Unit 2177: Advanced Structural Analysis and Material Mechanics

1. Stress and Strain Analysis

1.1 Introduction to Stress and Strain

• Definition of stress and strain
• Axial, shear, and torsional loading
• Stress-strain relationships and material behavior

1.2 Types of Stress

• Normal stress (axial and bending)
• Shear stress (direct and torsional)

1.3 Strain Measures

• Linear strain
• Shear strain
• Poisson's ratio effects

1.4 Stress-Strain Diagrams for Different Materials

• Elastic, plastic, and viscoelastic behavior
• Isotropic vs anisotropic materials

2. Mohr's Circle for 2D Stress Analysis

2.1 Fundamentals of Mohr’s Circle

• Concept and construction
• Coordinate transformation of stresses

2.2 Principal Stresses and Maximum Shear Stress

• Determination using Mohr’s circle
• Orientation of principal planes

2.3 Applications and Problem Solving

• Stress analysis in beams and shafts
• Combined loading scenarios

3. Deflection of Beams

3.1 Beam Theory Fundamentals

• Types of beams and loading conditions
• Bending moment and shear force diagrams

3.2 Methods for Calculating Deflections

• Double integration method
• Moment-area theorems
• Superposition principle

3.3 Analysis of Common Beam Configurations

• Cantilever, simply supported, and fixed beams
• Effect of concentrated and distributed loads

4. Buckling Analysis

4.1 Introduction to Buckling

• Concept of stability and failure modes

4.2 Euler’s Critical Load

• Derivation and assumptions
• Column end conditions and effective length

4.3 Buckling Modes

• Flexural buckling
• Torsional and flexural-torsional buckling

4.4 Design Applications

• Safety factors and design codes
• Practical considerations in structural design

5. Energy Methods in Structural Analysis

5.1 Principle of Conservation of Energy

5.2 Virtual Work Method

• Virtual displacement and virtual force concepts

5.3 Strain Energy

• Calculation for axial, bending, and torsional deformations

5.4 Castigliano’s Theorems

• First and second theorems and applications

6. Failure Theories

6.1 Overview of Material Failure

6.2 Maximum Normal Stress Theory

6.3 Maximum Shear Stress Theory (Tresca Criterion)

6.4 von Mises Stress Criterion

6.5 Comparison and Applicability

• Ductile vs brittle materials

7. Fracture Mechanics

7.1 Fundamentals of Crack Propagation

7.2 Stress Intensity Factor (K)

7.3 Fracture Toughness (K_IC)

7.4 Modes of Fracture

• Mode I (opening), Mode II (sliding), Mode III (tearing)

7.5 Application in Failure Analysis and Design Optimization

8. Fatigue Analysis

8.1 Introduction to Fatigue Phenomenon

8.2 S-N Curves (Wöhler Curves)

8.3 Fatigue Life Prediction Methods

8.4 Effects of Stress Concentrations and Defects

8.5 Design Considerations to Mitigate Fatigue Failure

9. Advanced Topics in Composite Materials

9.1 Introduction to Composite Materials

• Definitions and classifications

9.2 Mechanics of Laminated Structures

• Lamina and laminate properties
• Classical Laminate Theory (CLT)

9.3 Failure Modes in Composites

• Matrix cracking, fiber breakage, delamination

9.4 Design Considerations

• Optimization of layup sequences
• Trade-offs between strength, stiffness, and weight

9.5 Applications and Case Studies