Mechanical_Engineers_Handbook.pdf

Mechanical Engineer's Handbook

Academic Press Series in Engineering

Series Editor

J. David Irwin

Auburn University

This a series that will include handbooks, textbooks, and professional reference

books on cutting-edge areas of engineering. Also included in this series will be single-

authored professional books on state-of-the-art techniques and methods in engineer-

ing. Its objective is to meet the needs of academic, industrial, and governmental

engineers, as well as provide instructional material for teaching at both the under-

graduate and graduate level.

The series editor, J. David Irwin, is one of the best-known engineering educators in

the world. Irwin has been chairman of the electrical engineering department at

Auburn University for 27 years.

Published books in this series:

Control of Induction Motors

2001, A. M. Trzynadlowski

Embedded Microcontroller Interfacing for McoR Systems

2000, G. J. Lipovski

Soft Computing & Intelligent Systems

2000, N. K. Sinha, M. M. Gupta

Introduction to Microcontrollers

1999, G. J. Lipovski

Industrial Controls and Manufacturing

1999, E. Kamen

DSP Integrated Circuits

1999, L. Wanhammar

Time Domain Electromagnetics

1999, S. M. Rao

Single- and Multi-Chip Microcontroller Interfacing

1999, G. J. Lipovski

Control in Robotics and Automation

1999, B. K. Ghosh, N. Xi, and T. J. Tarn

Mechanical

Engineer's

Handbook

Edited by

Dan B. Marghitu

Department of Mechanical Engineering , Auburn University,

Auburn, Alabama

San Diego San Francisco New York Boston London Sydney Tokyo

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Table of Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Contributors ........................................ xv

CHAPTER 1

Statics

Dan B. Marghitu, Cristian I. Diaconescu, and Bogdan O. Ciocirlan

1. Vector Algebra ...................................... 2

1.1 Terminology and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Product of a Vector and a Scalar . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Zero Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Unit Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6 Vector Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.7 Resolution of Vectors and Components . . . . . . . . . . . . . . . . . . 6

1.8 Angle between Two Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.9 Scalar (Dot) Product of Vectors . . . . . . . . . . . . . . . . . . . . . . . 9

1.10 Vector (Cross) Product of Vectors . . . . . . . . . . . . . . . . . . . . . . 9

1.11 Scalar Triple Product of Three Vectors . . . . . . . . . . . . . . . . . . 11

1.12 Vector Triple Product of Three Vectors . . . . . . . . . . . . . . . . . . 11

1.13 Derivative of a Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2. Centroids and Surface Properties .......................... 12

2.1 Position Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 First Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Centroid of a Set of Points . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 Centroid of a Curve, Surface, or Solid . . . . . . . . . . . . . . . . . . . 15

2.5 Mass Center of a Set of Particles . . . . . . . . . . . . . . . . . . . . . . 16

2.6 Mass Center of a Curve, Surface, or Solid . . . . . . . . . . . . . . . . 16

2.7 First Moment of an Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.8 Theorems of Guldinus±Pappus . . . . . . . . . . . . . . . . . . . . . . . 21

2.9 Second Moments and the Product of Area . . . . . . . . . . . . . . . . 24

2.10 Transfer Theorem or Parallel-Axis Theorems . . . . . . . . . . . . . . 25

2.11 Polar Moment of Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.12 Principal Axes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3. Moments and Couples ................................. 30

3.1 Moment of a Bound Vector about a Point . . . . . . . . . . . . . . . . 30

3.2 Moment of a Bound Vector about a Line . . . . . . . . . . . . . . . . . 31

3.3 Moments of a System of Bound Vectors . . . . . . . . . . . . . . . . . 32

3.4 Couples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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