RESEARCH AND APPLICATION OF LARGE HEIGHT DIFFERENCE WHEEL SPOKE STRUCTURE
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摘要: 针对外环高度变化较大可能引起轮辐结构径向索受压的问题，通过设置刚性撑杆代替部分受压的径向索，解决了采用传统轮辐结构无法成形的难题。推导出轮辐结构的预应力态求解公式，考虑结构自重和索夹重量等的影响，通过反复迭代确定内环各节点的标高，形成索-杆混合结构找形分析方法。对大高差轮辐结构的受力性能进行较为全面的分析，考察了外环高差、径索系杆以及附加环索等参数的影响。计算分析结果表明：大高差轮辐结构在承受长轴方向半跨活荷载和风荷载作用时较为不利，但个别径索或撑杆失效不会引起结构连续倒塌。随着外环高差加大，撑杆数量相应增多，短轴构件及长轴上径索的内力增大，长轴下径索的内力减小。在长度较大的径索中部设置系杆，能够有效地协调上、下径索之间的变形。在长轴附近设置附加环索，可以通过增强相邻径索之间的联系，提高屋面支承结构的竖向刚度。大高差轮辐结构设置刚性撑杆的成形方法已成功应用于厦门新体育中心体育场工程。Abstract: According to the problem that the radial cable of a wheel spoke structure may be compressed due to the large change of the height of its outer ring, the rigid strut is introduced to replace the partially compressed radial cable, which solves the problem that the traditional wheel spoke structure cannot be formed. The prestressed state solution formula of the wheel spoke structure is deduced, considering the influence of the self-weight of the structure and the weight of the cable clamp, etc., the elevation of each node of the inner ring is determined through repeated iterations, and the form-finding method for the hybrid cable-strut structure analysis is formed. The mechanical performance of the wheel spoke structure with large height difference is analyzed comprehensively, and the influence of the parameters such as the height difference of the outer ring, the radial cable tie rod and the additional ring cable are investigated. The analysis results show that: the wheel spoke structure with large-height-difference is relatively unfavorable when it is subjected to the half-span live load and wind loading in the long axis direction, but the failure of individual radial cables or struts will not cause the structure to collapse continuously. As the height difference of the outer ring increases, the number of struts increases accordingly, the internal force of the members on short-axis and the upper radial cable on long-axis increases, and the internal force of the lower radial cable on long-axis decreases. Tie rods are arranged in the middle of the long radial cable, which can effectively coordinate the deformation between the upper and lower radial cables. By setting additional ring cables near the long axis, the vertical stiffness of the roof support structure can be improved by strengthening the connection between the adjacent radial cables. The forming method of setting rigid struts in the wheel spoke structure with large height difference has been successfully applied to the Xiamen New Sports Center Stadium Project.
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图 4 大高差轮辐结构的剖面
Figure 4. Section of the wheel spoke structure with large height difference
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图 9 大高差轮辐结构内环索夹节点
Figure 9. Large height difference wheel spoke structure inner ring cable clamp connections
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图 11 大高差轮辐结构的前3阶振型模态
Figure 11. First 3rd order vibration mode of the wheel spoke structure with large height difference
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图 12 长轴上径索失效时结构的响应
Figure 12. Response of the structure when the upper radial cable on the long axis fails
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图 13 短轴上径索失效时结构的响应
Figure 13. Response of structure when the upper radial cable on the short axis fails
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图 14 短轴撑杆失效时结构的响应
Figure 14. Response of the structure when the strut on short axis fails
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图 15 径索应力比随外环高差的变化情况
Figure 15. Variation of radial cables stress ratio with outer ring height difference
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图 16 撑杆数量占比与外环高差的关系
Figure 16. Relationship between the proportion of struts and outer ring height difference
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图 17 内环高差和构件应力比随外环高差的变化
Figure 17. Variation of inner ring height difference and component stress ratio with outer ring height difference
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图 18 结构竖向变形与外环高差的关系
Figure 18. Relationship between the maximum vertical deformation of structure and outer ring height difference
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图 20 轮辐结构长轴系杆端节点编号
Figure 20. Numbering of tie rod end nodes on long axis of wheel spoke structure
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图 21 设置系杆前后轮辐结构长轴径索的变形 /mm
Figure 21. The deformation of long axis radial cable of wheel spoke structure before and after setting tie rod
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图 23 长轴上径索竖向变形随环索数量的变化
Figure 23. Change of vertical defection along the upper radial cable on long axis with number of additional ring cables
表 1 径向索/杆的内力
Table 1 Internal force of radial cable/strut
编号 上径索 下径索/杆 本文/kN 有限元/kN 误差/(%) 本文/kN 有限元
/kN误差/(%) 1 460.6 472.8 2.61 1723.1 1708.5 0.85 2 481.3 477.6 0.77 1702.0 1687.5 0.86 3 551.8 547.7 0.75 1546.6 1533.0 0.88 4 875.6 869.5 0.70 1137.7 1126.8 0.96 5 1375.7 1340.8 2.57 470.4 491.5 4.39 6 1796.1 1831.9 1.97 −152.2 −157.4 −3.36 7 2077.9 2093.6 0.75 −602.2 −630.9 −4.65 8 2214.3 2218.9 0.21 −845.7 −860.0 −1.68 9 2260.0 2258.3 0.08 −948.9 −956.9 −0.84 10 2263.6 2260.6 0.13 −981.8 −986.2 −0.45 11 2265.6 2257.7 0.35 −988.2 −991.6 −0.34 
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表 2 荷载工况组合
Table 2 Combination of load conditions
工况类别 工况1 工况2 工况3 荷载组合 恒载 恒载+活1 恒载+活2 工况类别 工况4 工况5 工况6 荷载组合 恒载+活3 恒载+0°风 恒载+90°风
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表 3 活荷载布置对结构内力和变形的影响
Table 3 Influence of live load arrangement on internal force and deformation of the structure
荷载工况 内力/kN 最大竖向
位移/mm短轴
上径索短轴
下撑杆长轴
下径索长轴
上径索最小
索力1.3恒+1.5活1 2364 −1068 815 1342 81 255.7 1.3恒+1.5活2 2348 −1061 703 1462 110 188.6 1.3恒+1.5活3 2325 −1039 809 1329 75 258.5
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表 4 上径索参数与挠度
Table 4 Parameter and deflection of upper radial cables
编号 单索跨度l/m 支座高差c/m 索力T/kN 挠度w/mm 式(8) FEM 误差δ/(%) 1 33.5 16.0 460.6 489.0 461.3 5.83 2 31.9 13.9 481.3 445.2 433.9 2.57 3 28.3 9.7 551.8 347.2 337.7 2.78 4 24.1 5.4 875.6 202.5 200.2 1.12 5 19.9 1.9 1375.7 96.5 99.3 2.89 6 16.2 0.5 1796.1 49.8 51.3 3.02 7 13.1 1.8 2077.9 28.7 29.7 3.37 8 10.7 2.6 2214.3 18.4 18.9 2.71 9 9.0 2.9 2260.0 12.9 13.3 3.05 10 8.0 3.0 2263.6 10.3 10.5 2.33 11 7.6 3.0 2265.6 9.4 9.6 1.92 注：δ=[ABS(式(2)−FEM)/FEM]×100%。
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表 5 节点位移随系杆数量的变化
Table 5 Variation of displacement with the number of tie rods
系杆
数量节点位移/mm P0 Pu1 Pd1 Pu2 Pd2 Pu3 Pd3 0 14.5 415.4 35.6 589.4 40.2 471.3 28.4 1 61.3 287.1 161.6 245.0 245.0 322.5 132.8 2 72.6 232.8 193.4 300.9 231.4 237.4 171.8 3 76.9 206.5 206.5 251.4 251.4 189.7 189.7
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表 6 径索索力随系杆数量的变化
Table 6 Variation of radial cable force with the number tie rods
系杆数量 索力/kN 上径索 下径索 0 768.0 1450.1 1 637.5 1570.3 2 613.5 1607.3 3 602.7 1622.5
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