Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2019/2020
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Docente Martinelli Luca
Cfu 5.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

The course expands on the topics studied during the undergraduate level course of Strength of Materials (Scienza delle Costruzioni) extending the solutions for shear and torsion to hollow and thin walled cross-sections, presenting solution methods for statically indeterminate structures, including thermal loading, and applying the acquired knowledge to check the strength and stability of structural elements frequently found in chemical and petrochemical structures.

Risultati di apprendimento attesi

At the end of the course the students will know how to find the stress-state in statically indeterminate structures, in which equilibrium alone is not sufficient to completely define it.  The students will have knowlege of the the load limits on a structure before the strength of the material is exceeded or loss of equilibrium is reached for instability of the static equilibium state, and will be able to compute the expected displacements of a structure due to a given loading.

The students will be able to apply the knowledge acquired to the solution of simple problems related to practical situation in elements frequently found in chemical and petrochemical plants, such as distillation towers, pressure vessel, pipes.


Argomenti trattati
  1. Review of: stress state, strain state, constitutive law for elastic materials, calculation of support reactions in statically determinate structures, sketching diagrams of internal force components.

  2. Deepening of the De Saint Venant cases: Shear and torsion in thin walled sections (open and closed).

  3. Strain energy in beams.

  4. Generalities on energy theorems for planar beams: Clapeyron’s, Betti’s, Maxwell’s and Castigliano’s theorems.

  5. Elastic line equation for beams: deflection and displacement calculation for statically indeterminate beams. Effect of supports’ settlement and of thermal loading.

  6. Principle of virtual work for a deformable continuum. Kirchhoff's theorem on the uniqueness of the solution of the elastic problem. The principle of virtual work for systems of plane beams: calculation of displacements and solution of statically indeterminate beam structures. Effect of support settlement and of thermal loading.

  7. Stability of elastic equilibrium. The static method for determination of the critical load. Euler theory for slender columns. Effect of boundary conditions and of imperfections. Limitations of the Euler theory and normative methods for checking compressed elements. Lateral instability of beams in bending.

  8. Mohr's circle, principal stresses, yield strength and theories of failure for materials

  9. Generalities on plastic design of planar steel beams: pastic moments, plastic hinges sequence, collapse mechanisms


A sound knowledge of Statics and of the undergraduate course of "Scienza delle Costruzioni" (Strength of Materials) is required.

Modalità di valutazione

During the course there will be two intemediate written tests (one in the middle of the course and one at the end) to verify the understanding and the knowldege of the specific topics dealt with within the course (through theoretical questions in open form) and the ability of the student in applying them to the check of the strength and stability of plane frames and structures (through the solution of numerical problems).

If both tests will be judged as positive, then a mark for the course will be proposed to the student (50% from the first test and 50% from the second). If any of the test is not satisfactory,  the teacher may require an oral interview. During the oral interview it will be verified the student's learning about the contents of lessons, seminars, biography, and practical exercises. At the end of the oral interview the student will receive the mark (50% form the outcome of the two written tests + 50% from the outcome of the oral interview).

If a student fails any of the two written tests, or does not attend them, he will be required to sit a written exam modelled on the union of the written tests. If the written exam will be judged as positive, then a mark for the course will be proposed to the student. If the exam is not satisfactory, the teacher may require an oral interview. The mark will be formed 50% form the outcome of the written exam + 50% from the outcome of the oral interview.

The student can, in any case ask for an oral interview should he/she be not satisfied with the mark proposed.


Risorsa bibliografica facoltativaFerdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek, Mechanics of Materials, ISBN: 978-0073398235
Risorsa bibliografica facoltativaM. G. Mulas, Lezioni di scienza delle costruzioni, Editore: Esculapio
Risorsa bibliografica facoltativaL. Corradi Dell'Acqua, Meccanica delle Strutture, Editore: Mc-Graw Hill
Risorsa bibliografica facoltativaL. Malvern, Introduction to the mechanics of a continuous medium, Editore: Prentice Hall
Risorsa bibliografica facoltativaV.D. da Silva, Mechanics and Strength of Materials, Editore: Springer, Anno edizione: 2007
Risorsa bibliografica facoltativaT.H.G. Megson, Structural and Stress Analysis, third Edition, Elsevier, Editore: Elsevier, Anno edizione: 2014

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Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 50:00 75:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
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schedaincarico v. 1.6.9 / 1.6.9
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