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Appendix A: Matrix Algebra

Intro to Matrix Algebra [PDF]

Determinant of a matrix using minors Theory [YOUTUBE 4:41]

Determinant of a matrix using cofactors Theory [YOUTUBE 3:26]

Determinant of a matrix using minors Example [YOUTUBE 6:26]

Determinant of a matrix using cofactors Example [YOUTUBE 5:31]

A real life problem of setting up simultaneous linear equations [YOUTUBE 5:23]

Writing simultaneous linear equations in matrix form  [YOUTUBE 5:25]

Can we divide two matrices?  [YOUTUBE 5:39]

Inverse of matrices Example  [YOUTUBE 3:40]

Using concept of inverse to solve a set of equations  [YOUTUBE 2:27]

Finding the inverse of a matrix Theory [YOUTUBE 4:32]

Finding the inverse of a matrix Example  [YOUTUBE 7:03]

Appendix B: Transformation of Stresses and Strains

Transformation of Stresses [LIVESCRIBE 13:55]

2.1 Introduction

Deformations of unidirectional lamina under load  [ PDF]   [PPT]

2.2 Review of Definitions

Review of definitions   [PDF  [PPT]

2.3 Hooke's Law for Different Types of Materials

3D stiffness and compliance matrices   [PDF  [PPT]

2.4 Hooke's Law for a Two Dimensional Unidirectional Lamina

Stiffness and compliance matrices for a unidirectional lamina   [PDF  [PPT]

2.5 Hooke's Law for a Two Dimensional Angle Lamina

Stress-strain relationship for an angle lamina   [PDF  [PPT]

2.6 Engineering Constants of an Angle Lamina

Engineering constants of an angle lamina   [PDF  [PPT]

Problem 2.27 [PDF]

Problem 2.28 [PDF]

Problem 2.29 [PDF]

Problem 2.32 [LIVESCRIBE 9:03]

Background to #2.32: Linear Regression With Zero Intercept: Derivation [YOUTUBE 9:32]

Test problem#3 [problem statement] [LIVESCRIBE Parta 1:34] [LIVESCRIBE Part b 3:08] [LIVESCRIBE Partc 3:46]

2.7 Invariant Form of Stiffness and Compliance Matrices for an Angle Lamina

Invariant form of transformation matrices   [PDF  [PPT]

2.8 Strength Failure Theories of an Angle Lamina.

Maximum stress failure theory   [PDF  [PPT]

Maximum strain failure theory   [PDF  [PPT]

Tsai-Hill failure theory   [PDF  [PPT]

Tsai-Wu failure theory   [PDF  [PPT]

Comparison of failure theories   [PDF  [PPT]

Test problem#4 [problem statement] [LIVESCRIBE 6:53 ]

2.9 Hygrothermal Stresses and Strains in a Lamina

Hygrothermal stresses and strains   [PDF  [PPT]