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, students are expected to acquire the knowledge required to understand the operating principles, thermodynamic cycles and energy conversion processes characterizing gas turbine plants, steam power plants, hydraulic turbines and internal combustion engines. Students will develop the capability to interpret the operating behaviour of thermal and hydraulic machines, analysing their performance both under design and off-design operating conditions. Students will be able to evaluate the influence of the main design and operating parameters on efficiency, power output and overall system performance through the application of mass, energy and thermodynamic balance equations. They will also acquire the capability to analyse and apply the main regulation and control methods adopted for thermal and hydraulic machines, understanding their role in ensuring stable, efficient and reliable operation under variable load conditions. Through numerical exercises and application examples, students will develop the ability to solve engineering problems related to the performance evaluation of thermal machines, propulsion systems and power generation plants, critically interpreting the obtained results from both thermodynamic and operational perspectives. The course will additionally provide students with the methodological tools required to analyse technological solutions aimed at improving the energy efficiency and environmental sustainability of thermal machines and propulsion systems. In particular, students will develop awareness of the engineering approaches currently adopted to reduce fuel consumption and pollutant emissions in gas turbines and internal combustion engines, as well as of the technological evolution supporting the development of more sustainable mobility and energy conversion systems.

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)

For a profitable attendance of the course, students are expected to possess the fundamental knowledge of thermodynamics, fluid mechanics and heat transfer typically acquired in basic thermal sciences courses. In particular, students should be familiar with the principles of mass and energy conservation, thermodynamic properties of fluids, thermodynamic transformations and basic fluid-dynamic analysis. A prior background on the fundamental principles of fluid machinery and energy conversion systems is also recommended in order to facilitate the understanding of the operating behaviour and performance analysis of thermal and hydraulic machines. Basic knowledge of applied mechanics and energy systems is beneficial for understanding the operating behaviour, regulation and performance analysis of thermal and hydraulic machines.

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 ==> 1 h - Steam Power Plants - Recap of fundamentals of the Rankine-Hirn Cycle ==> 1.5 h - Analysis of real power plants and of the main technology trends ==> 1.5 h - Environmental issues: overview plants pollutant emissions and on the aftertreatment technologies ==> 1.5 h - Alternative Fuels: Bio & e-fuels - Off-Design Operation. ==> 4.5 h - Gas Turbine Plants: - Analysis of real power plants and of the main technology trends ==> 3 h - Environmental issues: overview plants pollutant emissions and on the aftertreatment technologies ==> 1.5 h - Use of Alternative Fuels: bio and e-fuels ==> 1.5h - From the ideal Cycle to the real one: analysis of the main sources of loss and of the most important operating parameters ==> 3 h - Off-Design Operation ==> 4.5 h - Hydraulic Turbine Technologies - Introduction: comparison among different methodologies to produce electricity from renewable sources ==> 1 h - Key Features of main categories of Hydraulic turbines and their operating parameters ==>3 h - Definition of Turbine regulation and performance curves ==> 1 h - Analysis of the Main Turbine Categories (Pelton, Francis, Kaplan) ==> 6 h - Internal Combustion Engines: - Introduction: comparison among different engine categories and configurations ==> 4.5 h - Efficiency analysis ==> 4.5 h - Overview on the main technologies to improve the performance and the efficiency of the engine ==>3 h - Analyses of the engine pollutant emissions and of their aftertreatment technologies ==> 3 h -Alternative fuels: biofuels and e-fuels ==> 1.5 h

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)

The course is organised through theoretical lectures and classroom exercise sessions covering all the topics presented during the course. The theoretical lectures are aimed at introducing the thermodynamic, fluid-dynamic and operational principles governing thermal and hydraulic machines, with particular reference to gas turbine plants, steam power plants, hydraulic turbines and internal combustion engines. Specific attention is devoted to energy conversion processes, machine performance, regulation methods and operating behaviour under design and off-design conditions. Each theoretical topic is complemented by numerical exercises and application examples aimed at applying the presented methodologies to the analysis and performance evaluation of thermal machines and energy conversion systems. The exercise sessions are intended to strengthen the students’ capability to solve engineering problems and critically interpret the obtained results. The course may also include laboratory activities and/or technical visits to industrial or experimental facilities, allowing students to observe real energy conversion systems and thermal machines operating in practical applications.

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

Lecture slides; Exercises; Exercise with solutions ; Lab exercises; Multimedia materials;

Thermal machines and structural mechanics (Thermal Machines)

Lecture slides; Video lectures (current year);

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;

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 40 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 1.20 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 8/15. 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.