Schaum's Outline Of Engineering Mechanics Statics

321 Pages·2021·55.418 MB·English

by  Merle C. Potter, W. G. McLean, Charles L. Best, E. W. Nelson

SCHAUM'S®
outlines
Statics
00_Potter-Statics_FM_i-xii.indd 1 07/08/20 5:53 PM
This page intentionally left blank
00_Potter-Statics_FM_i-xii.indd 2 07/08/20 5:53 PM
SCHAUM’S®
outlines
Statics
Seventh Edition
MERLE C. POT TER, P.E., B.S.M.E., M.S., Ph.D.
Emeritus Professor of Mechnical Engineering
Michigan State University
E. W. NELSON, B.S.M.E., M.Adm.E.
Engineering Supervisor, Retired
Western Electric Company
CHARLES L. BEST, B.S.M.E., M.S., Ph.D.
Emeritus Professor
Lafayette College
W. G. McLEAN, B.S.E.E., Sc.M., Eng.D.
Emeritus Director of Engineering
Lafayette College
Schaum’s Outline Series
New York Chicago San Francisco Athens London Madrid
Mexico City Milan New Delhi Singapore Sydney Toronto
00_Potter-Statics_FM_i-xii.indd 3 07/08/20 5:53 PM
Copyright © 2021, 2020, 2010, 1998, 1988, 1978, 1972 by McGraw Hill. All rights reserved. Except as permitted under the
United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means,
or stored in a database or retrieval system, without the prior written permission of the publisher.
ISBN: 978-1-26-046289-0
MHID: 1-26-046289-7
The material in this eBook also appears in the print version of this title: ISBN: 978-1-26-046288-3,
MHID: 1-26-046288-9.
eBook conversion by codeMantra
Version 1.0
All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trade-
marked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringe-
ment of the trademark. Where such designations appear in this book, they have been printed with initial caps.
McGraw-Hill Education eBooks are available at special quantity discounts to use as premiums and sales promotions or for use in
corporate training programs. To contact a representative, please visit the Contact Us page at www.mhprofessional.com.
This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold
with the understanding that neither the author nor the publisher is engaged in rendering legal, accounting, securities trading, or
other professional services. If legal advice or other expert assistance is required, the services of a competent professional person
should be sought.
—From a Declaration of Principles Jointly Adopted by a Committee of the
American Bar Association and a Committee of Publishers and Associations
TERMS OF USE
This is a copyrighted work and McGraw-Hill Education and its licensors reserve all rights in and to the work. Use of this work
is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the
work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit,
distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill Education’s prior consent. You
may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to
use the work may be terminated if you fail to comply with these terms.
THE WORK IS PROVIDED “AS IS.” McGRAW-HILL EDUCATION AND ITS LICENSORS MAKE NO GUARANTEES
OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED
FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA
HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUD-
ING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR
PURPOSE. McGraw-Hill Education and its licensors do not warrant or guarantee that the functions contained in the work will
meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill Education nor its licensors
shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages
resulting therefrom. McGraw-Hill Education has no responsibility for the content of any information accessed through the work.
Under no circumstances shall McGraw-Hill Education and/or its licensors be liable for any indirect, incidental, special, punitive,
consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of
the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or
cause arises in contract, tort or otherwise.
Preface
This book is designed to supplement standard texts, primarily to assist students of engineering and science in
acquiring a more thorough knowledge and proficiency in Statics. It is based on the authors’ convictions that
numerous solved problems constitute one of the best means for clarifying the basic principles. While this book
will not mesh precisely with any one text, the authors feel that it can be a very valuable adjunct to all.
The previous editions of this book have been very favorably received. This edition incorporates SI units only.
The authors attempt to use the appropriate mathematics available to students at the sophomore level. Thus the
vector approach is applied in those chapters where its techniques provide a simplicity in theory and problems.
On the other hand, we have not hesitated to use scalar methods elsewhere, since they provide entirely adequate
solutions to most of the problems. Chapter 1 is a complete review of the minimum number of vector definitions
and operations necessary for the entire book, and applications of this introductory chapter are made throughout
the book.
Chapter topics correspond to material usually covered in a standard Statics course. Most chapters contain the
appropriate derivations along with examples that illustrate the basic principles. The text material is followed by
sets of solved and supplementary problems. The solved problems present methods of analysis, provide practical
examples, and bring into sharp focus those fine points that, along with examples, enable the student to apply the
basic principles correctly and confidently. The many supplementary problems serve as a review of the material
covered in each chapter.
This book was originally the first part of Engineering Mechanics Statics and Dynamics, a Schaum’s Outline.
The decision was made to separate “Statics” and “Dynamics” into two books since it is most common to have
separate courses in engineering curricula. The material on first and second moments in the last two chapters
is most often included in “Statics” but also is used when studying “Strength of Materials” and “Dynamics.” It
saves time in those two courses if included in “Statics.” It may or may not be included in the Statics course at
a particular college.
In the first edition, the authors gratefully acknowledged their indebtedness to Paul B. Eaton and J. Warren
Gillon. In the second edition, the authors received helpful suggestions and criticism from Charles L. Best and
John W. McNabb. Also in that edition, Larry Freed and Paul Gary checked the solutions to the problems. For this
seventh edition, the authors thank William Best for checking the solutions to the new problems and reviewing
the added new material. For typing the manuscripts of the third and fourth editions, we are indebted to Elizabeth
Bullock.
E. W. Nelson
C. L. Best
W. G. McLean
M. C. Potter
v
00_Potter-Statics_FM_i-xii.indd 5 07/08/20 5:53 PM
About the Authors
MERLE C. POTTER has B.S. and M.S. degrees from Michigan Technological University and M.S. and
Ph.D. degrees from The University of Michigan. He has coauthored books on “Fluid Mechanics, Thermody-
namics, Thermal Sciences, Differential Equations, Advanced Engineering Mathematics, Statics, Dynamics,
and Strength of Materials” in addition to numerous engineering exam review books. His research involved
fluid flow stability and energy-related topics. In addition to several teaching awards, ASME awarded him
the 2008 James Harry Potter Gold Medal. He is Professor Emeritus of Mechanical Engineering at Michigan
State University and continues to write and golf.
E. W. NELSON graduated from New York University with a B.S.M.E. and an M.Adm.E. He taught mechani-
cal engineering at Lafayette College and later joined the engineering organization of the Western Electric
Company (now Lucent Technologies). Retired from Western Electric, he is currently a Fellow of the American
Society of Mechanical Engineers. He is a registered Professional Engineer and a member of Tau Beta Pi and
Pi Tau Sigma.
CHARLES L. BEST is Emeritus Professor of Engineering at Lafayette College. He holds a B.S. in M.E. from
Princeton, an M.S. in Mathematics from Brooklyn Polytechnic Institute, and a Ph.D. in Applied Mechanics from
Virginia Polytechnic Institute. He is coauthor of two books on engineering mechanics and coauthor of another
book on FORTRAN programming for engineering students. He is a member of Tau Beta Pi.
W. G. McLEAN is Emeritus Director of Engineering at Lafayette College. He holds a B.S.E.E. from Lafayette
College, an Sc.M. from Brown University, and an honorary Eng.D. from Lafayette College. Professor McLean is
the coauthor of two books on engineering mechanics, is past president of the Pennsylvania Society of Professional
Engineers, and is active in the codes and standards committees of the American Society of Mechanical Engineers.
He is a registered Professional Engineer and a member of Phi Beta Kappa and Tau Beta Pi.
vi
00_Potter-Statics_FM_i-xii.indd 6 26/08/20 1:41 PM
Contents
Chapter 1 Vectors 1
1.1 Definitions 1
1.2 Addition of Two Vectors 1
1.3 Subtraction of a Vector 3
1.4 Zero Vector 4
1.5 Composition of Vectors 4
1.6 Multiplication of Vectors by Scalars 4
1.7 Orthogonal Triad of Unit Vectors 4
1.8 Position Vector 5
1.9 Dot or Scalar Product 6
1.10 The Cross or Vector Product 8
1.11 Vector Calculus 9
1.12 Dimensions and Units 10
The International System (SI) 10
Solved Problems 11
Supplementary Problems 15
Chapter 2 Operations with Forces 19
2.1 The Moment of a Force 19
2.2 A Couple 21
2.3 Replacing a Single Force 22
2.4 Coplanar Force Systems 23
2.5 Notes 24
Solved Problems 24
Supplementary Problems 29
Chapter 3 Resultants of Coplanar Force Systems 33
3.1 Coplanar Forces 33
3.2 Concurrent System 33
3.3 Parallel System 34
3.4 Nonconcurrent, Nonparallel System 34
3.5 Resultants of Distributed Force Systems 35
Solved Problems 36
Supplementary Problems 45
Chapter 4 Resultants of Noncoplanar Force Systems 55
4.1 Noncoplanar Force Systems 55
4.2 Concurrent System 55
4.3 Parallel System 56
vii
00_Potter-Statics_FM_i-xii.indd 7 07/08/20 5:53 PM
viii Contents
4.4 Nonconcurrent, Nonparallel System 57
Solved Problems 59
Supplementary Problems 64
Chapter 5 Equilibrium of Coplanar Force Systems 69
5.1 Equilibrium of a Coplanar Force System 69
5.2 Two-Force Members 69
5.3 Concurrent Systems 70
5.4 Parallel Systems 71
5.5 Nonconcurrent, Nonparallel Systems 71
5.6 Remarks—Free-Body Diagrams 72
Solved Problems 73
Supplementary Problems 84
Chapter 6 Equilibrium of Noncoplanar Force Systems 103
6.1 Equilibrium of a Noncoplanar Force System 103
6.2 Concurrent Systems 103
6.3 Parallel Systems 104
6.4 Nonconcurrent, Nonparallel Systems 105
Solved Problems 106
Supplementary Problems 117
Chapter 7 Trusses and Cables 125
7.1 Trusses and Cables 125
7.2 Trusses 125
7.2.1 Method of Joints 125
7.2.2 Method of Sections 126
7.3 Cables 127
7.3.1 Parabolic 127
7.3.2 Catenary 128
Solved Problems 129
Supplementary Problems 138
Chapter 8 Forces in Beams 149
8.1 Beams 149
8.2 Shear and Moment 149
8.3 The Shear Diagram 151
8.4 The Moment Diagram 152
Solved Problems 153
Supplementary Problems 158
Chapter 9 Friction 163
9.1 General Concepts 163
9.2 Laws of Friction 164
9.3 Belt Friction and Brake Bands 164
9.4 Rolling Resistance 165
9.5 Jackscrew 166
Solved Problems 167
Supplementary Problems 179
00_Potter-Statics_FM_i-xii.indd 8 07/08/20 5:53 PM
Contents ix
Chapter 10 Virtual Work 197
10.1 Virtual Displacement and Virtual Work 197
10.2 Equilibrium 197
10.3 Stable Equilibrium 197
10.4 Unstable Equilibrium 198
10.5 Neutral Equilibrium 198
10.6 Summary of Equilibrium 199
Solved Problems 199
Supplementary Problems 207
Chapter 11 First Moments and Centroids 211
11.1 Centroid of an Assemblage 211
11.2 Centroid of a Continuous Quantity 211
11.3 Theorems of Pappus and Guldinus 212
11.4 Center of Pressure 213
Solved Problems 213
Supplementary Problems 229
Chapter 12 Moments of Inertia 245
12.1 Moment of Inertia of an Area 245
12.2 Polar Moment of Inertia of an Area 245
12.3 Product of Inertia of an Area 246
12.4 Parallel Axis Theorem 246
12.5 Composite Area 247
12.6 Rotated Set of Axes 247
12.7 Mohr’s Circle 247
12.8 Moment of Inertia of a Mass 247
12.9 Product of Inertia of a Mass 248
12.10 Parallel Axis Theorem for a Mass 249
12.11 Composite Mass 249
Solved Problems 252
Supplementary Problems 275
Practice Final Exam 285
Appendix A SI Units 293
Appendix B First Moments and Centroids 297
Appendix C Moments of Inertia of Areas and Masses 301
Index 303
*The video icon next to an exercise indicates that the exercise is also available as a video with step-by-step instructions.
These videos are available on the Schaums.com website by following the instructions on the inside front cover.
00_Potter-Statics_FM_i-xii.indd 9 12/09/20 1:35 PM