Civil Engineering Reference
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M
N
Loading
M
or
N
1
4
N
cr,y
3
6
M
pl
M
pl,r
2
7
N
M
(
M
,
N
)
max
beam
N
= 0
126
4
column
M
= 0
First yield
3
7
interaction
beam-column
5
5
0
In-plane deflection
Figure 7.2
In-plane behaviour of a beam-column.
m
M
m
M
m
M
(1 +
)/
L
N
Bending moment
-
EI
y
d
2
2
w
/d
x
L
Nw
w
x
m
M
[1 - (1 +
)
x
/
L
]
N
m
M
(1 +
)/
L
M
M
(a) Beam-column
(b) Bending moment distribution
Figure 7.3
In-plane bending moment distribution in a beam-column.
beam-columns,theseendmomentsareindependentofthedeflections,andhaveno
effectontheelasticbucklingload
N
cr
,
y
=
π
2
EI
y
/
L
2
.(Theyarethereforequitedif-
ferentfromtheendrestrainingmomentsdiscussedinSection3.6.3whichincrease
withtheendrotationsandprofoundlyaffecttheelasticbucklingload.)Thebeam-
columnispreventedfrombendingabouttheminoraxisoutoftheplaneoftheend
moments, and is assumed to be straight before loading.
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