paper: ding et al
Analysis of static wind effects on the membrane canopy roof of a large stadium Synopsis This paper reports the results of wind tunnel tests used to investigate the spatial variation of wind pressure over a large cantilevered roof covered by a membrane. The dominant effect is development of large upwards suction. To prevent wrinkling, the membrane has to be prestressed. The paper reports options for pre-stressing and other methods which add to roof stiffness.
Fig 1. External view of stadium
Prof. J. M. Ding PhD, FIStructE, 1RSE President of the Architectural Design and Research Institute of Tongji University, Shanghai
Introduction Being light and flexible structural systems, membrane-structure canopy roofs over large stadia are particularly sensitive to the effects of wind. Such structures have been constructed extensively worldwide but the roofs remain a major concern if they are constructed in areas that may be subjected to extreme wind conditions (e.g. typhoons). In these areas, wind loading and the corresponding behaviour of the membrane structure dictate overall stability and safety. Studies on the characteristics of wind load on canopy roofs have been investigated by a number of researchers using wind tunnel tests. From these studies, data on wind pressure distributions and wind-induced vibration have been procured for design. Nakamura, et. al. (1992) performed wind tunnel tests on a rigid model of an arch-supported membrane-structure canopy roof. And it is not surprising that the aerodynamic behaviour of the Olympic Stadium canopy in Rome was similarly studied via a series of wind tunnel tests1. Wind tunnel tests have been undertaken to provide loading data for the design of several membrane stadia grandstand roofs in China. However, the characteristics of wind load on such large-scale stadia are generally very complex, and canopies of non-typical form need to be investigated in detail. Effective wind resistant analysis and design can only be undertaken safely if the wind load characteristics are fully understood2. This paper focuses on the Qinhuangdao stadium shown in Fig 1. The stadium is situated near the sea and designed to accommodate 35 000 spectators. The membrane structure canopy roof is saddle-shaped. In plan the canopy (Fig 2) is elliptical with dimensions of 246m × 230m and the roof is symmetrical along its minor axis. The levels of the roof leading edge over the grandstand are 36.4m, 32m and 20.6m on the western, eastern and southern/northern sides respectively. In appearance the roof exhibits a robust dynamic and aesthetically curvilinear form. Wind tunnel tests3 of the model structure were performed in the boundary-layer wind tunnel of the State Key Laboratory for Disaster Reduction in Civil Engineering at Tongji University (2002). The test model is rigid model, both the under structure and roof canopy are simulated in the test, and pressures on both upper and lower roof surfaces were recorded simultaneously. Considering the periphery surrounding, A terrain roughness is simulated in the test, due to the turbulence flow being simulated, Reynold’s number is not significant in this test. Based on data from these wind tunnel tests, the distribution characteristics of mean wind pressure and root-mean-square (rms) wind pressure were then analysed in detail. Thereafter, the static wind effect on a typical membrane canopy segment was studied. This included consideration of the effects of membrane initial prestress, wind-resistant cable, distance between arches and arch height-to-span ratio of the canopy.
Canopy structure The entire canopy is composed of 24 basic tension units, whose support structure is shown in Fig 3. The trailing edges of the units are tensioned with cables. The leading edges are 28|The Structural Engineer – 21 November 2006
Z. J. He PhD
fixed onto the arches of an inner ring truss whilst the side edges are fixed onto the upper chords of adjacent trusses and steel-pipe arches support the inner areas of the tension unit. PVC-coated polyester with a PVDF top coating is applied to the 0.91mm thick membrane, whose elastic modulus is 630N/mm2 and has a Poisson’s ratio of 0.3. The entire canopy is supported by 24 trusses, all of which are fixed onto the top of concrete columns through a series of front struts, suspended cables, back struts and tie-down struts. The longest cantilever measured 40m. To strengthen the canopy roof, the inner ring truss at the tip of the cantilever and the outer ring truss at the cantilever rear were connected Fig 2. Plan of stadium canopy
Structural Engineer with the Architectural Design and Research Institute of Tongji University, Shanghai
Y. Zhou MSc, 1RSE Structural Engineer with the Architectural Design and Research Institute of Tongji University, Shanghai Received: 09/05 Modified: 11/05 Accepted: 12/05 Keywords: Canopies, Roofs, Membranes, Stadia, Qinhuangdao Stadium, China, Wind Pressure, Testing © J. M. Ding, Z. J. He and Y. Zhou
Fig 3. Canopy support structure
paper: ding et al
Fig 4. Mean wind pressure variation with wind direction 4a) Leading edge
4b) Middle part
wind loading on other more conventional structures. A canopy roof has various elevations and a strong flow separation arises at the upper surface when wind attacks the roof front. Thus, a large area is subjected to negative pressure extending from the leading edge back to the trailing edge. Additionally, flow separation is suppressed and positive pressure builds up under the lower surface because the inclined stand structure below accelerates the flow underneath the canopy. Consequently, under the combined pressure effect of the upper and lower surfaces, the resulting effect on the canopy roof is a high suction force upwards. Even the shorter –canopies still exhibit high suction. Just the magnitude is smaller than the longer canopies. As flow speed is decreased, turbulence occurs. This is caused by obstructions at the opposite end of grandstand making flow separation almost impossible. Hence, the maximum wind pressure of 1.45kpa occurs at the leading edge at a wind angle of 45º instead of the normal 90º angle. At the trailing edge, the maximum wind pressure is 1.77kpa, occurring at a wind angle of 270º. Without conducting wind tunnel tests, such high wind pressures would be neither known nor validated.
Distribution characteristic of root-mean-square wind pressure
4c) Trailing edge
For flexible structural systems such as membrane canopies, the dynamic effects of fluctuating wind cannot be ignored in wind-resistant analysis. Fig 5 shows the variation of rms wind pressure coefficients with wind angle for three locations of the largest tension unit at a typical measuring point located at the western end of the grandstand.
Fig 5. (right) RMS wind pressure coefficient variation with wind direction 5a) Leading edge
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 with the Engineering Construction Code of Shanghai4 (2002). The design strength of the membrane was therefore taken as 30.75N/mm2.
5b) Middle part
Distribution characteristic of mean wind pressure The roof at the western end of the grandstand has the largest cantilever and this is also the highest roof point. Its structural performance is therefore critical and is the roof part most affected by wind. Wind tunnel tests validated the magnitude of wind pressure in this locality. Fig 4 shows the variation of mean wind pressures at typical measuring points varying with wind direction angle (see Fig 2) at three locations on the largest tension unit. This unit is at the western end of the grandstand and is symmetrical about its short axis. From Fig 4, it is clear that the characteristic wind load on the canopy roof is quite different from that of the horizontal wind load. Moreover at any wind direction angle, suction is the dominant condition for design. When the frontal canopy roof (wind angle 0º~180º) is subjected to wind, the magnitude of the pressure at the leading edge is much larger than that at either the trailing edge or the middle part. However, when the back of the canopy roof is subjected to wind loading, the magnitude of the wind pressure at the trailing edge is then much larger than that at the leading edge and middle part. On large-cantilevered canopies, the distribution of wind loading is unusual. Furthermore, the nature of the distribution is relatively complex and differs from that of horizontal
5c) Trailing edge
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paper: ding et al
Fig 6. Initial shape and stress of membrane 6a) Initial shape
that many areas of the membrane were predicted to wrinkle, resulting in slackening of the membrane and computation divergence.
Adjustment of initial pre-stress
6b) Major principal stress S1 (N/m2)
6c) Minor principal stress S2 (N/m2) Fig 7. (right) Membrane principal stress distribution 7a) Major principal stress S1 (N/m2)
The magnitude of rms is higher at the measured points on the edge than at other parts on the canopy roof. The variation rule of the rms is similar to that of the mean wind pressure i.e. at an attack angle of 45°~90°, the rms value at the leading edge is 0.2 while the rms at the trailing edge is 0.3 at a wind angle of 270°~315°. The rms value of the middle part is about 0.08. Similarly, the rms value of the trailing edge is larger than the leading edge rms at the most disadvantageous angle of attack. This is due to the obstruction caused by the canopy roof opposite.
7b) Minor principal stress S2 (N/m2)
Wind-resistant analysis of typical membrane canopy Analysis model From the foregoing discussion of wind load characteristics, it can be seen that the highest wind pressure occurs at the roof trailing edge. However, the membrane at this edge has a high wind-resistance resulting from the tension effect added by the edge cable. Consequently, the next most critical part for design is the canopy leading edge. Hence for design, only the membrane canopy between adjacent arches on the leading edge is analysed for the action of static wind pressure. The arch spans are approximately 20.5m whilst their bowed height is 3.5m and the distance apart of adjacent arches is about 8.05m. Initial membrane pre-stressing was 20N/cm (0.22E+7N/m2). An analysis model is shown in Fig 6 and the initial shape was developed using a non-linear form-finding routine. Analysis showed that the pre-stress distribution within the membrane was relatively uniform. That means that we get a doubly curved surface, in which the stress distribution is even, isotropic stress field.
Preliminary analysis of static wind effect Pressures derived from wind tunnel tests were applied to the model and a non-linear analysis performed. Computation divergence occurred when the wind pressure reached 25% of the total pressure and the membrane vertical deformation at termination was 0.232m. Fig 7(a) shows the distribution of membrane principal stress, S1. The major principal stress from 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 parts of the membrane reduces to zero. Consequently this shows 30|The Structural Engineer – 21 November 2006
Fig 8. Load – displacement curve
Fig 9. Load – stress curve
From the initial analysis, a large wrinkled area was predicted and this implied instability under wind suction. To overcome this, membrane pre-stress was increased to 25N/cm as a trial and the non-linear analysis repeated. Figs 8 and 9 are the subsequent results of load-displacement and load-stress responses curves respectively of a joint at the canopy centre. The gradient of the load-displacement curve in Fig 8 shows an initial increase followed by a decrease indicating that the membrane stiffness varies with wind pressure magnitude. In Fig 9, the minor principal stress (S2) decreases initially with increasing load and then increases with increasing load after reaching a minimum value of 0.79 N/mm2. Although the prestress was increased by only by 5 N/cm (0.55 N/mm2), it was sufficient to prevent the minor principal stress (S2) from reducing to zero. Thus, membrane stability is ensured and membrane wrinkling does not occur. Further, the load-S1 curve is similar to the load-displace-
paper: ding et al
Fig 10. Membrane deformation
Fig 11. Stiffening of membrane using wind-resistant cable
Fig 12. Displacement– distance of adjacent arches curve
Influence of arch separation distance and bowed height/span ratio The arch separation distance and the bowed height/span ratio are decisive factors influencing the wind-resistant performance of a membrane canopy when the pre-stressing condition and arch span are kept constant. Figs 12 and 13 are the results of a study on the variation of the maximum displacement and the maximum major principal stresses (S1max) with arch separation distance and with bowed height/span ratio. From these figures, it can be seen that the maximum displacement and S1max decrease significantly with increasing bowed height/span ratio when the arch distance remains constant. This implies that increasing bowed height/span ratio should enhance membrane stiffness. The maximum displacement and S1max will also increase significantly with increasing arch distance when the ratio is less than 0.20. Similarly, the membrane stiffness could be increased. Further, the maximum displacement and S1max are insensitive to the variation of the arch distance when this ratio is more than 0.225, which in turn implies that variations of the arch distance have little or no influence on membrane stiffness. As the bowed height/span ratio is in practice not large, the arch distance becomes the decisive factor influencing windresistant performance of any arch-supported membrane structure.
Conclusion
Fig 13. S1max– distance of adjacent arches curve
ment curve and this indicates that the variation of S1 has a significant influence on canopy stiffness. Due to the form of membrane canopy, the resultant of S1 acts vertically downward. So, the major principal stress S1 has a dominant effect on membrane stiffness. Deformation of the model membrane is shown in Fig 10. Compared with Fig 6(a), we can find that the shape of the membrane has developed a quantitative change from its original anticlastic form to the synclastic form shown here. But the fluctuating maximum displacement of the centre node is unacceptably high at 0.731m and this could result in fatigue failure of the fittings.
Wind tunnel tests and non-linear finite element analyses were used to investigate the characteristics of wind load and static wind effects on a membrane structure canopy roof of a large-scale stadium and of a typical membrane canopy respectively. Negative wind pressure (suction) is the dominant load for the design of membranes for large-cantilevered canopy structure roofs with membranes. The studies showed that at the same location of the canopy, the variation rules of mean wind pressure and root-mean-square wind pressure coefficient are similar at different angles of wind attack. Wind pressures on the leading edge are much larger than on other parts of the structure when the front of canopy roof is subjected to wind. At the same time, wind pressures at the trailing edge are much larger than on other parts when the back of the canopy roof is subjected to wind. Detailed analysis indicates that the membrane canopy at the leading edge is very sensitive to wind loading. Increasing initial pre-stress is ineffective for increasing overall stiffness but could be effective in preventing wrinkling. Installing a wind-resistant cable is a better alternative to improving the canopy wind-resistant performance overall. Membrane stiffness increases with increasing bowed height/span ratio when the arch span and initial pre-stress are kept constant. Membrane stiffness increases with increasing arch distance provided this ratio is less than 0.20, and the variation of arch distance has little influence on membrane stiffness when the same ratio is greater than 0.225.
REFERENCES
Wind-resistant cable as stiffener for membrane Membrane structure canopy roofs can be stiffened either by increasing their pre-stressing force or by installing a windresistant cable as shown in Fig 11. Detailed analysis indicates that increasing the pre-stressing force is an ineffective stiffening method and one that will result in construction difficulty and in the major principle stress, S1, exceeding membrane ultimate tensile strength. An alternative is to install a wind-resistant cable (bold line shown in Fig 11) parallel to the arches and detailed studies for this solution indicated that the arrangement significantly decreased both displacement and major principal stresses.
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Nakamura, O., Tamura, Y., Miyashita, K. and Itch, M.: ‘A case study of wind pressure and wind-induced vibration of a large span open-type roof’, J. Wind Engineering and Industrial Aerodynamics, 1992, 52, 237-248 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 Industrial Aerodynamics, 1994, 41-44, 1435-1446 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 Engineering Construction Code of Shanghai, (DGJ08-97-2002) Specification of Membrane Structures, China 21 November 2006 – The Structural Engineer|31
