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External Pressure Coefficients on Saw-tooth and

Mono-sloped Roofs

Authors:

Bo Cui, Ph.D. Candidate, Clemson University, 109 Lowry Hall, Clemson, SC 29634-

0911, [email protected] O. Prevatt, Assistant Professor, Clemson University, 314 Lowry Hall, Clemson,

SC 29634-0911, Phone: 864-656-5941, [email protected]

ABSTRACT

A wind tunnel study to investigate wind pressures on single and multi-span saw-tooth

roofs for a 1:100 geometrical scale model of a 1ow-rise building was carried out in

atmospheric boundary layer wind tunnel at the Wind Load Test Facility at ClemsonUniversity. The purpose of this investigation was to further investigate wind loads on low

rise buildings with mono-sloped and saw-tooth roofs and study the validity of ASCE 7-02

specification on these buildings. By using larger models and a higher density of pressuretap than in previous studies, a greater resolution of the pressure variations was achieved.

The paper presents representative results of the study that includes point and area-

averaged wind pressure coefficients on models with varying spans and building heights.

Local peak pressures and area-averaged pressures obtained in this study are comparedwith the design values specified in ASCE 7-02 and with results of previous wind tunnel

studies. The results presented showed no significant difference in wind pressures

between the windward span of the saw-tooth roof and the mono-sloped roof. Comparingresults with ASCE 7-02 suggest that the current wind design provisions for mono-sloped

roofs may be un-conservative.

KEYWORDS: Low-rise building; wind-tunnel modeling; external pressure

coefficients, saw-tooth, mono-sloped roof

INTRODUCTION

Codified provisions for saw-tooth roofs have been included in building design guidelinesin the Australian Standard [AS 1170.2, 1989] and in the ASCE 7 since 1995 [ASCE 7

1995] . The current version of [ASCE 7-02] provides the specific values for saw-tooth,

multi-span gable and mono-sloped roofs shown in Table 1 below. From the table it isapparent that saw-tooth roofs should be designed for significantly higher wind loads at

the corners and edges of the building when compared to gable-roof or multi-span gable

buildings, For example, the roofing system installed on a high corner of a saw-tooth roof

would be designed an external pressure coefficient of -4.1, while a similar corner locationon a mono-sloped roof would be designed for an external pressure coefficient of -2.9.

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Roofing systems in US pre-dating the ASCE 7-95 were designed based on the lower

design values prescribed for gable roof buildings (i.e. -2.6 at corners). Despite this fact,of higher design wind loads, forensic investigations of two roofing systems installed on

saw-tooth buildings in Massachusetts found no unusual signs of increased failure of these

systems from high wind loads. This discrepancy in wind design provisions needs to be

investigated to determine the validity of current design value relative to prior results fromwind tunnel studies. This experimental investigation was conducted to use to turn the

validity of current design code values for saw-tooth roof and mono-sloped roofs.

Roof slope 10 < < 30 (degrees)Area 10ft2 Area = 100ft2 Area 500ft2

Roof Zone

Shape1 2 3 1 2 3 1 2 3

Saw-tooth (Span A) -2.2 -3.2 -4.1 -1.6 -2.3 -3.7 -1.1 -1.6 -2.1

Saw-tooth (Span BCD) -2.2 -3.2 -2.6 -1.6 -2.3 -2.6 -1.1 -1.6 -1.9

Mono-slope -1.3 -1.6 -2.9 -1.1 -1.2 -2.0 -1.1 -1.2 -2.0

Gable (27 > 7) -0.9 -1.7 -2.6 -0.8 -1.2 -2.0 -0.8 -1.2 -2.0Multi-Gable -1.6 -2.2 -2.7 -1.4 -1.7 -1.7 -1.4 -1.7 -1.7

TABLE 1EXTERNAL PRESSURE COEFFICIENTS FORGABLE,MONO-SLOPED AND SAW-TOOTH ROOFS (ASCE7-02)

[NORMALIZED TO 3-SECOND GUST WIND SPEED AT MEAN ROOF HEIGHT]

LITERATURE REVIEW

[Holmes,

1987] investigated local and area-averaged pressures on saw-tooth roof

buildings based on wind tunnel tests on a 1:200 scaled, 5-span saw-tooth model with a

roof slope of 20 degrees. The peak local pressure and area-averaged (32m

2

+/-) windpressure coefficients were found to be -7.6 and -3.86, respectively, normalized to the

mean wind speed at eave height, at the high corner of the windward span (span A).Extending this research to mono-sloped, 2 and 4-span saw-tooth roof buildings, [Saathoff

and Stathopoulos, 1992] investigated peak local and area-averaged pressure coefficients,

using 1:400 scale models with roof slopes of 15 degrees. These researchers concludedthat the peak local wind pressure coefficients occurring at the high corners and high

edges of the mono-sloped and windward span of the saw-tooth roof buildings were

approximately the same, at -9.8 and -10.2, respectively, (normalized to the mean wind

velocity at the lower eave height). In addition, they found that the peak local windpressure coefficient at the low corner of the saw-tooth roof significantly exceeded the

values observed on the mono-sloped model (i.e. -7.9 vs. -4.7).

While these previous research results provided valuable wind load design informationfor mono-sloped and saw-tooth roof buildings, there is an unexplained difference in peak

wind loads in ASCE 7 for mono-sloped and saw-tooth roofs that are not supported in

previous research results. To address these questions, the Clemson University windtunnel study was conducted using larger models and a higher density of pressure taps to

provide greater resolution of the area-averaged pressure coefficients than was previously

possible. In addition, the study includes the effect of building height and number of spans

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on wind pressure distributions. Table 2 compares the experimental setups of two previous

tests with the current study at the Wind Load Test Facility (WLTF).

Saathoff and

Stathopoulos (1992)

Holmes

(1987)Present Study

Clemson (2006)

Model Scale 1:400 1:200 1:100

Prototype building

dimension

64 ft 200 ft 48 ft

tall

40 ft 128 ft 40 ft

tall

26 ft 98 ft 53 ft tall 38 ft tall

23 ft tall

Model dimensions 1.91in 6in 2.03in2.36in 7.68in

2.34in

3.12in 11.76in 6.36in 4.56in

2.76in

Roof Slope (degrees) 15 20 21

No. pressure taps 66 taps 60 taps 290 taps

Minimum tributary area

per tap53.8 ft2 34.4 ft2 4.34ft2

Number of span oftested model

1, 2 and 4 span 5 span 1 ,2 , 3, 4, & 5 span

Exposure category Open country Open country Open country

Wind directions

(degrees)

0o, 30-150o in 15o

increments & 180o20-60o in 5o

increments

0350o in 10o deg for 53ft1-span & 5-span,

90-270o in 10o incr. othertests

Turbulence at low

eave/mean roof height0.2 0.2 0.18

TABLE 2COMPARISON OF CLEMSON UNIVERSITY WLTFS WIND TUNNEL TEST SETUP WITH PRIORTESTS BY

SAATHOFF ET. AL. AND BY HOLMES.

EXPERIMENTAL CONDITIONS

The wind tunnel studies were conducted out in the boundary layer wind tunnel of the

Wind Load Test Facility (WLTF) at Clemson University. The wind tunnel is an open-

flow wind tunnel with a 48-feet long test section, and a cross-section measuring 10 ft. by7 ft. We simulated upwind terrain using a 1:100 geometric scale and modeled the velocity

profile and turbulence intensity for open country exposures. The wind speed at gradient

height in the tunnel was approximately 12.5 m/s. The wind velocity and turbulence

intensity profiles obtained in this experiment (normalized to 10 m. height at full-scale)are presented in the Figure 1.

The building model consisted of five similarly shaped Plexiglas models, one of which

having 290 pressure taps installed in the roof as shown in Figure 2. This instrumented

model was interchanged with the other models of different spans to measure the pressuredistributions on the entire saw-tooth building.

Pressure data from the wind tunnel was collected using eight Scanivalve ZOC33electronic pressure scanning modules connected to a RAD3200 digital remote A/D

converter interfacing the pressure scanners with a PC. The pressure taps were attached to

the pressure scanners by 12-in. long vinyl tubes having a 0.063 in. internal diameterRestrictors were installed in each tube to ensure a flat frequency response. Pressure data

were sampled at a rate of 300 samples per second and recorded for a 120-second sample

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time. Based on the velocity scale of 1:4 and the 1:100 length scale ratio of the wind-

tunnel the sample corresponds to a full-scale record of approximately 15 minutes.

FIGURE 1WIND VELOCITY AND TURBULENCE INTENSITY PROFILE (REFERENCE HEIGHT =10 m AT FULL SCALE)

FIGURE 2MODEL USED IN STUDY AND TAP LOCATIONS

0

10

20

30

40

50

60

7080

90

100

0.0 0.3 0.6 0.9 1.2 1.5

0

10

20

30

40

50

60

7080

90

100

0.10 0.15 0.20 0.25 0.30

Turbulence

Intensity

UTest/Uref

z0=0.036mASCE

Wind

HC- high corner

LC- low corner

HE- high edgeLE - low edge

SE - slope edge

HC

HE

HC

SE

IN

Span

A

Span

B

Span

C

Span

D

Span

E

SE

5 Spans @26 = 130

INSTRUMENTED SPAN

IN - interior

LC

LE

LC

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To normalize the pressures, a Pitot tube, located 12 in. below the wind tunnel ceiling,

was used as a reference for dynamic wind pressure. The test pressure coefficients weredetermined using the mean wind speed at the Pitot tube height and then normalized to 3-

second gust wind speed at mean roof height, for the purpose of comparison with ASCE

values. Equivalent wind pressure coefficients were calculated using the following

equations:

phsASCE GCVP2

,32

1= (1)

testpPitotTest CVP ,2

2

1= (2)

Assuming thenTestASCE PP =

2

,3

,

2

2

,3

,

2

2

12

1

)(hs

testpPitot

hs

testpPitot

eqpV

CV

V

CV

GC ==

(3)

where was calculated by the Equation 4 provided by [Simiu and Scanlan, 1996]hsV ,3

)

)(5.2

)3(1(

0

,3

z

hLn

scVV hhs

+= (4)

P denotes wind pressure, denotes air density, 3s gust wind speed at mean roof

height,

hsV ,3

PitotV the mean wind speed at the Pitot tube height in the wind tunnel, the

wind pressure coefficient normalized to 3s gust wind speed at the mean roof height,

the wind pressure coefficient normalized to the mean wind speed at the Pitot tube

height in the wind tunnel,

pGC

testpC

,

hV mean wind speed at mean roof height,z0 roughness length,

h mean roof height, equivalent GCeqpGC )( p which is converted by test Cp.

Area-averaged wind pressure coefficients are necessary for the design of cladding and

components with larger tributary areas. While previous studies pneumatically averagedpressures over large areas, for this experiment, a numerical analysis method was used. To

calculate area-averaged wind pressure coefficients based on the following equations:

=

=

=n

in

i

i

i

jipjareap

A

ACC

1

1

),(),( (5)

),( jareapC denotes instantaneous area averaged wind pressure coefficient,

instantaneous point wind pressure coefficient at time-step j, n the number of taps in the

area and tributary area of the ith tap in the averaged area limitation. Using the time

history the statistic values of area-averaged wind pressure coefficients can be obtained.

),( jipC

iA

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RESULTS AND ANALYSIS

Peak Local Negative Wind Pressure Coefficient Distribution

For the purpose of comparing extreme (minimum) wind pressure coefficients on a mono-

sloped roof and on varying span number saw-tooth roofs, mono-sloped and 2, 3, 4 and 5span saw-tooth roof models with 53 ft mean roof height in full scale were tested in thewind tunnel. Following the convention of ASCE, the windward and leeward spans of the

saw-tooth buildings were denoted as spans A and E, respectively, with spans B, C and D

denoting the middle spans. The pressure distributions for the high corners and the highedges of the windward spans of the saw-tooth roof buildings had similar shapes as the

mono-sloped roof model. The spatial variation of peak negative pressure coefficients on

mono-sloped and span A of the 5-span saw-tooth roof models are shown in Figure 3. The

contour plots for the middle spans are similar with one another (not shown here). For theleeward spans, minimum wind pressure coefficient contours for the different span

number models were also very similar.

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

-4

-3.5

-3

-2.5

-2

-2

-2

-2

-2

-2

-1.5

-1.5

-1

.5

-1.5

-1

.5

-2 -1

.5

-2

.5

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

-4-3.5

-3.5

-3-3

-3

-2.5

-2.5

-2.5

-2

-2

-2

-2

-2

-1.5

-1.5

-1.5

-1.5

-1.5

-2

-2-1.5

-4

-2

CL

Mono-sloped Roof Span A of Saw-tooth Roof

FIGURE 3CRITICALNEGATIVE WIND PRESSURE COEFFICIENTS ON EACH SPAN OF 5-SPAN SAW-TOOTH ROOF (53

MEAN ROOF HEIGHT)

The most critical negative wind pressure coefficients always occurred in the high

corner of the mono-sloped and on the windward span (span A) of the saw-tooth roofs.

The critical wind direction varied from 220 to 240 for all buildings.o o

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Figure 4 presents the extreme point negative wind pressure coefficients at each zoneof the mono-sloped and the 2-5 span saw-tooth roofs with a mean roof height 53 ft. The

values in the high corners and high edges on span A of the multi-span saw-tooth and the

mono-sloped roofs were very similar. In the high corner the peak value for the 2-5 span

saw-tooth roofs was -4.6 and -4.3 for the mono-sloped roof. In the high edges the peak

values were -2.8 and -2.74, respectively. The peak negative wind pressure coefficient onthe span A was higher than on other spans. The maximum value on the middle spans and

leeward spans of the 2- through 5-span saw-tooth roofs was -2.9. For these spans theextreme peak negative wind pressure coefficient occurred in the low corners. The

maximum value in magnitude was -3.99. For span A the measured peak negative wind

pressure coefficient was -3.87 for the 2- to 5- span saw-tooth roofs, a value lower than thepeak value in the high corner of span A, but 29% higher than for the mono-sloped roof (-

2.99).

As the number of spans increased, the peak value in every zone changed. For span A

of the saw-tooth roof models and mono-sloped roof model this variation in the highcorner and in the high edge was less than 10%, the maximum and minimum values being

-4.31 and -4.61 respectively. The variation in other regions on span A was from 14% to25%. On the leeward span (span E), the peak values in each zone varied from 7% to 21%.The largest variation occurred in the sloped edge zone.

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

HC LC SE HE LE IN

Mono 2-A 3-A 4-A 5-A

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

HC LC SE HE LE IN

2-E 3-E 4-E 5-E

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

HC LC SE HE LE IN

3-B 4-B 4-C 5-B 5-C 5-D

Mono: mono-sloped roof;

2, 3, 4 and 5: the number of spans for a roofA: windward span; E: leeward span

3-B: middle span of 3-span roof;

4-B, 4-C: middle spans of 4-span roof;

5-B, 5-C, 5-D: middle spans of 5-span roof;

FIGURE 4PEAKNEGATIVE WIND PRESSURE COEFFICIENTS ON MONO-SLOPED ROOF AND VARYING SPAN SAW-TOOTH

ROOF (53ft MEAN ROOF HEIGHT)

Area-averaged Wind Pressure Coefficients

Increasing the tributary areas caused a sharp reduction in the wind pressure coefficientsfrom point pressures through 100 sq. ft. In the corner zones, the tributary area of a 2-tap

combination is approximately equal to 10 sq. ft. As the tributary areas increased from 10

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sq. ft. to 100 sq. ft., the negative wind pressure coefficients at the high corners decreasedbetween 30% to 50%.

The reduction caused by the increase in area from 100 sq. ft to 150 sq. ft was less

than 20% for the high corners. A similar reduction (30% to 50%) in pressure coefficients

is seen for the low corners and along the sloping edge zones. There were some

differences in extreme area-averaged negative wind pressure coefficients between thevarious span of the model, of less than 30% (Figure 5).

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1 10 100 1000

M

2A

3A

4A

5A

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1 10 100 1000

3B

4B

4C

5B

5C

5D

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1 10 100 1000

2E

3E

4E

5E

M: mono-sloped roof;2, 3, 4 and 5: the number of spans of a roof

A: windward span; E: leeward span

3-B: middle span of 3-span roof;4-B, 4-C: middle spans of 4-span roof;

5-B, 5-C, 5-D: middle spans of 5-span roof;

FIGURE 5PEAKNEGATIVE WIND PRESSURE COEFFICIENTS IN HIGH CORNER OF MONO-SLOPED ROOF AND EACH SPANOF THE 2-THROUGH 5-SPAN SAW-TOOTH ROOFS

Effect of Building Height on Negative Wind Pressure Coefficients

As expected, the extreme wind negative pressure coefficients were affected by the mean

roof height of the model. Figure 6 shows the comparisons of the area-averaged extreme

negative wind pressure coefficients for the three mean roof heights of 23 ft, 38 ft and 53ft. In the high corner zone of the mono-sloped roof and the windward span (span A) of

the saw-tooth roofs, these coefficients were in the range of -4.3 to -5.5. For the middle

and leeward spans (Spans BCDE) of the saw-tooth roof, the critical point negative windpressure coefficients were in the range of -2.4 to -3.6. The maximum variation in the

critical area-averaged negative wind pressure coefficients between two models of

different heights was up to 30%.

The peak area-averaged negative wind pressure coefficients in the high corner on the23 ft mono-sloped roof were larger than on 38 ft and on 53 ft mono-sloped roof models.

However for the extreme value in the high corner on the 5-span saw-tooth roof, the peak

area-averaged values occurred on the model having the 38 ft mean roof height. Thecritical area-averaged negative wind pressure coefficients in high corner on span A of

saw-tooth roofs and on mono-sloped roofs were very similar. (Note that 23M in Figure

6 denotes mono-sloped building (M), having a mean roof height of 23 ft (23) and so on.)

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FIGURE 6AREA-AVERAGEDNEGATIVE WIND PRESSURE COEFFICIENTS IN HIGH CORNER OF MONO-SLOPED AND 5-

SPAN SAW-TOOTH ROOFS WITH MEAN ROOF HEIGHTS OF 23 ft,38ft, AND 53 ft.

Comparison of Wind Tunnel Results with ASCE7-02 and Previous Research

The peak negative pressure coefficients for the mono-sloped roof building were almost

identical to the peak negative coefficients on the windward span (span A) of the 5-span

saw-tooth roof (Figure 7). As expected, peak negative pressure coefficients for themiddle and leeward spans (spans BCDE) were lower than for the windward span values.

FIGURE 7COMPARISONS OF MOST CRITICAL EXPERIMENTAL NEGATIVE WIND PRESSURE COEFFICIENTS AND ASCE

VALUES WITH PREVIOUS RESEARCH RESULTS

Our single point peak negative pressure coefficient of -5.49 was, as expected, well above

the -4.26 value reported by Saathoff et al., who used the average pressure coefficients

derived from results on ten 16-second long pressure time-histories. Of interest to note,however, is the near identical peak negative pressure coefficients obtained by Saathoff et.

al. for the mono-sloped and saw-tooth roofs. Thus, one should expect little difference in

the peak negative pressure coefficients between saw-tooth and mono-sloped buildings.

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1 10 100 1000

23M -6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1 10 100 1000

23A -6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1 10 100 1000

23BCDE

38A38M 38BCDE53A53M

53BCDE

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1 10 100 1000

Saw_A Mono

Saw-BCDE Saathoff -Mono

Saathoff -Saw-A Holmes -Saw-A

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1 10 100 1000

Saw_ A Saw-BCDE

Saathoff Holmes

High Corner Low Corner

Saw-tooth ASCE A

Mono ASCE Saw-tooth ASCE BCD

Saw-tooth ASCE A

Saw-tooth ASCE BCD

Point wind pressure coefficient

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The area-averaged negative pressure coefficients that we obtained by numericallyintegrating the results over several tributary areas revealed a sharp reduction in pressure

coefficients for tributary areas greater than 10 sq. ft. for both the mono-sloped and saw-

tooth roofs. The reductions occurred at smaller tributary areas than provided in the

current ASCE 7 design pressure coefficient reduction with areas. (Figure 7). The area-

averaged values reported by Saathoff et. al. for mono-sloped and saw-tooth buildingswere also nearly identical and, except for the negative pressure coefficient on the saw-

tooth roof at 150 sq. ft., all values exceeded the ASCE 7 design pressure coefficient forthe windward span of a saw-tooth roof building. The graph of area-averaged negative

pressure coefficients on the middle and leeward spans suggest that the negative pressure

coefficients in the low corner on areas less than approximately 25 sq. ft. exceeds theASCE 7 design values.

CONCLUSIONS

Preliminary results presented in this paper and corroborated by previous research suggest

that the peak minimum pressure coefficients for mono-sloped and saw-tooth roofbuildings should be approximately the same. ASCE7-02 provides lower design negative

wind pressure coefficients for mono-sloped roofs than the results reported here, that may

not be supported by the experimental results. Further work is continuing to investigate thesensitivity of extreme pressure coefficients in repeated tests before firm conclusions will

be made and to evaluate mono-sloped buildings with different aspect ratios. The extreme

wind pressure coefficients at the high corner on the windward span was approximately atleast 30% larger than those measured on the other middle or leeward spans. The ASCE7-

02 design pressure coefficients appear low for the low corner zones of the middle and

leeward spans of the saw-tooth roof. This research found no significant variation in low

corners negative pressure coefficients between spans for areas larger than 25 sq. ft.

The most critical area-averaged negative wind pressure coefficients on saw-toothroofs varied with building height. This variation was up to 30% in the high corner.

ACKNOWLEDGEMENTS

The authors wish to acknowledge the generous support of the Department of CivilEngineering at Clemson University, Floridas Department of Consumer Affairs, NOAA

and South Carolina Sea Grant Consortium in providing graduate assistant support.

REFERENCES:

[1] SAA, Minimum Design Loads on Structures (1989),Australian Standard AS 1170.2, StandardsAssociation of Australian.[2] ASCE, Minimum Design Loads for Buildings and Other Structures (1995), ASCE7-95, ASCE.[3] ASCE, Minimum Design Loads for Buildings and Other Structures (2002), ASCE 7-02, ASCE[4] Holmes, J.D. Wind Loading of Multi-span Buildings First National Structural Engineering Conf.,

Melbourne, Australia, Aug. 26-28 (1987)

[5] Saathoff Patrick J. and Stathopoulos Theodore Wind Loads on Buildings with Saw-tooth Roofs,Journal of Structural Engineering, Vol. 118 No. 2 Feb. 1992 Page 429-446

[6] Simiu Emil, Scanlan Robert H. , Wind Effects on Structures: Fundamentals and Applications toDesign , 1996, John Wiley & Sons, WC, WY.

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