical principles, mathematical models, and design methodologies.

Applying Knowledge and Understanding

At the end of the course, students will be able to:

• model dynamic structural systems with one or multiple degrees of freedom;
• evaluate the main dynamic properties of structures;
• perform seismic analyses using response spectrum and modal analysis procedures;
• assess the influence of ductility and damping on structural response;
• design and verify seismic isolation and supplemental damping systems;
• evaluate the effectiveness of traditional strengthening techniques for existing structures;
• develop numerical models using structural analysis software;
• critically compare different seismic protection strategies and structural upgrading solutions.

Making Judgements

Students will develop the ability to interpret the results of dynamic and seismic analyses, critically evaluating their reliability and limitations. They will also be able to compare alternative design solutions for seismic risk mitigation and assess their advantages and drawbacks with respect to project objectives.

Communication Skills

Students will be able to present theoretical concepts and design choices using appropriate technical and scientific terminology and to critically discuss the results of numerical analyses and real-world case studies.

Learning Skills

Students will acquire the methodological tools required to independently deepen their knowledge of advanced topics in structural dynamics, earthquake engineering, and innovative seismic protection technologies.

Required Prerequisites

The following knowledge is considered important:

• equilibrium of force systems;
• kinematics and statics of rigid bodies;
• stress and strain states in solids;
• mechanical behaviour of materials;
• stiffness and deformability concepts;
• basic principles of structural analysis;
• fundamentals of linear algebra and matrix computation.

Such knowledge is typically acquired through courses in Structural Mechanics, Strength of Materials, and related disciplines.

1. Fundamentals of Structural Dynamics

1. Single-degree-of-freedom (SDOF) oscillator.
2. Undamped free vibrations.
3. Damped free vibrations.
4. Response to harmonic excitations.
5. Resonance and dynamic amplification factor.
6. State-space formulation of dynamic response.
7. Step and impulse response.
8. Elastic response spectrum.

2. Multi-Degree-of-Freedom Systems

1. Equations of motion of MDOF systems.
2. Mode shapes and natural frequencies.
3. Modal orthogonality.
4. Classical modal analysis.
5. Classical and non-classical damping.
6. Introduction to complex modal analysis.

3. Seismic Analysis of Structures

1. Modelling of seismic excitation.
2. Response-spectrum modal analysis.
3. Modal participation factors.
4. Participating masses.
5. Modal combination procedures.
6. Elastic and design response spectra.
7. Ductility and inelastic behaviour.
8. Principles of seismic design according to current codes.

4. Seismic Protection Systems

1. Principles of seismic isolation.
2. Elastomeric and sliding isolation devices.
3. Mechanical behaviour and constitutive modelling of seismic isolators.
4. Design of base-isolated buildings.
5. Supplemental energy dissipation systems.
6. Viscous, hysteretic, and viscoelastic dampers.
7. Modelling and design of damped structures.

5. Seismic Retrofitting and Innovative Applications

1. Seismic upgrading and retrofitting strategies.
2. Seismic isolation systems applied to existing buildings.
3. Tuned Mass Dampers (TMDs) and damping towers.
4. Hybrid isolation and damping systems.
5. Critical analysis of national and international case studies.
6. Assessment of benefits in terms of seismic demand reduction and structural resilience enhancement.

6. Numerical and Design Applications

1. FEM and DMEM modelling of structures subjected to seismic actions.
2. Numerical implementation of seismic isolators and dampers.

[T1] Slides e dispense fornite dai docenti durante il corso.

[T2] Chopra A.K., Dynamics of Structures: Theory and Applications to Earthquake Engineering, 5th Edition, Pearson.

Supplementary References

[T3] Clough R.W., Penzien J., Dynamics of Structures, Computers & Structures Inc.

[T4] Muscolino G., Dinamica delle Strutture, McGraw-Hill Italia.

[T5] Dolce M., Ponzo F.C., Di Cesare A., Arleo G., Progetto di Edifici con Isolamento Sismico, IUSS Press.

[T6] Christopoulos C., Filiatrault A., Principles of Passive Supplemental Damping and Seismic Isolation, IUSS Press.

Additional material

Articoli scientifici, linee guida tecniche, documenti normativi e casi studio reali saranno messi a disposizione dal docente durante il corso per approfondire particolari applicazioni di isolamento sismico, dissipazione supplementare di energia e controllo delle vibrazioni.

Learning Assessment Procedures

Student learning is assessed through:

• discussion of a design project developed during the course;
• oral examination covering the topics addressed in the course.

The design project consists of the modelling and seismic analysis of a structure, with particular emphasis on the use of innovative seismic protection systems such as base isolation devices, supplemental damping systems, or passive vibration control systems.

The oral examination evaluates:

• knowledge and understanding of the course topics;
• ability to apply theoretical concepts to engineering problems;
• critical interpretation of analysis results;
• proper use of technical and scientific terminology;
• ability to establish connections among different topics covered in the course.

The design project contributes to the final grade and is intended to assess the student's ability to independently apply the acquired knowledge.

Grading Criteria

Fail (<18/30)

Fragmentary or inadequate knowledge, poor application skills, and inappropriate use of technical terminology.

18-21/30

Basic knowledge of the main topics and limited application skills.

22-25/30

Fair knowledge of the subject, with the ability to perform analyses and interpretations with limited critical autonomy.

26-28/30

Good theoretical and practical knowledge, ability to develop independent reasoning and critically discuss results.

29-30 cum laude

Comprehensive and in-depth knowledge, excellent critical thinking skills, full command of analytical and design methods, and outstanding technical communication abilities.

Learning assessment may also be carried out online should conditions require it. To ensure equal opportunities and compliance with current regulations, students may request a personal meeting to discuss compensatory and/or dispensatory measures based on specific educational needs. Students may also contact the departmental CInAP representative (Centro per l'Integrazione Attiva e Partecipata - Services for Students with Disabilities and/or Specific Learning Disorders).

1. Derive the equation of motion of a single-degree-of-freedom oscillator and discuss its dynamic response.
2. Explain the physical meaning of damping and compare the main damping models used in structural analysis.
3. Define the concept of response spectrum and explain its use in seismic analysis.
4. Discuss the meaning of modal participation factor and participating mass.
5. Illustrate the assumptions underlying response-spectrum modal analysis.
6. Explain the difference between elastic and design response spectra.
7. Describe the inelastic behaviour of structures and the role of ductility in seismic design.
8. Explain the physical principles of seismic isolation and its advantages over conventional design approaches.
9. Describe the mechanical behaviour of elastomeric isolators and sliding isolation devices.
10. Explain the operating principles of viscous and hysteretic dampers.
11. Compare a conventional structure and a seismically protected structure in terms of seismic demand and expected performance.
12. Discuss a real case study involving seismic retrofitting through base isolation.
13. Discuss a real case study involving seismic retrofitting through traditional strengthening techniques.
14. Explain the operating principles of Tuned Mass Dampers (TMDs) and their major structural engineering applications.
15. Describe the advantages and limitations of innovative seismic protection systems for both new and existing structures.
16. Present and critically discuss the design project developed during the course.