Civil Engineering Reference
In-Depth Information
Parabolic transition curve
F
"
cr
= 0.55
F
y
Euler curve
F
"
cr
=
0.55
F
y
2
E
L
= 5.55
r
y
F
y
FIGURE 7.3
Lateral-torsional buckling curve for flexural compression.
The parabolic transition equation is
B
L
r
y
2
F
cr
=
A
−
,
(7.23)
which becomes
L
r
y
2
0.55
F
y
6.3
F
cr
=
0.55
F
y
−
,
(7.24)
2
E
π
with
F
cr
=
A
=
0.55
F
y
(
when
L
/
r
y
=
0
)
,
0.55
F
y
6.3
(
when
F
cr
=
B
=
0.55
F
y
/2 and
L
/
r
y
is given by Equation 7.22
)
.
2
E
π
AREMA (2008) recommends a conservative approach using Equations 7.20 and
7.24 independently and adopting the larger of the two buckling stresses,
F
cr
or
F
cr
,
for the design of flexural me
mber
s. AREMA (2008) also restricts beam and girder
slenderness to
L/r
y
≤
5.55
E
/
F
y
in order to preclude Euler buckling.
It should be noted that Equations 7.20 and 7.24 are developed based on the assump-
tionofauniformmoment(noshearforces).Momentgradientsrelatingtoconcentrated
or moving load effects on simply supported beams and girders can be considered
through the use of modification factors (Salmon and Johnson, 1980). Modification
factors,
C
b
, based on loading and support conditions are available in the literature on
structural stability. The equations for pure and warping effects are then
0.13
,
π
EC
b
F
cr
=
Ld(
√
1
(7.25)
+ υ
)
/
bt
L
r
y
2
0.55
F
y
6.3
F
cr
=
0.55
F
y
−
.
(7.26)
2
EC
b
π
