


Politecnico di Torino  
Academic Year 2016/17  
06IHRMK Fundamentals of structural mechanics 

1st degree and Bachelorlevel of the Bologna process in Energy Engineering  Torino 





Subject fundamentals
The course is placed in between the basic subjects of the first three semesters (calculus and physics) and the more applied subjects and design courses of the following semesters, realizing an ideal connection among them. In the course, the fundamental theoretical principles of the mechanical behavior of elastic solids are presented, in order to allow, in particular, the analysis of beams and frame structures.

Expected learning outcomes
The student is supposed to get acquainted with the theoretical principles listed in the following, being able to apply them to the solution of the proposed practical problems. More in details, with reference to statically determinate or indeterminate systems, the student must be able to calculate: the constrain reaction forces; the diagrams of internal beam reaction (axial and shear force, bending moment) and the elastic line; the internal stresses based on the Saint Venant principle. Moreover, the student must be able to apply the strength criteria for threedimensional state of stress and to verify the stability of a compressed truss.

Prerequisites / Assumed knowledge
Basic knowledge of calculus (function diagrams, derivatives and integrals, matrix calculus and Eigenproblems solution) and physics (principles of statics and kinematics).

Contents
GEOMETRY OF AREAS: centroid, static moment, moment of inertia, product of inertia, principal axes and moments of inertia.
STATICALLY DETERMINATE BEAM SYSTEMS: statics and kinematics, plane constraints, hypostatic systems, determination of constraint reactions with auxiliary equations and with the graphical method; internal beam reactions; indefinite equations of equilibrium for plane beams; threehinged arches; closedframe structures; trusses. ANALYSIS OF STRAIN AND STRESS: strain tensor; dilations and shearing strains; principal directions of strain; cubic dilation. Stress tensor; principal directions of stress; plane stress condition; Mohr’s circle. Indefinite equations of equilibrium; boundary equations of equivalence; principle of virtual work for deformable bodies. ELASTIC CONSTITUTIVE LAW AND STRENGTH CRITERIA: Linear elasticity; elastic potential; Young modulus and Poisson’s coefficient; problem of a linear elastic body: Clapeyron’s theorem; Betti’s reciprocal theorem; isotropy; Tresca’s and Von Mises’ strength criteria. THE SAINT VENANT PROBLEM: fundamental hypotheses; centered axial force; flexure; eccentric axial force and biaxial flexure; central cores of inertia; torsion; shearing force; beam strength analysis. CALCULUS OF ELASTIC DISPLACEMENTS AND STATICALLY INDETERMINATE BEAM SYSTEMS: equation of the elastic line; determination of elastic displacements with the principle of virtual works; method of forces; equations of congruence written with the principle of virtual works; Simpson’s integration rule. ELASTIC INSTABILITY: compressed beams with different constrain conditions. 
Delivery modes
Exercises carried out in classroom: application of the theoretical principles to the solution of practical structural mechanics problems.

Texts, readings, handouts and other learning resources
A. Carpinteri (2013) Structural Mechanics Fundamentals. CRC Press.

Assessment and grading criteria
The final examination consists of a written and oral examination. The written part (duration 2h and 20m) requires solving one statically determined and one statically indeterminate structure. It is necessary to pass the written part to be admitted at the oral part of the exam. The oral part consists of two o three questions, where usually the first question is applicative. Depending on the number of applicants, the first question could require writing answer prior to the oral discussion.

