Academic Year 2015/2016 - 2° Year

ING-IND/14 - 9 CFU - 1° Semester

**STRESS TENSOR**

Stress definition and dimensions, Stress tensor, Invariants, Stress space coordinates, change of physical reference system, principal stresses and directions.

Examples & Exercises.

**STRAIN TENSOR**

Strain definition and dimensions, Strain tensor, Invariants, dilatational and distortional components.

Examples & Exercises.

**STRESS-STRAIN RELATIONSHIPS**

Elasticity matrix (vector representation of stress and strain), Yield criteria, basic concepts about plastic response and failure in special cases (uniaxial, torsional stress), path dependence.

Examples & Exercises.

**STRUCTURAL PROPERTIES OF AREAS **

Beam, Center of mass, Centroid, 1st order (“static”) and 2nd order (“inertia”) sectional moments, Huygens–Steiner theorem.

**STATICS OF BEAMS**

Definitions, De Saint Venant’s principle, Constraints and DOF, Normal and shear forces, Bending and torsion moments, Equations of statics for single beams, Unstable, Isostatic and Hyperstatic beams, Diagrams of Axial and Shear forces, Diagrams of Bending and torsion moments, Multiple-beams plane structures Truss structures, method of joints, method of sections

**STRESSES AND STRAINS WITHIN DEFORMED BEAMS**

Tension-compression (stress, strain, deformed shape),

Bending (Navier formula, strains distributions, equation of axis curvature, deformed beam shapes, bending of highly-curved solids), Shear (stress, strain and deformed shape of solid and thin-walled cross sections, shear center), Torsion (stress, strain and deformed shape of solid and thin-walled axisymmetrical cross sections, non-symmetric cross sections, principles about warping).

**BUCKLING OF COLUMNS**

Euler critical load, eccentric compression, effect of constraints, higher order buckling, membrane buckling, wrinkling.

**THERMAL EFFECTS **

Relaxation, Creep, viscoelastic response, principal material models

**FATIGUE OF MATERIALS**

Time dependent loads, difference between fatigue and high strain rate, Wohler curves, uniaxial symmetric, pulsating and intermediate loading histories, Testing methods, basic concepts about multiaxial fatigue.

**NOTCH EFFECTS **

Shape variations, uniaxial vs-triaxial stress states, geometry-material interaction, notch effect on static and fatigue response, Notch factor curves for main notch shapes

**DESIGN OF BASIC MECHANICAL COMPONENTS **

Flexural and torsional springs, specific energy parameter, main basic configurations and design problems.

Possible loads on shafts, Combined torsion, bending, shear and axial loads, bearing-load schemes, notch effect and fatigue considerations, safety factors.

**DESIGN OF PIPES, VESSELS AND SUPPORTING STRUCTURES**

Biaxial stress states, Thin sheets, Membranal behavior, typical basic configurations of pipes and vessels, positive and negative pressure effects, shape discontinuities, hatches and flange junctions, bolted joining and leakage pressure, supporting structures, internal pressure-induced loads and external loads.