9. CALCULATION EXAMPLES OF LVL STRUCTURES Beam properties: Bending strength edgewise fm,0,edge,k = 44 N/mm2 Shear strength edgewise fv,0,edge,k = 4,2 N/mm2 Compression perpendicular to grain edgewise fc,90,edge,k = 6 N/mm2 Modulus of elasticity E0,k = 11 600 N/mm2 Modulus of elasticity E0,mean = 13 800 N/mm2 Modulus of rigidity G0,edge,k = 600 N/mm2 Modulus of rigidity G0,edge,mean = 400 N/mm2 Area of cross section A =2 x b∙h = 40800 mm2 Section modulus Wy = 2 x b∙h2/6 = 2,72∙106 mm3 Moment of inertia Iy = 2 x b∙h3/12 = 5,44∙108 mm4 Moment of inertia Iz = 2 x h∙b3/12 = 8,84∙106 mm4 Torsion moment of inertia Itor = 2 x 0,3∙h∙b3 = 3,18∙107 mm4 Moment stiffness of the joist EIy = 13800 N/mm2 ∙ 5,44∙108 mm4 = 7,51∙1012 Nmm2 Shear rigidity of the joist GA = 600 N/mm2 ∙ 40800 mm2 = 2,45∙107 N Modification factor kmod for medium-term, SC1 = 0,8 Modification factor kdef for SC1 = 0,6 Material safety factor γM (default value in EC5) =1,2 Size effect factor kh = (300/400)0,15 = 0,96 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. Most critical ultimate limit state (ULS) load combination: E_(d,ULS) = γ_G∙(g_(1,k)+g_(2,k))+ γ_Q∙q_k (4.1) E_(d,ULS) =1,15∙(6m ∙1,0 kN/m^2+0,2 kN/m )+1,5∙6m∙2,0 kN/m^2 E_(d,ULS)= 25,1 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_(1,k)+g_(2,k))+ γ_Q∙q_k (4.1) E_(d,SLS) =1,0∙(6m ∙1,0 kN/m^2+0,2 kN/m )+6,0∙1,0∙2,0 kN/m^2 E_(d,SLS)= 18,2 kN/m 9.3 DOUBLE LVL 48 P RIDGE BEAM FOR ROOF Single-span ridge beam of the roof in a one family house is LVL 48 P double beam 2x51x400 mm. Span length is L = 4000 mm, width of the loading area 6000 mm and roof rafters connected to the sides of the beam at spacing s = 1200 mm. Support length is 120 mm. Snow load sk is 2,5 kN/m2, own weight of the roof structure is 1,0 kN/m2 and own weigh of the beam is 0,2 kN/m. Service class SC1. d,ULS = G ∙ ( 1,k + 2,k)+ Q∙ k (4.1) d,ULS =1,15∙ (6m ∙ 1,0 kN/m2 + 0,2 kN/m ) + 1,5∙ 6m∙ 2,0 kN/m2 d,ULS = 25,1 kN/m d,SLS = G ∙ ( 1,k + 2,k)+ Q∙ k (4.1) d,SLS =1,0∙ (6m ∙ 1,0 kN/m2 + 0,2 kN/m )+ 6,0∙ 1,0∙ 2,0 kN/m2 d,SLS = 18,2 kN/m d = d,ULS ∙ ∙ 2/8 = 25,1 kN/m∙ (4m)2/8 = 50,3 kNm = d = 2,7 5 2 0,3 kNm ∙ 10 mm = 18,5 N/mm2 d,ULS = G ∙ ( 1,k + 2,k)+ Q∙ k (4.1) d,ULS =1,15∙ (6m ∙ 1,0 kN/m2 + 0,2 kN/m ) + 1,5∙ 6m∙ 2,0 kN/m2 d,ULS = 25,1 kN/m d,SLS = G ∙ ( 1,k + 2,k)+ Q∙ k (4.1) d,SLS =1,0∙ (6m ∙ 1,0 kN/m2 + 0,2 kN/m )+ 6,0∙ 1,0∙ 2,0 kN/m2 d,SLS = 18,2 kN/m d = d,ULS ∙ ∙ 2/8 = 25,1 kN/m∙ (4m)2/8 = 50,3 kNm = = 50,3 kNm = 18,5 N/mm 188 LVL Handbook Europe
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