CHAPTER 2: Macromechanics of a Lamina Worked Out Examples

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

None

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)