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Unformatted text preview: Chapter 2 Stress and Strain-- Axial Loading Statics – deals with undeformable bodies (Rigid bodies) Mechanics of Materials – deals with deformable bodies-- Need to know the deformation of a boy under various stress/strain state-- Allowing us to computer forces for statically indeterminate problems. The following subjects will be discussed: • Stress-Strain Diagrams • Modulus of Elasticity • Brittle vs Ductile Fracture • Elastic vs Plastic Deformation • Bulk Modulus and Modulus of Rigidity • Isotropic vs Orthotropic Properties • Stress Concentrations • Residual Stresses 2.2 Normal Strain under Axial Loading δ ε = = normal strain L lim δ δ ε ∆ → ∆ = = ∆ x d x dx For variable cross-sectional area A, strain at Point Q is: The normal Strain is dimensionless. 2.3 Stress-Strain Diagram Ductile Fracture Brittle Fracture Some Important Concepts and Terminology: 1. Elastic Modulus 2. Yield Strength – lower and upper Y.S. -- σ y 0.2% Yield Strength 3. Ultimate Strength, σ ut 4. Breaking Strength or Fracture Strength 5. Necking 6. Reduction in Area 7. Toughness – the area under the σ- ε curve 8. Percent Elongation 9. Proportional Limit 2.3 Stress-Strain Diagram 100 %- B o o L L L 100 % B o A A A- Percent elongation = Percent reduction in area = ( / ) ε ε = Σ∆ = Σ ∆ t L L 2.4 True Stress and True Strain Eng. Stress = P/A o True Stress = P/A A o = original area A = instantaneous area Eng. Strain = True Strain = δ o L l ε = = ∫ o L t L o dL L n L L (2.3) L o = original length L = instantaneous length Where E = modulus of elasticity or Young’s modulus 2.5 Hooke's Law: Modulus of Elasticity2....
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