9. CALCULATION EXAMPLES OF LVL STRUCTURES The stiffness (EI)bracing of the bracing lines can be estimated according to EN1995-1-1, Annex B Mechanically jointed beams. For simplification, also the top flange of the transverse bracing is modelled as a 22x100 C14 board and the stiffness of the 2 bracing lines are divided for the whole floor span length. (EI)_bracing=n∙2∙E_(0,mean)∙((b_0∙〖h_0〗^3/12+γ∙b_0∙h_0∙(h/2+h_0/2)^2 ))/l_0 where n = number of bracing lines in each span = 2 E0,mean = mean modulus of elasticity of C14 flanges 7000 N/mm2 b0 = width of tension/compression chord = 100 mm h0 = thickness of tension/compression chord = 22 mm h = depth of joist = 240 mm s0 = Spacing of the nailing between blocking and flanges = 200 mm l0 = span length of the bracing line = width of the floor= 5 m ρk = characteristic density (C14: 350 kg/m3) d = diameter of the nail 2.5 mm for nails 2,5x60 mm The deflection under F =1 kN point load w=min{█((F∙l^2)/(42∙k_δ∙(EI)_l )@(F∙l^3)/(48∙s∙(EI)_l ))┤ (4.82) k_δ=∜((EI)_b/(EI)_l =) ∜((3,11∙〖10〗^3)/(1,79∙〖10〗^6 ))=0,2 (4.84) w=min{█((1kN∙(4,5m)^2)/█(42∙0,2∙1,79∙(〖10〗^6 Nm^2)/m@ )@(1kN∙(4,5m)^3)/(48∙0,4∙1,79∙(〖10〗^6 Nm^2)/m))┤=min{█(1,3 mm@ @2,7 mm)┤=1,3 mm According to the Finnish national Annex of EC5, for the span length L= 4500mm the requirement is w ≤ 0,6 mm and according to the Austrian national annex w ≤ 0,5 mm which are not fulfilled by the structure. The performance can be improved by transverse bracing by 2 blockings lines with tension boards close to the centre of the span and cross battens 45x45 c/c 400 mm underneath the floor. =���9,5Hz� −1� ∙ �4,5m� ∙ 3,11∙ 10 Nm /m� =11 = 4 (0,4+ 0,6 40) + 200 = 4 (0,4+ 0,6∙ 11) 120∙ 5∙ 4,5 + 200 = 0,010 ≤150( 1 −1) =0,011→ (4.78) =min� ∙ 2 42∙ ∙( )l ∙ 3 48∙ ∙( )l (4.82) =�( )b ( )l = 4 �3,11∙103 1,79∙106 4 =0,2 (4.84) =min ⎩⎪ ⎨ ⎪⎪⎧ 1kN∙ (4,5m)2 42∙ 0,2∙ 1,79∙ 106Nm2 m 1kN∙ (4,5m)3 48∙ 0,4∙ 1,79∙ 106Nm2 m =min�1,3 mm 2,7 mm = 1,3 mm ( )bracing = ∙ 2∙ 0,mean ∙ � 0 ∙ ℎ 0 3 12 + ∙ 0 ∙ ℎ0 ∙ (ℎ/2+ℎ0/2)2� 0 ser = k 1,5 ∙ 0,8 30 = 454 N/mm = 1 1+ 2 ∙ 0 ∙ ℎ0 ∙ 0 ∙ 0 ser ∙ 0 2 = 1 1+π2 ∙ 7000 N/mm2 ∙ 22 mm∙ 100 mm∙ 200 mm 454N/mm∙ (5000 mm)2 =min ⎩⎪ ⎨ ⎪⎪⎧ 1kN∙ (4,5m)2 42∙ 0,2∙ 1,79∙ 106Nm2 m 1kN∙ (4,5m)3 48∙ 0,4∙ 1,79∙ 106Nm2 m =min�1,3 mm 2,7 mm = 1,3 mm ( )bracing = ∙ 2∙ 0,mean ∙ � 0 ∙ ℎ 0 3 12 + ∙ 0 ∙ ℎ0 ∙ (ℎ/2+ℎ0/2)2� 0 ser = k 1,5 ∙ 0,8 30 = 454 N/mm = 1 1+ 2 ∙ 0 ∙ ℎ0 ∙ 0 ∙ 0 ser ∙ 0 2 = 1 1+π2 ∙ 7000 N/mm2 ∙ 22 mm∙ 100 mm∙ 200 mm 454N/mm∙ (5000 mm)2 1. Decking panel, 2. Floor joists, 3. Transverse tension board (C18, min 22x100) under the joists fixed with 2,8x75 nails to the joists and blockings, 4. Blocking 182 LVL Handbook Europe
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