Zhuo et al. / J Zhejiang Univ Sci A 2008 9(9):1201-1207 1201 Journal of Zhejiang University SCIENCE A ISSN 1673-565X (Print); ISSN 1862-1775 (Online) www.zju.edu.cn/jzus; www.springerlink.com E-mail: [email protected] Tensile force correction calculation method * for prestressed construction of tension structures Xin ZHUO†1, Guo-fa ZHANG1, Koichiro ISHIKAWA2, Dao-an LOU3 (1Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China) (2Department of Architecture and Civil Engineering, Fukui University, Fukui 910-8507, Japan) (3Zhejiang Zhancheng Construction Group Co., Ltd., Hangzhou 310005, China) †E-mail: [email protected] Received Nov. 27, 2007; revision accepted June 2, 2008 Abstract: Factors such as errors during the fabrication or construction of structural components and errors of calculation as- sumption or calculation methods, are very likely to cause serious deviation of many strings’ actual prestressing forces from the designed values during tension structure construction or service period, and further to threaten the safety and reliability of the structure. Aiming at relatively large errors of the prestressing force of strings in a tension structure construction or service period, this paper proposes a new finite element method (FEM), the “tensile force correction calculation method”. Based on the measured prestressing forces of the strings, this new method applies the structure from the zero prestressing force status approach to the measured prestressing force status for the first phase, and from the measured prestressing force status approach to the designed prestressing force status for the second phase. The construction tensile force correction value for each string can be obtained by multi-iteration with FEM. Using the results of calculation, the strings’ tensile force correction by group and in batch will be methodic, simple and accurate. This new calculation method can be applied to the prestressed correction construction simulation analysis for tension structures. Key words: Tension structures, Prestressed construction, High precision doi:10.1631/jzus.A0720090 Document code: A CLC number: TU3; TU7 INTRODUCTION ago. Some studies put emphasis on investigation of experiments (Tagawa et al., 1994; Yamagata et al., Tension structures, such as prestressed spatial 1994; Kawaguchi and Abe, 1999; Miyasato et al., grid structures and suspend-dome, etc., combine the 1999). Some studies focus on the analysis theories rigid beams or rods with the flexible strings. The and the calculation methods (Saiton et al., 2001; structural efficiencies of such new types of structural Dong et al., 2003; Zhuo and Ishikawa, 2004; Zhuo systems are enhanced because the structural rigidity is and Yuan, 2004; Zhuo et al., 2004; Lu and Shen, increased and the distribution of forces in the whole 2005). The key for constructing tension structures is structure is improved by the string’s prestressing the prestressed construction of many strings. It is force. Scholars have studied the analysis theories and unable to calculate accurately the string’s prestressing calculation methods for this structure system (Saiton force of tension structures in the structural design or et al., 1993; Kawaguchi et al., 1993; Chen and Li, construction simulation analysis, because such 2005; Zhang et al., 2004; 2005). However, the re- non-ideal factors as the errors of calculation assump- search topics concerning the mechanics analysis in tion or calculation methods, the errors of fabrication the course of construction were just begun a few years or construction of structural components, the effects of construction or temperature loads, and the effects * Project (No. 50678157) supported by the National Natural Science of the material deformation or friction of structural Foundation of China components, etc., are unavoidable. These non-ideal 1202 Zhuo et al. / J Zhejiang Univ Sci A 2008 9(9):1201-1207 factors are very likely to cause the actual prestressing analysis is started at the “zero prestressing force forces of many strings deviating seriously from the status” of the structure, and ended at the “measured designed values during a tension structure construc- prestressing force status” of the structure with tion course or service period, and thus the safety and prestressing force errors. The subsistent tensile force reliability of the structure would be threaten. In order calculation values of each string are forced to meet to achieve high precision control of the prestressing the measured values through structural finite element forces of the tension structure, the work of construc- analysis. In the second phase, the starting point of tion correction is absolutely necessary. analysis is the “measured prestressing force status”, The mechanics analysis of tension structures in and the ending point is the ideal “designed the course of construction has been a hot research prestressing force status” of the structure. The error topic in recent years. Research has basically solved status continuously approaches and finally reaches the issue of mechanics analysis and calculation the ideal status through structural analysis and cal- method of tension structures in the course of intro- culation, so the construction tension correction values ducing initial prestressing forces construction (Saiton of each string could be obtained. et al., 2001; Dong et al., 2003; Zhuo and Ishikawa, The traditional concept of prestressing force 2004; Zhuo and Yuan, 2004; Zhuo et al., 2004; Lu and should be changed and fractionized, because the Shen, 2005), but not the issue of analysis and calcu- construction correction of string’s prestressing forces lation method of high precision controlling of in a tension structure includes the factors of time and prestressing forces for tension structures based on space. Assume n groups of strings in a tension struc- measured data during construction or service period. ture tensioned in n batches. The parameters are de- Aiming at the tension structures with big errors in fined as follows: (1) construction control tensile force j prestressing force during construction or service pe- Ti (k,m)—the prestressing force construction control- riod, a new calculation method, so-called “tensile ling value of the ith string in the jth batch tensioning j force correction calculation method”, is put forward construction; (2) subsistent tensile force Fi (k,m)— in this paper. Based on the values of the strings’ the prestressing force value of the ith string in the jth measured prestressing forces, the tensile force cor- batch tensioning construction; (3) target tensile force rection value, which means the string’s tensile force Pi(m)—in the first analysis phase, it is the prestressing control values in actual construction correction of force measured value of the ith string after the struc- each string, can be obtained by this calculation ture construction completed or in the service period; method. The calculation results showed that the in the second analysis phase, it is the prestressing string’s tensile force correction construction work by force value of the ith string which should meet, i.e., group and in batch is methodic, simple and accurate. the prestressing force design value of the string. Where m is the step of analysis phase, m=1, 2; k is the step of iteration, k=1, 2, 3, …; i refers to the ith string, PRINCIPLE OF TENSILE FORCE CORRECTION i=1, 2, 3, …, n; j is the tension construction sequence CALCULATION METHOD number, j=1, 2, 3, …, n. The tensile force correction calculation uses the Many strings’ measured prestressing forces in a iteration approximation methods. The second phase tension structure have large errors, and should be analysis is carried out after the first phase. The cal- carried out by group and in batch construction cor- culation principles and methods of the two analysis rection method. Here, the group, as a space parameter, phases are basically the same. The analysis methods refers to some strings tensioned at the same time, and and the calculation procedures could be summarized the batch, as a time parameter, refers to the sequence as follows: of the strings tensioned. The groups and the batches (1) For the first iteration, the structural geomet- should be decided on the distribution of the strings in rical nonlinear finite element method (FEM) analysis the structure and the actual construction conditions. is performed in terms of the construction tensioning The prestressed construction correction analysis sequence. When calculating the strings of the jth is divided into two phases. In the first phase, the group in the ith batch of tensioning, the construction Zhuo et al. / J Zhejiang Univ Sci A 2008 9(9):1201-1207 1203 control tensile forces of strings are forced to be equal correction tensioning method by group and in batch. j to the target tensile forces, i.e., Ti (1,m)= Pi(m), and This is the final target of the calculation method in j the subsistent tensile forces Fi (1,m) of other strings this paper as well as the high precision control of which have been tensioned in structure are calculated prestressed construction for tension structures. at the same time. All of the subsistent tensile forces of Calculating construction control tensile each batch of strings have changed except that of the j force Ti (k,m) last batch strings when calculating the nth group of the last batch of the strings. The value of tension force j j change of each group of strings is ΔFi (2,m)=Ti (1,m)− Calculating the strings of the jth group in the ith batch j Fi (1,m). of tensioning (2) For the second iteration, the construction control tensile force value of each group of strings in the first iteration is modified by compensating the Calculating value of tension force change of each group of strings ΔF j(k,m) value of tension change. The construction control i tensile force of the strings in the second iteration is j j j Ti (2,m)=Ti (1,m)+ΔFi (2,m).