Civil Engineering Reference
In-Depth Information
N
r
N
r
N
N
c
c
N
r
N
r
EI
r
,L
r
EI
r
,L
r
EI ,
cc
EI ,
cc
N
N
c
c
(b) Antisymmetric
buckling mode
(c) Symmetric buckling
mode
(a) Frame and loads
Figure 8.8
Pinned base portal frame.
For portal frames with pinned bases
C
=
1.2
(8.11)
and for antisymmetric buckling as shown in Figure 8.8b,
ρ
c
=
3
/(
10
R
+
12
)
(8.12a)
and
ρ
r
=
1
(8.12b)
in which
R
=
(
I
c
/
L
c
)/(
I
r
/
L
r
)
(8.13)
For symmetric buckling as shown in Figure 8.8c,
4.8
+
12
R
(
1
+
R
H
)
2.4
+
12
R
(
1
+
R
H
)
+
7
R
2
R
H
ρ
c
=
(8.14a)
and
ρ
r
=
12
R
+
8.4
RR
H
12
R
+
4
(8.14b)
in which
R
H
=
(
L
r
/
L
c
)
sin
θ
R
(8.15)
inwhich
θ
R
istheinclinationoftherafter.Aworkedexampleoftheapplicationof
this method is given in Section 8.5.5.
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