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THEORY & ANALYSIS ---OF--- YEONG-81N YANG Departmenl of Civil EngIneering National Taiwan UniYerslty SHYH-RONG KUO DepaItrTIent 01 Harbof and RiYer National Taiwan El~.*.·-~_~o"'ilQ ooean UrWersitY PRENTICE HALL New York London Toronlo Sydney Tokyo Singapore Fint poobI,ohooI I~ by --~ sa. A ~ (.......) .... LId _ o . . i p wt 11oct • • 006·11 ,..... I'ao\jq Ro.d S_o:Ill o I~ Simon A Scnuol definit ions. with only. limited number of operalions performed 011 them. Ortly suucturrs thaI are of \Ix frame Iype. and composed of solid cross sealoas are ronsideml ill lhc lUI, whicta include in pania.>lar the following four calegories o f .IlI\ICtIlrcS: uusscs. pllllll frames. spKe fn.mes, and curved beams. Eadt of these fOUl calcSOries is C/Jvend in • "parale chaptel, u«pcthe Jpace frames, whid! ". coyered by two ehaplers. The lUI hn been organized in a ptogIessive mantler in Ihal il sc.rtS wilh lhe simpiesl theory of lrusses and ends wil h lhe mosl compliated theo)ry of curved bc:ams, followed by • chapter on nonlintil solulion pr-oc:edure$. In ChapleT I. the "nins, and oonsIltuli~e laws thlt are 10 be u.sed tlIrougiloul the boot are filS! introduced. The principle of virtual displacements llUillble for incRmenUlI farm"laliom of the lIgrangian type is the:n delived, whid\ l.ys • very IIItlural foundal.ion for .11 the theories to be dcli~ed in laltt ehaplCrs. In the firsl half of Orapler 2, Cl)nvcntionallincar Ilnalysis procedures for framed structUles Ire oullined, followed by • review of the qualilY lests for line.r and nonUnell finlle elements. Of Ihese IeSU, Ille rigid body Ies! appua 10 be of pamnount imposance .inoc il provides Ihe guidelincs for alatLalina the element forces in a Slcp-by-SlCp nonlinear aIIIIlysis. The planar and space truss clements are derived in wessa. Jviii OJap'er 3. Of paniClllar inte~ in this chapteT is the formulation of 1M pi'"O«dure for obtaining exKl solmions for trusses of . ny complexity loaded into the range of large suains. Two key issues are addressed in this regard: tile updating \If material coRStants and tile aolcuJatioll of bar fOI"«5. In a.lplcr 4, planar frame elemen15, as wen as buckling differential equations and nalUral boundary conditions, Ire derived for lwo-dimensional beams based on tbe Bernoulli-Euler hypDthesis of plane sections. This chapler gives us I very good example of how pDwerfultbe rigid body \eSI can be. II can be used nOi only in the tesl of a finile elemenl and ils underlying tbeory, but also for calculating the member fOl"ccs in an incremental nonliDe.af analysis. One key step in the buckling analysis of space frames is that an phys.ical relalions ~ld be established (or lhe buckling configuration of a wuaure, based on tile Pfinciple$ of continuum m«hanics. By Slicking rll1T1 ly t\l Ihis rule, In loalytiao) appro;och based on the COm_ monly used buckling equations is prUenled in OIapicr 5 for Ihe analysis o( the lateral buckling IoIod of some simple (rames, whicb are tlIt:n iranslated into the finite elemenl equations in ClI'plCf 6. The physical link belwun the two a~ helps in Tcsolving some existing conlrOversies on the illH:kling of space: frames. Also presented in a.apler 6 is I general thne-dimensional elemenl suitable for the analysis of space framcs. In OIaptet 7, a comprehensive treatment o( the bl>CkJing of Cllrved bea./n$ is Pf~nted. One (eature of the curv.d beam equations presented in this chapler is that they can be derived either from the principle of virtual displacements or (rom the SlTaight beam equations. By sticking to the rule that IU physical relations should be established for !he buckling configuration of a struclUle, il is demOnSlnlted that the straighl-ileam element can be employed 10 y~ld solutions that are as accurate as lho$e by the QIfVed_