European Technical Approval ETA-12/0087 - ETA-Danmark

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Page 24 of 26 of European Technical Approval no. ETA-12/0087 B l ef,b Heat insulation on rafters with alternatively inclined screws A ß 1 2 6 5 l ef,r 90° - = 0° to 60° α 1 α 2 4 3 90° - = 0° to 60° H 1 counter batten 2 insulation 3 vapour barrier 4 sheating 5 compressive screw 6 rafter Mechanical model Depending on the screw spacing and the arrangement of tensile and compressive screws with different inclinations the battens are loaded by significant bending moments. The bending moments are derived based on the following assumptions: • The tensile and compressive loads in the screws are determined based on equilibrium conditions from the actions parallel and perpendicular to the roof plane. These actions are constant line loads q⊥ and q ⎢⎢. • The screws act as hinged columns supported 10 mm within the batten or rafter, respectively. The effective column length consequently equals the length of the screw between batten and rafter plus 20 mm. • The batten is considered as a continuous beam with a constant span l = A + B. The compressive screws constitute the supports of the continuous beam while the tensile screws transfer concentrated loads perpendicular to the batten axis. The screws are predominantly loaded in withdrawal or compression, respectively. The screw’s normal forces are determined based on the loads parallel and perpendicular to the roof plane: Compressive screw: Tensile screw: ⎛ qII ⋅sin α 2 + q⊥ ⋅cos α ⎞ 2 F c,Ed = (A + B) ⋅⎜ − ⎟ sin ( α + α ) ⎝ 1 2 ⎠ ⎛ qII ⋅sin α1 − q⊥ ⋅cos α ⎞ 1 F t,Ed = (A + B) ⋅⎜ ⎟ ⎝ sin ( α 1 + α2 ) ⎠ Counter batten
Page 25 of 26 of European Technical Approval no. ETA-12/0087 The bending moments in the batten follow from the constant line load q⊥ and the load components perpendicular to the batten from the tensile screws. The span of the continuous beam is (A + B). The load component perpendicular to the batten from the tensile screw is: ⎛ qII ⋅sin α1 ⋅sin α2 − q⊥ ⋅cos α1 ⋅sin α2 ⎞ F ZS,Ed = (A + B) ⋅⎜ ⎟ ⎝ sin( α 1 + α2 ) ⎠ Where: qII Constant line load parallel to batten q⊥ Constant line load perpendicular to batten α1 Angle between compressive screw axis and grain direction Angle between tensile screw axis and grain direction α2 A positive value for FZS means a load towards the rafter, a negative value a load away from the rafter. Design of the screws The load-carrying capacity of the screws shall be calculated as follows: Screws loaded in tension: 0.8 0.8 ⎧ ⎪ fax,d ⋅ d ⋅ lef ,b ⎛ ρb,k ⎞ fax,d ⋅d ⋅ lef ,r ⎛ ρr,k ⎞ f ⎫ tens,k ⎪ Fax, α,Rd = min ⎨ ⋅⎜ ⎟ ; ⋅⎜ ⎟ ; ⎬ ⎪1.2 ⋅cos² α + sin ² α ⎝ 350 ⎠ 1.2 ⋅cos ² α + sin ² α ⎝ 350 ⎠ γ ⎩ M2 ⎪⎭ Screws loaded in compression: 0.8 0.8 ⎧ ⎪ fax,d ⋅d ⋅l ef ,b ⎛ ρb,k ⎞ fax,d ⋅ d ⋅ lef ,r ⎛ ρr,k ⎞ κc ⋅ N ⎫ pl,k ⎪ Fax, α,Rd = min ⎨ ⋅⎜ ⎟ ; ⋅⎜ ⎟ ; ⎬ ⎪1.2 ⋅cos² α + sin ² α ⎝ 350 ⎠ 1.2⋅ cos² α + sin ² α ⎝ 350 ⎠ γ ⎩ M1 ⎪⎭ where: fax,d design value of the axial withdrawal parameter of the threaded part of the screw in the rafter or batten, fax,d does not apply for wood-based panels except plywood, LVL or crosslaminated timber/solid wood panels d outer thread diameter of the screw lef,b lef,r ρb�k ρr�k penetration length of the threaded part of the screw in the batten penetration length of the threaded part of the screw in the rafter, lef ≥ 40 mm characteristic density of the batten [kg/m³] characteristic density of the rafter [kg/m³] α angle α1 or α2 between screw axis and grain direction, 30° ≤ α� ≤ 90°, 30° ≤ α2 ≤ 90° ftens,k γM1, γM2 κc · Npl,k characteristic tensile capacity of the screw partial factor according to EN 1993-1-1 or to the particular national annex Buckling capacity of the screw
Page 1 and 2: ETA-Danmark A/S Kollegievej 6 DK-29
Page 3 and 4: Page 3 of 26 of European Technical
Page 7 and 8: 3 Attestation of Conformity and CE
Page 11 and 12: ETA- Zul-0001-DaBau ø 8 ln Page 11
Page 13 and 14: ETA-Zul-0003-IngBau_Ø6 L Page 13 o
Page 15 and 16: ETA-Zul-0005 IngBAU-Ø10 L Page 15
Page 21 and 22: Mechanical model Page 21 of 26 of E
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European Technical Approval ETA-12/0087 - ETA-Danmark

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