结构机械制造工艺学模拟试题答桉.docx
- 文档编号:6269600
- 上传时间:2023-05-09
- 格式:DOCX
- 页数:12
- 大小:152.69KB
结构机械制造工艺学模拟试题答桉.docx
《结构机械制造工艺学模拟试题答桉.docx》由会员分享,可在线阅读,更多相关《结构机械制造工艺学模拟试题答桉.docx(12页珍藏版)》请在冰点文库上搜索。
结构机械制造工艺学模拟试题答桉
Chapter3(Chapter7inbook)
AnalysisofstaticallyDeterminateTruss
§1.Introduction
Atrussisdefinedasastructureformedbyagroupofmemberswhichareassumedtobeconnectedbypinsanduniformincross-section.
Trussesusematerialveryefficientlyandareconsequenteconomicalforspanninglongdistances.Theyarecommonlyusedinbridges,towersandroof.Crane,etc.
AclassictrussisshowninFig.3-1
Fig.3-1
Thetrussiscomprisedbychordsandwebs.Chordscanbedividedintotopandbottom,andwebintoverticalanddiagonal.
Thepointatwhichwebmembersconnecttochordiscalledpanelpoint(joint).
Thelengthbetweentwojointsonthesamechordiscalledpanel.
Thefollowingassumptionsaremadeinordertosimplifytheanalysisoftrusses:
a)Trussmembersareconnectedtogetherattheirendsbyfrictionlesspins.
Fig.3-2
b)Thecentroidalaxesofmembersareallstraightlines.thosemeetingatajointallintersectatacommonpoint.
Fig.3-3
c)Externalloadsandreactionsareappliedonthetrussonlyatitsjoints.
Fig.3-4
Accordingtoaboveassumptionsmembersofatrussaresubjectedtoaxialforceonly.Inotherwords,themembersinatrussarealltwo-forcemembers.
Itiscustomarytodesignatethetensionasthepositiveaxialforceandcompressionasthenegative.
Fig.3-5
§2.ClassificationofTrusses
1.Simpletruss
Aplanetrussisformedbybeginningtriangle,andthenunitsoftwocomponentsareaddedonthetriangle.Trussesformedinthiswayarecalledsimpletrusses.
Fig.3-6
2.Compoundtruss
Twoormoretrussesareconnectedaccordingtotworigidpiecesruleorthreerigidpiecesrule,thetrussesformedinthiswayaretermedcompoundtrussed.
Fig.3-7
3.Complextruss
Trussesthatcannotbeclassifiedaseithersimpletrussesorcompoundarecalled.
Fig.3-8
§3.MethodofJoints
Inthismethodbyasectionpassedcompletelyaroundajoint,thejointisisolatedfromtherestoftruss.
Theequilibriumequations
and
maybeappliedtothejointfreebodytodeterminetheunknownforcesinmembersmeetingthere.
Thiscanalwaysbedonesuccessivelyintheorderreversetothattheyweresetup(built)insimpletrusses.
Ingeneral,theaxialforceNofaninclinedmemberwillberesolvedintothehorizontalcomponentXandverticalcomponentYinthecalculation(Fig.3-9).
Fig.3-9
LengthofAB=L,itsprojectioninhorizontal
andinvertical
.
Similarly:
theaxialforce=N,projectionofNinhorizontal=x,invertical=y.
Twotrianglesaresimilartoeachother.
So:
(3-1)
WecanobtainedcomponentsX,Yusingthisformula.
Inthecalculationitiscustomarytoassumetheunknownaxialforcestobetension.Iftheobtainedsolutionisanegativeone,itindicatesthattheaxialforceiscompression.
Fig.3-10
Ex.3-1
Find(determine)forcesofmembersusingjointsmethod.
Fig.3-11
Solution:
(1)Wedeterminedthereactionsofentiretrussatfirst.
;
Wecanfindthattheordersetupofthistrussis1,2,……8,or8,7…2,1
Weisolatethejointsreversetotheorder.
(2)Joint1isisolatedasfreebody.
Wesupposetheaxialforcesofmembers12,13arepositiveforcesasFig.3-12.
Fig.3-12
Accordingtoequilibriumequation.
(compression)
Equation(3-1)
Wealsohave,
(tension)
Joint2:
Fig.3-13
Joint3:
Fig.3-14
(compression)
Joint4,5,6,7,8canbedonelikethis.
Axialforcesofallmemberscanbefound.
Inthecalculation,itisnecessarytodrawafreebodysketch.
Thememberinwhichtheaxialforceisequaltozeroiscalledinactivemember.
Inthefollowingcases,theinactivemembersmaybedeterminedeasilybythemethodofjoints.
A.Ifnoloadisappliedatajointbetweenonlytwotrussmembers,boththetwomembersareinactivemembers.
Fig.3-15
B.IfaconcentratedloadPactingatajointbetweentwotrussmembersisalongoneofthememberaxes,theothermemberisinactivemember.
Fig.3-16
C.Ifnoloadisappliedatajointbetweenthreemembers,ofwhichtwolieonthesameline,thethirdoneisinactivememberandtheaxialforcesoftheothertwomembersarethesame.
D.Ifnoloadisappliedatajointbetweenfourmembers,ofwhichtwolieonthesamelineandothertwolieontheothersameline,theforceoftwomembersonthesamelinearethesame.
Fig.3-16
§4.MethodofSections
Iftheaxialforceinonlyonememberisdesiredandforacompoundtruss,themethodofjointsislessconvenient,themethodofsectionsmaybeappliedtodeterminetheunknownsinthesemembers.
Themethodofsectionsinvolves
isolatingaportionofthetrussbycuttingcertainmembersand
solvingfortheaxialforcesinthesememberswiththeequilibriumequationsfortheisolatedfreebody.
Ingeneral,onlytheremembersarecutbyasection,becausethreeunknownscanbeobtainedbythreestaticallyequilibriumequations.
Ex.3-2(Fig.3-17)
Fig.3-17
Determinetheinternalforcesofa,b,cmembers.
Solution:
(1)Findreactionsofthetruss
;
(2)Passsection
-
throughmembersa,b,c,taketheleftportionofthetrussasfreebody(Fig.3-18).
Fig.3-18
(3)Find
(4)Also,
(5)
Insomespecialcases,althoughfourormoremembersarecutbyasection,wecanstilldeterminesomeunknownforceamongthemprovidedthattheforcescomplywithsomerules.
Howtodetermineinternalforceofmember1(
)(Fig.3-19)
Fig.3-19
PasssectionⅠ-Ⅰthoughtrussasshown(indicated)bythedashlinesinFig.3-19.
Although5membersarecut,force
canbefoundbecauseallmemberscutbysectionintersectatthesamepointCexcept
.
ForthetrussshowninFig.3-20,sectionⅠ-Ⅰcut5members.Itisobviousthatmember5isinactivemember;wesetcoordinationsystemX,YshowninFig.Wecanfindforceofmember1becauseofforcesinmembers2,3,4areparallelandperpendicatetoX.
Fig.3-20
;
canbeobtained.
Themethodofjointsandthemethodofsectionsmaybecombinedwhenatrussisanalyzed.
Ex.3-3P90
Findforceinmember1,2.
Fig.3-21
Solution:
(1)Reactions=60kN
(2)PasssectionⅠ-Ⅰthoughthetrusstaketheleftportionasfreebody.shownin3-22.
areparalleleachotherandhorizontal.
Fig.3-22
So
Then,takejointBasfreebody(3-23)
;
Fig.3-23
canfind
.
Problems:
P112,7-2(b),(c);P113(a)
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 结构 机械制造 工艺学 模拟 试题