WIND UPLIFT CALCULATIONS
BS 5534: Part 1: 2003: The British Standard Code of Practice for Slating and Tiling, recommends the following for plain tiles with nibs: Where nailed, plain tiles should have minimum fixings in accordance with the following:
For rafter pitches below 60 degrees, two nails should be used in each tile in at least every fifth course.
For pitches of 60 degrees and above, two nails should be used in every tile.
At verges and abutments and at each side of valleys and hips, the end tile in every course should be nailed or otherwise mechanically fixed.
At eaves and top edges, two courses of tiles should be nailed or otherwise mechanically fixed. Nails should not be less than 2.65mm in diameter and of a length which gives at least 15mm penetration into the batten. (The CRTC recommend that nails of 3.35 diameter should be used).
However it must be stressed that there will be situations where fixing the tiles at the minimum requirement may not be enough to prevent tiles being dislodged in high winds.
The following calculations can be used to establish whether a higher level of fixing is required.
Note: The calculation must not be used to justify using a lower level of fixing than the minimum recommended in BS 5534.
The following sections, A and B,show how the predicted wind uplift force for a particular project and its location can be determinined. The calculations in section C provide the resistance to the wind force and the comparison of uplift force to resistance is given in section D. Section E gives examples of the calculations.
A Basic wind uplift equation
It is assumed that the force the wind could exert directly on the windward side of the building will act as a vacuum force on the lee side of the building and it is this vacuum that causes the tiles to lift off the roof. Therefore, it is taken that the uplift force is equal to the force applied to the windward side of the building and conventionally this is given a negative sign.
Force = Pressure x Area
Uplift force (Ft) = dynamic pressure of wind (qs) x pressure coefficient (Cpe
- Cpi) x area (At)
The dynamic pressure of the wind is proportional to the wind speed and the pressure coefficient converts the wind speed to a pressure and this takes into consideration the external and internal pressures on the roof. The coefficients have been derived from wind tunnel testing where windspeed and pressure generated were measured.
Cp e is the external pressure coefficient
Cp i is the internal pressure coefficient
Therefore,
Ft = qs (Cpe -Cpi) At
Where,
qs = 0.613 Ve
2
and, 0.613 is an experimentally determined constant and Ve is the effective wind velocity where, Ve = Vb . Sa . Sb . Sd . Ss . Sp
and, Vb is the site wind speed which is obtained from the 50 year return wind speed map of the UK (given in BS 6399 and BS 5534).
Sa is a factor that takes the altitude into consideration and,
where the topography is not significant, Sa = 1 + s, and
where the topography is significant, Sa = 1 + s , or, 1 + 0.001 T + 1.2 -S,
and the greater value is taken.
ΔS is the site altitude
ΔT is the base altitude of the topographical feature Ψ is the slope
S is a factor that allows for the position of the building on the slope
NOTE : Significant topography, and the calculation methods for T , and S are described in BS 6399.
Sb is a factor that takes into consideration the effective height of the building, whether the
building is in a town or country environment and the distance from the sea or large open
expanse of water. The method of establishing the effective height and the related values of Sb
are given in BS 6399.Sd is a wind direction factor and usually given the value 1 which allows for wind from all
directions. A lower figure can be entered if there is a single or predominant wind direction.
Ss is a wind season factor which is usually set at the value 1 which allows for wind at all times
of the year. A lower figure can be used if there is a significant variation in the wind loads in
the different seasons.
Sp is a probability factor which is assumed to be 1 if the expected wind return rate is once in
fifty years. Other figures can be used if different return periods are anticipated.
Cpe is the external pressure coefficient and values can be obtained from BS 6399.
Cpi
is the internal pressure coefficient and the values can be obtained from BS 6399.
At is the exposed area of the tile and is usually calculated from the product of the batten
gauge (Ga) the cover width (B) of the tiles.
Therefore,
Ft = 0.613 [Vb .Sa . Sb . Sd . Ss . Sp ]2
(Cpe -Cpi) At
B Modifications to calculation method introduced by BS 5534
1. The Cpe - Cpi
is replaced by Cpt which can be used for most common applications and
when the values of Cpt were calculated from BS 6399 they were modified to ensure that
the values obtained were consistent with the values obtained from the previous CP3 standard.
2. A factor D was introduced to allow for the air permeability of the tiles.
3. An S factor was introduced to allow for the shielding effect of the underfelt, when
used.
4. The uplift force equation including the BS 5534 modifications is:
Ft = 0.613 [Vb .Sa . Sb . Sd . Ss . Sp ]2
. Cpt . (B.Ga). D. S
C Calculation of resistance to uplift (Fc)
Two actions resist the wind uplift force; the dead weight of the tiles and the resistance of the any
fixing (nails, clips, mortar etc.).
1. The dead weight of the tile
The weight of the tile must be converted to a force and component of the gravity force acting on
the tile vertical to its face must be calculated.
The following equation can be used :
W = Wg x 0.9 x 9.81 x cos (rafter pitch - tile to rafter pitch)
where,
W resisting force acting vertical to surface of tile due to self weight in Newtons
Wg is the conventional weight of the tile in kilograms
0.9 is a safety factor to take into consideration variations in the weights of the tiles
9.81 is factor to convert kilograms weight to Newtons
cos (rafter pitch - tile-to-rafter-pitch) corrects gravity for to give the component acting
vertical to the surface of the tile.
2. Fixing resistance
Information on nail resistance and mortar strength is provided in BS 5268 and BS 5534.
The resistance of nails is given in Newtons per mm of penetration of type of wood used. Mortar
strengths are given in Newtons per mm2
for the type of mortar mix used. The total resistance is
calculated taking into consideration the nail penetration or the area of mortar contact.
D Comparison of uplift force with resistance
The moments of the forces are compared. The action of the forces needs to be considered to identify the fulcrum points and the length of the lever arms through which the forces act.
Thus the uplift force is taken to act at the central point of the exposed part of the tile and through a lever are that rotates round the corner of the batten and the tile nib. The self weight is take to act through the centre of gravity of the tile and the lever again rotates round the batten and the tile nib.
The lever arm for the nail resistance is the distance from the point where the nail penetrates the batten and the batten tile nib contact rotation point.
Normal practice is to make a number of trail calculations with different fixing patterns until values that exceed the uplift force are achieved.
E Calculation examples
1. Uplift force calculation
Plain tiles (Town Site)
Assume :
Duo-pitched roof, general and local areas, 40 rafter pitch, Newcastle area, town position and no
buildings with 45 m, 2 kilometres from the sea, 30 m above sea level, no significant topographical
features and 7.5 m to ridge.
Ft = 0.613 [Vb .Sa . Sb . Sd . Ss . Sp ]2
. Cpt . (B.Ga). D. S
Vb
24 m / s BS 6399 figure 6
Sa 1.03 1 + 0. 001 s where s is height of site above sea level
Sb 1.615 BS 6399 table 4 He = 7.5 m; 2 km from sea; town position; no
significant topographical features
Sd 1 BS 6399 2.2.2.3
Ss 1 BS 6399 2.2.2.4
Sp 1 BS 6399 2.2.2.5
Cpt -0.11 BS 5534 table 8 general area
-0.13 BS 5534 table 8 local area
B 0.165 m width of tile in metres
Ga 0.1 m gauge in metres
D 2.70 BS 5534 table 9 air permeability factor
S 1 BS 5534 table 10 underfelt shielding factor
When the values given above are substituted in the basic equation the following values are obtained:
Ft = -4.78 N general area
Ft = - 5.658 N local area
Plain tiles (Country Site)
Assume :
Duo-pitched roof, general and local areas, 40 rafter pitch, Newcastle area, country position and
no buildings with 45 m, 2 kilometres from the sea, 100 m above sea level, no significant
topographical features and 7.5 m to ridge.
Ft = 0.613 [Vb .Sa . Sb . Sd . Ss . Sp ]2
. Cpt . (B.Ga). D. S
Vb
24 m / s BS 6399 figure 6
Sa 1.10
Sb 1.7 BS 6399 table 4 He = 7.5 m; 2 km from sea; country position; no
significant topographical features
Sd 1 BS 6399 2.2.2.3
Ss 1 BS 6399 2.2.2.4
Sp 1 BS 6399 2.2.2.
Cpt -0.11 BS 5534 table 8 general area
-0.13 BS 5534 table 8 local area
B 0.165 m width of tile in metres
Ga 0.1 m gauge in metres
D 2.70 BS 5534 table 9 air permeability factor
S 1 BS 5534 table 10 underfelt shielding factor
When the values given above are substituted in the basic equation the following values are obtained:
Ft = -6.051 N general area
Ft = - 7.15 N local area
Plain tiles (Country Site; Significant Topography)
Assume :
Duo-pitched roof, general and local areas, 40 rafter pitch, Newcastle area, town position and no
buildings with 45 m, 10 kilometres from the sea, base 30 m above sea level, hill (slope 0.3 100m base
length and site 30 m windward side of ridge, and building height 7.5 m to ridge.
Ft = 0.613 [Vb .Sa . Sb . Sd . Ss . Sp ]2
. Cpt . (B.Ga). D. S
Vb
24 m / s BS 6399 figure 6
Sa 1.1765 1 + 0.001 t + 1.2 eS
t = 30 m, where t is base height of site above sea level BS 6399
2.2.2.2.3
e = 0.3, where e is effective slope of the topographical feature BS 6399
2.2.2.2.3
S = 0.407, where S is the topographical location factor BS 6399 2.2.2.2.3 &
amendment table G2
Sb 1.615 BS 6399 table 4 He = 7.5 m; 2 km from sea; town position; no
significant topographical features
Sd 1 BS 6399 2.2.2.3
Ss 1 BS 6399 2.2.2.4
Sp 1 BS 6399 2.2.2.5
Cpt -0.11 BS 5534 table 8 general area
-0.13 BS 5534 table 8 local area
B 0.165 m width of tile in metres
Ga 0.1 m gauge in metres
D 2.70 BS 5534 table 9 air permeability factor
S 1 BS 5534 table 10 underfelt shielding factor
When the values given above are substituted in the basic equation the following values are obtained:
Ft = -6.52 N general area
Ft = -7.71 N local area
2 Calculation of uplift resistance
Self weight
Weight of plain tile 1.2kg
Force component perpendicular to tile surface :
W = 1.2 x 0.9 x 9.81 x cos (40 -10) N
= 9.17 N
Nail resistance
Assume :
A 2.65mm diameter nail with a type A batten has a resistance of 1.5 N per mm of penetration (BS
5268 part 2)
BS 5534 3.6.3.4.2.(b) recommends a factor of 3 is applied to this value.
Nail penetration is assumed to be 17mm
Therefore:
nail resistance = 17 x 1.5 x 3 = 76.4 N, and,
for two nails the value is 153 N.
The following factor (Kn ) may be used to reduce the resistance to where some courses are not
nailed.
Where, n = 1 Kn = 1 all courses nailed
n = 2 Kn = 0.379 every 2nd course nailed
n = 3 Kn = 0.184 every 3rd course nailed
n = 4 Kn = 0.102 every 4th course nailed
n = 5 Kn = 0.058 every 5th course nailed
The Kn factors have been calculated using the equation given in BS 5534 3.6.3.4.
= -1.1316 Nm local area
Example 2
Mu = Ft x Lf = -6.051 x 0.2 = -1.2102 Nm general area
= -7.15 x 0.2 = -1.43 Nm local area
Example 3
Mu = Ft x Lf = -6.52 x 0.2 = -1.304 Nm general area
= -7.71 x 0.2 = -1.542 Nm local area
Self weight moment
Mw is the restoring moment due to self weight and is given by :
Mw = Fw x Lw = 9.17 x 0.12 = 1.10 Nm
The residual uplift forces after the self weight moment is subtracted are
3 Comparison of uplift and resistance moments
Uplift moment
The uplift moment Mu is given by Ft x Lf, where Lf is the lever arm from the batten nib rotation point to the centre of the exposed area of the tile
Example 1
Mu = -0.0 Nm general area
= -0.0316 Nm local area
Example 2
Mu = -0.1102 Nm general area
= -0.33 Nm local area
Example 3
Mu = -0.204 Nm general area
= -0.442 Nm local area
1st comparison
When the uplift moments are compared to the restoring moment due to self weight it
can be seen that the self weigh only exceeds the requirement in the general area of the
first example and that in all other cases nailing will be required.
Nail Resistance Moments
Mn is the restoring moment due to the nail resistance and is given by :
Mn = Fn x Ln = 153 x 0.013 = 1.989 Nm twice nailed tiles
Applying the reduction factors for unnailed courses the following values are obtained
n = 1 Kn = 1.989 Nm
n = 2 Kn = 0.754 Nm
n = 3 Kn = 0.370 Nm
n = 4 Kn = 0.238 Nm
n = 5 Kn = 0.115 Nm
2nd Comparison
When the residual uplift moments are compared with the nail resistance values a
nailing specification that exceeds the residual value would be considered safe for that
site.
