Structural mechanics

The module of Structural Mechanics aims at providing students with the fundamentals to understand, analyze, and critically assess the structural behavior of key components in power plants during service. The Structural Mechanics module covers the following topics: analytical models describing the mechanical behavior of structural materials, static failure mechanisms, and fatigue failure — including high-cycle fatigue, low-cycle fatigue, and thermomechanical fatigue — affecting both materials and components. Design and verification practices for pressure vessels will also be addressed, following both analytical methods and standards.

Thermal machines and structural mechanics (Thermal Machines)

This course aims at providing the students with the fundamentals necessary to understand and critically analyze the performance of the main topologies of powerplants. The course will also provide a comprehensive overview of the state-of-the-art technologies capable to improve the plant efficiency and to reduce its pollutant emissions. Finally particular attention will be devoted to the regulation strategies in order to assess the impact of the off-design operations on the efficiency of the plants.

Structural mechanics

The Structural Mechanics module aims to provide students with the knowledge required to understand the failure behavior of structural components under both static and cyclic loading conditions. It also enables them to perform the main calculations involved in the structural design and verification of pressure vessels and related components, in accordance with the technical guidelines defined by applicable standards. By the end of the module, students are expected to be able to carry out preliminary design and verification of key components used in power plants.

Thermal machines and structural mechanics (Thermal Machines)

At the end of the course the student is expected to be able to perform a preliminary design a new powerplant and/or to critically analyze the performance and the key operating parameters of an existing one. Moreover, he should be able to identify the most suitable methodologies to regulate the power output of the plant and to select the most suitable technologies to either increase its efficiency or reduce its pollutant emissions.

Structural mechanics

The Structural Mechanics module requires prior knowledge of fundamental topics in Strength of Materials. In particular, students are expected to be familiar with the stress state of beams in the elastic range, including axial, bending, and torsional loading conditions, as well as with the basic principles of stress and strain theory and the mechanical properties of metallic materials.

Thermal machines and structural mechanics (Thermal Machines)

In order to fruitfully attend the course, the student should have previously acquired the basic knowledge of Thermodynamics, Fluid Mechanics and Fluid Machines theory.

Structural mechanics

The Structural Mechanics module aims to provide an overview of the following topics: 3D stress and strain status. Stress vector and tensor. Principal stresses and principal directions. Stress status invariants. Hydrostatic and deviatoric stress status. Mohr circles for stress. Main loading conditions for beams. Deformation kinematics. Strain vector and tensor. Principal strains. Relation between stress and strain: Hooke’s law. Static resistance. Tensile test. Brittle and ductile materials. Failure criteria for brittle and ductile materials. Static safety factor against static failure. Effect of temperature on mechanical properties of metallic materials. Creep. Notch effect and stress intensity factor. Notch effect in static failure. Fatigue resistance. Phenomena related to fatigue and characteristic parameters. Whoeler (SN) diagrams: fatigue limit. SN material diagram estimation. Influence of mean stress: Haigh diagram. Influence of load, of dimensions, of surface finish and of notch. Component fatigue limit. Haigh diagram and SN component curves. Fatigue safety factor. Fatigue with variable amplitude stresses. Multiaxial fatigue. Cyclic and thermo-mechanic cyclic behavior: low-cycle fatigue, isothermal and thermomechanical. Parameters describing low cycle fatigue behavior and corresponding constitutive models. Parameters describing thermomechanical fatigue behavior and corresponding constitutive models. Damage models: classification, uniaxial models, multiaxial models. Residual life estimation. Case studies. Pressure vessels. Definition of the problem, differential equilibrium equation and its solution. Determination of stress status generated by internal and external pressure and by thermal gradient. Pipings. Axialsymmetric plates: axialsimmetric shells. Edge effect. Bolted joints, design and verification.

Thermal machines and structural mechanics (Thermal Machines)

Introduction Overview on the energy scenario & motivation for thermal machine analyses Steam Power Plants • Recap of fundamentals of the Rankine-Hirn Cycle • Analysis of real power plants and of the main technology trends • Environmental issues: overview plants pollutant emissions and on the aftertreatment technologies • Off-Design Operation. Gas Turbine Plants: • Recap of fundamentals of the Brayton Joule • From the ideal Cycle to the real one: analysis of the main sources of loss and of the most important operating parameters • Analysis of real power plants and of the main technology trends • Environmental issues: overview plants pollutant emissions and on the aftertreatment technologies • Off-Design Operation. Hydraulic Turbine Technologies* • Introduction: comparison among different methodologies to produce electricity from renewable sources • Key Features of main categories of Hydraulic turbines and their operating parameters • Definition of Turbine regulation and performance curves Wind Turbine Technologies • Introduction: comparison among different methodologies to produce electricity from renewable sources • Key Features of main categories of Wind turbines and their operating parameters • Definition of Turbine regulation and performance curves Internal Combustion Engines: • Introduction: comparison among different engine categories and configurations with a focus on powerplant applications • Efficiency analysis • Definition of internal combustion engine operating parameters and characteristic curves • Overview on the main technologies to improve the performance and the efficiency of the engine • Analyses of the engine pollutant emissions and of their aftertreatment technologies • Alternative fuels: biofuels and e-fuels *This topic could be skipped if already analyzed and discussed in …….

Structural mechanics

Thermal machines and structural mechanics (Thermal Machines)

Structural mechanics

The theoretical part of the course will cover the required topics through the development of analytical models and equations, as well as the discussion of case studies. Classroom tutorials will focus on formulating and solving practical problems related to the topics covered in the lectures, with the aim of deepening the understanding of theoretical concepts and providing students with insight into the role and influence of key parameters in structural analysis and design. A 1.5 hourse laboratory session will also be held, during which strains on a pressure vessel will be measured and compared with analytical predictions.

Thermal machines and structural mechanics (Thermal Machines)

Exercises: • 1st Exercise: numerical exercises on the regulations of steam power plants: 3 hours • 2rd Exercise: numerical exercises on the regulations of turbogas power plants: 3 hours • 3th Exercise: numerical exercises on hydraulic turbines: 3 hours • 4th Exercise: numerical exercises on internal combustion engines: 4.5 hours Laboratory (1.5 hour): • Overview on the main internal combustion engine components • Overview on the measurement systems to characterize the performance and the pollutant emissions of the engine.

Structural mechanics

Students are warmly invited to attend both theory lectures and tutorials to better understand the content of the slides shared by the professor on the web teaching portal. Suggested books are: • Shigley's mechanical engineering design, Richard G. Budynas, McGraw-Hill Education • A textbook of machine design, R.S. Khurmi J.K. Gupta, McGraw-Hill Education • F. Cesari, D. Martini, I recipienti in pressione, Pitagora Editrice Bologna, 2012.

Thermal machines and structural mechanics (Thermal Machines)

The student is suggested to attend lectures and exercises, to use the notes provided by the teacher for the preparation of the exam, since there is no single text dealings with all the topics covered in the course. Possible books to deepen single topics, when needed, for future professional activity, are the following: • M.J. Moran, H.N. Shapiro, “Fundamentals of Engineering Thermodynamics”, 5th ed., John Wiley & Sons. • S.L. Dixon, C.A. Hall, “Fluid Mechanics and Thermodynamics of Turbomachinery”, 6th ed., Butterworth-Heinemann, Elsevier. • S.A. Korpela, “Principles of Turbomachinery”, Wiley & Sons. • Heywook J., Internal Combustion Engine fundamentals

Structural mechanics

Slides; Esercizi; Esercizi risolti; Esercitazioni di laboratorio; Materiale multimediale ;

Thermal machines and structural mechanics (Thermal Machines)

Slides; Video lezioni dell’anno corrente;

Structural mechanics

Modalità di esame: Prova scritta (in aula); Prova orale obbligatoria; Prova pratica di laboratorio; Elaborato scritto prodotto in gruppo;

Thermal machines and structural mechanics (Thermal Machines)

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa;

Structural mechanics

Exam: Written test; Compulsory oral exam; Practical lab skills test; Group essay;

Thermal machines and structural mechanics (Thermal Machines)

Exam: Written test; Optional oral exam;

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Structural mechanics

The exam consists of two parts: a written test (numerical exercises) and an oral test (theory). The written test lasts 1.5 hours and includes two exercises, one for each module of the course. The type and complexity of the exercises are similar to those covered during class tutorials. Consultation of notes or any external material is not permitted during the written test, except for a single A3 sheet prepared by the student, containing formulas. The oral test will be scheduled according to a calendar published within one day after the written exam. It consists of one question on theoretical topics. To be admitted to the oral test, the student must obtain a score of at least 18/30 in both written exercises. During the oral test, students are required to bring a printed report of the experimental lab activity on strain measurement in pressure vessels. This report will be discussed with the professor, and up to 2 bonus points may be awarded and added to the average score (written + oral) of the Structural Mechanics module. At the end of the oral test, a score will be assigned for each module, based on the results of both the written and oral tests. The exam is considered passed only if the student obtains a grade of at least 18/30 in both the written and the oral tests. The final grade is calculated as the average of the scores obtained in the two modules. The written test is intended to assess the ability to solve practical problems involving material properties, failure mechanisms, and load-bearing models, reflecting real-world applications. The oral test evaluates the student's ability to reason beyond standard exercises, particularly in handling analytical models describing the behavior of materials and structures under operating conditions. This includes both the understanding of model assumptions and their application to case studies.

Thermal machines and structural mechanics (Thermal Machines)

- Written test (duration: 1h 25 m): it is divided into two parts: o The first part is composed by 8 multiple-choice questions to be answered within 30 minutes. The questions are concerned with the theory topics, but a few of them will require the solution of short numerical problems. Each correct answer will score 2 points, each blank (not given) answer will bring 0 points, and each wrong answer will bring -0.5 points. Each question will have only one correct answer. The maximum score for the first part is 16/15. o The second part will require the solution of two exercises within 1 hours, in the form of essay questions. The maximum score is 15/15. In order to be admitted to the second part, it is necessary to get a score >= 8/16 from the first part o The exam is not passed if the score from the first written part is strictly lower than 8/15 OR the one from the second part is strictly lower than 9/15. o The final mark of the written test is given by the sum of the two parts. The maximum achievable mark of the written part is 26/30. In order to achieve higher marks, the student has to attend the oral exam. - Oral Test: the student will discuss with the commission about the main topics of the course, and he may be asked to provide some of the mathematical demonstrations shown during the lessons. With the oral test, the student may increase or decrease the mark achieved during the written part of the exam. All the students with a sufficient mark (>=18) may ask the commission to attend the oral test.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.