SN030

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N

NCC

CCII: Mono-symmetrical uni

: Mono-symmetrical uni form

form members under bendin

members under bendin g

g

and axial compression

This NCCI gives a

This NCCI gives a method for the elastic verification of method for the elastic verification of mono-symmetrical uniformmono-symmetrical uniform members und

members under bending and er bending and axial compressaxial compressionion

6. Information Information about about LTLT Beam Beamfreeware to freeware to calculate calculate the the elastic elastic critical critical moment moment 1313 7. 7. References References 1414 F F r r i i d d a a y y , , S S e e p p t t e e m m b b e e r r 1 1 9 9 , , 2 2 0 0 0 0 8 8 i i a a l l i i s s c c o o p p y y r r i i g g h h t t - - a a l l l l r r i i g g h h t t s s r r e e s s e e r r v v e e d d . . U U s s e e o o f f t t h h i i s s d d o o c c u u m m e e n n t t i i s s s s u u b b j j e e c c t t t t o o t t h h e e t t e e r r m m s s a a n n d d c c o o n n d d i i t t i i o o

n n s s o o f f t t h h e e A A c c c c e e s s s s S S t t e e e e l l L L i i c c e e

n n c c e e A A g g r r e e e e m m e e n n t t

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1. Scope

This NCCI provides information for dealing with mono-symmetrical uniform members subjected to bending and axial compression satisfying the following conditions:

 The verification is restricted to the elastic behaviour of the member  The cross-section is symmetrical about the weak axis

 The flanges and the web are made of the same steel grade  The loads create bending moments about the strong axis only

 The axial load is expected to be applied at the centroid of the cross-section  The web is made of a solid plate of constant thickness

 The effects of the fillet welds are not taken into account

Note 1: Such a mono-symmetrical cross-section is susceptible to torsional-flexural buckling |3|.

Note 2: This kind of cross-section can be found, for instance, in composite structures where the upper flange of the beam is connected to a composite slab by means of shear connectors. Then, the following calculations are required in the non-composite stage when the fresh concrete acts only as an external load. In this case, the smaller flange is generally mainly in compression.

This kind of cross-section can be found also in welded cross-sections when a higher resistance to torsional-flexural buckling is needed for the member. In this case, the smaller flange is generally mainly in tension.

Note 3: Cellular beams or beams made of two different hot-rolled profiles are not covered by this NCCI.

2. Notations and geometrical properties of the

cross-section

The dimensional characteristics of the cross-section are shown in Figure 2.1.

F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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b₂ b₁ h t₂ t₁ t_w h_w G y y z z z_G S z_SC h_s 1 2 Key: 1 Top fibre 2 Bottom fibre Figure 2.1 Notations

The geometrical properties are the followings |2|, |8|, |10|:

 Area 2 2 w w 1 1 t h t b t b A= + + (1)

 Position of the centroid from the bottom fibre of the cross-section

A t b h t t h t h t b z 2 ) 2 ( ) 2 ( 22 2 w 2 w w 1 1 1 G + + + − = (2)

 Second moment of area about the strong axis y-y

2 G 2 2 2 2 G w 2 w w 2 G 1 1 1 3 w w 3 2 2 3 1 1 y 2 2 ... ... 2 12 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ₊ ₋ + + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ₋ ₋ + + + = z t t b z h t t h z t h t b h t t b t b I (3)

 Second moment of area about the weak axis z-z

12 3 w w 2 3 2 1 3 1t b t h t b I _z = + + (4)

 Elastic section modulus:

G y top y, el, z h I W − = (5) G y bottom y, el, z I W = (6) F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 i a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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 Position of the shear centre S from the bottom fibre of the cross-section: 1 3 1 2 3 2 1 3 1 s 2 SC 2 b t b t t b h t z + + = (7)

 St Venant torsional constant

3 3 w w 3 2 2 3 1 1 T t h t b t b I = + + (8)  Warping constant:

(

)

(

)

2 2 3 2 1 3 1 2 3 2 1 3 1 z 2 s w t b t b t b t b I h I + = (9)

3. Member resistance according to EN 1993-1-1

3.1 General

As bending is expected to occur about the strong axis, the verification of member stability is based on Clause (6.3.3) of EN 1993-1-1 |4| with M z,Ed = 0.

Nevertheless, the method given in Clause (6.3.3) is restricted to uniform members with double symmetric cross-sections. But, it may be extended to uniform members with mono-symmetric cross-sections (mono-symmetrical about the weak axis) when the following conditions are satisfied:

 the elastic resistance is the only one to be considered (elastic resistance of the whole

section for Class 1, 2 or 3 sections and elastic resistance of the effective cross-section for Class 4 cross-cross-sections),

 χ _y and χ _z must be replaced by χ _min = min( χ _y, χ _z,χ _TF) in (6.61) and (6.62) if χ _y and

z

χ are the reduction factors due to flexural buckling and χ _TF is the reduction factor for

torsional-flexural buckling (see Section 5.2),

 In Table A.2 of Annex A, the equivalent uniform moment factors must be limited to:

y cr, Ed 0 , my 1 N N C ≥ − (10)

Therefore, such members should satisfy |1|, |9|: 1 1 M Rk y, LT Ed y, Ed y, M1 Rk min Ed ₊ +Δ _≤ γ χ γ χ M M M k N N yy (11) 1 M1 Rk y, LT Ed y, Ed y, M1 Rk min Ed ₊ +Δ _≤ γ χ γ χ M M M k N N zy (12) F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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where: and are respectively the design values of the compression force and the maximum moments about the y-y axis along the member,

Ed

N M _y,_Ed

is the moment due to the shift of the centroidal axis in the case of Class 4 cross-sections (see Section 3.3),

Ed y,

M Δ

and are respectively the characteristic resistance to normal force and the characteristic moment resistance about the y-y axis,

Rk

N M _y,_Rk

M1

γ is the partial factor for resistance of members to instability ,

min

χ is the relevant reduction factor: χ _min = min( χ _y, χ _z,χ _TF),

LT

χ is the reduction factor due to lateral torsional buckling (see Section 5.1),

and are interaction factors.

yy

k k _zy

yy

k and k _zy have been derived from two alternative approaches provided in Annex A

(alternative Method 1) and Annex B (alternative Method 2) of EN 1993-1-1 |4|. Method 1 (see Section 3.3) has been established to provide an accurate fully-theoretical derived set of

formulae. Method 2 is simpler than Method 1. It has been established to be a user-friendly set of formulae. The National Annex may give a choice from alternative Methods 1 or 2.

Note: It is important to notice that, in both cases, the resistance of the cross-sections must be checked at each end of the member.

3.2 Susceptibil ity to torsion al deformations

Some moment factors depending on the susceptibility of the member to experience torsional deformations, it is necessary to clarify the boundary of this phenomenon.

The susceptibility to torsional deformations depends on the value of λ 0 , the non dimensional

slenderness for lateral torsional buckling due to uniform bending moment. The limiting value λ 0,lim is the following:

4 TF cr, Ed z cr, Ed 1 lim , 0 0,2 1 1 _⎟⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = N N N N C λ (13)

where: N _cr,_z is the elastic flexural buckling force about the z-z axis,

is theelastic torsional-flexural buckling force (see Section 5.2),

TF cr,

N

is a factor depending on the bending moment distribution and end restraint conditions (see Section 4).1

C

 If λ 0 ≤ λ 0,lim, the member is not susceptible to torsional deformations. In that case,

lateral torsional buckling is also prevented and χ _LT =1.

 If λ 0 >λ 0,lim, the member is susceptible to torsional deformations.

F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 i a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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3.3 Elastic resistance obtained from alternative Method 1

(Annex A)

 Class 1, 2 and 3 cross-sections

For Class 1, 2 and 3 cross-sections, the member should satisfy: 1 M1 y y el, LT Ed y, yy M1 y min Ed ₊ _≤ γ χ γ χ W f M k f A N (14) 1 M1 y y el, L Ed y, zy M1 y min Ed ₊ _≤ γ χ γ χ W f M k f A N T (15) where: y cr, Ed y mLT my yy 1 N N C C k − = (16) y cr, Ed z mLT my zy 1 N N C C k − = (17) in which: y cr, Ed y y cr, Ed y 1 1 N N N N χ μ − − = (18) z cr, Ed z z cr, Ed z 1 1 N N N N χ μ − − = (19)

is the elastic flexural buckling force about the y-y axis,

y cr,

N

is the elastic flexural buckling force about the z-z axis,

z cr,

N

and are uniform moment factors depending on the susceptibility of the member to torsional deformations (see hereinafter).

my

C C _mLT

 Class 4 cross-sections

For Class 4 cross-sections, equations (14) and (15) become: 1 M1 y y eff, LT Ed y N, Ed y, yy M1 y eff min Ed ₊ + _≤ γ χ γ χ W f N e M k f A N (20) F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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1 M1 y y eff, LT Ed y N, Ed y, zy M1 y eff min Ed ₊ + _≤ γ χ γ χ W f N e M k f A N (21)

where: is the shift of the centroid of the effective area calculated under pure compression,

y N,

e

is the effective area determined under pure compression,

eff

A

is the effective section modulus about the y-y axis determined under bending only,

y eff,

W

and are interaction factors defined by equations (16) and(17).

yy

k k _zy

 Influence of the susceptibility to torsional deformations

• If the member is not susceptible to torsional deformations: (see my,0 my C C = Table A.2 in EN 1993-1-1 |4|) 0 , 1 mLT = C and: χ _LT =1

• If the member is susceptible to torsional deformations: then: LT y LT y my,0 my,0 my 1 ) 1 ( a a C C C ε ε + − +

= (see Table A.2 in EN 1993-1-1 |4|)

and: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = TF cr, Ed z cr, Ed LT 2 my mLT 1 1 N N N N a C C where: y el, Ed Ed y, y W A N M =

ε for Class 1, 2 and 3 cross-sections

or: eff,y eff Ed Ed y, y W A N M = ε

for Class 4 cross-sections

and: 1 0 y T LT = − ≥ I I a F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 i a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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3.4 Elastic resistance obtained from alternative Method 2

(Annex B)

 Class 1, 2 and 3 cross-sections

For Class 1, 2 and 3 cross-sections, the member should satisfy: 1 M1 y y el, LT Ed y, yy M1 y min Ed ₊ _≤ γ χ γ χ W f M k f A N (22) 1 M1 y y el, LT Ed y, zy M1 y min Ed ₊ _≤ γ χ γ χ W f M k f A N (23) where: ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + ≤ ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + = M1 y min Ed my M1 y min Ed y my yy 1 0,6 1 0,6 γ χ γ χ λ f A N C f A N C k (24)

k zy depends on the susceptibility of the member to torsional deformations (see below).  Class 4 cross-sections

For Class 4 cross-sections, equations (14) and (15) become: 1 M1 y y eff, LT Ed y N, Ed y, yy M1 y eff min Ed ₊ + _≤ γ χ γ χ W f N e M k f A N (25) 1 M1 y y eff, LT Ed y N, Ed y, zy M1 y eff min Ed ₊ + _≤ γ χ γ χ W f N e M k f A N (26) where: ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + ≤ ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + = M1 y eff min Ed my M1 y eff min Ed y my yy 1 0,6 1 0,6 γ χ γ χ λ f A N C f A N C k (27)

depends on the susceptibility of the member to torsional deformation (see below).

zy

k

The equivalent moment factor C _my is given in Table B.3 in EN 1993-1-1 |4|.

 Influence of the susceptibility to torsional deformations Members not susceptible to torsional deformations:

yy

zy 0,8k

k = (28)

Therefore, because the first terms of equations (22) and (23) or(25) and (26)are the same, in that case, the most critical relationship is the first one of each set respectively.

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Members susceptible to torsional deformations:

(

)

(

)

M1 y min Ed mLT M1 y min Ed mLT z zy 25 , 0 05 , 0 1 25 , 0 05 , 0 1 γ χ γ χ λ f A N C f A N C k − − ≥ − − =

for Class 1, 2 or 3 cross-sections (29)

(

)

(

)

M1 y eff min Ed mLT M1 y eff min Ed mLT z zy 25 , 0 05 , 0 1 25 , 0 05 , 0 1 γ χ γ χ λ f A N C f A N C k − − ≥ − − =

for Class 4 cross-sections (30)

The equivalent moment factor C _mLT is given in Table B.3 in EN 1993-1-1 |4|.

4. Evaluation of the elastic critical moment

In the case of a member of uniform cross-section symmetrical about the weak axis, the critical moment for lateral torsional buckling is:

( )

₍

₎

₍

₎

⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ − − − + π + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ π = ₂ _g ₃ _j 2 ₂ _g ₃ _j z 2 T 2 z z w 2 w z 2 z z 2 1 cr C z C z C z C z EI GI L k I I k k L k EI C M (31)

where: L is the length of the member between points where lateral restraint is provided, , and are factors depending on the loading and the end restraint conditions (see

1

C C ₂ C ₃

Table 4.1 and Table 4.2),

is the effective length factor that refers to the end rotation about the z axis,

z

k

is the effective length factor that refers to the end warping,

w k s a g z z z = −

(

)

∫

+ − = A dA z y z I z z 2 2 y s

j 0,5 ( (approximations are given hereinafter |6|)

is the coordinate of the point of load application,

a

z

and: z_s is the coordinate of the shear centre: ( z_s = z_G −z_SC according to notations given in Figure 2.1). F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 i a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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The effective length factors, k _z and k _w, take the following values:

• 0,5 full restraint at both ends,

• 0,7 one end fixed and one end free,

• 1,0 no restraint,

the normal conditions of restraint at each end being:

• k _z =1,0 free to rotate about the z axis and restraint against lateral movements,

• k _w =1,0 free to warp but restraint against rotation about the longitudinal axis.

 Sign conventions for , z z_a, z_g and z_j

The sign conventions for , , z z_a z_g and z_j are defined in Figure 4.1. They are the followings:

• z is positive from the centroid of the cross-section to the compression flange,

• z_a is positive when the loads have a destabilising effect,

• _g is positive when the loads act towards the shear centre from their point of application.

z

• _j is positive when the flange with the larger value of is in compression at the point of the larger bending moment.

z I z G y z S zs za>0 G y z S zs za<0 3 2 zg>0 zg<0 z j>0 z j<0 1 2 3 1 1 Loading direction 2 Compression 3 Tension

Figure 4.1 Sign convention for z, z a z g and z j

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 Approximations for z_j |6|

If and are respectively the width and the thickness of the compression flange and if and are those of the tension flange, then:

c b t _c b_t t t t 3 t c 3 c c 3 c f t b t b t b + = β (32)

If: β _f>0,5, then z_j may be taken equal to z_j =0,4h_s(2β _f−1) and if: β _f <0,5, then z_j may be taken equal to z_j = 0,5h_s(2β _f−1)

Table 4.1 Values of C 1 and C 3 for end moment loading (for k z = 1)

C₁ C₃ ψ +1,00 1,00 1,00 +0,75 1,14 0,99 +0,50 1,31 0,99 +0,25 1,52 0,98 0,00 1,77 0,94 -0,25 2,05 0,85 ψ.M M ψ.M M -1≤ψ≤1 -0,50 2,33 0,68 -0,75 2,57 0,37 -1,00 2,55 0,00

Table 4.2 Values of factors C ₁ , C ₂ and C ₃ for cases with transverse loading (for k_z = 1)

Loading and support

conditions Bending moment diagram C1 C2 C3

1,13 0,45 0,52 2,57 1,55 0,75 1,35 0,63 1,73 1,68 1,64 2,64 F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 i a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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5. Evaluation of the non dimensional slenderness

5.1 Non dimensional slenderness for lateral torsion al

buckling

The non dimensional slenderness for lateral torsional buckling, λ LT depends on the

slenderness for lateral torsional buckling λ _LT :

cr y y el, LT M f W =

λ for Class 1, 2 and 3 cross-sections (33)

cr y y eff, LT M f W =

λ for Class 4 cross-sections (34)

The reduction factor χ _LT for lateral torsional buckling is then (EN 1993-1-1 §6.3.2 |4|):

2 LT 2 LT LT LT 1 λ φ φ χ − + = (35) where: φ _LT =0,5 _⎢⎣⎡1+α _LT

(

λ LT−0,2

)

+λ LT2 _⎥⎦⎤

• If the cross-section is such as h/b_c ≤2 , then α _LT = 0,49 (buckling curve c)

• If the cross-section is such as h/b_c >2, then α LT = 0,76 (buckling curve d)

where: b_c is the width of the compression flange.

5.2 Non dimensional slenderness for torsional-flexural

buckling

The non dimensional slenderness λ TF for torsional-flexural buckling is obtained by:

cr y TF N f A =

λ for Class 1, 2 or 3 cross-sections,

and: cr y eff TF N f A =

λ for Class 4 cross-sections,

where: N cr = min( N cr,TF ; N cr,T);

T cr,

N is theelastic torsional buckling force,

N _cr,_TF is theelastic torsional-flexural buckling force.

These buckling forces are given by the following relationships:

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⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ _π + = ₂ T cr, w 2 T 0 T cr, L EI GI I A N (36) where: 2 s z y

0 I I Az

I = + +

(

)

(

)

(

)

(

)

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ₊ − + − + + = _cr,_z _cr,_T 0 z y 2 T cr, z cr, T cr, z cr, z y 0 TF cr, ₂ 4 N N I I I N N N N I I I N (37) T cr,

L is generally taken as the member length.

The reduction factor χ _TF for torsional-flexural buckling is then:

2 TF 2 TF TF TF 1 λ φ φ χ − + = (38) where: φ _TF =0,5 _⎢⎣⎡1+α _TF

(

λ TF −0,2

)

+λ TF2 _⎥⎦⎤

• If the cross-section is such as t _f_min ≤40mm, then α TF = 0,49 (buckling curve c) • If the cross-section is such as t _f_min >40mm, then α _TF = 0,76 (buckling curve d)

. ) , min( _sup _inf

min

f t t

t =

6. Information about LT

Beam

_{freeware to calculate}

the elastic critical moment

It is to be noted that, in order to help in solving the calculation of for different loading and support conditions, a freeware is available. Named LT Beam, it may be downloaded from CTICM site (www.cticm.com). This software allows determining the elastic critical moment for mono-symmetrical uniform members with various loading cases including the effect of the position of the applied load. A short presentation in English in available in Chapter 7.3 of |5|

and in French in |7|. cr M F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 i a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

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7. References

1 N. Boissonnade, R. Greiner & J.P. Jaspart

“Rules for Member stability in EN 1993-1-1. Background documentation and design guidelines” - ECCS Technical Committee 8 “Stability” (to be published).

2 A. Bureau

“Résistance plastique en flexion composée d’une section en I mono-symétrique” – Construction Métallique, n°1-1997, pp. 41-52.

3 A. Bureau

“Flambement par torsion et par flexion-torsion d’une barre comprimée” – Construction Métallique, n°2-2004, pp. 39-54.

4 EN 1993-1-1:2004

“Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings”

5 ECSC Steel RTD Programme “Lateral Torsional Buckling in Steel and Composite Beams” N° 7210-PR-183 (1999-2002)

Final Technical Report – Book 2: “Design Guide” - Chapters 3 and 7.3.

6 Eurocode 3 – “Calcul des structures en acier – Partie 1-1: Règles générales et règles pour les bâtiments”

Eyrolles Paris, 1996.

7 Y. Galéa

“Moment critique de déversement élastique de poutres fléchies. Présentation du logiciel LTBEAM” – Construction Métallique, n°2-2003, pp. 47-76.

8 M. Pignataro, N. Rizzi and A. Luongo

“Stability, bifurcation and post-critical behaviour of elastic structures” – Development in Civil Engineering, vol. 39, Elsevier, 1991.

9 M. Villette

“Analyse critique du traitement de la barre comprimée et fléchie et propositions de nouvelles formulations” – PhD Thesis, University of Liège, Belgium, 14 January 2005.

10 B.Z. Vlassov

“Pièces longues et voiles minces” – 2ème édition, Éditions Eyrolles, Paris, 1962.

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Quality Record

RESOURCE TITLE NCCI: Mono-symmetrical uniform members under bending and axial

compression

Reference(s)

ORIGINAL DOCUMENT

Name Compan y Date

Created b y Jean-Pierre Muzeau CUST 21/12/2005

Technical content checked by Alain BUREAU CTICM 21/12/2005

Editorial content checked by D C Iles SCI March 2006

Technical content endorsed by the following STEEL Partners:

1. UK G W Owens SCI 10/3/06

2. France Alain Bureau CTICM 10/3/06

3. Sweden A Olsson SBI 10/3/06

4. Germany C Müller RWTH 10/3/06

5. Spain J Chica Labein 10/3/06

Resource approved by Technical Coordinator

G W Owens SCI 24/6/06

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F r i d a y , S e p t e m b e r 1 9 , 2 0 0 8 i a l i s c o p y r i g h t - a l l r i g h t s r e s e r v e d . U s e o f t h i s d o c u m e n t i s s u b j e c t t o t h e t e r m s a n d c o n d i t i o n s o f t h e A c c e s s S t e e l L i c e n c e A g r e e m e n t

SN030

N

NCC

CCII: Mono-symmetrical uni

: Mono-symmetrical uni form

form members under bendin

members under bendin g

g

and axial compression

and axial compression

Contents

Contents

1.

Scope

2.

Notations and geometrical properties of the

cross-section

(

)

(

)

3.

Member resistance according to EN 1993-1-1

3.1

General

3.2 Susceptibil ity to torsion al deformations

3.3 Elastic resistance obtained from alternative Method 1

(Annex A)

3.4 Elastic resistance obtained from alternative Method 2

(Annex B)

(

)

(

)

(

)

(

)

4.

Evaluation of the elastic critical moment

( )

( )

(

)

(

)

(

)

∫

5.

Evaluation of the non dimensional slenderness

5.1 Non dimensional slenderness for lateral torsion al

buckling

(

)

5.2 Non dimensional slenderness for torsional-flexural

buckling

(

)

(

)

(

)

(

)

(

)

6.

Information about LT

freeware to calculate

the elastic critical moment

7.

References

Quality Record

₍

₎

₍

₎

_{freeware to calculate}