9. CALCULATION EXAMPLES OF LVL STRUCTURES ULS design Bending moment resistance M_d = E_(d,ULS)∙s∙L^2/8 = 4,03kN/m^2∙0,4m∙〖(4,5m)〗^2/8 = 4, σ_(m,d)=M_d/W=(4,1 kNm)/(4,32〖∙10〗^5 mm^3 )=9,5 N/mm^2 f_(m,0,edge,d)=k_mod/γ_M ∙k_h∙f_(m,0,edge,k) (4.3) f_(m,0,edge,d)=0,8/1,2∙1,034∙44 N/mm^2 =30,3 N/mm^2 σ_(m,d)≤f_(m,0,edge,d) →OK Lateral torsional buckling is prevented by the fixing of the decking. Shear resistance V_d = E_(d,ULS)∙s∙L/2 = 4,03kN/m^2∙0,4m∙4,5m/2 = 3,6 kN τ_(v,d)=〖3∙V〗_d/(2∙A)=(3∙3,6 kN)/(2 ∙10 800mm^2 )=0,5 N/mm^2 f_(v,0,edge,d)=k_mod/γ_M ∙f_(v,0,edge,k)=0,8/1,2∙4,2 N/mm^2 =2,8 N/mm^2 τ_(m,d)≤f_(v,0,edge,d) →OK Compression perpendicular to the grain F_(c,90,d) = V_d = 3,6 kN σ_(c,90,d)=F_(c,90,d)/A_ef =F_(c,90,d)/(b∙(l_s (4.14) σ_(c,90,d)=3,6kN/(45 mm∙(45 mm+15mm k_(c,90)∙f_(c,90,edge,d)=k_(c,90)∙k_mod/γ_M ∙ (4.13) k_(c,90)∙f_(c,90,edge,d)=1,0∙0,8/1,2∙6 N/mm^2=4 (kc,90 Table 4.7) σ_(c,90,d)≤k_(c,90)∙f_(m,0,edge,d) →OK SLS design Instantaneous deflection w_inst = w_(inst,g) + w_(inst,q) w_(inst,g)=(5〖∙g〗_(d,SLS)∙ (4.74) d,SLS = G ∙ ( 1,k + 2,k)+ G ∙ k (4.1) d,SLS =1,0∙ (0,6 kN/m2 + 0,3 kN/m2 )+1,0∙ 2,0 kN/m2 d,SLS = 2,9 kN/m2 d = d,ULS ∙ ∙ 2/8 = 4,03kN/m2 ∙ 0,4m∙ (4,5m)2/8 = 4,1 kNm m,d = d = 4,32 4,1 kNm ∙ 105mm3 = 9,5 N/mm2 m,0,edge,d = mod M ∙ h ∙ m,0,edge,k (4.3) m,0,edge,d = 0 1 , , 8 2∙ 1,034∙ 44 m N m2 = 30,3 N/mm2 m,d ≤ m,0,edge,d →OK d = d,ULS ∙ ∙ /2 = 4,03kN/m2 ∙ 0,4m∙ 4,5m/2 = 3,6 kN d,SLS = G ∙ ( 1,k + 2,k)+ G ∙ k (4.1) d,SLS =1,0∙ (0,6 kN/m2 + 0,3 kN/m2 )+1,0∙ 2,0 kN/m2 d,SLS = 2,9 kN/m2 d = d,ULS ∙ ∙ 2/8 = 4,03kN/m2 ∙ 0,4m∙ (4,5m)2/8 = 4,1 kNm m,d = d = 4,32 4,1 kNm ∙ 105mm3 = 9,5 N/mm2 m,0,edge,d = mod M ∙ h ∙ m,0,edge,k (4.3) m,0,edge,d = 0 1 , , 8 2∙ 1,034∙ 44 m N m2 = 30,3 N/mm2 m,d ≤ m,0,edge,d →OK d = d,ULS ∙ ∙ /2 = 4,03kN/m2 ∙ 0,4m∙ 4,5m/2 = 3,6 kN v,d = 3∙ d 2∙ = 3∙ 2 3,6 kN ∙ 10 800mm2 = 0,5 N/mm2 v,0,edge,d = mod M ∙ v,0,edge,k = 0 1 , , 8 2∙ 4,2 m N m2 = 2,8 N/mm2 m,d ≤ v,0,edge,d →OK c,90,d = d = 3,6 kN c,90,d = c,90,d ef = c,90,d ∙� support+15 mm� (4.14) c,90,d = 3,6kN 45 mm∙ (45 mm+ 15mm) = 1,35 N/mm2 c,90 ∙ c,90,edge,d = c,90 ∙ mod M ∙ c,90,edge,k (4.13) c,90 ∙ c,90,edge,d =1,0∙ 0,1 8,2∙ 6 N/mm2 =4N/mm2 (kc,90 Table 4.7) c,90,d ≤ c,90 ∙ m,0,edge,d →OK inst = inst,g + inst,q inst,g =5∙ d,SLS∙ ∙ 4 384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2 8∙ mean (4.74) inst,g = 2,69 mm + 0,17 mm = 2,86 mm inst,q = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8∙ mean = 5,97 mm+ 0,38 mm = 6,35 mm inst = 2,86 mm + 6,34 mm = 9,2 mm inst ≤ 400 =4 4 5 0 0 0 0 = 11,3 mm→OK ∙� ∙ ∙ ∙ ∙ ∙ ∙ ∙ v,d = 3∙ d 2∙ = 3∙ 2 3,6 kN ∙ 10 800mm2 = 0,5 N/mm2 v,0,edge,d = mod M ∙ v,0,edge,k = 0 1 , , 8 2∙ 4,2 m N m2 = 2,8 N/mm2 m,d ≤ v,0,edge,d →OK c,90,d = d = 3,6 kN c,90,d = c,90,d ef = c,90,d ∙� support+15 mm� (4.14) c,90,d = 3,6kN 45 mm∙ (45 mm+ 15mm) = 1,35 N/mm2 c,90 ∙ c,90,edge,d = c,90 ∙ mod M ∙ c,90,edge,k (4.13) c,90 ∙ c,90,edge,d =1,0∙ 0,1 8,2∙ 6 N/mm2 =4N/mm2 (kc,90 Table 4.7) c,90,d ≤ c,90 ∙ m,0,edge,d →OK inst = inst,g + inst,q inst,g =5∙ d,SLS∙ ∙ 4 384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2 8∙ mean (4.74) inst,g = 2,69 mm + 0,17 mm = 2,86 mm inst,q = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8∙ mean = 5,97 mm+ 0,38 mm = 6,35 mm inst = 2,86 mm + 6,34 mm = 9,2 mm inst ≤ =4500 = 11,3 mm→OK 216 (255) 0,edge,d = 0 1 , , 8 2∙ 1,034∙ 44 m N m2 = 30,3 N/mm2 m,d ≤ m,0,edge,d →OK Lateral torsional buckling is prevented by the fixing of the decking. Shear resistance d = d,ULS ∙ ∙ /2 = 4,03kN/m2 ∙ 0,4m∙ 4,5m/2 = 3,6 kN v,d = 3∙ d 2∙ = 3∙ 2 3,6 kN ∙ 10 800mm2 = 0,5 N/mm2 v,0,edge,d = mod M ∙ v,0,edge,k = 0 1 , , 8 2∙ 4,2 m N m2 = 2,8 N/mm2 m,d ≤ v,0,edge,d →OK Compression perpendicular to the grain , , d = 3,6 kN c,90,d = c,90,d ef = c,90,d ∙� support+15 mm� (4.14) c,90,d = 3,6kN 45 mm∙ (45 mm+ 15mm) = 1,35 N/mm2 c,90 ∙ c,90,edge, = c,90 ∙ mod M ∙ c,90,edge,k (4.13) , ∙ c,90,edge,d =1,0∙ 0,1 8,2∙ 6 N/mm2 =4N/mm2 (kc,90 Table 4.7) c,90,d ≤ c,90 ∙ m,0,edge,d →OK SLS design Instantaneous deflection inst = inst,g + inst,q , = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8∙ mean = 2,69 mm+ 0,17 mm = 2,86 mm (4.74) ,q = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8∙ mean = 5,97 mm+ 0,38 mm = 6,35 mm inst = 2,86 mm + 6,35 mm = 9,2 mm 180 LVL Handbook Europe
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