4.3 Applications of the Principle of Virtual Work 994.3 ApplicationsofthePrincipleofVirtualWork....................................................
Wehavenowseenthattheprincipleofvirtualworkmaybeusedeitherintheformofimposedvirtual
displacementsorintheformofimposedvirtualforces.Generallytheformerapproach,aswesawin
Example4.1,isusedtodetermineforces,whilethelatterisusedtoobtaindisplacements.
Forstaticallydeterminatestructures,theuseofvirtualdisplacementstodetermineforcesystemsis
arelativelytrivialuseoftheprinciple,althoughproblemsofthistypeprovideausefulillustrationofthe
method.Therealpowerofthisapproachliesinitsapplicationtothesolutionofstaticallyindeterminate
structures.However,theuseofvirtualforcesisparticularlyusefulindeterminingactualdisplacements
ofstructures.Weshallillustratebothapproachesbyexamples.
Example 4.2
Determine the bending moment at the point B in the simply supported beam ABC shown in
Fig.4.8(a).
We determined the support reactions for this particular beam in Example 4.1. In this example,
however,weareinterestedintheactualinternalmoment,MB,atthepointofapplicationoftheload.
Therefore,wemustimposeavirtualdisplacement,whichwillrelatetheinternalmomentatBtothe
appliedloadandexcludeotherunknownexternalforces,suchasthesupportreactions,andunknown
internalforcesystems,suchasthebendingmomentdistributionalongthelengthofthebeam.Therefore,
Fig.4.8
Determination of bending moment at a point in the beam of Example 4.2 using virtual work.