9. CALCULATION EXAMPLES OF LVL STRUCTURES Geometry conditions: Minimum distance to edge a2,CG in stud ≥ 4d = 4∙6,0 mm = 24 mm. Stud thickness 51 mm/2 = 25,5 mm → Screw size 6,0x140 mm is OK for the stud Min. screw spacing a1 in stud ≥ 10d = 60 mm Min. screw spacing a2 in beam ≥ 5d = 30 mm → a1 in the stud is more critical Distance to edge of the beam a2,CG ≥ 4d = 24 mm. When the screwing angle is 45°, the beam thickness t1/2 = 25,5 mm gives the minimum distance. Maximum number of screws in the connection: 1+((h_beam – 2 ∙ min a_(2,CG) ))/((min a_(1,stud) / sin 45°) )=1+((200 mm – 2 ∙ 25,5 mm))/((60 mm / sin 45°) )=1+(149 mm)/(85 mm)=2,79 → 2 screws are chosen for the connection, so that the heads of the screws are 20 mm and 110 mm from the bottom edge of the beam. 1+�ℎbeam – 2 ∙ min 2,CG� �min 1,stud / sin 45°� = 1 + (200 mm – 2 ∙ 25,5 mm) (60 mm / sin 45°) = 1 + 18459mmmm = 2,79 Minimum distance to the beam end a1,CG ≥ 10d = 60 mm. Therefore the end of the bean shall exceed the stud edge. Effective penetration length lef,1 in ledger beam is l_(ef,1)=l_(g,1)=t_1/sin〖45°〗 -l_u=(51 mm)/(sin 45°)-17 mm=55 mm Penetration length in wall stud l_(g,2)=l-t_1/sin〖45°〗 =140 mm-(51 mm)/(sin45°)=68 mm For the beam the angles in the connections are: α = 45°, β = 45° and ε = 90° and for the stud they are: α = 45°, β = 0° and ε = 45°. ef,1 = g,1 = t1 sin45° −lu = 5 si 1 n mm45° −17 mm = 55 mm Penetration length in wall stud g,2 = − 1 sin45° = 140 mm−51 sin m 45 m ° = 68 mm k = 0,9 T,k (cos + sin ) (5.33) T,k =min⎨⎩⎧max� ax,90,1,k g,1; head,k h2� k a�0,8� ax,ε,2,k g,2 tens,k (5.31) ax,ε,k = ax ∙ ax,90,k 1,5 cos2 + sin2 � k a�0,8 (5.32) ef,1 = g,1 = t1 sin45° −lu = 5 si 1 n mm45° −17 mm = 55 mm Penetration length in wall stud g,2 = − 1 sin45° = 140 mm−51 sin m 45 m ° = 68 mm k = 0,9 T,k (cos + sin ) (5.33) T,k =min⎨⎩⎧max� ax,90,1k g,1; head,k h2� k a�0,8� ax,ε,2k g,2 tens,k (5.31) ax,ε,k = ax ∙ ax,90,k 1,5 cos2 + sin2 � k a�0,8 (5.32) Connection capacity The characteristic load-carrying capacity of the tension screw connection, see Figure 5.11(b), is calculated by the equation: Rk=n0,9 R T,k (cos α+μ sin α) (5.33) LVL Handbook Europe 201
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