Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (1): 217-224.doi: 10.13229/j.cnki.jdxbgxb20190867

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Analytical method for elongation of stayed-cable with catenary configuration

De-shan SHAN(),Xiao ZHANG,Xiao-yu GU,Qiao LI   

  1. School of Civil Engineering，Southwest Jiaotong University，Chengdu 610031，China
  • Received:2019-09-05 Online:2021-01-01 Published:2021-01-20

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Abstract:

In order to meet the requirements of unstressed length and elongation control for stay cable during its installation， the analytical method for calculating the elongation of the stay cable with catenary configuration is discussed. First， the geometric equation of the stay cable with catenary configuration is obtained by applying the force equilibrium condition to the stay cable， and the analytical expressions of the cable length and its elongation under a certain given cable tension are acquired by direct integration. Moreover， the analytical expressions of the cable elongation under varying cable tension are obtained by using the deformation coordination condition. Then， the equivalent elastic modulus for stay cable with catenary configuration is discussed based on strain equivalence. It is verified that the equivalent elastic modulus for the stay cable with catenary configuration can be simplified to the equivalent elastic modulus for the stay cable with parabolic configuration. Taking the real parameters of the stay cables of a certain cable-stayed bridge with composite/hybrid girder as the case study， the analytical expressions of stay cable length and its corresponding elongation under a given cable tension are verified by numerical integration and simplified formulas respectively. Furthermore， the analytical expressions for the elongation of stay cable with varying cable tension are verified by the Nlabs finite element and equivalent elastic modulus method. The results show that the proposed analytical expressions can simply and directly figure out the exact elongation of stay cable， which provide the theory and straight forward method for the unstressed length of stay cable and the elongation control of stay cable during its installation.

Key words: civil engineering, stay cable, catenary configuration, elongation, parabolic configuration

CLC Number: 

  • U448

Fig.1

Coordinate system of stay cable"

Fig.2

Stay cable deformation under cable tensions TN1and TN2"

Fig.3

Surrogate straight rod with equivalent elastic modulus"

Fig.4

Approximate calculation of Esec for initial tension of stay cable"

Fig.5

Number of stay cable"

Table 1

Parameters of stay cables"

索号钢束规格索长/m索号钢束规格索长/m
ZN1M250?4395.218BN1M250?4395.740
ZN2M250?37102.747BN2M250?37103.637
ZN3M250?37110.259BN3M250?37111.484
ZN4M250?37118.312BN4M250?37119.840
ZN5M250?43126.783BN5M250?43128.574
ZN6M250?43135.787BN6M250?43137.801
ZN7M250?43146.672BN7M250?50148.888
ZN8M250?50157.413BN8M250?50159.813
ZN9M250?50168.569BN9M250?55171.135
ZN10M250?50180.101BN10M250?55182.817
ZN11M250?55191.881BN11M250?55194.731
ZN12M250?61203.900BN12M250?55206.865
ZN13M250?61216.121BN13M250?61219.185
ZN14M250?61228.512BN14M250?61231.650
ZN15M250?73241.047BN15M250?61244.267
ZN16M250?73253.706BN16M250?61256.987
ZN17M250?73266.474BN17M250?73269.806
ZN18M250?73279.331BN18M250?73282.707
ZN19M250?73292.271BN19M250?85296.683
ZN20M250?73305.283BN20M250?85308.723
ZN21M250?85318.358BN21M250?85313.023
ZS1M250?3791.274BS1M250?5596.099
ZS2M250?3799.436BS2M250?55103.565
ZS3M250?37107.445BS3M250?55110.055
ZS4M250?37115.793BS4M250?55116.216
ZS5M250?43124.395BS5M250?61122.024
ZS6M250?43133.479BS6M250?61127.999
ZS7M250?43144.144BS7M250?61135.001
ZS8M250?50154.718BS8M250?61141.864
ZS9M250-50165.734BS9M250?73149.004
ZS10M250?50177.157BS10M250?73156.412
ZS11M250?55188.836BS11M250?73164.000
ZS12M250?55200.770BS12M250?73171.770
ZS13M250?55212.918BS13M250?73179.732
ZS14M250?61225.246BS14M250?73187.799
ZS15M250?61237.727BS15M250?73196.987
ZS16M250?61250.338BS16M250?73204.283
ZS17M250?73263.062BS17M250?73212.623
ZS18M250?73275.885BS18M250?73221.184
ZS19M250?73288.792BS19M250?85229.732
ZS20M250?73301.775BS20M250?85238.348

Fig.6

Comparison of third tensile elongation of cable by different algorithms（unit: mm）"

Fig.7

Comparison of second tensile elongation increment of cable（unit:mm）"

Fig.8

Comparison of third tensile elongation increment of cable（unit:mm）"

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