**Mechanics and Strength of Materials by Vitor Dias da Silva**

## Contents of Mechanics and Strength of Materials

- Part I Introduction to the Mechanics of Materials
- Introduction
- General Considerations
- Fundamental Definitions
- Subdivisions of the Mechanics of Materials
- The Stress Tensor
- Introduction
- General Considerations
- Equilibrium Conditions
- Equilibrium in the Interior of the Body
- Equilibrium at the Boundary
- Stresses in an Inclined Facet
- Transposition of the Reference Axes
- Principal Stresses and Principal Directions
- The Roots of the Characteristic Equation
- Orthogonality of the Principal Directions
- Lam´e’s Ellipsoid
- Isotropic and Deviatoric Components of the Stress Tensor
- Octahedral Stresses
- Two-Dimensional Analysis of the Stress Tensor
- Stresses on an Inclined Facet
- Principal Stresses and Directions
- Mohr’s Circle
- Three-Dimensional Mohr’s Circles
- Conclusions
- Examples and Exercises
- The Strain Tensor
- Introduction
- General Considerations
- Components of the Strain Tensor
- Pure Deformation and Rigid Body Motion
- Equations of Compatibility
- Deformation in an Arbitrary Direction
- Volumetric Strain
- Two-Dimensional Analysis of the Strain Tensor
- Introduction
- Components of the Strain Tensor
- Strain in an Arbitrary Direction
- Conclusions
- Examples and Exercises
- Constitutive Law
- Introduction
- General Considerations
- Ideal Rheological Behaviour – Physical Models
- Generalized Hooke’s Law
- Introduction
- Isotropic Materials
- Monotropic Materials
- Orthotropic Materials
- Isotropic Material with Linear Visco-Elastic
- Behaviour
- Newtonian Liquid
- Deformation Energy
- General Considerations
- Superposition of Deformation Energy in the Linear Elastic Case
- Deformation Energy in Materials with Linear Elastic Behaviour
- Yielding and Rupture Laws
- General Considerations
- Yielding Criteria
- Theory of Maximum Normal Stress
- Theory of Maximum Longitudinal Deformation
- Theory of Maximum Deformation Energy
- Theory of Maximum Shearing Stress
- Theory of Maximum Distortion Energy
- Comparison of Yielding Criteria
- Conclusions About the Yielding Theories
- Mohr’s Rupture Theory for Brittle Materials
- Concluding Remarks
- Examples and Exercises
- Part II Strength of Materials
- Fundamental Concepts of Strength of Materials
- Ductile and Brittle Material Behaviour
- Stress and Strain
- Work of Deformation Resilience and Tenacity
- High-Strength Steel
- Fatigue Failure
- Saint-Venant’s Principle
- Principle of Superposition
- Structural Reliability and Safety
- Uncertainties Affecting the Verification of Structural Reliability
- Probabilistic Approach
- Semi-Probabilistic Approach
- Safety Stresses
- Slender Members
- Definition of Slender Member
- Conservation of Plane Sections
- Axially Loaded Members
- Introduction
- Dimensioning of Members Under Axial Loading
- Axial Deformations
- Computation of Internal Forces
- Elasto-Plastic Analysis
- An Introduction to the Prestressing Technique
- Composite Members
- Position of the Stress Resultant
- Stresses and Strains Caused by the Axial Force
- Effects of Temperature Variations
- Non-Prismatic Members
- Slender Members with Curved Axis
- Slender Members with Variable Cross-Section
- Non-Constant Axial Force – Self-Weight
- Stress Concentrations
- Examples and Exercises
- Bending Moment
- General Considerations
- Pure Plane Bending
- Pure Inclined Bending
- Composed Circular Bending
- The Core of a Cross-Section
- Deformation in the Cross-Section Plane
- Influence of a Non-Constant Shear Force
- Non-Prismatic Members
- Slender Members with Variable Cross-Section
- Slender Members with Curved Axis
- Bending of Composite Members
- a Linear Analysis of Symmetrical Reinforced
- Concrete Cross-Sections
- Nonlinear bending
- Deflections Caused by the Shear Force
- Introduction
- Rectangular Cross-Sections
- Symmetrical Cross-Sections
- Thin-Walled Cross-Sections
- Statically Indeterminate Frames Under Bending
- Equation of Two Moments
- Equation of Three Moments
- Elasto-Plastic Analysis Under Bending
- Examples and Exercises
- Torsion
- Introduction
- Circular Cross-Sections
- Torsion in the Elasto-Plastic Regime
- Closed Thin-Walled Cross-Sections
- Applicability of the Bredt Formulas
- General Case
- Introduction
- Hydrodynamical Analogy
- Membrane Analogy
- Rectangular Cross-Sections
- Open Thin-Walled Cross-Sections
- Optimal Shape of Cross-Sections Under Torsion
- Examples and Exercises
- Structural Stability
- Introduction
- Fundamental Concepts
- Computation of Critical Loads
- Post-Critical Behaviour
- Effect of Imperfections
- Effect of Plastification of Deformable Elements
- Instability in the Axial Compression of a Prismatic Bar
- Euler’s Problem
- Prismatic Bars with Other Support Conditions
- Safety Evaluation of Axially Compressed Members
- Optimal Shape of Axially Compressed
- Cross-Sections
- Instability Under Composed Bending
- Introduction and General Considerations
- Safety Evaluation
- Composed Bending with a Tensile Axial Force
- Examples and Exercises
- Stability Analysis by the Displacement Method
- Introduction
- Simple Examples
- Framed Structures Under Bending
- Stiffness Matrix of a Compressed Bar
- Stiffness Matrix of a Tensioned Bar
- Linearization of the Stiffness Coefficients
- Examples of Application
- Energy Theorems
- General Considerations
- Elastic Potential Energy in Slender Members
- Theorems for Structures with Linear Elastic Behaviour
- Clapeyron’s Theorem
- Castigliano’s Theorem
- Menabrea’s Theorem or Minimum Energy
- Theorem
- Betti’s Theorem
- Maxwell’s Theorem
- Theorems of Virtual Displacements and Virtual Forces
- Theorem of Virtual Displacements
- Theorem of Virtual Forces
- Considerations About the Total Potential Energy
- Definition of Total Potential Energy
- Principle of Stationarity of the Potential Energy
- Stability of the Equilibrium
- Elementary Analysis of Impact Loads
- Examples and Exercises