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Thermal behavior of large-span reticulated domes covered by ETFE membrane roofs under solar radiation
Thin-Walled Structures 115 (2017) 1–11
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Full length article
Thermal behavior of large-span reticulated domes covered by ETFE membrane roofs under solar radiation
MARK
⁎
Zhongwei Zhaoc, Hongbo Liua,b,c, , Zhihua Chena,c a b c
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China School of Engineering, Edinburgh of university, Edinburgh EH93FB, UK School of Civil Engineering, Tianjin University, Tianjin 30007, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Large-span reticulated domes Membrane roof Solar radiation Non-uniform thermal load Non-uniform thermal effect Field monitoring
A strong non-uniform temperature was induced by solar radiation for the large-span reticulated domes with ETFE membrane roof, which may induce a significant thermal stress and thermal deformation. In order to obtain the temperature distribution and thermal behavior of large-span reticulated domes with ETFE membrane under solar radiation, a long term field monitoring and numerical analysis were conducted in this paper. Based on the results of both field monitoring and the numerical analysis, the following conclusions were obtained: 1) shelter effects of glass and membrane varies widely. 2) Daily temperature variation can be reduced by a large degree due to introduction of membrane. 3) Average temperature of components is increased by membrane due to ‘greenhouse effect’.4) The seasonal temperature variation has little effect on the components which located at upper part of spatial latticed shell structures, the internal force can be released by deformation. 5) Thermal response of bottom ring beam is reduced by installation temperature and double supports.
1. Introduction With the advantages light weight, fast assembly, spanning capability and ease to form various attractive geometrical appearance, the large-span reticulated domes have been widely used in various buildings, such as sport stadiums and gymnasiums, exhibition centers, airport, factory buildings and so on [1–3]. In order to more beautiful and energy saving, the ETFE membrane or glass materials were widely used as roof for large-span reticulated domes to allow some solar radiation come into indoor, for example of the Eden Project (Fig. 1) in the United Kingdom and Yujiabu Station in China (Fig. 2). For the large-span reticulated domes with ETFE membrane roof, the solar radiation can arrive to the steel member surfaces in both construction and operation. Based on the previous studies [4–9], the temperature of steel members is not only much higher than ambient air temperature but also much non-uniform because of the high solar radiation transmittance of ETFE membrane or glass, which always induce a significant thermal stress and thermal deformation. Therefore, it is important to take into account the thermal effect induced by solar radiation for the large-span steel structures with ETFE membrane or glass roof in the design process. Many researches were carried out in past years to evaluate the stability [10–12], seismic performance [13–15], dynamic performance
⁎
under blast loading [16,17] and dynamic behavior under wind loading [18,19]. Alinia [20–22] has carried out some research on the thermal effect of large-span steel structures under both uniform thermal load and non-uniform thermal load. Liu [4–6] have carried out systematic investigation on the non-uniform thermal effect of large-span steel structures exposed to solar radiation directly through experiment and numerical analysis. However, no research referred to the thermal effect of large-span reticulated domes covered by ETFE membrane or glass roof, which of thermal effect were different that exposed to solar radiation directly. In this paper, the thermal effect of the large-span reticulated domes covered by ETFE membrane or glass roof was studied through a longterm monitoring and numerical analysis. 2. Structural information of Yujiabu Railway Station Yujiabu Railway Station Building is located in Tianjin, China. A conch-shaped single-layer steel lattice structure was designed to cover a large space, which is 142 m in length, 80 m in width, and 24 m in height as shown in Fig. 3. The main members of the whole structure are 72 curved steel box girders that intersect each other, as shown in Fig. 4. The appearance of the structure is similar to a conch. Ten kinds of nodes different from each other were used. Every member’s torsion has
Corresponding author at: State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (H. Liu).
http://dx.doi.org/10.1016/j.tws.2017.01.025 Received 27 June 2016; Received in revised form 15 December 2016; Accepted 18 January 2017 0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
Thin-Walled Structures 115 (2017) 1–11
Z. Zhao et al.
the analysis on the temperature distribution of large span steel structures under solar radiation based ASHRAE model in ANSYS software. 4.1. Boundary condition For any steel members exposed to solar radiation, the heat flow acting on its surface includes convection heat, solar radiation and long wave radiation among ground, sky and steel surface. Therefore, the temperature boundary condition for the steel members exposed to solar radiation is defined as:
λ
∂T ∂n
= h [Ta (t ) − T ] + qS (t ) + qL (t )
(1)
Γ
20
where h is heat convection coefficient (w / m C ); Ta is ambient air temperature; qS is solar radiation (w / m2 ); qL is long wave radiation (w / m2 );λ is thermal conductivity (w / m2 0C ). Fig. 1. The reticulated dome of Eden Project in United Kingdom.
4.2. Solar radiation The ASHRAE clear-sky model was adopted in this study to calculate the solar radiation striking the surface of steel members. In this model, the total global solar radiation is assumed to be the sum of direct radiation, diffuse radiation, and the solar radiation reflected from the surrounding surface.
different angles to keep the configuration smooth. The steel structure was covered by ETFE membrane and glass, as shown in Fig. 5. The bottom ring beam (BRB) is constraint by 36 supports, including 5 single-direct supports and 31 double-direct supports as shown in Fig. 6, and the supports are constrained by concrete corbels. There is a spherical bearing between top and bottom plate and the center of the spherical are set to the same for double supports to ensure that it can rotate in a degree.
⎡ ⎤ GdV qs = ε (GD + Gd + GR ) = ε ⎢max(cos θ , 0) + C + ρg Fwg (sin β + C ) ⎥ ⎣ ⎦ GdH (2)
GND 3. Field monitoring scheme
where ε is the solar absorption coefficient. The solar radiation absorption is affected by its color and smoothness of steel plates. 0.6 was adopted in this study based on the test data. The meaning of other parameters can be found in [4–6].
A temperature and stress monitoring system designed for the steel structure of Yujiabu Railway Station was installed in July 2014. There were 44 temperature sensors and 22 strain gages were installed. 4 temperature sensors and 2 strain gages were installed in each steel member. Arrangement of monitoring members was shown as in Fig. 7. Fig. 8 showed installation positions of monitoring sensor on each component in detail. Four temperature sensors and two stress sensors were installed on middle part of each component. Temperature sensors were installed on each side of the component and stress sensors were installed on top and bottom of the components. The section of component located at skylight is circle and the others are rectangular section. Fig. 9 shows actual structure under solar radiation and monitoring sensors on each component.
4.3. Long wave radiation The long wave radiation on the surface of steel plates can be expressed by Stefan-Boltzmann equation:
ql = εf σ (F
wg
4 (Tg4 − T 4 ) + F (Tsky − T 4 )) ws
(3)
where εf is the ratio of the radiation emitted by a surface; σ is StefanBoltzmann constant=5.67 × 10−8W /(m2⋅K 4 ); Tsky is the effective temperature of sky, usually calculated by Ta − 6 ; Tg is the ground temperature.
4. Numerical analysis
4.4. Comparison of results The finite element model of the structure constitutes of beam
A three-dimensional transient thermal FE model was developed for
Fig. 2. The reticulated dome of Yujiabu Station in China.
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Fig. 3. Overview of Yujiabu Railway Station in different stages.
compared, shown as in Fig. 11. It is clear that the temperature and stress obtained by numerical analysis were generally consistent with the monitoring results. Reasons attributing to the discrepancies might be due to variance in the solar radiation model. As the complexity of the algorithm, the shadow effect among components was not taken into account which is the main cause of difference between temperature
element and Beam 188 in ANSYS was adopted, support at the bottom of the structure was constraint in radial and vertical direction. The temperature field derived by numerical method was shown as in Fig. 10. The temperature-time curves of each monitoring component on 1th August derived by field monitoring and numerical analysis was
Fig. 4. Sections and joints of Yujiabu Railway Station.
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Fig. 7. Distribution of monitoring components. Fig. 5. Location of membrane and glass.
derived by FEM method and field monitoring.
5. Long-term monitoring results of temperature 5.1. Analysis of seasonal temperature change The monitoring was conducted from July 31, 2014 to September 8, 2015. The monitoring results of temperature were shown in Fig. 12. Detailed locations of each component can be found in Fig. 7. The monitoring was started before installation of membrane. As shown in Fig. 12, the monitoring process can be divided into mainly two periods, i.e. before and after installation of membrane. Through the comparison of monitoring results obtained before and after membrane installation, it was concluded that the variation of daily temperature is smaller after installation of membrane due to the membrane preventing some solar radiation into steel member surface. The max temperature before membrane installation is about 55 ℃ and occurred at component 1, 2 and 5, because these components were directly exposed to solar radiation. The maximum temperature of other components was smaller with value of 40 ℃ due to shelter of accessory structure for solar radiation. The max temperature at component 1 is 35 ℃ in summer of 2015 after membrane installation, which was about 20 ℃ lower than it before membrane installation because of shelter effect of membrane.
Fig. 8. Positions of temperature sensors and strain gauges.
The max temperature at component 2 and 5 in summer of 2015 after membrane installation is only 5 ℃ smaller than that before installation of membrane, because the component 2 and 5 is located below glass skylight not membrane. Therefore, it was concluded that shelter effect of glass is much smaller than membrane for solar radiation. Results shown in Fig. 12(b) and (d) indicate that the max value of temperature was decreased by about 5 ℃. But the average value of temperature in summer of 2014 is about 2.5 ℃ higher than that in 2015. This is caused by enclosed space after installation of membrane
Fig. 6. The arrangement of supports.
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Fig. 9. Installation of temperature sensor and stress sensor.
monitored were above 0 ℃. But the average daily air temperature in Tianjin in winter is about −8 ℃ as shown in Fig. 13. Considering no air conditioner installed in the building, it was concluded that heat insulation effect of the membrane is pretty good. The max temperature of steel structure under membrane is about 45 ℃, which is 15 ℃ lower than that of steel structure directly exposed to solar radiation and also 15 ℃ higher than ambient air temperature.
and glass, the energy cannot be released immediately. The max temperature value at component 3 in summer of 2014 is almost the same as that in summer of 2015, because Component 3 was in shade of other components was lightly affected by solar radiation. But even so, the average temperature in summer of 2014 is also about 2.5 ℃ higher than that in 2015. Component 11 is different from other monitoring components as it shown in Fig. 12(f), and its daily temperature variation is very small. The reason for that was Component 11 was located at bottom ring beam of the structure, which was covered by concrete wall and is lightly affected by solar radiation or weather condition. In addition, Different from other components, the average temperature at component 11 in summer of 2014 is lower than that in 2015. It was clearly seen from Fig. 12 that all of the temperature
5.2. Influence of membrane on daily temperature change The influence of membrane on daily temperature change was studied in this section. The symbol T1~T4 indicate the temperature monitored during August 1, 2014 to August 4, 2014 and T1′~T4′ indicate the temperature monitored during August 1, 2015 to August 4,
Fig. 10. Contour of temperature field under solar radiation at 12 o′clock.
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60 6
Max(FEM) Min(FEM) T1 T2 T4
55 50
4 2 Stress (MPa)
45
S1 S2 S1(FEM) S2(FEM)
40 35 30
0 -2 -4
25
-6
20
-8
15 2
4
6
8
10
12
14
16
18
20
22
0
24
2
4
Clock hour
a) The temperature–time curve for co
6
8
10 12 14 Clock hour
16
18
20
22
24
b) The stress–time curve for compone
mponent 5
nt 6 Fig. 11. Comparison of results.
shown mentioned above cannot support pull force. The bottom ring beam can contract freely without internal force occurred.
2015. It was concluded from Fig. 14 that the min monitoring temperature after membrane installation is generally higher than that before membrane installation. On the contrary, the max temperature is reduced due to membrane installation. That is to say, the daily temperature change is reduced by membrane. It can also be observed from the results that the increasing velocity of temperature under membrane lag behind that without membrane.
6.2. Influence of membrane on daily stress variation To investigate the influence of membrane on structural daily stress variation in detail, the monitoring results during August 1, 2014 to August 4, 2014 and August 1, 2015 to August 4, 2015 were shown in Fig. 16. S1′ and S2′ indicate the results monitored after membrane installation. S1 and S2 indicate the results monitored before membrane installation. It can be clearly seen in Fig. 16 that the daily variation of stress will be reduced in a large degree due to the existence of membrane. The max daily variation of stress without membrane is about 14 MPa and it is reduced to 7 MPa after the membrane was installed. It can also be concluded from results shown in Fig. 16d), e) and f) that the stress of bottom and upper surface of these components change in a parallel manner. This indicate the variation of daily temperature mainly cause change of axial force. Bending moment of the other components will change with variation of temperature.
6. Long-term monitoring results of thermal stress 6.1. Analysis of stress during monitoring process Monitoring results of component stress are shown as in Fig. 15. The monitoring period was divided into seven sub phase. Duration of each sub phase was shown at the end of Fig. 15. I and II indicate the period before installation of membrane. It was concluded that the change tendency of the stress is similar to the temperature. The stress will decrease with temperature. The change magnitude of stress is within 20 MPa during one year, which indicates that the influence of seasonal temperature change on the monitored components is small. This is not in consistent with traditional opinion. In fact, the latticed shell can deform freely when the temperature load was applied because of high ratio of rise-to-span. Even so, the influence of thermal load is remarkable on the components near support. It can be seen from results shown in Fig. 15 that stress of the upper and bottom surface of components will deviate from each other as the temperature changes. This indicates bending moment will occur when the latticed shell deforms with temperature difference. Change of component stress is a complex mechanism as the structure is an integrity influence by temperature load. At the same time, the component stress is also closely related to installation sequence and installation temperature. Generally speaking, change magnitude of stress in summer of 2015 is smaller than that in summer of 2014. This is caused by the existence of membrane. Results shown in Fig. 15b) indicate that S2 is smaller than S1 in winter. But S2 will exceed S1 in summer. Bending moment direction in this component will reverse as temperature changes. It can be seen from Fig. 15e) that the stress variation of the bottom ring beam is also within 20 MPa. This is caused by the installation temperature of bottom ring beam. The bottom ring beam was installed in summer of 2013. So the installation temperature was high. Bottom ring beam will contract in winter. At the same time, the double support
6.3. Comparison of stress in summer and winter In this section, monitoring results during January 15, 2015 to January 20, 2015 and July 15, 2015 to July 20, 2015were compared to investigate influence of seasonal temperature difference on structural thermal behavior. Only part of the results were listed due to limited space, as shown in Fig. 17. It can be concluded from the results that value of S1 and S2 is almost equal in summer. This indicates that the components mainly suffer axial force in summer. The difference between S1 and S2 increases in winter which indicates the bending moment increase with the temperature. The reason attributing this phenomenon is that the stress sensor were installed in summer, so the stress in summer can be seen as starting point in a certain degree. At the same time, it can be seen that the max stress difference in summer and winter is within 20 MPa. The daily stress variation in summer is almost equal to that in winter. 7. Conclusions 1) Long term monitoring of aconch-shaped latticed shell structure was conducted, the temperature and stress condition before and after 6
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60
60
40
30
30
20
20
10
10
60
With membrane Maximum
40
Average
Ju ne
Ju ly Ju ly
Ju ne
Ma y
l Ap ri
Au gu st Se pte mb er Oc tob er No ve mb er De ce mb er
Ju ly
Ju ne
Ma y
Ap ril
h Ma rc
Ja nu ary
Fe bru ary
Month
Month
c) Component 3
d) Component 5 60
60
Ma rch
0 Oc tob er No ve mb er De ce mb er
With membrane
With membrane
50
T1 T2 T4 T3
T1 T2 T4 T3
40 30
30 Average
20
20
Average
10
10
Minimum
e) Component 9
f) Component 11
Fig. 12. Time history of temperature at different components.
7
Ju ly
Ju ne
Au gu st Se pte mb er Oc tob er No ve mb er De ce mb er
Ju ly
Ju ne
Ma y
Ap ril
Ma rch
Au gu st Se pte mb er Oc tob er No ve mb er De ce mb er Ja nu ary Fe bru ary
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Month
Ma y
0
0
Ap ril
Au gu st Se pte mb er
Ma y
10
0
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30 20
With membrane
Maximum
50
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40
b) Component 2
Ja nu ary Fe bru ary
50
Ap ril
Month
a) Component 1 T1 T2 T3 T4
Ma rch
Au gu st Se pte mb er Oc tob er No ve mb er De ce mb er
e
Month
60
T1 T2 T3
0
Ju ly
Ju n
Ma y
Ap r il
Ma rc h
Au gu st Se pte mb er Oc to b er No ve mb er De ce mb er Ja nu ary Fe bru ary
0
Average
Fe bru ary
40
With membrane
50
T1 T2 T3 T4
Ja nu ary
Maximum
Maximum
Ja nu ary Fe bru ary
50
With membrane
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Highest Lowest
3)
20 10
4)
0 -10
6)
Ju ly
Ju ne
M ay
il A pr
A ug us Se t pt em be r O ct ob er N ov em be r D ec em be r Ja nu ra ry Fe br ua ry M ar ch
5)
Month
Fig. 13. The air temperature in Tianjin, China.
that directly exposed to solar radiation. Meanwhile, the temperature of steel structure under glass is 5 ℃ lower than that directly exposed to solar radiation. Average temperature in summer of 2015 is 2.5 ℃ higher than that in summer of 2014 due to ‘greenhouse effect’. The max temperature of components under membrane is 15 ℃ higher than air temperature. The min temperature of structure under membrane is about 8℃ higher than min air temperature in winter and the max temperature is 15 ℃ higher than max air temperature in summer. Change tendency of every component is similar to curves of seasonal temperature. All decrease along with decrease of temperature. Different parts of the structure have different sensitivity to thermal load. Components located near supports are more sensitive to thermal load. But in this project, it was released by introduction of double supports. Monitoring results indicate that axial stress change caused by seasonal temperature difference was within 20 MPa.
Acknowledgements
installation of membrane were derived. The results were compared to investigate influence of membrane on thermal an mechanical behavior of the conch-shaped latticed shell structure. 2) Shelter effect of glass is much smaller than membrane. The temperature of steel structure under membrane is 20 ℃ lower than
This work was supported by the National Natural Science Foundation of China (51208355).
Fig. 14. Influence of membrane on daily temperature of steel structures.
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Fig. 15. Time history of stress at different components.
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Fig. 16. Influence of membrane on daily stress variation.
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Fig. 17. Comparison of stress in summer and winter.
[12] Aitziber López, I.ñigo Puente, Miguel A. Serna, Direct evaluation of the buckling loads of semi-rigidly jointed single-layer latticed domes under symmetric loading, Eng. Struct. 29 (1) (2007) 101–109. [13] Z.W. Yu, X.D. Zhi, F. Fan, C. Lu, Effect of substructures upon failure behavior of steel reticulated domes subjected to the severe earthquake, Thin-Walled Struct. 49 (9) (2011) 1160–1170. [14] W.Z. Liu, J.H. Ye, Collapse optimization for domes under earthquake using a genetic simulated annealing algorithm, J. Constr. Steel Res. 97 (2014) 59–68. [15] Huidong Zhang, Qinghua Han, Yuanfeng Wang, Yan Lu, Explicit modeling of damping of a single-layer latticed dome with an isolation system subjected to earthquake ground motions, Eng. Struct. 106 (2016) 154–165. [16] Ximei Zhai, Yonghui Wang, Ming Huang, Performance and protection approach of single-layer reticulated dome subjected to blast loading, Thin-Walled Struct. 73 (2013) 57–67. [17] Jialu Ma, Feng Fan, Chengqing Wu, Xudong Zhi, Counter-intuitive collapse of single-layer reticulated domes subject to interior blast loading, Thin-Walled Struct. 96 (2015) 130–138. [18] Yasushi Uematsu, Motohiko Yamada, Akira Inoue, Takeshi Hongo, Wind loads and wind-induced dynamic behavior of a single-layer latticed dome, J. Wind Eng. Ind. Aerodyn. 66 (3) (1997) 227–248. [19] Yasushi Uematsu, Osamu Kuribara, Motohiko Yamada, Akihiro Sasaki, Takeshi Hongo, Wind-induced dynamic behavior and its load estimation of a single-layer latticed dome with a long span, J. Wind Eng. Ind. Aerodyn. 89 (14–15) (2001) 1671–1687. [20] M.M. Alinia, S. Kashizadeh, Effect of flexibility of substructures upon thermal behaviour of spherical double layer space truss domes, Part I: uniform thermal loading, J. Constr. Steel Res. 62 (4) (2006) 359–368. [21] M.M. Alinia, S. Kashizadeh, Effect of flexibility of substructures upon thermal behaviour of spherical double layer space truss domes, Part II: gradient & partial loading, J. Constr. Steel Res. 62 (7) (2006) 675–681. [22] M.M. Alinia, S. Kashizadeh, Effects of support positioning on the thermal behaviour of double layer space truss domes, J. Constr. Steel Res. 63 (3) (2007) 375–382.
References [1] S.Z. Shen, Recent advances on the fundamental research of spatial structures in China, J. Int. Assoc. Shell Spat. Struct. 47 (2) (2006) 93–100. [2] Z.W. Yu, X.D. Zhi, F. Fan, C. Lu, Effect of substructures upon failure behavior of steel reticulated domes subjected to the severe earthquake, Thin-Walled Struct. 49 (9) (2011) 1160–1170. [3] M. Mazzolani Federico, 3D aluminium structures, Thin-Walled Struct. 61 (2012) 258–266. [4] H.B. Liu, Z.H. Chen, Q.H. Han, B.B. Chen, Y.D. Bu, Study on the thermal behavior of aluminum reticulated shell structures considering solar radiation, Thin-Walled Struct. 85 (2014) 15–24. [5] H.B. Liu, Z.H. Chen, B.B. Chen, X. Xiao, X.D. Wang, Studies on the temperature distribution of steel plates with different paints under solar radiation, Appl. Therm. Eng. 71 (2014) 342–354. [6] H.B. Liu, X.W. Liao, Z.H. Chen, Q. Zhang, Thermal behavior of spatial structures under solar irradiation, Appl. Therm. Eng. 87 (2015) 328–335. [7] Y.Q. Wang, C.C. Lin, Y.J. Shi, Experimental study on the temperature of steel members in sunshine, J. Build. Struct. 140–147 (2010) 140–147. [8] X.F. Jin, F. Fan, S.Z. Shen, Effect of non-uniform temperature field under sunshine on the structure supporting the reflector of a large radio telescope-FAST, China Civ. Eng. J. 41 (11) (2008) 71–77 (in Chinese). [9] Z. Fan, Z. Wang, J. Tian, Analysis on temperature field and determination of temperature upon healing of large-span steel structure of the National Stadium, J. Build. Struct. 28 (2) (2007) 32–40. [10] F. Fan, J.C. Yan, Z.G. Cao, Elasto-plastic stability of single-layer reticulated domes with initial curvature of members, Thin-Walled Struct. 60 (2012) 239–246. [11] Aitziber López, I.ñigo Puente, Miguel A. Serna, Numerical model and experimental tests on single-layer latticed domes with semi-rigid joints, Comput. Struct. 85 (7–8) (2007) 360–374.
11
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Full length article
Thermal behavior of large-span reticulated domes covered by ETFE membrane roofs under solar radiation
MARK
⁎
Zhongwei Zhaoc, Hongbo Liua,b,c, , Zhihua Chena,c a b c
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China School of Engineering, Edinburgh of university, Edinburgh EH93FB, UK School of Civil Engineering, Tianjin University, Tianjin 30007, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Large-span reticulated domes Membrane roof Solar radiation Non-uniform thermal load Non-uniform thermal effect Field monitoring
A strong non-uniform temperature was induced by solar radiation for the large-span reticulated domes with ETFE membrane roof, which may induce a significant thermal stress and thermal deformation. In order to obtain the temperature distribution and thermal behavior of large-span reticulated domes with ETFE membrane under solar radiation, a long term field monitoring and numerical analysis were conducted in this paper. Based on the results of both field monitoring and the numerical analysis, the following conclusions were obtained: 1) shelter effects of glass and membrane varies widely. 2) Daily temperature variation can be reduced by a large degree due to introduction of membrane. 3) Average temperature of components is increased by membrane due to ‘greenhouse effect’.4) The seasonal temperature variation has little effect on the components which located at upper part of spatial latticed shell structures, the internal force can be released by deformation. 5) Thermal response of bottom ring beam is reduced by installation temperature and double supports.
1. Introduction With the advantages light weight, fast assembly, spanning capability and ease to form various attractive geometrical appearance, the large-span reticulated domes have been widely used in various buildings, such as sport stadiums and gymnasiums, exhibition centers, airport, factory buildings and so on [1–3]. In order to more beautiful and energy saving, the ETFE membrane or glass materials were widely used as roof for large-span reticulated domes to allow some solar radiation come into indoor, for example of the Eden Project (Fig. 1) in the United Kingdom and Yujiabu Station in China (Fig. 2). For the large-span reticulated domes with ETFE membrane roof, the solar radiation can arrive to the steel member surfaces in both construction and operation. Based on the previous studies [4–9], the temperature of steel members is not only much higher than ambient air temperature but also much non-uniform because of the high solar radiation transmittance of ETFE membrane or glass, which always induce a significant thermal stress and thermal deformation. Therefore, it is important to take into account the thermal effect induced by solar radiation for the large-span steel structures with ETFE membrane or glass roof in the design process. Many researches were carried out in past years to evaluate the stability [10–12], seismic performance [13–15], dynamic performance
⁎
under blast loading [16,17] and dynamic behavior under wind loading [18,19]. Alinia [20–22] has carried out some research on the thermal effect of large-span steel structures under both uniform thermal load and non-uniform thermal load. Liu [4–6] have carried out systematic investigation on the non-uniform thermal effect of large-span steel structures exposed to solar radiation directly through experiment and numerical analysis. However, no research referred to the thermal effect of large-span reticulated domes covered by ETFE membrane or glass roof, which of thermal effect were different that exposed to solar radiation directly. In this paper, the thermal effect of the large-span reticulated domes covered by ETFE membrane or glass roof was studied through a longterm monitoring and numerical analysis. 2. Structural information of Yujiabu Railway Station Yujiabu Railway Station Building is located in Tianjin, China. A conch-shaped single-layer steel lattice structure was designed to cover a large space, which is 142 m in length, 80 m in width, and 24 m in height as shown in Fig. 3. The main members of the whole structure are 72 curved steel box girders that intersect each other, as shown in Fig. 4. The appearance of the structure is similar to a conch. Ten kinds of nodes different from each other were used. Every member’s torsion has
Corresponding author at: State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (H. Liu).
http://dx.doi.org/10.1016/j.tws.2017.01.025 Received 27 June 2016; Received in revised form 15 December 2016; Accepted 18 January 2017 0263-8231/ © 2017 Elsevier Ltd. All rights reserved.
Thin-Walled Structures 115 (2017) 1–11
Z. Zhao et al.
the analysis on the temperature distribution of large span steel structures under solar radiation based ASHRAE model in ANSYS software. 4.1. Boundary condition For any steel members exposed to solar radiation, the heat flow acting on its surface includes convection heat, solar radiation and long wave radiation among ground, sky and steel surface. Therefore, the temperature boundary condition for the steel members exposed to solar radiation is defined as:
λ
∂T ∂n
= h [Ta (t ) − T ] + qS (t ) + qL (t )
(1)
Γ
20
where h is heat convection coefficient (w / m C ); Ta is ambient air temperature; qS is solar radiation (w / m2 ); qL is long wave radiation (w / m2 );λ is thermal conductivity (w / m2 0C ). Fig. 1. The reticulated dome of Eden Project in United Kingdom.
4.2. Solar radiation The ASHRAE clear-sky model was adopted in this study to calculate the solar radiation striking the surface of steel members. In this model, the total global solar radiation is assumed to be the sum of direct radiation, diffuse radiation, and the solar radiation reflected from the surrounding surface.
different angles to keep the configuration smooth. The steel structure was covered by ETFE membrane and glass, as shown in Fig. 5. The bottom ring beam (BRB) is constraint by 36 supports, including 5 single-direct supports and 31 double-direct supports as shown in Fig. 6, and the supports are constrained by concrete corbels. There is a spherical bearing between top and bottom plate and the center of the spherical are set to the same for double supports to ensure that it can rotate in a degree.
⎡ ⎤ GdV qs = ε (GD + Gd + GR ) = ε ⎢max(cos θ , 0) + C + ρg Fwg (sin β + C ) ⎥ ⎣ ⎦ GdH (2)
GND 3. Field monitoring scheme
where ε is the solar absorption coefficient. The solar radiation absorption is affected by its color and smoothness of steel plates. 0.6 was adopted in this study based on the test data. The meaning of other parameters can be found in [4–6].
A temperature and stress monitoring system designed for the steel structure of Yujiabu Railway Station was installed in July 2014. There were 44 temperature sensors and 22 strain gages were installed. 4 temperature sensors and 2 strain gages were installed in each steel member. Arrangement of monitoring members was shown as in Fig. 7. Fig. 8 showed installation positions of monitoring sensor on each component in detail. Four temperature sensors and two stress sensors were installed on middle part of each component. Temperature sensors were installed on each side of the component and stress sensors were installed on top and bottom of the components. The section of component located at skylight is circle and the others are rectangular section. Fig. 9 shows actual structure under solar radiation and monitoring sensors on each component.
4.3. Long wave radiation The long wave radiation on the surface of steel plates can be expressed by Stefan-Boltzmann equation:
ql = εf σ (F
wg
4 (Tg4 − T 4 ) + F (Tsky − T 4 )) ws
(3)
where εf is the ratio of the radiation emitted by a surface; σ is StefanBoltzmann constant=5.67 × 10−8W /(m2⋅K 4 ); Tsky is the effective temperature of sky, usually calculated by Ta − 6 ; Tg is the ground temperature.
4. Numerical analysis
4.4. Comparison of results The finite element model of the structure constitutes of beam
A three-dimensional transient thermal FE model was developed for
Fig. 2. The reticulated dome of Yujiabu Station in China.
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Fig. 3. Overview of Yujiabu Railway Station in different stages.
compared, shown as in Fig. 11. It is clear that the temperature and stress obtained by numerical analysis were generally consistent with the monitoring results. Reasons attributing to the discrepancies might be due to variance in the solar radiation model. As the complexity of the algorithm, the shadow effect among components was not taken into account which is the main cause of difference between temperature
element and Beam 188 in ANSYS was adopted, support at the bottom of the structure was constraint in radial and vertical direction. The temperature field derived by numerical method was shown as in Fig. 10. The temperature-time curves of each monitoring component on 1th August derived by field monitoring and numerical analysis was
Fig. 4. Sections and joints of Yujiabu Railway Station.
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Fig. 7. Distribution of monitoring components. Fig. 5. Location of membrane and glass.
derived by FEM method and field monitoring.
5. Long-term monitoring results of temperature 5.1. Analysis of seasonal temperature change The monitoring was conducted from July 31, 2014 to September 8, 2015. The monitoring results of temperature were shown in Fig. 12. Detailed locations of each component can be found in Fig. 7. The monitoring was started before installation of membrane. As shown in Fig. 12, the monitoring process can be divided into mainly two periods, i.e. before and after installation of membrane. Through the comparison of monitoring results obtained before and after membrane installation, it was concluded that the variation of daily temperature is smaller after installation of membrane due to the membrane preventing some solar radiation into steel member surface. The max temperature before membrane installation is about 55 ℃ and occurred at component 1, 2 and 5, because these components were directly exposed to solar radiation. The maximum temperature of other components was smaller with value of 40 ℃ due to shelter of accessory structure for solar radiation. The max temperature at component 1 is 35 ℃ in summer of 2015 after membrane installation, which was about 20 ℃ lower than it before membrane installation because of shelter effect of membrane.
Fig. 8. Positions of temperature sensors and strain gauges.
The max temperature at component 2 and 5 in summer of 2015 after membrane installation is only 5 ℃ smaller than that before installation of membrane, because the component 2 and 5 is located below glass skylight not membrane. Therefore, it was concluded that shelter effect of glass is much smaller than membrane for solar radiation. Results shown in Fig. 12(b) and (d) indicate that the max value of temperature was decreased by about 5 ℃. But the average value of temperature in summer of 2014 is about 2.5 ℃ higher than that in 2015. This is caused by enclosed space after installation of membrane
Fig. 6. The arrangement of supports.
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Fig. 9. Installation of temperature sensor and stress sensor.
monitored were above 0 ℃. But the average daily air temperature in Tianjin in winter is about −8 ℃ as shown in Fig. 13. Considering no air conditioner installed in the building, it was concluded that heat insulation effect of the membrane is pretty good. The max temperature of steel structure under membrane is about 45 ℃, which is 15 ℃ lower than that of steel structure directly exposed to solar radiation and also 15 ℃ higher than ambient air temperature.
and glass, the energy cannot be released immediately. The max temperature value at component 3 in summer of 2014 is almost the same as that in summer of 2015, because Component 3 was in shade of other components was lightly affected by solar radiation. But even so, the average temperature in summer of 2014 is also about 2.5 ℃ higher than that in 2015. Component 11 is different from other monitoring components as it shown in Fig. 12(f), and its daily temperature variation is very small. The reason for that was Component 11 was located at bottom ring beam of the structure, which was covered by concrete wall and is lightly affected by solar radiation or weather condition. In addition, Different from other components, the average temperature at component 11 in summer of 2014 is lower than that in 2015. It was clearly seen from Fig. 12 that all of the temperature
5.2. Influence of membrane on daily temperature change The influence of membrane on daily temperature change was studied in this section. The symbol T1~T4 indicate the temperature monitored during August 1, 2014 to August 4, 2014 and T1′~T4′ indicate the temperature monitored during August 1, 2015 to August 4,
Fig. 10. Contour of temperature field under solar radiation at 12 o′clock.
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shown mentioned above cannot support pull force. The bottom ring beam can contract freely without internal force occurred.
2015. It was concluded from Fig. 14 that the min monitoring temperature after membrane installation is generally higher than that before membrane installation. On the contrary, the max temperature is reduced due to membrane installation. That is to say, the daily temperature change is reduced by membrane. It can also be observed from the results that the increasing velocity of temperature under membrane lag behind that without membrane.
6.2. Influence of membrane on daily stress variation To investigate the influence of membrane on structural daily stress variation in detail, the monitoring results during August 1, 2014 to August 4, 2014 and August 1, 2015 to August 4, 2015 were shown in Fig. 16. S1′ and S2′ indicate the results monitored after membrane installation. S1 and S2 indicate the results monitored before membrane installation. It can be clearly seen in Fig. 16 that the daily variation of stress will be reduced in a large degree due to the existence of membrane. The max daily variation of stress without membrane is about 14 MPa and it is reduced to 7 MPa after the membrane was installed. It can also be concluded from results shown in Fig. 16d), e) and f) that the stress of bottom and upper surface of these components change in a parallel manner. This indicate the variation of daily temperature mainly cause change of axial force. Bending moment of the other components will change with variation of temperature.
6. Long-term monitoring results of thermal stress 6.1. Analysis of stress during monitoring process Monitoring results of component stress are shown as in Fig. 15. The monitoring period was divided into seven sub phase. Duration of each sub phase was shown at the end of Fig. 15. I and II indicate the period before installation of membrane. It was concluded that the change tendency of the stress is similar to the temperature. The stress will decrease with temperature. The change magnitude of stress is within 20 MPa during one year, which indicates that the influence of seasonal temperature change on the monitored components is small. This is not in consistent with traditional opinion. In fact, the latticed shell can deform freely when the temperature load was applied because of high ratio of rise-to-span. Even so, the influence of thermal load is remarkable on the components near support. It can be seen from results shown in Fig. 15 that stress of the upper and bottom surface of components will deviate from each other as the temperature changes. This indicates bending moment will occur when the latticed shell deforms with temperature difference. Change of component stress is a complex mechanism as the structure is an integrity influence by temperature load. At the same time, the component stress is also closely related to installation sequence and installation temperature. Generally speaking, change magnitude of stress in summer of 2015 is smaller than that in summer of 2014. This is caused by the existence of membrane. Results shown in Fig. 15b) indicate that S2 is smaller than S1 in winter. But S2 will exceed S1 in summer. Bending moment direction in this component will reverse as temperature changes. It can be seen from Fig. 15e) that the stress variation of the bottom ring beam is also within 20 MPa. This is caused by the installation temperature of bottom ring beam. The bottom ring beam was installed in summer of 2013. So the installation temperature was high. Bottom ring beam will contract in winter. At the same time, the double support
6.3. Comparison of stress in summer and winter In this section, monitoring results during January 15, 2015 to January 20, 2015 and July 15, 2015 to July 20, 2015were compared to investigate influence of seasonal temperature difference on structural thermal behavior. Only part of the results were listed due to limited space, as shown in Fig. 17. It can be concluded from the results that value of S1 and S2 is almost equal in summer. This indicates that the components mainly suffer axial force in summer. The difference between S1 and S2 increases in winter which indicates the bending moment increase with the temperature. The reason attributing this phenomenon is that the stress sensor were installed in summer, so the stress in summer can be seen as starting point in a certain degree. At the same time, it can be seen that the max stress difference in summer and winter is within 20 MPa. The daily stress variation in summer is almost equal to that in winter. 7. Conclusions 1) Long term monitoring of aconch-shaped latticed shell structure was conducted, the temperature and stress condition before and after 6
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Fig. 13. The air temperature in Tianjin, China.
that directly exposed to solar radiation. Meanwhile, the temperature of steel structure under glass is 5 ℃ lower than that directly exposed to solar radiation. Average temperature in summer of 2015 is 2.5 ℃ higher than that in summer of 2014 due to ‘greenhouse effect’. The max temperature of components under membrane is 15 ℃ higher than air temperature. The min temperature of structure under membrane is about 8℃ higher than min air temperature in winter and the max temperature is 15 ℃ higher than max air temperature in summer. Change tendency of every component is similar to curves of seasonal temperature. All decrease along with decrease of temperature. Different parts of the structure have different sensitivity to thermal load. Components located near supports are more sensitive to thermal load. But in this project, it was released by introduction of double supports. Monitoring results indicate that axial stress change caused by seasonal temperature difference was within 20 MPa.
Acknowledgements
installation of membrane were derived. The results were compared to investigate influence of membrane on thermal an mechanical behavior of the conch-shaped latticed shell structure. 2) Shelter effect of glass is much smaller than membrane. The temperature of steel structure under membrane is 20 ℃ lower than
This work was supported by the National Natural Science Foundation of China (51208355).
Fig. 14. Influence of membrane on daily temperature of steel structures.
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Fig. 15. Time history of stress at different components.
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Fig. 16. Influence of membrane on daily stress variation.
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Fig. 17. Comparison of stress in summer and winter.
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