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 kC 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 Nc 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 beam where lateral displacement 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; and Wy is the section modulus about the strong axis y. m,d ≤ crit ∙ m,d (4.38) (EC5 6.33) � m,d crit m,d� 2 + c,0,d c,z c,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, 2 m, when 1,4 < rel,m (4.40) (EC5 6.34) m,d ≤ crit ∙ m,d (4.38) (EC5 6.33) � m,d crit m,d� 2 + c,0,d c,z c,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, 2 m, when 1,4 < rel,m (4.40) (EC5 6.34) m,d ≤ crit ∙ m,d (4 � m,d crit m,d� 2 + c,0,d c,z c,0,d ≤1 (4 crit =� 1, when rel,m≤0,75 1,56−0,75 rel,m, when 0,75 < rel,m≤1,4 1 rel, 2 m, when 1,4 < rel,m (4 rel,m=� m,k m,crit (4 m,crit = y,crit y = � 0,05 0,05 tor ef y (4 tor = 1 ∙ ℎ ∙ 3 m,d ≤ crit ∙ m,d (4 � m,d crit m,d� 2 + c,0,d c,z c,0,d ≤1 (4 crit =� 1, when rel,m≤0,75 1,56−0,75 rel,m, when 0,75 < rel,m≤1,4 1 rel, 2 m, when 1,4 < rel,m (4 rel,m=� ,k m,crit (4 m,crit = y,crit y = � 0,05 0,05 tor ef y (4 tor = 1 ∙ ℎ ∙ 3 fm,d is the design bending strength; kcrit is a factor that takes into account the reduced bending buckling. In the case where a combination of moment My about the strong axis force Nc exists, the stresses should satisfy the following expression ( m,d crit m,d) 2 + c,0,d c,z c,0,d ≤1 (4 For beams with an initial lateral deviation from straightness within the 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 r2 el,m when 1,4 < rel,m (4 The factor kcrit may be taken as 1,0 for a beam where lateral displace edge is prevented throughout its length and where torsional rotation supports The relative slenderness for bending should be taken as rel,m=√ m,k m,crit (4 where σm,crit is the critical bending stress calculated according to the c stability, using 5-percentile stiffness values. The critical bending stre m,crit = y,crit y = √ 0,05 0,05 tor ef y (4 where E0,05 is the fifth percentile value of modulus of elasticity para G0,05 is the fifth percentile value of shear modulus parallel to 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 su load configuration, according to Table 4.9; Wy is the section modulus about the strong axis y. In the case of rectangular cross sections: tor = 1 ∙ ℎ ∙ 3 where 1 =1 3(1−0,63∙ ℎ ) LVL Handbook Europe 129
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