Chapter 1: forces and moments

1.1 Introduction

1.2 Units

1.3 Forces in mechanics of materials

1.4 Concentrated forces

1.5 Moment of a concentrated force

1.6 Distributed forces-force and moment restraint

1.7 Internal forces and stresses---stress resultants

1.8 Restraint forces and restraint force resultants

1.9 Summary and conclusions

Chapter 2: static equilibrium

2.1 Introduction

2.2 free body diagrams

2.3 Equilibrium-concentrated forces

2.4 Equilibrium-distributed forces

2.5 Equilibrium in three dimensions

2.6 Equilibrium-internal forces and stresses

2.7 summary and conclusions

Chapter 3: Displacement, strain, and material properties

3.1 Introduction

3.2 Displacement and strain

3.3 compatibility

3.4 Linear material properties

3.5 Some simple solutions for stress, strain, and displacement

3.6 Thermal strain

3.7 Engineering materials

3.8 Fiber reinforced composite laminates

3.9 Plan for the following chapters

3.10 summary and conclusions

Chapter 4: classical analysis of the axially loaded slender bar

4.1 Introduction

4.2 Solutions from the theory of elasticity

4.3 derivation and solution of the governing equations

4.4 The statically determinate case

4.5 The statically indeterminate case

4.6 Variable cross sections

4.7 Thermal stress and strain in an axially loaded bar

4.8 Shearing stress in an axially loaded bar

4.9 Design of axially loaded bars

4.10 Analysis and design of pin-joined trusses

4.11 Work and energy- Castiglione’s second theorem

4.12 Summary and conclusions

Chapter 5: A general method for the axially loaded slender bar

5.1 Introduction

5.2 Nodes, elements, shape functions, and the Element stiffness matrix

5.3 The assembled global equations and their solution

5.4 General methods—distributed applied loads

5.5 Variable cross sections

5.6 Analysis and design of pin-joined trusses

5.7 Summary and conclusions

Chapter 6: Torsion

6.1 Introduction

6.2 Torsional displacement, strain, and stress

6.3 Derivation and solution of the governing equations

6.4 Solutions from the theory of elasticity

6.5 Torsional stress in thin walled cross sections

6.6 Work and energy–torsional stiffness in a thin walled tube

6.7 Torsional stress and stiffness in multicell sections

6.8 Torisonal stress and displacement in thin walled open sections

6.9 General (Finite Element) method

6.10 Continuously variable cross sections

6.11 Summary and conclusions

Chapter 7: Classical analysis of the bending of beams

7.1 Introduction

7.2 Area properties-sign conventions

7.3 Derivation and solution of the governing equations

7.4 The statically determinate case

7.5 Work and energy-castigliano’s second theorem

7.6 The statically indeterminate case

7.7 Solutions from the theory of elasticity

7.8 Variable cross sections

7.9 Shear stress in non rectangular cross sections-thin walled cross sections

7.10 Design f beams

7.11 Large displacements

7.12 Summary and conclusions

Chapter 8: A general method (FEM) for the bending of beams

8.1 Introduction

8.2 Nodes, elements, shape functions, and the element stiffness matrix

8.3 The global equations and their solution

8.4 Distributed loads in FEM

8.5 Variable cross sections

8.6 Summary and conclusions

Chapter 9: More about stress and strain , and Material properties

9.1 Introduction

9.2 Transformation of stress in two dimensions

9.3 Principal axes and principal stresses in two dimensions

9.4 Transformation of strain in two dimensions

9.5 Strain rosettes

9.6 Stress transformation and principal stresses in three dimensions

9.7 Allowable and ultimate stress , and factors of safety

9.8 Fatigue

9.9 Creep

9.10 Orthotropic materials-composites

9.11 Summary and conclusions

Chapter 10: Combined loadings on slender bars-thin walled cross sections

10.1 Introduction

10.2 Review and summary of slender bar equations

10.3 Axial and torsional loads

10.4 Axial and bending loads-2D frames

10.5 Bending in two planes

10.6 Bending and torsion in thin walled open sections-shear center

10.7 Bending and torsion in thin walled closed sections-shear center

10.8 Stiffened thin walled beams

10.9 Summary and conclusions

Chapter 11: Work and Energy methods-virtual work

11.1 Introduction

11.2 Introduction o the principle of virtual work

11.3 Static analysis of slender bars by virtual work

11.4 Static analysis of 3D and 2D solids by virtual work

11.5 The element stiffness matrix for plane stress

11.6 The element stiffness matrix for 3D solids

11.7 Summary and conclusions

Chapter 12: Structural analysis in two and three dimensions

12.1 Introduction

12.2 The governing equations in two dimensions plane stress

12.3 Finite elements and the stiffness matrix for plane stress

12.4 Thin flat plates-classical analysis

12.5 Thin flat plates – FEM analysis

12.6 Shell structures

12.7 Stiffened shell structures

12.8 Three dimensional structures – classical and FEM analysis

12.9 Summary and conclusions

Chapter 13: Analysis of thin laminated composite material structures

13.1 Introduction to classical lamination theory

13.2 Strain displacement equations for theory

13.3 Stress-strain relations for a single lamina

13.4 Stress resultants for laminates

13.5 CLT constitutive for description

13.6 Determining laminae stress/strains

13.7 Laminated plates subject to transverse loads

13.8 Summary and conclusion

Chapter 14: Bucking

14.1 Introduction

14.2 The equations for a beam with combined lateral and axial loading

14.3 Buckling of a column

14.4 The beam column

14.5 The finite element method for bending and bucking

14.6 Buckling of frames

14.7 Buckling of thin plates and other structures

14.8 Summary and conclusions

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