Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Linear algebra, vectors, mathematical analysis, ordinary and linear differential equations, geometry, main concepts on material point and rigid bodies mechanics.

The course intends to provide the fundamental basis of structural analysis by developing the theoretical principles which allows to understand the mechanical behavior of elastic solids and, in particular, of elastic beam structures. The course tackles the main problems related to the analysis of isostatic and hyperstatic structures, the essential knowledge of solid mechanics, the study of the strain and stress state and the capacity of evaluating beam structures strength and deformability.

The student will be able to apply his knowledge in order to develop critical and practical skills, which are necessary for the structural analysis. Concerning with the area of the comprehension of a structural system, the student will obtain the capability to analyze isostatic and hyperstatic structures, compute the stresses in a beam and perform safety verifications. These abilities will be gained through the development of exercises, which require the use of those models presented during the lectures.

The presented theory and the discussed problems represent a basic theoretical tools in the design of any structural system. These concepts are essential in order to interpret, analyze, model and solve more complex problems related to structural analysis.

1. RIGID BODY KINEMATICS Rigid body motion External and internal constraints Rigid bodies systems Kinematical analysis Kinematical classification of structures 2. RIGID BODY STATICS Static characterization of constraints Equilibrium equations Static classification of structures Constraint reactions Static matrix Superposition principle 3. INTERNAL ACTIONS Definition of a beam Internal actions in 3D: N, Tx, Ty, Mx, My, Mt, and in 2D: N, M, T Internal actions diagrams Equilibrium differential equations Jump conditions (concentrated loads) and boundary conditions. 4. AREAS GEOMETRY Total area First order moments and center of mass Second order moments Huyghens theorem principal axes of inertia Inertia tensor 5. KINEMATICS OF DEFORMABLE BODIES Elementary deformations: stretch ration, shear strain, area and volume variations Strain tensor Principal axes - strain invariants 6. STATICS OF DEFORMABLE BODIES Definition of stress Theorem of Cauchy Stress tensor Mohr's circle Triaxial, uniaxial, plane stress state Spherical and deviatoric stresses Principal axes Equilibrium equations 7. CONSTITUTIVE LAWS Uniaxial test Generalized linear elastic costitutive law Homogeneity and isotropy Strain energy 8. THEORY OF ELASTIC BEAMS Saint Venant's problem Normal force Flexure Eccentric normal force - Jourawski's approximated shear theory Torsion (circular, rectangular and thin-walled cross-sections) Elastic line differential equations 9. FAILURE CRITERIA AND STRENGTH VERIFICATIONS Local failure Tresca, Beltrami, Von Mises criteria Strength verification and project 10. PRINCIPLE OF VIRTUAL WORKS Principle of virtual works (P.L.V.) 11. STABILITY OF EQUILIBRIUM Critical load for concentrated elasticity systems - Eulers problem Eulerian load

The learming evaluation is divided into two parts: - a written test, consisting in the solution of two exercises to be completed in three hours; - an oral exam, consisting in the discussion of the main theoretical concepts and some application exercises.

In order to have a positive result, the student must prove to: - have reached a good understanding of the main theoretical and application concepts of the mechanics of rigid bodies and deformable bodies; - be able to use autonomously and in a correct way the models and the main methods of analysis of isostatic and hyperstatic structures and solve problems related to the evaluation of beam structures strength and deformability; - be capable to clearly expose the principal ideas and concepts of structural analysis.

During the written and oral tests, the professor will evaluate the autonomous ability of the student to set up and solve problems related to the topics of the course. Moreover, the professor will evaluate the abilities to use the main methods, theoretical models and tools of structural analysis.

The written test is preparatory to the oral exam. In order to access to the oral exam, the student must obtain at least the passing mark, equivalent to 18/30, at the written test. In order to have an overall positive result, the student must obtain at least the passing mark, equivalent to 18/30, at both written and oral tests. The maximum evaluation mark, equivalent to 30/30 with lode, is obtained by proving an exhaustive knowledge of the contents of the course and a full autonomy in aswering the questions and solving problems. The minimum evaluation mark, equivalent to 18/30, is reserved to those student who prove to be able to solve problems with a sufficient knowledge of the methods and models of structural mechanics.

Lenci, Lezioni di Meccanica Strutturale, Pitagora. Menditto, Lezioni di Scienza delle Costruzioni, Pitagora. Gambarotta, Nunziante, Tralli, Scienza delle Costruzioni, McGraw-Hill. Corradi dell'Acqua, Meccanica delle Strutture, McGraw-Hill. Comi, Corradi dell'Acqua, Introduzione alla Meccanica Strutturale, McGraw-Hill. Exercise book of Scienza delle Costruzioni for Ingegneria Meccanica and Ingegneria Edile-Architettura, Prof. Lenci, available at C.L.U.A.

- Ingegneria Edile (Corso di Laurea Triennale (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

Tel (+39) 071.220.1, Fax (+39) 071.220.2324

P.I. 00382520427