On the wind-loading mechanism of roofing elements

Journal of Industrial Aerodynamics, 4 (1979) 415--427

415

© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

ON THE WIND-LOADING MECHANISM O F R O O F I N G ELEMENTS*

C. KRAMER, H.J. GERHARDT and H.-W. KUSTER

Fluid Mechanics Laboratory, Fachhochschule Aachen (F. R. G.)

Summary The outer, wind-exposed layer of many roofing systems is wind permeable. The wind load on a roofing element of such systems is determined by the pressure difference across the roofing element. Only the external pressure distribution induced largely by the building flow field is given in wind-loading codes. The application of the codes to wind-permeable roofing systems usually leads to very conservative wind loads. This paper describes the wind-loading mechanism for three widely used roofing elements. The experimental results obtained give a reliable basis for designing more economic roofing systems.

1. Introduction

Generally the wind load on a roofing element is created by the difference of the external and the internal pressure, the latter acting on the downward surface of the element. As shown in the schematic (Fig.l), the net wind load is determined b y the building flow field, the wind gustiness and t h e element flow field. While these parameters directly influence the external pressure distribution on the roofing element, the development _of the internal pressure, depending on these parameters indirectly, is governed b y a dynamic response which is different for various roofing elements. Roofing elements are, for example, tiles, paving blocks and sealing membranes. The pressure distribution on the external r o o f surface is well known from numerous investigations (for flat roofs see the paper "Wind Pressures on Block-type Buildings" by the authors in these Proceedings and the reference given; for pitched roofs see Chien et al. [1], and Eaton, Mayne and Cook [2] ). The investigation of the internal pressure has obtained very little attention. This paper presents the first results of studies into the wind-loading mechanism for tiles, paving blocks and sealing membranes. 2. Wind loading o n tiles

The external pressure on a tile on a wind-exposed r o o f is determined by the external pressure distribution on the r o o f due to the flow field around *Paper presented at the 3rd Colloquium on Industrial Aerodynamics, Aachen, June ]4--16, 1978.

416

response. behavJour

__•[ __•._[ ._•

building flow field

wind gustiness element flow field

external pressure distribution

internal pressure distribution

f

l net wind load

Fig.1. Net wind load on roofing elements as the difference between external and internal pressure distribution.

the building and by the surface flow acting on the protruding and curved external shape of the tile. The external pressure distribution on the r o o f depends on the r o o f pitch and the geometric properties of the building. Tiles are normally used on roofs with a pitch angle a >i 15 ° . Data for the distribution of the mean pressure coefficient on the r o o f surface are usually based on wind-tunnel results obtained for building models with s m o o t h and impermeable r o o f surfaces. In those experiments, the influence of external shape of the tile on the pressure distribution is n o t taken into account. Experimental data for s m o o t h r o o f surfaces obtained by the authors and taken from Chien et al. [1] are summarized in Fig.2 for various building dimensions H/B and L/B and a pitch angle a = 15 ° . To simplify the application of the data, the roof area has been divided into comer, edge, and middle regions. The diagrams (Fig.2) are based on the locally highest Cp values for all wind directions. From Fig.2 and similar diagrams for a = 30 ° and 45 ° , the simplified external pressure distributions (Fig.3) have been deduced. Fig. 3 is generally valid for pitched-roofed buildings and seems to be useful for codinjz purposes. The contribution to the external wind pressure due to the surface flow was first investigated by Hazelwood [3]. Surface flow is only i m p o r t a n t at the windward side of the r o o f where the flow is n o t separated. The greatest effect occurs for wind direction normal to the eave (a = 0 ° ). Fig. 4 shows as an ex-

417

0=15 o

c o r n e r region

cp~,

2

/

I

i

,

i

0.5

1

L

®=15 o I

1.5

H B

CPmI

edge region

~

m

1

1.5

Cp

mt

L

-f-;

H_ B

. . . .

C~-1

e = 30 °

0.5

.........

%:-,.~

middle region

-2

]

-1 ~

2

0.5

.....

_~

.

1

L_ B

1.5

®= 45 o L

Ii

14 B

Fig.2. Pressure coefficients, averaged for corner, edge and middle regions of a 15° pitch roof. Fig.3. Simplified pressure distributions for roofs with various pitch angle. (The values for corner, edge and middle regions marked in the diagram for e = 15 ° have to be taken from Fig. 2. )

U

FH Aachen

/

HAZELWOOD (3)

,,p

f

Fig.4. Pressure distribution on tiles due to surface flow (a = 0°).

418

ample, the typical pressure distribution for a = 0 ° taken from Hazelwood [3] and obtained by the authors at 1/6 scale tilesin model tests. The pressure distribution,indicating an acceleration region at the eaveward end of the tileand a stagnation zone in front of the overlap of the tilein the upper row, results in an upward-lifting moment. The predominant geometric parameter for the pressure distribution is the tilethickness t related to the non-overlapping length I. Based on this parameter, the BSI Code "Slating and Tiling" [4] gives a general procedure for calculatingthe uplift loading on tiles due to the surface flow. Fluctuations of the surface flow velocity caused by instabilitiesof the flow field over the roof will change the pressure distribution and make the tilesclatter. As mentioned above, the total wind load on tilesis the result of the external wind pressure and the pressure underneath the tiled surface. Following an idea firstformulated by Hazelwood [3], the pressure in the space underneath the tilescan be assumed to be governed by the external pressure distribution and the wind permeability of the tiled surface. For a roof without an underlay between spars and tiles,this space is relativelylarge. Neglecting openings in the gable walls, the pressure inside the space corresponds roughly to the pressure averaged over the whole roof area, which is approximately the pressure of the wind flow. For this case, the total load on the tilescorresponds to the external pressure distribution. W h e n the wind load exceeds a certain value, the tilesare lifted up and the permeability of the roof surface increases rapidly. If this happens in a region with low external pressure, the wind load on the tileswill decrease. However, if the lifting-upoccurs due to surface flow action on the windward side, the stagnation effect will lead to an increase of the internal pressure and to an increase of the up-liftingtileload. A physically valid description of the response behaviour of the internal pressure seems to be rather difficultfor this particular case. If an underlay is fixed on the spars, the space underneath the tilesis considerably reduced. Hazelwood [3] showed by experiments illustratedin Fig.5 that, due to the relativelyhigh permeability of the tiled surface, the time constant for the equilibration of the pressure difference across the tilesis negligibly small compared with the gust time. Underneath the tiles,the pressure equilibration is less obstructed in the channels formed by the battens than for a direction across the battens. Because the pressure loss at the relatively low equilibrating flow velocitiesin the batten space channels is small, the assumption of a constant pressure m a y be sufficient for practical purposes. The absolute value of this pressure is somewhere between the m a x i m u m value of the external pressure distribution along the batten space channel. It depends on the permeability of the tilesand the external pressure distribution. Figs. 6 and 7 give some examples of internal and external pressure distributions obtained in the wind tunnel with a 1/6 scale model roof. For all wind directions,the resulting net load is significantlylower than the load calculated from only the external pressure distribution. The difference between the external pressure and the batten space pressure is lower for wind direc-

419 underlay

curtain

ropidlY ?',

I

failing ~ I' essure

atmospheric ~

pre~u~ S

J/~,f /

batten space

I/so - - - -

-~ .

I

i

--~

¼osec b a t t e n space

pr~re~

curtain released

~

time

Fig.5. Determination of the time constant for the equilibration of the external pressure and the batten space pressure for roofs with an underlay (taken from Hazelwood [3] .).

tions a = 0 ° than for wind directions 45 ° ~< a ~< 90 ° . Thus, higher loads due to this pressure difference may be expected if the load due to the surface flow is small, and vice versa. This should be taken into consideration in wind-loading codes. The following conclusions may be drawn. (1) The wind load on tiles consists of two components: the load due to the difference of external and internal pressure distribution over the roof, and the load resulting from the external pressure distribution over the tile due to the surface flow. (2) The surface flow is only important on the windward side of the r o o f and creates reasonable up-lifting m o m e n t s only for wind directions roughly perpendicular to the eave. (3) For a small batten space, e.g. limited by an impermeable and sufficiently stiff underlay, the time constant of the equilibration process between external and internal pressure distribution is negligibly small, compared with the gust time, for c o m m o n l y used tiles. (4) The pressure along the batten space channels is nearly constant and the load due to the difference between external pressure and batten space pressure is small compared to the load acting on an impermeable r o o f surface due to the external pressure distribution.

420

H = 0.25; e-~-= 1

-4 ~ / 7 - / I / / , v / / / i / / r / / ! / / 1 / R ( ~.A~/ /// /,/ / /// /// /I/ / / / '/ ,,,os~--~D / i 7 / / / / / / / / / / / / / / 1 / ~, I '/~/ / / / /J' / I I / I I / / / I / / f / = i~/ / 1 / / J / ,' / J / ~ / ,'.1/ / 7 /

/.
/1~~ S

,8

~=0°J

external pressure distribution

tiles

c,=o°~

internal pressure distribution in batten space

~=°°J

resulting load distribution

Fig.6. Distribution of external pressure, batten space pressure and resulting load for a roo w i t h a n u n d e r l a y ( a = 0% 0 = 3 0 ° ).

421

-~B=0.25; ~ =I

Af. external pressure distribution

~

J

internal pressure distribution in batten space Cp I

resulting load distribution Fig.7. Distribution of external pressure, batten space pressure and resulting load for a roof w i t h a n u n d e r l a y (~ = 9 0 ° , 0 = 3 0 °).

422 3. Wind load o n f i a t - r o o f p r o t e c t i o n layers In order to protect the sealing membrane, flat roofs are often covered with gravel or concrete blocks. These layers have to withstand the wind action and to prevent the roofing system from lifting up due to wind forces. The main problem for gravel layers is gravel scouring due to tangential wind forces [5,6]. Usually, concrete blocks are placed on the r o o f with gaps in between them and with a spacing from the surface underneath the blocks. This is necessary to allow for water drainage and for vapour diffusion when using an "inverse r o o f " (thermal insulation above the sealing membrane). Porous blocks with channels formed in the b o t t o m surface have the same effect. The wind loading on these blocks is very similar to the wind loading on tiles, because the outer surface is permeable and a space exists b e t w e e n the blocks and the impermeable r o o f sealing. As shown in Fig.8 for an external pressure distribution corresponding to the "worst case" of flat-roof wind loading, the air flow across the blocks at a region of high negative pressure difference will flow into the space underneath the blocks in regions of the r o o f where the pressure difference is smaller. Therefore, in the space underneath the blocks, an equilibrating flow is established. In contrast to the batten space on a tiled roof, the cross-section of the space underneath the blocks is small, resulting in a high resistance for the equilibrating flow. Therefore, a noticeable pressure difference in this space will occur in the direction of the external pressure gradient. Fig.9 is a schematic of a two-dimensional section model used to measure (in full scale) the pressure distribution underneath the blocks as a function of the external pressure gradient. The external pressure gradient could be varied b y the diffuser angle of the channel above the blocks. Due to the flow restriction b e t w e e n the blocks and the impermeable surface, the pressure difference across the blocks in regions of high suction is smaller than for a tiled roof. Also, the influence of the surface flow on the

%~t = CP,,xte,-r,~q"

~~,~j

ITTTTTT volume

flow

~½1ttt ,

equilibration flow

. . / ~ / P e x t e r nat

\roof

seolir~j_

Fig.8. Schematic o f f l o w properties o f a permeable layer o f concrete blocks o n a fiat roof.

423

I

- 500 I Oli 0

\,p~, ..... ~ -~'internQl ~ 0.5

"interna 1.0

1.5m

2.0 x

Fig.9. I n t e r n a l p r e s s u r e as a f u n c t i o n o f e x t e r n a l p r e s s u r e d i s t r i b u t i o n f o r a p e r m e a b l e l a y e r o f c o n c r e t e b l o c k s o n a flat s u r f a c e .

up-lifting of the blocks is smaller. Because the block surface is flat and there is no angle of incidence even at high surface flow velocities, no lift will occur. Therefore, the difference between the up-lifting wind load calculated from the external pressure difference and the actual wind load for blocks on flat roofs may be greater than for tiles. The following conclusions may be drawn. (1) The wind load on concrete blocks protecting a flat roof is determined by the difference of the external pressure distribution over the r o o f and the pressure distribution in the space between the concrete blocks and the impermeable roof surface. (2) The resulting net wind load m a y be significantly lower compared to the wind load on an impermeable flat roof surface. (3) Due to the higher resistance for the equilibrating flow underneath the permeable layer, and due to the flat outer surface, the net wind load acting on concrete blocks is smaller than for tiles at the same external wind pressure distribution. 4. Wind loading o f roofing membranes on flat roofs The total wind load of a roofing membrane, on a flat roof, either loosely lying or with pointwise mechanical fixation, is the difference between the external pressure distribution and the pressure underneath the membrane. For m a n y practical applications, the pressure below the r o o f membrane differs from the static pressure in the undisturbed wind flow. Therefore, the calculation of wind loading using pressure measurement data on the surface of building models alone is n o t correct. During a gust, the membrane will be lifted up due to the outer wind suction. If the structure below the roofing membrane has low or negligible permeability, a negative pressure difference relative to the undisturbed static pressure will occur in the space between the membrane and the roof structure. Therefore, the load is lower than the difference between the external pressure distribution and the undisturbed static pressure. The lower the wind permeability of the structure, the shorter the time constant for pres-

424

sure equilibration. In contrast to the underlay action for a tiled roof, the actual wind load on a roofing membrane may be significantly reduced when the time constant is large compared to the gust time. The area of a gravelled roof where scouring occurred may be taken as an example of a loosely lying membrane. Fig.10 shows a test set-up for the measurement of the time constant for this particular application. The external wind force on the gravel-free zone is simulated by a crane acting on a sheetF, s

A

crane

I ~ m o m e t e r /,,"q~>(

O,~uo_

O,,O,o,emeo,

\~2

X seating membrane & ,

load cell

T &

.

~SEo, e:,oo / \~ I_gyer (fort! s

~

X

i

~

/

j

metal

/

/ ~ - -

/

plate

pressure tab / g r a v e

~PO.7m ~

i

Fig.10. Test set-up to determine the time constant for pressure change under a lifted-up membrane on a flat roof.

F~

,

F = l i f t i n g - u p force ~p = pressure difference across membrane

~'P ,

~o°o 4 ~ooo t

A , ~ ~,

. I Pa I

~

. ~,,~

IW&, "~'"

. ,. ,

.

I

~

~

I mm

~,oot'OOOl/~o~,~ ....... ~

-~:o

~oooI ~ooo

"""'

~,,~,,,,,L,,

looo 4 30001 I

0

t~o

~

oAOOOo .

~/

.

.

.

.

.

5

.

.

~

.

.

.

10

I,..... .

.

.

.

.

15

.

/. .

.

.

t ~°

.... .

20

.

f

90

sec

time

Fig.11. Typical registration of an experiment with the test set-up shown in Fig.lO.

425

metal plate underneath the membrane. In a similar way to roofing practice, the concrete ground simulating the r o o f structure is separated from the membrane by a protection felt. The crane force, the lifting-up height and the pressure difference across the membrane in the lifted-up zone are measured as functions of time. F i g . l l is a typical registration for a test w i t h o u t a gravel layer. The serrated force curve is due to the incontinuous crane action necessary to keep the load approximately constant for a certain time. At the beginning of the lifting-up action, the crane force F c r a n e = 2750 N corresponds well to the product of the pressure difference times the sheet-metal plate area (6.000 Pa X 0.38 m 2 = 2.310 N). The resulting load on the membrane is small compared to the outer simulated wind load. After the load acts on the membrane for approximately 15 s, the pressure difference decreases from 6000 Pa to less than 2000 Pa, while the membrane is lifted up only 6 cm. The time constant for the pressure equilibration is approximately 16.5 s. As long as the membrane around the lifted-up area does n o t form folds, the leakage is relatively small. Forming folds may be easily avoided b y appropriate fixation of the membrane borders at the edges of the roof. The pressure difference across the membrane acts like a spring holding the membrane down; the spring constant decreases with time. This spring constant is represented b y the quotient Ap/A V, where V denotes the volume underneath the membrane and can be determined from the lifting-up height s. In general, the coefficient Ap/A V has to be related to the circumference of the lifted-up area. Fig.12 shows the dependence on time for this circumference-

Ap/AV U

2,0 10s (N/m 6)

\

1.5t0 5

I 1'0"10s

---

\\

without grave[ with grave[ (w=aOON/a2}

0.510s

0

5

10

15

20 t (sec)

Fig.12. Circumference-related "spring constant" for membranes with and without gravel covering as a function of time.

related spring constant. The influence of the gravel load is astonishingly small. Using these results, a calculation of the membrane stress and the lifted-up height was carried o u t under the following assumptions: (a) gravel load, w = 800 N m - 2 ; (b) polyester protection felt (300 g m-2); (c) gravel blow-off in regions where Cp = --3; (d) distribution of the pressure coefficient according to the German Code of

426

Practice DIN 1055 Teil 45; (e) pressure difference underneath the membrane in the lifted-up area 1500 Pa at a gust stagnation pressure of 1000 Pa; and (f) membrane deformation in the lifted-up area approximated by a catenian curve.

The results are summarized in Table 1. The largest value (Ap/A V ) / U = 19230 N m -6 obtained after 14 s for a roof width B = 5 m and a length of the gravel-free zone l = 0.625 m is much lower than the smallest value obtained from the experiments. For all other cases, ( A p / A V ) / U is even smaller. Therefore, the lifting-up heights will be considerably smaller than the values Y m e m b r a n e calculated with the assumptions stated above. Because the time span of 14 s is much longer t h a n the gust time for the highest gust within a 50 year period, i.e. 40 m s-~ corresponding to a stagnation pressure Apstag = 1000 Pa during a 5 s gust, taking into account the effect of wind impermeability seems to be justified. In conclusion, we can say the following. TABLE1 B

Smean

l

b

(m)

(m)

(m)

5

0.038

0.625

10

0.0923

1.25

V

U

p/V

t

(m)

(m 3)

(m)

(Nm-')

(s)

1

0.024

3.25

19230

14

2

0.048

5.25

5950

1

0.115

4.5

2900

2

0.231

6.5

1000

5

0.577

12.5

520

B = r o o f w i d t h ; Smean = m e a n lifted u p h e i g h t ; l = l i f t e d - u p l e n g t h ; b = l i f t e d - u p w i d t h ; V = v o l u m e u n d e r l i f t e d - u p m e m b r a n e ; U = c i r c u m f e r e n c e o f the lifted-up area.

(1) The effective wind load during a gust acting on a roofing membrane on a fiat r o o f with a low wind permeability is considerably lower than the loads deduced from the external pressure distribution. (2) The fixation of the roofing membrane borders at the edges of the roof should be sealed as tightly as possible. Low wind permeability is more important than the strength of the fixation. (3) For a r o o f corresponding to items (1) and (2), gravel blow-off is of minor importance from the wind-loading point of view. The weight of the gravel layer per unit area need n o t be greater than the m a x i m u m gust dynamic pressure at roof height times the pressure coefficient averaged over the roof area, e.g. Cp = --0.8 for buildings with L / B > 1.5 and H / B > 1. (4) Perforations of the roof membrane due to vents, etc., should be avoided in the roof-edge region.

427

References 1 N. Chien et al., Wind-tunnel studies of pressure distribution of elementary building forms, Iowa Institute of Hydraulic Research, State University of Iowa, 1951. 2 K.J. Eaton, J.R. Mayne and N.J. Cook, Wind loads on low-rise buildings -- effects of of roof geometry, Proc. 4th Int. Conf. on Wind Effects on Buildings and Structures, Heathrow, 1975. 3 R.A. Hazelwood, Wind loading, Paper given to Fluid Mechanics Research Meeting at the NPL, London, 1976. 4 British Standards Institution, Code of Practice BS 5534, Part 1 (1978), Slating and Tiling. 5 R.J. Kind, Tests to determine wind speeds for scouring and blow-off of roof top gravel, Proc. 4th Conf. on Wind Effects on Buildings and Structures, Heathrow, 1975. 6 C. Kramer and H.J. Gerhardt, Windkr~fte auf flachen und wenig geneigten Dachfl~/chen, Dokumentation zum 2. Kolloquium fiber Industrieaerodynamik, Aachen, Januar 1976.