Estimation of cables’ tension of cable-stayed footbridge using measured natural frequencies

MATEC Web of Conferences, Jan 2017

This paper presents analysis of cables’ tension of steel cable-stayed footbridge using their field-test natural frequencies. A vibration method is usually used for the measured cable tension during the construction of cable systems stiffened with inclined cables. Practical formulas for the vibration method applied herein, mainly based on cable-sag and vertical angle effects (a survey measurement), have been verified on the one-tower steel cable-stayed bridge. The bridge is situated in Sieradz (Poland) and it was the structure with the longest span concerning all the cable-stayed bridges in Poland until 1999. The obtained cable axial forces for estimated natural frequencies of low- and high-order modes are verified using FEM models. The final conclusions drawn on the basis of conducted studies can be useful for technical diagnosis, monitoring programs and repair works of similar class of cable-stayed bridges.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://www.matec-conferences.org/articles/matecconf/pdf/2017/21/matecconf_dyn2017_00006.pdf

Estimation of cables’ tension of cable-stayed footbridge using measured natural frequencies

MAT EC Web of Conferences Estimation of cables' tension of cable-stayed footbridge using measured natural frequencies Przemysław Jakiel 1 Zbigniew Mańko 0 0 International University of Logistic and Transport , Soltysowicka, No. 19B, 51-168 Wrocław , Poland 1 Opole University of Technology , Katowicka Street, No 48, 45-061 Opole , Poland This paper presents analysis of cables' tension of steel cablestayed footbridge using their field-test natural frequencies. A vibration method is usually used for the measured cable tension during the construction of cable systems stiffened with inclined cables. Practical formulas for the vibration method applied herein, mainly based on cablesag and vertical angle effects (a survey measurement), have been verified on the one-tower steel cable-stayed bridge. The bridge is situated in Sieradz (Poland) and it was the structure with the longest span concerning all the cable-stayed bridges in Poland until 1999. The obtained cable axial forces for estimated natural frequencies of low- and high-order modes are verified using FEM models. The final conclusions drawn on the basis of conducted studies can be useful for technical diagnosis, monitoring programs and repair works of similar class of cable-stayed bridges. 1 Introduction A knowledge of cable tensions is very important concerning suitable geometry of the cablestayed bridges and it allows to create their detailed calculation models [ 1 ]. The cable axial force can be estimated by the method using measured natural frequencies, which depend not only on axial force but on flexural stiffnes, cable sag and inclination of the cable chord as well. According horizontal cable configuration with relatively small sag the cable tension F we can obtain from well known formula F = A L2f2/g (A - cross section area, - material density, L - length, f – natural frequency, g - gravitational acceleration) applicable for firstorder mode only, but the result may be burden with error concerning longer tendons [ 2 ]. In this paper, verification of the accurate method which allows to estimate the cable axial force using measured its natural frequencies, taking into consideration aforementioned material and geometrical parameters is presented. Considering the very slender tendons, i.e. those that are the structural members in the cable-stayed bridges for instance is difficult to excite the cable artificially to first or secondorder mode oscillation. In this case, one should use the results obtained from stationary vibrations, in which modes of high order are usually dominant. So called vibration method proposed by Zui, Shinke and Namita [ 3 ] is herein briefly described with unification of practical formulas, and applied to the results of natural frequencies obtained from the measurement conducted on a cable-stayed pedestrian bridge in Sieradz (Poland) and the accuracy is confirmed using FEM models [ 4 ]. 2 Short description of footbridge structure The cable-stayed footbridge in Sieradz was built in 1978 for pedestrian traffic and emergency vehicle, e.g. fire engine. The total length of this bridge is 142 m with effective spans equal to 9.12+75.88+3x19.00 m, respectively. The steel superstructure consists of one portal tower, consisted of closed, rectangular cross-section, cable system arranged in harp layout and an orthotropic plate deck (Fig. 1a). Total height of the tower transversally braced in the locations of cable joints is 43.48 m. The cables are fixed to the tower and anchored to the deck. The tower is rigidly fixed to the main girders and supported by the steel hinge bearings situated on a pier P2 (Fig. 1b). LC1 - dead load LC2 - dead and live loads live load C1 C2 C3 A1 P1 P2 P3 P4 A2 CL Asphalt 40 mm Steel deck plate 10 mm 4200/2 b) c) a) The steel deck structure, which is 4.10 m wide, is composed of two I-beams 550 mm main girders, the openwork and plain girder double-tee cross-beams of 525 mm and 250 mm high respectively (Fig. 1c). The cross-beams are alternately spaced: the major ones 7.40 m and the minor ones 1.90 m. The steel plate orthotropic deck consists of 10 mm thick plate and the longitudinal stiffening ribs (12×200). The plate deck is directly topped with a 50 mm thick layer of asphalt [ 5 ]. The cables are made of helical wires closed by the z-profile wires in the cross-section in diameter of 48 mm. A peculiar feature of this bridge are the rocker bearings at each support except the pier P2, which enable limited longitudinal and vertical displacements of the spans at their supports. 3 Vibration method’s formula A simplified algorithm of presented herein the vibration method is used for free-oscilation frequencies of the cable with its span length denoted as L, sag d and angle of cable inclination α (Fig. 2a) [ 3 ]. Introducing a dimensionless parameter (1): L F / EJ , (1) DYN-WIND'2017 where EJ is flexural rigidity of cable, the range of application of the method is specified as any region (...truncated)


This is a preview of a remote PDF: https://www.matec-conferences.org/articles/matecconf/pdf/2017/21/matecconf_dyn2017_00006.pdf

Przemysław Jakiel, Zbigniew Mańko. Estimation of cables’ tension of cable-stayed footbridge using measured natural frequencies, MATEC Web of Conferences, 2017, 107, DOI: 10.1051/matecconf/201710700006