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Butterworth-Heinemann is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA Linacre House, Jordan Hill, Oxford OX2 8DP, UK Copyright © 2009, International Codes Council. All rights reserved. ALL RIGHTS RESERVED. This Structural Analysis: In Theory and Practice is a copyrighted work owned by the International Code Council, Inc. Without advance permission from the copyright owner, no part of this book may be reproduced, distributed, or transmitted in any form or by any means, including without limitation, electronic, optical or mechanical means (by way of example and not limitation, photocopying, or recording by or in an information storage retrieval system). For information on permission to copy material exceeding fair use, please contact Publications, 4051 West Flossmoor Road, Country Club hills, IL 60478-5795. Phone 1-888-ICC-SAFE (422-7233) Trademarks: “International Code Council,” and the “International Code Council” logo are trademarks of the International Code Council, Inc. Library of Congress Cataloging-in-Publication Data Application submitted British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN: 978-1-85617-550-0 For information on all Butterworth–Heinemann publications visit our Web site at www.elsevierdirect.com Printed in the United States of America 08 09 10 11 12 10 9 8 7 6 5 4 3 2 1 Foreword It is with great pleasure that I write this foreword to Structural Analysis: In Theory and Practice, by Alan Williams. Like many other engineers, I have uti- lized Dr. Williams ’ numerous publications through the years and have found them to be extremely useful. This publication is no exception, given the extensive experience and expertise of Dr. Williams in this area, the credibil- ity of Elsevier with expertise in technical publications internationally, and the International Code Council (ICC) with expertise in structural engineering and building code publications. Engineers at all levels of their careers will find the determinate and indeter- minate analysis methods in the book presented in a clear, concise, and practical manner. I am a strong advocate of all of these attributes, and I am certain that the book will be successful because of them. Coverage of many other impor- tant areas of structural analysis, such as Plastic Design, Matrix and Computer Methods, Elastic-Plastic Analysis, and the numerous worked-out sample prob- lems and the answers to the supplementary problems greatly enhance and rein- force the overall learning experience. One may ask why, in this age of high-powered computer programs, a com- prehensive book on structural analysis is needed. The software does all of the work for us, so isn't it sufficient to read the user’s guide to the software or to have a cursory understanding of structural analysis? While there is no question that computer programs are invaluable tools that help us solve complicated problems more efficiently, it is also true that the soft- ware is only as good as the user’s level of experience and his/her knowledge of the software. A small error in the input or a misunderstanding of the limita- tions of the software can result in completely meaningless output, which can lead to an unsafe design with potentially unacceptable consequences. That is why this book is so valuable. It teaches the fundamentals of struc- tural analysis, which I believe are becoming lost in structural engineering. Having a solid foundation in the fundamentals of analysis enables engineers to understand the behavior of structures and to recognize when output from a computer program does not make sense. Simply put, students will become better students and engineers will become better engineers as a result of this book. It will not only give you a better understanding of structural analysis; it will make you more proficient and efficient in your day-to-day work. David A. Fanella, Ph.D., S.E., P.E. Chicago, IL March 2008 Part One Analysis of Determinate Structures 1 Principles of statics Notation F force fi angle in a triangle opposite side Fi H horizontal force l length of member M bending moment P axial force in a member R support reaction V vertical force WLL concentrated live load wDL distributed dead load θ angle of inclination 1.1 Introduction Statics consists of the study of structures that are at rest under equilibrium conditions. To ensure equilibrium, the forces acting on a structure must bal- ance, and there must be no net torque acting on the structure. The principles of statics provide the means to analyze and determine the internal and external forces acting on a structure. For planar structures, three equations of equilibrium are available for the determination of external and internal forces. A statically determinate struc- ture is one in which all the unknown member forces and external reactions may be determined by applying the equations of equilibrium. An indeterminate or redundant structure is one that possesses more unknown member forces or reactions than the available equations of equilib- rium. These additional forces or reactions are termed redundants. To determine the redundants, additional equations must be obtained from conditions of geo- metrical compatibility. The redundants may be removed from the structure, and a stable, determinate structure remains, which is known as the cut-back structure. External redundants are redundants that exist among the external reactions. Internal redundants are redundants that exist among the member forces. 4 Structural Analysis: In Theory and Practice 1.2 Representation of forces A force is an action that tends to maintain or change the position of a struc- ture. The forces acting on a structure are the applied loads, consisting of both dead and imposed loads, and support reactions. As shown in Figure 1.1 , the simply supported beam is loaded with an imposed load WLL located at point 3 and with its own weight wDL, which is uniformly distributed over the length of the beam. The support reactions consist of the two vertical forces located at the ends of the beam. The lines of action of all forces on the beam are parallel. WLL wDL 12 3 Figure 1.1 In general, a force may be represented by a vector quantity having a magni- tude, location, sense, and direction corresponding to the force. A vector repre- sents a force to scale, such as a line segment with the same line of action as the force and with an arrowhead to indicate direction. The point of application of a force along its line of action does not affect the equilibrium of a structure. However, as shown in the three-hinged portal frame in Figure 1.2 , changing the point of application may alter the internal forces in the individual members of the structure. 100 kips 100 kips 75 kips 25 kips 25 kips 75 kips 50 kips 50 kips 50 kips 50 kips (i) (ii) Figure 1.2 Collinear forces are forces acting along the same line of action. The two hor- izontal forces acting on the portal frame shown in Figure 1.3 (i) are collinear and may be added to give the single resultant force shown in (ii). Principles of statics 5 50 kips 20 kips 30 kips 2323 1 41 4 (i) (ii) Figure 1.3 Forces acting in one plane are coplanar forces. Space structures are three- dimensional structures and, as shown in Figure 1.4 , may be acted on by non- coplanar forces. Figure 1.4 In a concurrent force system, the line of action of all forces has a common point of intersection. As shown in Figure 1.5 for equilibrium of the two-hinged arch, the two reactions and the applied load are concurrent. Figure 1.5 6 Structural Analysis: In Theory and Practice It is often convenient to resolve a force into two concurrent components. The original force then represents the resultant of the two components. The direc- tions adopted for the resolved forces are typically the x- and y-components in a rectangular coordinate system. As shown in Figure 1.6 , the applied force F on the arch is resolved into the two rectangular components: sHFϭ co θ ϭ θ VFsin F V θ H Figure 1.6 The moment acting at a given point in a structure is given by the product of the applied force and the perpendicular distance of the line of action of the force from the given point. As shown in Figure 1.7 , the force F at the free end of the cantilever produces a bending moment, which increases linearly along the length of the cantilever, reaching a maximum value at the fixed end of: ϭ MFl The force system shown at (i) may also be replaced by either of the force systems shown at (ii) and (iii). The support reactions are omitted from the fig- ures for clarity. l FFF F Forces ϭϭ 11222 1 F M Fl Moment Fl Fl Fl (i) (ii) (iii) Figure 1.7 Principles of statics 7 1.3 Conditions of equilibrium In order to apply the principles of statics to a structural system, the structure must be at rest. This is achieved when the sum of the applied loads and sup- port reactions is zero and there is no resultant couple at any point in the struc- ture. For this situation, all component parts of the structural system are also in equilibrium. A structure is in equilibrium with a system of applied loads when the result- ant force in any direction and the resultant moment about any point are zero. For a system of coplanar forces this may be expressed by the three equations of static equilibrium: ∑ H ϭ 0 ∑V ϭ 0 ∑ ϭ M 0 where H and V are the resolved components in the horizontal and vertical directions of a force and M is the moment of a force about any point.
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