Engineering Statics Engineering Statics M. Rashad Islam Colorado State University – Pueblo Md Abdullah Al Faruque Rochester Institute of Technology Bahar Zoghi State University of New York – Farmingdale Sylvester A. Kalevela Colorado State University – Pueblo First edition published 2021 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN © 2021 Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, LLC Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Library of Congress Cataloging-in-Publication Data Names: Islam, M. Rashad, author. | Al Faruque, Md Abdullah, author. | Zoghi, Bahar, author. | Kalevela, Sylvester A., author. Title: Engineering statics/M. Rashad Islam, Colorado State University Pueblo, Md Abdullah Al Faruque, Rochester Institute of Technology, Bahar Zoghi, State University of New York--Farmingdale, Sylvester A. Kalevela, Colorado State University Pueblo. Description: First edition. | Boca Raton: CRC Press, 2021. | Includes bibliographical references and index. Identifiers: LCCN 2020020323 (print) | LCCN 2020020324 (ebook) | ISBN 9780367561062 (hardback) | ISBN 9781003098157 (ebook) Subjects: LCSH: Statics. Classification: LCC TA351 .I85 2021 (print) | LCC TA351 (ebook) | DDC 620.1/053--dc23 LC record available at https://lccn.loc.gov/2020020323 LC ebook record available at https://lccn.loc.gov/2020020324 ISBN: 978-0-367-56106-2 (hbk) ISBN: 978-1-003-09815-7 (ebk) Typeset in Computer Modern font by KnowledgeWorks Global Ltd. Contents Preface ................................................................................................................................ ix About the Authors ..............................................................................................................xi Chapter 1 Introduction ......................................................................................................1 1.1 Mechanics ...............................................................................................1 1.2 Principles of Mechanics ..........................................................................1 1.3 Basic Quantities ......................................................................................3 1.4 Basics of Units ........................................................................................3 1.4.1 Types of Units .............................................................................3 1.4.2 Unit Systems ...............................................................................4 1.5 Rounding Off ..........................................................................................6 1.6 Support Types .........................................................................................7 1.7 Loading Types ......................................................................................10 1.8 Beam Types ..........................................................................................13 1.9 Engineering Practice ............................................................................13 Chapter 2 Coplanar Force Systems .................................................................................15 2.1 General .................................................................................................15 2.2 Concurrent Forces.................................................................................17 2.2.1 Two-Force Systems ...................................................................17 2.2.2 More Than Two-Force Systems ................................................23 2.3 Non-concurrent Forces .........................................................................29 2.3.1 Centroid ....................................................................................29 2.3.2 Moment .....................................................................................30 2.3.3 Loads and Resultant .................................................................31 Practice Problems...........................................................................................35 Chapter 3 Equilibrium of Particle and Rigid Body .........................................................41 3.1 Concept of Equilibrium ........................................................................41 3.2 Particle versus Rigid Body ...................................................................41 3.3 Idealization of Structures ......................................................................41 3.4 Free-Body Diagrams ............................................................................43 3.5 Application of Equilibrium Equations to Particles ...............................45 3.6 Application of Equilibrium Equations to Rigid Bodies ........................59 Practice Problems...........................................................................................79 Chapter 4 Trusses ............................................................................................................95 4.1 Truss Structure .....................................................................................95 4.2 Zero-Force Members ............................................................................97 v vi Contents 4.3 Direct-Force Members ..........................................................................99 4.4 Method of Joints .................................................................................100 4.5 Method of Sections .............................................................................106 4.6 Determinacy and Stability ..................................................................116 Practice Problems.........................................................................................119 Chapter 5 Arches, Cables and Pulleys ..........................................................................127 5.1 General ...............................................................................................127 5.2 Arches .................................................................................................127 5.3 Cables .................................................................................................134 5.3.1 Uniformly Loaded Cable ........................................................135 5.3.2 Non-Uniformly Loaded Cable ................................................138 5.4 Pulleys ................................................................................................144 Practice Problems.........................................................................................150 Chapter 6 Frame Structures ..........................................................................................155 6.1 Truss Versus Frame ............................................................................155 6.2 Frame Analysis ...................................................................................155 Practice Problems.........................................................................................167 Chapter 7 Axial Force, Shear Force and Bending Moment in Beams ..........................171 7.1 Internal Reactions ...............................................................................171 7.2 Internal Reactions Diagrams ..............................................................178 Practice problems .........................................................................................189 Chapter 8 Space Force Systems ....................................................................................195 8.1 General ...............................................................................................195 8.2 Vector Method ....................................................................................195 8.2.1 Scalars versus Vectors ............................................................195 8.2.2 Vector Representation .............................................................195 8.2.3 Position Vector ........................................................................197 8.3 Vector Products...................................................................................202 8.4 Projection of Vector ............................................................................202 8.5 Resultant of Vectors ............................................................................203 Practice Problems.........................................................................................212 Chapter 9 Centroids of Area ......................................................................................... 217 9.1 Centroids ............................................................................................. 217 9.2 Centroid of Regular Areas ..................................................................217 9.3 Centroid of Composite Areas ............................................................. 217 9.4 Centroid of Irregular Areas ................................................................225 9.4.1 Centroid of Rectangle .............................................................226 Contents vii 9.4.2 Centroid of Triangle ..............................................................227 9.4.3 Centroid of Quarter Circle ....................................................228 9.4.4 Centroid of an Irregular Section ...........................................231 Practice Problems.......................................................................................233 Chapter 10 Moment of Inertia of Area ..........................................................................239 10.1 Moment of Inertia ............................................................................239 10.2 Radius of Gyration and Section Modulus ....................................... 240 10.3 Moment of Inertia of Common Sections ..........................................241 10.4 Moment of Inertia of Composite Sections .......................................243 10.5 Parallel Axis Theorem for Moment of Inertia ................................ 244 10.6 Moment of Inertia of Irregular Areas ..............................................260 10.6.1 The Moment of Inertia of a Rectangle.................................261 10.6.2 The Moment of Inertia of an Irregular Section ....................261 Practice Problems .....................................................................................263 Chapter 11 Friction........................................................................................................269 11.1 Static and Kinetic Frictions ................................................................269 11.2 Friction in Wedges ..............................................................................274 11.3 Belt Friction ........................................................................................280 Practice Problems .......................................................................................284 Index ................................................................................................................................293 Preface This textbook is intended for engineering and applied engineering undergraduate students of subjects such as civil engineering, mechanical engineering, civil engineering technol­ ogy, mechanical engineering technology, architecture, construction engineering, construc­ tion management, etc. It is also suitable for applied science students who are pursuing a two-year degree with or without the intention to transfer to four-year-degree programs. The cutting-edge statics theory required for engineering has been described using plain text, appropriate equations, figures and worked out examples. Examples are mostly taken from the real world and are solved using step-by-step explanations. The authors believe that this text will be helpful for engineering, applied engineering and applied science students to understand and apply statics to succeed in their degree programs and careers. The authors would like to express their sincere gratitude to Rafid Shams Huq from Stamford University, Arifur Rahman from Khulna University of Engineering & Technology, Jarrett Schirmer from Colorado State University-Pueblo, for reviewing the book. The authors also thank their good friends who helped by providing photos. Students of Colorado State University, Pueblo, who helped to identify some issues during the classroom experi­ ment are acknowledged as well. The book has been thoroughly inspected with the help of professional editors to fix typos, editorial issues, and poor sentence structure. Despite this, if there is any issue, please excuse us and report it to [email protected]. Any suggestion to improve this book or any issue reported will be fixed in the next edition with proper acknowledgment. Thank you. The Authors ix