Structural Mechanics

Code: -
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ICAR/08
Introduction to the foundations of continuum mechanics. Kinematics of deformation. Linearization. The concept of stress. Constitutive equations. Elastic response. Work and energy. Theorem of virtual work. Simple problems in linear elasticity. Restraints and reactions. Statically determinate structures. Evaluation of internal forces (axial force and bending moment) under a variety of applied loads. The Euler-Bernoulli model of beam. Analysis of small deflections of beams. Statically redundand structures. Methods of solution. The stress status in a 3D beam subject to axial force, bending moment, shear and torque.

Lesson hours:

72

Practice hours:

-

Propaedeuticities:

General physics, Mathematical analysis II, Mathematical Physics

Credits:

9

Types of examinations:

The final exam will be both written and oral

Teacher:

-

Objectives:

Understanding of the principles and methods for the analysis of strength and behaviour of solids and structures. Awareness of the foundations and critical usage of the main models in the analysis of solids and structures.

Contents:

[2 CFU] One-dimensional continuum: Static of beam systems: constraints, reactions. Diagrams of internal stresses for beams with straight axis. Derivation of the deflection line. Force and displacement methods. The principle of virtual forces and virtual displacements for beam systems. Evaluation of moments of inertia of 2D domains. Influence lines.

[3 CFU] Three-dimensional continuum: Basics of Tensor Algebra. Definition of the main deformation measures and their expression as a function of the displacement field. Linearization of deformation measures. Infinitesimal strain and rotation tensors: mechanical interpretation of their components. Local and global balance laws. Property of the Cauchy stress. Principal stresses. Mohr’s circles. Hydrostatic and deviatoric components of the stress tensor. Constitutive laws of linear elastic isotropic materials. Conservativeness of the elastic energy: statements of Clapeyron and Betti’s theorems for the Cauchy model.

[2 CFU] Saint Venant’s model: Axial force and bending moments. Relations between neutral and bending axes. Kernel of a section. Properties of antipolarity between the center of pressure and the neutral axis. Culmann’s ellipse. Shear: Jourawski’s theory. Center of twist. Thin-walled beams having open and closed cross-sections: Bredt’s formulas.

[2 CFU] Verification and analysis of structures: Isotropic yield criteria for ductile materials (Tresca, von Mises) and those for fragile materials (Mohr-Coulomb). Concept of equivalent stress. Euler’s critical load. Analysis of sections subject to bending and axial actions as well as shear and torque.

Teaching materials:

Beer Johnston DeWolf Mazurek – Mechanics of materials