PDF Free Download | 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