1-s2.0-S0167610505000863-main

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Journal of Wind Engineering

and Industrial Aerodynamics 93 (2005) 843–855

0167-6105/$ -

doi:10.1016/j

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Wind effects of parapets on low buildings:Part 2. Structural loads

Gregory A. Kopp�, Christian Mans, David Surry

Alan G. Davenport Wind Engineering Group, Boundary Layer Wind Tunnel Laboratory,

University of Western Ontario, London, Ont., Canada N6A 5B9

Received 14 May 2004; received in revised form 23 August 2005; accepted 26 August 2005

Available online 10 October 2005

Abstract

The present paper, Part 2 in a four part series, focuses on the effects of solid, perimetric parapets

on the wind-induced structural loads on low-rise buildings. Roof and wall pressures were measured

at more than 500 locations simultaneously for five parapet heights (h ¼ 0, 0.46, 0.9, 1.8 and 2.7m in

equivalent full-scale dimensions) and three building heights (H ¼ 4:6, 9.1 and 18.3m) with plan

dimensions 31.1 by 61.6m and a 12on 12 gable roof slope. The data were obtained in simulated open

country and suburban terrain conditions, at a scale of 1:100, in a boundary layer wind tunnel. It was

observed that the distance from the eaves edge to the reattachment point for winds normal to the wall

increases from x=H�0:4 for h=ðH þ hÞ ¼ 0 to x=H ¼ 1:8 for h=ðH þ hÞ ¼ 0:23. While mean and

fluctuating point pressure distributions tend to decrease in magnitude with h, the increased areas of

separated flow lead to increased loads for interior frames with the taller parapets.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Wind loads; Low-rise buildings; Building codes; Parapets

1. Introduction

While the influence of parapets on local pressure coefficients has been the topic ofnumerous experimental studies, the effect of parapets on structural loads has remainedlargely unexamined. This is likely due to the comments made by Leutheusser [1] 40 yearsago, when he stated that (also quoted in [2]) the ‘‘pertinent design information listed in

see front matter r 2005 Elsevier Ltd. All rights reserved.

.jweia.2005.08.005

nding author. Tel.: +1519 661 3338; fax: +1 519 661 3339.

dress: [email protected] (G.A. Kopp).

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ARTICLE IN PRESSG.A. Kopp et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 843–855844

building codes for flat-roofed structures without parapets applies unchanged also to thesebuildings when equipped with parapets.’’ Baskaran and Stathopoulos [2,3], examining onlythe most basic of structural loads, made a similar conclusion, finding that parapets causeno significant change in the overall lift and drag forces on low buildings. In contrast, weshowed in Part 1 [4] of this work, that parapets do have a significant effect of theaerodynamics of low buildings, at least over the smaller areas associated with componentand cladding loads. Given this result, it is worthwhile to re-visit the effects of parapets onstructural loads. Thus, the objective of the present paper is to examine the effects ofparapets on the structural loads for low buildings.This paper is the second part in a four part series on the wind effects of parapets on low

buildings: the reader is referred to Part 1 [4] for details on the basic aerodynamic effects ofparapets on the point pressure distributions and area-averaged loads relevant tocomponents and cladding design; to Part 3 [5] for details on the parapet loads and toPart 4 [6] for load mitigation strategies using parapets. Every effort has been made toensure that the present paper is reasonably self-contained, but without unnecessaryduplication of information. Many more details on this project can be found in [7–10].

2. Experimental details

Wind loads on low buildings depend on the many factors pertaining to buildinggeometry and the upstream boundary layer characteristics. In [4], we discuss our choicesfor the model scales used in the project. For the present part, a scale model of 1:100 waschosen. For the boundary layer simulation, we matched our previous wind tunnel set-up ofthe terrain used for the National Institute of Standards and Technology (NIST)aerodynamic database for low buildings [11,12]. The open country terrain is characterizedby a roughness length, zo, of 0.03m in open country and 0.3m for suburban terrainroughness, similar to Part 1. Only the open country terrain results are presented herein.The experiments matched the ESDU 82026 mean profiles [13], ESDU 83045 turbulenceintensities [14], and ESDU 740031 velocity spectra [15] for the specified target terrainroughness lengths. A detailed discussion of the flow simulation for the present part can befound in Ho et al. [11] and is not repeated here.An exploded plan view of the 1:100 model is shown in Fig. 1, which has equivalent full-

scale plan dimensions of 31.1m by 61.6m (102 ft by 202 ft) and a 12on 12 gable roof slope.

The nearly flat roof slope is representative of the majority of commercial and industrial lowbuildings used in practice and was chosen for this reason. The model was constructed foran earlier study, and has been modified for the present purposes. Pressure time series wererecorded at more than 500 locations over the surface of the model, concentrated over onehalf of the building. The model was designed to slide through the floor of the wind tunnel,allowing three eaves heights to be examined, namely, H ¼ 4:6, 9.1 and 18.3m (15, 30 and60 ft). These are indicated by the dashed lines in Fig. 1. For the 4.6m building, the pressuretaps below the dashed lines do not represent taps on the building itself as these were belowthe tunnel floor. Note that throughout the paper, equivalent full-scale dimensions willused, assuming the length scale of 1:100.Acrylic parapet members, with a nominal thickness of 0.30m (1.0 ft), were added around

the perimeter of the model. The thickness of the parapet was chosen to be as thin aspossible, yet rigid. The parapets had the same 1

2on 12 gable shape as the building. Five

parapet heights were considered, namely, h ¼ 0, 0.46, 0.9, 1.8 and 2.7m (0, 1.5, 3.0, 6.0 and

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WIND

31.1m

7.6m

18.3m

9.1m

4.6m

61.6 m

Fra

me

1

Fra

me

2

Fra

me

3

Fra

me

4Bay 1 Bay2

L=

W=

B=

Y

X

α

Fig. 1. Pressure tap layout and definition of wind direction.

G.A. Kopp et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 843–855 845

9.0 ft). The parapet heights were chosen to bound the range of possible values for thesebuilding heights. (A 2.7m parapet on a 4.6m building would not be common, but it maybe on an 18.3m building where h=ðH þ hÞ ¼ 0:13.) Note also that only uniform perimetricparapets were examined; no isolated (single wall) parapets were studied in this part.

Pressure measurements were made using the parameters listed in Table 1; further detailscan be found in [4]. In addition, the maximum blockage was less than 2%, while theReynolds number based on roof height varied between 4.2� 104 and 1.7� 105. Full-scaleReynolds numbers would be larger by the length scale multiplied by the velocity scale, sothe present experiments are more than two orders of magnitude low. Pressures weresampled for the 17 wind directions listed in Table 1 (and defined in Fig. 1).

3. Definitions of the structural loads

Seven structural responses were calculated on an assumed main wind force resistingsystem for each model configuration using the time series obtained from wind tunneltesting. These responses were selected to envelope the major structural actions important

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Table 1

Details pertaining to measurement configurations and data acquisition

Plan dimensions, W�L 31.1m� 61.6m (102 ft� 202 ft)

Eaves height, H 4.6, 9.1, 18.3m (15, 30, 60 ft)

Roof slope 1/2 on 12 gable roof

Parapet heights 0, 0.46, 0.9, 1.83, 2.74m (0, 1.5, 3, 6, 9 ft)

Upstream terrain roughness, zo 0.03 & 0.3m (0.10 & 1.0 ft)

Wind angles (degrees) 0, 15, 30, 35, 40, 45, 50, 55, 60, 75, 90, 120, 135, 150, 180, 200, 225

Number of taps 518

Sampling frequency 400Hz

Low pass filter cut-off frequency 200Hz

Sampling time 120 s

Reference wind tunnel speed 13.7m/s (45 fps)

Model scale 1:100

G.A. Kopp et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 843–855846

to designing a building with frames of uniform spacing. All loads were calculated assuminga typical frame spacing of 7.6m (25 ft), consistent with values used in earlier analyses [e.g.,12,17]. The frame locations with respect to the pressure tap layout are shown in Fig. 1.Two area-averaged loads were calculated: bay uplift and horizontal thrust. These areglobal load actions, and do not depend on any assumed structural system. Frame upliftwas also calculated. Four bending moments covering two major types of structural systemswere calculated on each of the frames: the moments at the ridge and at the knees of a framepinned at the base, and the moments at the knees of a frame pinned at the base and at theridge. Only the bay uplift and the ridge bending moment for a two-pinned frame will bediscussed herein in order to illustrate the major effects of parapets. The reader is referred to[7] for further results and numerous additional plots.The response coefficients were determined by integrating the pressure time series

obtained at each tap location weighted by the ratio of the tributary area of the tap to thetotal area being considered. For example, bay uplift coefficients are obtained by

CuðtÞ ¼

PwibiCpiðtÞ

BW=2, (1)

where Cpi, wi and bi are the pressure coefficient, tributary width and tributary breadthassociated with tap i, W is the building width, and B is the bay width. In this case, we useW/2 since only half of the bay (i.e., from eaves edge to ridge) is considered.All of the moment response coefficients are determined by

CMðtÞ ¼

PwibiILiIMiCpiðtÞ

W 2B, (2)

where IMi is the moment influence coefficient relating the local frame load (from thepressure at tap i) to the moment in question and ILi is a linearly varying influencecoefficient to account for load sharing between frames. These influence coefficients wereobtained in the same manner as earlier analyses [12,17]. The influence coefficients vary foreach particular moment and for each structural system assumed. To calculate the momentinfluence coefficients on the two-pinned frames, the stiffness of the frame girders relative tothe stiffness of the columns was assumed to be unity. In order to keep this stiffness ratioconstant, the moment of inertia of the column cross-section was varied. The ratio of the

ARTICLE IN PRESSG.A. Kopp et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 843–855 847

girder moment of inertia to that of the column (i.e., Ig/Ic) was taken as the ratio of thebuilding width to the eaves height. Further details can be found in [7].

As in the other parts, the peak pressure and area-averaged load coefficients presented inthe study are not the absolute worst coefficients recorded within the sample time, but areLieblein-fitted statistical peaks. This involves dividing the recorded time series into tenequal segments and performing the Lieblein BLUE formulation [18] with the peak valuestaken from each of 10 segments. The resulting mode and dispersion of the type I extremevalue distributions were used to determine the mean 1

2h (full scale) peak value for each

pressure and load coefficient reported herein. These are believed to be more statisticallystable quantities than the actual recorded peaks.

4. Aerodynamic effects of parapets on structural loads

4.1. Bay uplift

It was shown in Part 1 [4] that parapets have a significant effect on the local(components and cladding) loads on the roofs of low buildings. This type of loading isprimarily caused by the suctions induced by the corner vortices that occur for corneringwind directions. The strength of the corner vortices were shown to be strengthened by lowparapets, while the extent of these vortices on the surface was expanded. For highparapets, fairly uniform pressures were observed. For many structural loads, the importantdirections are for wind normal to one of the walls. Here, we examine the aerodynamiceffects of parapets for this wind direction.

Fig. 2 shows the mean and root-mean-square (rms1; i.e., standard deviation) pressurecoefficients along the line of taps at midspan for a wind direction normal to the roof (901).The reattachment point is often determined from surface pressure data as the location justbeyond the peak value of the mean suction, where the rms values are maximum. One cansee that for the case with no parapet, h ¼ 0, this occurs around x=H�0:4 and increasesdramatically with increasing h so that for h=ðH þ hÞ ¼ 0:091, x=H�0:8, h=ðH þ hÞ ¼ 0:17,x=H�1:1 and h=ðH þ hÞ ¼ 0:23, x=H�1:8. This trend was also clearly observed in flowvisualizations (not shown here). The increase is not one-to-one in h or h+H so that, again,the extent of the edge vortices is significantly expanded for larger h as were the cornervortices. For a building with H ¼ 9:1m the distance from the edge to the reattachmentpoint increases from roughly 4m for h ¼ 0 to 16m for h ¼ 2:7m. This latter distancecorresponds roughly to the ridge, which could have significant implications for roofs withsteeper slopes, but also has implications for winds parallel to the ridge where reattachmentwould be beyond the second bay, rather than the middle of the first bay.

Also observed in Fig. 2 is that peak values of both the mean and rms pressurecoefficients decrease near the edge with increased h, with the distributions becoming moreuniform for the higher parapets. Larger values in these pressure coefficients are observed atdistances further from the edge, as compared to the no parapet case. One final observationis that Cp0 increases just upstream of the leeward parapet, accounting for the upward trendat x=H�3 (see also Fig. 5).

1We will use the abbreviation rms for the standard deviation of the fluctuations (i.e., with the mean removed)

throughout this work.

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-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.20.0 1.0 2.0 3.0 4.0

x/H

Cp

H=4.6m, h=0mH=9.1m, h=0H=18m, h=0H=9.1m, h=0.46mH=9.1m, h=0.91mH=9.1m, h=1.8mH=9.1m, h=2.7m

H=4.6m, h=0mH=9.1m, h=0H=18m, h=0H=9.1m, h=0.46mH=9.1m, h=0.91mH=9.1m, h=1.8mH=9.1m, h=2.7m

0.0

0.1

0.2

0.3

0.4

0.0 1.0 2.0 3.0 4.0x /H

Cp'

(a)

(b)

Fig. 2. Distributions of the (a) mean, Cp, and (b) rms, Cp0, pressure coefficients along the building midplane, L/2,

for a wind normal to the ridge (901) in the open country exposure.


The question to be answered from these observations is whether the expanding area ofsuction beneath these edge vortices increases more rapidly than the corresponding decreasein the strength of the peak point suctions. This can be examined with the bay uplift (thebays are defined in Fig. 1). Fig. 3 depicts the peak bay uplift for bays 1 and 2 vs. windangle. In these figures, the uplift coefficients (negative values are upwards, consistent withthe definition of pressures) are normalized by

Cu;Bay1 ¼ jMINðCuÞj, (3)

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-1.25

-1

-0.75

-0.5

-0.25

00 30 60 90 120 150 180

wind angle (°)

Cu,

min

/Cu,

Bay

1

h/(H+h)= 0

h/(H+h)=0. 048

h/(H+h)=0. 091

h/(H+h)= 0.17

h/(H+h)= 0.23

-1.25

-1

-0.75

-0.5

-0.25

00 30 60 90 120 150 180

wind angle (°)

Cu,

min

/Cu,

Bay

2

h/(H+h)= 0

h/(H+h)=0.048

h/(H+h)=0.091

h/(H+h)=0.017

h/(H+h)= 0.23

(a)

(b)

Fig. 3. Uplift minima for (a) bay 1 and (b) bay 2 vs. wind angle in the open country terrain for an eaves height of

H ¼ 9:1m.

G.A. Kopp et al. / J. Wind Eng. Ind. Aerodyn. 93 (2005) 843–855 849

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-0.5

-0.25

0

0.25

0.5

0.750 30 60 90 120 150 180

wind angle (°)

Cu,

max

/Cu,

Bay

1

h/(H+h)= 0

h/(H+h)=0. 048

h/(H+h)=0. 091

h/(H+h)= 0.17

h/(H+h)= 0.23

Fig. 4. Uplift maxima for bay 1 vs. wind angle in the open country terrain for an eaves height of H ¼ 9:1m.


where MIN(Cu) is evaluated for a particular bay (i.e., for Bay 1, in this case) over all windangles for h ¼ 0. To maintain signs, the absolute value is taken in (3). This normalizationallows an easy comparison of the relative effects of the parapets particularly for oppositesigned loads, such as the maxima in Fig. 4. Interested readers are referred to St. Pierreet al. [12] for a comparison of bay uplift (panel) loads, for similar building sizes, tothose in current building codes and past experiments. It should also be noted thatCu;Bay2 ¼ 0:79Cu;Bay1.It is clear from Fig. 3 that for the 2.7m parapet on the 9.1m high building

(h=ðH þ hÞ ¼ 0:23), the peak loads are increased by about 25% for both bays. Also, sincethere are few points in either plot where the magnitude is below that of the no parapet case,one can conclude that the expanding ‘‘footprint’’ of the edge vortices dominates thediminished magnitude of the suctions. This is consistent with our observations for the localloads in Part 1. Again, it is important to note that the increased loading is dependent on h.For h=ðH þ hÞ ¼ 0:048, there is virtually no increase; by h=ðH þ hÞ ¼ 0:091, the increase inthe worst coefficients are 14% and 9% for bays 1 and 2, respectively.There are some other interesting observations, as well. For bay 2, the influence of the

separated flow for a wind angle of 01 leads to dramatic increases in the uplift, though 901remains the most important wind angle for this bay. For bay 1, the important wind anglechanges from 01 to cornering wind directions (30–401), presumably because of thediminishing size of the quiescent zone between the two corner vortices (see Fig. 6 in Part 1).The other significant effect caused by parapets is the occurrence of downward acting

loads on the roof in front of a leeward parapet. Significant downward loading can occurover large areas, as illustrated in Fig. 4. Downward acting bay loads with a magnitude of


over 50% of the peak uplift for the building with no parapet are observed for all bays. Thisload increases significantly with parapet height.

As mentioned in Part 1, the pressure distributions in the separated flow zones shouldscale with H and be similar for constant values of h/(H+h). Fig. 5 shows that this isapproximately the case for h=ðH þ hÞ ¼ 0:091. The collapse is not perfect, perhaps due tothe influence of varying wind conditions at the different eaves heights (from H ¼ 4:6 to18.3m) but could also be due to effects of the plan dimensions and parapet thickness notbeing geometrically similar with respect to H. What this means in practice is that the

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.20.0 1.0 2.0 3.0 4.0

x/H

Cp

H=4. 6m

H=9. 1m

H=18m

0.0

0.1

0.2

0.3

0.0 1.0 2.0 3.0 4.0x/H

Cp'

H=4.6m

H=9.1m

H=18m

(a)

(b)

Fig. 5. Distributions of the (a) mean and (b) rms pressure coefficients, for constant h=ðH þ hÞ ¼ 0:091, along the

building midplane for a wind normal to the ridge (901) in the open country exposure.


aerodynamic loads should be normalized by (H+h), as should the parapet heights.(The exceptions to this are for the downward acting loads due to the large positivepressures that occur on the roof near the windward side of a leeward parapet and thewall pressures, as shown in Part 3 [5]. In the former case, the load coefficients are wellscaled by h. This is because the flow is reattached on the roof and the pressures around theleeward parapet behave like those for a wall on the ground. In other words, H is lessrelevant in this case.)

4.2. Ridge bending moment

Fig. 6 depicts minima and maxima of the ridge bending moment for a two-pinned framefor frames 1 and 2. These values are normalized by the minimum value of CM for the sameframe, but with h ¼ 0, considering all wind angles, just as was done for the bay uplift.Thus, for frame 1, the normalizing value is

CM;Frame1 ¼ jMINðCMÞj. (4)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

00 30 60 90 120 150 180

wind angle (°)

CM

,min

/CM

,Fra

me1

h/(H+h)=0h/(H+h)=0.048h/(H+h)=0.091h/(H+h)=0.17h/(H=h)=0.23


-1.2

-1

-0.8

-0.6

-0.4

-0.2

00 30 60 90 120 150 180

wind angle (°)

CM

,min

/CM

,Fra

me2

-0.4

-0.2

0

0.2

0.4

0.6

0.80 30 60 90 120 150 180

wind angle (°)

CM

,max

/CM

,Fra

me2

(a) (b)

(c)


Fig. 6. (a) Minimum ridge bending moment for frame 1 and (b) minimum and (c) maximum ridge bending

moments for frame 2 on the building with H ¼ 9:1m vs. wind angle in the open country exposure.


To maintain signs, the absolute value is taken in (4). Note that the frame 2 minimumis only 65% of that for frame 1, i.e., CM;Frame2 ¼ 0:65CM;Frame1. Interestingly, the effectsof parapets on frame 1 are quite different compared to those for frame 2; for frame 1the parapets are seen to reduce the value of the worst moment, while for frame 2the worst moments are increased. This is typical of many of the structural loads, whichdepend on the details of the pressure distribution (including frame uplift). The increasinglength to the reattachment point alters the distributions of the loading, as shown above.For the ridge bending moment, the increase is not severe, only about 10% for h=ðH þ hÞ ¼

0:17 and 5% for h=ðH þ hÞ ¼ 0:091; however, for other responses, the effects can begreater [7].

Parapets have a second significant effect on the ridge bending moment, shown in Fig.6(c) (and on other moments not shown here), that is, on the positive moments. When thereis no parapet in place the largest maxima is relatively small, less than 20% of themagnitude of CM,Frame2. However, the significant downward loading induced by theleeward parapets for normal winds acts to increase CM,max to significant magnitudes, inthis case, for example, to 50% of CM,min for h=ðH þ hÞ ¼ 0:17. Therefore, these downwardacting pressures affect not only the vertical loading, as indicated in [4], but also thestructural moments. Many current wind load standards do not account for this type ofloading, which is clearly exacerbated by the presence of parapets.

4.3. Discussion

In [12], St. Pierre et al. compared the existing wind load provisions for large, gable-roofed buildings with recent and historical experimental data [11,17], similar to thoseobtained here, but for h ¼ 0. They made several observations but found that, in general,the different standards significantly underestimated the loads on the end frames. Bettermatches were found for interior frames, primarily because the wind tunnel loads drop inmagnitude while the code loads remain nearly constant. Parapets tend to increase theloading proportionally more for interior frames, compared to end frames, due to theincreased distance from the eaves edge to the reattachment point. So, two approaches toaltering the wind load provisions could be made to account for the effects of parapets. Onthe one hand, one could increase the pressure coefficients, e.g., GCp, to account for theunderestimation on the end frames. This would bring an increase for the interior frameswhich would effectively envelope the effects of parapets (as shown in [7]) while beingconservative for h ¼ 0. On the other hand, one could develop a set of coefficients, whichwould depend on h/(H+h). For h/(H+h) in the range up to 0.17, the effects on structuralloads responding to suctions on the roof are minimal and could possibly be neglected.However, the downward acting pressures, which have affects on every frame for windsapproximately normal to the walls, should be considered.

5. Conclusions

The results of a systematic study on the effects of parapets on structural loads for lowbuildings indicate that parapets are not benign, as earlier concluded by Leutheusser [1].The distance from the flow separation at the eaves edge to the first reattachment point onthe roof for normal winds increases significantly with h/(H+h), being roughly 0.4H forh=ðH þ hÞ ¼ 0 and increases to 1.8H for h=ðH þ hÞ ¼ 0:23. This leads to an increased load


of about 10% on interior frames for h=ðH þ hÞp0:09, with a greater increase for higherparapets. Bay uplift is increased on end bays by similar amounts, while structural loadssuch as bending moments or frame uplift are not affected significantly. Downward actingloads near leeward parapets have a significant effect on moments, leading to considerablemagnitudes of opposite sign compared to the normal roof suctions; the ASCE 7 does notcurrently account for such loading.

Acknowledgements

This work was made possible through the financial support of the Metal BuildingManufacturers Association and the American Iron and Steel Institute. The on-goinginterest of Dr. Lee Shoemaker is greatly appreciated. The authors wish to thank Dr. EricHo for many useful conversations and his help with the data handling. G.A. Koppgratefully acknowledges the support of the Canada Research Chairs Program.

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[18] J. Lieblein, Efficient methods of extreme value methodology, National Bureau of Standards Report No.

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