9. CALCULATION EXAMPLES OF LVL STRUCTURES Instantaneous deflection w_inst = w_(inst,g) + w_(inst,q) w_(inst,g)=(5〖∙g〗_(d,SLS)∙s∙L^4)/(〖384∙E〗_mean∙I)+〖〖6/5∙g〗_(d, (4.74) w_(inst,g)=1,30 mm+0,49 mm=1,79 mm w_(inst,q)=(5〖∙q〗_(d,SLS)∙s∙L^4)/(〖384∙E〗_mean∙I)+(6/5∙〖q_(d,SLS)∙s∙L〗 mm+1,08 mm=3,95 mm w_inst=1,79 mm+3,95 mm=5,5 mm Final deflection w_(net,fin) = (1+k_def)∙w_(inst,g) + (1+ψ_2∙k_def)∙w_(inst,q) (4.73) Note: For the snow load in Finnish National annex: ψ2 = 0,2. w_(net,fin) = (1+0,6)∙1,79 mm + (1+0,2∙0,6)∙3,95 mm = 7,3 mm When the requirement is w_(net,fin)≤L/300=2300/300=7,7 mm→OK The lintel beam fulfils the design requirements. However, in practice the required support lengths are quite long and for windows a more strict deflection limit can be required. Therefore a double lintel 2x45x260 mm or a 69x300 mm lintel from LVL 36 C could be a more suitable choice. c,90,d = c,90,d ef = c,90,d ∙� support+15 mm� (4.14) c,90,d = 25,6kN 45mm∙ (150mm + 15mm) = 3,4 N/mm2 c,90 ∙ c,90,edge,d = c,90 ∙ mod M ∙ c,90,edge,k =1,0∙ 0 1 , , 8 2∙ 6 N/mm2 = 4 N/mm2 c,90,d ≤ c,90 ∙ m,0,edge,d →OK (4.13) inst = inst,g + inst,q inst,g =5∙ d,SLS∙ ∙ 4 384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2 8∙ mean (4.74) inst,g = 1,30 mm + 0,49 mm = 1,79 mm inst,q = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5∙ d,SLS ∙ ∙ 2 8∙ mean = 2,87 mm+ 1,08 mm = 3,95 mm = 1,79 mm + 3,95 mm = 5,5 mm net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) net,fin = (1+0,6)∙ 1,79 mm + (1 + 0,2∙ 0,6)∙ 3,95 mm = 7,3 mm When the requirement is net,fin ≤3 L 00 =2 3 3 0 0 0 0 = 7,7 mm→OK inst,g = 1,30 mm + 0,49 mm = 1,79 mm inst,q = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5∙ d,SLS ∙ ∙ 2 8∙ mean = 2,87 mm+ 1,08 mm = 3,95 mm = 1,79 mm + 3,95 mm = 5,5 mm net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) net,fin = (1+0,6)∙ 1,79 mm + (1 + 0,2∙ 0,6)∙ 3,95 mm = 7,3 mm When the requirement is net,fin ≤3 L 00 =2 3 3 0 0 0 0 = 7,7 mm→OK SLS design 222 (253) inst,g 5∙ d,SLS∙ ∙ 4 384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2 8∙ mean (4.74) inst,g = 5 ∙ d,SLS ∙ ∙ 4 384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8 ∙ mean = 1,30 mm+ 0,49 mm = 1,79 mm inst,g = 1,30 mm + 0,49 mm = 1,79 mm inst,q = 5 ∙ d,SLS ∙ ∙ 4 384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8 ∙ mean = 2,87 mm+ 1,08 mm = 3,95 mm = 1,79 mm + 3,95 mm = 5,5 mm Final deflection net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) Note: For the snow load in Finnish National annex: ψ2 = 0,2 net,fin = (1 + 0,6) ∙ 1,79 mm + (1 + 0,2 ∙ 0,6) ∙ 3,95 mm = 7,3 mm When the requirement is net,fin ≤3 L 00 , 2 3 3 0 0 0 0 = 7,7 mm → OK The lintel beam fulfils the design requirements. However, in practice the required support lengths are quite long and for windows a more strict deflection limit can be required. Therefore a double lintel 2x45x260 mm or a 69x300 mm lintel from LVL 36 C could be a more suitable choice. 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. 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 223 (255) inst,g =5∙ d,SLS∙ ∙ 4 384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2 8∙ mean (4.74) inst,g = 5 ∙ d,SLS ∙ ∙ 4 384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8 ∙ mean = 1,30 mm+ 0,49 mm = 1,79 mm inst,g = 1,30 mm + 0,49 mm = 1,79 mm inst,q = 5 ∙ d,SLS ∙ ∙ 4 384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8 ∙ mean = 2,87 mm+ 1,08 mm = 3,95 mm = 1,79 mm + 3,95 mm = 5,5 mm Final deflection net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) Note: For the snow load in Finnish National annex: ψ2 = 0,2 net,fin = (1 + 0,6) ∙ 1,79 mm + (1 + 0,2 ∙ 0,6) ∙ 3,95 mm = 7,3 mm When the requirement is net,fin 3 L 00 , 2303000mm= 7,7 mm → OK The lintel beam fulfils the design requirements. However, in practice the required support lengths are quite long and for windows a more strict deflection limit can be required. Therefore a double lintel 2x45x260 mm or a 69x300 mm lintel from LVL 36 C could be a more suitable choice. 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. 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 LVL Handbook Europe 187
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