The course aims at giving the basic knowledge needed to understand the structural assessment of machine elements, by defining the parameters that describe applied loading and strength of materials. The calculation methods used to assess the stress state in simple structural elements are presented, with focus on cases of industrial interest and failure under monotonic loading.

Knowledge
Statics: properties, equilibrium, calculation methods.
Stress and strain analysis: components, mathematical / physical properties, tools for calculation and measurement.
Mechanical behaviour of materials: elasticity, strength, failure.
Fundamental loading modes in the one-dimensional structural element: tension, bending, torsion, shear and induced stresses.
Internal forces in the structures, diagrams and related properties.
Stress risers: notches and cracks.



Skills
Calculating the reaction forces in a structure.
Operating on stress and strain components.
Strength calculation of a material subjected to given stress conditions.
Calculating the stresses in a one-dimensional structural element subjected to fundamental loading conditions (tension, bending, torsion, shear).
Assessing the distribution of the internal forces in simple structures.
Performing basic calculations on parts containing notches o cracks.

Contents of the courses on Mathematics and Physics, in particular calculus, basic matrix algebra and eigenvalue/eigenvector problems, as well as basic knowledge of kinematics (translational and rotational motion) and statics (force, moment, equilibrium).

1. Statics (10 hours). Lectures: refreshment and advancement on fundamentals of statics (force, moment, resultant, equivalence), point and distributed loads, constraints, hyperstaticity; free body diagram, translational and rotational equilibrium. Classroom exercises: operations on forces, calculation of unknown reactions.
2. Stress (8 hours). Lectures: normal (direct) and tangential (shear) components, stress vector and stress tensor; principal stresses and directions; Mohr’s circles. Classroom exercises: calculations on stress components, search for principal stresses and directions; construction of Mohr’s circles and their use to assess principal stresses and directions.
3. Strain (6 hours). Lectures: rigid body motion and deformation, normal and shear strains, principal strains and directions; stress-strain elastic relationship (Hooke’s law), strain energy; resistance strain gauges, principles, gauge properties, circuits, rosettes. Classroom exercises: calculations on strain components, search for principal stresses and directions; elastic strains, strain gauge measurements and related calculations.
4. Static strength of materials (4 hours). Lectures: tensile testing, specimens, machines, measured properties; brittle and ductile behaviour, failure criteria and ideal stresses; safety factor. Classroom exercises: strength calculation under given states of stress, safety factor, choice of the material.
5. One-dimensional structural element (24 hours). Lectures: cross-sectional properties, first moment of area and centroid, second moment of area, principal axes and moments; St. Venant’s problem, hypotheses and limits, internal forces, extensional, flexural and torsional behaviour; shear stresses in thin walled sections, shear centre. Classroom exercises: determination of the cross sectional properties, calculation of the stresses in parts subjected to tension, bending, torque and shear.
6. Elementary structures (24 hours). Lectures: internal forces and diagrams, elastic deflection equation and solution by double integration; hints on statically undetermined cases; hints on 3D structures; trusses, calculation of normal forces; buckling, Euler’s column. Classroom exercises: diagrams of normal force, shear, bending moment; deformed shape of elementary structures; normal forces in simple trusses; instability.
7. Stress risers (4 hours). Lectures: effects of a notch, causes, stress concentration factor, effects on the static failure; fundamentals of fracture mechanics, crack, stresses ahead of the crack tip, toughness. Classroom exercises: basic calculations on elements containing notches or cracks.

The course is based on lectures and classroom exercises. Lessons are intended to present the theoretical basis of the topics; classroom exercises show the solutions of sample problems.
Lectures and classroom exercises are given by means of the dashboard, slide projections are reserved to special needs.

Downloadable from the web portal
Course notes (covering the whole content of the course).
Slides (available for most of the lessons, although ordinarily not used).
Weekly assignments.

Optional textbooks
A. Somà: "Fondamenti di Meccanica Strutturale "; Levrotto & Bella, Torino, 2012.
F. Curà, G. Curti: "Fondamenti di Meccanica Strutturale"; CLUT, Torino, 2006.

The exam consists of a written part, that enables to achieve a score up to 27/30, and an optional oral part, by which it is possible to achieve a higher score. The written part, to be completed in two and a half hours, includes theoretical questions (weight ¼) and practical exercises (weight ¾), involving the same contents and difficulties encountered in the weekly assignments (when solving the exercises, it is allowed to use textbooks and notes in printed form). The oral part is a discussion on the topics of the syllabus, aimed at assessing the comprehension of the physical phenomena involved and of the calculation methods.
The knowledge is assessed on the basis of the given answers, the skills on the basis of the ability in solving problems.