This book is intended to provide the student with a clear andthoroughpresentation of the theory and application of structuralanalysis as itapplies to trusses, beams, and frames. Emphasis isplaced on developingthe students ability to both model and analyzea structure and toprovide realistic applications encountered inprofessional practice.
For many years now, engineers have been using matrix methodstoanalyze structures. Although these methods are most efficient forastructural analysis, it is the authors opinion that studentstaking a firstcourse in this subject should also be well versed insome of the moreimportant classicial methods. Practice in applyingthese methods willdevelop a deeper understanding of the basicengineering sciences ofstatics and mechanics of materials. Also,problem-solving skills arefurther developed when the varioustechniques are thought out andapplied in a clear and orderly way.By solving problems in this way onecan better grasp the way loadsare transmitted through a structure andobtain a more completeunderstanding of the way the structure deformsunder load. Finally,the classicial methods provide a means of checkingcomputer resultsrather than simply relying on the generated output.
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Content Revision. Each section of the text was carefullyreviewedto enhance clarity. This has included incorporating the newASCE/SEI 07-10 standards on loading in Chapter 1, an improvedexplanationof how to draw shear and moment diagrams and thedeflection curveof a structure, consolidating the material onstructures having avariable moment of inertia, providing furtherdiscussion for analyzingstructures having internal hinges usingmatrix analysis, and adding anew Appendix B that discusses some ofthe common features used forrunning current structural analysiscomputer software.
Problems. Most of the problems in the book depictrealisticsituations encountered in practice. It is hoped that thisrealism willboth stimulate the students interest in structuralanalysis and developthe skill to reduce any such problem from itsphysical description to amodel or symbolic representation to whichthe appropriate theory canbe applied. Throughout the book there isan approximate balance ofproblems using either SI or FPS units. Theintent has been to develop
ContentsThis book is divided into three parts. The first partconsists of sevenchapters that cover the classical methods ofanalysis for staticallydeterminate structures. Chapter 1 provides adiscussion of the varioustypes of structural forms and loads.Chapter 2 discusses the determinationof forces at the supports andconnections of statically determinate beamsand frames.The analysisof various types of statically determinate trussesis given inChapter 3, and shear and bending-moment functions anddiagrams forbeams and frames are presented in Chapter 4. In Chapter 5,theanalysis of simple cable and arch systems is presented, andinChapter 6 influence lines for beams, girders, and trusses arediscussed.Finally, in Chapter 7 several common techniques for theapproximateanalysis of statically indeterminate structures areconsidered.
The third part of the book treats the matrix analysis ofstructures usingthe stiffness method.Trusses are discussed inChapter 14, beams in Chap-ter 15, and frames in Chapter 16. Areview of matrix algebra is given inAppendix A, and Appendix Bprovides a general guide for usingavailable software for solvingproblem in structural analysis.
STRAN. Developed by the author and Barry Nolan, apracticingengineer, STRAN is a downloadable program for use withStructuralAnalysis problems. Access STRAN on the Companion Website,www.pearsonhighered.com/hibbeler and follow the links for theStructuralAnalysis text. Complete instructions for how to use thesoftware areincluded on the Companion Website.
This chapter provides a discussion of some of the preliminaryaspectsof structural analysis. The phases of activity necessary toproduce astructure are presented first, followed by an introductionto the basictypes of structures, their components, and supports.Finally, a briefexplanation is given of the various types of loadsthat must beconsidered for an appropriate analysis and design.
When designing a structure to serve a specified function forpublic use,the engineer must account for its safety, esthetics, andserviceability,while taking into consideration economic andenvironmental constraints.Often this requires several independentstudies of different solutionsbefore final judgment can be made asto which structural form is mostappropriate.This design process isboth creative and technical and requiresa fundamental knowledge ofmaterial properties and the laws ofmechanics which govern materialresponse. Once a preliminary design of astructure is proposed, thestructure must then be analyzed to ensure thatit has its requiredstiffness and strength. To analyze a structure properly,certainidealizations must be made as to how the members are supportedandconnected together. The loadings are determined from codes andlocalspecifications, and the forces in the members and theirdisplacementsare found using the theory of structural analysis,which is the subjectmatter of this text. The results of thisanalysis then can be used to
1redesign the structure, accounting for a more accuratedetermination ofthe weight of the members and their size.Structural design, therefore,follows a series of successiveapproximations in which every cyclerequires a structural analysis.In this book, the structural analysis isapplied to civilengineering structures; however, the method of analysisdescribedcan also be used for structures related to other fieldsofengineering.
Types of Structures. The combination of structural elementsandthe materials from which they are composed is referred to as astructuralsystem. Each system is constructed of one or more of fourbasic types ofstructures. Ranked in order of complexity of theirforce analysis, they areas follows.
1response spectrum. Once this graph is established, theearthquakeloadings can be calculated using a dynamic analysis basedon the theoryof structural dynamics. This type of analysis isgaining popularity,although it is often quite elaborate andrequires the use of a computer.Even so, such an analysis becomesmandatory if the structure is large.
In this chapter we will direct our attention to the most commonformof structure that the engineer will have to analyze, and thatis onethat lies in a plane and is subjected to a force system thatlies in thesame plane. We begin by discussing the importance ofchoosing anappropriate analytical model for a structure so that theforces in thestructure may be determined with reasonable accuracy.Then the criterianecessary for structural stability are discussed.Finally, the analysis ofstatically determinate, planar,pin-connected structures is presented.
2.1 Idealized StructureAn exact analysis of a structure cannever be carried out, since estimatesalways have to be made of theloadings and the strength of thematerials composing the structure.Furthermore, points of applicationfor the loadings must also beestimated. It is important, therefore,that the structural engineerdevelop the ability to model or idealize astructure so that he orshe can perform a practical force analysis of themembers. In thissection we will develop the basic techniques necessaryto dothis.
Idealized models used in structural analysis that representpinned andfixed supports and pin-connected and fixed-connectedjoints are shownin Figs. 23a and 23b. In reality, however, allconnections exhibit somestiffness toward joint rotations, owing tofriction and material behavior.In this case a more appropriatemodel for a support or joint might bethat shown in Fig. 23c. If thetorsional spring constant the joint isa pin, and if the joint isfixed.k: q ,
When selecting a particular model for each support or joint, theengineermust be aware of how the assumptions will affect the actualperformanceof the member and whether the assumptions are reasonablefor thestructural design. For example, consider the beam shown inFig. 24a,which is used to support a concentrated load P. The angleconnection atsupport A is like that in Fig. 21a and can thereforebe idealized as atypical pin support. Furthermore, the support at Bprovides an approximatepoint of smooth contact and so it can beidealized as a roller. The beamsthickness can be neglected since itis small in comparison to the beamslength, and therefore theidealized model of the beam is as shown inFig. 24b.The analysis ofthe loadings in this beam should give results thatcloselyapproximate the loadings in the actual beam.To show that themodelis appropriate, consider a specific case of a beam made ofsteel with (8000 lb) and One of the major simplifications made herewasassuming the support at A to be a pin. Design of the beam usingstandardcode procedures* indicates that a W would be adequateforsupporting the load. Using one of the deflection methods ofChapter 8, therotation at the pin support can be calculated as FromFig. 24c, such a rotation only moves the top or bottom flangeadistance of This smallamount would certainly be accommodated bythe connection fabricated asshown in Fig. 21a, and therefore thepin serves as an appropriate model.
As a first example, consider the jib crane and trolley in Fig.25a. Forthe structural analysis we can neglect the thickness of thetwo mainmembers and will assume that the joint at B is fabricatedto be rigid.Furthermore, the support connection at A can be modeledas a fixedsupport and the details of the trolley excluded. Thus,the members of theidealized structure are represented by twoconnected lines, and the loadon the hook is represented by a singleconcentrated force F, Fig. 25b.This idealized structure shown hereas a line drawing can now be usedfor applying the principles ofstructural analysis, which will eventuallylead to the design of itstwo main members.
Beams and girders are often used to support building floors.Inparticular, a girder is the main load-carrying element of thefloor, whereasthe smaller elements having a shorter span andconnected to the girdersare called beams. Often the loads that areapplied to a beam or girder aretransmitted to it by the floor thatis supported by the beam or girder.Again, it is important to beable to appropriately idealize the system as aseries of models,which can be used to determine, to a close approxi-mation, theforces acting in the members. Consider, for example, theframingused to support a typical floor slab in a building, Fig. 26a.Herethe slab is supported by floor joists located at evenintervals, and thesein turn are supported by the two side girdersAB and CD. For analysis itis reasonable to assume that the jointsare pin and/or roller connectedto the girders and that the girdersare pin and/or roller connected to thecolumns. The top view of thestructural framing plan for this system isshown in Fig. 26b. Inthis graphic scheme, notice that the linesrepresenting the joistsdo not touch the girders and the lines for the girdersdo not touchthe columns. This symbolizes pin- and/ orroller-supportedconnections. On the other hand, if the framing planis intended torepresent fixed-connected members, such as those thatare welded 2ff7e9595c
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