Statics Mechanics of Materials

Statics

1 General Principles

1.1 Mechanics

1.2 Fundamental Concepts

1.3 Units of Measurement

1.4 The International System of Units

1.5 Numerical Calculations

1.6 General Procedure for Analysis


2 Force Vectors

2.1 Scalars and Vectors

2.2 Vector Operations

2.3 Vector Addition of Forces

2.4 Addition of a System of Coplanar Forces

2.5 Cartesian Vectors

2.6 Addition of Cartesian Vectors

2.7 Position Vectors

2.8 Force Vector Directed Along a Line

2.9 Dot Product


3 Force System Resultants

3.1 Moment of a Force—Scalar Formulation

3.2 Cross Product

3.3 Moment of a Force—Vector Formulation

3.4 Principle of Moments

3.5 Moment of a Force about a Specified Axis

3.6 Moment of a Couple

3.7 Simplification of a Force and Couple System

3.8 Further Simplification of a Force and Couple System


4 Equilibrium of a Rigid Body

4.1 Conditions for Rigid-Body Equilibrium

4.2 Free-Body Diagrams

4.3 Equations of Equilibrium

4.4 Two- and Three-Force Members

4.5 Free-Body Diagrams

4.6 Equations of Equilibrium

4.7 Characteristics of Dry Friction

4.8 Problems Involving Dry Friction

4.9 Frictional Forces on Flat Belts

4.10 Frictional Forces on Screws


5 Structural Analysis

5.1 Simple Trusses

5.2 The Method of Joints

5.3 Zero-Force Members

5.4 The Method of Sections

5.5 Frames and Machines


6 Center of Gravity, Centroid, and Moment of Inertia

6.1 Center of Gravity, Center of Mass, and the Centroid of a Body

6.2 Composite Bodies

6.3 Resultant of a Distributed Loading

6.4 Moments of Inertia for Areas

6.5 Parallel-Axis Theorem for an Area

6.6 Moments of Inertia for Composite Areas


7 Stress and Strain

7.1 Introduction

7.2 Internal Resultant Loadings

7.3 Stress

7.4 Average Normal Stress in an Axially Loaded Bar

7.5 Average Shear Stress

7.6 Allowable Stress

7.7 Design of Simple Connections

7.8 Deformation

7.9 Strain


Mechanics of Materials

8 Mechanical Properties of Materials

8.1 The Tension and Compression Test

8.2 The Stress—Strain Diagram

8.3 Stress—Strain Behavior of Ductile and Brittle Materials

8.4 Hooke’s Law

8.5 Strain Energy

8.6 Poisson’s Ratio

8.7 The Shear Stress—Strain Diagram


9 Axial Load

9.1 Saint-Venant’s Principle

9.2 Elastic Deformation of an Axially Loaded Member

9.3 Principle of Superposition

9.4 Statically Indeterminate Axially Loaded Member

9.5 The Force Method of Analysis for Axially Loaded Members

9.6 Thermal Stress

9.7 Stress Concentrations


10 Torsion

10.1 Torsional Deformation of a Circular Shaft

10.2 The Torsion Formula

10.3 Power Transmission

10.4 Angle of Twist

10.5 Statically Indeterminate Torque-Loaded Members

*10.6 Solid Noncircular Shafts

10.7 Stress Concentration


11 Bending

11.1 Shear and Moment Diagrams

11.2 Graphical Method for Constructing Shear and Moment Diagrams

11.3 Bending Deformation of a Straight Member

11.4 The Flexure Formula

11.5 Unsymmetric Bending

11.6 Stress Concentrations


12 Transverse Shear

12.1 Shear in Straight Members

12.2 The Shear Formula

12.3 Shear Flow in Built-Up Members


13 Combined Loadings

13.1 Thin-Walled Pressure Vessels

13.2 State of Stress Caused by Combined Loadings


14 Stress and Strain Transformation

14.1 Plane—Stress Transformation

14.2 General Equations of Plane-Stress Transformation

14.3 Principal Stresses and Maximum In-Plane Shear Stress

14.4 Mohr’s Circle—Plane Stress

14.5 Absolute Maximum Shear Stress

14.6 Plane Strain

14.7 General Equations of Plane-Strain Transformation

*14.8 Mohr’s Circle—Plane Strain

14.9 Strain Rosettes

14.10 Material-Property Relationships


15 Design of Beams and Shafts

15.1 Basis for Beam Design

15.2 Prismatic Beam Design

*15.3 Fully Stressed Beams


16 Deflection of Beams and Shafts

16.1 The Elastic Curve

16.2 Slope and Displacement by Integration

*16.3 Discontinuity Functions

16.4 Method of Superposition

16.5 Statically Indeterminate Beams and Shafts—Method of Superposition


17 Buckling of Columns

17.1 Critical Load

17.2 Ideal Column with Pin Supports

17.3 Columns Having Various Types of Supports

*17.4 The Secant Formula

*17.5 Inelastic Buckling


Appendices

A. Mathematical Review and Expressions

B. Geometric Properties of An Area and Volume

C. Geometric Properties of Wide-Flange Sections

D. Slopes and Deflections of Beams

Fundamental Problems Partial Solutions and Answers

Answers to Selected Problems

Index