28|The Structural Engineer 21 November 2006

paper: ding et al

SynopsisThis paper reports the results of wind tunnel tests used toinvestigate the spatial variation of wind pressure over alarge cantilevered roof covered by a membrane. Thedominant effect is development of large upwards suction.To prevent wrinkling, the membrane has to be pre-stressed. The paper reports options for pre-stressing andother methods which add to roof stiffness.

IntroductionBeing light and flexible structural systems, membrane-struc-ture canopy roofs over large stadia are particularly sensitiveto the effects of wind. Such structures have been constructedextensively worldwide but the roofs remain a major concernif they are constructed in areas that may be subjected toextreme wind conditions (e.g. typhoons). In these areas, windloading and the corresponding behaviour of the membranestructure dictate overall stability and safety.

Studies on the characteristics of wind load on canopy roofshave been investigated by a number of researchers usingwind tunnel tests. From these studies, data on wind pressuredistributions and wind-induced vibration have been procuredfor design. Nakamura, et. al. (1992) performed wind tunneltests on a rigid model of an arch-supported membrane-struc-ture canopy roof. And it is not surprising that the aerody-namic behaviour of the Olympic Stadium canopy in Romewas similarly studied via a series of wind tunnel tests1. Windtunnel tests have been undertaken to provide loading data forthe design of several membrane stadia grandstand roofs inChina. However, the characteristics of wind load on suchlarge-scale stadia are generally very complex, and canopiesof non-typical form need to be investigated in detail. Effectivewind resistant analysis and design can only be undertakensafely if the wind load characteristics are fully understood2.

This paper focuses on the Qinhuangdao stadium shown inFig 1. The stadium is situated near the sea and designed toaccommodate 35 000 spectators. The membrane structurecanopy roof is saddle-shaped. In plan the canopy (Fig 2) iselliptical with dimensions of 246m 230m and the roof issymmetrical along its minor axis. The levels of the roofleading edge over the grandstand are 36.4m, 32m and 20.6mon the western, eastern and southern/northern sides respec-tively. In appearance the roof exhibits a robust dynamic andaesthetically curvilinear form.

Wind tunnel tests3 of the model structure were performedin the boundary-layer wind tunnel of the State KeyLaboratory for Disaster Reduction in Civil Engineering atTongji University (2002). The test model is rigid model, boththe under structure and roof canopy are simulated in the test,and pressures on both upper and lower roof surfaces wererecorded simultaneously. Considering the peripherysurrounding, A terrain roughness is simulated in the test, dueto the turbulence flow being simulated, Reynolds number isnot significant in this test. Based on data from these windtunnel tests, the distribution characteristics of mean windpressure and root-mean-square (rms) wind pressure werethen analysed in detail. Thereafter, the static wind effect ona typical membrane canopy segment was studied. Thisincluded consideration of the effects of membrane initial pre-stress, wind-resistant cable, distance between arches andarch height-to-span ratio of the canopy.

Canopy structureThe entire canopy is composed of 24 basic tension units,whose support structure is shown in Fig 3. The trailing edgesof the units are tensioned with cables. The leading edges are

fixed onto the arches of an inner ring truss whilst the sideedges are fixed onto the upper chords of adjacent trusses andsteel-pipe arches support the inner areas of the tension unit.PVC-coated polyester with a PVDF top coating is applied tothe 0.91mm thick membrane, whose elastic modulus is630N/mm2 and has a Poissons ratio of 0.3. The entire canopyis supported by 24 trusses, all of which are fixed onto the topof concrete columns through a series of front struts,suspended cables, back struts and tie-down struts. Thelongest cantilever measured 40m. To strengthen the canopyroof, the inner ring truss at the tip of the cantilever and theouter ring truss at the cantilever rear were connected

Analysis of static wind effects on themembrane canopy roof of a large stadium

Prof. J. M.DingPhD, FIStructE,1RSE President of theArchitectural Designand Research Instituteof Tongji University,Shanghai

Z. J. HePhDStructural Engineerwith the ArchitecturalDesign and ResearchInstitute of TongjiUniversity, Shanghai

Y. ZhouMSc, 1RSEStructural Engineerwith the ArchitecturalDesign and ResearchInstitute of TongjiUniversity, Shanghai

Received: 09/05Modified: 11/05Accepted: 12/05Keywords: Canopies,Roofs, Membranes,Stadia, QinhuangdaoStadium, China, WindPressure, Testing

J. M. Ding, Z. J. Heand Y. Zhou

Fig 1.External view of stadium

Fig 2.Plan of stadium canopy

Fig 3.Canopy supportstructure

21 November 2006 The Structural Engineer|29

paper: ding et al

together to form a huge canopy roof with spatial rigidity.The membrane material had a characteristic limiting

tensile strength of 123N/mm2. Under short-term design loads,a safety factor of 4 was used for its design in accordance withthe Engineering Construction Code of Shanghai4 (2002). Thedesign strength of the membrane was therefore taken as30.75N/mm2.

Distribution characteristic of mean wind pressureThe roof at the western end of the grandstand has the largestcantilever and this is also the highest roof point. Its struc-tural performance is therefore critical and is the roof partmost affected by wind. Wind tunnel tests validated themagnitude of wind pressure in this locality. Fig 4 shows thevariation of mean wind pressures at typical measuring pointsvarying with wind direction angle (see Fig 2) at three loca-tions on the largest tension unit. This unit is at the westernend of the grandstand and is symmetrical about its shortaxis.

From Fig 4, it is clear that the characteristic wind load onthe canopy roof is quite different from that of the horizontalwind load. Moreover at any wind direction angle, suction isthe dominant condition for design. When the frontal canopyroof (wind angle 0~180) is subjected to wind, the magnitudeof the pressure at the leading edge is much larger than thatat either the trailing edge or the middle part. However, whenthe back of the canopy roof is subjected to wind loading, themagnitude of the wind pressure at the trailing edge is thenmuch larger than that at the leading edge and middle part.

On large-cantilevered canopies, the distribution of windloading is unusual. Furthermore, the nature of the distribu-tion is relatively complex and differs from that of horizontal

wind loading on other more conventional structures. A canopyroof has various elevations and a strong flow separationarises at the upper surface when wind attacks the roof front.Thus, a large area is subjected to negative pressure extend-ing from the leading edge back to the trailing edge.Additionally, flow separation is suppressed and positive pres-sure builds up under the lower surface because the inclinedstand structure below accelerates the flow underneath thecanopy. Consequently, under the combined pressure effect ofthe upper and lower surfaces, the resulting effect on thecanopy roof is a high suction force upwards. Even the shortercanopies still exhibit high suction. Just the magnitude issmaller than the longer canopies.

As flow speed is decreased, turbulence occurs. This iscaused by obstructions at the opposite end of grandstandmaking flow separation almost impossible. Hence, themaximum wind pressure of 1.45kpa occurs at the leadingedge at a wind angle of 45 instead of the normal 90 angle.At the trailing edge, the maximum wind pressure is 1.77kpa,occurring at a wind angle of 270. Without conducting windtunnel tests, such high wind pressures would be neitherknown nor validated.

Distribution characteristic of root-mean-squarewind pressureFor flexible structural systems such as membrane canopies,the dynamic effects of fluctuating wind cannot be ignored inwind-resistant analysis. Fig 5 shows the variation of rmswind pressure coefficients with wind angle for three loca-tions of the largest tension unit at a typical measuring pointlocated at the western end of the grandstand.

Fig 4.Mean wind pressurevariation with winddirection4a) Leading edge

4b) Middle part

5b) Middle part

4c) Trailing edge

5c) Trailing edge

Fig 5. (right)RMS wind pressurecoefficient variationwith wind direction5a) Leading edge

30|The Structural Engineer 21 November 2006

paper: ding et al

The magnitude of rms is higher at the measured points onthe edge than at other parts on the canopy roof. The varia-tion rule of the rms is similar to that of the mean wind pres-sure i.e. at an attack angle of 45~90, the rms value at theleading edge is 0.2 while the rms at the trailing edge is 0.3at a wind angle of 270~315. The rms value of the middlepart is about 0.08. Similarly, the rms value of the trailing edgeis larger than the leading edge rms at the most disadvanta-geous angle of attack. This is due to the obstruction causedby the canopy roof opposite.

Wind-resistant analysis of typical membrane canopyAnalysis modelFrom the foregoing discussion of wind load characteristics, itcan be seen that the highest wind pressure occurs at the rooftrailing edge. However, the membrane at this edge has a highwind-resistance resulting from the tension effect added bythe edge cable. Consequently, the next most critical part fordesign is the canopy leading edge. Hence for design, only themembrane canopy between adjacent arches on the leadingedge is analysed for the action of static wind pressure. Thearch spans are approximately 20.5m whilst their bowedheight is 3.5m and the distance apart of adjacent arches isabout 8.05m. Initial membrane pre-stressing was 20N/cm(0.22E+7N/m2). An analysis model is shown in Fig 6 and theinitial shape was developed using a non-linear form-findingroutine. Analysis showed that the pre-stress distributionwithin the membrane was relatively uniform. That meansthat we get a doubly curved surface, in which the stressdistribution is even, isotropic stress field.

Preliminary analysis of static wind effectPressures derived from wind tunnel tests were applied to themodel and a non-linear analysis performed. Computationdivergence occurred when the wind pressure reached 25% ofthe total pressure and the membrane vertical deformation attermination was 0.232m. Fig 7(a) shows the distribution ofmembrane principal stress, S1. The major principal stressfrom Fig 7(b) is larger than the initial pre-stress(2.2E+6N/m2), with the maximum value being 0.832E+7N/m2

(8.32N/mm2) while the minor principal stress at most partsof the membrane reduces to zero. Consequently this shows

that many areas of the membrane were predicted to wrinkle,resulting in slackening of the membrane and computationdivergence.

Adjustment of initial pre-stressFrom the initial analysis, a large wrinkled area was predictedand this implied instability under wind suction. To overcomethis, membrane pre-stress was increased to 25N/cm as a trialand the non-linear analysis repeated. Figs 8 and 9 are thesubsequent results of load-displacement and load-stressresponses curves respectively of a joint at the canopy centre.

The gradient of the load-displacement curve in Fig 8 showsan initial increase followed by a decrease indicating that themembrane stiffness varies with wind pressure magnitude. InFig 9, the minor principal stress (S2) decreases initially withincreasing load and then increases with increasing load afterreaching a minimum value of 0.79 N/mm2. Although the pre-stress was increased by only by 5 N/cm (0.55 N/mm2), it wassufficient to prevent the minor principal stress (S2) fromreducing to zero. Thus, membrane stability is ensured andmembrane wrinkling does not occur.

Further, the load-S1 curve is similar to the load-displace-

Fig 6.Initial shape andstress of membrane6a) Initial shape

6b) Major principalstress S1 (N/m2)

6c) Minor principalstress S2 (N/m2)

7b) Minor principalstress S2 (N/m2)

Fig 8.Load displacementcurve

Fig 9.Load stress curve

Fig 7. (right)Membrane principalstress distribution7a) Major principalstress S1 (N/m2)

21 November 2006 The Structural Engineer|31

paper: ding et al

ment curve and this indicates that the variation of S1 has asignificant influence on canopy stiffness. Due to the form ofmembrane canopy, the resultant of S1 acts vertically down-ward. So, the major principal stress S1 has a dominant effecton membrane stiffness.

Deformation of the model membrane is shown in Fig 10.Compared with Fig 6(a), we can find that the shape of themembrane has developed a quantitative change from its orig-inal anticlastic form to the synclastic form shown here. Butthe fluctuating maximum displacement of the centre node isunacceptably high at 0.731m and this could result in fatiguefailure of the fittings.

Wind-resistant cable as stiffener for membrane Membrane structure canopy roofs can be stiffened either byincreasing their pre-stressing force or by installing a wind-resistant cable as shown in Fig 11. Detailed analysis indi-cates that increasing the pre-stressing force is an ineffectivestiffening method and one that will result in constructiondifficulty and in the major principle stress, S1, exceedingmembrane ultimate tensile strength. An alternative is toinstall a wind-resistant cable (bold line shown in Fig 11)parallel to the arches and detailed studies for this solutionindicated that the arrangement significantly decreased bothdisplacement and major principal stresses.

Influence of arch separation distance and bowedheight/span ratioThe arch separation distance and the bowed height/spanratio are decisive factors influencing the wind-resistantperformance of a membrane canopy when the pre-stressingcondition and arch span are kept constant. Figs 12 and 13 arethe results of a study on the variation of the maximumdisplacement and the maximum major principal stresses(S1max) with arch separation distance and with bowedheight/span ratio.

From these figures, it can be seen that the maximumdisplacement and S1max decrease significantly with increas-ing bowed height/span ratio when the arch distance remainsconstant. This implies that increasing bowed height/spanratio should enhance membrane stiffness. The maximumdisplacement and S1max will also increase significantly withincreasing arch distance when the ratio is less than 0.20.Similarly, the membrane stiffness could be increased.Further, the maximum displacement and S1max are insensi-tive to the variation of the arch distance when this ratio ismore than 0.225, which in turn implies that variations of thearch distance have little or no influence on membrane stiff-ness.

As the bowed height/span ratio is in practice not large, thearch distance becomes the decisive factor influencing wind-resistant performance of any arch-supported membranestructure.

ConclusionWind tunnel tests and non-linear finite element analyseswere used to investigate the characteristics of wind load andstatic wind effects on a membrane structure canopy roof of alarge-scale stadium and of a typical membrane canopyrespectively.

Negative wind pressure (suction) is the dominant load forthe design of membranes for large-cantilevered canopy struc-ture roofs with membranes. The studies showed that at thesame location of the canopy, the variation rules of mean windpressure and root-mean-square wind pressure coefficient aresimilar at different angles of wind attack. Wind pressures onthe leading edge are much larger than on other parts of thestructure when the front of canopy roof is subjected to wind.At the same time, wind pressures at the trailing edge aremuch larger than on other parts when the back of the canopyroof is subjected to wind.

Detailed analysis indicates that the membrane canopy atthe leading edge is very sensitive to wind loading.Increasing initial pre-stress is ineffective for increasingoverall stiffness but could be effective in preventing wrin-kling. Installing a wind-resistant cable is a better alterna-tive to improving the canopy wind-resistant performanceoverall.

Membrane stiffness increases with increasing bowedheight/span ratio when the arch span and initial pre-stressare kept constant. Membrane stiffness increases withincreasing arch distance provided this ratio is less than 0.20,and the variation of arch distance has little influence onmembrane stiffness when the same ratio is greater than0.225.

1. Nakamura, O., Tamura, Y., Miyashita, K. and Itch, M.: A case study of wind pressureand wind-induced vibration of a large span open-type roof, J. Wind Engineering andIndustrial Aerodynamics, 1992, 52, 237-248

2. Borri, C., Majowiecki, M. and Spinelli, P.: Wind response of a large tensile structure:The new roof of the Olympic Stadium in Rome, J. Wind Engineering and IndustrialAerodynamics, 1994, 41-44, 1435-1446

3. State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University,(2002) Wind tunnel test study of the wind load distribution of Qinhuangdao Stadium,China

4. Engineering Construction Code of Shanghai, (DGJ08-97-2002) Specification ofMembrane Structures, China

REFERENCES

Fig 10.Membranedeformation

Fig 11.Stiffening ofmembrane usingwind-resistant cable

Fig 12.Displacementdistance of adjacentarches curve

Fig 13.S1max distance ofadjacent archescurve