2.1 Introduction
Learning Objectives:
1) Recognize how a composite lamina mechanical behavior is different from that of an isotropic layer.
2) Review the matrix algebra concepts needed for the course from EML3041 Computational Methods course
3) Review the transformation of stresses and strains from the EML3500 Mechanics of Solids course
Videos
Appendix A: Matrix Algebra
Title: Adding Two Matrices
Title: Subtracting Two Matrices
Title: Multiplying Two Matrices
Title: A real life problem of setting up simultaneous linear equations
Title: Writing simultaneous linear equations in matrix form
Title: Can we divide two matrices?
Title: Some statements about the inverse of matrices
Title: Inverse of matrices: Example
Title: Using concept of inverse to solve a set of equations
Title: Finding the inverse of a matrix: Theory
Title: Finding the inverse of a matrix: Example
Title: Finding the inverse of a matrix by adjoints: Theory
Title: Finding the inverse of a matrix by adjoints: Example
Slide Shows
Worked Out Examples
Appendix B: Transformation of Stresses and Strains: Transformation of Stresses [PDF]
Handouts
None
Flashcards
Flashcards for Section 2.1 Introduction Slideshow
Flashcards for Appendix A: Matrix Algebra Slideshow
Flashcards for Appendix B: Transformation of Stresses and Strains Slideshow
Quiz
None
2.2 Review of Definitions
Learning Objectives:
1) Review definition of stress
2) Review definition of strain
3) Review definition of elastic moduli
4) Review definition of strain energy.
Videos
None
Slide Shows
Worked Out Examples
None
Handouts
None
Flashcards
Review of Definitions Slideshow
Quiz
2.3 Hooke’s Law for Different Types of Materials
Learning Objectives:
1) Develop stress–strain relationships for different types of materials
Videos
None
Slide Shows
Worked Out Examples
None
Handouts
None
Flashcards
Hooke’s Law for Different Types of Materials Slideshow
Quiz
2.4 Hooke’s Law for a Two Dimensional Unidirectional Lamina
Learning Objectives:
1) Develop stress–strain relationships for a unidirectional/bidirectional lamina.
Videos
None
Slide Shows
Worked Out Examples
None
Handouts
None
Flashcards
Hooke’s Law for a Two Dimensional Unidirectional Lamina Slideshow
Quiz
2.5 Hooke’s Law for a Two Dimensional Angle Lamina
Learning Objectives:
1) Develop stress–strain relationships for an angle lamina.
Videos
None
Slide Shows
Worked Out Examples
None
Handouts
None
Flashcards
Hooke’s Law for a Two Dimensional Angle Lamina Slideshow
Quiz
2.6 Engineering Constants of an Angle Lamina
Learning Objectives:
1) Develop formulas for engineering constants of an angle lamina
Videos
None
Slide Shows
Worked Out Examples
Problem 2.27 [PDF]
Problem 2.28 [PDF]
Problem 2.29 [PDF]
Problem 2.32 [PDF]
Background to #2.32: Linear Regression With Zero Intercept: Derivation
10 degree ply problem – Finding Ex [PDF] (Question asked in a test)
10 degree ply test – Misalignment of strain gauges [PDF] (Question asked in a test)
Handouts
None
Flashcards
Engineering Constants of an Angle Lamina Slideshow
Quiz
2.7 Invariant Forms of Stiffness and Compliance Matrices for Angle Lamina
Learning Objectives:
1) Develop invariant forms of compliance and stiffness matrix
Videos
None
Slide Shows
Worked Out Examples
Writing a transformed reduced stiffness matrix in fewer invariants [PDF]
Handouts
None
Flashcards
Invariant Forms of Stiffness and Compliance Matrices for Angle Lamina Slideshow
Quiz
2.8 Strength Failure Theories of Angle Lamina
Learning Objectives:
1) Define strength ratio
2) Use four failure criteria for failure of angle laminas
Videos
None
Slide Shows
Worked Out Examples
Off-axis shear strength using maximum stress failure theory [PDF] (A question asked in the test)
Handouts
None
Flashcards
Strength Failure Theories of Angle Lamina Slideshow
Quiz
2.9 Hygrothermal Stresses and Strains in a Lamina
Learning Objectives:
1) Develop hygrothermal coefficients for angle lamina
Videos
None
Slide Shows
Worked Out Examples
Finding coefficients of moisture expansion of an angle ply [PDF] (A question asked in a test)
Handouts
None
Flashcards
Hygrothermal Stresses and Strains in a Lamina Slideshow
Quiz