Structural AnalySiS SkillS For Practice
Structural Analysis:Skills for PracticeJames H. Hanson, PhD, PERose-Hulman InstituteofTechnology221 River Street, Hoboken NJ 07030A01 HANS8789 01 SE FM.indd 102/11/18 8:58 PM
Senior Vice President Courseware Portfolio Management:Engineering, Computer Science, Mathematics, Statistics,and Global Editions: Marcia J. HortonDirector, Portfolio Manager: Engineering, ComputerScience, and Global Editions: Julian PartridgeExecutive Portfolio Manager: Holly StarkPortfolio Management Assistant: Amanda PerfitManaging Producer, ECS and Mathematics: Scott DisannoSenior Content Producer: Erin AultProject Manager: Rose KernanManager, Rights and Permissions: Ben FerriniOperations Specialist: Maura Zaldivar-GarciaInventory Manager: Bruce BoundyProduct Marketing Manager: Yvonne VannattaField Marketing Manager: Demetrius HallMarketing Assistant: Jon BryantCover Design: Black Horse DesignsCover Image: Thomas Kelley/AlamyComposition: Integra Publishing ServicesCover Printer: Phoenix Color/HagerstownPrinter/Binder: Lake Side Communications, Inc. (LSC)Typeface: TimesTenLTStd 10/12Copyright 2020 Pearson Education, Inc., Hoboken, NJ 07030. All rights reserved. Manufactured in the United States ofAmerica. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibitedreproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying,recording, or otherwise. For information regarding permissions, request forms and the appropriate contacts within the PearsonEducation Global Rights & Permissions department, please visit www.pearsoned.com/permissions/.Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial capsor all caps.The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development,research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty ofany kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing,performance, or use of these programs.Library of Congress Cataloging-in-Publication DataNames: Hanson, James H., author.Title: Structural analysis : skills for practice / James H. Hanson, PhD, PE,Rose-Hulman Institute of Technology.Description: First edition. Pearson, [2019] Includesbibliographical references and index.Identifiers: LCCN 2018028853 ISBN 9780133128789 ISBN 0133128784Subjects: LCSH: Structural analysis (Engineering)Classification: LCC TA645 .H374 2019 DDC 624.1/7—dc23LC record available at https://lccn.loc.gov/2018028853ISBN 10:0-13-312878-4ISBN 13: 978-0-13-312878-9A01 HANS8789 01 SE FM.indd 202/11/18 8:58 PM
ContentsPreface ixMotivation for a New Text ixHomework Problems and Example Structure xi01Evaluating Results 1Loads and Structure Idealization 21.1 Loads 41.2 Load Combinations 111.3 Structure Idealization 281.4 Application of Gravity Loads 351.5 Application of Lateral Loads 491.6 Distribution of Lateral Loads by Flexible Diaphragm 59Homework Problems 672Predicting Results 823Cables and Arches 1184Internal Force Diagrams 1705Deformations 2346Influence Lines 2962.1 Qualitative Truss Analysis 842.2 Principle of Superposition 942.3 Bounding the Solution 982.4 Approximating Loading Conditions 102Homework Problems 1093.1 Cables with Point Loads 1203.2 Cables with Uniform Loads 1403.3 Arches 152Homework Problems 1634.1 Internal Forces by Integration 1724.2 Constructing Diagrams by Deduction 1924.3 Diagrams for Frames 205Homework Problems 2165.1 Double Integration Method 2365.2 Conjugate Beam Method 2475.3 Virtual Work Method 257Homework Problems 2776.1 The Table-of-Points Method 2986.2 The Müller-Breslau Method 3126.3 Using Influence Lines 322Homework Problems 329iiiA01 HANS8789 01 SE FM.indd 302/11/18 8:58 PM
7Introduction to Computer Aided Analysis 3368Approximate Analysis of Indeterminate Trussesand Braced Frames 3727.1 Computer Results Are Always Wrong 3387.2 Identifying Mistakes 3407.3 Checking Fundamental Principles 3427.4 Checking Features of the Solution 350Homework Problems 3598.1 Indeterminate Trusses 3748.2 Braced Frames with Lateral Loads 3848.3 Braced Frames with Gravity Loads 401Homework Problems 4179Approximate Analysis of Rigid Frames 4369.1 Gravity Load Method 4389.2 Portal Method for Lateral Loads 4589.3 Cantilever Method for Lateral Loads 4739.4 Combined Gravity and Lateral Loads 490Homework Problems 49710 Approximate Lateral Displacements 51410.1 Braced Frames—Story Drift Method 51610.2 Braced Frames—Virtual Work Method 52610.3 Rigid Frames—Stiff Beam Method 54210.4 Rigid Frames—Virtual Work Method 55010.5 Solid Walls—Single Story 56510.6 Solid Walls—Multistory 575Homework Problems 58311 Diaphragms 61611.1 Distribution of Lateral Loads by Rigid Diaphragm 61811.2 In Plane Shear: Collector Beams 63311.3 In Plane Moment: Diaphragm Chords 645Homework Problems 66112 Force Method 67412.1 One Degree Indeterminate Beams 67612.2 Multi-Degree Indeterminate Beams 69112.3 Indeterminate Trusses 699Homework Problems 71113 Moment Distribution Method 72613.1 Overview of Method 72813.2 Fixed-End Moments and Distribution Factors 73013.3 Beams and Sidesway Inhibited Frames 73413.4 Sidesway Frames 754Homework Problems 777ivA01 HANS8789 01 SE FM.indd 402/11/18 8:58 PM
14 Direct Stiffness Method for Trusses 79214.1 Overview of Method 79414.2 Transformation and Element Stiffness Matrices 79514.3 Compiling the System of Equations 80714.4 Finding Deformations, Reactions, and Internal Forces 81514.5 Additional Loadings 827Homework Problems 84115 Direct Stiffness Method for Frames 85415.1 Element Stiffness Matrix in Local Coordinates 85615.2 Element Stiffness Matrix in Global Coordinates 86215.3 Loads Between Nodes 86815.4 Finding Deformations, Reactions, and Internal Forces 877Homework Problems 886Index900vA01 HANS8789 01 SE FM.indd 502/11/18 8:58 PM
Combine this.viA01 HANS8789 01 SE FM.indd 602/11/18 8:58 PM
With the Power of Mastering Engineering forStructural Analysis: Skills for PracticeMasteringTM is the teaching and learning platform that empowers every student.By combining trusted authors’ content with digital tools developed to engage students andemulate the office hours experience, Mastering personalizes learning and improves resultsfor each student.Empower each learnerEach student learns at a different pace. Personalized learning, including optional hints andwrong-answer feedback, pinpoints the precise areas where each student needs practice, givingall students the support they need — when and where they need it — to be successful.Learn more at www.pearson.com/mastering/engineeringviiA01 HANS8789 01 SE FM.indd 702/11/18 8:58 PM
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PrefaceMotivation for a New TextLet’s be realistic, most structural analysis performed in practice is done ona computer. So why do we need another text on how to perform a nalysisby hand? Because most structural analysis is performed using a computer.That might sound like circular logic, but think about it for a moment. A texton hand methods for structural analysis should be focused on skills neededto complement computer aided analysis, and I couldn’t find one of those.If you ask experienced engineers, there are three practical reasonsfor performing hand calculations: 1) some problems are faster to solveby hand than by computer, 2) hand methods can be more efficient in thepreliminary design phase where we don’t yet know the member properties, and 3) hand methods make up many of the tools practitioners use forevaluating detailed analysis results. The topics in this text were carefullychosen to support these three purposes. That meant developing severalchapters dedicated to skills used by experienced engineers but not foundin other textbooks (e.g., approximate analysis of braced frames, approximating drift, analysis of rigid diaphragms).Yes, computers have made it possible for us to design structures thatcould not have been designed before. Nevertheless, even today moststructures could still be designed by hand. It is the increase in efficiencythat makes computers indispensable in the modern design process. Withthat increased efficiency, however, also comes the ability to make errorsfaster than ever before. Therefore, it is especially important that new engineers learn the skills for and develop the habit of evaluating the reasonableness of structural analysis results.The evaluation skills presented in this text are the result of a ten yearproject to gather experience from practicing structural engineers and incorporate it in the classroom based on principles from cognitive science.Students following a traditional curriculum and practitioners both tookan exam to measure their ability to identify the most reasonable answerand explain why. As expected, practitioners outperformed the students.With the curriculum presented in this text, however, students performedmuch better on the exam than students following the traditional curriculum. In fact, they cut the gap with practitioners in half.The curriculum in this text emphasizes developing intuition for reasonable answers and cultivating the habit of predicting results. Intuitionallows experienced practitioners to know if a result is not reasonablewithout giving it conscious thought. The fastest way to develop intuitionis to practice evaluation skills routinely and to reflect on the thought process we used. That reflection is called metacognition and is fostered inmost of the homework problems in this text. Expert evaluators of resultswill tell you that they start by predicting results. There are important reasons from cognitive psychology for why it should be in that order, so predicting results before performing detailed analysis is a routine part of theA01 HANS8789 01 SE FM.indd 9ix02/11/18 8:58 PM
homework and example problems in this text. These skills and habits arevaluable not only for students going on to practice structural engineering,but for our students going into any field of engineering.So while developing a new text, why not address other issues studentsbring up about their structural analysis textbooks and courses. One suchissue is not seeing how the theory connects with the real world. It is difficult for someone new to structural engineering to make the connectionbetween stick figures on a page and real structures they see in the world.To help students make this connection, every example and homeworkproblem is based on a real-world structure with a scenario motivating therequested analysis.Another issue is the amount of detail in the examples. Students learna lot by reviewing worked examples and reflecting on why each stepis taken. To help in that learning, the examples in this text carry unitsthroughout all calculations and the examples don’t skip steps. In addition, the calculations are augmented with comments explaining why different steps were performed and what the results mean.OrganizationEach chapter begins with Motivation: a brief description of why the topics in that chapter are important to practice structural engineering. Mostof the sections within the chapters are organized with the following format: Introduction, How-To, Section Highlights (boxed and shaded for easyidentification), and Example Problems (boxed for easy identification). Thehomework problems are grouped at the end of each chapter and are easilyidentified by a ribbon down the side of the page.Homework Problems and Example StructureThe homework format is another product of the ten year study. Thehomework problems are structured to achieve three goals: 1) developintuition, 2) practice the concept, and 3) accurately evaluate results.Most homework problems begin with students making a guess aboutsome part of the solution in order to promote development of intuition.It is important to the development process that students make a guesswithout fear of being wrong. Therefore, this part should be graded basedon whether it was done or not. If students believe that the quality of theguess will impact their score, they will wait until after they have generated a solution before writing down their guess.The middle part of each homework problem emphasizes applicationof the concepts covered in that section of the text. This is the traditionalhand calculation portion.Since many of the hand methods in this text are useful for evaluating computer analysis results, homework problems for about half of thechapters also require that the student calculate the result using structuralanalysis software. The student is asked to verify fundamental principlesfor their result (i.e., all equations of equilibrium are satisfied) and f eaturesof the graphical solution (e.g., segment of constant shear diagram valuewhere there is no applied load).xA01 HANS8789 01 SE FM.indd 1002/11/18 8:58 PM
The student is then asked to make a comprehensive argument thatthe computer analysis results are reasonable. For full credit, the studentshould use all of the previous parts of the homework problem (exceptthe guess) to demonstrate that the computer results are reasonable:hand solution(s), verification of fundamental principles, and verificationof features of the graphical solution. In this argument the hand solutionpart of the homework might have used an approximate analysis method.In those cases, the student should recognize that the hand and computersolutions should not match perfectly. The student will need to decidewhether the difference is acceptable or not.Grading AdviceEach problem that starts with an initial guess ends with reflection onthat guess. The student is asked to compare the initial guess with thecomputer results and reflect on why the two are similar or different.Again, if the instructor wants to successfully promote developmentof intuition, the students must feel that there is no disadvantage tohaving an initial guess that does not match the computer result. Anexample rubric that can be used to score this reflection is shown in thefollowing table:Full Credit (10)Adequate (7)Marginal (5)Unacceptable (0)If the guessand solutiongenerallymatch:Explains how previous experienceand/or fundamental principles ledto a guess thatmatched.Identifies previousexperienced and/orfundamental principles that guided theguess.Attempts to explain whythe guess matched the solution, but shows little understanding of pertinent fundamental principles and/orfeatures of the solution.No demonstrationof understanding of why theguess matched thesolution.If the guessand solutiongenerally donot match:Explains why guessdoes not matchbased on previousexperience and/or fundamentalprinciples.Identifies fundamental principles and/or features of thesolution that could beused to explain thedifference.Attempts to explain thedifference, but shows littleunderstanding of pertinentfundamental principlesand/or features of thesolution.No demonstrationof understandingof why the guessdid not match thesolution.Examples of how to apply the rubric to score student reflections are alsoavailable.Using Structural Analysis SoftwareThis text is not based on the use of a specific structural analysis softwareprogram. Any structural analysis program that can model 2D trusses andframes will be sufficient. Note that in order to model braced frames, theprogram must allow specification of pinned connections in an otherwiserigid frame.xiA01 HANS8789 01 SE FM.indd 1102/11/18 8:58 PM
If students do not already have access to structural analysis software,they can obtain free software via the internet. For example, basic use ofthe program MASTAN2 can be taught in a single lecture. The program isavailable for free download from the following website:www.mastan2.comInstructor ResourcesThe single objective of this text is to prepare your students with skills andhabits for the practice of engineering, regardless of the specialty. Trustthe process. Do all the steps. The organization of the example and homework problems is based on how experienced engineers approach analysisand is supported by cognitive science.All instructor resources are available for download at www.pearsonhighered.com. If you are in need of a login and password for this site,please contact your local Pearson representative.Mastering EngineeringThis online tutorial and assessment program allows you to integratedynamic homework with automated grading of the calculation parts ofproblems and personalized feedback. MasteringTM Engineering allowsyou to easily track the performance of your entire class on an assignmentby-assignment basis, or the detailed work of an individual student. Formore information visit www.masteringengineering.com.Instructor Solutions ManualFully worked-out solutions to the homework problems.PowerPoint Lecture ImagesAll figures from the text are available in PowerPoint for your lecture needs. These are used to give students real visual examples of thephenomena.Learning CatalyticsThis “bring your own device” student engagement, assessment and classroom intelligence system enables you to measure student learning during class, and adjust your lectures accordingly. A wide variety of questionand answer types allows you to author your own questions, or you can usequestions already authored into the system. For more information visitwww.learningcatalytics.com or click on the Learning Catalytics link insideMastering Engineering.Prerequisite CoursesThis text is constructed assuming that students have already completedstatics and mechanics of materials courses; therefore, topics such as determinate truss analysis have been omitted.xiiA01 HANS8789 01 SE FM.indd 1202/11/18 8:58 PM
AcknowledgmentsI am blessed to be able to share this approach to teaching structural analysis with you. The old phrase “It takes a village” is so true. All of mystudents over the years have inspired me and helped me in creating thistext. I greatly appreciate their hard work and feedback. My colleaguesin Civil and Environmental Engineering at Rose-Hulman have been extremely supportive of me as I focused on making this available to you.There is nothing we won’t do for each other to provide a better studentexperience.The approach to structural analysis and verification of results uniqueto this text is a direct result of what I learned from interviews with dozensof experienced structural engineers. Their passion and input really madethis text about skills for practice.The team that Pearson assembled to help me in this process has beenstellar. Their unified focus has been to bring my vision to life in order tohelp you. Part of that team is faculty reviewers, and their feedback madethis text so much better. Some of them want to remain anonymous, butothers agreed to allow me to thank them publicly: Bechara Abboud, Temple UniversityTomasz Arciszewski, George Mason UniversityMikhail Gershfeld, California State Polytechnic UniversityThomas H. Miller, Oregon State UniversityGokhan Pekcan, University of Nevada – RenoHayder A. Rasheed, Kansas State UniversityHung-Liang (Roger) Chen, West Virginia UniversityHusam Najm, Rutgers UniversitySteven Vukazich, San Jose State UniversityThis text doesn’t happen without the support of my friends and family, especially the love of my life Diane. Because they believe in sharingmy passion with you, they sacrificed and encouraged me. For example,all of the photos in this text were tak
9 Approximate Analysis of Rigid Frames 436 9.1 Gravity Load Method 438 9.2 Portal Method for Lateral Loads 458 9.3 Cantilever Method for Lateral Loads 473 9.4 Combined Gravity and Lateral Loads 490 Homework Problems 497 10 Approximate Lateral Displacements 514 10.1 Braced Frames—Story Drift Method 516
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