Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 9324520, 11 pages

https://doi.org/10.1155/2017/9324520

## Experimental and Analytical Investigation of Deformations and Stress Distribution in Steel Bands of a Two-Span Stress-Ribbon Pedestrian Bridge

^{1}Department of Bridges and Special Structures, Vilnius Gediminas Technical University (VGTU), LT-10223 Vilnius, Lithuania^{2}Research Laboratory of Innovative Building Structures, VGTU, LT-10223 Vilnius, Lithuania

Correspondence should be addressed to V. Gribniak; tl.utgv@kainbirg.rotkiv

Received 1 February 2017; Revised 9 April 2017; Accepted 30 April 2017; Published 29 May 2017

Academic Editor: Fabrizio Greco

Copyright © 2017 G. Sandovic et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The article is dedicated to the analysis of problems related to design of pedestrian bridges with flexible ribbon bands made of steel. The study is based on test results of a bridge model that has two spans (each with a length of five meters). A simplified analytical technique has been proposed for predicting vertical deformations of the bridge structure subjected to symmetrical or asymmetrical loading patterns. The technique also allows assessing the tension forces in the ribbons, which are very important for design of such structures. The analysis reveals the importance of the flexural rigidity of the ribbons that might cause significant redistribution of stresses within the steel bands.

#### 1. Introduction

Monumental engineering structures, particularly bridges, are omnipresent in every society, regardless of culture, religion, geographical location, and economic development [1, 2]. The stress-ribbon structural scheme can be considered as one of the most efficient for pedestrian bridges [3–5]. A deck (often prestressed concrete slabs) with a catenary shape forms the stress-ribbon structure. The load-bearing structure consists of slightly sagging cables (tensioned bands), bedded in a thin slab. The traffic is often placed directly on the slab embedding the cables. Compared with other structural types, the stress-ribbon system can be considered extremely simple though requiring massive anchorage blocks due to very large tensile stresses induced in the cables. The smooth curved shape of the bridge is well tailored to the environment: the height of the bridge girder is the smallest among all known bridge types [1, 3]. Three common structural schemes exist for the stress-ribbon bridges [1, 3, 6–8]: prefabricated concrete slabs suspended on steel cables, prestressed concrete structures, and steel band systems. Due to the specific static and dynamic characteristics, these constructions are mainly used for pedestrian and bicycle traffic [3, 7, 8].

Stress-ribbon bridges are often constructed by using a multispan layout that is a consequence of exploitation conditions [1, 3, 6]. To avoid stress concentrations, connection joints of the ribbons are constructed as flexible hinges [1, 8, 9]. The structural behaviour of such bridges, however, is complicated due to the movement (horizontal displacement) of intermediate supports under traffic load [10, 11]. An ideally flexible ribbon is also just a theoretical assumption [12, 13]. To ensure the adequacy of analytical predictions, these nonlinear effects must be included into mathematical models [9, 10, 14].

The first experimental studies of stress-ribbon bridge models were carried out in the Czech Republic and Germany [3, 7, 14–16]. In this context, a scaled model of a combined (supported arch) bridge over Radbuza river (Czech Republic) should be mentioned. The model (scale 1 : 10, span length 10.35 m) was constructed by using a steel pipe as a bearing component [14]. A multispan prestressed concrete bridge model was also tested in the Czech Republic [3]. The first bridge with ribbons made of carbon fibre reinforced polymer sheets was constructed in TU Berlin (Germany) in 2007. It had 13 m span [16].

Notwithstanding the current experimental and analytical studies, the behaviour of bridges with ribbons made of steel bands has not been fully explored [7]. The lack of clarity is mainly related to the absence of experimental studies related to the structural behaviour of multispan bridges of such structure. Besides, the frequently neglected flexural stiffness of the ribbons might be important to ensure adequate assessment of the stress distribution [12]. Therefore, the current research is dedicated to the deformation analysis of a two-span pedestrian bridge with flexible steel ribbon bands and a total length of 10 m. A simplified analytical technique is proposed for predicting vertical deformations of the bridge structure subjected to symmetrical and asymmetrical loads. To simplify the iterative calculations, the elastic and kinematic deformation components are separated. The predictions are validated against test data of the bridge.

#### 2. Analytical Technique for Deformation Analysis of the Two-Span Bridge

##### 2.1. Assumptions

The ribbon bands are the main components of the considered bridge. The deformation state of the ribbon bands is described by kinematic and elastic components. The behaviour of the ribbon is assumed to be geometrically nonlinear. The flexural stiffness of the band is completely neglected (i.e.,* EI* = 0). A second-order parabolic shape describes the deformations of the strip subjected to the dead load. The effect of horizontal movement of the supports and the initial deformation state (sagging in the middle of a span) of the ribbons are accounted for as well.

##### 2.2. Symmetrical Loading

The calculation scheme is presented in Figure 1. The vertical displacements of the strips, the horizontal displacements of the supports, and the tension forces in the bands are the unknowns. The length of the leftmost strip due to the elastic deformation can be calculated by the following formula [17–19]: where is the sag of the leftmost ribbon; is the vertical displacement of the middle point of the leftmost ribbon; is the span; is the horizontal displacement of the leftmost support; is the displacement of the middle support. Taking an expression of the length of the unloaded strip into account, (1) can be rearranged as where the tension (thrust) forces in the leftmost strip due to the complex action of the distributed dead and live loads can be expressed as while the thrust force associated with the effect of the dead load can be obtained from the following: Here* EA* is the axial stiffness of the band; is the effective (live) load.