9. CALCULATION EXAMPLES OF LVL STRUCTURES Loading combinations Snow load at roof level qk = μ1 ∙ Ce ∙ sk. Form factor μ1 = 0,8, when roof angle is less than 30° and in normal conditions Ce = 1,0 → qk = 0,8 ∙ 1,0∙2,5 N/m2 = 2,0 kN/m2. Accidental load combination of fire in the ultimate limit state (ULS): Ed,ULS,fi = γG ∙ (g1,k + g2,k) + ψ1 ∙ γQ ∙ qk Ed,ULS,fi =1,0 ∙ (8m ∙ 1,0 kN/m2 + 0,2 kN/m ) + 0,4 ∙ 1,0 ∙ 8m ∙ 2,0 kN/m2 Ed,ULS,fi = 14,6 kN/m Note: Safety factors γG, ψ1 and γQ are according to Finnish National annex of Eurocode 0. ULS design Bending moment resistance M_d = E_(d,ULS,fi)∙s∙L2/8 = 14,6 kN/m∙(4m)^2/8 = 29,2 kNm σ_(m,d)=M_d/W=(29,2 kNm)/(1,52〖∙10〗^6 〖 mm〗^3 )=19,2 N/mm^2 f_(m,d,fi)=(k_(mod,fi) 〖∙k〗_fi∙k_h)/γ_(M,fi) ∙f_(m,edge,k) f_(m,d,fi)=(1,0∙1,1∙(300mm/344mm)^0,15)/1,0∙44 N/mm^2 =47,4 N/mm^2 σ_(m,d)≤f_(m,d,fi) →OK Lateral torsional buckling The beam is loaded on the top side and the purlins won’t act as supports against lateral torsional buckling for 30min fire exposure. Therefore according to Table 4.9 and EN1995-1-2, clause 4.3.2 (1) and the effective length Lef of the beam is L_ef=0,9∙L + 2∙h = 0,9 ∙ 4000mm + 2 ∙ 344mm = 4288mm. σ_(m,crit)=M_(y,crit)/W_y =(π√(E_0,05 I_z G_0,05 I_tor ))/(l_ef W_y ) (4.42) σ_(m,crit)= (π√(10600 N/mm^2∙1,31∙〖10〗^7 〖 mm〗^4∙400N/mm^ 〖1,52∙10〗^6 〖 mm〗^3 ) σ_(m,crit)= 25,8 N/mm^2 λ_rel=√(f_(m,k)/σ_(m,crit) )=√((44 N/mm^2)/(25,8 N/mm^2 ))= 1,36 (4.41) when 0,75<λ_(rel,m)≤1,4 ,k_crit=1,56-0,75∙λ_(rel,m)=1,56-0,75∙1,36=0,58 k_crit∙ f_(m,d,fi)=0,58 ∙47,4 N/mm^2=27,5 N/mm^2 σ_(m,d)=19,2 N/mm^2≤k_crit∙ f_(m,d)→OK (4.38) d = d,ULS,fi ∙ ∙ 2/8 = 14,6 kN/m∙ (4m)2/8 = 29,2 kNm m,d = d = 1,5 2 2 9,2 kNm ∙ 106 mm3 = 19,2 N/mm2 m,d,fi = mod,fi ∙ fi ∙ h M,fi ∙ m,edge,k m,d,fi = 1,0∙ 1,1∙ �33 04 04 mm mm� 0,15 1,0 ∙ 44 m N m2 =47,4 m N m2 m,d ≤ m,d,fi →OK ef =0,9∙ + 2∙ ℎ = 0,9 ∙ 4000mm + 2 ∙ 344mm = 4288mm. m,crit = y,crit y = � 0,05 0,05 tor ef y (4.42) m,crit = π�10600 N/mm2 ∙ 1,31∙ 107 mm4 ∙ 400N/mm2 ∙ 4,71∙ 107 ∙ mm4 4288 mm∙ 1,52∙ 106 mm3 m,crit = 25,8 N/mm2 d = d,ULS,fi ∙ ∙ 2/8 = 14,6 kN/m∙ (4m)2/8 = 29,2 kNm m,d = d = 1,5 2 2 9,2 kNm ∙ 106 mm3 = 19,2 N/mm2 m,d,fi = mod,fi ∙ fi ∙ h M,fi ∙ m,edge,k m,d,fi = 1,0∙ 1,1∙ �33 04 04 mm mm� 0,15 1,0 ∙ 44 m N m2 =47,4 m N m2 m,d ≤ m,d,fi →OK ef =0,9∙ + 2∙ ℎ = 0,9 ∙ 4000mm + 2 ∙ 344mm = 4288mm. m,crit = y,crit y = � 0,05 0,05 tor ef y (4.42) m,crit = π�10600 N/mm2 ∙ 1,31∙ 107 mm4 ∙ 400N/mm2 ∙ 4,71∙ 107 ∙ mm4 4288 mm∙ 1,52∙ 106 mm3 m,crit = 25,8 N/mm2 rel =� m,k m,crit =�44 N/mm2 25,8 N/mm2 = 1,36 (4.41) when 0,75 < rel,m≤1,4 , crit =1,56−0,75∙ rel,m=1,56−0,75∙ 1,36=0,58 crit ∙ m,d,fi =0,58 ∙ 47,4 N/mm2 = 27,5 N/mm2 m,d = 19,2 N/mm2 ≤ crit ∙ m,d →OK (4.38) d = d,ULS,fi ∙ /2 = 14,6 kN/m∙ 4,0m/2 = 29,2 kN v,d = 3∙ d 2∙ = 3∙ 2 29,2 kN ∙ 26488 mm2 = 1,7 N/mm2 v,d,fi = mod,fi ∙ fi M,fi ∙ v,0,edge,k = 1,0∙1,0 1,1∙ 4,2 m N m2 = 4,6 N/mm2 m,d ≤ v,d,fi →OK 212 LVL Handbook Europe
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