工程科学与技术   2017, Vol. 49 Issue (5): 13-21

1. 天津城建大学 天津市土木建筑结构防护与加固重点实验室，天津 300384;
2. 北京工业大学 工程抗震与结构诊治北京市重点实验室，北京 100124

Analysis of Rigid Bracing Dome with Broken Cable (Rod)
GAO Zhanyuan1, XUE Suduo2
1. Tianjin Key Lab. of Civil Structure Protection and Reinforcement,Tianjin Chengjian Univ.,Tianjin 300384,China;
2. Beijing Key Lab. of Earthquake Eng. and Structural Retrofit,Beijing Univ. of Technol.,Beijing 100124,China
Abstract: Rigid bracing dome is a new type of cable structure and broken cables (rods) analysis is very important for the failure mechanism and collapse performance of vcts structure.The structural mechanical properties of the broken cable (or rod) are analyzed by the Newmark time integration method of the transient dynamics.The response rate and dynamic magnification factor are given,and the influence degree of the broken cable (or rod) on the structure is analyzed by these parameters.The members are divided into global sensitivity components,local sensitivity components and insensitive components through the cable (or rod) breaking caused by the destruction of strength and excessive displacement of the other cables.The importance coefficient of the member is defined,and component importance is analyzed.Research shows that because the inner and outer ring rod,outer oblique rod or outer support rod is break,the structure will undergo a progressive collapse and are global sensitivity component.Lateral upper cable,middle upper cable,internal upper cable,middle oblique rod,internal oblique rod and internal support rod are locally sensitive components.The component importance of outer ring rod is the first,and internal upper cable is the last.
Key words: rigid bracing dome    broken cables (or rods) analysis    sensitivity    component importance

1 基本理论

 $\rho = \frac{{{S_{{\text{稳}}}} - {S_{{\text{静}}}}}}{{{S_{{\text{静}}}}}}$ (1)
 $R = \displaystyle\frac{{{S_{{\text{最大}}}}}}{{{S_{{\text{静}}}}}}$ (2)

2 静力分析

 图1 劲性支撑穹顶结构 Fig. 1 Rigid bracing dome

 图2 静载作用下结构的变形图和应力图 Fig. 2 Deformation and stress of structure under static load

3 断索（或杆）分析

1）外脊索

 图3 1号外脊索破断 Fig. 3 No. 1 lateral upper cable is broken

1号外脊索破断，只对断索位置附近的杆件有较大影响，其他位置的杆件影响程度均较小。结构并未此发生连续倒塌，故外脊索为局部敏感性构件。

2）中脊索

 图4 21号中脊索破断 Fig. 4 No. 21 middle upper cable is broken

21号中脊索破断，只对1号轴、2号轴及20号轴上的杆件有较大影响，对其它杆件影响不大，未引起整个结构的连续倒塌。因此，中脊索为局部敏感性构件。

3）内脊索

 图5 41号内脊索破断 Fig. 5 No. 41 internal upper cable is broken

41号内脊索破断，只对1号、2号及20号轴上的杆件及节点有较大影响，对其他杆件及节点影响不大，并未引起整个结构的连续倒塌。因此，内脊索为局部敏感性构件。

4）外斜杆

 图6 61号外环杆破断时结构的位移图 Fig. 6 After breaking outer ring rod, displacement of the structure

5）中斜杆

 图7 81号中斜杆破断 Fig. 7 No.81 outer oblique rod is broken

81号中斜杆发生断裂时，结构只在断杆位置附近发生较大的振动，其他位置的节点和杆件振动幅度均较小。中斜杆断裂以后，局部发生破坏，但振动稳定后整个结构安全，因此，中斜杆为局部敏感性构件。

6）内斜杆

 图8 101号内斜杆破断 Fig. 8 No.101 internal oblique rod is broken

7）外环杆、内环杆、外撑杆

 图9 结构的位移图 Fig. 9 Structure displacement diagram

121号外环杆或141号内环杆或161号外撑杆发生破断，大部分脊索内力为零，出现过大位移，结构发生连续倒塌，因此外环杆、内环杆和外撑杆均为全局敏感性构件。

8）内撑杆

 图10 181号内撑杆破断 Fig. 10 No.181 outer support rod is broken

4 杆件重要性分析

 ${\beta _j} = \frac{{\displaystyle\sum\limits_{i = 1}^n {(| {{\rho_{xi}}} | +| {{\rho _{yi}}} | + | {{\rho_{{\text z}i}}} |)} }}{{3n}}$ (3)

5 结　论

1）提出的响应变化率和动力响应系数能充分反映断索（杆）后结构性能，并通过其判断索（杆）的敏感性。

2）外环杆、内环杆、外斜杆和外撑杆破断后结构多数索出现松弛，结构出现过大位移，发生连续倒塌，其为全局敏感性构件。

3）中斜杆、内斜杆、外脊索、中斜索、内脊索或内撑杆破断后，影响在断索（或杆）附近，其他位置的杆件影响均较小，这些杆件为局部敏感性杆件。

4）外脊索和中脊索破断后，会导致相应位置的部分斜杆出现压应力，但并未发生失稳。外脊索、中脊索和内脊索破断都会引起相应部位的索出现松弛。

5）杆件重要性系数能反映杆件对整体结构的重要性，通过其对杆件重要性进行排序。环杆的重要性尤为重要。外环杆的杆件重要性排在首位，内脊索的重要性排在末位。外侧杆件比相应的内侧杆件的杆件重要。全局敏感性杆件重要性排序较高，局部敏感性的杆件重要性居中，不敏感性构件重要性较低。通过杆件重要性分析，可为进一步连续倒塌分析提供依据。

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