4. STRUCTURAL DESIGN OF LVL STRUCTURES 4.3.11 Tapered beams The influence of the taper on the bending stresses parallel to the surface shall be taken into account. The design bending stresses, σm,α,d and σm,0,d (see Figure 4.21) may be taken as: σ_(m,α,d)=σ_(m,0,d)=(6M_d)/(bh^2 ) (4.49) (EC5 6.37) At the outermost fibre of the tapered edge, the stresses should satisfy the following expression: σ_(m,α,d)≤k_(m,α)∙f_(m,d) (4.50) (EC5 6.38) where σm,α,d is the design bending stress at an angle to grain; fm,d is the design bending strength; and km,α is calculated as follows: For tensile stresses parallel to the tapered edge: k_(m,α)=1/√(1 + (f_(m, (4.51)32 Figure 4.21. Single-tapered beam. α is the angle between the tapered edge and the grain direction of the beam (EC5 Figure 6.8). where a={█(0,75 for LVL-P@1,0 for LVL-C)┤ (4.52)32 For compressive stresses parallel to the tapered edge: k_(m,α)=1/√(1 + (f_(m,d (4.53)32 where b={█(1,5 for LVL-P@1,0 for LVL-C)┤ (4.54)32 It is not necessary to take km,α into consideration in the resistance against lateral torsional buckling of the beam equation (4.38). The effects of combined axial force and bending moment shall be taken into account. When the tapered edge is under tension stress, km,α is used to reduce the bending strength in the equations for combined stresses equation (4.17) and (4.18). When the tapered edge is under compression stress, km,α is used to reduce the bending strength in the equations for combined stresses equations (4.19) and (4.20). Figure 4.22. Strength reduction factor km,α for tensile or compression stress parallel to the tapered edge. Left LVL 48 P, right LVL 36 C. m,α,d = m,0,d =6 d ℎ2 (4.49) (EC5 6.37) m,α,d ≤ m,α ∙ m,d (4.50) (EC5 6.38) m,α = 1 �1 + � m,d ∙ v,d tan � 2+ � m,d t,90,d tan2 � 2 (4.51)32 m,α,d = m,0,d =6 d ℎ2 (4.49) (EC5 6.37) m,α,d ≤ m,α ∙ m,d (4.50) (EC5 6.38) m,α = 1 �1 + � m,d ∙ v,d tan � 2+ � m,d t,90,d tan2 � 2 (4.51)32 =�0,75 for LVL−P 1,0 for LVL−C (4.52) m,α = 1 �1 + � m,d ∙ v,d tan � 2+ � m,d c,90,d tan2 � 2 =�1,5 for LVL−P 1,0 for LVL−C v,max,d = m,0,max,d ∙ tan 90,max,d = m,0,max,d ∙ tan2 =�0,75 for LVL−P 1,0 for LVL−C (4.52)3 m,α = 1 �1 + � m,d ∙ v,d tan � 2+ � m,d c,90,d tan2 � 2 =�1,5 for LVL P 1,0 for LVL−C v,max,d = m,0,max,d ∙ tan 90,max,d = m,0,max,d ∙ tan2 155 (255) m,α 1 √1 + ( m,d ∙ v,d tan ) 2 + ( m,d t,90,d tan2 ) 2 (4.51)32 where = { 01, 7, 05ffoorrLLVVLL−−CP (4.52)32 For compressive stresses parallel to the tapered edge: m,α = 1 √1 + ( m,d ∙ v,d tan ) 2 + ( m,d c,90,d tan2 ) 2 (4.53)32 Where = { 1 1 , , 5 0 f f o o r r L L V V L L −− P C (4.54)32 It is not necessary to take km,α into consideration in the resistance against lateral torsional buckling of the beam equation (4.38). The effects of combined axial force and bending moment shall be taken into account. When the tapered edge is under tension stress, km,α is used to reduce the bending strength in the equations for combined stresses equation (4.17) and (4.18). When the tapered edge is under compression stress, km,α is used to reduce the bending strength in the equations for combined stresses equations (4.19) and (4.20). It is recommended to have the tapered edge on the compressive side, especially for LVL-P, since the tension perpendicular to grain strength ft,90,edge,k is low, which can lead to cracks and brittle failure. LVL-C may be used for special shapes, also when the tapered edge is on the tensile side, as its ft,90,edge,k is higher due to the cross veneers and it behaves more ductile. Figure 4.21 shows the km,α factors as a function of the angle α. m,α = 1 √1 + ( m,d ∙ v,d tan ) 2 + ( m,d t,90,d tan2 ) 2 (4.51)32 where = { 01, 7, 05ffoorrLLVVLL−−CP For compressive stresses parallel to the tapered edge: m,α 1 √1 + ( m,d ∙ v,d tan ) 2 + ( m,d c,90,d tan2 ) 2 (4.53)32 Where = { 1 1 , , 5 0 f f o o r r L L V V L L −− P C It is not necessary to take km,α into consideration in the resistance against buckling of the beam equation (4.38). The effects of combined axial force moment shall be taken into account. When the tapered edge is under ten used to reduce the bending strength in the equations for combined stress and (4.18). When the tapered edge is under compression stress, km,α is us bending strength in the equations for combined stresses equations (4.19) It is recommended to have the tapered edge on the compressive side, es since the tension perpendicular to grain strength ft,90,edge,k is low, which ca brittle failure. LVL-C may be used for special shapes, also when the taper tensile side, as its ft,90,edge,k is higher due to the cross veneers and it behav Figure 4.21 shows the km,α factors as a function of the angle α. Figure 4.21. Strength reduction factor km,α for tensile or compression stres tapered edge. Left LVL 48 P, right LVL 36 C. For high pitched roof beams (α ≥ ~10°) the maximum shear stress v,max,d perpendicular to the grain 90,max,d shall be calculated at the point of the m moment stress with the equations: 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 0 5 10 15 20 25 30 35 40 45 Reduction factor km,α α LVL 48 P km,α,tension km,α,compression 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 0 5 10 15 20 25 30 35 40 45 Reduction factor km,α α LVL 36 C km,α,tension km,α,compression 132 LVL Handbook Europe
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