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Steel Portal Frame EC3 RUNET software
16.10.7 Lateral torsional buckling for uniform members
ΕΝ 1993-1-1:2005 § 6.3.2
Lateral torsional buckling of uniform members in bending.
M
Ed
1
(ΕΝ 1993-1-1, 6.54)
M b
,
Rd
M b
,
Rd
LT
W y
1
f y
(ΕΝ 1993-1-1, 6.55)
W
=
y
W pl
,
y
for class 1, 2 cross-sections,
W y
=
W el
,
y
for class 3 cross-sections,
W
=
y
W eff
,
y
for class 4 cross-sections.
The reduction factor
is determined from the non-dimensional slenderness
LT
LT
LT
LT
1
2
LT
2
LT
1
(ΕΝ 1993-1-1, 6.56)
LT
0 .
5 1
LT
LT
0 .
2
2
LT
LT
W y f y
M cr
The imperfection factor
which corresponds to the appropriate buckling curve a,b,c,d:
Buckling curve
Imperfection factor α
LT a b C d
0.21 0.34 0.49 0.76
Recommended values for torsional buckling curves:
Rolled Sections h/b<2 buckling curve a, h/b>2 buckling curve b
Welded sections h/b<2 buckling curve c, h/b>2 buckling curve d
The critical elastic moment for lateral torsional buckling is computed according to Annex F of
Eurocode 3-1-1 (1992).
M cr
C
1
2
EI
2
z
k k w
2
I
I w z
2
2
GI
EI z t
C
2
Z g
C
3
Z j
2
C
2
Z g
C
3
Z j
C1, C2, C3, coefficients depending on the loading conditions and support conditions, for a beam with uniform bending moment diagram C1=1.000, C2=0.000, C3=1.000 for a beam with parabolic bending moment diagram C1=1.132, C2=0.459, C3=0.525
I
St. Venant torsional constant,
t
I
warping constant,
w
I
second moment of inertia about the weak axis,
z
L
beam length between the support points,
k
, k w
coefficients depending on the support conditions,
Z g
distance of shear center from point of load application
Copyright
RUNET Software www.runet-software.com 39
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