Scientia Iranica, Vol. 15, No. 5, pp 507{515c Sharif University of Technology, October 2008

Impact of Table Size on the Performanceof Thermo-Plastic Roo�ng Systems

Under Wind Uplift Pressures

S.M. Zahrai1

Roo�ng systems have always been vulnerable to strong wind uplift pressures. Wind forces havedynamic e�ects on structures, as they change in time and space. Therefore, a dynamic means ofevaluating roo�ng systems is necessary in order to identify the component of the system havingthe least resistance to wind uplift forces. Although researchers worldwide have conducted testson roo�ng structures, they have all used various table sizes, as there is still no standard chambersize for experimental purposes. This paper aims to study the impact of table size on roo�ngsystem performance. To achieve this objective, extensive analytical work has been conductedto investigate the performance of roo�ng systems subjected to wind pressure. Analytical resultscompared well with those obtained from experimental work, validating the numerical modeling.This paper presents some of these result comparisons. It was found that an increase in tablewidth beyond a certain level, about 3 m for cases considered here, did not signi�cantly changethe results, while the rate of fastener load change might be high for a smaller table width. Thisspeci�c limit depends on the roo�ng system con�guration. Furthermore, a larger membranewidth (fastener row spacing) would increase the width of the ideal table. Ideal table sizes werealso suggested for various con�gurations having a TPO (Thermo-Plastic Ole�ns) membrane andcorrection factors were eventually developed for di�erent table sizes.

INTRODUCTION-PROBLEMIDENTIFICATION

Wind e�ects must be taken into account when design-ing roo�ng systems, since, as in all structures, they arevulnerable to strong wind uplift pressures and severedamage [1]. The wind resistance rating of roo�ngsystems is based on standardized test methods. InNorth America, existing test methods include FactoryMutual (FM 4470 and 4471) [2] and UnderwritersLaboratories (UL 580 and 1897). In both cases, themanufacturer assembles the roo�ng system, togetherwith its respective components in a test chamber asshown in Figure 1. To evaluate the wind upliftresistance, air pressure is applied until the structuralfailure of the system occurs, e.g. membrane tearingand/or fastener pull out.

1. Center of Excellence in Infrastructural Engineering andManagement, School of Civil Engineering, Tehran Uni-versity, Tehran, Iran. E-mail: mzahrai@ut.ac.ir

Figure 1. E�ect of table size on the roo�ng systemresponse.

For experimental purposes, roo�ng system speci-mens are generally placed in a testing apparatus whosesize is normally far less than the size of the realroof. Although the system con�guration (e.g. fastenerspacing and membrane width) is the same as that ofthe real structure and the specimen is subjected tothe same amount of suction pressure, the fastener loadand membrane de ection might be di�erent from realvalues. This is mainly because the testing rig edges

508 S.M. Zahrai

would clamp the membrane and, therefore, resist someof the applied pressure, particularly so for narrowertables. If the testing table is wide enough, the resultswould be realistic and reliable. Nevertheless, how wideis adequate and how much does the answer to this ques-tion depend upon the roo�ng system con�guration?

Current test methods consider di�erent table sizesfor the performance evaluation of roo�ng structures.For instance, FM tests use a table size of 5 ft by 9 ft(1524 by 2743 mm) or 12 ft by 24 ft (3658 by 7315mm), depending on the roo�ng system. A chambersize of 10 ft by 10 ft (3048 by 3048 mm) is usedby the UL standard. Figure 2 shows a number ofexisting chambers being used worldwide. Researche�orts in recent decades by a North American roo�ngconsortium, the Special Interest Group for DynamicEvaluation of Roo�ng Systems (SIGDERS) establishedat the National Research Council of Canada, haveled to the development of a facility, which makesit possible to evaluate roof systems dynamically [3].A table size of 2000 by 6000 mm is used by theSIGDERS test protocol. The table size and its impacton the roo�ng system performance are questionable inorder to achieve identical results by di�erent testingmethods. As a matter of fact, there is a need for testingstandards and special guidelines to specify a uniquetable size and/or to recommend correction factors whenchambers with other sizes have to be used.

Careful examination reveals that table size playsan important role in evaluating roo�ng systems andshould be selected properly to obtain realistic winduplift resistance. For example, the use of smaller tableswould increase the edge e�ects on the results, par-ticularly for roo�ng systems having larger membranewidths, i.e. spacing between fastener rows. On theother hand, using larger or wider tables would makethe system response slower. Despite the signi�canceof table dimensions to the author's knowledge, therestill exist no clear criteria and/or speci�c standard tosuggest an ideal table size. A number of parameterscan in uence the required table size, in particularFastener Spacing (Fs), Fastener Row spacing (Fr)and membrane Elasticity (E), that would be closelyrelated to fastener forces and membrane de ections.Zahrai and Baskaran developed an analytical model toinvestigate the wind resistance performance of Modi�edBituminous (Mod-Bit) roo�ng systems [4,5]. Afterbeing veri�ed through experimental studies, the ana-lytical model was used to investigate the e�ect of tablesize on the roo�ng system performance. It was foundthat an increase in the table width beyond a certainlevel (depending on the system con�guration) did notsigni�cantly change the system response. Systemswith greater fastener spacing generally increased therequired table width.

In this paper, the testing facility, the SIGDERS

dynamic load cycle and the Factory Mutual (FM),another evaluation method which is a static wind uplifttest used commonly in North America, are brie ydescribed. Using these tools and techniques, this paperstudies the responses of roo�ng systems under upliftpressure conditions. The experimental results weresubsequently used for comparison with those obtainedby extensive analytical work, in order to validatethe numerical modeling. In this way, the improvedanalytical model could be used to study the impactof table size on performance. The objectives of thepresent study in chronological order are:

� To develop a numerical model simulating experi-mental results,

� To investigate the e�ect of table size on roo�ngsystem responses,

� To identify an ideal table size for which no changesare introduced into the system response,

� To develop correction factors for tables smaller thanthe ideal one.

APPLIED LOAD PROCEDURE

Factory Mutual Standard

The standard test currently in most common use inNorth America is the FM static test (FM 1986). Inthis static test, a pressure of 1436 Pa (30 psf) is appliedfrom the bottom of the test specimen and held forone minute. The pressure is increased by 718 Pa (15psf) each minute until the test specimen fails [2]. Atest assembly that successfully sustains a pressure of4309 Pa (90 psf), for example is given a windstormclassi�cation of I-90.

SIGDERS Load Cycle

The SIGDERS load cycle was developed based on ex-tensive wind tunnel studies of full-scale roo�ng systemsmeasuring 3048 mm by 3048 mm (10 ft by 10 ft). Thesestudies were carried out in the NRC's 9000 mm by9000 mm (30 ft by 30 ft) wind tunnel. The load cycleconsists of eight load sequences with di�erent pressureranges. The eight load sequences can be dividedinto two groups: Group 1 represents wind-inducedsuction over a roof assembly and Group 2 representsthe e�ects on a building of exterior wind uctuations,combined with constant interior pressure [6]. Internalpressure variations have been explicitly codi�ed inthe recent North American Wind Standards by ASCE1997, NBCC 1995 [7,8]. Details of the method by whichthe load cycle was developed can be found elsewhere [9].

The above test methods can be conducted in theDynamic Roo�ng Facility (DRF) established at theInstitute for Research in Construction at the National

Impact of Table Size on Roo�ng System Performance 509

Figure 2. Tested table sizes for evaluation of roo�ng system performance.

Research Council of Canada (IRC/NRC). The DRFconsists of a bottom frame of adjustable height uponwhich roof specimens are installed and a movabletop chamber (see [3] for more details). The DRFoperation is controlled by a HP mainframe computerusing feedback signals. The computer regulates thefan speed, in order to maintain the required pressurelevel in the chamber. Operation of the ap valvesimulates the gusts. Closing the ap valve allows

pressure existence in the chamber and opening thevalve bleeds the pressure.

EVALUATION OF TPO SYSTEM

System Details

TPO roof assemblies with various con�gurations wereevaluated under the two di�erent testing methods

510 S.M. Zahrai

Figure 3. (a) Roo�ng system layout for thermoplastic membranes; (b) Longitudinal section of TPO roo�ng system; (left)seam detail, (right) edge detail; (c) The enhanced �nite element model; (d) Seam details considered in the proposednumerical model.

(FM and SIGDERS). Similar system layout and in-strumentation locations were used for the specimens.To monitor the response of the roof system, typicaldesign parameters of pressure, force and de ection weremeasured (Figure 3a). Load cells and optical de ectionsensors, respectively, measured the tensile forces in thefasteners and in the uplift movement of the membranecenter point. As shown in Figures 3a and b, thetested roo�ng system consisted of all three main roo�ngcomponents: A 0.76 mm (22-Ga) thick steel deck witha pro�le height of 38 mm (1.5 in) and a ute width of150 mm (5.9 in), 100 mm by 1500 mm by 3000 mm (4 inthick by 4 ft by 8 ft) polyisocyanurate (ISO) insulationboards, mechanically attached to the steel deck, andmembrane.

MembraneThe present study focuses on the behavior of thoseroo�ng systems in which thermoplastic membranesare used as the waterproof component. Two mainkinds of thermoplastic membrane: PolyVinyl Chloride(PVC) and ThermoPlastic ole�ns (TPO) are used in

single-ply roofs. In this study, 1829 mm (6 ft) widereinforced polyethylene-based TPO membrane sheetsare used. In the early 1990's, TPO was introduced intothe roo�ng market, due to its outstanding ecologicalpro�le with regard to environmental aspects [10]. Acomplete overview of PVC and TPO roo�ng membraneperformance has been documented by Rossiter andParoli [11] and Beer [12], respectively.

The details of a typical seam are shown in Fig-ure 3b, where the seam has an overlap of 127 mm (5 in),with the fastener placed 38 mm (1.5 in) from the edgeof the under sheet and 89 mm (3.5 in) from the edge ofthe overlapping sheet. The portion of the seam beyondthe fastener row was welded with hot air, such that awaterproof top surface was obtained. The width of thewelded portion varied between 38 and 45 mm (1.5 and1.75 in).

Figure 3b also shows a typical detail at the edge ofthe DRF frame. Gaskets were placed above and belowthe membrane, between the membrane and the frame,to ensure the air-tightness of the chamber. Piecesof wood, 76 mm (3 in) in diameter, were �xed to

Impact of Table Size on Roo�ng System Performance 511

Figure 4. Typical de ected shape of the proposednumerical model.

the membrane outside the chamber, to prevent themembrane from slipping during the test. The fourseams shown in Figure 4 indicate the fastener locations.For the tested system, membrane sheets were fastenedat 152, 305 and 457 mm (6, 12 and 18 in for di�erentcon�gurations) intervals along the seam. Fastenerswere 127 mm (5 in) long with a plastic disc of 51 mm(2 in) in diameter.

NUMERICAL MODELING APPROACH

To achieve the objectives of this paper, the presentstudy takes advantage of the numerical modellingapproach. Finite Element (FE) analysis is gener-ally done by dividing the whole assembly model ofconcern into many smaller parts. FE techniquesa�ord large exibility in exploring scenarios whichare too expensive or, in some cases, impossible toset up experimentally. In addition to economicaladvantages, the analytical models are generally fasterfor solving complex problems where there is a need toinvestigate the impact of various in uencing parame-ters.

Roo�ng can be a good application for FE analysis,as some membrane materials have large deformationsthat make some conventional analysis methods inap-propriate. The FE model is also helpful for studyingthe roo�ng performance using larger test tables wherethere is less edge e�ect and the holding fasteners takemore load than the table edges. Keeping the aboveadvantages in mind, a three-step approach is followedin this study: (i) Development of a FE model, astypically shown in Figure 4, (ii) Veri�cation of the FEmodel with experimental data for limited benchmarkcon�gurations and (iii) Investigation of the e�ect oftable size on the roo�ng system performance, using thevalidated FE model.

FE Model

Figure 3c shows the FE model, being 6 m in length and2 m wide (the same as the roo�ng system dimensionsin the experimental program shown in Figure 3a),proposed to simulate the behaviour of roof specimensin the lab. For simplicity, the membrane alone wasconsidered in the numerical modelling, due to its muchgreater exibility compared to those of the insulationand steel deck. In other words, the de ection of thesteel deck was ignored and fasteners were assumed asspring supports for the membrane, in addition to theedge supports.

For each case, a rectangular grid of nodes andelements was used in order to discretize the membrane.Numerical modelling grids, consisting of 4-node shellelements for the membrane (about 1.04 mm thick withan equivalent modulus of elasticity of 300 MPa) andsprings for the fasteners (axial sti�ness of 20 N/mm),were located in the seam areas. The membrane at thefastener locations was modelled to represent the hardplastic fastener discs (3 mm thick with a diameter of50 mm (2 in) and a modulus of elasticity of 500 MPa).

ABAQUS version 5.7 [13] is a commercially avail-able �nite element program with nonlinear analysiscapability, which was used to carry out all the analysesand obtain numerical results. The large strains anddeformations that occur during the loading of themembrane require that a geometry nonlinearity (largedeformation theory) be considered. Small load incre-ments were considered to accommodate the exibilityof the single-ply membranes.

Some of the features of the FE model developmentare brie y explained in the following. The geometrynonlinear behaviour of the membrane was accountedfor by using �ner meshes, particularly around the seamareas and end supports. Larger size elements couldcause the FE equations not to converge. Seam detailswere simply modelled by doubling the thickness ofthe shell element at the seam areas, as schematicallyillustrated in Figure 3d, in order to simulate the splicedregion of the membrane. Di�erent material propertieswere simulated for fastener discs in the seam areasusing shell elements. Fixed bar type elements wereused to simulate fastener attachments with the steeldeck.

VALIDATION OF THE PROPOSED MODEL

A roo�ng system with a single-ply TPO membranewas initially selected to validate the �nite elementmodel. Three Fr/Fs con�gurations (67 in/12 in, 48in/18 in, and 72 in/18 in) or (1700/300, 1220/460 and1830/460 in mm) were considered. A typical de ectedshape for the membrane is shown in Figure 4, wheremembrane ballooning occurs between fastener rows and

512 S.M. Zahrai

table edges. To collect benchmark data, experimentswere carried out for these systems at the DynamicRoo�ng Facility (DRF), using FM and SIGDERS testprotocols described in the previous sections. Thistesting program provided six sets of data to validateand improve the FE model.

RESULTS AND DISCUSSION

The average values of two characteristic parameters,i.e. fastener loads at the center of the seam andde ections at the center of the membrane width,measured from the DRF experiments, were comparedwith the output of the FE analyses. These comparisonsdemonstrated that the FE analytical model is a validtool that can be used to predict the fastener forcesof test specimens at any pressure level. A typicalexample of the fastener load comparison is shown inFigure 5a, for the �rst con�guration (Fr/Fs = 67 in/12in). For this case, an under-estimation of 7% bythe FE model has been noticed. Similar comparisonsfor the 48 in/18 in and 72 in/18 in con�gurations,respectively, revealed 2% and 10% deviations (thistime, over-estimations as presented in Figures 5b and5c) of the analytical model from the measured fastenerloads in the DRF experiments. As illustrated in Fig-ure 6, more di�erence was observed in the membranedeformations, due to some slippage that occurred in thetests, particularly for the roo�ng con�gurations withsmaller membrane width. Therefore, the tensile forcesof the fasteners were usually considered for comparisonpurposes.

DEVELOPMENT OF TABLE SIZECORRECTION FACTORS

As mentioned earlier, each test protocol has its owntable size, giving some related results not necessarilyidentical to those obtained by other testing methods.In this section, the focus is to determine ideal tablesize and develop corresponding correction factors. Itis noteworthy that changing table length does notsigni�cantly a�ect the wind resistance response (seethe membrane ballooning between two rows of fastenersin Figure 1) and here, accordingly, was kept constant(2 m, the same as DRF tests). The above-validatedFE model was used to investigate the e�ect of tablewidth on the system performance. The ideal tablewidth must demonstrate no changes in the roo�ngsystem response. While maintaining the same TPOroo�ng system and the same applied pressure (30psf), the table width was changed by 12 ins (305mm) increments, in order to carry out several sim-ulations for di�erent Fr/Fs con�gurations. A rangeof 31 in to 199 in was considered for the tablewidth.

Figure 5. Model validation; comparison of the FEsimulation results for fastener tensile force withexperimental data: (a) 67 in/12 in, (b) 48 in/18 in and (c)72 in/18 in con�gurations.

Impact of Table Size on Roo�ng System Performance 513

Figure 6. Model validation; comparison of the FEsimulation results for membrane de ection withexperimental data; (a) 67 in/12 in, (b) 48 in/18 in and (c)72 in/18 in con�gurations.

Figure 7. Fastener tensile load versus table width forthree roo�ng system con�gurations.

The impact of table width on the fastener forcesfor the three Fr/Fs con�gurations considered here,is presented in Figure 7, where the rate of fastenerload change is high for a table width less than 3m. In all cases, increasing the table width, madethe fastener forces approach the tributary load (i.e.pressure multiplied by the tributary area) for thatfastener. Also, note that having the same size fastenerspacing, Fs, a larger membrane width (fastener rowspacing, Fr), increases the width of the ideal table. Thefollowing criteria were used to identify the appropriatetable width: \Fastener load is constant or change in thefastener load is within 5% from the one table width tothe next". In other words, if the change in the fastenertensile force is less than 5% while increasing the tablewidth by 12 in, the new table width is ideal and thereis no need to further increase the width. For instance,115 in was obtained as the ideal table width for the67 in/12 in con�guration, with 4% change in fastenerforce (Figure 7).

With this approach, correction factors shouldbe considered for tables smaller than the ideal one.Based on the relationship between fastener load andtable width (Figure 8a), the fastener load should bemultiplied by the correction factor, Cf , for tables witha smaller width. A typical example is also shown inFigure 8a for a 67 in/12 in con�guration. In such a case,while the ideal table width is 115 in (2.92 m), a cor-rection factor of 1.26 should be applied to the fastenerforce if a table width of 78 in (2 m) is used. Note thatthe other parameters, such as the applied pressure andmembrane layout, were kept constant. Figure 8b showsa comparison of the correction factor curves for variouscon�gurations in an attempt to achieve characteristiccurves and generalized guidelines. Complementaryresearch is underway to investigate the issue for other

514 S.M. Zahrai

Figure 8. Developed correction factors for various table sizes for (a) Three considered system con�gurations; (b) Di�erentcases for comparison.

membranes through dynamic analyses.

CONCLUSIONS

An analytical model was developed to simulate thewind resistance response of single-ply roo�ng systemsused frequently in building structures subjected towind loads. Numerical results for various systemcon�gurations compared well with those obtained byexperimental work, based on di�erent test protocols(average values for the results of dynamic testingby SIGDERS method were considered for comparisonpurposes). The analytical model was also used toinvestigate the e�ect of table size on the roo�ngsystem performance. It was found that an increasein table width beyond a certain level (e.g. about3 m for the cases considered in this study) did notsigni�cantly change the results, while the rate offastener load change might be high for a smaller tablewidth. This speci�c limit depends on the roo�ngsystem con�guration. Furthermore, having the samesize of fastener spacing, a larger membrane width(fastener row spacing) increases the width of the idealtable.

Several numerical analyses were carried out toobtain the relationship between fastener force and tablewidth for various con�gurations and developed tablesize correction factors applicable to smaller tables.More research considering other membranes and dy-namic analyses has been in progress at IRC/NRC, inorder to establish guidelines for table size correctionfactors to be applied to the results given by di�erenttest protocols. It is ideal for roo�ng designers to

have software capable of performing complete systemdesigns.

ACKNOWLEDGMENT

The SIGDERS consortium, consisting of manufactur-ers, building owners and associations, has supportedthe presented research. Their support and commitmentare greatly appreciated.

REFERENCES

1. Smith, T.L. \Improving wind performance of me-chanically attached single-ply membrane roof systems:Lessons from hurricane Andrew", Proceedings of theIX Congress, International Waterproo�ng Association,Amsterdam, pp 321-348 (1995).

2. Factory Mutual Research \Approval standard: ClassI roof covers (4470)", Norwood, Massachusetts, USA(1986).

3. Baskaran, A. and Lei, W. \A new facility for dynamicwind performance evaluation of roo�ng systems", Pro-ceedings of the Fourth International Symposium onRoo�ng Technology, NRCA/NIST, Washington, D.C.,USA, pp 168-179 (1997).

4. Zahrai, S.M. and Baskaran, B.A. \Numerical evalu-ation for the e�ect of table size on roof wind upliftresistance. Part 1: Thermoplastic roo�ng systems", In-ternal Report No. IRC-IR-709, Institute for Researchin Construction, National Research Council, Canada,pp 32 (1999).

5. Zahrai, S.M. and Baskaran, A. \Table size e�ect onevaluation of roo�ng Mod-Bit systems", 5th Interna-

Impact of Table Size on Roo�ng System Performance 515

tional Conference on Building Envelope, pp 319-324(NRCC-45006), June 2001, Ottawa, Canada (2001).

6. Zarghamee, M.S. \Wind e�ects on single-ply roo�ngsystems", Journal of Structural Engineering, 116(1),pp 177-187 (1990).

7. ASCE, \Minimum design loads for buildings and otherstructures", ASCE Standard 7-95, American Society ofCivil Engineers, Reston, Va., p 13 (1997).

8. NBCC \National building code of Canada", NationalResearch Council of Canada, Ottawa, Canada, p 145(1995).

9. Baskaran, A. and Chen, Y. \Wind Load cycle develop-ment for evaluating mechanically attached single plyroofs", Journal of Wind Engineering and IndustrialAerodynamics, 77-78, Sept.-Dec., pp 83-96 (1998).

10. Beer, H.R. \Flexible polyole�n roo�ng membranes:Properties and ecological assessment", Proceedingsof Waterproo�ng Technology & Environment, IWACongress, pp 81-89 (1995).

11. Rossiter, W.J. Jr. and Paroli, R.M. \Performance ofpolyvinyl chloride roo�ng: An overview", Proceedingsof the Sustainable Low-Slope Roo�ng Workshop, OakRidge National Laboratory, pp 15-29 (1996).

12. Beer, H.R. \Longevity and ecology of polyole�n roofmembranes", Proceedings of the Fourth InternationalSymposium on Roo�ng Technology, pp 14-21 (1997).

13. ABAQUS User's Manual, Hibbitt, Karlsson &Sorensen, Inc., Pawtucket, RI (1997).