Civil Engineering Reference
In-Depth Information
60
Zero
interaction
50
L
2
/
L
1
= 5
40
30
L
2
/
L
1
= 1
20
L
2
/
L
1
= 0.2
Q
1
Q
2
Q
1
10
L
1
L
2
L
1
0
0 10 20 30 40
(
2
EI
w
/GI
t
L
2
)=0
Q
1
L
1
2
/ (
EI
z
GI
t
)
K
=
Dimensionless buckling load
(a) Three span beam
(b) Buckling load combinations
Figure 6.23
Elastic buckling load combinations of symmetrical three span beams.
[12]areshowninFigure6.22. Similardiagramshavebeenproduced[44]fortwo
span beams of narrow rectangular section.
6.8.2 Beams with general loading
Whenmorethanonesegmentofabracedorcontinuousbeamisloaded,thebuck-
ling loads can be determined by analysing the interaction between the segments.
This has been done for a number of continuous beams of narrow rectangular
section [44], and the results for some symmetrical three span beams are shown in
Figure6.23.Theseindicatethatastheloads
Q
1
ontheendspansincreasefromzero,
sodoesthebucklingload
Q
2
ofthecentrespanuntilamaximumvalueisreached,
and that a similar effect occurs as the centre span load
Q
2
increases from zero.
TheresultsshowninFigure6.23suggestthattheelasticbucklingloadinteraction
diagramcanbecloselyandsafelyapproximatedbydrawingstraightlinesasshown
in Figure 6.24 between the following three significant load combinations:
1 When only the end spans are loaded (
Q
2
=
0), they are restrained during
bucklingbythecentrespan,andthebuckledshapehasinflectionpointsinthe
end spans, as shown in Figure 6.21b. In this case the buckling loads
Q
1
can
bedeterminedbyusing
R
1
=
R
2
=
R
4
=
1
/(
1
+
3
L
2
/
2
L
1
)
inthetabulations
of [12].
2 Whenonlythecentrespanisloaded(
Q
1
=
0),itisrestrainedbytheendspans,
and the buckled shape has inflection points in the centre span, as shown in
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