Optimization of hanger inclination in a tied arch bridge

7/26/2019 Optimization of hanger inclination in a tied arch bridge

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2ndConference for PhD students in Civil Engineering

CE-PhD 2014, 10-13 December 2014,Cluj-Napoca, Romaniawww.cephd.ro

Optimization of hanger inclination for a tied-arch bridge

VLAD Mihai*1, GAVRIL Kollo*2

1,2 Technical University of Cluj-Napoca, Faculty of Civil Engineering. 15 C Daicoviciu Str., 400020, Cluj-

Napoca, Romania

Abstract

This paper is based on the study of alternatives to determine the best hanger arrangement for a

road tied-arch bridge. In this paper are analyzed several hanger configurations. For each case it

was performed a first order static analysis, using load models according to EN 1991-2. Theanalysis was performed with an automatic calculation program for structures, thus determining the

strain and state of efforts in each case studied. Following preliminary dimensioning of sections we

need to determine the optimum hanger configuration which is the most economical. The question

that comes when designing a tied arch bridge considering all the financial constraints is: How does

the number of hangers and their angle influence the distribution of efforts in tied-arch bridges?

Keywords:Tied-arch bridge, hangers, efforts, tension.

1. Introduction

One of the main feature of the arch bridge is the transmition of external forces to arch ends.When arches are situated under the deck, these external forces are transmitted directly to the land,

imposing land with high load capacity and high costs of foundations. Tied-arch bridges, use the

deck to take the role as the tension member taking the forces generated in the ends. In general, arch

bridges are suitable for openings between 70-200 meters distance range where other type of bridges

require large sections or other support systems such as stay cables.

The most common functions for determining the arch shape are the parabola and catenary

arc. For concrete arches, where self weight is the determining factor, the best solution is to define a

catenary arch. For steel arches where superimposed dead loads are determinants it is recommended

to define a parabolic arch.

The large number of possibilities that can be adopted in arch bridges, such as bridges with

the deck above, underneath or in between the arches, offers designers the possibility to adapt to the

conditions imposed by landscape. Is an efficient solution for crossing medium spans.

This paper aims to identify the optimal arrangements of hangers for a tied arch bridge with

respect to all the variables such as: efforts in arches, ties and hangers.

Depending on the inclination of hangers, tied arch bridges are classified as:

With vertical hangers

With inclined hangers

Depending on the stiffness of the suspensions can be:

With rigid hangers

Vlad Mihai: Tel./ Fax.: +40 747 608 995E-mail address: [email protected]


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With elastic hangers

The tied arch bridges appear in different hanger layouts. The general layout of the hangershave been greatly improved with the development of modern computing technology. Understanding

of the behavior of structures with large number of static indeterminacy was conditioned by thedevelopment of computers. Three main layouts are presented further: The Langer system, theNielsen Sistem and the Network configuration system.

Langer system requires a deck with high rigidity, who plays the role of a tie for the flexiblearches. The deck is suspended by vertical hangers.

Nielsen system consists of a single rigid beam, reinforced with a system of hangers. In this

system, the hangers are inclined and work as a variable-section truss with rigid bottom

flange. Nielsen system, patented by Danish engineer Octavius F. Nielsen in 1926, was

used in the construction of over 60 bridges at that time.

The network of inclined hangers is an improved version of the Nielsen system, with the

exception that in this case the hangers cross each other at least once. This arrangement of

the hangers determine very slender structures and thus reduced material consumption.

Inclined hanger network system was patented by Professor Per Tveit from Norway in the

1950s, from the study of the distribution of bending moment bridges Nielsen system.

The purpose of this paper is to investigate the influence of different hanger arrangements

using three-dimensional finite element models. For this study the goal was to determine the most

suitable solution for a road bridge over the Somes river , with a span of 100 meters, consisting of

two inclined steel arches, located on a road with two traffic lanes, subjected to medium traffic.

Defining parameters to identify the most effective hanger arrangement requires a complex

process that involves several variables such as cost, aesthetics, efficiency and some of the local

constraints imposed by landscape. Regarding hangers, the demanding criterion is to reduce the

number of the compressed hangers and to reduce the maximum axial force in them.

Fig. 1. Tied arch bridge with Langer configuration of hangers

Fig. 2. Tied arch bridge with Nielsen configuration of hangers

Fig. 3. Tied arch bridge with network configuration of hangers


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2. Case study

The case study is a road bridge with a span of 100 meters, consisting of two circular hollow

section steel arches with a height of 17 meters, inclined inward 15 degrees after tie beam axis,connected by circular hollow section tie-beams (Fig. 4).The slenderness of the arch f/l=0.17. Tie

beams are transversaly connected by means of steel double T section crossbeams positioned at a

equal distantance of 5 meters and arches are connected by circular hollow sections bracings. An

reinforced concrete top slab linked by elastic connectors to the crossbeams completes the composite

deck as shown in Fig. 5.

Hangers were modeled as rigid truss elements to evaluate the first order effects , so that in

cases where hangers appear relaxed, they actually supposed to axial compression. Both links at the

top with arches, and bottom with tie beams are pinned in fork connectors (Fig. 6). Each hanger is

applied an initial unit pretension force. Conditioned by vertical movement of the deck, the tension

must be adjusted properly after aplying the superimposed loads.

Fig. 5. Main Span Cross Section

Fig. 4. Main Span General Layout

Fig. 6. Fork connector


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2.1 First order structural analysis

The bridge was modeled in the finite element analysis software Midas Civil, with all the

elements defined as General Beam elements with the exeception of hangers which were modeled as

truss members. The model was created as a spatial structure.

In this analysis were considered all the loads acording to EN 1991-2 such as selfweight,

superimposed dead loads, wind, braking force, vehicle impact force. For the moving load analysis

were considered loading models according to EN 1991-2. The first model is the Load Model 1 with

the tandem system changing its position throughout all crossbeams that constitute the deck and the

uniformed distribued load (UDL) placed throughout the entire bridge deck. The second model

consideret is Load Model 2, and the third model consideret is Load Model 4.

In Fig. 7 is shown that the closer the hangers are to the arch ends, the lower the tension . In

this configuration there arent any relaxed hangers which mean a well optimized angle of

inclination for the hangers. The tension in hangers are between 1013 kN and 621 kN in the Ultimate

Limit State analysis

As we can see in Fig. 8, the transvers bending moments are considerably higher than arches

or tie beams bending moments. This indicate a good distribution of efforts along the arches and tie

beams, which are mostly subjected to compression and tension. The maximum bending moment in

the arch in Ultimate Limit State analysis is only 765 kNm. The tie beams are subjected to higher

bending moments than the arches, with a maximum of 1545 kNm. The bending moments in cross

beams are more than three times higher than bending moments in arches with a maximum of 2487

kNm.

Fig. 7. Axial force in hangers in Ultimate Limit State analysis

Fig. 8. Bending moments in Ultimate Limit State analysis


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In Fig. 9 shows that compression is uniformly distributed along the arches an tension is also

uniformly distributed along the tie beams. Small variations can be seen determined by the distance

between the anchor location of the hangers. The maximum compression in arches in Ultimate Limit

State is 9510 kN and the maximum tension in tie beams is 7930 kN.

The maximum displacement in Service Limit State is 0.126 centimeters, value which is

under the recommended by EUROCODE ratio L/750.

2.2 Data analysis

In the network tied system the inclined hangers cross each other at least twice. In general

this type of arrangement lead to lower consumption of materials and slender structures. In Langer

system the assimetric load produce considerable deformations in both arches and tie beams ,while

using the inclined system with variable slope, cosiderable deformations only occur in the tie beam

which means a this system provides a better distribution of efforts in the arch.

Favorable behavior of this system is due to the rigidity of the network of hangers .Thetransverse bending moments determined are greater than the longitudinal bending.

This method follows the same concept as the Nielsen system. Unlike constant inclination

Fig. 9. Axial force in Ultimate Limit State analysis

Fig. 10. Displacements in Ultimate Limit State analysis


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system, in this system the slope of each hanger is variable by a linear function.

An optimization of the "wheel spokes" is documented and Schanack Brunn, who concluded

that if every hanger decomposes in two hangers and the resultant hanger forces is orientated toward

the center of the circle determined by the arch radius. The only variable involved is the angle

between adjacent hangers at their intersection.

Some case studies studied by Per Tveit and offered relevant results helping designers to

understand better this type of structure and made possible an easier approach to designing a

network tied arch bridge.

Maximum axial force in the arch tends to be smaller as the inclination is greater. Bending

moment results from the analysis show that the more inclined hangers, the smaller the bending

moment.

The hanger angle variation does not appear to significantly influence the tie beam axial

force and bending moments along the beam decreases with increasing angle.

Comparing to a vertical hangers system, in this configuration we get a 30% lighter structure.

Fig. 11. Axial force variation in hangers in inclined hanger

system with variable slope depending on the angle variation

Fig. Error! No text of specified style in document.12. Number of

relaxed hangers in inclined hanger system with variable slope

Fig. Error! No text of specified style in document.14. Bending

moment variation in tie beam in inclined hanger system with

variable slope depending on the angle variation

Fig. Error! No text of specified style in document.13 Bending

moment variation in arch in inclined hanger system with

variable slope depending on the angle variation


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3. ConclusionsIn this study, for the opening of 100 m, it can be seen more effective the network system

with inclined hangers than the vertical hanger system. This system provides a better structural

efficiency compared to the configuration with vertical hangers.

Following the analysis we can draw the following conclusions:

The lowest tension in hangersis obtained in vertical hanger configuration. However, this

configuration shows large arch bending and tie beams moments.

The system with inclined hangers is the best solution for this case study. In this

configuration we get the lowest compression and bending moments in beams arches and tie.

Maximum tension of hangers not only affects the ultimate limit state, but play a role in

resistance to fatigue, thus a fatigue analysis should be performed.Buckling length of arch varies depending on the number and position of the hangers. A

comprehensive analysis of the phenomenon should be performed to optimize structural buckling of

the bridge.

4. Acknowledgements

This paper is supported by the Sectorial Operational Programme Human Resources

Development POSDRU/159/1.5/S/137516 financed from the European Social Fund and by the

Romanian Goverment

5. References[1]

. Midas Civil Users Manual.[2] Departament of Civil Engineering of the University of Porto. Jose Miguel, Freitas Castro .

Design of arch bridges.pg 1-94.[3] Delft University of technology. T.J.M. Smit Design and construction of a railway arch bridge with a

network hanger arrangement . Journal of Civil Engineering Research 2013 pg 1-214.

[4]

Tveit P., Optimal design of of Network Arches, Contribution to the IABSE Symposium inMelbourne, Australia, 2002

[5] Tveit P., Preliminary design of network arch road bridges Examples with spans of 135 and 160meters, Internet Edition, Grimstad, Norway, 2003. Retrieved from http://pchome.grm.hia.no/~ptveit/on 03/05/2009

[6]

Tveit P., Preliminary Design of Network arch road bridges, with examples spanning 93 and 120metres. Internet Edition, Grimstad, Norway, 2003. Retrieved from http://pchome.grm.hia.no/~ptveit/on 03/24/2009

Fig. Error! No text of specified style in document.15. Axial

force variation in arch in inclined hanger system with

variable slo e de endin on the an le variation

Fig. Error! No text of specified style in document.16. Axial force

variation in tie beam in inclined hanger system with variable

slope depending on the angle variation


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[7]

Tveit P., Revision of Erection of optimal Network Arches, Grimstad, Norway, 2003. InternetEdition. Retrieved from http://pchome.grm.hia.no/~ptveit/ on 03/24/2009

[8]

European Committee for Standardization, Eurocode 1: Actions on structures Part 2: Trafficloads on bridges. Brussels. 2003.

[9]

European Committee for Standardization, Eurocode: Basis of structural design. Brussels. 2000.[10] European Committee for Standardization, Eurocode 3: Design of steel structures Part 2: Steel

bridges. Brussels. 2006.

Optimization of hanger inclination in a tied arch bridge

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