SLS design 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,SLS)∙s∙L〗^2/(〖8∙G〗_mean A)=2,76mm+0,61mm=3,36mm w_(inst,q)=(5〖∙q〗_(d,SLS)∙s∙L^4)/(〖384∙E〗_mean∙I)+〖〖6/5∙q〗_(d,SLS)∙s∙L〗^2/(〖8∙G〗_mean A)=5,33mm+1,18mm=6,51mm w_inst=3,36 mm+6,51 mm=9,9 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)∙3,36 mm + (1+0,2∙0,6)∙6,51 mm = 12,7 mm When the requirement is w_(net,fin)≤L/300=4000/300=13,3mm→OK = = 50,3 c,90,d = c,90,d ef = c,90,d ∙� support+15 mm� (4.14) c,90,d = 50,3kN 2∙ 51mm∙ (120mm + 15mm) = 3,7 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 = 2,76mm + 0,61mm = 3,36mm inst,q = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5∙ d,SLS ∙ ∙ 2 8∙ mean = 5,33mm + 1,18mm = 6,51mm inst = 3,36 mm + 6,51 mm = 9,9 mm net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) For the snow load in Finnish national annex: ψ2 = 0,2 net,fin = (1+0,6)∙ 3,36 mm + (1 + 0,2∙ 0,6)∙ 6,51 mm = 12,7 mm When the requirement is net,fin ≤ 300 =4 3 0 0 0 0 0 =13,3mm→OK 9. CALCULATION EXAMPLES OF LVL STRUCTURES , ∙ , ∙ ∙ , , ∙ ∙ ∙ , 300 4 3 0 0 0 0 0 , 226 (255) inst = 3,36 mm + 6,51 mm = 9,9 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) ∙ 3,36 mm + (1 + 0,2 ∙ 0,6) ∙ 6,51 mm = 12,7 mm When the requirement is net,fin ≤ 300 , 4003000mm= 13,3mm → OK 9.4 Roof purlin Single-span purlins of the roof of an unheated (service class 2) portal frame hall are 45x240 LVL 48 P beams. Roof angle is 15°, span length is L = 4000 mm, spacing s = 900 mm and the purlins are perpendicular to the roof plane having a side support line at the middle of the span. Support length is 45mm. Snow load sk is 2,5 kN/m2 and own weight of the roof structure is 0,30 kN/m2. For simplification there is no wind load in the example. The purlins are connected to the sides of the portal frame beams and they act also as lateral torsional buckling supports. Therefore the purlins have an axial load of Nk = 3 kN mainly from snow load. 190 LVL Handbook Europe
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