Objectives
The aim of the course is to teach the fundamental principles and tools of the continuum mechanics and theory of elasticity for the development of the structural analysis. The objective is the evaluation of the safety state of structural elements subjected to various loading conditions. To this end, the general equations governing the structural analysis are given in order to determine the displacement, the strain and the stress fields, taking into account the specific material response and its ability to resist to the external actions. Particular interest is paid to the case of the structural analysis of beam systems.
Course program
0) Technical theory of beam (24 hours) Differential equation of the beam. Statically indeterminate structures: method of forces. 1) Strain analysis (6 hours). Continuous and deformable medium. Change of configuration. Strain tensor. Small strain model. 2) Stress analysis (10 hours). Stress. Cauchy theorem. Stress tensor. Equilibrium equations. Mohr circles. 3) Virtual work principle (2 hours). Virtual work principle. Virtual displacement theorem. Virtual force theorem. 4) Constitutive law (4 hours). Constitutive law. Elasticity. Isotropic materials. 5) Elasto-static problem (4 hours). Elasto-static problem. Theorem of superposition. Uniqueness of the solution. Clapeyron theorem. Betti theorem. Navier equations. 6) Saint Venant problem (18 hours). The Saint Venant principle. Axial force. Bending. Torsion. Shear. 7) Strength criteria (4 hours). Ductile and brittle behaviour of materials. Tresca and Mises criteria.
Books
Video lessons. Notes of the course.
Evaluation mode
- The evaluation of the student takes place through a written test followed by an oral test. - In order to be able to take the oral test, the student must have passed the written test with a positive result. - The student who passes the written test, can take the oral test in any round, trying to take the oral test within one year of passing his written test. - The written test lasts five hours and aims to verify the student's ability to solve numerically problems of practical interest. The written test consists of the following six exercises: 1) Statically indeterminate structure via method of forces and PLV. 2) Differential equation of the beam or method of moments. 3) Strain analysis. 4) Plane stress analysis via Mohr circles or eigenvalue-eigenvector method. 5) Transverse section subjected to eccentric axial force. 6) Transverse section subjected to shear and/or torsion. - A necessary
