STATICS AND KINEMATICS OF RIGID BODY SYSTEMS. Forces and torques. Resultant and resultant moment of a system of applied forces. Equivalent systems of forces. Elementary equivalence operations. Equilibrium of a rigid body or a system of rigid bodies. Cardinal equations of statics. Plane systems of forces. Forces distributed on a volume (force of gravity), on a surface, on a line; concentrated forces and torques. Constraint reactions for smooth, fixed and bilateral constraints; static characterization of external and internal plane constraints. Search for balanced reactive states. Isostatic, hyperstatic, labile, degenerate structures. Characteristics of internal stress in beam systems: normal stress, shear stress, bending moment, twisting moment; indefinite equilibrium equations for the straight axis beam. General formula of rigid displacements. Kinematic characterization of internal and external constraints. Bonded settlements. Kinematic problem. Static-kinematic duality. Alignment theorems of kinematic chains.
INTRODUCTION TO THE THEORY OF ELASTIC STRUCTURES. Limits of the rigid body model. Elementary deformable model: rod, linear elastic bond. Equations of equilibrium, congruence and constitutive link for the straight rod. The linear elastic problem; solution methods: force method and displacement method for the straight rod. Equation of the elastic line for the single beam and for the beam systems.
ELASTIC BEAM AND BEAM SYSTEMS. Differential relationships between transverse displacement of the axis line, rotation of the straight section and flexural curvature; curvature due to thermal distortions or bending moment; integration of the equation of the elastic line. Characteristics of deformation (flexural and torsional curvature, extension, sliding); elastic bond between stress and strain characteristics.
CONTINUOUS OF CAUCHY. ANALYSIS OF THE STATE OF VOLTAGE. The Cauchy tension. Cauchy lemma. Decomposition of the Cauchy voltage vector. Cauchy's formula. Indefinite and boundary equilibrium equations. Principal tensions and directions around the point. Triaxial, cylindrical and spherical stress states. Voltage diverter. Octahedral voltage. Main reference. Circumferences of Mohr. Plane state of tension, purely tangential and uniaxial. Isostatic lines.
RESISTANCE CRITERIA. The resistance criteria in uniaxial and triaxial regimes. Strength criteria for brittle materials: Galileo-Rankine. Strength criteria for ductile materials: Tresca, Octahedral tension (Huber-Mises-Henchy).
