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3.9 WIND LOADING
Timber is frequently associated with buildings of lightweight construction, and the general lack of mass usually requires attention to be paid to wind loading as it affects not only the stresses in individual members and the overall stability but connections and anchorages. The wind loading for which structures must be designed in the UK is calculated from BS 6399-2.
BS 6399-2 and the previous wind code CP3: ChV: Part 2 both predict the maximum gust load on a component or part of a building or the entire structure that is then used in static design. Both codes require the derivation of a design or effective wind speed that is converted to a dynamic wind pressure which with the relevant pressure coefficients, gives the wind forces acting on the building, part or component.
For the majority of sites in the UK the designer, when using CP3: ChV: Part 2, had only to assess the site exposure (S2), as the other factors relating to topogra- phy, statistical return period and wind direction (S1, S3 and S4) were generally assumed to be unity. The pressure coefficients for buildings were defined from the geometry of simple rectangular plan shapes.
BS 6399: Part 2, on the other hand, provides alternative methods for deriving both the effective wind speed and the pressure coefficients for a building part or component. This leads to computational procedures that range from the simple (hand calculator) to the complex (programmable calculator or computer based).
To arrive at the effective wind speed, BS 6399: Part 2 offers three basic methods:
• Method 1 The Standard method
• Method 2 The Directional method for effective wind speed, with Standard method pressure coefficients (as described in clause 3.4.2 of the code)
• Method 3 The Directional method for effective wind speed, with Directional method pressure coefficients.
For hand calculations the designer will find Method 1 the simplest for buildings located in country areas, while Method 2 will be more advantageous in towns.
Method 3 essentially requires a software driven solution.
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All three methods use the same procedure to determine the site wind speed (Vs) which is derived from the basic wind speed (Figure 6 of the Code) and the effects of wind direction, seasonal or duration effect and the probability of occurrence.
They all have an ‘altitude factor’ – Method 1 includes altitude with topography whereas Methods 2 and 3 take into account only altitude (with the effects of topography for Methods 2 and 3 being included in the factor Sb– see below).
The site wind speed is then factored by Sbto allow for terrain and building effects. The value of Sb is determined by the distance of the site from the sea, whether the site is located in the country or in a town and the effective height of the building.
The effective height of a building is derived from clause 1.7.3.3 and is related to the upwind shielding effects of other buildings or permanent obstructions. In country terrain there is usually little benefit available from upwind shielding but in towns the effects are very significant. The Note to clause 1.7.3.3 gives guidance on the height of surrounding buildings that may be assumed in the absence of specific measurements. With this assumed height the dimension Xmay be taken as 20 m where no plan dimensions exist.
For Method 1 the factor Sb is given in Table 4 of the Code. When using Methods 2 and 3, Sb is calculated from the equations and tables in clause 3.2.3.2. With Method 2, the gust factor (gt) is taken as a fixed value of 3.44 for a diagonal dimension aof 5 m whereas in the more complex Method 3, gtis a variable factor depending upon the effective height and the dimension a.
Methods 1 and 2 then return to clause 2.1.2 for the derivation of dynamic pressure and wind forces using relatively simple external and internal pressure coefficients. Method 3 proceeds to clause 3.1.2 using more comprehensive but likewise more complicated pressure coefficients.
Division of the height of a building into parts, e.g. storey heights – a procedure often followed in timber designs when using CP3: ChV: Part 2 – is not permitted in BS 6399: Part 2 unless the building height exceeds the horizontal dimension of the elevation facing the wind. This is a very unlikely geometrical proportion for a timber building. It is therefore essential that the designer takes full account of upwind shielding and uses Method 2 where possible. In these particular circum- stances the resulting wind forces, particularly in a town, will in most cases be less than those derived from CP3: ChV: Part 2.
Consider as an example a typical pair of semidetached two-storey flat-roofed houses located in the city of Leeds at an altitude of 120 m. The distance from the site to the edge of the city to the north, south and west is 5 km and the distance to the east is 1.5 km. It is assumed that there are no topographical features such as an escarpment affecting the wind calculation. The eaves height is 6 m (2 storeys
¥3 m) with plan dimensions of the building 10 m ¥8 m. The houses are surrounded by similar buildings. As the orientation of such a dwelling relative to the cardinal points is not definable in a large development, the maximum likely site wind speed is calculated and the wind forces calculated from the corresponding pressure. To simplify the calculation only the wind forces acting on the long elevation will be considered.
Example
Using CP3: ChV: Part 2
Basic wind speed 45 m/s S2(3B) =0.60 (3 m) and 0.67 (6 m) S1 =S3 =S4 =1.00 for the top storey Vs =0.67 ¥45 =30.00 m/s
for the bottom storey Vs =0.60 ¥45 =27.00 m/s
the dynamic pressure q=0.613 ¥302=552 N/m2for the top storey q=0.613 ¥272=447 N/m2for the bottom storey Combined cpe on the windward and leeward elevations is [+0.7 -(-0.25)] =0.95 Total wind force on long elevation is 3 ¥10 ¥0.95(552 +447)/1000 =28.47 kN Using BS 6399: Part 2, Method 1
Basic wind speed Vb = 22.5 m/s (note: the wind speed is for 1 hour’s duration whereas the previous Code was on a 3 second basis)
The effective height is 6(Hr) -1.2 ¥6(H0) +0.2 ¥20(X) =2.8 m
Using the worst parameters with the altitude factor Sa=1.12 and Sd =Ss=Sp=1.0 gives
The minimum distance to the sea is 95 km, and as the distance into the town is less than 2 km, country conditions have to be assumed; hence, from Table 4,
Sb =1.31 for He=2.8 m, in the country, 100 km from the sea
(Note: if the effects of upwind shielding are ignored, i.e. He=6.0 m, then Sb=1.48, Ve=37.30 m/s and qs=853 N/m2)
The cpe values for a ratio of (plan dimension parallel to wind/eaves height) =1.33 are
and to arrive at the wind forces it is necessary to calculate the diagonal dimension aof the elevation under consideration. This dimension agives the factor cawhich is a size effect for the size of the wind gust (smaller dimension gusts have higher pressures in simple terms):
For alternative B in this figure, the wind force on the elevation is then,
where Cr, the dynamic augmentation factor, is 0.01 approximately and can be ignored for timber structures. Hence
P=33.5 kN, which is 17% higher than the CP3: ChV: Part 2 value.
Using BS 6399: Part 2, Method 2
Consider for this example only the cardinal points for the alternative wind directions in Table 3.1. (In a full calculation the wind directions should be in 30°
increments, not 90°.)
P=0 85 10. ¥ ¥6¥0 93 1 056. ¥ . ¥668 1( +Cr) 1000
a= 102+82 =12 8. m and hence from Figure 4, ca=0 93. 0 778. - -( 0 278. )=1 056.
Ve=1 31. ¥25 20. =33 01. m /s and qs=0 613. ¥33 01. 2=668N / m2 Vb=1 12. ¥22 5. =25 20. m /s
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The critical design pressure is 497 N/m2. It can be seen that the maximum value of Sbdoes not now give the maximum design wind pressure because this maximum Sbis used with a lower value of Vsdue to the direction factor. By making these refinements the value of qs is now 34% lower than with Method 1.
The wind force on the long elevation is calculated as for Method 1 but using the lower value of qs, i.e.
This is some 12.5% less than the CP3: ChV: Part 2 method but the effort required is considerably greater. To obtain the most economical return from BS 6399: Part 2 tabulated data, ‘ready reckoners’ or a software solution are a necessity if only to determine the dynamic wind pressure.
The above example demonstrates some of the intricacies of BS 6399-2 in relation to the effects of wind on the walls of a building. The calculation for the effects of wind on roof structures is more complex because the number of pressure zones on a duopitch roof is at least 6 and with pitches in the range 15° to 45° there can be alternative +ve and -ve pressure coefficients for a particular zone. This certainly complicates stability calculations and makes the stress calculations for a roof truss close to impossible without making overall simplifying assumptions such as taking uniform pressures on the windward and leeward slopes equal to the maximum values derived from BS 6399-2.
Where there is a net wind uplift or a net overturning moment due to wind BS 5268-3 for trussed rafters calls for a factor of safety of 1.4, i.e. the wind
P=0 85 10. ¥ ¥6¥0 93 1 056. ¥ . ¥497 1000=24 9. kN Table 3.1 Cardinal points vs. wind directions
North East South West
0° 90° 180° 240°*
Altitude Sa 1.12 1.12 1.12 1.12
Direction Sd 0.78 0.74 0.85 1.0
Seasonal Ss 1.0 1.0 1.0 1.0
Probability Sp 1.0 1.0 1.0 1.0
Vs=Sa·Sd·Ss·Sp 19.66 18.65 21.42 25.20
Distance, sea (km) 90 90 330 80
Distance, town (km) 5.0 1.5 5.0 5.0
Sc 0.771 0.854 0.765 0.777
Tc 0.624 0.649 0.624 0.624
gt 3.44 3.44 3.44 3.44
St 0.209 0.209 0.209 0.209
Tt 1.85 1.85 1.85 1.85
Sh 0 0 0 0
Sb=ScTc(1 +(gtStTt) +Sh) 1.21 1.29 0.95 1.13
Ve=SbVs 23.79 24.06 20.35 28.48
qs=0.613 ¥Ve2 347 N/m2 355 N/m2 254 N/m2 497 N/m2
* The value of Sdis 1.0 at 240° and 0.99 at true west (270°), so the worst condition has been taken.
action must be multiplied by 1.4 and the result must not be greater than the dead load or permanent load value or restoring moment (including the contribu- tion from holding down straps, etc.). This principle should be applied to all timber structures.