基于比值更新的索穹顶结构找力分析方法

姜正荣; 刘小伟; 石开荣; 林全攀

doi:10.3969/j.issn.0258-2724.20180201

基于比值更新的索穹顶结构找力分析方法

doi: 10.3969/j.issn.0258-2724.20180201

姜正荣^1,2,,
刘小伟¹,
石开荣^1,2, ,,
林全攀¹

基金项目: 广州市科技计划项目（1563000257）；亚热带建筑科学国家重点实验室开放课题（2019ZB27）

详细信息

作者简介:
姜正荣（1971—），男，副教授，博士，研究方向为大跨度空间结构，E-mail：zhrjiang@scut.edu.cn

通讯作者:
石开荣（1978—），男，副教授，博士，研究方向为预应力钢结构，E-mail：krshi@scut.edu.cn

中图分类号: TU394
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出版历程
- 收稿日期: 2018-03-19
- 修回日期: 2018-08-12
- 网络出版日期: 2018-12-21
- 刊出日期: 2020-02-01

Method of Force-Finding Analysis Based on Ratio Updating for Cable Domes

摘要

摘要: 为了快速高效求解索穹顶结构的预应力分布，提出了一种基于比值更新的找力新方法. 以不断更新的索预应力比值来分配拉索预应力，以索力和位形作为收敛控制参数，迭代得到满足精度要求的预应力分布. 基于此，首先对索穹顶结构进行了不考虑重力影响的找力分析，验证了该方法的正确性；其次当考虑重力影响且每个索段划分为多个单元时，可引入沿索长的索水平分力这一不变量，将索力的比值替换为索水平分力的比值. 结果表明：基于比值更新的找力分析方法计算速度快，位形偏差小，精度高；考虑重力影响的找力分析结果与不考虑重力影响相差较大（最大为19.34%），索穹顶结构的找力分析宜考虑重力的影响；将每个索段划分为单个单元和多个单元的找力分析结果相差甚微（最大仅0.05%），当索预应力较大且索长较短时，可将每个索段划分为单个单元以简化求解预应力分布.
- 索穹顶结构 /
- 找力分析 /
- 基于比值更新的找力分析方法 /
- 索水平分力
Abstract: In order to determine the prestress distribution of cable domes efficiently, a new method of force-finding analysis based on ratio updating was proposed. In this method, values of cable prestresses are pre-assumed and then constantly adjusted according to the continuously updated ratio of cable prestress; the precise prestress distribution of cable dome is acquired by iterations using the cable force and geometric shape as convergence control parameters. In this way, a force-finding analysis of cable domes is first conducted without considering the gravity effect, which verifies the effectiveness of this method. When the gravity is considered, each cable segment is divided into multiple units. An invariant, the cable force’s horizontal component along the length is introduced and the ratio of cable force is then replaced by that of the horizontal component force to deal with the situation with gravity. The results show that the method of force-finding analysis based on ratio updating is characterized by fast computational speed, small geometric shape deviation, and high precision. The results of force-finding analysis considering the influence of gravity are significantly different from those without considering gravity, and the maximum deviation reaches 19.34%. Thus, the influence of gravity should be taken into account in force-finding analysis of cable domes. In addition, whether each cable segment is divided into one unit or multiple units, the results of force-finding analysis make little difference (0.05% maximum deviation). Therefore, in cases when the cable prestress is large and cable length is short, each cable segment could be divided into only one unit to simplify the solving process of prestress distribution.
- cable dome /
- force-finding analysis /
- method of force-finding analysis based on ratio updating /
- horizontal component force of cable

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图 1 分析模型

Figure 1. Analytical model

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图 2 索杆预应力分布

Figure 2. Cable-strut prestress distribution

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图 3 索段s示意

Figure 3. Schematic diagram of cable segment s

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图 4 索杆预应力分布

Figure 4. Cable-strut prestress distribution

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表 1 截面参数

Table 1. Section parameter

索杆编号	截面面积/mm²	索杆编号	截面面积/mm²
JS1	2 494.03	HS1	5 202.03
JS2	3 271.03	SLH	1 424.03
JS3	3 671.03	XLH	2 494.03
XS3	1 669.03	YG1	6 633.03
XS2	3 671.03	YG2	3 280.03
XS1	4 195.03	YG3	2 749.03
HS2	3 671.03

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表 2 预应力分布对比

Table 2. Comparison of prestress distributions

索杆编号	预应力			预应力比值
索杆编号	文献[18]/kN	本文方法/kN	偏差/%	文献[18]	本文方法	偏差/%
JS1	435.33	435.33	0.00	1.000	1.000	0.00
JS2	715.33	715.09	−0.03	1.643	1.643	0.00
JS3	1 492.00	1 491.26	−0.05	3.427	3.426	−0.03
XS3	276.00	275.75	−0.09	0.634	0.633	−0.16
XS2	764.33	764.02	−0.04	1.756	1.755	−0.06
XS1	1 001.00	1 000.39	−0.06	2.299	2.298	−0.04
HS2	1 451.67	1 451.14	−0.04	3.335	3.333	−0.06
HS1	1 819.33	1 818.41	−0.05	4.179	4.177	−0.05
SLH	834.00	833.49	−0.06	1.916	1.915	−0.05
XLH	521.00	520.93	−0.01	1.197	1.197	0.00
YG1	−339.00	−338.83	−0.05	−0.779	−0.778	−0.13
YG2	−140.33	−140.23	−0.07	−0.322	−0.322	0.00
YG3	−57.67	−57.53	−0.24	−0.132	−0.132	0.00

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表 3 找力后控制点竖向位置与设计初始态偏差值

Table 3. Deviation of the control point’s vertical position after force finding from that in the initial state of design

节点编号	控制点偏差/mm
B	0.045
C	0.045
D	0.097
E	0.097
F	0.030
G	0.030

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表 4 找力后控制点竖向位置与设计初始态偏差值

Table 4. Deviation of the control point’s vertical position after force finding from that in the initial state of design mm

节点编号	划分为 1 个单元	划分为 3 个单元
B	0.028	0.047
C	0.028	0.047
D	0.104	0.085
E	0.104	0.085
F	0.031	0.025
G	0.031	0.025

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表 5 找力分析结果对比

Table 5. Comparison of force-finding analysis results

索杆编号	节点编号	不考虑重力影响/kN	考虑重力影响				偏差3/%
索杆编号	节点编号	不考虑重力影响/kN	划分为 1 个单元/kN	偏差1/%	划分为 3 个单元/kN	偏差2/%	偏差3/%
JS1	D	435.33	435.35	0.00	435.19	−0.03	−0.04
JS1	F	435.33	435.35	0.00	435.45	0.03	0.02
JS2	B	715.09	735.73	2.89	735.40	2.84	−0.04
JS2	D	715.09	735.73	2.89	735.97	2.92	0.03
JS3	A	1 491.26	1 619.21	8.58	1 618.81	8.55	−0.02
JS3	B	1 491.26	1 619.21	8.58	1 619.46	8.60	0.02
XS3	D	275.75	296.43	7.50	296.56	7.55	0.04
XS3	G	275.75	296.43	7.50	296.28	7.45	−0.05
XS2	B	764.02	870.19	13.90	870.42	13.93	0.03
XS2	E	764.02	870.19	13.90	869.90	13.86	−0.03
XS1	A	1 000.39	1 193.29	19.28	1 193.83	19.34	0.05
XS1	C	1 000.39	1 193.29	19.28	1 192.67	19.22	−0.05
HS2	E	1 451.14	1 652.77	13.89	1 652.73	13.89	0.00
HS2	E₁	1 451.14	1 652.77	13.89	1 652.73	13.89	0.00
HS1	C	1 818.41	2 169.04	19.28	2 168.97	19.28	0.00
HS1	C₁	1 818.41	2 169.04	19.28	2 168.97	19.28	0.00
SLH	F	833.49	833.50	0.00	833.46	0.00	0.00
SLH	F₁	833.49	833.50	0.00	833.46	0.00	0.00
XLH	G	520.93	559.98	7.50	559.97	7.49	0.00
XLH	G₁	520.93	559.98	7.50	559.97	7.49	0.00
YG1		−338.83	−392.08	−15.72	−392.08	−15.72	0.00
YG2		−140.23	−153.91	−9.76	−153.91	−9.76	0.00
YG3		−57.53	−59.82	−3.98	−59.82	−3.98	0.00
注：偏差1、2 分别表示将每根索段划分为 1 和 3 个单元时，考虑重力影响的找力分析结果与不考虑重力影响的找力分　析结果之间的偏差；偏差 3 表示将每根索段划分为 1 及 3 个单元时，考虑重力影响的找力分析结果之间的偏差；E₁、　C₁、F₁、G₁分别为水平构件 HS2、HS1、SLH、XLH 的另一端.

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