LVL Handbook EUROPE

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4. STRUCTURAL DESIGN OF LVL STRUCTURES
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0 25 50 75 100 125 150 175 200 225 250
Buckling factor k
C
Slendernes ratio λ
Buckling factor kc for LVL
LVL 32 P
LVL 48 P
LVL 36 C
LVL 25 C
Figure 4.18. Buckling coefficient kc of different LVL classes for different slenderness ratios λ.
4.3.9.3 Beams subjected to either bending or
combined bending and compression– Lateral
torsional buckling (LTB)
Lateral torsional stability shall be verified both in the case
where only a moment My exists about the strong axis y and
where a combination of moment My and compressive force
N c exists.
In the case where a bending moment M exists only on one
axis, the stresses should satisfy the following expression:
σ_(m,d) ≤ k_crit ∙f_(m,d) (4.38) (EC5 6.33)
where
σm,d is the design bending stress;
fm,d is the design bending strength; and
kcrit is a factor that takes into account the reduced bending
strength due to lateral buckling.
In the case where a combination of moment My about the
strong axis y and compressive force Nc exists, the stresses
should satisfy the following expression
(σ_(m,d)/(k_crit f_(m,d) ))^2+σ_(c,0,d) (4.39) (EC5 6.35)
For beams with an initial lateral deviation from straightness
within the limits defined in Section 10 of Eurocode 5, kcrit may
be determined from expression:
k_crit={█(1,when
(4.40) (EC5 6.34)
The factor kcrit may be taken as 1,0 for a beamwhere lateral dis-
placement of its compressive edge is prevented throughout its
length and where torsional rotation is prevented at its supports
The relative slenderness for bending should be taken as
λ_(rel,m)=√(f_(m,k)/σ_(m,crit) ) (4.41) (EC5 6.30)
where σm,crit is the critical bending stress calculated according
to the classical theory of stability, using 5-percentile stiffness
values. The critical bending stress should be taken as:
σ_(m,crit)=M_(y,crit)/W_y =(π√(E_ (4.42) (EC5 6.31)
where
E0,05 is the fifth percentile value of modulus of elasticity
parallel to grain;
G0,05 is the fifth percentile value of shear modulus parallel to
grain; Note: Gedge,0,05 of LVL shall be used;
Iz is the second moment of area about the weak axis z;
Itor is the torsional moment of inertia;
lef is the effective length of the beam, depending on the
support conditions and the load configuration,
according to Table 4.9;
Wy is the section modulus about the strong axis y.
m,d ≤ crit ∙ m,d (4.38) (EC5 6.33)
� ,d critm,d� 2 + c,0,d c,zc,0,d ≤ 1 (4.39) (EC5 6.35)
crit = � 1, when rel,m ≤ 0,75
1,56 − 0,75 rel,m, when 0,75 < rel,m ≤ 1,4
1
rel,m2 , when 1,4 < rel,m (4.40) (EC5 6.34)
m,d ≤ crit ∙ m,d (4.38) (EC5 6.33)
� m,d critm,d�2 + c,0,d c,zc,0,d ≤ 1 (4.39) (EC5 6.35)
crit = � 1, when rel,m ≤ 0,75
1,56 − 0,75 rel,m , when 0,75 < rel,m ≤ 1,4
1
rel,m2 , when 1,4 < rel,m (4.40) (EC5 6.34)
m,d ≤ crit ∙ m,d
� m,d critm,d�2 + c,0,d c,zc,0,d ≤ 1
crit = � 1, when rel,m ≤ 0,75
1,56 − 0,75 rel,m, when 0,75 < rel,m ≤ 1,4
1
rel,m2 , when 1,4 < rel,m
rel,m = � m,k m,crit
m,crit = y,crit y = � 0,05 0,05 toref y
tor = 1 ∙ ℎ ∙ 3
m,d ≤ crit ∙ m,d
� m,d critm,d�2 + c,0,d c,zc,0,d ≤ 1
crit = � 1, when rel,m ≤ 0,75
1,56 − 0,75 rel,m, when 0,75 < rel,m ≤ 1,4
1
rel,m2 , when 1,4 < rel,m
rel,m = � ,k m,crit
m,crit = y,crit y = � 0,05 0,05 toref y
tor = 1 ∙ ℎ ∙ 3
fm,d is the design bending strength;
kcrit is a factor that takes into account the reduced bendin
buckling.
In the case where a combination of moment My about the strong a
force Nc exists, the stresses should satisfy the following expressio
( m,d critm,d)2 + c,0,d c,zc,0,d ≤ 1
For beams with an initial lateral deviation from straightness within
Section 10 of Eurocode 5, kcrit may be determined from expression
crit = { 1 when rel,m ≤ 0,75
1,56 − 0,75 rel,m when 0,75 < rel,m ≤ 1,4
1
rel,m2 hen 1,4 < rel,m
The factor kcrit may be taken as 1,0 for a beam where lateral displa
edge is prevented throughout its length and where torsional rotati
supports
The relative slenderness f r be ding should be taken as
rel,m = √ m,k m,crit
where σm,crit is the critical bending stress calculated according to th
stability, using 5-percentile stiffness values. The critical bending st
m,crit = y,crit y = √ 0,05 0,05 toref y
where
E0,05 is the fifth percentile value of modulus of elasticity pa
G0,05 is the fifth percentile value of shear modulus parallel
LVL shall be used;
Iz is the second moment of area about th weak axis z;
Itor is the torsional moment of in rtia;
l
ef is the effective length f he beam, depending on the
load configuration, according to Table 4.9;
Wy is th section modulus about the strong axis y.
In the case of rectangular cross sections:
tor = 1 ∙ ℎ ∙ 3
where
LVL Handbook Europe 129