Teaching - Università Roma Tre

THEORY OF ELASTICITY AND ANALYSIS OF STRUCTURES (objectives)

Code

20801971

Language

ITA

Type of certificate

Profit certificate

Credits

9

Scientific Disciplinary Sector Code

ICAR/08

Contact Hours

72

Type of Activity

Core compulsory activities

Teacher	TOMASSETTI GIUSEPPE (syllabus) Introduction to Algebra and Vector and Tensor Calculus Kinematics of Rigid Bodies The Rigid Body Model Rigid Displacements General Formula for Infinitesimal Rigid Displacement Scalar Representation Planar Rigid Displacements Systems of Rigid Bodies Kinematic Characterization of Constraints Definitions Kinematic Characterization of External Constraints Kinematic Characterization of Internal Constraints Constraint Failures The Kinematic Problem Problem Statement Analytical Kinematic Classification Direct Kinematic Classification Gradient Method for Solving the Kinematic Problem Definitions. Kinematic Chains. Statics of Rigid Bodies Static Characterization of Constraints Static Characterization of External Constraints Static Characterization of Internal Constraints The Static Problem Cardinal Equations of Statics Problem Statement Static Classification Static-Kinematic Duality Beam Kinematics Deformation Process Displacements and Rotations Displacement Sectional Rotation Hypothesis of Small Displacements Boundary Conditions on Displacements and Rotations External Constraints: Kinematic Characterization Strain Measurements Axial Deformation Angular Shear Bending Curvature Implicit Congruence Equations Timoshenko Model Euler-Bernoulli Model Kinematic Problem Discontinuities in the Kinematic Problem Static of Beams Problem Statement External Forces Internal Actions Indeterminate Equations of Equilibrium Static Problem Laws and Diagrams of Load Characteristics Discontinuities in the Static Problem General Rules for Tracing Load Characteristic Diagrams Linear Elastic Relation for the One-Dimensional Beam Axial Behavior Flexural Behavior Shear Behavior Thermal Distortions Uniform Temperature Variation Butterfly Temperature Variation Linear Temperature Variation Constitutive Equations for the One-Dimensional Beam Elastic Problem for the Beam Problem Statement: Given and Unknown Analytical Formulation: Resolvent Equations Solution Euler-Bernoulli Model Timoshenko Model Solution Strategies Systems of Beams Method of Displacements: The Elastic Line Elastic Line Axial Problem Flexural Problem: Euler-Bernoulli Model Observations Elastic Line in Systems of Beams Kinematic and Static Performance of Internal Constraints Identity of Virtual Works. Duality. General Definitions Work Congruent System Balanced System External Virtual Work Internal Virtual Work Virtual Work Theorem Calculation of Displacements and Rotations in Isostatic Structures Method of Forces Once Hyperstatic Systems Multiple Times Hyperstatic Systems Müller-Breslau Equations Lattice Structures and Continuous Beams Lattice Structures Node Method Ritter's Section Method Continuous Beams: Three-Moment Equation The Continuous Medium: Deformation Analysis Deformation Process Deformation Analysis in the Surroundings: Strain Tensor Mechanical Interpretation of ε Components Meaning of Diagonal Components εx, εy, εz Meaning of Off-Diagonal Components γxy, γxz, γyz Decomposition of the Deformation Process Cubic Dilatation Cauchy's Strain Formula - Principal Directions of Strain Triaxial Strain State Cylindrical Strain State Principal Reference - Mohr's Circles Congruence Equations The Continuous Medium: Stress Analysis Cauchy's Stress Cauchy's Lemma Decomposition of Cauchy's Stress Vector Cauchy's Stress Formula Indeterminate Equilibrium Equations Stresses and Principal Directions Principal Reference Stress States Isostatic Lines Mean Stress, Deviatoric Stress, and Octahedral Stress Mohr's Circles Plane Stress State or Biaxial Stress Purely Tangential Stress State Uniaxial Stress State Linear Elastic Relation Isotropic Materials: Generalized Hooke's Law Elastic Equilibrium Problem: Direct Formulation and Energetic Aspects Saint-Venant's Problem Problem Statement Saint-Venant's Postulate Simple and Composite Loads Solution Semi-Inverse Method Stress State Indeterminate Equilibrium Equations Congruence and Constitutive Relation Equations Static Equivalence Centric Axial Force. Pure Bending Centric Axial Force Uniform Pure Bending Pure Bending My Deviated Bending. Torsion, Bending-Torsion Uniform Deviated Bending Torsion Torsion in Circular Sections Compact Circular Section Hollow Circular Section Torsion in Compact Sections of Any Shape Hydrodynamic Analogy for Tangential Stresses Thin Rectangular Section Open Sections Composed of Thin Rectangles Thin-Walled Sections: Bredt's Theory Composite Thin Sections Bending and Shear Distribution of Normal Stresses Distribution of Shear Stresses: Jourawsky's Approximate Treatment Intuitive Considerations Problem Equations Jourawsky's Formula Applicability of Jourawsky's Formula Open Thin Sections Thin Rectangular Section Double-T Thin Section U and H Thin Sections Closed Thin Sections Symmetric Box Section Shear Straight Along y Deviated Shear Symmetric Compact Sections Combined Shear and Torsion Loading Shear Center Shear and Torsional Tangential Stresses Strength Criteria Strength Criteria for Ductile Materials Strength Criteria for Brittle Materials Structural Instability Phenomenon Stability Analysis in Rigid Beams with Elastic Constraints Euler's Column Stability Curves, Slenderness Structural Verification Verification of Beams in Operating Conditions Extension of Saint-Venant's Theory Strength Criteria for the Solid of Saint-Venant Operational Procedure for Structural Verification Geometry of Areas Area and Centroid Moments of Inertia Transport Formulas (without Rotation Formulas) Principal Moments of Inertia Central Ellipse of Inertia Notable Cases Recurring Static Schemes Cantilever Simply Supported Beam Fixed-Supported Beam Two-End Fixed Beam Continuous Beam Frame" (reference books) Hibbeler: Mechanics of Materials
Dates of beginning and end of teaching activities	From 25/09/2023 to 22/12/2023
Delivery mode	Traditional
Attendance	not mandatory
Evaluation methods	Written test Oral exam