4. STRUCTURAL DESIGN OF LVL STRUCTURES 4.3.9 Stability of LVL members LVL cross sections are usually slender, as it is economical to produce panel billets and cut thin and high or deep beams and stud dimensions. Stability calculation is therefore particularly important for LVL beams. Column stability and lateral torsional stability shall be verified using the characteristic stiffness properties E0,05 and G0,05. 4.3.9.1 Members subjected to combined bending and axial compression or tension Roof rafters of pitched roofs are typical members which shall be analysed for combined bending and compression. According to Eurocode 5, the expressions (4.17) & (4.18) or (4.19) & (4.20) shall be fulfilled. For combined bending and axial tension the following expressions shall be satisfied: σ_(t,0,d)/f_(t,0,d) +σ_(m,y,d)/(k_(m,α (4.17) (EC5 6.17) σ_(t,0,d)/f_(t,0,d) +k_m σ_(m,y,d) (4.18) (EC5 6.18) For combined bending and axial compression the following expressions shall be satisfied: (σ_(c,0,d)/f_(c,0,d) )^2+σ_(m,y,d)/( (4.19) (EC5 6.19) (σ_(c,0,d)/f_(c,0,d) )^2+k_m σ_(m, (4.20) (EC5 6.20) where km makes allowance for re-distribution of stresses and the effect of inhomogeneities of the material in cross-section. For rectangular LVL cross sections km = 0,7 and for other cross sections km = 1,0; and km,α is a factor for combined stresses in tapered beams, see subsection 4.3.11. For straight beams km,α =1,0. 4.3.9.2 Columns subjected to either compression or combined compression and bending When both λrel,z ≤ 0,3 and λrel,y ≤ 0,3 the stresses should satisfy the expressions (4.19) and (4.20) of combined bending and axial compression. In all other cases the stresses, which will be increased due to deflection, should satisfy the expressions (4.29) and (4.30). σ_(c,0,d)/〖k_(c,y)∙f〗_(c,0,d) +σ_(m (4.29) (EC5 6.23) σ_(c,0,d)/〖k_(c,z)∙f〗_(c,0,d) +k_m∙σ (4.30) (EC5 6.24) k_(c,y)=1/(k_y+√(k_y^2-λ_(rel,y)^2 )) (4.31)(EC5 6.25) k_(c,z)=1/(k_z+√(k_z^2-λ_(rel,z)^2 (4.32) (EC5 6.26) k_y=0,5(1+β_c (λ_(rel,y)-0,3)+λ_(rel,y)^2 (4.33) (EC5 6.27) k_z=0,5(1+β_c (λ_(rel,z)-0,3)+λ_(rel,z)^2 (4.34) (EC5 6.28) Factor βc is 0,10 for LVL members within the straightness limit of L/500. The limit is defined in Eurocode 5, Section 10 as the deviation from straightness measured midway between the supports of frame members, columns and beams where lateral instability can occur. The relative slenderness ratio should be taken as: λ_(rel,y)=λ_y/π √(f_(c,0,k)/E_0,05 ) (4.35) (EC5 6.21) λ_(rel,z)=λ_z/π √(f_(c,0,k)/E_0,05 ) (4.36) (EC5 6.22) Where λy and λrel,y are the slenderness ratio corresponding to bending about the y-axis (deflection in the z-direction); λz and λrel,z are the slenderness ratio corresponding to bending about the z-axis (deflection in the y-direction); and E0,05 is the characteristic value of modulus of elasticity parallel to the grain. For rectangular cross section the slenderness of a member is defined as: λ=l_c/i=l_c/√((I/A) )=l_c/√((((bh^3)/12))/bh)=√12 (4.37) where lc is the buckling length; and h is the height of the member in the direction of the buckling analysis. The buckling coefficient kc for different LVL classes and slenderness ratios are shown in Figure 4.18 and Table 4.8. The values are very similar for all shown LVL classes. More advanced instructions on determining the effect of an angle to the grain on LVL strength properties may be found in the manufacturers’ technical documentation. t,0,d t,0,d + m,y,d m,α m,y,d + m m,z,d m,z,d ≤1 (4.17) (EC5 6.17) t,0,d t,0,d + m m,y,d m,α m,y,d + m,z,d m,z,d ≤1 (4.18) (EC5 6.18) � c,0,d c,0,d� 2 + m,y,d m,α m,y,d + m m,z,d m,z,d ≤1 (4.19) (EC5 6.19) � c,0,d c,0,d� 2 + m m,y,d m,α m,y,d + m,z,d m,z,d ≤1 (4.20) (EC5 6.20) t,0,d t,0,d + m,y,d m,α m,y,d + m m,z,d m,z,d ≤1 (4.17) (EC5 6.17) t,0,d t,0,d + m m,y,d m,α m,y,d + m,z,d m,z,d ≤1 (4.18) (EC5 6.18) , , , , m,y,d m,α ,y,d + m , , , , (4.19) (EC5 6.19) � c,0,d c,0,d� 2 + m m,y,d m,α m,y,d + m,z,d m,z,d ≤1 (4.20) (EC5 6.20) t, , t, , m,y,d m,α ,y,d + m , , , , (4.17) (EC5 6.17) t,0,d t,0,d + m m,y,d m,α m,y,d + m,z,d m,z,d ≤1 (4.18) (EC5 6.18) � c,0,d c,0,d� 2 + m,y,d m,α m,y,d + m m,z,d m,z,d ≤1 (4.19) (EC5 6.19) � c,0,d c,0,d� 2 + m m,y,d m,α m,y,d + m,z,d m,z,d ≤1 (4.20) (EC5 6.20) t,0, t,0,d + m,y,d m,α m,y,d + m ,z, m,z,d ≤1 (4.17) (EC5 6.17) t,0, t,0,d + m m,y,d m,α m,y,d + ,z, m,z,d ≤1 (4.18) (EC5 6.18) � c,0, c,0,d� 2 + m,y,d m,α m,y,d + m ,z, m,z,d ≤1 (4.19) (EC5 6.19) � c,0, c,0,d� 2 + m m,y,d m,α m,y,d + ,z, m,z,d ≤1 (4.20) (EC5 6.20) c,0,d c,y∙ c,0,d + m,y,d m,α∙ m,y,d + m∙ m,z,d m,z,d ≤1 (4.29) (EC5 6.23) c,0,d c,z∙ c,0,d + m∙ m,y,d m,α∙ m,y,d + m,z,d m,z,d ≤1 (4.30) (EC5 6.24) c,y = 1 y+� y2− rel, 2 y (4.31) (EC5 6.25) c,0,d c,y∙ c,0,d + m,y,d m,α∙ m,y,d + m∙ , , m,z,d ≤1 (4.29) (EC5 6.23) c,0,d c,z∙ c,0,d + m∙ m,y,d m,α∙ m,y,d + , , m,z,d ≤1 (4.30) (EC5 6.24) c,y = 1 y+� y2− rel, 2 y (4.31) (EC5 6.25) c,0,d c,y∙ c,0,d + m,y,d m,α∙ m,y,d + m∙ m,z,d m,z,d ≤1 (4 c,0,d c,z∙ c,0,d + m∙ m,y,d m,α∙ m,y,d + m,z,d m,z,d ≤1 (4 c,y = 1 y+� y2− rel, 2 y (4 c,z = 1 z+� z2− rel, 2 z (4 y =0,5�1+ c� rel,y −0,3�+ rel, 2 y� (4 z =0,5�1+ c� rel,z −0,3�+ rel, 2 z� (4 rel,y = y � c,0,k 0,05 (4 rel,z = z � c,0,k 0,05 (4 = c = c �� � = c �� 1ℎ23� ℎ =√12� cℎ� c,0,d c,y∙ c,0,d ,y,d ,α∙ ,y,d ∙ ,z,d ,z,d (4 c,0,d c,z∙ c,0,d ∙ ,y,d ,α∙ ,y,d ,z,d ,z,d (4 c,y 1 y+� y2− rel, (4 c,z 1 z+� z2− rel, (4 y � c� rel,y 0,3� rel, � (4 z � c� rel,z 0,3� rel, � (4 rel,y y c,0,k 0,05 (4 rel,z z c,0,k 0,05 (4 c c �� � c � 1ℎ23� ℎ c c,0,d c,y∙ c,0,d + m,y,d m,α∙ m,y,d + m∙ ,z,d m,z,d ≤1 (4 c,0,d c,z∙ c,0,d + m∙ m,y,d m,α∙ m,y,d + ,z,d m,z,d ≤1 (4 c,y = 1 y+� y2− rel, 2 y (4 c,z = 1 z+� z2− rel, 2 z (4 y =0,5�1+ c� rel,y −0,3�+ rel, 2 y� (4 z =0,5�1+ c� rel,z −0,3�+ rel, 2 z� (4 rel,y = y � c,0,k 0,05 (4 rel,z = z � c,0,k 0,05 (4 = c = c �� � = c �� 1ℎ23� ℎ =√12� cℎ� c,0,d c,y∙ c,0,d + m,y,d ,α∙ m,y,d + m∙ ,z,d ,z, ≤1 (4 c,0,d c,z∙ c,0,d + m∙ m,y,d m,α∙ m,y,d + ,z,d m,z,d ≤1 (4 c,y = 1 y+� y2− rel, 2 y (4 c,z = 1 z+� z2− rel, 2 z (4 y c� rel,y rel, 2 y� z =0,5�1+ c� rel,z −0,3�+ rel, 2 z� (4 rel,y = y � c,0,k 0,05 (4 rel,z = z � c,0,k 0,05 (4 = c = c �� � = c �� 1ℎ23� ℎ =√12� cℎ� c,0,d c,y∙ c,0, m,y,d m,α∙ m,y,d + m∙ ,z,d ,z, c,0,d c,z∙ c,0,d + m∙ m,y,d m,α∙ m,y,d + ,z,d m,z,d ≤1 (4 ,y y+� y2− , 2 y c,z = 1 z+� z2− rel, 2 z y =0,5� c� rel,y 0,3� rel, 2 y� (4 z =0,5�1+ c� rel,z −0,3�+ rel, 2 z� (4 ,y y , , , rel,z = z � c,0,k 0,05 (4 = c = c �� � = c �� 1ℎ23� ℎ =√12� cℎ� c,0,d c,y∙ c,0,d m,y,d m,α∙ m,y,d m∙ , , , , c,0,d c,z∙ c,0,d m∙ m,y,d m,α∙ m,y,d m,z,d m,z,d 1 (4 ,y y y2 2 y c,z 1 z+� z2− rel, 2 z (4 y =0,5� c� rel,y 0,3� rel, 2 y� (4 z =0,5� c� rel,z 0,3� rel, 2 z� (4 rel,y y c,0,k 0,05 (4 rel,z z c,0,k 0,05 (4 c c �� � c �� 1ℎ23� ℎ √12� cℎ� , , ,y∙ , , m,y,d m,α∙ ,y,d + m∙ , , , , c,0,d c,z∙ c,0,d + m∙ m,y,d m,α∙ m,y,d + m,z,d m,z,d ≤1 (4 c,y 1 y+� y2− rel, 2 y c,z = 1 z+� z2− rel, 2 z y =0,5�1+ c� rel,y −0,3�+ rel, 2 y� (4 z =0,5�1+ c� rel,z −0,3�+ rel, 2 z� (4 y y , , , rel,z = z � c,0,k 0,05 (4 = c = c �� � = c �� 1ℎ23� ℎ =√12� cℎ� LVL Handbook Europe 127
RkJQdWJsaXNoZXIy MjU0MzgwNw==