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PEDESTRIAN BRIDGE OVER RIVER NAUSTA IN NAUSTDAL, NORWAY.

DESIGN OF TWO ALTERNATIVES: SUSPENDED BRIDGE AND STRESS-

RIBBON BRIDGE

Felice ALLIEVI

Structural Engineer

DOF Engineers

Director

f.allievi@dofengineers.com

Teresa CABALLERO ROSELL

Structural Engineer

DOF Engineers

Engineer

t.caballero@dofengineers.com

Fernando IBÁÑEZ CLIMENT

Structural Engineer

DOF Engineers

Director

f.ibanez@dofengineers.com

Gaute MO

Structural Engineer

DOF Engineers

Director

g.mo@dofengineers.com

SUMMARY

This paper summarizes two pedestrian bridge alternatives given for crossing river Nausta and the

Highway 5: a suspended bridge and a stress ribbon bridge. The stress ribbon alternative is 305m

long, with five equal spans of 61m. The overall length of the bridge will make it one of the world’s

longest in its category. The concrete supports have arched shape; the deck is formed by 350mm

deep precast concrete panels with No2 Φ105mm bearing cables and No4 Φ125mm post-

tensioning cables. The bridge, due to slope limitation, has a sag/span ratio of 1/61. The suspension

alternative is 261 m long, with two lateral spans 58.5m long and the central span between towers

144m long. The two Φ125mm catenary cables are curved in plan due to the position of anchorages

in deck and towers. The deck is a composite section suspended by Φ25mm hangers positioned

every 3m. The towers are formed by No 4 columns connected on top and at deck level.

KEY-WORDS: Bridge, Pedestrian, Suspended, Stress-Ribbon, Pre-stressing, Non

Linearity

1. Introduction

Naustdal is a classic U-shaped valley in Norway through which runs Nausta, an approximately

100m wide river. On both sides we find roads: local road in the east and National road 5 in the

west. Further east is mainly residential areas and west of Highway 5 is the village center, with

shops, schools, council offices, sports facilities etc. People need to cross though any of the existing

road bridges, forcing them to deviate 1 kilometer north or south. During floods water occupies the

entire area between the municipal road and highway 5. The bridge over the river is thus necessary

to achieve good communication between residential areas in the east, and the village center in the

west.

The preliminary project has been submitted at this moment, it has been performed in an

interdisciplinary collaboration between Degree of Freedom Engineers and Multiconsult, and based

on the two chosen bridge options from the Conceptual project issued on 2012: a suspended bridge

and a stress ribbon bridge.

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This paper will describe the two alternatives, focusing on the structural behavior of each, the main

challenges that the design team had to face for each, and the solutions proposed.

Figure 1. Naustdal valley looking south Figure 2. Planning area

The Client requested the following main items:

- Modern but not monumental, the bridge shall become an icon for the city of Naustdal;

- Preserve the existing natural park along the river sides.

Norwegian legislation obliges to comply with additional conditions:

- Design life of bridge to be 100 years;

- Deck width is set to 3.5m between inner sides of handrails, as a minimum;

- A minimum clear height must be maintained and verified due to the deflection under the

frequent load combination or from maximum deformations due to temperature, creep &

shrinkage. Over road: The minimum clear height is to be 4.9m. Over water: The maximum

flood level (200 year return period) is at level 1.8m;

- Maximum vertical slope allowed limited to 5%. TEK10 obliges to limit maximum slope to 5%

but allows exceeding up to 8.3% under certain circumstances herein satisfied;

- Along and adjacent the river, on both sides, an area with 3m width should be respected, to

accommodate for pedestrians (e.g. fishermen) passing underneath the bridge;

- Along and adjacent the road, the safety zone is defined in Håndbok 185. Any column/arch

adjacent to Rv5 (road) will be protected with guardrail, hence there is no requirement for

designing any columns/arches for collision load.

Figure 3. Suspended bridge alternative

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Figure 4. Stress-ribbon bridge alternative

2. Suspended Bridge Alternative

2.1. Description of the structure

The bridge will have a total length of 261 m. There are two side spans 58.5m long, plus the central

span between towers 144m long.

Figure 5. Plan and Elevation

Figure 6. Typical section A-A Figure 7. Elevation Detail: tower

The bridge section is a composite deck, formed by a concrete 250mm thick slab and No2 steel

channels on the edges. There are transversal I shape floor beams and a horizontal cross-bracing

formed by steel pipes that are placed at the bottom flanges level, aiding in increasing significantly

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the torsional stiffness of the deck whilst allowing for simple connections of longitudinal profiles,

since those are open. The towers are made by No4 rectangular tapered box sections. There are

No2 suspension cables running from abutments sides to the tower top, creating a curved geometry

both in plan and elevation.

2.2. Design criteria

2.2.1. Materials

For the abutments and foundations it has been used concrete B45 with reinforcing steel B500NC.

Regarding the steel elements, for the plates it has been used steel S355N, S355J2 for the hot

rolled sections and S355H for the structural hollow sections. The cables used in the design of the

bridge are Bridon Locked coil strand LC.

2.2.2. Loads

It has been considered a superimposed dead load for the 50mm finish brushed mortar pavement of

1.25kN/m2, and the handrail is 0.60kN/m (each one). Regarding the traffic, when the loaded spans

are long the code allows for a reduction so that the final uniform load is 3kN/m2. The loads on the

pedestrian parapets are 1.5kN/m, whether vertical or horizontal. No snow loads are considered

because they are smaller than traffic loads. The wind on deck loads are 1.8kN/m in the direction

transverse to bridge deck, 0.9kN/m in the longitudinal direction and ±1.25·b kN/m in the vertical

direction. Finally, the uniform temperature variations are 39.4ºC for expansion and 38ºC for

contraction.

2.3. Description of the FE model

The bridge has been modeled with frame elements. The model is built so that non-linear behavior

of the cables is considered.

Figure 8. FE model: overall 3D view and Tower detail

In order to simplify the model, the deck frames have been assigned a steel box section with

dimensions 4000x1000mm and 14mm thickness; the mechanical properties of this section are

modified to match the actual bridge deck section properties, in particular the torsional stiffness. In

order to obtain the modifying factors for these properties, we have created auxiliary cantilever FE

models subject to the same point loads and moment at their ends: one of them with the box section

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used in the model, and the other with the actual composite deck section. The factors are obtained

by comparing the resultant displacements and rotations for the same loads on those models.

The deck allows for longitudinal movement UX at both ends, but it is fully fixed to the tower

columns.

The towers consist of 4 inclined legs; their top ends meet at the location where catenary cables are

supported. The columns cross section are steel squared hollow sections, dimensions vary from

400x400mm in the top and bottom ends to 600x600mm as shown in figure 8. The 4 columns of

each tower are simply supported at their base.

The cables have been modeled also as frames with actual cross sections given by the

manufacturer for LC-125 (main cables) and for LC-25 (hangers). All hanger frames have releases

so that they can only work axially. The catenary cables are simply supported at their ends, but on

top of the towers there are 2 frames with proper releases modelling the actual supports.

Initial geometry of the main cables

It has been performed a Non-linear analysis: the stiffness matrix is formed for the final equilibrium

geometry for each load combination. But in order to reach that final geometry the software needs

to start from geometry similar to the final one, otherwise convergence problems may occur. That is

why we obtain first the geometry for the permanent loads as per procedure in Figure 9:

Figure 9. Procedure to obtain main cable initial geometry

Once we introduce the geometry obtained by procedure in Figure 9 and the model is loaded with

the permanent loads, then the catenary cables would reach the expected tension T0=3600kN

(force normal to hanger planes) but extending ΔL=490mm because of this tension. Since we do

not want this elongation to occur from the original position previously, then we need to introduce a

pre-stress action in the cable at FEM. Temperature load shortening associated is ΔT=-166ºC.

For any additional live load the resultant deformed shape is close enough to the initial geometry so

that no convergence problems occur anymore.

2.4. Results: verification SLS and ULS

The model shows a good static-deformation behavior with a maximum deflection in vertical

direction of 220 mm, meaning ratio span/displacements of 655 well inside the limit of 350.

All the elements have been verified to ULS load combinations. For the steel deck the maximum

Von Misses stress is 145MPa while for the towers 230MPa. Regarding the cables, the tension

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force in the main cables vary between 3600-6445kN while in the hangers the range of tension

force is 15-205kN; the maximum axial force has been checked according with the producer limit.

These results presented show that the design of the bridge is not governed by the stress in steel

elements but by the dynamics because of the bridge typology.

The dynamic analysis has been performed according to BS [1], as per the steps described in

Figure 10:

Figure 10. Dynamic analysis

The conclusions from the dynamic analysis are:

- Vertical accelerations: maximum values are below the limit set by [1] alim=1.86m/s2 for the

bridge category. They also comply with the Eurocode criteria (alim=0.7m/s2).

- Horizontal accelerations: for a group of 15 pedestrians fully synchronized, the resultant

accelerations do also comply with Eurocode criteria, that sets the alim=0.2m/s2.

Per the checks done at this phase, no resonance due to pedestrians is expected to occur.

3. Stress ribbon Alternative

3.1. Description of the structure

The stress ribbon alternative has been chosen due to the singularity of the solution and the

simplicity, clarity and elegance of the design. The stress ribbon deck comprises 350mm deep

precast concrete sections with No2 Φ105mm bearing cables and No4 Φ125mm post-tensioning

cables.

The bridge has been designed to be built accordingly with the standard procedure set up by

Strasky [2]: i.e. abutments and towers are built on site, bearing cables are placed over support, the

prefabricated RC elements positioned on bearing cables and slide to their final position, post-

tensioning cables placed inside the two canals, concreting the canal and top layer and finally post-

tension the cables.

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Figure 11. Plan and Elevation

Figure 12. Typical section A-A Figure 13. Elevation Detail: typical span

3.2. Design criteria

3.2.1. Materials

The materials chosen are reinforced concrete B45 in abutments and foundations with Rebars

made of B500NC. Cables are Bridon Spiral strand SS, being 4 no SS 125 post-tensioning cables

and 2 no SS 105 bearing cables.

3.2.2. Loads

In addition to Self-weight, Superimposed dead load from the flexible rubber pavement is set to

0.85kN/m2. Handrail is treated separately as 0.25kN/m loading (each one). Permanent loads

include also shrinkage set to εcs=256·10-4 and modelled as a temperature load, and Cable pre-

stressing loads. Bearing cables include F=4250kN (since there are 2 cables, total force is 8500kN);

post tensioning cables F=6920kN (since there are 4 cables, total force is 27680kN).

Traffic loads of 12.95kN/m have been considered, with a maximum torsional load of 3.25kN·m/m.

With respect to horizontal loads, it has been considered 1.3kN/m. When required, loads on

pedestrian parapet were set to 1.5kN/m, vertical or horizontal.

Snow loads have not considered since they are smaller than traffic, but wind on deck is 1.6kN/m

transversally, 0.8 kN/m in the longitudinal direction and ±5 kN/m in the vertical direction.

Finally, thermal actions include ΔT expansion of 20.3ºC and contraction of 24ºC. The linear

temperature difference component is 22.5ºC for heat and 8ºC for cool.

3.3. Description of the FE model

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The model consists of frame elements. The deck frames are joined to the bearing cables by means

of ultra-rigid transverse beams located every 1m. They are also connected to the towers by using

these ultra-rigid frames.

Figure 14. Detail of bridge elements (deck, bearing cables, post-tensioning cables, rigid constrain)

Figure 15. Conceptual chart of the stage non-linear analysis (from Strasky [2])

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3.3.1. General static system

The static system of the bridge is very simple from a geometric point of view, but very complex in

the analysis of the non-linear stages. Each element (deck, bearing cables and post-tensioning

cables) needs to be placed in the correct sequence with the associated tension, and the final

geometry of each step has to be calculated through an iterative non-linear process (form-finding).

3.3.2. Boundary conditions

- The bearing cables are simply supported at both east and west ends.

- The tower columns are fully fixed to the ground at their base.

3.4. Results: verification SLS and ULS

The maximum vertical sag occurs at the end of the panel-hanging process, before post-tensioning

the cables. The vertical deformation is measured from the reference line that joins the deck at

towers location for each span. The maximum deformation has to be check at t=∞ and with DT>0:

the results calculated is Uz=1010 mm approximately equal to limit vertical sag = L/50 = 61000/50=

1220mm.

Figure 16. SLS displacement (SDL+DTe at t=∞)

The tension in the cables varies during the life of the structure due to the long term concrete effect

and to the temperature variation. The maximum values calculated are: 5675 kN for each bearing

cables and 15795 kN for each post-tensioning cables. Especially the negative DT (usually very big

in Norway) are very challenging for this type of structure, because they cause loss of compression

in the deck meaning less bending moment capacity. An iterative process has been set to optimize

all the parameters.

The concrete sections for the bridge deck have been post-processed in order to calculate the

required reinforcement at each deck frame: the top and bottom longitudinal reinforcement, for the

most unfavorable case where area requested is A≈150cm2, could be Φ25 c/c 150mm, which is a

feasible layout. For the towers no special design is required, as they will be executed in situ.

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3.5. Conclusions

The suspended alternative is a suitable alternative for the client’s requirements. The most

characteristic features in this particular case are the curved cables in plan and the geometry of the

towers, with 4 legs. The calculations for this preliminary phase show that the structure design is

governed by pedestrian comfort, and represents a challenge regarding the dynamics of the bridge.

Aero-elastic instabilities produced by wind flow in the valley need also to be verified at future

stages.

The stress-ribbon alternative is very challenging in the Norwegian climate environment, big

temperature variation occur during the life of the structure meaning that large post-tensioning

forces have to be used. The limitations on the maximum slope and the fact that the tower heads

are not all at same absolute elevation (meaning that there is an average slope to add to slopes by

the catenary shapes) also force to have initial reduced sag with respect to other stress ribbon

found in bibliography. This leads to a structure more slender and sensitive to thermal contraction.

The preliminary calculation undertaken shows the feasibility of the structure, but also underlines

the strong conceptual challenges to be faced in realizing a stress-ribbon structure in Norway.

[1] National Annex to BS EN 1991-2:2003, Eurocode 1: Actions on structures - Part 2: Traffic

loads on bridges

[2] Stress ribbon Stress Ribbon and Cable-supported Bridges - J Strasky – 2011