Civil Engineering Reference
In-Depth Information
6.6.3 Elastic end restraints
6.6.3.1 General
When a beam forms part of a rigid-jointed structure, the adjacent members
elastically restrain the ends of the beam (i.e. they induce restraining moments
whichareproportionaltotheendrotations).Theserestrainingactionssignificantly
modifytheelasticbucklingmomentofthebeam.Fourdifferenttypesofrestraining
moment may act at each end of a beam, as shown in Figure 6.17.They are
(a) the major axis end moment
M
which provides restraint about the major axis,
(b) the bottom flange end moment
M
B
, and
(c) thetopflangeendmoment
M
T
,whichproviderestraintsabouttheminoraxis
and against end warping, and
(d) the axial torque
T
0
which provides restraint against end twisting.
6.6.3.2 Major axis end moments
The major axis end restraining moments
M
vary directly with the applied loads,
andcanbedeterminedbyaconventionalin-planebendinganalysis.Thedegreeof
restraintexperiencedatoneendofthebeamdependsonthemajoraxisstiffness
α
y
oftheadjacentmember(whichisdefinedastheratiooftheendmomenttotheend
rotation).Thismaybeexpressedbytheratio
R
1
oftheactualrestrainingmomentto
themaximummomentrequiredtopreventmajoraxisendrotation.Thus
R
1
varies
from 0 when there is no restraining moment to 1 when there is no end rotation.
Forbeamswhicharesymmetricallyloadedandrestrained,therestraintparameter
x
M
T
T
0
d
f
M
y
M
B
z
Figure 6.17
End-restraining moments.
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