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 ∙ 2,75 N/m2 = 2,2 kN/m2. The most critical ultimate limit state (ULS) load combination: E_(d,ULS )= γ_G∙g_k+ γ_Q∙q_k (4.1) E_(d,ULS )= 1,15∙(5m∙1,0 kN/m^2 )+1,5∙5m∙2,2 kN/m^2=22,3 kN/m Note: Safety factors γG and γQ are according to Finnish National annex of Eurocode 0. The most critical serviceability limit state (SLS) load combination: E_(d,SLS) = γ_G∙g_k + γ_Q∙q_k (4.1) E_(d,SLS) = 1,0∙(5m∙1,0 kN/m^2+1,0∙5m∙2,2kN/m^2=16,0 kN/m ULS design Bending moment resistance M_d= E_(d,ULS)∙s∙L^2/8 = 22,3kN/m∙〖(2,3m)〗^2/8 = 14,7 kNm σ_(m,d)=M_d/W=(14,7 kNm)/(6,75〖∙10〗^6 mm^3 )=21,8 N/mm^2 f_(m,0,edge,d)=k_mod/γ_M ∙k_h∙f_(m,0,edge,k)=0,8/1,2∙1,00∙44 N/mm^2 =29,3 N/mm^2 σ_(m,d)≤f_(m,0,edge,d) →OK Lateral torsional buckling The lintel beam is laterally supported to wall studs in 600mm spacing and the load is applied via them. Therefore the effective length is Lef = 600mm (See table 4.9). 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∙2,28∙〖10〗^6 mm^4∙400N/mm^2 ∙8,20∙〖10〗^6∙ 〗^5 mm^3 ) σ_(m,crit)=72,2 N/〖mm〗^2 λ_rel=√(f_(m,k)/σ_(m,crit) )=√((44 N/mm^2)/(72,2N/mm^2 ))= 0,78 (4.41) when 0,75<λ_(rel,m)≤1,4 ,k_crit=1,56-0,75∙λ_(rel,m)=1,56-0,75∙0,78=0,97 d,ULS = G ∙ k + Q∙ k (4.1) d,ULS = 1,15∙ �5m∙ 1,0 m kN2�+1,5∙ 5m∙ 2,2 kN/m2 = 22,3 kN/m d,SLS = G ∙ k + Q∙ k (4.1) d,SLS = 1,0∙ (5m∙ 1,0 kN/m2 +1,0∙ 5m∙ 2,2kN/m2 = 16,0 kN/m d = d,ULS ∙ ∙ 2/8 = 22,3kN/m∙ (2,3m)2/8 = 14,7 kNm m,d = = 6,7 1 5 4,7 kNm ∙ 106mm3 = 21,8 N/mm2 m,0,edge,d = mod M ∙ h ∙ m,0,edge,k = 0 1 , , 8 2∙ 1,00∙ 44 m N m2 = 29,3 N/mm2 m,d ≤ m,0,edge,d →OK m,crit = y,crit y = � 0,05 z 0,05 tor ef y (4.42) m,crit = π�10600 N/mm2 ∙ 2,28∙ 106mm4 ∙ 4 m 0 m0N2 ∙ 8,20∙ 106 ∙ mm4 600mm∙ 6,75∙ 105mm3 m,crit =72,2 / 2 =� m,k m,crit =�44 N/mm2 72,2N/mm2 = 0,78 (4.41) when 0,75 < rel,m≤1,4 , crit =1,56−0,75∙ rel,m=1,56−0,75∙ 0,78=0,97 crit ∙ m,d =0,97 ∙ 29,3 N/mm2 = 28,6 N/mm2 m,d ≤ crit ∙ m,d → d = d,ULS ∙ ∙ /2 = 22,3kN/m∙ 2,3m/2 = 25,6 kN d,ULS = G ∙ k + Q∙ k (4.1) d,ULS = 1,15∙ �5m∙ 1,0 m kN2�+1,5∙ 5m∙ 2,2 kN/m2 = 22,3 kN/m d,SLS = G ∙ k + Q∙ k (4.1) d,SLS = 1,0∙ (5m∙ 1,0 kN/m2 +1,0∙ 5m∙ 2,2kN/m2 = 16,0 kN/m d = d,ULS ∙ ∙ 2/8 = 22,3kN/m∙ (2,3m)2/8 = 14,7 kNm m,d = = 6,7 1 5 4,7 kNm ∙ 106mm3 = 21,8 N/mm2 m,0,edge,d = mod M ∙ h ∙ m,0,edge,k = 0 1 , , 8 2∙ 1,00∙ 44 m N m2 = 29,3 N/mm2 m,d ≤ m,0,edge,d →OK m,crit = y,crit y = � 0,05 z 0,05 tor ef y (4.42) m,crit = π�10600 N/mm2 ∙ 2,28∙ 106mm4 ∙ 4 m 0 m0N2 ∙ 8,20∙ 106 ∙ mm4 600mm∙ 6,75∙ 105mm3 m,crit =72,2 / 2 =� m,k m,crit =�44 N/ 2 72,2N/mm2 = 0,78 (4.41) when 0,75 < rel,m≤1,4 , crit =1,56−0,75∙ rel,m=1,56−0,75∙ 0,78=0,97 crit ∙ m,d =0,97 ∙ 29,3 N/mm2 = 28,6 N/mm2 m,d ≤ crit ∙ m,d → d = d,ULS ∙ ∙ /2 = 22,3kN/m∙ 2,3m/2 = 25,6 kN , = G ∙ k + Q∙ k (4.1) d,ULS = 1,15∙ �5m∙ 1,0 m kN2�+1,5∙ 5m∙ 2,2 kN/m2 = 22,3 kN/m d,SLS = G ∙ k + Q∙ k (4.1) d,SLS = 1,0∙ (5m∙ 1,0 kN/m2 +1,0∙ 5m∙ 2,2kN/m2 = 16,0 kN/m d = d,ULS ∙ ∙ 2/8 = 22,3kN/m∙ (2,3m)2/8 = 14,7 kNm m,d = = 6,7 1 5 4,7 kNm ∙ 106mm3 = 21,8 N/mm2 m,0,edge,d = mod M ∙ h ∙ m,0,edge,k = 0 1 , , 8 2∙ 1,00∙ 44 m N m2 = 29,3 N/mm2 m,d ≤ m,0,edge,d →OK m,crit = y,crit y = � 0,05 z 0,05 tor ef y (4.42) m,crit = π�10600 N/mm2 ∙ 2,28∙ 106mm4 ∙ 4 m 0 m0N2 ∙ 8,20∙ 106 ∙ mm4 600mm∙ 6,75∙ 105mm3 m,crit =72,2 / 2 =� m,k m,crit =�44 N/mm2 72,2N/mm2 = 0,78 (4.41) when 0,75 < rel,m≤1,4 , crit =1,56−0,75∙ rel,m=1,56−0,75∙ 0,78=0,97 crit ∙ m,d =0,97 ∙ 29,3 N/mm2 = 28,6 N/mm2 m,d ≤ crit ∙ m,d → d = d,ULS ∙ ∙ /2 = 22,3kN/m∙ 2,3m/2 = 25,6 kN , ∙ ∙ (4.1) , ∙ � ∙ 1,0 m kN ∙ ∙ , ∙ ∙ (4.1) ,SLS ∙ ∙ ∙ ∙ , ∙ ∙ ∙ , = 6,7 1 5 4,7 kNm ∙ , ,edge, ∙ ∙ , ,edge, = 0 1 , , 8 2∙ ∙ 44 m N m , ≤ , ,edge, ,crit y,crit y � 0,05 z 0,05 tor ef y ,crit ∙ ∙ ∙ 4 m 0 m0N∙ ∙ ∙ ∙ ∙ ,crit ,k ,crit 44 / 2 72, / 2 rel, 1,4 , crit ∙ rel, ∙ crit ∙ , ∙ , ≤ crit ∙ , → , ∙ ∙ ∙ LVL Handbook Europe 185
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