Civil Engineering Reference
In-Depth Information
R
1
is related to the stiffness
α
y
of each adjacent member by
α
y
=
EI
y
L
2
R
1
1
−
R
1
.
(6.49)
Although the major axis end moments are independent of the buckling deforma-
tions, they do affect the buckling load of the beam because of their effect on the
in-planebendingmomentdistribution(seeSection6.2.1.4).Manyparticularcases
have been studied, and tabulations of buckling loads are available [5, 12, 13,
33-35].
6.6.3.3 Minor axis end restraints
On the other hand, the flange end moments
M
B
and
M
T
remain zero until the
bucklingloadofthebeamisreached,andthenincreaseinproportiontotheflange
endrotations.Again,thedegreeofendrestraintcanbeexpressedbytheratioofthe
actualrestrainingmomenttothemaximumvaluerequiredtopreventendrotation.
Thus, the minor axis end restraint parameter
R
2
(which describes the relative
magnitude of the restraining moment
M
B
+
M
T
) varies between 0 and 1, and the
endwarpingrestraintparameter
R
4
(whichdescribestherelativemagnitudeofthe
differentialflangeendmoments(
M
T
−
M
B
)/
2)variesfrom0whentheendsarefree
towarpto1whenendwarpingisprevented.Theparticularcaseofsymmetrically
restrainedbeamswithequalandoppositeendmoments(Figure6.18)isanalysedin
Section6.13.1.Itisassumedforthisthattheminoraxisandendwarpingrestraints
taketheformofequalrotationalrestraintswhichactateachflangeendandwhose
1.0
M
M
L
0.5
(a) Elevation
M
B
+M
T
x
M
B
+M
T
0
v
0
0.2 0.4
0.6 0.8 1.0
Restraint parameter
R
(b) Plan on centroidal axis
(c) Effective length factors
Figure 6.18
Elastic buckling of end-restrained beams.
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