9. CALCULATION EXAMPLES OF LVL STRUCTURES The embedment strength of 2,5x60 mm round nail in LVL 36 C and LVL 48P fh,k = 0,082∙ρk∙d-0,3 = 0,082∙480∙2,5-0,3 = 29,9 N/mm2 When the nails are produced from wire with tensile strength fu = 600 N/mm2, the characteristic value of the yield moment My,k for round nails is My,k = 0,3∙fu∙d2,6 = 0,3∙600∙(2,5)2,6 = 1949 Nmm The influence of rope effect based on the axial withdrawal capacity Fax,k of round nails is negligible. With these properties FV,nail,Rk is as the minimum of failure modes (a)-(f) F_(V,nail,Rk)=min{█(2,02 (a)@2,47 (b)@0,94 (c)@0,78 (d)@0,92 (e)@0,62 (f))┤=0,62 kN F_(f,Rd)=k_mod/γ_M ∙1,2∙F_(V,nail,Rk)=1,1/1,3∙1,2∙0,62 kN=0,63 kN kmod = 1,1 for instantaneous load (wind load) in service class 1 γM = 1,3 for connections (default value in EC5) F_(V,Rd)=(F_(f,Rd)∙b∙c)/s=(0,63 kN∙1200 mm∙0,96)/(100 mm)=7,3 kN Shear buckling of the panel may be disregarded, when the stud spacing bnet / t ≤ 100. b_net/t=(600 mm)/(27 mm)=22 ≤100 →OK In order to with stand a horizontal force FV,Ed = 7,3 kN, the diaphragm panel shall be anchored at the bottom corners for the external forces F_(t,Ed)=F_(c,Ed)= (F_(V,Rd)∙h)/b=(7,3kN∙2500 mm)/(1200 mm)=15,2 kN The contact area between perimeter stud and the end of the horizontal sole plate shall be verified for compression perpendicular to the grain. σ_(c,90,d)≤k_(c,90) 〖∙f〗_(c,90,d) σ_(c,90,d)=F_(c,90,d)/A_ef =F_(c,90,d)/(l∙(b+30 mm))=15,2kN/(150 mm ∙ (51 mm+30 mm) )=1,3N/ mm^2 kc,90 is 1,4 for LVL-P flatwise and fc,90,k is 2,2 N/mm2. γM =1,2 (default value in EC5) k_(c,90)∙f_(c,90,flat,d)=1,4∙1,1/1,2∙2,2 N/mm^2 =2,8 N/mm^2>σ_(c,90,d)→OK Anchoring can be done with e.g. Rothoblaas WHT340 brackets for tension loads and Titan TFC200 brackets for shear loads. V,nail,Rk =min⎪⎨ ⎩ ⎪⎧2,02 ( ) 2,47 ( ) 0,94 ( ) 0,78 ( ) 0,92 ( ) 0,62 ( ) = 0,62 kN f,Rd = mod M ∙ 1,2∙ V,nail,Rk = 1 1 , , 1 3∙ 1,2∙ 0,62 kN = 0,63 kN V,Rd = f,Rd ∙ ∙ = 0,63 kN∙ 1200 mm∙ 0,96 100 mm = 7,3 kN net = 62070 mmmm = 2 2 ≤100 →OK t,Ed = c,Ed = V,Rd ∙ ℎ = 7,3kN∙ 120205m0m0 mm = 15,2 kN c,90,d ≤ c,90 ∙ c,90,d V,nail,Rk =min⎪⎨ ⎩ ⎪⎧2,02 ( ) 2,47 ( ) 0,94 ( ) 0,78 ( ) 0,92 ( ) 0,62 ( ) = 0,62 kN f,Rd = mod M ∙ 1,2∙ V,nail,Rk = 1 1 , , 1 3∙ 1,2∙ 0,62 kN = 0,63 kN V,Rd = f,Rd ∙ ∙ = 0,63 kN∙ 1200 mm∙ 0,96 100 mm = 7,3 kN net = 62070 mmmm = 2 2 ≤100 →OK t,Ed = c,Ed = V,Rd ∙ ℎ = 7,3kN∙ 120205m0m0 mm = 15,2 kN c,90,d ≤ c,90 ∙ c,90,d V,nail,Rk ⎪⎨ ⎩ 2,02 ( ) 2,47 ( ) 0,94 ( ) 0,78 ( ) 0,92 ( ) 0,62 ( ) = 0,62 kN f,Rd mod ∙ 1,2∙ V,nail,Rk = 1 1 , , 1 3∙ 1,2∙ 0,62 kN = 0,63 kN V,Rd f,Rd ∙ ∙ = 0,63 kN∙ ∙ 0,96 net = 62070 mmmm = 2 2 t,Ed c,Ed V,Rd ∙ ℎ = 7,3kN∙ 120205m0m0 mm = 15,2 kN c,90,d ≤ c,90 ∙ c,90,d V,nail,Rk =min⎪⎨ ⎩ ⎪⎧2,02 ( 2,47 ( 0,94 ( 0,78 ( 0,92 ( 0,62 ( ) = 0,62 kN f,Rd = mod M ∙ 1,2∙ V,nail,Rk = 1 1 , , 1 3∙ 1,2∙ 0,62 kN = 0,63 kN V,Rd = f,Rd ∙ ∙ = 0,63 kN∙ 1200 mm∙ 0,96 100 mm = 7,3 kN net = 62070 mmmm = 2 2 ≤100 →OK t,Ed = c,Ed = V,Rd ∙ ℎ = 7,3kN∙ 120205m0m0 mm = 15,2 kN c,90,d ≤ c,90 ∙ c,90,d c,90,d = c,90,d ef = c,90,d ∙ ( + 30 mm) = 15,2kN 150 mm ∙ (51 mm+ 30 mm) = 1,3N/mm2 c,90 is 1,4 for LVL-P flatwise and fc,90,k is 2,2 N/mm2. c,90 ∙ c,90,flat,d =1,4∙ 1 1 , , 1 2∙ 2,2 m N m2 = 2,8 N/mm2 > c,90,d →OK ∙ ∙ 245 (255) The contact area between perimeter stud and the end of the horizontal sole plate shall be verified for compression perpendicular to the grain. c,90,d ≤ c,90 ∙ c,90,d c,90,d = c,90,d ef = c,90,d ∙ ( + 30 mm) =150 mm ∙ (51 mm+ 30 mm) = 1,3N/mm2 is 1,4 for LVL-P flatwise and fc,90,k 2. Material safety factor γM (default value in EC5) = 1,2 c,90 ∙ mod M ∙ c,90,flat,k = 1,4 ∙ 11,,12 ∙ 2,2 mNm2 = 2,8 N/mm2 > c,90,d →OK Anchoring can be done with e.g. Rothoblaas WHT340 brackets for tension loads and Titan TFC200 brackets for shear loads. 9.11 Main beam of roof structure in 30min fire exposure Single-span main beam of a flat roof structure is GLVL 48 P beam 133x400 mm. Span length is L = 4000 mm, width of the loading area 8000 mm and roof purlins are on the top of the beam. Support length is 100 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. The structure fulfils the ULS and SLS requirements in normal temperature where wnet,fi ≤ L/300 has been the most critical requirement. The fire resistance R30 of the beam needs to be verified for fire exposure on all sides of the beam. 210 LVL Handbook Europe
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