(

*STRUCTURAL MECHANICS AND NUCLEAR CONSTRUCTIONS*)

CdSINGEGNERIA NUCLEARE

Codice519II

CFU12

PeriodoAnnuale

LinguaInglese

The student who completes successfully the course will achieve the ability to perform structural calculations of complex components of a nuclear power plant such as pressure vessels, steam generators, piping, pumps and valves. The student will be able to apply the failure criteria by plastic collapse, incremental plastic strain and thermal ratcheting and will be able to demonstrate advanced knowledge of the relevant standards such as ASME III and ASME XI.

The student who completes the course successfully will have the ability to perform structural calculations of complex components of a nuclear power plant such as pressure vessels, steam generators, piping, pumps and valves. He or she will be able to apply the failure criteria by plastic collapse, incremental plastic strain and thermal ratcheting. He or she will be able to demonstrate advanced knowledge of the relevant standards such as ASME III and ASME XI.

**Assessment criteria of knowledge**

- The student will be assessed on his capabilities to discuss the main course contents using appropriate terminology.
- An exercise/report will be performed by the student ad discussed during the oral examination. The student must demonstrate the ability to put into practice and to execute, with critical awareness, the activities illustrated or carried out under the guidance of the teacher during the course.

- The student will be assessed on his/her demonstrated ability to discuss the main course contents using the appropriate terminology. - In the written report, the student must demonstrate the ability to put into practice and to execute, with critical awareness, the activities illustrated or carried out under the guidance of the teacher during the course.

Methods:

- Final oral exam
- Written report

Further information:

Specific criterium of evaluation : the student will be evaluated weighting the home made written report (30%) and the oral exam ( 70%)

**Skills**

The following main skills are provided by the course:

- Capability to understand structural problems geometry and boundary conditions;
- Capability to apply the proper theory (simplified or general) and solution method for evaluating stress and strain state;
- Capability to perform the limit analysis of structures;
- Capability to evaluate the linear-elastic fracture mechanics;
- Capability to assess thermal ratcheting and shake down;
- Capability to perform seismic assessment;
- Capability to adopt standards (ASME III and XI) for vessel, pump, valve and piping design.

**Skills**

The following main skills are provided by the course:

- Capability to understand structural problems geometry and boundary conditions;
- Capability to apply the proper theory (simplified or general) and solution method for evaluating stress and strain state;
- Capability to perform the limit analysis of structures;
- Capability to evaluate the linear-elastic fracture mechanics;
- Capability to assess thermal ratcheting and shake down;
- Capability to perform seismic assessment;
- Capability to adopt standards (ASME III and XI) for vessel, pump, valve and piping design.

**Assessment criteria of skills**

During the oral interview, the skills acquired by the students will be assessed, evaluating the comprehension degree and capability to connect different topics of the course.

During the oral interview, the skills acquired by the students will be assessed, evaluating the comprehension degree and capability to connect different topics of the course.

**Behaviours**

Students will acquire/develop awareness on structural analysis of nuclear power plant main components and sensibility and understanding of their implementation in nuclear plants.

Students will acquire/develop awareness on structural analysis of nuclear power plant main components and sensibility and understanding of their implementation in nuclear plants.

**Assessment criteria of behaviours**

The oral interview will ascertain the personal attitude of the student by proposing questions and problems related to structural analysis of nuclear power plant components.

The oral interview will ascertain the personal attitude of the student by proposing questions and problems related to structural analysis of nuclear power plant components.

**Prerequisites**

Knowledge and skills on beam structures theory (isostatic and hyperstatic) and knowledge of the main concepts of the continuum mechanics constitute the prerequisites for this course

Knowledge and skills on beam structures theory (isostatic and hyperstatic) and knowledge of the main concepts of the continuum mechanics constitute the prerequisites for this course.

**Teaching methods**

Front and distance (live online by Microsoft Teams) lectures with the support of slides are provided. Task-based teaching, problem-based teaching and inquiry-based teaching are performed. A written exercise/report will be assigned to the students on topics developed during the lectures and solved by themselves.

Delivery: face to face

Attendance: very important

Learning activities:

- attending lectures
- preparation of oral/written report
- individual study

Teaching methods:

- Lectures
- Task-based learning/problem-based learning/inquiry-based learning
- project work

**Syllabus**

The specific topics of the course are:

- the methods of the elasticity theory applied to plates and shells solicited by mechanical loads and temperature gradients;
- the theory of limit analysis for the determination of the collapse load of plates, shells and beams;
- the theory of linear elastic fracture mechanics;
- the determination of seismic loads by means of modal analysis theory;
- failure criteria for plastic collapse, incremental plastic strain and thermal ratcheting;
- the relevant standards such as ASME III and ASME XI

The specific topics of the course are:

STRUCTURAL MECHANICS

**1) – Recall of the principles of beam theory**

- (stresses, strains in one-dimensional structures, criteria of resistance of ductile materials, Geometry of masses and static moments, Statically indeterminate beams: methods for opening the indeterminacy and examples).

**2) -The theory of the bending plates**

- elastic surface of a circular plate loaded by a uniform distribution of moments on the contour, determined starting from the constitutive equations;

- bending of circular plates: determination and solution of the differential equation of the elastic surface for some particular cases

- state of stress and strain of the bending of circular plates simply supported or clamped on the contour and subjected to a uniform load. Sizing with resistance criteria

- calculation of the stress and strain state of annular plates variously constrained and loaded

- differential equation of the elastic surface of plates of general shape: - rectangular plates variously constrained and loaded; determination of the solution with the use of double and simple series. applications to particular cases.

**3) - Shell theory**

-determination of the equilibrium equations, congruence and constitutive of shells in the membrane regime

- stress state of axially symmetric shells subjected to own weight. Resistance checks;

determination of the stress state of containers containing liquids; equilibrium equations of cylindrical shells in the membrane regime

- application of the membrane theory to cylindrical shells filled with liquid with a varied axis inclined on the horizontal

- constitutive equation of a shell of revolution in the membrane regime and determination of the displacements.

- bending theory of cylindrical shells: determination of equilibrium equations. Deformations and displacements of a cylindrical shell in bending regime: interpretation and approximation of the constitutive equations; determination of the differential equations of the displacements of the average surface

- application of the bending theory of cylindrical shells and comparison with the results of the membrane theory; cylindrical tanks containing liquid; discontinuity analysis and congruence conditions for variously constrained cylinders

- bending stresses at the intersection between a cylindrical shell and a spherical shell

**4) - Thermal stresses**

- condition of existence of the thermal stresses in an unconstrained continuum

- thermal stresses in structures with external constraints (beams and plates)

- thermal stresses in thin disks, in a sphere and in a plate. Extension of the results of the thin cylinder plate

- thermal stresses in slabs and thin cylinders

- thermal stresses in thin cylinders with free edge and temperature gradient in the thickness

- numerical determination of thermal stresses in shells and plates

**5) - Limits analysis of beams, plates and shells**

- theory of the limit analysis of structures; equilibrium and geometric equations of spherical shells; principle of virtual works; rigid-plastic behaviour of the materials

- limit analysis theorems; yield conditions of shells; yield conditions approximated to limited interaction. Flow rule (link between strain rate and yield condition).

- collapse load of variously constrained circular plates

- limit analysis of cylindrical shells: application to cylindrical shells under pressure with variously constrained ends

- limit analysis of spherical shells: application to a spherical shell sector with variously constrained ends

**6) - Linear Elastic Fracture Mechanics **

- Principles and criteria of fracture mechanics; transition temperature; tests for the determination of NDT and resilience

- Standard tests for determining the KIC. Fracture mechanics verification according to ASME III and XI standards

**NUCLEAR CONSTRUCTIONS**

**7) - Seismic analysis**

- designt and seismic verification of a nuclear plant and its components;

-simulation with concentrated parameters of a structure and determination of the equations of motion.

-resolution of the equations of motion with modal analysis; method of response spectra

**8) - ASME standards**

- ASME standards for the verification of the components of a nuclear plant. Limits and loading conditions

- primary, secondary and peak stresses. Verification of the failure modes typical of pressure vessels

- analysis of operational transients to which a nuclear reactor pressure vessel is subjected

- categorization of the stresses of a pressure vessel according to ASME III standards

- shakedown condition in pressurized vessels

- Thermal Ratcheting in pressure vessels

**9) Components of a nuclear power plant with light water reactors**

- technology and sizing of pressure vessels of light water reactors - application of the ASME standards to the design of the Pressure Vessel of a PWR.

- Steam generator: material and design problems

- sizing and manufacturing technology of steam generators for pressurized water nuclear reactors;

- Sizing and manufacturing technology of pumps

- sizing and manufacturing technology of valves of the primary circuit of a nuclear plant.

- design of the piping of the primary circuit of a light water reactor and manufacturing technology

The specific topics of the course are: -the methods of the elasticity theory applied to plates and shells solicited by mechanical loads and temperature gradients. - the theory of limit analysis for the determination of the collapse load of plates, shells and beams. - the theory of linear elastic fracture mechanics - the determination of seismic loads by means of modal analysis theory - failure criteria for plastic collapse, incremental plastic strain and thermal ratcheting -the relevant standards such as ASME III and ASME XI

Recommended reading includes the following works: - Notes of the teacher - Relevant Standards ( ASME III- Sect NB and ASME XI) Further bibliography will be indicated during the lectures.

There are not variations (about program, exam, bibliography etc.) for non-attending students.

Lectures will be provided live .

The student preparation will be evaluated during one final oral test. It consists of an interview between the candidate and exam commission, during which the candidate will discuss the topics of the course and could be requested to also solve written problems/exercises in front of the commission.

The student must prepare, for being admitted to the final oral test, a written exercise/report assigned by the lecturers, about one of the main topics of the course.

The exam is considered passed if the student provides sufficiently correct answers to the proposed questions.

It is not possible to pass the test if the candidate shows an inability to express him/herself in a clear manner using the correct terminology, or if the candidate does not respond sufficiently to questions regarding the most fundamental part of the course. The final test will not have a positive outcome if the candidate repeatedly demonstrates an incapacity to relate and link parts of the programme with notions and ideas that he/her must combine in order to correctly respond to a question.

It is not required to pass intermediate tests, follow seminar or lab activities for attending the exam.

Stages, internships and collaborations with third parts are not required for this course.

For any further information, students can contact the lecturers via email: donato.aquaro@unipi.it, alessio.pesetti@unipi.it.