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) Elements of Algebra and Vector and Tensor Calculus Kinematics of Rigid Bodies The Rigid Body Model Rigid Displacements General Formula for Infinitesimal Rigid Displacement Planar Rigid Displacements Systems of Rigid Bodies Kinematic Characterization of Constraints Kinematic Characterization of External Constraints Kinematic Characterization of Internal Constraints Settlement Constraints The Kinematic Problem Kinematic Classification by Analytical Means Kinematic Classification by Direct Means Graphical 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 Position of the Problem Static Classification Static-Kinematic Duality Kinematics of Beams The Deformation Process Displacements and Rotations Displacement Rotation of Sections Small Displacement Assumption Boundary Conditions on Displacements and Rotations External Constraints: Kinematic Characterization Strain Measurements Axial Strain Angular Slip Bending Curvature Implicit Equations of Compatibility Timoshenko Model Euler-Bernoulli Model Kinematic Problem Discontinuities in the Kinematic Problem Statics of Beams Position of the Problem External Forces Internal Actions Indeterminate Equations of Equilibrium Static Problem Laws and Diagrams of Stress Characteristics Discontinuities in the Static Problem General Rules for Plotting Stress Characteristic Diagrams Linear Elastic Link for One-Dimensional Beams Axial Behavior Bending Behavior Shear Behavior Thermal Distortions Uniform Thermal Variation Butterfly Thermal Variation Linear Thermal Variation Constitutive Equations for One-Dimensional Beams The Elastic Problem for Beams Euler-Bernoulli Model Timoshenko Model Beam Systems Displacement Method: The Elastic Line Elastic Line Axial Problem Bending Problem: Euler-Bernoulli Model Elastic Line in Beam Systems Kinematic and Static Performance of Internal Constraints Virtual Work Identity. Duality. Work Congruent System Equilibrium System External Virtual Work Internal Virtual Work Virtual Work Theorem Calculation of Displacements and Rotations in Isostatic Structures Force Method Once Hyperstatic Systems Multiple Hyperstatic Systems Müller-Breslau Equations Truss Structures and Continuous Beams. Truss Structures Node Method Ritter's Section Method Continuous Beams: Three-Moment Equation Continuum Mechanics: Deformation Analysis Deformation Process Deformation Analysis in the Vicinity: 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 Volumetric Dilatation Cauchy's Formula for Deformation - Principal Directions of Deformation Triaxial Deformation State Cylindrical Deformation State Principal Reference - Mohr's Circles Compatibility Equations Continuum Mechanics: Stress Analysis Cauchy Stress Cauchy's Lemma Decomposition of the Cauchy Stress Vector Cauchy's Formula Indeterminate Equations of Equilibrium Stresses and Principal Directions Principal Reference Stress States Isostatic Lines Mean Stress, Deviatoric Stress, and Octahedral Stress Mohr's Circles Plane or Biaxial Stress State Purely Shear Stress State Monoaxial Stress State Linear Elastic Link Isotropic Materials: Generalized Hooke's Law The Problem of Elastic Equilibrium: Direct Formulation and Energy Aspects Saint-Venant Problem Saint-Venant Postulate Simple and Combined Stresses Semi-Inverse Method Indeterminate Equations of Equilibrium Compatibility and Constitutive Equations Concentrated Normal Force. Straight Bending Concentrated Normal Force Uniform Straight Bending Deflected Bending. Tensile Bending, Compressive Bending Uniform Deflected Bending Compressive (Tensile) Deflected Bending Eccentric Normal Force Uniform Torsion Torsion in Circular Sections Compact Circular Section Hollow Circular Section Torsion in Any Shape Compact Sections Hydrodynamic Analogy for Shear Stresses Thin Rectangular Section Open Sections Made of Thin Rectangles Thin-Walled Hollow Sections: Bredt's Theory Composite Thin Sections Bending and Shear Distribution of Normal Stresses Distribution of Shear Stresses: Approximate Treatment by Jourawsky Problem Equations Jourawsky's Formula Applicability of Jourawsky's Formula Open Thin Sections Thin Rectangular Section Thin Double-T Section Thin U and H Sections Closed Thin Sections Symmetrical Hollow Section Straight Shear according to y Deflected Shear Symmetrical Compact Sections Combined Shear and Torsion Stress Shear Center Shear and Torsion Shear Stresses Strength Criteria and Introduction to Plasticity Ductile and Brittle Materials Linear Elastic Model and Plastic Behavior The Concept of Yielding Elasto-Plastic Constitutive Relationship Yielding Mechanisms and Plasticity Criteria Stress-Strain Diagrams for Elasto-Plastic Materials Plasticity in Bending: Yield Moments Effects of Plastic Behavior in Beams and Structural Elements Calculation of Safety Factors in Plastic Regime Limit Analysis of Structures Methods for Determining Plastic Hinges in Hyperstatic Structures Structural Verification in Plastic Field The Phenomenon of Structural Instability Stability Analysis in Rigid Beams with Elastic Constraints Euler's Column Stability Curves, Slenderness Structural Verifications Verification of Beams under Operating Conditions Extension of Saint-Venant Theory Strength Criteria for Saint-Venant Solids Operational Procedure for Structural Verification Geometry of Areas Area and Centroid Moments of Inertia Transport Formulas (without Rotation Formulas) Principal Moments of Inertia Central Inertia Ellipse Notable Cases Recurring Static Schemes Cantilever Simply Supported Beam Fixed-Supported Beam Beam Fixed at Both Ends Continuous Beam Frame (reference books) Hibbeler, R. C. (2017). Mechanics of Materials (SI Units). Boston: Pearson.
Dates of beginning and end of teaching activities	From 23/09/2024 to 23/12/2024
Delivery mode	Traditional
Attendance	not mandatory
Evaluation methods	Written test Oral exam