This textbook has been written for the engineering students. This textbook covers the essentials of solid mechanics with reference to basic load-bearing members—straight bars, thin-walled cylindrical and spherical pressure vessels, circular shafts, beams undergoing simple bending, and columns. It concisely elucidates the corresponding fundamental assumptions, important equations, and their range of validity without formal derivations. Subsequently, this textbook contains several carefully selected examples to illustrate sequence of steps in the analysis of forces, stresses and displacements, or stability. It further deals with combined loading, stress and strain transformations, energy methods, and failure analysis using commonly employed criteria. This textbook is a handy, yet complete, resource for graduate and postgraduate engineering students. It will also be a ready reference for a practicing engineers or graduate students preparing for an interview or a competitive examination.
Author(s): K. Bhaskar, T. K. Varadan
Publisher: Springer
Year: 2022
Language: English
Pages: 167
City: Cham
Preface
Contents
About the Authors
1 Preliminaries
1.1 State of Stress at a Point
1.2 Principle of Complementary Shear
1.3 The Assumption of Small Displacements and Rotations
1.4 State of Strain at a Point
1.5 Strain–Displacement Relations
1.6 Linear Constitutive Law
1.7 Plane Stress and Plane Strain
1.8 Two-Dimensional Stress Transformation
1.9 Principal Planes and Principal Stresses
1.10 Maximum In-Plane Shear Stress
1.11 Strain Transformation and Principal Strains
1.12 Mohr’s Circle
1.13 Notable Points About 2-D Transformation
1.14 Failure Criterion for Brittle Materials
1.15 Yield Criteria for Ductile Materials
1.16 Statically Determinate and Indeterminate Structures
1.17 St. Venant’s Principle
2 Straight Bars
2.1 Straight Bar
2.2 Assumptions
2.3 Final Formulae
2.4 Range of Applicability
2.5 Illustrative Problems
3 Thin-Walled Pressure Vessels
3.1 Thin-Walled Vessels
3.2 Assumptions
3.3 Final Formulae
3.4 Range of Applicability
3.5 Illustrative Problems
4 Circular Shafts
4.1 Circular Shaft
4.2 Assumptions
4.3 Final Formulae
4.4 Range of Applicability
4.5 Illustrative Problems
5 Beams—Shear Force and Bending Moment
5.1 Beam Undergoing Simple Bending
5.2 Shear Force and Bending Moment
5.3 Relations Between Loading, Shear Force, and Bending Moment
5.4 Shear Force and Bending Moment Diagrams (SFD, BMD)
5.5 Bending Moment Diagram by Parts
6 Beams–Stresses
6.1 Engineering Beam Theory—Assumptions
6.2 Final Formulae
6.3 Range of Applicability
6.4 Illustrative Problems
7 Beams–Deflections
7.1 Engineering Beam Theory—Kinematics of Deformation
7.2 Deflection Analysis
7.3 Final Formulae
7.4 Specification of Boundary Conditions
7.5 Range of Applicability
7.6 Illustrative Problems
7.6.1 Double Integration Method
7.6.2 Moment-Area Method
7.6.3 Superposition Method
7.6.4 Statically Indeterminate Beams
8 Combined Loading, Stress Transformation, Failure Criteria
8.1 Combined Loading
8.2 Stress and Strain Transformation
8.2.1 Use of Transformation Rules
8.2.2 Mohr’s Circle
8.3 Use of Failure Criteria
9 Long Columns
9.1 Column
9.2 Perfect and Imperfect Columns
9.3 Assumptions
9.4 Final Formulae
9.5 Illustrative Problems
10 Energy Methods
10.1 Assumptions
10.2 Final Formulae
10.3 Illustrative Problems
Index
