基于影响矩阵的桁架结构预应力损失识别方法

刘艳辉; 张阳阳; 刘军校; 任鹏; 卓彪

doi:10.3969/j.issn.0258-2724.20180107

基于影响矩阵的桁架结构预应力损失识别方法

doi: 10.3969/j.issn.0258-2724.20180107

基金项目: 国家重点研究课题（2016YFC0802205-9）；国家自然科学基金资助项目（51378427）

详细信息

作者简介:
刘艳辉（1969—），女，副教授，研究方向为混凝土结构设计理论，E-mail：yhliu@swjtu.edu.cn

中图分类号: TU378.6
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- 文章访问数: 466
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- 被引次数: 0
出版历程
- 收稿日期: 2018-03-18
- 修回日期: 2018-10-15
- 网络出版日期: 2019-05-30
- 刊出日期: 2019-10-01

Prestress Loss Identification Method Based on Influence Matrix in Truss Structure

摘要

摘要: 为计算出每束预应力钢束实时的预应力损失，依据预应力桁架结构观测变形，基于位移影响矩阵原理提出一种预应力损失识别方法. 通过有限元分析，建立预应力损失值与桁架结构观测点位移值之间的关系方程，并依据极小值优化原理，获得预应力损失值. 研究表明：当单位预应力损失取30%～50%时，得到的位移影响矩阵计算预应力损失时误差最小，约为1%～2%；三角形桁架1/4跨度和3/4跨度处位移观测点对预应力损失的敏感性最高. 最后，以黔渝线上某高铁站房的大跨钢筋预应力桁架结构为例，验证了该方法的正确性.
- 桁架结构 /
- 结构变形 /
- 位移影响矩阵 /
- 预应力损失计算
Abstract: In order to calculate the real-time prestress loss of prestressed strands according to the observed deformation of prestressed truss structure, a prestress loss identification method based on displacement influence matrix is proposed. By finite element analysis, the relationship between the prestress loss and displacement of the observation point on the truss structure is formulated. Moreover, according to the minimum principle, the prestress loss is obtained. The results show that when the unit prestress loss ranges between 30% and 50%, there is minimum error around 1%–2% in calculating prestress loss with displacement influence matrix; the displacement observation point is most sensitive to prestress loss, when it is located at the 1/4 span and 3/4 span of the truss. Finally, by taking an example of the long-span prestressed truss structure near a high-speed railway station on the Qian-Yu line, the accuracy of the method is verified.
- truss Structure /
- structural deformation /
- displacement influence matrix /
- prestress loss calculation

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图 1 预应力损失计算流程

Figure 1. Flow chart of prestress loss calculation

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图 2 桁架结构一详图

Figure 2. No.1 Truss structure diagram

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图 3 桁架一腹杆截面详图

Figure 3. No.1 truss web member sections

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图 4 桁架一观测点位置

Figure 4. Locations of No.1 truss observation points

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图 5 桁架一预应力损失引起观测点位移变化

Figure 5. Displacement variations of No.1 truss observation points due to prestress loss

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图 6 桁架二详图

Figure 6. No.2 Truss structure diagram

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图 7 桁架二腹杆截面详图

Figure 7. No.2 Truss web member sections

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图 8 桁架二预应力损失引起观测点位移变化值

Figure 8. Displacement variations of observation points on No.2 truss due to prestress loss

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图 9 C40混凝土徐变系数和收缩应变

Figure 9. C40 concrete creep coefficient and shrinkage strain

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图 10 桁架观测点位置

Figure 10. Locations of truss observation points

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表 1 精确度验算1（单位预应力损失取10%）

Table 1. Checking calculation of accuracy with unit prestress loss of 10%

假设预应力损失	反算预应力损失	相对误差	假设预应力损失	反算预应力损失	相对误差	假设预应力损失	反算预应力损失	相对误差
6.00	5.65	5.91	15.00	13.90	7.35	30.00	27.64	7.86
7.00	6.85	2.20	20.00	19.52	2.39	50.00	48.92	2.16
8.00	7.35	8.15	30.00	28.19	6.04	40.00	36.57	8.57
9.00	8.92	0.92	20.00	19.75	1.27	30.00	29.49	1.71
10.00	9.84	1.62	15.00	14.40	3.98	20.00	18.63	6.85

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表 2 精确度验算2（单位预应力损失取30%）

Table 2. Checking calculation of accuracy with unit prestress loss of 30%

假设预应力损失	反算预应力损失	相对误差	假设预应力损失	反算预应力损失	相对误差	假设预应力损失	反算预应力损失	相对误差
6.00	5.96	0.62	15.00	14.81	1.25	30.00	29.65	1.15
7.00	6.98	0.21	20.00	19.93	0.37	50.00	49.85	0.31
8.00	8.09	1.18	30.00	29.81	0.64	40.00	39.67	0.83
9.00	8.98	0.28	20.00	19.93	0.36	30.00	29.90	0.34
10.00	10.04	0.40	15.00	14.97	0.21	20.00	19.75	1.24

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表 3 精确度验算3（单位预应力损失取50%）

Table 3. Checking calculation of accuracy with unit prestress loss of 50%

假设预应力损失	反算预应力损失	相对误差	假设预应力损失	计算预应力损失	相对误差	假设预应力损失	反算预应力损失	相对误差
6.00	5.95	0.85	15.00	14.85	1.00	30.00	29.71	0.96
7.00	6.97	0.37	20.00	19.94	0.32	50.00	49.86	0.28
8.00	8.01	0.11	30.00	29.76	0.79	40.00	39.48	1.30
9.00	8.99	0.14	20.00	19.97	0.17	30.00	29.96	0.13
10.00	10.06	0.64	15.00	15.05	0.34	20.00	19.87	0.64

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表 4 精确度验算4（单位预应力损失取100%）

Table 4. Checking calculation of accuracy with unit prestress loss of 100%

假设预应力损失	反算预应力损失	相对误差	假设预应力损失	反算预应力损失	相对误差	假设预应力损失	反算预应力损失	相对误差
6.00	6.14	2.34	15.00	15.36	2.42	30.00	30.67	2.23
7.00	6.89	1.54	20.00	19.71	1.43	50.00	49.22	1.57
8.00	8.06	0.81	30.00	29.92	0.28	40.00	39.67	0.83
9.00	8.87	1.49	20.00	19.70	1.51	30.00	29.54	1.53
10.00	10.12	1.20	15.00	15.16	1.06	20.00	20.01	0.03

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表 5 观测点位移数据计算值

Table 5. Calculation results of observation point displacement

观测点	各组预应力无损失时	钢束组1预应力损失	钢束组2预应力损失	钢束组3预应力损失	钢束组4预应力损失	钢束组5预应力损失
1	7.009	6.775	7.475	6.878	6.993	7.000
2	11.980	11.664	12.252	12.044	11.932	11.949
3	12.331	12.030	12.443	12.364	13.012	12.270
4	3.521	3.341	4.055	3.456	3.508	3.516
5	9.930	9.619	10.332	10.024	9.911	9.908
6	11.010	10.695	11.207	11.062	12.068	10.967
7	10.100	9.868	10.177	10.123	10.556	10.308

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表 6 预应力损失识别系数计算

Table 6. Identification coefficients of prestress loss

项目	σ_%
项目	10%	20%	25%	20%	30%
理论值	0.333 3	0.666 6	0.833 3	0.660 0	1.000 0
计算值	0.334 6	0.667 0	0.837 0	0.666 4	0.998 3

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