Stress and Strain – Chapter 1 eBook – Strength of Materials

1.1 Introduction 1.1
1.2 Deformations in Solids 1.1
1.2.1 Increase or Decrease in Length Due to Axial Loads 1.1
1.2.2 Angular Deformation Due to a Force Parallel to the Cross-Section 1.2
1.2.3 Bending, Deformation Due to a Moment in the Plane of the Axis of the Member 1.2
1.2.4 Twisting, Deformation Due to a Moment in the Plane Perpendicular
to the Axis of the Member 1.2
1.3 Axial Loading (Tension-Compression) 1.3
1.3.1 External Forces or Loads 1.3
1.3.2 Internal Forces 1.3
1.3.3 Tension and Compression 1.3
1.3.4 Stress 1.3
1.3.5 Strain 1.4
1.4 Stress-Strain Curve for Mild Steel (Tensile Test on Mild Steel) 1.4
1.4.1 Proportional Limit 1.5
1.4.2 Elastic Limit 1.5
1.4.3 Yield Point 1.5
1.4.4 Ultimate Stress 1.5
1.4.5 Breaking Point (Fracture) 1.5
1.4.6 Ductile and Brittle Materials 1.5
1.4.7 Proof Stress 1.6
1.5 Hooke’s Law 1.6
1.5.1 Modulus of Elasticity (Young’s Modulus) 1.6
1.6 Working Stress and Factor of Safety 1.7
1.7 Composite Bars (Bars in Series) 1.11
1.7.1 Procedure of Analysis (Bars in Series) 1.11
1.8 Statically Indeterminate Axially Loaded Bars in Series 1.15
1.9 Axially Loaded Bars with Composite Cross-Section 1.19
1.9.1 Procedure of analysis (Composite Cross-Sections) 1.19
1.10 Bars with Uniformly Varying Cross-Section 1.30
1.10.1 Uniformly Varying Circular Cross-Section 1.30
1.10.2 Uniformly Varying Rectangular Cross-Section 1.32
1.11 Deformation of a Vertical Bar Under its Own Weight 1.34
1.12 Lateral Strain and Poisson’s Ratio 1.35
1.12.1 Lateral Strain 1.35
1.12.2 Poisson’s Ratio 1.35
1.13 Volumetric Strain and Bulk Modulus 1.36
1.13.1 Volumetric Strain 1.36
1.13.2 Bulk Modulus K 1.36
1.13.3 Volumetric Strain in a Rectangular Block 1.37
1.13.4 Volumetric Strain in a Cylindrical Bar 1.37
1.13.5 Principle of Superposition 1.37
1.14 Shear Force, Shear Stress and Shear Strain 1.41
1.14.1 Modulus of Rigidity or Shear Modulus 1.41
1.14.2 Single Shear and Double Shear 1.41
1.14.3 Complementary Shear 1.42
1.15 Relation Between Young’s Modulus, Bulk Modulus and Modulus of Rigidity 1.44
1.15.1 Relation Between Young’s Modulus E and Bulk Modulus K 1.44
1.15.2 Relation Between Young’s Modulus and Shear Modulus 1.45
1.15.3 Relation Between Young’s Modulus E, Shear Modulus G and Bulk Modulus K 1.45
• Summary 1.47
• Exercise 1.48