ABSTRACT
Solving Eq. (8.1.6) for ci in terms of the nodal variables Vi and B; and substituting the results into Eq. (8.1.4) give
where
3x2 2x3 Il1(x) = 1-[2 + 13
2x2 x3 H2(x) =X--~-+ r
3x2 2x3 H3(x) = [2-13
x2 x3 H4(x) = -~ + [2
(8.1.7)
(8.1.8)
(8.1.9)
Figure8.1.3HermitianBeamElement
where [B]- {H"H"H"H"}-1234(8.1.10)
andthecorrespondingelementnodaldegreesoffreedomvectoris{de}={v101v282 }T.1 InEq.(8.1.10),doubleprimedenotesthesecondderivativeofthefunctionandlinEq. (8.1.9)isthelengthofabeamelement.AssumingthebeamrigidityEIisconstant withintheelement,theelementstiffnessmatrixis
[ 12
6l
6ll2/2 -6[ 4[2
(8.1.11)
Incasethebeamrigidityisnotconstantwithinabeamelement,theintegralinEq. (8.1.9)mustbeevaluatedincludingEIasafunctionofx.Ifthebeamelementis relativelyshort,forexampleinarefinedmesh,theaveragevalueofEIfortheelement maybeusedwithEq.(8.1.11)forasimpleandreasonableapproximation.
