2) Consider the following steel Ibeam, which has a constant crosssection as described below, and a modulus of E = 200 GPa. The distance a = 0.2 m. The distributed load has a value of and the point load, P=400 N
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BeamsandFrames
1)Connectionconstraints
Thephysicalconstructionoftwodifferentbeamconnectionsareshown:
a)AnIbeamisconnectedtoafloorslabthroughaslottedbolthole
b)AnIbeamisconnectedtoacolumnthroughananglebracket.
Whatsimplifiedsupportconditionswouldyouusetorepresentthephysicalconstructioninthetwo
cases?Explainyourreasons.
2)Beamwithdistributedandpointloads(MATLAB,LISA,ANSYS)
ConsiderthefollowingsteelIbeam,whichhasaconstantcrosssectionasdescribedbelow,anda
modulusofE=200GPa.Thedistancea=0.2m.
Thedistributedloadhasavalueofw=12kN/mandthepointload,P=400N
a)Byhand/usingMATLABwith2elementsandthestandardshapefunctionsdetermine:
thereactionforcesatthetwowalls
thedeflection,thebendingmomentandthebendingstressatthetwolocationsofinterest:
o thelocationofthepointmass
o thelocationametersfromtherightwall
Yoursolutionmustinclude:
A. Elementalstiffnessmatrixforeachelement
B. Theglobalstiffnessmatrixfortheentirebeam
C. Theloadvectorfortheentirebeam
D. Theboundaryconditionstheentirebeam
E. WriteouttheFEAsysteminmatrixformandclearlyexplainwhateachmatrixrepresents.
F. Nodaldisplacementsolution
G. Thereactionforces
H. Thedeflectionatthetwoselectedpoints
I. Thebendingmomentandbendingstressesatthetwoselectedpoints
J. TheMatlabscriptandcommentsprovidingdetailedexplanationofeachlineofcode(Note
thatyouwillbebuildingonthiscodeforthenextproblem,sobesuretocommentyourcode
well)
b)UseLISAtoperformthesameanalysis,butuseatotalof4elementstocompletethemodel,placinga
nodeatthespecifiedlocations.ComparethefollowingbetweentheMATLABandLISAsolution:
Nodaldisplacements
BendingMoment
Thereactionforces
c)UseANSYStoperformthesameanalysisasLISA.Confirmthenodaldisplacementsandthebending
momentsbetweentheLISAandANSYSsolutions.Explain,basedontheunderlyingmodelusedwhythe
answersmaynotbeidentical.
3)Framewithpointloadanddistributedload(MATLAB,LISA)
Theplaneframeisalmostidenticaltothebeamintheprevious
problem,exceptthattheportionoftheframewithoutthe
distributedloadismountedatanangleasshown.
a)Describethedifferencesintheassemblyoftheglobalstiffness
matrixforthisproblemcomparedtothepreviousbeamproblem.
b)Clearlydescribeallofthenodalvariablesthatcanbe
calculatedandexplainwhytherearemorethanintheprevious
problem.
c)UsingbothMATLABandLISA,findandcomparethenodalvaluesassociatedwithnode2andclearly
explainwhattheyrepresent,andwhytheyarereasonable.
Note:youshouldbeabletoreusemostofyourcodefromproblem2withmodifications.
4)Framewithpointloadanddistributedload(LISA,ANSYS)
Thebikeframeshowninthefigurebelowhashollowcirculartubes(24mmouterdiameterand2mm
thick)andismadeofaluminumalloywithE=70GPa.
a)Canareasonablyaccuratemodelbedevelopedforthismodelin2Dspace?Providerationalforyour
answer.
b)UseeitherLISAorANSYSWorkbenchtodeterminethedeformationandstressesusinga2Dframe
modelforthisbicycle.
c)UseLISAtodeterminethedeformationandstressesoftheframemembersforthemodelasshown.
CompareyourLISAresultswiththefollowingANSYSresultsandidentifyanydifferencesinnodal
displacements,andelementstresses,aswellasdifferencesinthewaythattheresultsareinterpolated
betweenNodes.
Thetotaldeformationplotforthebicycleframe:Thedirectstressplot:
d)Comparetheresultsfromb)andc),assessyouranswertoparta)andexplainanydifferences.
NotesforusingLISA:
1.Tofixtherotationatanode,selectthedesirednode,andthenusetheOnselectednodescommand
toapplyanNewrotzofzero.
2.Modelthedistributedloadbyapplyingtheequivalentforceandmomentoneachofthenod
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