The aim of this document together with the ETA 16/0583 is to facilitate the determination of design values.

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1 GUIDANCE PAPER VELUX MODULAR SKYLIGHTS SELF-SUPPORTING RIDGELIGHT Determination of design values 1. Introduction The aim of this document together with the ETA 16/0583 is to facilitate the determination of design values. By means of structural calculations and the design values it can be demonstrated, whether the requirements of the load bearing capacity of a specific kit, installed in a given building on a given location, are met. ETA 16/0583 contains information on the kit, e.g. the static system, hardware, cross section of the profiles, as well as the characteristic values. For convenience, a number of the relevant characteristic values are repeated in this document. The load bearing capacity of the glazing is not subject to this document. 2. Principle The design load bearing capacities (1) Rd and Cd shall be calculated using the following equations (see ETAG 010, and ): and where: R d = R k/(ɣmr*k t*k u*k θ) C d = C k/(ɣ MC*C t*c u*c θ) R k = load bearing capacity (ULS) calculated in accordance with ETA 16/0583 C k = load bearing capacity () calculated in accordance with ETA 16/0583 ɣmr = partial safety factor for ULS ɣmc = partial safety factor for K t = effect of duration for ULS C t = effect of duration for K u = effect of aging/environment for ULS C u = effect of aging/environment for K θ = effect of temperature for ULS C θ = effect of temperature for (1) Without self-weight. The self-weight, including partial safety factors, shall be calculated in accordance with Clause 6. 1 / 11

2 3. Partial safety factors, magnification and reduction factors Whenever possible internationally and/or nationally determined parameters shall be taken into account. By default, the parameters shown in Table 1 and Table 2 and Table 5 are recommended. The recommended parameters are based on BÜV-Empfehlung Tragende Kunststoffbauteile im Bauwesen [TKB] - Entwurf, Bemessung und Konstruktion - Stand 08 / 2010 (BÜV) and some European standards and VELUX test reports. Table 1: Partial safety factors Partial safety factor ɣmr ɣmc Frame profiles at connections 1,5 (1) Not relevant Bolt/Rivet/Bracket/Rotating shoe/mounting clamp 1,25 (2) Not relevant Frame profiles 1,2 (1) 1,1 (3) (1) See BÜV Tablelle E-1 (2) See EN :2005, section 2.2 (3) See BÜV Abschnitt 5.5 Table 2: Magnification and reduction factors K t (1) (2) ULS 10 minutes 1,10 C t 1 week 1,48 1 week 1,08 3 months 1,66 (1) (4) 3 months 1,11 6 months 1,71 6 months 1,11 25 years 2,02 25 years 1,15 10 minutes 1,02 Ku (1) (3) 1,2 Cu (1) (5) 1,2 Kθ (1) 0 C (6) 0,95 Cθ (1) 0 C (6) 1,00 20 C (6) 1,00 20 C (6) 1,00 40 C (7) 1,35 40 C (7) 1,05 60 C (6) 1,50 60 C (6) 1,05 80 C (6) 2,05 80 C (6) 1,10 (1) K t = A f, 1 Ct = AE (see ETAG 010: 2002, section 6.3 and Annex H, BÜV Abschnitt 5.2) 1 K u = A f, 2 Cu = AE (see ETAG 010: 2002, section 6.3 and Annex H, BÜV Abschnitt 5.2) 2 K θ = A f, 3 Cθ = AE (see ETAG 010: 2002, section 6.3 and Annex H, BÜV Abschnitt 5.2) 3 (2) See BÜV Tabelle B-1a and Gleichung 8.2. (3) See BÜV Tabelle B-2. (4) See BÜV Tabelle B-1b and Gleichung 8.2. (5) See BÜV Tabelle B-2. (6) See VELUX test reports no and (7) Conservative approximation based on measurements from VELUX test reports nos and / 11

3 4. Design values of small scale test The design values of the small-scale tests can be calculated as shown in Table 3. Table 3: Characteristic and design values Property Tensile strength Compression strength Bending strength E-modulus G-modulus Shear strength Characteristic values see ETA 16/0583 Annex D.1 832,9 MPa 465 MPa 1257 MPa 39,5 GPa 41,6 GPa (1) 3,1 GPa 3,4 GPa (2) 53,8 MPa Design values see Table 1 and Table 2 above ULS= Characteristic value / (ɣmr *Kt*Ku*Kθ) = Characteristic value / (ɣmc*ct*cu*cθ) (1) Mean value, confidence level 75%, unknown standard deviation (See ISO :2014). (2) Mean value, confidence level 75%, unknown standard deviation (See ISO :2014). 3 / 11

4 5. Design values for the hardware connections The design values for the hardware connections are shown in Figure 1 and in Table 4 Figure 1: Applied forces to the hardware 4 / 11

5 Table 4: Characteristic and design values for hardware connections Element/Connection A: Top bolt connection (calculated minimum) 13,5 (1) B: Bottom rivet connection (calculated minimum) C: Top corner bracket/frame connection 7,3 Characteristic values [kn] see ETA 16/0583 Annex D.2 15,8 (2) D: Bottom corner bracket/frame connection in 18 14,6 (= R1, see Annex D.3) E: Bottom corner bracket/frame connection in 180 5,1 F: Bottom corner bracket/frame connection in 270 4,0 G: Rotating shoe/mounting clamp/roof connection in 90 18,4 H: Rotating shoe/mounting clamp/roof connection in ,8 Design values [kn] see Table 1 and Table 2 above ULS= Characteristic value / (ɣmr *Kt*Ku*Kθ) : Not relevant J: Top corner bracket/frame connection in 270 4,0 K: Top corner bracket/frame connection in ,7 (= R2, see Annex D.3) L: Top corner bracket/frame connection in 310 5,3 M: Bottom corner bracket/frame connection in 230 5,3 (1) Strength of the bolt itself: 17,6 kn (2) Strength of the rivet itself: 20,0 kn 5 / 11

6 6. Self-weight The self-weight (including hardware, lining, cladding and flashing) of the fixed roof window (Gf and gf) and the openable roof window (Gv and gv) shall be calculated as follows: and where: G f = (W-12) * (L-96) * t*25* (W+L) *57*10-6 [kn] g f = G f /(W*L)* 10 6 [kn/m 2 ] G v = (W-12) * (L-96) * t*25 * (W+L) * 96 * 10-6 [kn] g v = G v /(W*L)* 10 6 [kn/m 2 ] W = Width of the roof window in mm L = Height of the roof window in mm t = Total thickness of glass in mm Table 5: Partial safety factors for permanent action (self-weight): Unfavourable Favourable Reference ɣg,sup ɣg,inf ULS 1,35 1,0 EN 1990:2007, Table A1.2(B), Eq. 6.10b 1,0 1,0 EN 1990:2007, Table A1.4 6 / 11

7 7. Examples of design values for the load bearing capacity The examples of design values for load bearing capacity are shown in Table 6. Table 6: Characteristic and design load bearing capacities for application examples Characteristic values [kn/m 2 ] see ETA 16/0583 Annex E.1 Design values (without self-weight) [kn/m 2 ] 3 months duration, 20 C. Application examples α ULS ULS 1/300 1/150 1/300 1/ ,3 2,1 5,1 1,88 0,86 2, ,7 2,4 5,6 2,32 0,98 2,84 Type: 2x HVC T (1000mm x 2400mm) Glazing: 22 mm glass in total 35 11,1 2,7 6,3 2,74 1,15 3, ,6 3,1 7,3 3,17 1,38 3,76 Application examples Characteristic values [kn/m 2 ] see ETA 16/0583 Annex E.1 α ULS Design values (without self-weight) [kn/m 2 ] 10 minutes, 60 C. (1) ULS 1/300 1/150 1/300 1/ ,3 2,0 3,4 1,94 1,39 2, ,0 2,0 3,4 2,18 1,37 2,21 Type: 2x HVC (1000mm x 2400mm) Glazing: 14 mm glass in total 35 5,6 1,9 3,4 2,39 1,34 2, ,2 1,9 3,3 2,59 1,31 2,15 (1) See VELUX test report / 11

8 8. Calculation example (design values) For the calculations example Asymmetric wind load the same example as Annex E.2 in ETA-16/0583 is used. Asymmetric wind load To demonstrate the calculation procedure, a VELUX openable modular skylight self-supporting ridgelight application under asymmetric wind load is examined. 2 x HVC (1000mm x 2400mm). Glazing: 14mm glass in total. Load duration 10 min and temperature of 60 o C. The pitch is α = 25. Partial safety factors are taken from this document when nothing ells is stated and can be seen in table 7. Table 7: Partial safety factors used in calculation example for Asymmetric wind load ULS Frame profiles at connections: ɣmr = 1,5 - Frame profiles: ɣmr = 1,2 ɣmc = 1,1 Time dependency: Kt,10 min = 1,1 Ct,10 min = 1,02 Aging/environment dependency: Ku = 1,2 Cu = 1,2 Temperature dependency: Kθ,60 o = 1,5 Cθ,60 o = 1,05 Variable Load: ɣq,1 = 1,5 (1) ɣq,1 = 1,0 (1) Permanent action, unfavourable: ɣg,sup = 1,35 ɣg,sup = 1,0 Permanent action, favourable: ɣg,inf = 1,0 ɣg,inf = 1,0 (1) Taken from EN 1990:2007 Self-weight, half of one module: G v = 1 2 ((W 12) (L 96) t (W + L) ) = 1 2 (( ) ( ) ( ) ) = 0.72kN G v,sup,d = G v γ G,sup = 0.72kN 1,35 = 0,97kN G v,inf,d = G v γ G,inf = 0.72kN 1,00 = 0,72kN In this example, the wind peak velocity pressure is set to 0,8kN/m 2 and the shape factor is set to 0,5 for compressed side and -0,5 for suction side. Hence, the characteristic load is q c = q s = 0,8kN/m 2 0,5 = 0,4kN/m 2 P c = 1 2 0,4kN/m2 1,0m 2,4m = 0,48kN, on half of a module where P c denotes the equivalent concentrated load. Vertical and horizontal component of the characteristic load: P SV = P CV = 0,48kN cos(25) = 0,44kN, P SH = P CH = 0,48kN sin(25) = 0,20kN 8 / 11

9 Hence the design loads are determined: P c,d = P c γ Q,1 = 0,48kN 1,5 = 0,72kN P SV,d = P CV,d = P SV γ Q,1 = 1,5 0,44kN = 0,66kN P SH,d = P CH,d = P SH γ Q,1 = 1,5 0,20kN = 0,30kN Design reactions in bottom brackets: R V1R,d 2 2,4m cos(25) = (0,66kN + 0,97kN) 2,4m cos(25) 3 2 (0,66kN 0,72kN) 2,4m cos(25) 1 2 (0,30kN + 0,30kN) 2,4m sin(25) 1 2 R V1R,d = 1,17kN R H1R,d 2,4m sin(25) = 1,17kN 2,4m cos(25) 0,72kN 2,4m 1 2 0,97 2,4m cos(25) 1 2 R H1R,d = 0,61kN R V1L,d 2 2,4m cos(25) = (0,66kN + 0,97kN) 2,4m cos(25) 1 2 (0,66kN 0,72kN) 2,4m cos(25) 3 2 +(0,30kN + 0,30kN) 2,4m sin(25) 1 2 R V1L,d = 0,52kN R H1L,d 2,4m sin(25) = 0,52kN 2,4m cos(25) + 0,72kN 2,4m 1 2 0,97kN 2,4m cos(25) 1 2 R H1L,d = 0,93kN Design reaction force resultant in left bottom bracket: 2 2 R 1L,d = R H1L,d + R V1L,d = 1,07kN angle to horizontal 29 Angle of reaction force relative to module, denoted as v frame : v frame = 29 o 25 o = 4 o The reaction angle is relatively close to direction D, hence the resistance in this direction is used for the proof (see Annex D.2 in ETA-16/0583) R D,k 14,6kN R D,d = = γ MR K t,10 min K u K θ,60 o 1,5 1,1 1,2 1,5 = 4,92kN 1,07kN < 4,92kN OK Design reaction force resultant in right bottom bracket: 2 2 R 1R,d = R H1R,d + R V1R,d = 1,32kN angle to horizontal 55 Angle of reaction force relative to module: v frame = 55 o 25 o = 20 o The reaction angle is close to direction D, hence the resistance in this direction is used for the proof (see Annex D.2 in ETA-16/0583): 1,32kN < 4,92kN OK 9 / 11

10 Design reactions in the top bracket: R H2L,d = R H2R,d = R H1L,d P SH,d = 0,63kN R V2L,d = R V2R,d = P SV,d + R V1L,d G V,inf,d = 0,46kN Reaction force resultant in the top bracket: 2 2 R 2L,d = R 2R,d = R H2L,d + R V2L,d = 0,78kN The R2L,d reaction angle to horizontal is 36 and the angle relative to the module is 191. Here, the angle is determined as shown in Annex D.2 in ETA-16/0583. The reaction angle is relatively close to direction K, hence the resistance in this direction is used for the proof (see Annex D.2 in ETA-16/0583): R K,k 10,7kN R K,d = = γ MR K t,10 min K u K θ,60 o 1,5 1,1 1,2 1,5 = 3,60kN 0,78kN < 3,60kN OK The R2R reaction angle to horizontal is 36 and the angle relative to the module is 169. The reaction angle is again relatively close to direction K, hence the proof is the same as for R2L: 0,78kN > 3,60kN OK Design bending in frame and casement profile: The line load from self-weight perpendicular to the module is denoted g p,d and line load from the wind pressure is denoted p c,d. The ridgelight s span width is equal to the module height, plus 149 mm to allow for the brackets, see Figure 1 g p,d = G V,sup.d cos (25) 0,92 cos (25) = = 0,33kN/m, on half of a module (2,4 + 0,149)m (2,4 + 0,149)m p c,d = 1 2 0,40kN/m2 1,5 1,0m = 0,30kN/m, on half of a module M d = 1 8 (g p,d + p c,d ) L 2 = 1 8 (0,33 + 0,30)kN/m (2,40m + 0,149m)2 = 0,51kNm M frame,d = M d I frame I frame +I casement = 0,51kNm Design capacity of frame and casement: σ R,k σ R,d = γ MR K t,10 min K u K θ,60 o 0,669 0,669+0,930 = 0,21kNm = 1257N/mm2 1,2 1,1 1,2 1,5 = 529N/mm2 Here, the characteristic bending strength is taken from Annex D.1 in ETA-16/0583. σ frame,d M frame,d W y,frame = 0, Nmm 9, mm 3 = 21,6N/mm2 529N/mm 2 M casement,d = M d I casement I frame +I casement = 0,51kNm 0,930 0,669+0,930 = 0,30kNm σ casement,d M casement,d W y,casement = 0, Nmm 16, mm 3 = 18,1N/mm2 529N/mm 2 10 / 11

11 Second moment of area and Section modulus are taken from Annex C.1 and C.4 in ETA-16/0583. The rotation of the main axis is ignored, as it has little influence on the result, and the resulting stress is much lower than the bending strength. The shear force is generally taken in combination by the frame and casement profile, but near the ends of the module, the entire shear force is taken by the frame profile. Largest shear force is in the right module in this example: V frame,d = R V1R,d cos(25) R H1R,d sin(25) = 2,43kN cos(25) 3,32kN sin (25) = 0,80kN Design capacity shear stress of frame: τ frame,r,k τ frame,r,d = γ MR K t,10 min K u K θ,60 o = 53,8N/mm2 1,2 1,1 1,2 1,5 = 22,6N/mm2 Here, the characteristic shear strength is taken from Annex D.1 in ETA-16/0583. τ frame,d = V frame,d A web 0, N = 3,0mm 60mm+3,5mm 106mm 1,5N/mm2 22,6N/mm 2 Design deflection of the module at mid length, perpendicular to the module: γ MC C t,10 min C u C θ,60 o = 1,1 1,02 1,2 1,05 = 1,41 u = (g p,d +p c,d ) L 4 E (I frame +I casement ) γ MC C t,10 min C u C θ,60 o = (0,33+0,30)N/mm (2400mm) N 1,41 = 7,5mm < L mm 2 (0, mm 4 +0, mm 4 ) 300 = 8mm E is the E-modulus mean value, taken from D.1 note 2 in ETA-16/ / 11

The aim of this document together with ETA-17/0467 is to facilitate the determination of design values.

GUIDANCE PAPER VELUX MODULAR SKYLIGHTS SELF-SUPPORTING RIDGELIGHT Determination of structural design values 1. Introduction The aim of this document together with ETA-17/0467 is to facilitate the determination