MCG3145 - ADVANCED STRENGTH OF MATERIALS

Advanced Strength of Materials / Résistance des Matériaux

MCG 3145 / 3545 ADVANCED STRENGTH OF MATERIALS / RÉSISTANCE DES MATÉRIAUX OUTLINE OF COURSE MATERIAL 1 Stress 1.1 Part A 1.2 1.3 1.4 1.5 Part B 1.6 1.7 1.8 1.9 1.10

Introduction General Concepts of Stress Method of Sections Definition of Stress Stress Tensor Differential equations of equilibrium (Symmetry of stress tensor) Stress Analysis of Axially Loaded Bars Maximum Normal Stress in Axially Loaded Bars Stresses on Inclined Sections in Axially Loaded Bars Shear Stresses Analysis for Normal and Shear Stresses Member Strength as a Design Criterion

2 Strain 2.1 2.2 2.3 2.4 2.5 2.6 2.7

Introduction The Tension Test and the Normal Strain Stress-Strain Relationships Hooke’s Law Further Remarks on Stress-Strain Relationships Poisson’s Ratio Thermal Strain and Deformation

3 Axial Deformation of Bars: Statically Determinate Systems 3.1 Introduction 3.2 Deformation of Axially Loaded Bars 3.3 Saint-Venant’s Principle and Stress Concentration 3.5 Elastic Strain Energy for Uniaxial Stress 3.7 Dynamic and Impact Loads 5 Generalized Hooke’s Law and Pressure Vessels 5.1 Introduction Part A Constitutive Relationships for Shear 5.2 Stress-Strain Relationships for Shear 5.3 Elastic Strain Energy for Shear Stresses Part B Generalized Concepts of Strain and Hooke’s Law 5.4 Mathematical Definition of Strain 5.5 Strain Tensor 5.6 Generalized Hooke’s Law for Isotropic Materials 5.7 E, G and  Relationships 5.8 Dilatation and Bulk Modulus Part C Thin-walled Pressure Vessels 5.9 Cylindrical and Spherical Pressure Vessels Y. M. Haddad LECTURE NOTES


5.10 Part D 5.11 5.12

Remarks on Thin-walled Pressure Vessels Thick-walled Cylinders Introduction Solution of the General Problem

6 Torsion 6.1 Introduction 6.2 Application of the Method of Sections Part A Torsion of Circular Elastic Bars 6.3 Basic Assumptions for Circular Members 6.4 The Torsion Formula 6.5 Remarks on the Torsion Formula 6.6 Design of Circular Members in Torsion for Strength 6.7 Stress Concentration 6.8 Angle of Twist of Circular Members Part D Torsion of Thin-walled Tubular Members 6.16 Thin-walled Hollow Members 8 Symmetric Beam Bending Introduction Basic Kinematic Assumption The Elastic Flexure Formula 8.5 Application of the Elastic Flexure Formula 8.6 Stress Concentration 8.7 Elastic Strain Energy in Pure Bending 8.9 Beams of Composite Cross Section 9 Unsymmetric (Skew) Beam Bending 9.1 Introduction Part A Doubly Symmetric Cross Sections 9.2 Bending about Both Principal Axes 9.3 Elastic Bending with Axial Loads 9.4 Inelastic Bending with Axial Loads 10 Shear Stresses in Beams 10.1 Introduction 10.2 Preliminary Remarks 10.3 Shear Flow 10.4 The Shear Stress Formula for Beams 10.5 Warpage of Plane Sections Due to Shear 10.6 Some Limitations of the Shear Stress Formula 10.8 Shear Center 11 Shear Stresses in Beams 11.1 Introduction Part A Transformation of Stress 11.2 The Basic Problem 11.3 Transformation of Stress in Two-dimensional Problems Y. M. Haddad LECTURE NOTES


11.4 Principal Stresses in Two-dimensional Problems 11.5 Maximum Shear Stresses in Two-dimensional Problems 11.6 Mohr’s Circle of Stress for Two-dimensional Problems 11.7 Construction of Mohr’s Circle of Stress Transformation 11.8 Principal Stresses for a General State of Stress 11.9 Mohr’s Circle of Stress for a General State of Stress Part B Transformation of Strain 11.10 Strain components in Two-Dimensions 11.11 Transformation of Stress in Two-Dimensions 11.12 Mohr’s Circle for Two-dimensional Strain 12 Yield and Fracture Criteria 12.1 Introduction 12.2 Maximum Shear-Stress Theory 12.3 Maximum Distortion-energy Theory 12.4 Comparison of Maximum-shear and Distortion-energy Theories for Plane Stress 12.5 Maximum Normal-stress Theory 12.6 Comparison of Yield and Fracture Criteria 12.7 Failure Surface for Brittle Materials 16 Columns 16.1 Introduction 16.2 Examples of Instability 16.3 Criteria for Stability of Equilibrium Part A Column Buckling Theory 16.4 Euler Load for Columns with Pinned Ends 16.5 Euler Load for Columns with Different End Restrains Part B Design of Columns 16.11 General Considerations 16.12 Concentrically Loaded Columns 17 Energy and Virtual Work

Y. M. Haddad LECTURE NOTES