0 - Content

Millau Bridge

Contents :

1 - Tension, Compression, and Shear

1.1 Introduction to Mechanics of Materials
1.2 Normal Stress and Strain
1.3 Mechanical Properties of Materials
1.4 Elasticity, Plasticity, and Creep
1.5 Linear Elasticity, Hooke's Law, and Poisson's Ratio
1.6 Shear Stress and Strain
1.7 Allowable Stresses and Allowable Loads
1.8 Design for Axial Loads and Direct Shear

2 - Axially Loaded Members

2.1 Introduction
2.2 Changes in Lengths of Axially Loaded Members
2.3 Changes in Length Under Nonuniform Conditions
2.4 Statically Indeterminate Structures
2.5 Thermal Effects, Misfits, Prestrains
2.6 Stresses on Inclined Sections
2.7 Strain Energy
2.8 Impact Loading
2.9 Repeated Loading and Fatigue
2.10 Stress Concentrations
2.11 Nonlinear Behavior

3 - Torsion

3.1 Introduction
3.2 Torsional Deformations of a Circular Bar
3.3 Circular Bars of Linearly Elastic Materials
3.4 Nonuniform Torsion
3.5 Stresses and Strains in Pure Shear
3.6 Relationship Between Moduli of Elasticity E and G
3.7 Transmission of Power by Circular Shafts
3.8 Statically Indeterminate Torsional Members
3.9 Strain Energy in Torsion and Pure Shear
3.10 Thin-Walled Tubes
3.11 Stress Concentrations in Torsion

4 - Shear Forces and Bending Moments

4.1 Introduction
4.2 Types of Beams, Loads, and Reactions
4.3 Shear Forces and Bending Moments
4.4 Relationships Between Loads, Shears Forces, and Bending Moments
4.5 Shear-Force and Bending-Moment Diagrams

5 - Stresses in Beams (Basic Topics)

5.1 Introduction
5.2 Pure Bending and Nonuniform Bending
5.3 Curvature of a Beam
5.4 Longitudinal Strains in Beams
5.5 Normal Stresses in Beams (Linearly Elastic Materials)
5.6 Design of Beams for Bending Stresses
5.7 Nonprismatic Beams
5.8 Shear Stresses in Beams of Rectangular Cross Section
5.9 Shear Stresses in Beams of Circular Cross Section
5.10 Shear Stresses in the Web of Beams with Flanges
5.11 Built-Up Beams and Shear Flow
5.12 Beams with Axial Loads
5.13 Stress Concentration in Bending

6 - Stresses in Beams (Advanced Topics)

6.1 Introduction
6.2 Composite Beams
6.3 Transformed-Section Method
6.4 Doubly Symmetric Beams with Inclined Loads
6.5 Bending of Unsymmetric Beams
6.6 The Shear-Center Concept
6.7 Shear Stresses in Beams of Thin-Walled Open Cross Section
6.8 Shear Stresses in Wide-Walled Open Sections
6.9 Shear Centers of Thin-Walled Open Sections
6.10 Elastoplastic Bending

7 - Analysis of Stress and Strain

7.1 Introduction
7.2 Plane Stress
7.3 Principal Stresses and Maximum Shear Stresses
7.4 Mohr's Circle for Plane Stress
7.5 Hooke's Law for Plane Stress
7.6 Triaxial Stress
7.7 Plane Strain

8 - Applications of Plane Stress (Pressure Vessels, Beams, and Combined Loadings)

8.1 Introduction
8.2 Spherical Pressure Vessels
8.3 Cylindrical Pressure Vessels
8.4 Maximum Stresses in Beams
8.5 Combined Loadings

9 - Deflections of Beams

9.1 Introduction
9.2 Differential Equations of the Deflection Curve
9.3 Deflections by Integration of the Bending-Moment Equation
9.4 Deflections by Integration of the Shear-Force and Load Equations
9.5 Methods of Superposition
9.6 Moment-Area Method
9.7 Nonprimsmatic Beams
9.8 Strain Energy of Bending
9.9 Castigliano's Theorem
9.10 Deflection Produced by Impact
9.11 Temperature Effects

10 - Statically Indeterminate Beams

10.1 Introduction
10.2 Types of Statically Indeterminate Beams
10.3 Analysis by the Differential Equations
10.4 Methods of Superposition
10.5 Temperature Effects
10.6 Longitudinal Displacements at the Ends of a Beam

11 - Columns

11.1 Introduction
11.2 Buckling and Stability
11.3 Columns with Pinned Ends
11.4 Columns with Other Support Conditions
11.5 Columns with Eccentric Axia Loads
11.6 The Secant Formula for Columns
11.7 Elastics and Inelastic Column Behavior

12 - Review of Centroids and Moments of Inertia

12.1 Introduction
12.2 Centroids of Plane Areas
12.3 Centroids of Composite Areas 
12.4 Moments of Inertia of Plane Areas
12.5 Parallel-Axis Theorem for Moments of Inertia
12.6 Polar Moment of Inertia
12.7 Products of Inertia
12.8 Rotation of Axes
12.9 Principal Axes and Principal Moments of Inertia



Preface :

Mechanics of Materials is a basic engineering subject that must be understood by anyone concerned with the strength and physical performance of structures, whether those structures are man-made or natural. The subject matter includes such fundamental concepts as stresses and strains, deformations and displacements, elasticity and inelasticity, strain energy, and load-carrying capacity. These concepts underlie the design and analysis of a huge variety of mechanical and structural systems.

At the college level, mechanics of materials is usually taught during the sophomore and junior years. The subject is  required for most students majoring in mechanical, structural, civil, biomedical, aeronautical, and aerospace engineering.

Stephen Timoshenko

Probably the most famous name in the field of applied mechanics and as the world's most outstanding pioneer in applied mechanics. Stephen P. Tymoshenko  December 22, 1878 – May 29, 1972), was a Ukrainian engineer who is reputed to be the father of modern engineering mechanics. He was a founding member of the Ukrainian Academy of Sciences.
He wrote many of the  seminal works in the areas of engineering mechanics, elasticity and strength of materials, many of which are still widely used today.