Prefacexcovered in the course, these sections are highly visible and can be easily referred to by thestudents if needed in a later course or in engineering practice. For convenience all optionalsectionshavebeenindicatedbyasterisks.ChapterOrganizationIt is expectedthat students using this text will have completed a coursein statics.However,Chap.1isdesignedtoprovidethemwithan opportunitytoreviewtheconceptslearned inthatcourse, while shear and bending-moment diagramsarecovered in detail in Secs.5.1 and 5.2.Theproperties of moments and centroids of areasaredescribed in AppendixA;thismaterialcanbeusedto reinforcethediscussion of the determination ofnormal and shearing stressesin beams (Chaps. 4, 5, and 6).The first four chapters of the text are devoted to the analysis of the stresses and of thecorresponding deformations in various structural members,considering successively axial load-ing,torsion,and purebending.Each analysis isbased ona fewbasic concepts:namely,theconditions of equilibrium of the forces exerted on the member, the relations existing betweenstress and strain in the material, and the conditions imposed by the supports and loading of themember.The study of each type of loading is complemented by a large number of conceptapplications, sample problems, and problems to be assigned, all designed to strengthen thestudents'understanding of the subject.The concept of stress at a point is introduced in Chap. 1, where it is shown that an axialload can produce shearing stresses as well as normal stresses,depending upon the sectionconsidered.Thefact that stressesdepend upontheorientationof the surfaceon whichtheyare computed is emphasized again in Chaps.3and 4 in thecases of torsion and pure bending.However, the discussion of computationaltechniques-such as Mohr's circle-used for thetransformation of stress at a point is delayed until Chap.7, after students have had the oppor-tunitytosolveproblemsinvolvingacombinationofthebasicloadingsandhavediscoveredforthemselvestheneedforsuchtechniques.Thediscussion in Chap.2 of the relation between stress and strain in various materialsincludesfiber-reinforcedcompositematerials.Also,the study of beams undertransverse loadsiscovered intwoseparatechapters.Chapter5isdevotedtothedeterminationofthenormalstresses in a beam and to the design of beams based on the allowable normal stress in thematerial used (Sec.5.3).Thechapterbegins with a discussion of the shear and bendingmomentdiagrams(Secs.5.1and5.2)andincludesanoptional sectionontheuseofsingularityfunctions for thedetermination of the shear and bendingmoment in abeam (Sec.5.4).Thechapter endswith an optional section on nonprismaticbeams (Sec.5.5)Chapter 6 is devoted to the determination of shearing stresses in beams and thin-walledmembersundertransverseloadings.Theformulaforthe shearflow,q=VQ/l,isderivedinthe traditional way. More advanced aspects of the design of beams, such as the determinationof theprincipal stresses at the junction of theflangeand web of a W-beam,are considered inChap.8,an optional chapterthatmaybecovered afterthetransformations of stresseshavebeen discussed in Chap.7.The design oftransmission shafts is inthat chapterfor thesamereason, as well as the determination of stresses under combined loadings that can now includethe determination of the principal stresses, principal planes, and maximum shearing stress atagivenpoint.Statically indeterminate problems are first discussed in Chap.2 and considered through-outthetextforthevarious loadingconditions encountered.Thus,studentsarepresented atanearly stagewith amethod of solutionthat combines the analysis of deformations with theconventional analysis of forces used in statics.In this way,theywill have becomethoroughlyfamiliar with this fundamental method by the end of the course. In addition, this approachhelps the students realizethatstressesthemselves are staticallyindeterminateand can becom-puted only by considering the corresponding distribution of strains
x Preface covered in the course, these sections are highly visible and can be easily referred to by the students if needed in a later course or in engineering practice. For convenience all optional sections have been indicated by asterisks. Chapter Organization It is expected that students using this text will have completed a course in statics. However, Chap. 1 is designed to provide them with an opportunity to review the concepts learned in that course, while shear and bending-moment diagrams are covered in detail in Secs. 5.1 and 5.2. The properties of moments and centroids of areas are described in Appendix A; this material can be used to reinforce the discussion of the determination of normal and shearing stresses in beams (Chaps. 4, 5, and 6). The first four chapters of the text are devoted to the analysis of the stresses and of the corresponding deformations in various structural members, considering successively axial loading, torsion, and pure bending. Each analysis is based on a few basic concepts: namely, the conditions of equilibrium of the forces exerted on the member, the relations existing between stress and strain in the material, and the conditions imposed by the supports and loading of the member. The study of each type of loading is complemented by a large number of concept applications, sample problems, and problems to be assigned, all designed to strengthen the students’ understanding of the subject. The concept of stress at a point is introduced in Chap. 1, where it is shown that an axial load can produce shearing stresses as well as normal stresses, depending upon the section considered. The fact that stresses depend upon the orientation of the surface on which they are computed is emphasized again in Chaps. 3 and 4 in the cases of torsion and pure bending. However, the discussion of computational techniques—such as Mohr’s circle—used for the transformation of stress at a point is delayed until Chap. 7, after students have had the opportunity to solve problems involving a combination of the basic loadings and have discovered for themselves the need for such techniques. The discussion in Chap. 2 of the relation between stress and strain in various materials includes fiber-reinforced composite materials. Also, the study of beams under transverse loads is covered in two separate chapters. Chapter 5 is devoted to the determination of the normal stresses in a beam and to the design of beams based on the allowable normal stress in the material used (Sec. 5.3). The chapter begins with a discussion of the shear and bendingmoment diagrams (Secs. 5.1 and 5.2) and includes an optional section on the use of singularity functions for the determination of the shear and bending moment in a beam (Sec. 5.4). The chapter ends with an optional section on nonprismatic beams (Sec. 5.5). Chapter 6 is devoted to the determination of shearing stresses in beams and thin-walled members under transverse loadings. The formula for the shear flow, q 5 VQyI, is derived in the traditional way. More advanced aspects of the design of beams, such as the determination of the principal stresses at the junction of the flange and web of a W-beam, are considered in Chap. 8, an optional chapter that may be covered after the transformations of stresses have been discussed in Chap. 7. The design of transmission shafts is in that chapter for the same reason, as well as the determination of stresses under combined loadings that can now include the determination of the principal stresses, principal planes, and maximum shearing stress at a given point. Statically indeterminate problems are first discussed in Chap. 2 and considered throughout the text for the various loading conditions encountered. Thus, students are presented at an early stage with a method of solution that combines the analysis of deformations with the conventional analysis of forces used in statics. In this way, they will have become thoroughly familiar with this fundamental method by the end of the course. In addition, this approach helps the students realize that stresses themselves are statically indeterminate and can be computed only by considering the corresponding distribution of strains. bee98233_FM_i-xvi_1.indd x 11/15/13 10:21 AM
PrefacexiThe concept of plastic deformation is introduced in Chap.2, where it is applied to theanalysisof membersunderaxialloading.Problemsinvolvingtheplasticdeformation of circular shaftsand ofprismaticbeams arealso considered in optional sections of Chaps.3,4,and6.Whilesomeofthismaterialcanbeomitted atthechoiceoftheinstructor,itsinclusioninthe body of the text will help students realize the limitations of the assumption of a linearstress-strain relation and serve to caution them against the inappropriate use of the elastictorsion and flexure formulas.The determination of the deflection of beams is discussed in Chap. 9. The first part ofthe chapter is devoted to the integration method and to the method of superposition, with anoptional section (Sec.9.3) based on the use of singularity functions. (This section should beused onlyif Sec.5.4wascoveredearlier.)Thesecondpartof Chap.9isoptional.Itpresentsthemoment-areamethodintwolessons.Chapter 10, which is devoted to columns, contains material on the design of steel, alumi-num, and wood columns.Chapter 1l covers energymethods,including Castigliano's theorem.SupplementalResources for InstructorsFind the Companion Website for Mechanics of Materials at www.mhhe.com/beerjohnston.IncludedonthewebsitearelecturePowerPoints,animagelibrary,andanimations.Onthesiteyou'll also find theInstructor's Solutions Manual (password-protected and available to instruc-tors only)that accompanies the seventh edition.The manual continues the tradition of excep-tional accuracy and normally keeps solutions contained to a single page for easier reference.The manual includes an in-depth review of the material in each chapter and houses tablesdesignedtoassist instructors in creating a scheduleofassignmentsfortheir courses.Thevarioustopics covered in the text are listed in Table I, and a suggested number of periods to be spentoneachtopicisindicated.TableIIprovidesabriefdescriptionofallgroupsofproblemsandaclassification oftheproblems in eachgroupaccordingto the unitsused.A CourseOrganizationGuide providing sample assignment schedules is also found on the website.Viathewebsite,instructors canalsorequest access to C.O.S.M.o.S.,the CompleteOnlineSolutions Manual Organization System that allows instructors to create custom homework,quizzes, and tests using end-of-chapter problems from the text.McGraw-Hill Connect Engineering provides online presentationconnectassignment, and assessment solutions.It connects your studentsENGINEERINGwiththetools and resourcesthey'll need to achieve success.WithConnect Engineering you can deliver assignments, quizzes, and tests online.A robust set ofquestions and activities are presented and aligned with the textbook's learning outcomes. Asan instructor,you can editexisting questions and author entirelynew problems.Integrategrade reports easily with Learning Management Systems (LMS), such as WebCT and Blackboard-andmuchmore.ConnectPlusEngineeringprovides students withall theadvantagesof ConnectEngineering,plus24/7onlineaccesstoamedia-richeBook,allowingseamlessintegration oftext,media, and assessments.To learn more,visitwww.mcgrawhillconnect.com.ILEARNSMARTMcGraw-Hill LearnSmartisavailable as astandaloneproduct oran integratedfeature of McGraw-Hill ConnectEngineering.It is anadap-tive learning system designed to help students learn faster, study more efficiently, and retainmoreknowledgeforgreatersuccess.LearnSmartassessesastudent'sknowledgeofcoursecon-tentthrougha series ofadaptivequestions.Itpinpoints conceptsthe studentdoesnotunder-stand and maps out a personalized studyplan for success.This innovative studytool also hasfeatures that allow instructors to see exactly what students have accomplished and a built-inassessmenttool for graded assignments.Visitthefollowing site for a demonstration.www.LearnSmartAdvantage.com
xi Preface The concept of plastic deformation is introduced in Chap. 2, where it is applied to the analysis of members under axial loading. Problems involving the plastic deformation of circular shafts and of prismatic beams are also considered in optional sections of Chaps. 3, 4, and 6. While some of this material can be omitted at the choice of the instructor, its inclusion in the body of the text will help students realize the limitations of the assumption of a linear stress-strain relation and serve to caution them against the inappropriate use of the elastic torsion and flexure formulas. The determination of the deflection of beams is discussed in Chap. 9. The first part of the chapter is devoted to the integration method and to the method of superposition, with an optional section (Sec. 9.3) based on the use of singularity functions. (This section should be used only if Sec. 5.4 was covered earlier.) The second part of Chap. 9 is optional. It presents the moment-area method in two lessons. Chapter 10, which is devoted to columns, contains material on the design of steel, aluminum, and wood columns. Chapter 11 covers energy methods, including Castigliano’s theorem. Supplemental Resources for Instructors Find the Companion Website for Mechanics of Materials at www.mhhe.com/beerjohnston. Included on the website are lecture PowerPoints, an image library, and animations. On the site you’ll also find the Instructor’s Solutions Manual (password-protected and available to instructors only) that accompanies the seventh edition. The manual continues the tradition of exceptional accuracy and normally keeps solutions contained to a single page for easier reference. The manual includes an in-depth review of the material in each chapter and houses tables designed to assist instructors in creating a schedule of assignments for their courses. The various topics covered in the text are listed in Table I, and a suggested number of periods to be spent on each topic is indicated. Table II provides a brief description of all groups of problems and a classification of the problems in each group according to the units used. A Course Organization Guide providing sample assignment schedules is also found on the website. Via the website, instructors can also request access to C.O.S.M.O.S., the Complete Online Solutions Manual Organization System that allows instructors to create custom homework, quizzes, and tests using end-of-chapter problems from the text. McGraw-Hill Connect Engineering provides online presentation, assignment, and assessment solutions. It connects your students with the tools and resources they’ll need to achieve success. With Connect Engineering you can deliver assignments, quizzes, and tests online. A robust set of questions and activities are presented and aligned with the textbook’s learning outcomes. As an instructor, you can edit existing questions and author entirely new problems. Integrate grade reports easily with Learning Management Systems (LMS), such as WebCT and Blackboard—and much more. ConnectPlus® Engineering provides students with all the advantages of Connect Engineering, plus 24/7 online access to a media-rich eBook, allowing seamless integration of text, media, and assessments. To learn more, visit www.mcgrawhillconnect.com. McGraw-Hill LearnSmart is available as a standalone product or an integrated feature of McGraw-Hill Connect Engineering. It is an adaptive learning system designed to help students learn faster, study more efficiently, and retain more knowledge for greater success. LearnSmart assesses a student’s knowledge of course content through a series of adaptive questions. It pinpoints concepts the student does not understand and maps out a personalized study plan for success. This innovative study tool also has features that allow instructors to see exactly what students have accomplished and a built-in assessment tool for graded assignments. Visit the following site for a demonstration. www. LearnSmartAdvantage.com bee98233_FM_i-xvi_1.indd xi 11/15/13 10:21 AM
PrefacexiiSMARTBK"Powered by the intelligent and adaptive LearnSmartengine, SmartBook is the first and only continuously adaptive reading experience availabletoday.Distinguishing what students know from what they don't,and honing in on concepts theyare most likely to forget, SmartBook personalizes content for each student. Reading is no longera passive and linear experience but an engaging and dynamic one, where students are morelikely to master and retain important concepts, coming to class better prepared. SmartBookincludes powerful reports that identify specific topics and learning objectives students needto study.create"Craft your teaching resources to match the way you teach! With McGraw-Hill Create, www.mcgrawhillcreate.com, you can easily rearrange chapters, combine materialfrom other content sources, and quickly upload your original content, such as a course syllabusor teaching notes.Arrange your book to fit your teaching style. Create even allows you to per-sonalize your book's appearance by selecting the cover and adding your name, school, andcourse information. Order a Create book and you'll receive a complimentaryprint review copyin 3-5business days or a complimentary electronic review copy (eComp)via email in minutes.Go to www.mcgrawhillcreate.com today and register to experience how McGraw-Hill Createempowers youtoteachyourstudents yourway.AcknowledgmentsThe authors thank the many companies that provided photographs for this edition.We alsowish to recognize the efforts of the staff of RPK Editorial Services, who diligently worked toedit,typeset,proofread,andgenerallyscrutinizeall ofthisedition'scontent.Ourspecial thanksgo to Amy Mazurek (B.S. degree in civil engineering from the Florida Institute of Technology,and a M.S. degree in civil engineering from the University of Connecticut) for her work in thechecking and preparation of the solutions and answers of all the problems in this editionWe also gratefully acknowledge the help, comments, and suggestions offered by the manyreviewers and users of previous editions of Mechanics of Materials.John T. DeWolfDavid F Mazurek
Powered by the intelligent and adaptive LearnSmart engine, SmartBook is the first and only continuously adaptive reading experience available today. Distinguishing what students know from what they don’t, and honing in on concepts they are most likely to forget, SmartBook personalizes content for each student. Reading is no longer a passive and linear experience but an engaging and dynamic one, where students are more likely to master and retain important concepts, coming to class better prepared. SmartBook includes powerful reports that identify specific topics and learning objectives students need to study. Craft your teaching resources to match the way you teach! With McGrawHill Create, www.mcgrawhillcreate.com, you can easily rearrange chapters, combine material from other content sources, and quickly upload your original content, such as a course syllabus or teaching notes. Arrange your book to fit your teaching style. Create even allows you to personalize your book’s appearance by selecting the cover and adding your name, school, and course information. Order a Create book and you’ll receive a complimentary print review copy in 3–5 business days or a complimentary electronic review copy (eComp) via email in minutes. Go to www.mcgrawhillcreate.com today and register to experience how McGraw-Hill Create empowers you to teach your students your way. Acknowledgments The authors thank the many companies that provided photographs for this edition. We also wish to recognize the efforts of the staff of RPK Editorial Services, who diligently worked to edit, typeset, proofread, and generally scrutinize all of this edition’s content. Our special thanks go to Amy Mazurek (B.S. degree in civil engineering from the Florida Institute of Technology, and a M.S. degree in civil engineering from the University of Connecticut) for her work in the checking and preparation of the solutions and answers of all the problems in this edition. We also gratefully acknowledge the help, comments, and suggestions offered by the many reviewers and users of previous editions of Mechanics of Materials. John T. DeWolf David F. Mazurek xii Preface bee98233_FM_i-xvi_1.indd xii 11/15/13 10:21 AM
Guided TourChapter Introduction.Each chapter beginswithanintroductorysectionthat setsupthepurposeand goals of the chapter,describing in simpletermsthematerial that will be covered and its applicationto the solution of engineeringproblems.ChapterObjectivesprovide studentswithapreviewof chap-Introduction-ter topics.Conceptof StressChapterLessons.Thebodyofthetextisdividedinto units,each consisting of one or several theorysections,Concept Applications, one or severalSampleProblems,andalargenumberofhomeworkproblems.The Companion Website contains aCourse Organization Guide with suggestions on eachchapter lesson.Concept Appllcation 1.1ConceptApplications.Concept Appli-theuctire ofFig LIoe pape S,asunrodBCications are used extensively within individ-ofthe force Facin the roeEg-(1)t determinetheual theory sections to focus on specific0X10Ntopics,and they aredesigned to illustrate4 x104specificmaterial being presented and facili-X10P-+155MPtate its understanding.scenarSampleProblems.The Sample Prob-lemsareintendedtoshowmorecompre-hensive applications of the theory to the solution of engineeringproblems,and theyemploythe SMART problem-solvingmethodologythat students are encouraged to use in the solution of their assignedproblems.Sincethesampleproblemshavebeen setup inmuchthesame form that students will use in solving the assigned problems,theyservethedoublepurpose of amplifyingthetext anddemonstrat-MODELINGandHANALYSISing the type of neat and orderly work that students should cultivate in()5-1P-601their own solutions.In addition,in-problemreferencesand captions1-5-10Phavebeenaddedtothesampleproblemfiguresforcontextual linkageto the step-by-step solution.--HomeworkProblemSets.Over25%ofthenearly1500home-arenfttworkproblemsareneworupdated.Mostoftheproblemsareofaprac-plateht=20sceed175M1aritical nature and should appeal to engineering students.They areprimarily designed, however, to illustrate the material presented in the-d43textandtohelpstudentsunderstandtheprinciplesusedinmechanics2of materials.Theproblems aregrouped accordingtotheportions of175MPmaterial they illustrate and are arranged in order of increasing diffi-culty.Answers to a majority of theproblems aregiven at the end of theREFLECTENdbookProblemsforwhichtheanswersaregivenaresetinbluetypeinhad to recalculate d bathetext,whileproblemsforwhichno answer isgiven are set inredxili
xiii Guided Tour Chapter Introduction. Each chapter begins with an introductory section that sets up the purpose and goals of the chapter, describing in simple terms the material that will be covered and its application to the solution of engineering problems. Chapter Objectives provide students with a preview of chapter topics. Chapter Lessons. The body of the text is divided into units, each consisting of one or several theory sections, Concept Applications, one or several Sample Problems, and a large number of homework problems. The Companion Website contains a Course Organization Guide with suggestions on each chapter lesson. Concept Applications. Concept Applications are used extensively within individual theory sections to focus on specific topics, and they are designed to illustrate specific material being presented and facilitate its understanding. Sample Problems. The Sample Problems are intended to show more comprehensive applications of the theory to the solution of engineering problems, and they employ the SMART problem-solving methodology that students are encouraged to use in the solution of their assigned problems. Since the sample problems have been set up in much the same form that students will use in solving the assigned problems, they serve the double purpose of amplifying the text and demonstrating the type of neat and orderly work that students should cultivate in their own solutions. In addition, in-problem references and captions have been added to the sample problem figures for contextual linkage to the step-by-step solution. Homework Problem Sets. Over 25% of the nearly 1500 homework problems are new or updated. Most of the problems are of a practical nature and should appeal to engineering students. They are primarily designed, however, to illustrate the material presented in the text and to help students understand the principles used in mechanics of materials. The problems are grouped according to the portions of material they illustrate and are arranged in order of increasing difficulty. Answers to a majority of the problems are given at the end of the book. Problems for which the answers are given are set in blue type in the text, while problems for which no answer is given are set in red. 1 Introduction— Concept of Stress Stresses occur in all structures subject to loads. This chapter will examine simple states of stress in elements, such as in the two-force members, bolts and pins used in the structure shown. Objectives • Review of statics needed to determine forces in members of simple structures. • Introduce concept of stress. • Define diff erent stress types: axial normal stress, shearing stress and bearing stress. • Discuss engineer’s two principal tasks, namely, the analysis and design of structures and machines. • Develop problem solving approach. • Discuss the components of stress on diff erent planes and under diff erent loading conditions. • Discuss the many design considerations that an engineer should review before preparing a design. bee98233_ch01_002-053.indd 2-3 11/8/13 1:45 PM Concept Application 1.1 Considering the structure of Fig. 1.1 on page 5, assume that rod BC is made of a steel with a maximum allowable stress sall 5 165 MPa. Can rod BC safely support the load to which it will be subjected? The magnitude of the force FBC in the rod was 50 kN. Recalling that the diameter of the rod is 20 mm, use Eq. (1.5) to determine the stress created in the rod by the given loading. P 5 FBC 5 150 kN 5 150 3 103 N A 5 pr 2 5 pa 20 mm 2 b 2 5 p110 3 1023 m2 2 5 314 3 1026 m2 s 5 P A 5 150 3 103 N 314 3 1026 m2 5 1159 3 106 Pa 5 1159 MPa Since s is smaller than sall of the allowable stress in the steel used, rod BC can safely support the load. bee98233_ch01_002-053.indd 9 11/7/13 3:27 PM REFLECT and THINK: We sized d based on bolt shear, and then checked bearing on the tie bar. Had the maximum allowable bearing stress been exceeded, we would have had to recalculate d based on the bearing criterion. Sample Problem 1.2 The steel tie bar shown is to be designed to carry a tension force of magnitude P 5 120 kN when bolted between double brackets at A and B. The bar will be fabricated from 20-mm-thick plate stock. For the grade of steel to be used, the maximum allowable stresses are s 5 175 MPa, t 5 100 MPa, and sb 5 350 MPa. Design the tie bar by determining the required values of (a) the diameter d of the bolt, (b) the dimension b at each end of the bar, and (c) the dimension h of the bar. STRATEGY: Use free-body diagrams to determine the forces needed to obtain the stresses in terms of the design tension force. Setting these stresses equal to the allowable stresses provides for the determination of the required dimensions. MODELING and ANALYSIS: a. Diameter of the Bolt. Since the bolt is in double shear (Fig. 1), F1 5 1 2 P 5 60 kN. t 5 F1 A 5 60 kN 1 4p d2 100 MPa 5 60 kN 1 4p d2 d 5 27.6 mm Use d 5 28 mm ◀ At this point, check the bearing stress between the 20-mm-thick plate (Fig. 2) and the 28-mm-diameter bolt. sb 5 P td 5 120 kN 10.020 m210.028 m2 5 214 MPa , 350 MPa OK b. Dimension b at Each End of the Bar. We consider one of the end portions of the bar in Fig. 3. Recalling that the thickness of the steel plate is t 5 20 mm and that the average tensile stress must not exceed 175 MPa, write s 5 1 2P ta 175 MPa 5 60 kN 10.02 m2a a 5 17.14 mm b 5 d 1 2a 5 28 mm 1 2(17.14 mm) b 5 62.3 mm ◀ c. Dimension h of the Bar. We consider a section in the central portion of the bar (Fig. 4). Recalling that the thickness of the steel plate is t 5 20 mm, we have s 5 P th 175 MPa 5 120 kN 10.020 m2h h 5 34.3 mm Use h 5 35 mm ◀ A B d F1 P P F1 F1 1 2 b h t 5 20 mm d P P' 120 kN a t a d b 1 2 P1 2 P 5 120 kN t 5 20 mm h Fig. 1 Sectioned bolt. Fig. 2 Tie bar geometry. Fig. 3 End section of tie bar. Fig. 4 Mid-body section of tie bar. bee98233_ch01_002-053.indd 19 11/7/13 3:27 PM bee98233_FM_i-xvi_1.indd xiii 11/15/13 10:21 AM
GuidedTourxiyChapter Reviewand Summary.Eachchapter endswith a review and summary of the material covered in thatchapter. Subtitlesareused to help studentsorganizetheirReview and Summaryreviewwork,andcross-referenceshavebeenincludedtohelpthem find the portions of material requiring their specialattention.ReviewProblems.Aset of reviewproblems isincludedRg1.41)wattheend ofeachchapter.Theseproblemsprovidestudents(LS)further opportunityto apply themost important conceptsolntOofhesintroduced in the chapter.eAFofthand the imagnaud“e(LaReviewProblemson af thetroforcesM160TComputerProblemsComputerProblems.Computersmakeitpossibleforengineering students to solve a great number of challengingproblems.Agroupofsixormoreproblemsdesigned tobesolvedwithacomputercanbefoundattheendofeachchap-ter. These problems can be solved using any computerlanguage that provides a basis for analytical calculations.Developing the algorithm required to solveagiven problemwill benefit the students in two different ways: (1) it will helpthemgainabetterunderstandingofthemechanicsprinciplesinvolved; (2) it will provide them with an opportunity to applythe skills acquired in theircomputerprogramming coursetothe solution of a meaningful engineering problem
xiv Guided Tour Chapter Review and Summary. Each chapter ends with a review and summary of the material covered in that chapter. Subtitles are used to help students organize their review work, and cross-references have been included to help them find the portions of material requiring their special attention. Review Problems. A set of review problems is included at the end of each chapter. These problems provide students further opportunity to apply the most important concepts introduced in the chapter. Computer Problems. Computers make it possible for engineering students to solve a great number of challenging problems. A group of six or more problems designed to be solved with a computer can be found at the end of each chapter. These problems can be solved using any computer language that provides a basis for analytical calculations. Developing the algorithm required to solve a given problem will benefit the students in two different ways: (1) it will help them gain a better understanding of the mechanics principles involved; (2) it will provide them with an opportunity to apply the skills acquired in their computer programming course to the solution of a meaningful engineering problem. 44 Review and Summary This chapter was devoted to the concept of stress and to an introduction to the methods used for the analysis and design of machines and loadbearing structures. Emphasis was placed on the use of a free-body diagram to obtain equilibrium equations that were solved for unknown reactions. Free-body diagrams were also used to find the internal forces in the various members of a structure. Axial Loading: Normal Stress The concept of stress was first introduced by considering a two-force member under an axial loading. The normal stress in that member (Fig. 1.41) was obtained by s 5 P A (1.5) The value of s obtained from Eq. (1.5) represents the average stress over the section rather than the stress at a specific point Q of the section. Considering a small area DA surrounding Q and the magnitude DF of the force exerted on DA, the stress at point Q is s 5 lim¢Ay0 ¢F ¢A (1.6) In general, the stress s at point Q in Eq. (1.6) is different from the value of the average stress given by Eq. (1.5) and is found to vary across the section. However, this variation is small in any section away from the points of application of the loads. Therefore, the distribution of the normal stresses in an axially loaded member is assumed to be uniform, except in the immediate vicinity of the points of application of the loads. For the distribution of stresses to be uniform in a given section, the line of action of the loads P and P9 must pass through the centroid C. Such a loading is called a centric axial loading. In the case of an eccentric axial loading, the distribution of stresses is not uniform. Transverse Forces and Shearing Stress When equal and opposite transverse forces P and P9 of magnitude P are applied to a member AB (Fig. 1.42), shearing stresses t are created over any section located between the points of application of the two forces. A P' P Fig. 1.41 Axially loaded member with cross section normal to member used to define normal stress. A C B P P Fig. 1.42 Model of transverse resultant forces on either side of C resulting in shearing stress at section C. bee98233_ch01_002-053.indd 44 11/7/13 3:27 PM 47 Review Problems 1.59 In the marine crane shown, link CD is known to have a uniform cross section of 50 3 150 mm. For the loading shown, determine the normal stress in the central portion of that link. Fig. P1.59 A D C B 15 m 25 m 3 m 35 m 80 Mg 15 m 1.60 Two horizontal 5-kip forces are applied to pin B of the assembly shown. Knowing that a pin of 0.8-in. diameter is used at each connection, determine the maximum value of the average normal stress (a) in link AB, (b) in link BC. Fig. P1.60 B A C 0.5 in. 0.5 in. 1.8 in. 1.8 in. 45 60 5 kips 5 kips 1.61 For the assembly and loading of Prob. 1.60, determine (a) the average shearing stress in the pin at C, (b) the average bearing stress at C in member BC, (c) the average bearing stress at B in member BC. bee98233_ch01_002-053.indd 47 11/7/13 3:27 PM 51 Computer Problems The following problems are designed to be solved with a computer. 1.C1 A solid steel rod consisting of n cylindrical elements welded together is subjected to the loading shown. The diameter of element i is denoted by di and the load applied to its lower end by Pi, with the magnitude Pi of this load being assumed positive if Pi is directed downward as shown and negative otherwise. (a) Write a computer program that can be used with either SI or U.S. customary units to determine the average stress in each element of the rod. (b) Use this program to solve Probs. 1.1 and 1.3. 1.C2 A 20-kN load is applied as shown to the horizontal member ABC. Member ABC has a 10 3 50-mm uniform rectangular cross section and is supported by four vertical links, each of 8 3 36-mm uniform rectangular cross section. Each of the four pins at A, B, C, and D has the same diameter d and is in double shear. (a) Write a computer program to calculate for values of d from 10 to 30 mm, using 1-mm increments, (i) the maximum value of the average normal stress in the links connecting pins B and D, (ii) the average normal stress in the links connecting pins C and E, (iii) the average shearing stress in pin B, (iv) the average shearing stress in pin C, (v) the average bearing stress at B in member ABC, and (vi) the average bearing stress at C in member ABC. (b) Check your program by comparing the values obtained for d 5 16 mm with the answers given for Probs. 1.7 and 1.27. (c) Use this program to find the permissible values of the diameter d of the pins, knowing that the allowable values of the normal, shearing, and bearing stresses for the steel used are, respectively, 150 MPa, 90 MPa, and 230 MPa. (d) Solve part c, assuming that the thickness of member ABC has been reduced from 10 to 8 mm. Element n Element 1 Pn P1 Fig. P1.C1 Fig. P1.C2 0.2 m 0.25 m 0.4 m 20 kN C B A D E bee98233_ch01_002-053.indd 51 11/7/13 3:27 PM bee98233_FM_i-xvi_1.indd xiv 11/15/13 10:21 AM