Static and dynamic properties of three-tower suspension bridge and structural type selection of mid-tower
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摘要: 为探讨三塔悬索桥与两塔悬索桥静动力特性差异与中塔选型, 以泰州长江大桥为原型, 基于有限位移理论建立相应的两塔、三塔(混凝土中塔与钢中塔) 悬索桥的空间有限元模型, 分析了各种结构参数下的静力和地震效应。研究结果表明: 与两塔悬索桥相比, 由于中塔顶缺乏边缆的有效纵向约束, 三塔悬索桥整体刚度较小, 变形较大, 自振频率低; 汽车作用下主缆抗滑、桥塔受力、主梁挠跨比等在常规两塔悬索桥中很容易满足要求的指标, 但对三塔悬索桥却成为控制指标。三塔悬索桥的3个指标都与中塔抗推刚度密切相关, 但其对中塔抗推刚度的需求是矛盾的。“人”字形钢中塔三塔悬索桥的主缆抗滑安全系数为2.17, 汽车作用下桥塔最大应力为182 MPa, 最大挠跨比为1/210, 全部满足要求。可见, “人”字形钢中塔较好地兼顾了3个控制指标的需要, 做到了构件刚度和缆索体系刚度的优化, 是合理的中塔形式。Abstract: In order to discuss the static and dynamic properties differences between three-tower and two-tower suspension bridges, and select the rational structure type of mid-tower, based on the Taizhou Yangtze River Bridge, the 3D space finite element models of two-tower suspension bridge and three-tower suspension bridges with concrete mid-tower and steel mid-tower were set up by finite displacement theory and the static and seismal effects were analyzed under various structural parameters. Analysis result shows that compared with two-tower suspension bridge, because the mid-tower is lack of effective restraints from side cables, three-tower suspension bridge has lower total stiffness, lower natural frequency and larger deflection-to-span ratio of main girder. Under vehicle loads, the anti-slipping safety factor between main cable and saddle, the forces of mid-tower and the deflection-to-span ratio of main girder are not important for two-tower suspension bridge, but become controlling indices for three-tower suspension bridge. The indices are related to the anti-pushing rigidity of mid-tower, but have incompatible demands for the rigidity. Under vehicle loads, when the steel mid-tower with upside-down Y shape is selected, the anti-slipping safety factor between main cable and saddle of mid-tower is 2.17, the maximum stress of mid-tower is 182 MPa, the deflection-to-span ratio of main girder is 1/210, and they meet correlative demands. Obviously, due to the application of steel mid-tower, the indices are rationally considered, the stiffness optimization of components and cable system is achieved, so, it is an appropriate structure for mid-tower.
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图 4 汽车荷载作用下主梁竖向挠度包络
Figure 4. Vertical deflection envelopments of main girders under vehicle loads
图 5 单跨活载作用下主缆与主梁的变形
Figure 5. Deformations of main girder and main cable under live load on single span
图 6 挠跨比与主梁转角的关系
Figure 6. Relationships between deflection-to-span ratios and vertical angles of main girders
图 7 两塔与三塔(钢中塔) 主要1阶振型
Figure 7. Main first order vibration modes of two-tower suspension bridge and three-tower suspension bridge with steel mid-tower
表 1 汽车荷载作用下主梁位移
Table 1. Displacements of main girders under vehicle loads
计算模型 两塔 三塔(砼中塔) 三塔(钢中塔) 上挠 下挠 上挠 下挠 上挠 下挠 绝对数值 最大竖向位移/m 1.449 2.756 3.712 5.099 3.877 5.183 梁端水平位移/m 0.562 1.071 1.228 相对比值 最大竖向位移 1.00 1.00 2.56 1.85 2.68 1.88 梁端水平位移 1.00 1.91 2.19 注: 表中的相对比值均为三塔(混凝土中塔)、三塔(钢中塔) 计算值与两塔计算值的比值, 下同。 
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表 2 汽车荷载作用下主塔内力与位移
Table 2. Forces and displacements of towers under vehicle loads
计算模型 两塔 三塔(砼中塔) 三塔(钢中塔) 桥塔 边塔 中塔 边塔 中塔 绝对数值 塔顶位移/m 0.196 0.188 2.105 0.186 2.356 塔底纵向弯矩/ (MN·m) 237 231 2 460 229 2 848 相对比值 塔顶位移 1.00 0.96 10.74 0.95 12.02 塔底纵向弯矩 1.00 0.97 10.38 0.97 12.02
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表 3 汽车荷载作用下主缆抗滑安全系数
Table 3. Anti-slipping safety factors between main cables and saddles
计算模型 两塔 三塔(砼中塔) 三塔(钢中塔) 桥塔 边塔 中塔 边塔 中塔 抗滑安全系数 34.47 11.80 2.15 11.85 2.17
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表 4 纵风作用下梁塔水平位移
Table 4. Displacements of girders and towers under longitudinal wind
计算模型 两塔 三塔(砼中塔) 三塔(钢中塔) 边塔 中塔 边塔 中塔 绝对数值 梁端水平位移/m 0.247 0.362 0.312 塔顶位移/m 0.016 0.021 0.244 0.020 0.234 相对比值 梁端水平位移 1.00 1.47 1.26 塔顶位移 1.00 1.30 15.25 1.30 14.63
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表 5 横风作用下主梁内力与位移
Table 5. Forces and displacements of main girders under lateral wind
计算模型 两塔 三塔(砼中塔) 三塔(钢中塔) 绝对数值 跨中主梁横向位移/m 1.208 0.677 0.792 跨中主梁横向弯矩/ (MN·m) 376 285 305 中塔处主梁横向弯矩/ (MN·m) 541 593 相对比值 跨中主梁横向位移 1.00 0.56 0.66 跨中主梁横向弯矩 1.00 0.76 0.81 中塔处主梁横向弯矩 1.44 1.58
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表 6 横风作用下主塔内力与位移
Table 6. Forces and displacements of towers under lateral wind
计算模型 两塔 三塔(砼中塔) 三塔(钢中塔) 桥塔 边塔 中塔 边塔 中塔 绝对数值 塔顶横向位移/m 0.116 0.109 0.139 0.109 0.227 塔底横向弯矩/ (MN·m) 131 126 205 126 231 相对比值 塔顶横向位移 1.00 0.94 1.20 0.94 1.95 塔底横向弯矩 1.00 0.96 1.56 0.96 1.76
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表 7 结构自振特性
Table 7. Natural vibration characteristics of structures
振型阶次 两塔 三塔(砼中塔) 三塔(钢中塔) 频率/Hz 振型描述 频率/Hz 振型描述 频率/Hz 振型描述 1 0.071 1阶正对称侧弯 0.063 1阶反对称竖弯 0.067 1阶反对称竖弯 2 0.079 1阶反对称竖弯 0.071 1阶反对称侧弯 0.070 1阶反对称侧弯 3 0.118 2阶反对称竖弯 0.087 2阶反对称竖弯 0.092 1阶正对称侧弯 4 0.148 1阶正对称竖弯 0.095 1阶正对称侧弯 0.095 2阶反对称竖弯 5 0.200 2阶正对称竖弯 0.116 1阶正对称竖弯 0.117 1阶正对称竖弯 6 0.226 1阶反对称侧弯 0.118 3阶反对称竖弯 0.136 3阶反对称竖弯 0.382 1阶反对称扭转 0.319 1阶反对称扭转 0.286 1阶反对称扭转 0.327 1阶正对称扭转 0.329 1阶正对称扭转 0.330 1阶正对称扭转
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表 8 地震水平位移
Table 8. Horizontal displacements under earthquake
计算模型 两塔 三塔(砼中塔) 三塔(钢中塔) 绝对数值 梁端/m 1.181 1.237 0.865 边塔顶/m 0.074 0.091 0.135 中塔顶/m 0.831 0.713 相对比值 梁端 1.00 1.05 0.73 边塔顶 1.00 1.23 1.82 中塔顶 11.23 9.64
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表 9 地震内力
Table 9. Forces under earthquake
计算模型 两塔 三塔(砼中塔) 三塔(钢中塔) 桥塔 边塔 中塔 边塔 中塔 绝对数值 轴力/MN 50.8 52.0 46.1 65.3 25.1 剪力/MN 10.5 10.2 13.0 14.5 8.6 弯矩/ (MN·m) 472 435 1 240 580 1 052 相对比值 轴力 1.00 1.02 0.91 1.29 0.49 剪力 1.00 0.97 1.24 1.38 0.82 弯矩 1.00 0.92 2.63 1.23 2.23
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