Contents
- Introduction
- Body Force, Surface Force, and Stress Vector
- The State of Stress at a Point
- Normal and Shear Stress Components
- Rectangular Stress Components
- Stress Components on an Arbitrary Plane
- Digression on Ideal Fluid
- Equality of Cross Shears
- A More General Theorem
- Principal Stresses
- Stress Invariants
- Principal planes are orthogonal.
- A cubic equation has three real roots.
- Particular Cases
- Recapitulation
- The state of stress refers to the principal axes.
- Mohr’s Circles for the Three-Dimensional State of Stress
- Mohr’s Stress Plane
- Planes of Maximum Shear
- Octahedral Stresses
- The State of Pure Shear
- Decomposition into Hydrostatic and Pure Shear States
- Cauchy’s Stress Quadric
- Lame’s Ellipsoid
- The Plane State of Stress
- Differential Equations of Equilibrium
- Equilibrium equations for the plane stress state
- Boundary Conditions
- Equations of Equilibrium in Cylindrical Coordinates
- The Axisymmetric Case and the Plane Stress Case
- Analysis of Strain
- Introduction
- Deformations
- There is deformation in the vicinity of a point.
- Change in Length of a Linear Element
- Change in Length of a Linear Element—Linear Components
- Rectangular Strain Components
- The State of Strain at a Point
- We interpret gxy, gyz, and gxz as Shear Strain Components.
- Change in Direction of a Linear Element
- Cubical Dilatation
- Change in the angle between two line elements
- Principal Axes of Strain and Principal Strains
- Plane State of Strain
- The Principal Axes of Strain Remain Orthogonal after Strain
- Plane Strains in Polar Coordinates
- Compatibility Conditions
- Strain Deviator and its Invariants
- Problems
- Appendix: Compatibility Conditions
- Stress–Strain Relations for Linearly Elastic Solids
- Introduction
- Generalized Statement of Hooke’s Law
- Stress–Strain Relations for Isotropic Materials
- Modulus of Rigidity
- Bulk Modulus
- Young’s Modulus and Poisson’s Ratio
- Relations between the Elastic Constants
- Displacement Equations of Equilibrium
- Problems
- Theories of Failure or Yield Criteria and Introduction to Ideally Plastic Solid
- Energy Methods
- Bending of Beams
- Torsion
- Axisymmetric Problems
- Thermal Stresses
- Elastic Stability
- Introduction to Composite Materials
- Introduction to Stress Concentration and Fracture Mechanics
Preface
The book has undergone complete changes from its first two editions. The second edition provided the opportunity to correct typos and incorrect answers to some questions.
Additionally, in response to numerous comments, we added a section on connected devices, which received positive feedback. Many upper-level students have requested the inclusion of certain topics in this second-level course.
It was difficult to meet all the demands in a book of this type, but some important articles had to be included and a new text was needed. As previously published, the first five chapters concern the general analysis of the mechanics of simple objects.
The content of this chapter provides a solid foundation in the mechanics of dynamic structures that will enable the student to analyze and solve a variety of dynamic design problems encountered in practice. The second reason is that more and more equal ideas are being put forward. The literature provides numerous examples of applying the given equations to solve practical problems, irrespective of the conditions that yield these parameters. Treatment begins with a stress analysis of isotropic solids, a behavior analysis, and stress-strain relationships. These chapters are complex and contain material not commonly found in standard textbooks. Chapter 4 delves into the theory of failure or resignation, drawing a generalization from the ancient text. We advance this treatment because it is crucial to understand the potential causes of equipment malfunctions when applying all designs to power-related problems.
Practical application has greatly expanded Mohr’s theory of failure. Energy systems, one of the most significant issues, are the focus of Chapter 5’s detailed discussion. This section’s discussions hold significance as they are applicable to a wide range of problems. The content is boring, and Virtual Work discusses the theses of Castigliano, Kirchhoff, Mena Bria, Engesser, and Maxwell-Mohr. Various examples are given to illustrate the application of this statement. Examples include the bending of wood, bending centers, and curved lines, among others. Discussed in Chapter 6. This chapter also discusses the importance of the Euler-Bernoulli hypothesis in deriving the equations. Chapter 7 provides a more detailed discussion of torsion.
We discuss the torsion of circles, elliptical systems, equilateral triangles, small circles around multiple spheres, and more. Another notable addition in this section is the twisting of multiple rods. The general text does not incorporate this useful addition. Chapter 8 provides an analysis of asymmetric problems like pressure meters, rotating disks, shafts, and cylinders under both internal and external pressure. Tensions and tensions in the body due to the heat of the fire require special attention because they occur frequently. The thermoelectricity literature generally addresses these issues. Analysis of heat transfer problems is less complex than the traditional problems discussed in Advanced Solid Mechanics textbooks. Chapter 9 of this book covers the topic of heat sinks. Chapter 10 covers the problem of inelastic elasticity. In addition to the beam-column topics, this chapter introduces the student to the elasticity problem as an eigenvalue problem. This is an important concept for a student to appreciate. Energy methods such as Rayleigh-Ritz, Timoshenko, the use of trigonometric series, etc. find their place in this field.
See Chapter 11 for an introduction to synthetic mechanics. Modern technology and industrial processes apply to various materials. This chapter lays a solid foundation for the topic. Solid materials are a natural extension from isotropic solids to anisotropic materials. We cover topics such as orthotropic materials, off-axis loading, corner ply and cross ply laminate, material failure rates, and the impact of Poisson’s ratio. The study encompasses a substantial number of samples. Stress and rupture are important factors in research theory. Only a dedicated book can discuss these topics in a simple teaching style. However, a book of this type can provide a useful introduction to these important topics. Chapter 12 provides excellent information and many worked examples. The provided treatment allows for the safe solution of many practical problems.
Many numerical examples and problems use SI units, but some also use kgf, meter, and second units. We intentionally use kgf to measure strength and weight, allowing the student to become accustomed to using both units in daily life. When we use kgf units, we also provide their equivalents in SI units.
Download For Free in PDF Format