4. STRUCTURAL DESIGN OF LVL STRUCTURES Figure 4.26. Tension perpendicular to the grain stresses at the hole edges. (1) Risk of cracks due to the tension in perpendicular to grain 33. hd is the height of the hole for rectangular holes. For round holes hd = 0,7d may be used in the equation (4.59). Load distribution length lt,90 is l_(t,90)= {█(0,5∙(h_d+h (4.61) Verification of shear stress concentration at the hole edge shall fulfil the condition: τ_d=k_τ∙(1,5 ∙ V_d)/(b ∙ (h-h_d ) )≤f_(v,d) (4.62) Where k_τ=1,85∙(1+a/h)∙(h_d/h)^0,2 (4.63) τd is the design value of shear stress; kτ is the factor to determine maximum shear stress due to stress concentration; a is the length of a hole [mm], for round holes a = hd; and f(v,d) is the design value of edgewise shear strength Bending stress at the location of a rectangular hole is verified by the equations: (M_d/W_n + M_(o,d)/W_o )/f_(m,d) ≤1 (4.64) (M_d/W_n + M_(u,d)/W_u )/f_(m,d) ≤1 (4.65) where W_n=(b ∙ (h^2-h_d^2 ))/6 (4.66) M_(o,d)=A_o/(A_u+A_o )∙V_d∙a/2 (4.67) M_(u,d)=A_u/(A_u+A_o )∙V_d∙a/2 (4.68) A_o=b∙h_ro and W_o=(b ∙ h_ro^2)/6 (4.69) A_u=b∙h_ru and W_u=(b ∙ h_ru^2)/6 (4.70) Wo and Wu is the effective section modulus of the beam at the location of a hole [mm3] fm,d is the edgewise bending strength [N/mm2] Bending stress at the location of a round hole is verified by the equations: (M_d/W_n )/f_(m,d) ≤1 (4.71) The resistance of LVL-P beams at the location of holes maybe improved and larger hole sizes are allowed when they are reinforced by gluing wood-based panels such as plywood to both sides of the beam around the holes. Detailed design instructions are given e.g. in chapter F3.2 of the Austrian ÖNORM B 1995-1-1:2015 33. As LVL beams are thin, internal reinforcement with screws or glued-in-rods is not recommended. t,90,d = d∙ℎd 4∙ℎ ∙ �3−�ℎdℎ �2� +0,008∙ dℎr (4.59) ℎr =� min(ℎro; ℎru) for rectangular holes min(ℎro +0,15∙ ; ℎro +0,15∙ ) for round holes (4.60) t,90 = �0,5∙ (ℎd +ℎ) for rectangular holes 0,35∙ +0,5∙ ℎ for round holes (4.61) d = τ ∙ 1,5 ∙ d ∙ (ℎ−ℎd) ≤ v,d (4.62) τ =1,85∙ �1+ ℎ� ∙ �ℎdℎ �0,2 (4.63) t, , ∙ � ∙ r ; ∙ ; ∙ t, ∙ ∙ ∙ , ∙ ∙ ( ) ≤ , ℎ , d n + o,d o m,d ≤1 (4.64) d n + u,d u m,d ≤1 (4.65) where n = ∙ �ℎ2−ℎd2 6 � (4.66) o,d = o ∙ d ∙ d n + o,d o m,d ≤1 d n + u,d u m,d ≤1 n = ∙ �ℎ2−ℎd2 6 � o,d = o u+ o ∙ d ∙ 2 u,d = u u+ o ∙ d ∙ 2 o = ∙ ℎro and o = ∙ ℎr2 o 6 u = ∙ ℎru and u = ∙ ℎr2 u 6 d n m,d ≤1 d n + o,d o m,d 1 d n + u,d u m,d 1 n ∙ �ℎ2−ℎd2 o,d o u+ o ∙ d ∙ 2 u,d u u+ o ∙ d ∙ 2 o ∙ ℎro and o ∙ ℎr2 o 6 u ∙ ℎru and u ∙ ℎr2 u 6 d n m,d 1 d n o,d o , d n u,d u , , + ∙ 2 , + ∙ 2 ∙ ℎ ∙ ℎ d n , d n + o,d o m,d ≤1 d n + u,d u m,d ≤1 where n = ∙ �ℎ2−ℎd2 6 � o,d = o u+ o ∙ d ∙ 2 u,d = u u+ o ∙ d ∙ 2 o = ∙ ℎro and o = ∙ ℎr2 o 6 u = ∙ ℎru and u = ∙ ℎr2 u 6 d n m,d ≤1 d n + o,d o m,d ≤1 d n + u,d u m,d ≤1 where n = ∙ �ℎ2−ℎd2 6 � o,d = o u+ o ∙ d ∙ 2 u,d = u u+ o ∙ d ∙ 2 o = ∙ ℎro and o = ∙ ℎr2 o 6 u = ∙ ℎru and u = ∙ ℎr2 u 6 d n m,d ≤1 d n + o,d o m,d ≤1 d n + u,d u m,d ≤1 where n = ∙ �ℎ2−ℎd2 6 � o,d = o u+ o ∙ d ∙ 2 u,d = u u+ o ∙ d ∙ 2 o = ∙ ℎro and o = ∙ ℎr2 o 6 u = ∙ ℎru and u = ∙ ℎr2 u 6 d n m,d ≤1 d n o,d o , d n u,d u , , + ∙ 2 , + ∙ 2 ∙ ℎ ∙ ℎ d n , Figure 4.26. Tension perpendicular to the grain stresses at the hole edges. (1) Risk of cracks due to the tension in perpendicular to grain 33. (Kuva_97_2 f t90 in rectangular hole, Kuva_97_3 f t 90 in round hole) The tension perpendicular to the grain force Ft,90,d depends on the shear force Vd and bending moment Md at the edge of the hole: t,90,d = d∙ℎd 4∙ℎ ∙ [3−(ℎdℎ )2]+0,008 ∙ dℎr (4.59) where ℎr ={ min(ℎro;ℎru) for rectangular holes min(ℎro + 0,15 ∙ ; ℎro + 0,15 ∙ ) for round holes (4.60) is the height of the hole for rectangular holes. For round holes hd = 0,7d may be used in the equation (4.59). Load distribution length lt,90 is t,90 = { 0,5∙(ℎd + ℎ) for rectangular holes 0,35 ∙ + 0,5 ∙ ℎ for round holes (4.61) Verification of shear stress concentration at the hole edge shall fulfil the condition: d = τ ∙ 1,5 ∙ d ∙ (ℎ−ℎd) ≤ v,d (4.62) Where τ =1,85 ∙ (1+ ℎ) ∙ (ℎdℎ )0,2 (4.63) d is the design value of shear stress; τ is the factor to determine maximum shear stress due to stress concentration; LVL Handbook Europe 135
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