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# Worked example wind loading on portal frame

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### Worked example wind loading on portal frame

2. 2. 2 Portal frame building The principal dimensions of the portal frame building in this example are given in Figure A. Stage 1: Dynamic classiﬁcation This is a test to determine whether it is appropriate to use BS 6399-2 and to obtain the value of Cr, and is demonstrated in Calculation 1. Note A The value of Cr given by the classiﬁcation indicates that the building is 3.5% dynamic. α = 10˚ 6m H =7m W = 30 m L = 60 m Figure A Principal dimensions of the portal frame building Calculation 1 Dynamic classiﬁcation of the portal frame building Clause Action Notes 1.3.3.2 Building height above its base H=7m Use height to eaves 1.6.1 Read value of Kb from Table 1 Kb = 2 When in doubt, take next larger value 1.6.1 Using H and Kb, read Cr from Figure 3 Cr = 0.035 1.6.2 Check Cr < 0.25 If Cr > 0.1, get better value from Annex C If Cr > 0.25, BS 6399-2 is not applicable BS 6399 can be used Yes Stage 2: Design wind speed and dynamic pressure Notional site layout In accordance with §1.7.2 and the distances in Table A, the site is categorised as in-town terrain. We shall assume that the building is in an industrial estate, surrounded by buildings of a similar height, and is aligned with the ridge at 45° east of north. This gives four orthogonal cases – NW, NE, SE and SW (shown in Calculation 2) – that are the same as for the house in Part 2 (Figure C of Part 2). We shall assume that the spacing of the other buildings in the estate is unknown but typical. This gives an obstruction height Ho = 9.7 m and, from Q8 of Part 1, a spacing X = 20 m. Owing to the symmetry of the house, we need to consider only two orthogonal directions: q wind normal to the ridge θ = 0°, and q wind parallel to the ridge θ = 90°. Accordingly, the orthogonal cases SW for θ = 90° and NW for θ = 0° control the design, and the dynamic pressures for the other cases are not required. Stage 3: Pressure coefﬁcients and design loads Pressure coefficients on walls The scaling dimensions for the walls of the portal frame building are determined in Calculation 3 from the dimensions given in Figure A. The pressure coefficients for the walls of the building are shown in Figure B for θ = 0° (Case NW) and in Figure C for θ = 90° (Case SW). 2.8 m +0.6 Windward face Windward4.3) (D/H = 4.3) ( D/H = face -0.4 -0.8 -0.1 -1.3 14 m Side face (isolated) Side face (isolated) Leeward face (Leeward face (D/H = 4.3) D/H = 4.3) Figure B Pressure coefﬁcients for walls of the portal frame building θ = 0° Pressure coefficients on the roof The scaling dimensions for the walls of the portal frame building are determined in Calculation 4 from the dimensions given in Figure A. The pressure coefficients for the roof of the building are shown in Figure D (on page 4) for both orthogonal cases. Calculation 2 Dynamic pressures for the portal 3.9 m +0.6 Windward face Windward face (D/H = 4.3) ( D/H = 6.2) -0.4 Side face (isolated) Side face (isolated) -0.8 19.3 m Figure C Pressure coefﬁcients for walls of the portal frame building θ = 90° -1.3 -0.1 Leeward face Leeward face (D/H = 4.3) ( D/H = 6.2)
3. 3. 3 Note B Ready-reckoner gives values of Sb directly, avoiding the use of Sc, St, Tc and Tt factors. frame building by Option 2(b) Clause Action 2.2.1 Notes From Figure 6, basic wind speed Vb = 22.6 m/s Hourly mean speed 10 m above ﬂat open country From site plan, altitude of site ∆ = 120 m 1.3.3.1 2.2.2.2.1 2.2.2.2 2.1.1.2 2.2.2.3 Site less than halfway up hill From Equation 9, altitude factor Sa = 1.120 Orthogonal direction : NE SE SW 0.85 1.00 Topography not signiﬁcant Range of NE includes 0°, 30°, 60° and 90° NW 0.99 NE value is biggest of From Table 3, select biggest direction factor in range Sd = 0.78 2.2.2.1 Take from OS 1:50,000 mapping Using Figure 7, check for signiﬁcant topography = No 0.78, 0.73, 0.73 & 0.74 Ss and Sp taken as unity From Equation 8, site wind speed Vs = 19.74 21.52 25.31 25.06 m/s 1.3.3.4 Surrounded by similar buildings Select lowest obstruction height in range Ho = 9.7 9.7 9.7 9.7 m 20 20 20 m 7.6 7.6 7.6 m Spacing unknown but typical. Select furthest obstruction separation in range Xo = 20 E.2.1 displacement height Hd = 7.6 2.2.3.3 110 200 112 km 1.5 1.5 1.5 km Hr = 9.7 9.7 9.7 9.7 m Larger of He = Hr – Hd = 2.1 2.1 2.1 2.1 m or He = 0.4 Hr = 3.9 3.9 3.9 3.9 m Selected for range from Table A From Table A, shortest distance-in-town in range = 3.5 1.7.3.3 Hd = 1.2Ho – 0.2 Xo Selected for range from Table A From Table A, closest distance-to-sea in range = 110 1.7.3.1 See Q8 of Part 1 Deﬁned in Annex E. From Q10 of Part 1, Safe assumption for whole building Reference height at ridge See Q10 of Part 1 Option 2(b): use Equation 29 or ready-reckoner 3.2.3.2.3 From Table 22, factor Sc = 0.839 0.839 0.839 0.839 Logarithmic interpolation used in From Table 22, factor S t = 0.197 0.197 0.197 0.197 Tables 22 and 23, but linear interpolation From Table 23, factor Tc = 0.702 0.722 0.722 0.722 is adequate From Table 23, factor Tt = 1.687 1.687 1.687 1.687 3.4.2.1 Standard value of factor g t = 3.44 2.2.3.3 From Equation 29, terrain-&- 3.44 3.44 Equivalent to CP3 Class A 3.44 Equation 29 allows for building factor S b = 1.260 1.296 1.296 1.296 2.2.3.1 Now gust speed, equivalent to CP3 Class A effective wind speed Ve = 24.9 2.1.2.1 actual distance-in-town From Equation 12, 27.9 32.8 32.5 m/s Gust dynamic pressure, From Equation 1, dynamic pressure qs = 379.4 476.5 659.5 646.4 Pa equivalent to CP3 Class A Calculation 3 Scaling dimensions for walls of the portal frame building Clause Wind parallel to ridge, θ = 90°, case SW Wind normal to ridge, θ = 0°, case NW 1.3.3.2 Height H = 9.65 m Height of gable Height H = 7 m 1.3.4.3 Breadth B = 30 m Figure A, B = W Breadth B = 60 m 1.3.4.4 Depth D = 60 m Figure.A, D = L Depth D = 30 m 2.2.3.2 H < B, one part, Hr = 9.65 m 2.4.1.2 Span ratio D/H = 6.2 2.4.1.3 Scaling length b = 19.3 m Peak of gable See Table 5 Smaller of B or 2H Height of eaves Figure A, B = L Figure A, D = W H < B, one part, Hr = 7 m Span ratio D/H = 4.3 Scaling length b = 14 m Eaves See Table 5 Smaller of B or 2H Calculation 4 Scaling dimensions for roof of the portal frame building Clause Wind parallel to ridge, θ = 90°, case SW Wind normal to ridge, θ = 0°, case NW 1.3.3.2 Height H = 9.65 m = Hr 2.5.2.2 Scaling length bW = 19.3 m Height of ridge Smaller of W or 2H Height H = 9.65 m = Hr Scaling length bL = 19.3 m Height of ridge Smaller of L or 2H
4. 4. 4 1.93 m Note C For the wind angle θ = 0° and roof pitch of α = 10° the pressure coefﬁcients on the roof are always suctions. In determining horizontal components the asymmetric loads provisions of §2.1.3.7 will apply to the beneﬁcial action of the suctions on the upwind roof pitch. (See Q24 of Part 1.) 7.5 m -1.8 -0.4 -0.4 -0.6 -0.35 7.5 m -1.3 -0.8 -0.8 -0.6 -0.6 -0.8 1.4 m -1.3 -0.45 -0.45 -0.6 -0.35 -1.8 -1.55 -1.55 -1.0 -1.0 -1.55 1.4 m 9.65 m 9.65 m Figure D Pressure coefﬁcients for roof of the portal frame building θ = 0° and 90° 6m 6 m -1.3 -0.8 3.9 m Figure E Location and size of roller shutter door Internal pressure coefficients We shall assume that there is a 6 m-high roller shutter door spanning the full width of the end bay on one of the side walls. This will be assumed to be closed at the ultimate limit state, corresponding to Calculation 5. We will treat the door open as a serviceability limit state, corresponding to Calculation 6 (see Q46 of Part 1). Figure E shows the external pressure coefficients over the area of the door at wind angle θ = 90°. We shall take the typical porosity for curtain walling from Q44 of Part 1 as 3.5 × 10-4. We shall assume that all walls are equally permeable and the roof is impermeable. As the internal pressure, door closed, is set by the average flow of wind in and out of the distributed porosity, it is reasonable to take the average height of the walls as the reference height for internal pressure. Because the area of the side walls is twice the area of the gable walls, the average height is close to the eaves height and we shall use the eaves height as the reference height for the internal pressure. This is a pragmatic engineering decision. The reference height for the internal pressure caused by a dominant opening is the reference height for the wall in which the opening occurs, which is also the eaves height. Dynamic pressure Reference heights for the portal frame building are ridge height for the roof and the gable walls and eaves height for the side walls. The values at ridge height were derived in Calculation 2. Corresponding values of dynamic pressure at eaves height and for the serviceability limit are given in Table B. Table B Values of dynamic pressure for the portal frame building Reference height Ultimate Sp = 1 Serviceability Sp = 0.8 Application θ = 0° θ = 90° θ = 0° θ = 90° Hr = 7 m 547 Pa 558 Pa 350 Pa 357 Pa pe side walls, pi (see above) Hr = 9.7 m 646 Pa 660 Pa 414 Pa 422 Pa pe roof and gable Loading of roller shutter door Clearly wind loads occur on the roller shutter door only when it is closed, and values are derived in Calculation 7. We shall treat the door as a single structural element and use the average pressure coefficient over the area of the door. (See Q38 of Part 1.) Note E At higher values of roof pitch α the highestloaded purlin will be in the ﬁrst (ridge) or second purlin on the downwind slope. Remember that the loaded zones are deﬁned in plan so that the dimensions up the roof slope depend on the pitch angle. Highest-loaded purlin We shall assume that there are eight lines of purlins on each roof slope, spaced equally from eaves to ridge, giving a purlin spacing of 2.17 m in the plane of the roof. Inspection of the pressure coefficients in Figure D reveals that 6m 6m the highest-loaded purlin will be either the first (eaves) or second purlin on the upwind roof slope of the end bay, as 2.17 m 2.17 m shown in 1.42 m Calculations 8a (opposite) and 8b 1.93 m 9.65 m (on page 6). The relevant tributary Wind angleangle θ0˚ 0° Wind angle θθ= 90˚ = = Wind θ Wind angle = 90° areas are shown hatched in Figure F. Figure F Highest-loaded purlin
5. 5. 5 Note D With the door open, the large positive value of internal pressure for wind angle θ = 0° increases the net uplift on the roof, while the large negative value θ = 90° increases the load on the windward wall. Calculation 5 Internal pressure coefﬁcient for the case with the door closed Clause Action Notes Internal pressure coefﬁcient Cpi = –0.3 2.6.1.1 See Q43 of Part 1 From Equation 13, diagonal dimension a = 10 × 3√(volume of storey) = 10 × 3√(60 × 30 × (7 + 2.65/2)) = 248 m Includes roof space From Figure 4, size effect factor Ca = 0.646 2.1.3.4 Site in-town, line C Calculation 6 Internal pressure coefﬁcient for the case with the door open Clause Action From Q46 of Part 1, probability factor Sp = 0.8 2.2.2.5 2.6.2 Notes 2 year return From Equation 15, diagonal dimension is greater of diagonal Opening controls dimension of opening = √(62 + 62) = 8.5 m, the value or 0.2 ×3√(volume of storey) = 5.0 m, a = 8.5 m From Figure 4, size effect factor Ca = 0.952 2.1.3.4 Site in-town, line C Area of opening A1 = 6 × 6 m = 36 m2 Total surface area A2 = 3176 m2 Ratio, opening area to sum of remaining openings = 36 / ( 3125 × 3.5 × 10–4) = 32 Much greater than 3 From Table 17, internal pressure coefﬁcient Cpi = 0.9 × Cpe Wind angle θ = 0°, Cpi = +0.6 × 0.9 = +0.54 See Figure E Wind angle θ = 90°, Cpi = (–1.3 × 3.9 – 0.8 × 2.1) / 6 × 0.9 = –1.01 Calculation 7 Loads on the roller shutter door Clause Action Notes Diagonal dimension of door a = √(62 + 62) = 8.5 m 2.1.3.4 Site in-town, line C From Figure 4, size effect factor Ca = 0.952 θ = 0° Wind angle : 2.4.1 θ = 90° External pressure coefﬁcient averaged over door Cpe = 0.6 2.1.3.1 From Equation 2, pe = qs × Cpe × Ca = 547 × 0.6 558 × –1.125 × 0.952 = 312 Pa 2.1.3.2 × 0.952 = –598 Pa From Equation 3, pi = qs × Cpi × Ca = 547 × –0.3 558 × –0.3 × 0.645 = –106 Pa 2.1.3.3 Cpi and Ca from × 0.645 = –108 Pa earlier calculation From Equation 4, net pressure p = pe – pi = 418 Pa 2.1.3.5 See Figure E –1.125 –490 Pa Load on door P = p × A = 15.0 kN –17.6 kN Ultimate limit Calculation 8a Highest-loaded purlin (ultimate limit state) Clause Action Notes Eaves purlin Diagonal dimension a = 6.1 m 2.1.3.4 6.4 m From Figure 4, size effect factor Ca = 0.982 0.978 Site in-town, line C 13.02 m2 Loaded area A = 6.51 m2 2.1.3.5 Second purlin True area on slope θ = 0° θ = 90° From Table B, External qs = 646 Pa 660 Pa Internal qs = 547 Pa 558 Pa Ultimate limit, door closed 2.1.2 Loaded purlin Eaves purlin Second purlin Second purlin 2.5.2.4 Averaged Cpe = –1.55 –0.62 –0.99 2.1.3.1 pe = qs × Cpe × Ca = –983 Pa –392 Pa –639 Pa pi = qs × Cpi × Ca = –106 Pa –106 Pa –108 Pa Equation 4, net pressure, p = pe – pi = –877 Pa –286 Pa –531 Pa –3.72 kN –6.91 kN 2.1.3.2 2.1.3.3 2.1.3.5 (Ca =0.646) Load on purlin, P = p × A = –5.71 kN
8. 8. 8 Fifteen-storey tower surrounded by a two-storey podium L = 20 m The office tower consists of a 15-storey tower surrounded by a 2-storey podium. The storey height is 3 m and the tower has a 2 m-high parapet. The principal dimensions of the office tower in this example are given in Figure I. W = 15 m H = 47 m H= 6 m W = 40 m L = 40 m Figure I Principal dimensions of the ofﬁce tower Stage 1: Dynamic classiﬁcation Calculation 14 determines whether it is appropriate to use BS 6399-2 and obtain the value of Cr. Note J The value of Cr given by the classiﬁcation indicates that the building is only 5% dynamic. Calculation 14 Dynamic classiﬁcation of the ofﬁce building Clause Action Notes 1.3.3.2 Building height above its base H = 47 m Use height to top of parapet 1.6.1 Read value of Kb from Table 1 Kb = 1 When in doubt, take next larger value Using H and Kb, read Cr from Figure 3 Cr = 0.05 If Cr > 0.1, get better value from Annex C. Check Cr < 0.25 Yes If Cr > 0.25, BS 6399-2 is not applicable 1.6.2 Note K The combination of X = 20 m and maximum funnelling is not consistent but, since the spacing is unknown, it is a conservative assumption. Stage 2: Design wind speed and dynamic pressure Notional site layout In accordance with §1.7.2, and the distances in Table A, the site is categorised as in-town terrain. We shall assume that the building is in the commercial area of town and is aligned with the long axis at 45° east of north. This gives four orthogonal cases NW, NE, SE and SW that are the same as for the house in Part 2 (Figure C of Part 2). We shall assume that the surrounding buildings are a mixture of two and three-storeys (2.5 storeys on average), and that their spacing is unknown but typical. From Q8 of Part 1, this gives an obstruction height Ho = 2.5 × 3 = 7.5 m and a spacing X = 20 m. We shall further assume, since the spacing is unknown, that funnelling (see Q40 of Part 1) is at maximum along the sides of the podium. The design dynamic pressure at the top of the tower, Hr = 47 m, is determined in Calculation 15. As the tower and podium will be divided into a number of parts, we shall require dynamic pressures at a number of other reference heights, but their calculation is left as an exercise for the reader. Owing to the symmetry of the office tower, we need to consider only two orthogonal directions: q wind normal to the long face, θ = 0°, and q wind normal to the short face, θ = 90°. 4m -1.3 2.4 m 0.8 -0.8 -0.3 -1.6 0.6 -0.9 Windward face face Windward Side faceSide face -0.1 3m -1.3 2.4 m 0.8 -0.8 -0.3 -0.9 -0.1 -1.6 Windward face face Windward Side faceSide face Accordingly, the orthogonal cases SW for θ = 90° and NW for θ = 0° control the design, and the dynamic pressures for the other cases are not required. Leeward face face Leeward Wind angle θ = 0° 0.6 BS 6399-2 can be used Leeward face face Leeward Wind angle θ = 90° Figure J Pressure coefﬁcients for the walls of the ofﬁce tower and podium from Table 5 Stage 3: Pressure coefﬁcients and design loads Pressure coefficients on walls and roofs The scaling dimensions for the office tower are determined in Calculation 16 and for the podium in Calculation 17 (on page 10). Figure J shows the pressure coefficients for the walls of the office tower and podium.
9. 9. 9 Note L The ready-reckoner gives the values of Sb directly, avoiding the use of Sc, S t, Tc and Tt factors. Calculation 15 Dynamic pressures for ofﬁce building by Option 2(b) Clause Action Notes 2.2.1 From Figure 6, basic wind speed Vb = 22.6 m/s Hourly mean speed 10 m above ﬂat open country 1.3.3.1 2.2.2.2.1 2.2.2.2 2.1.1.2 2.2.2.3 From site plan, altitude of site ∆ = 120 m Site less than halfway up hill From Equation 9, altitude factor Sa = 1.120 Orthogonal direction : NE Topography not signiﬁcant Range of NE includes 0°, 30°, 60° and 90° SE SW NW 0.85 1.00 0.99 NE value is biggest of From Table 3, select biggest direction factor in range Sd = 0.78 2.2.2.1 Take from OS 1:50,000 mapping Using Figure 7, check for signiﬁcant topography = No 0.78, 0.73, 0.73 and 0.74 Ss and Sp taken as unity From Equation 8, site wind speed Vs = 19.74 21.52 25.31 25.06 m/s 1.3.3.4 Surrounded by similar buildings Select lowest obstruction height in range Ho = 7.5 7.5 7.5 7.5 m 20 20 20 m 5.0 5.0 5.0 m Spacing unknown, but typical. Select furthest obstruction separation in range X o = 20 E.2.1 displacment height Hd = 5.0 2.2.3.3 110 200 112 km 1.5 1.5 1.5 km 47 47 47 m 42 42 42 m Selected for range from Table A From Table A, shortest distance-in-town in range = 3.5 1.7.3.1 1.7.3.3 Other reference heights will be needed Reference height at parapet Hr = 47 See Q10 of Part 1 From Q10 of Part 1, effective height He = Hr – Hd = 42 Hd = 1.2Ho – 0.2 Xo Selected for range from Table A From Table A, closest distance-to-sea in range = 110 See Q8 of Part 1 Deﬁned in Annex E. From Q10 of Part 1, Option 2(b): use Equation 29 or ready-reckoner 3.2.3.2.3 From Table 22, factor Sc = 1.263 1.263 1.263 1.263 Logarithmic interpolation used in From Table 22, factor S t = 0.151 0.151 0.151 0.151 Tables 22 and 23, but linear interpolation From Table 23, factor Tc = 0.911 0.937 0.937 0.937 is adequate From Table 23, factor Tt = 1.286 1.197 1.197 1.197 3.4.2.1 Standard value of factor g t = 3.44 2.2.3.3 From Equation 29, terrain-&- 3.44 3.44 Equivalent to CP3 Class A 3.44 Equation 29 allows for building factor S b = 1.918 1.918 1.918 1.918 2.2.3.1 effective wind speed Ve = 37.9 2.1.2.1 actual distance-in-town Now gust speed, equivalent to CP3 Class A From Equation 12, 41.3 48.5 48.1 m/s Gust dynamic pressure, From Equation 1, dynamic pressure qs = 879 1044 1444 1416 Pa Calculation 16 Scaling dimensions for the ofﬁce tower Clause Wind angle, θ = 0° equivalent to CP3 Class A 90° Notes From roof of podium 1.3.3.2 Height of tower H = 41 m 41 m 1.3.4.3 Breadth B = 20 m 15 m Depth D = 15 m 20 m 1.3.4.4 2.2.3.2 Aspect ratio H/B = 2.1 2.7 Both H/B > 2. See Figure T 2.4.1.2 Span ratio D/H = 0.37 0.49 D/H < 1. See Table 5 2.4.1.3 Scaling length b = 20 m 15 m Smaller of B or 2H parapet height h = 2 m 2m Assume 2 m high parapet. 0.13 See Table 8 2.5.1.4 parapet height ratio h/b = 0.1 Figure K (on page 10) shows the zones of pressure coefficient on the roof of the tower and the podium for each wind direction. Note that the parapet of the tower reduces values in the A and B zones by a different amount in each wind direction because the ratio h/b differs.
10. 10. 10 Calculation 17 Scaling dimensions of the podium Clause Wind angle, θ = 0° = 90° Notes From roof of podium 1.3.3.2 Height of podium H =6m =6m 1.3.4.3 Breadth B = 40 m = 40 m 1.3.4.4 Depth D = 40 m = 40 m 2.2.3.2 Aspect ratio H/B = 0.15 = 0.15 = 10 = 10 D/H > 4. See Table 5 = 12 m = 12 m Smaller of B or 2H 2.4.1.2 Span ratio D/H 2.4.1.3 Scaling length b Clause 2.5.1.7 requires that we consider the effect of the presence of the tower on the pressure coefficients for the podium roof. The zones of additional pressure coefficients from §2.5.1.7 are given in Figure L and must be used with the dynamic pressure for the tower walls. Because the height of the tower gives a large dynamic pressure, these additional zones may control the design pressures on the podium roof. 1.2 m 6m 3m ±0.2 -2.0 -1.65 -1.14 ±0.2 10 m -0.7 2m -0.7 5m 1.2 m ±0.2 5m -1.75 6m ±0.2 -0.7 -1.4 -2.0 -1.2 5m -0.7 7.5 m 1.5 m -2.0 -2.0 Both H/B < 1, one part 3m Dynamic pressure Following §2.2.3.2, the value aspect ratio H/B Wind angle θ = 90° Wind angle θ = 0° for each direction allows the tower to be split Figure K Pressure coefﬁcients for the roofs of the ofﬁce tower and podium, into the parts shown in Figure M. These parts are used for determining overall lateral loads from Table 8 only and not cladding (see Q34 of Part 1). The Note M middle part, if it exists, may be split into as many slices as desired. We shall align the slices to the 3 m (Dynamic pressure) storey heights. The effective height for each part is taken as the height of the top of the part. Relevant Clause 2.2.3.2 does not values of design dynamic pressure for each effective height are given in Table C. apply to cladding and 3m 3m -1.4 components. See Q34 of Part 1. -0.3 10 m -0.8 -0.8 4m -1.3 7.5 m 0.8 -1.3 -0.8 7.5 m 7.5 m -0.3 3m -1.3 0.8 10 m -1.3 Wind angle θ = 0° -0.8 7.5 m Wind angle θ = 90° Figure L Additional pressure coefﬁcients for the podium roof from §2.5.1.7 Hr = 47 m Hr = 47 m H r = 32 m H r = 26 m Hr = 30 m H r = 27 m 27 m 24 m H r = 21 m Hr = 6 m Hr = 6 m Wind angle θ = 0° Figure M Reference heights for parts of the ofﬁce tower Wind angle θ = 90°