External Pressure Coefficients on Saw-tooth and Mono-sloped Roofs

Transcription

1 External Pressure Coefficients on Saw-tooth and Mono-sloped Roofs Authors: Bo Cui, Ph.D. Candidate, Clemson University, 109 Lowry Hall, Clemson, SC , David O. Prevatt, Assistant Professor, Clemson University, 314 Lowry Hall, Clemson, SC , Phone: , 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 Clemson University. 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 7-0 specification on these buildings. By using larger models and a higher density of pressure tap 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 areaaveraged wind pressure coefficients on models with varying spans and building heights. Local peak pressures and area-averaged pressures obtained in this study are compared with the design values specified in ASCE 7-0 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. Comparing results with ASCE 7-0 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 guidelines in the Australian Standard [AS 1170., 1989] and in the ASCE 7 since 1995 [ASCE ]. The current version of [ASCE 7-0] provides the specific values for saw-tooth, multi-span gable and mono-sloped roofs shown in Table 1 below. From the table it is apparent 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 location on a mono-sloped roof would be designed for an external pressure coefficient of.9.

2 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..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 from wind 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 < θ < 30 (degrees) Area 10ft Area = 100ft Area 500ft Roof Zone Shape Saw-tooth (Span A) Saw-tooth (Span BCD) Mono-slope Gable (7 θ > 7) Multi-Gable TABLE 1 EXTERNAL PRESSURE COEFFICIENTS FOR GABLE, MONO-SLOPED AND SAW-TOOTH ROOFS (ASCE 7-0) [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 1:00 scaled, 5-span saw-tooth model with a roof slope of 0 degrees. The peak local pressure and area-averaged (3m +/-) wind pressure 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, and 4-span saw-tooth roof buildings, [Saathoff and Stathopoulos, 199] investigated peak local and area-averaged pressure coefficients, using 1:400 scale models with roof slopes of 15 degrees. These researchers concluded that 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., respectively, (normalized to the mean wind velocity at the lower eave height). In addition, they found that the peak local wind pressure coefficient at the low corner of the saw-tooth roof significantly exceeded the values observed on the mono-sloped model (i.e vs. -4.7). While these previous research results provided valuable wind load design information for 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 wind tunnel 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

3 on wind pressure distributions. Table compares the experimental setups of two previous tests with the current study at the Wind Load Test Facility (WLTF). Saathoff and Holmes Stathopoulos (199) (1987) Model Scale 1:400 1:00 1:100 Prototype building dimension Model dimensions 64 ft 00 ft 48 ft tall 1.91in 6in.03in 40 ft 18 ft 40 ft tall.36in 7.68in.34in Present Study Clemson (006) 6 ft 98 ft 53 ft tall 38 ft tall 3 ft tall 3.1in 11.76in 6.36in 4.56in.76in Roof Slope (degrees) No. pressure taps 66 taps 60 taps 90 taps Minimum tributary area per tap 53.8 ft 34.4 ft 4.34ft Number of span of tested model 1, and 4 span 5 span 1,, 3, 4, & 5 span Exposure category Open country Open country Open country o in 10 o deg for 53ft Wind directions (degrees) 0 o, o in 15 o increments & 180 o 0-60 o in 5 o increments 1-span & 5-span, 9070 o in 10 o incr. other tests Turbulence at low eave/mean roof height TABLE COMPARISON OF CLEMSON UNIVERSITY WLTF S WIND TUNNEL TEST SETUP WITH PRIOR TESTS 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 openflow wind tunnel with a 48-feet long test section, and a cross-section measuring 10 ft. by 7 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 1.5 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 90 pressure taps installed in the roof as shown in Figure. This instrumented model was interchanged with the other models of different spans to measure the pressure distributions on the entire saw-tooth building. Pressure data from the wind tunnel was collected using eight Scanivalve ZOC33 electronic pressure scanning modules connected to a RAD300 digital remote A/D converter interfacing the pressure scanners with a PC. The pressure taps were attached to the pressure scanners by 1-in. long vinyl tubes having a 63 in. internal diameter Restrictors 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 10-second sample

4 time. Based on the velocity scale of 1:4 and the 1:100 length scale ratio of the windtunnel the sample corresponds to a full-scale record of approximately 15 minutes. 100 UTest/Uref 90 z0=36m FIGURE 1 WIND VELOCITY AND TURBULENCE INTENSITY PROFILE (REFERENCE HEIGHT = 10 m AT FULL SCALE) α Wind 5 = 130 INSTRUMENTED SPAN HC Turbulence Intensity ASCE SE LC HE IN LE HC SE LC Span A Span B Span C Span D Span E HC- high corner LC- low corner HE- high edge LE - low edge SE - slope edge IN - interior FIGURE MODEL USED IN STUDY AND TAP LOCATIONS

5 To normalize the pressures, a Pitot tube, located 1 in. below the wind tunnel ceiling, was used as a reference for dynamic wind pressure. The test pressure coefficients were determined 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: 1 PASCE = ρ V3s, hgc p (1) 1 P Test = ρ VPitotC p, test () Assuming P ASCE = P Test then 1 ρv PitotC p, test VPitotC p, test ( GC p ) eq = = 1 ρv V3s, h 3s, h (3) where was calculated by the Equation 4 provided by [Simiu and Scanlan, 1996] V 3s, h V 3 s, h β = Vh (1 + c(3s) ) (4) h.5ln( ) z P denotes wind pressure, ρ denotes air density, 0 V 3 s, h 3s gust wind speed at mean roof height, V Pitot the mean wind speed at the Pitot tube height in the wind tunnel, GC p 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 C, p test height in the wind tunnel, V h mean wind speed at mean roof height, z 0 roughness length, h mean roof height, ( GC p ) eq equivalent GCp which is converted by test C p. Area-averaged wind pressure coefficients are necessary for the design of cladding and components with larger tributary areas. While previous studies pneumatically averaged pressures 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 Ai C p( area, j) = C p( i, j) (5) n i= 1 Ai i= 1 C denotes instantaneous area averaged wind pressure coefficient, p( area, j) C p ( i, j) instantaneous point wind pressure coefficient at time-step j, n the number of taps in the area and A i 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.

6 STRUCTURES 006 RESULTS AND ANALYSIS Peak Local Negative Wind Pressure Coefficient Distribution For the purpose of comparing extreme (minimum) wind pressure coefficients on a monosloped roof and on varying span number saw-tooth roofs, mono-sloped and, 3, 4 and 5 span saw-tooth roof models with 53 ft mean roof height in full scale were tested in the wind 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 high edges 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 the leeward spans, minimum wind pressure coefficient contours for the different span number models were also very similar. C L Mono-sloped Roof Span A of Saw-tooth Roof -3 FIGURE 3 CRITICAL NEGATIVE 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. o o The critical wind direction varied from 0 to 40 for all buildings.

7 Figure 4 presents the extreme point negative wind pressure coefficients at each zone of the mono-sloped and the -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 -5 span saw-tooth roofs was -4.6 and -4.3 for the mono-sloped roof. In the high edges the peak values were.8 and.74, respectively. The peak negative wind pressure coefficient on the span A was higher than on other spans. The maximum value on the middle spans and leeward spans of the - through 5-span saw-tooth roofs was.9. For these spans the extreme peak negative wind pressure coefficient occurred in the low corners. The maximum value in magnitude was For span A the measured peak negative wind pressure coefficient was for the - to 5- span saw-tooth roofs, a value lower than the peak value in the high corner of span A, but 9% higher than for the mono-sloped roof (-.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 high corner and in the high edge was less than 10%, the maximum and minimum values being and respectively. The variation in other regions on span A was from 14% to 5%. On the leeward span (span E), the peak values in each zone varied from 7% to 1%. The largest variation occurred in the sloped edge zone..0 HC LC SE HE LE IN Mono -A 3-A 4-A 5-A Mono: mono-sloped roof;, 3, 4 and 5: the number of spans for 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;.0.0 HC LC SE HE LE IN 3-B 4-B 4-C 5-B 5-C 5-D HC LC SE HE LE IN -E 3-E 4-E 5-E FIGURE 4 PEAK NEGATIVE WIND PRESSURE COEFFICIENTS ON MONO-SLOPED ROOF AND VARYING SPAN SAW-TOOTH ROOF (53 ft MEAN ROOF HEIGHT) Area-averaged Wind Pressure Coefficients Increasing the tributary areas caused a sharp reduction in the wind pressure coefficients from point pressures through 100 sq. ft. In the corner zones, the tributary area of a -tap combination is approximately equal to 10 sq. ft. As the tributary areas increased from 10

8 sq. ft. to 100 sq. ft., the negative wind pressure coefficients at the high corners decreased between 30% to 50%. The reduction caused by the increase in area from 100 sq. ft to 150 sq. ft was less than 0% 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 the various span of the model, of less than 30% (Figure 5). M A 3A 4A.0 5A M: mono-sloped roof;, 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; 3B 4B 4C 5B.0 5C 5D E 3E 4E 5E.0 FIGURE 5 PEAK NEGATIVE WIND PRESSURE COEFFICIENTS IN HIGH CORNER OF MONO-SLOPED ROOF AND EACH SPAN OF THE - 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 3 ft, 38 ft and 53 ft. 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 For the middle and leeward spans (Spans BCDE) of the saw-tooth roof, the critical point negative wind pressure coefficients were in the range of.4 to 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 the 3 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. The critical 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 3M in Figure 6 denotes mono-sloped building (M), having a mean roof height of 3 ft (3) and so on.)

9 -6.0 3M M 53M 3A A 53A 3BCDE 38BCDE 53BCDE FIGURE 6 AREA-AVERAGED NEGATIVE WIND PRESSURE COEFFICIENTS IN HIGH CORNER OF MONO-SLOPED AND 5- SPAN SAW-TOOTH ROOFS WITH MEAN ROOF HEIGHTS OF 3 ft, 38 ft, AND 53 ft. Comparison of Wind Tunnel Results with ASCE7-0 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 the middle and leeward spans (spans BCDE) were lower than for the windward span values High Corner -6.0 Low Corner Saw-tooth ASCE A Saw-tooth ASCE A.0.0 Mono ASCE Saw-tooth ASCE BCD Saw-tooth ASCE BCD Saw_A Mono Saw-BCDE Saathoff -Mono Saathoff -Saw-A Holmes -Saw-A Saw_A Saw-BCDE Saathoff Holmes Point wind pressure coefficient FIGURE 7 COMPARISONS OF MOST CRITICAL EXPERIMENTAL NEGATIVE WIND PRESSURE COEFFICIENTS AND ASCE VALUES WITH PREVIOUS RESEARCH RESULTS Our single point peak negative pressure coefficient of was, as expected, well above the -4.6 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.

10 The area-averaged negative pressure coefficients that we obtained by numerically integrating 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 sawtooth roofs. The reductions occurred at smaller tributary areas than provided in the current ASCE 7 design pressure coefficient reduction with areas. (Figure 7). The areaaveraged values reported by Saathoff et. al. for mono-sloped and saw-tooth buildings were also nearly identical and, except for the negative pressure coefficient on the sawtooth roof at 150 sq. ft., all values exceeded the ASCE 7 design pressure coefficient for the 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 5 sq. ft. exceeds the ASCE 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 roof buildings should be approximately the same. ASCE7-0 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 the sensitivity 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 at least 30% larger than those measured on the other middle or leeward spans. The ASCE7-0 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 5 sq. ft. The most critical area-averaged negative wind pressure coefficients on saw-tooth roofs 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 Civil Engineering at Clemson University, Florida s 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., Standards Association of Australian. [] ASCE, Minimum Design Loads for Buildings and Other Structures (1995), ASCE7-95, ASCE. [3] ASCE, Minimum Design Loads for Buildings and Other Structures (00), ASCE 7-0, ASCE [4] Holmes, J.D. Wind Loading of Multi-span Buildings First National Structural Engineering Conf., Melbourne, Australia, Aug. 68 (1987) [5] Saathoff Patrick J. and Stathopoulos Theodore Wind Loads on Buildings with Saw-tooth Roofs, Journal of Structural Engineering, Vol. 118 No. Feb. 199 Page [6] Simiu Emil, Scanlan Robert H., Wind Effects on Structures: Fundamentals and Applications to Design, 1996, John Wiley & Sons, WC, WY.