Mechanics of Composite Materials OCW

Worked Out Examples

Chapter 1 Introduction 

Section 1.1 Introduction

Why Bending Rectangular Cross-Section Beam Mass for Same Deflection and Width is Inversely Proportional to E⅓/density [PDF] [HTML]

Section 1.2 Classification

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Section 1.3 Recycling Fiber-Reinforced Composites

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Section 1.4 Mechanics Terminology

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Chapter 2  Macromechanics of Lamina

Section 2.1 Mechanics Terminology

Transformation of Stresses: A Derivation [PDF] [HTML]

Transformation of Strains: A Derivation [PDF] [HTML]

Section 2.2 Review of Definitions

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Section 2.3 Hooke’s Law for Different Types of Materials

Compliance and Stiffness Matrix of a Three-Dimensional Orthotropic Material [PDF] [HTML]

Section 2.4 Hooke’s Law for a Two Dimensional Unidirectional Lamina

Finding elastic moduli and strain in a unidirectional lamina [PDF] [HTML]

Section 2.5 Hooke’s Law for a Two Dimensional Angle Lamina

Transformed Compliance and Stiffness Matrices and More [PDF] [HTML]

Section 2.6 Engineering Constants of an Angle Lamina

Finding engineering constants of an angle ply [PDF] [HTML]

Can Ex be smaller than E1 and E2? [PDF] [HTML]

Can Ex be greater than E1 and E2? [PDF] [HTML]

Is the major Poisson’s ratio for a lamina maximum at 45°? [PDF] [HTML]

Finding in-plane shear modulus G12 from regressed data [PDF] [HTML]

10 Degree-Ply Test – Finding Ex [PDF] [HTML] (Question asked in a test)

10 Degree Ply Test – Finding G12 [PDF] [HTML] (Question asked in a test)

10 Degree Ply Test – Strain Gage Misalignment [PDF] [HTML] (Question asked in a test)

Section 2.7 Invariant Forms of Stiffness and Compliance Matrices for Angle Lamina

Writing a transformed reduced stiffness matrix in fewer invariants [PDF] [HTML]

Section 2.8 Strength Failure Theories of Angle Lamina

Modified Maximum Stress Theory for Plane Stress [PDF] [HTML]

Off-axis shear strength using maximum stress failure theory [PDF] [HTML] (A question asked in the test)

Strength ratio using maximum stress failure theory [PDF] [HTML]

Strength ratio using maximum strain failure theory [PDF] [HTML]

Strength ratio using Tsai-Hill failure theory [PDF] [HTML]

Strength ratio using Tsai-Wu failure theory [PDF] [HTML]

Section 2.9 Hygrothermal Stresses and Strains in a Lamina

Finding coefficients of moisture expansion of an angle ply [PDF] [HTML] (A question asked in a test)


Chapter 3 Micromechanics of Lamina

Section 3.1 Introduction

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Section 3.2 Volume and Mass Fractions, Density and Void Content

Finding Density of an Intraply Hybrid Composite [PDF] [HTML]

Finding Void Fraction in a Lamina [PDF] [HTML]

Fiber Volume Fraction [PDF] [HTML]

Section 3.3 Evaluation of Four Elastic Moduli

Why are Halpin-Tsai Equations called semi-empirical? [PDF] [HTML]

Elastic Moduli using Halphin-Tsai with Circular Fibers in Square Array [PDF] [HTML]

Elastic Moduli using Halphin-Tsai with Rectangular Fibers in Hexagonal Array [PDF] [HTML]

Elastic Moduli using Mechanics of Materials [PDF] [HTML]

Section 3.4 Ultimate Strengths of a Unidirectional Lamina

Ultimate Longitudinal Compressive Strength of Lamina [PDF] [HTML]

Ultimate Longitudinal Tensile Strength of Lamina [PDF] [HTML]

Ultimate Transverse Compressive Strength of Lamina [PDF] [HTML]

Ultimate Transverse Tensile Strength in Lamina [PDF] [HTML]

Hybrid Composite Ultimate Strength [PDF] [HTML]

Hybrid Composite with 2 Fibers [PDF] [HTML]

Section 3.5 Coefficients of Thermal Expansion

Derivation of Transverse Thermal Expansion Coefficient [PDF] [HTML] This derivation is optional but you do need to know the formula inside-out

Longitudinal Coefficient of Thermal Expansion of Lamina [PDF] [HTML]

Transverse Coefficient of Thermal Expansion of Lamina [PDF] [HTML]

Deriving the Transverse Cofficient of Thermal Expansion Formula [PDF] [HTML]

Section 3.6 Coefficients of Moisture Expansion

Change in Volume [PDF] [HTML]

Longitudinal Coefficient of Moisture Expansion of Lamina [PDF] [HTML]

Transverse Coefficient of Moisture Expansion of Lamina [PDF] [HTML]


Chapter 4 Macromechanics of Laminate

Section 4.1 Introduction

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Section 4.2 Laminate Code

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Section 4.3 Stress-Strain Relationships for a Laminate

Finding the Bending Moment [PDF] [HTML]

Stress-Strain for Each Ply in a Laminate [PDF] [HTML]

Section 4.4 In-Plane and Flexural Modulus

Finding the In-Plane and Flexural Modulus [PDF] [HTML]

Section 4.5 Hygrothermal Effects in a Laminate

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Chapter 5 Failure Analysis and Design of a Laminate

Section 5.1 Introduction

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Section 5.2 Special Cases of Laminates

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Section 5.3 Failure Criterion for Laminate

Ply-by-Ply Failure using Tsai-Wu Failure Theory [PDF] [HTML]

Section 5.4 Design of a Laminate

Finding Formula for Shear Force per Unit Length for Drive Shaft Problem [PDF] [HTML]

Section 5.5 Other Mechanical Design Issues

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