영국 River Irwell Network Bridge 설계사례 (강아치교)

21. 4. 19 오후 7:59

 

This case study covers the following aspects:

 

1. Project Information

2. Advantages of Network Arch Bridges over Conventional Bowstring Arches

3. Modelling in midas Civil

4. Features for cable elements in midas Civil

5. Construction Stage Analysis

6. Moving Loads and Cables

7. Design and Checking Results

 


 

1. Project Information

 

The River Irwell Network Arch Bridge is the centerpiece of the Ordsall Chord project, which connects Manchester Train stations of Victoria and Piccadilly, as part of the Great Northern Rail Project. The bridge presents a peculiar squashed tennis racket shape and is the longest spanning asymmetric network arch rail bridge in the world. It was the first Network Arch Bridge to ever be built in the United Kingdom.

 

River Irwell Bridge
 Figure 1: River Irwell Bridge

 

The total span of the structure is 89m, with an arch rise of 13.57m (rise to span ratio: 0.1525). In order to achieve a continuous linear development of the lines of the structure at the northern end side, the transition between the curved and straight girder is obtained through the use of a non-structural reversed curvature arch component.

 

Bridge Elevation
 
Figure 2: Bridge Elevation
 
 
Reversed transitional arch component
 
Figure 3: Reversed transitional arch component
(© Knight Architects - https://www.knightarchitects.co.uk/projects/ordsall-chord)
 
 
Reversed transitional arch component installation
 
Figure 4: Reversed transitional arch component installation
(© Knight Architects - https://www.knightarchitects.co.uk/projects/ordsall-chord)

 

The bridge is 15.4m wide and carries two railway tracks in a curved alignment. Furthermore, it is designed for full LM71 loading (EN 1991-2:2003 + UK NA). The constraints regarding the space at which the bridge will be erected were accounted for in the design. The erection method is based on the use of temporal asymmetric towers in order to speed up construction and make use of the same towers to dismantle the previous truss bridge at this location.

 

 

Detailed Design Drawing
Figure 5: Detailed Design Drawing (© Network Rail)

 


 

 

2. Advantages of Network Arch Bridges over Conventional Bowstring Arches 

 

Typical bowstring arch bridges have vertical hangers or inclined hangers (Nielsen type). The tie closes the arch, taking in the spring (works in tension). This has the advantage of making arch bridges practical in sites with poor geotechnical conditions. Under UDL the arch is purely compressed and the tie-beam acts in tension.

 

Ayuntamiento de Palma del Río
 
Figure 6: © Ayuntamiento de Palma del Río http://palmadelrio.es/wordpress/en/sitios-de-interes/
 

 

Network arch bridges have inclined hangers crossing each other at least two times. The structural behavior is similar to a truss: arch structure in compression, tie beams in tension and shear forces taken by the hangers. The father of this type of bridge is Prof. Emeritus Per Tveit, who conducted considerable research on the subject since 1950.

 

Details of the Steinkjer Bridge
 
Figure 7: © Details of the Steinkjer Bridge (1963), Norway designed by Dr. Per Tveit (per.tveit@uia.no)

 

In the lecture by Dr.Per Tveit, he compared two arch bridges. One is an original bowstring arch and the other is a network arch bridge with the same span length as the bowstring arch. Dr. Per Tveit calculated the influence line for the bending moment for both arch bridges. The network arch showed lower influence lines for bending moments than that of a tied beam arch. The point is that the network arch can be a very effective structure which leads to materials and weight-saving for long-span bridges.

 

The Network Arch – Lectures by Dr. Per Tveit 
Figure 8: © The Network Arch – Lectures by Dr. Per Tveit (per.tveit@uia.no)
 
 
The Network Arch – Lectures by Dr. Per Tveit 
Figure 9: © The Network Arch – Lectures by Dr. Per Tveit (per.tveit@uia.no)

 

The River Irwell Network Arch Bridge analysis was studied using midas Civil as shown in the figure below. Two element models were created. Load conditions, boundary conditions, and all other conditions are the same except for the cable shape.

 

Network arch vs Bowstring arch 
Figure 10: Network arch vs Bowstring arch 

 

Analysis results have shown that the network arch bridge is a more effective structure than the bowstring arch bridge with regards to displacement, bending moments, and buckling.

 

Displacement result
 
Figure 11: Displacement result

 

 

p12
 
Figure 12: Bending moments result
 
 
Buckling mode shape at 3 mins. 
Figure 13 : Buckling mode shape at 3 mins. 

 

 

Recap of advantages of Network Arch Bridges over Bowstring Arches:

 

1. Network Arch bridges induce lower bending effects in members

2. Network Arch bridges show higher stiffness against deflections in members

3. Network Arch bridges show higher stiffness against lateral buckling

4. Network Arch bridges allow for higher redundancy in the cable-out case

5. Network Arch bridges allow for the design of slender structures

6. Network Arch bridges allow for savings in material and more economical designs


Network Arch bridges are suitable to efficiently cross longer spans, achieve higher redundancy levels, better material utilization, and overall more economical and environmentally less impactful designs.

 


 

3. Modelling in midas Civil

 

Bridge members have been modelled by using various elements in midas Civil. Arch and tie members consist of 3D beam elements. In order to consider a composite girder, the concrete slab of the girder is modelled using orthotropic plate elements with time-dependent properties. Truss elements are used for hangers. The connection of arch and ties has been modelled using isotropic plate elements. The use of plate elements for the fin plates allows for a better representation of the local stiffness of the knuckle joint connection in the global analysis model. This, in return, avoids unreal spikes in stresses and/or BM concentrations. It also allows for a more realistic interpretation of the local stiffness, which is a very important factor in capturing the behavior of the structure in terms of effects/displacements.

 

Model overview (© AECOM)
Figure 14 :Model overview (© AECOM)

 

 

The following modelling process was used in midas Civil.

 

Modelling process in midas CivilFigure 15 :Modelling process in midas Civil 

 

Some sections in the bridge are not typical sections. Those sections have been defined using Sectional Property Calculator (SPC). It allows the user to define various sections based on a drawing. The arch member consists of a lot of beam elements. However, the arch member had a tapered shape, so inputting the various sections into each element was a challenge. In this case, the Tapered Group function was used. It allows the user to define start/end sections and create all sections in between using linear or polynomial variations. Each section can be defined as a new section property (and imported in other models).

 

 

Sectional Property Calculator & Tapered Section PropertyFigure 16 :Sectional Property Calculator & Tapered Section Property

 

 

A model shape after using Tapered Group function      
Figure 17 : A model shape after using Tapered Group function        
 

    

In this model, the concrete slab has been modelled using orthotropic plate elements. Before modelling, three types of modelling method were considered:

 

  • Equivalent orthotropic material for RC plate

  • Using stiffness modifiers

  • Beams grillage

 

The equivalent orthotropic material for RC plate method is assigning equivalent orthotropic materials to plate elements. By using codified material properties in the equations on the right-hand side and by inverting the equations on the left-hand side using the results obtained we determine all necessary parameters for the equivalent reinforced concrete plate:all necessary parameters for the equivalent reinforced concrete plate:

 

After that, those results can be inputted into material properties directly.

 

 

Bending moment diagram due to the self-weight of PPC segments and concrete deck
 
Figure 18 : Bending moment diagram due to the self-weight of PPC segments and concrete deck
 
 

 

The second method consists of using a stiffness modifier function in SW. By using this function, we can control in-plane stiffness and out-of-plane stiffness by ratio. For this case, the Plate Stiffness Scale Factor function was used. This function has a grouping option so the user can apply it to the desired construction stage.

 

 

Plate Stiffness Scale Factor function
 
Figure 19 :Plate Stiffness Scale Factor function
 
 

The last method is to model the concrete slab using beam elements as a grillage model. In this case, the deck is modelled by using transverse composite section beams and longitudinal concrete-only beams using cracked section properties. Composite Section for C.S. function in midas Civil was used to consider composite sections during construction stage analysis.

 

Beams Grillage model
 
Figure 20 : Beams Grillage model

 

 

 

 
p21 
Figure 21 :Composite Section For C.S. function

 


 

4.Features for cable elements in midas Civil

 

Before discussing cable elements, let’s first look at a comparison between truss and cable elements.

The truss element:

  • Axial forces only element.
  • Considers decreased axial stiffness of element due to sag effects.
  • Does not calculate actual sag.
  • Tension/Compression only elements (If selected).
 
Truss element
Figure 22 :Truss element

 

The cable element:

  • Tension only elements
  • Non-linear in behavior due to sag effects (Non-linearity in geometry) – i.e. large displacement analysis
  • Directly reflects changes in stiffness due to changes in tension level in elements – i.e. explicitly calculates sag.

 

Cable element
 
Figure 23 : Cable element
 

 

Therefore, to use a cable element, the user needs to perform a full non-linear analysis, making use of the tangent stiffness. However, the non-linear analysis is not always necessary. Usually, non-linear analysis is used for long span bridges over 500m and when cable forces in the stage are low. It causes the sagging effects to be the dominant force. Midas Civil has been providing a peculiar feature to use cable elements easily.

 

When the user considers cable elements in a construction stage analysis, the following options should be considered. In order to conduct non-linear analysis, the user needs to switch on the non-linear analysis controls in the Construction Sequence panel. As the system is non-linear, superimposition is lost and Accumulative Stage effects are to be considered. The software will update the tangent stiffness of the cable at each stage and take into account large displacements by explicitly calculating the sag of the elements.

.
 
 
 
Nonlinear Analysis Control option in Construction Stage Analysis Control
Figure 24 : Nonlinear Analysis Control option in Construction Stage Analysis Control

 

 

The other option is the re-stressing of cables in force-control. Typically, the software requires the modeller to obtain the final stressing either by changing the element length (imposed elongation) or by deactivating and reactivating a new element by assigning first stressing into it. MIDAS Civil has introduced the concept of treating applied pretensions as “External” type forces. Through this option, the user can replace or add a new force into existing cable elements without deactivating or reactivating elements.

 

 

Cable-Pretension Force Control option in Construction Stage Analysis ControlFigure 25 : Cable-Pretension Force Control option in Construction Stage Analysis Control

 

Cable forces at the same element in different stagesFigure 26 : Cable forces at the same element in different stages

 

Here are two more functions regarding cable elements. The first one is Cable Force Tuning function. It allows the users to interactively change forces in cables and see results change in real-time on screen. This helps reduce the number of iterations required to find the optimum tensioning of cables based on displacement/stress/member forces or hanger loads.

 

Cable Force Tuning function
Figure 27 : Cable Force Tuning function

 

 

The other is the Unknown Load Factor function. It allows solving goal-seek problems using multiple constraints. This helps reduce the number of iterations required to find the optimum tensioning of cables based on displacement/stress/member forces or hanger loads constraints.

 

Unknown Load Factor functionFigure 28 : Unknown Load Factor function

 

From this function, the influence matrix for hangers was was obtained to quickly assess effect of stressing any given hanger on all other hangers.

 

The influence matrix for hangers in ULF function and excel sheetThe influence matrix for hangers in ULF function and excel sheet 2Figure 29: The influence matrix for hangers in ULF function and excel sheet

 


 

5. Construction Stage Analysis

 

After modelling for the whole bridge, several groups for elements, boundaries, and loads were created in midas Civil. midas Civil supports the construction stage analysis. The concept of the construction stage analysis is that several groups for elements, boundaries, and loads are activated or deactivated along the stage as the real-construction plan. Furthermore, additional steps can be defined in a construction stage so a lot of construction phases can be easily managed. In order to see the detailed process of construction stage analysis in this project, please refer to the video below (38:00~48:30).

 

Construction Stage Analysis in midas CivilConstruction Stage Analysis in midas Civil 2
Figure 30: Construction Stage Analysis in midas Civil
 
 

Additionally, certain boundary conditions such as Beam End Release can be applied to a desired construction stage by assigning the condition into a boundary group.

 

Beam End Release function for construction stage analysis  
Figure 31: Beam End Release function for construction stage analysis
 
 

 

6. Moving Loads and Cables

 

The moving load analysis is also conducted in midas Civil. The process of moving load analysis is:

1. Traffic lane definition

2. Vehicle definition

3. Load case definition

4. Run

 

p32-1The process of moving load analysis 1p32-2The process of moving load analysis 2
Figure 32: The process of moving load analysis
 

 

 

The Moving Load Tracer function can be found in the Results menu of midas Civil. It allows users to see distribution of moving load to assess specified effect.

 

Moving load tracer
Figure 33: Moving load tracer

 

When the user runs a moving load analysis with a model using cable elements, a warning message will show in midas Civil saying “Cable/Tension-only truss elements are converted to Truss elements for moving load analysis”. This means that midas Civil converts nonlinear elements into linear elements. When the moving load analysis is conducted with tension-only elements and truss elements for cables, the user can see the results below. Particularly, the model with the truss elements for cables shows truss elements under compression under a moving load case for the minimum case. When a moving load analysis is conducted in midas Civil, midas Civil shows enveloped results for the maximum and minimum case. In order to check corresponding forces, the user needs to check results using the Moving Load Tracer. Figure 34 shows the compressed truss elements, and compression here means relieving effects on cables.

 

Moving load results for cable elements and truss elements
Figure 34: Moving load results for cable elements and truss elements

 

Therefore, placing moving loads as static loads with tension-only elements in a “linearized” (superimposition) analysis will not capture the relieving effect in the cable. When MIDAS converts cables to linearized elements, which is a correct approach, it allows the user to use influence lines for moving load analysis.

 

Cable forces without relieved effect
Figure 35: Cable forces without relieved effect

 

 

Figure 36 shows the results for the combination of permanent loads and moving loads (the maximum case). There is a considerable change in final forces between the two systems. If cable/tension only truss elements are used for cables for a moving load analysis, midas Civil will ignore the relieving effect and imposition for all cables. The hangers as trusses is the real behavior result, and this is due to the fact that the stiffness of the structure is correctly captured. In order to correctly use cables, the user will need to place a moving load in the correct Influence line positions and run Non-linear analysis with the “Load cases created from Load Combinations” function.

 

Cable force results comparison
Figure 36: Cable force results comparison
 
 
 

 

7. Design and Checking Results

 
 

Structural element checks are carried out in accordance with BS EN 1992/1993/1994. Most plated elements are class 3 or 4, so local buckling is important in the design. Global stability was checked through non-linear buckling analyses carried out in MIDAS Civil, based on the buckling shapes obtained from linear buckling and by identifying the load factor associated with failure under the specific load condition and buckling shape, including imperfections as specified in BS EN 1993-2. Regarding cable-out load cases, accidental LL position extracted from moving load tracer and hangers removed. Equivalent static load technique used for this analysis (dynamic amplification factor applied to original hanger forces).

 
 
Analysis model in results view

Figure 37: Analysis model in results view

 

From midas model, the results regarding reaction forces, internal forces, and displacements at members of the bridge have been compared with real systems such as hydraulic jack, geometrical survey, and structural monitoring systems. The comparison results have shown that reasonable results obtained from the midas model.

 

Model vs Reality 1 Model vs Reality 2

Model vs Reality 3
Figure 38: Model vs Reality

 

 

 


 

Watch the full webinar video

 

 

 


 

Q&A

 

 

Question 1

Can we talk about the arch plan bracing design concept?

 

Answer 1

The wind bracing used for the River Irwell bridge is made up of K-bracing. In my opinion, this is the most typical bracing used for railway structures of this type and is basically the one shown in the MSc Thesis by Brunn & Schanack and in multiple papers by Professor Tveit.

The sections used on the River Irwell are rectangular hollow sections 380x400 with 12/15mm thicknesses.

The function of the bracing is obviously to carry wind loads and limit the buckling length of the single arches and connect the two in the out-of-plane response. This enhances the overall lateral buckling response of the structure. These members take self-weight, wind forces and the restraining forces from the arches due to out-of-plane deformations.

Their structural design was checked against the forces induced by the prominent buckling mode of the arches, scaling the imperfection at midpoint as per Eurocode 1993 and the other actions.

 


Question 2

Can you describe the various cases of cable loss?  Was there a case of direct impact into the stays by the train?  Did you just use PTI requirements for cable-stay bridges?

 

Answer 2

The scope of works included the check of any 4 adjacent cables snapping simultaneously. If I understand the question correctly, you are asking if the train load during derailment was applied in the model as an out-of-plane load and the models ran with non-linear analysis with dynamic effects of cables snapping (i.e. time history with material non linearities). If this is the question, no - The calculation was done by considering the PTI requirements (i.e. the incremental DAF to the static force). This is in line with what is recommended by the MIDAS support when dealing with cable-out cases (see the MIDAS Technical query forum).

 


Question 3

Did you assume any tension force is taken at the level of the deck?  Did you bound the solution by making the membrane-stiffness of the deck zero - in order to maximize tension in the tie beam?

 

Answer 3

The membrane stiffness in the deck was calculated for the fully cracked section longitudinally – i.e. the forces were maximized in the ties. The stiffness of the plate was not set to zero, but the longitudinal reinforcement was considered for the stiffness (this is lower than the full plate stiffness, but is not zero for the membrane effects).

 


Question 4

Thanks for the great presentation. Is aerodynamic effect taken into consideration in the fatigue check for the hanger?

 

Answer 4

Vortex shedding for the hangers was calculated and the cross-displacement determined (see BS EN 1991-1-:2005). This did not result in an impact to the fatigue life of the hangers due to wind alone.

Fatigue testing on the hangers was particularly demanding from the contract: each hanger diameter present on the bridge was tested to 2 million cycles to determine the behavior in fatigue, as the system was previously granted European Technical Approval under static loads only.

 


Question 5

I understand bearingless construction is preferred in UK. Why is this not used on this bridge?

 

Answer 5

True, but I have not seen it used for this type of structures. The only integral arch bridges I know of are mainly pedestrian and have been designed by Strasky (see here) – as far as I am aware these were not Network Arches.

Usually integral forms here in the UK are used for frame portals (on full height or piled abutment). The reference code for these types is PD6694-1 in the UK.

I don’t know of one network arch bridge which acts integrally with the substructure. I must admit I haven’t personally considered the case of making the structure integral neither. I’d be curious to see if it would have any advantage. If you do have material, please share it with me. Thank you!

 


Question 6

Presumably is there a limitation on span length?

 

Answer 6

Typical integral abutment bridges would be limited by the span. BA 42 suggests all highway bridge below 60m should be made integral where possible (this is due to lower expected maintenance costs). The span limit usually is dictated by what is practicable to design when soil ratcheting is considered. But this refers to “frame” type bridges, with abutments loaded directly by the backfill.

Some research has gone into ways of isolating the bridge structure from the backfill in later years. This would allow to reduce the associated strain ratcheting effects and help achieve longer spans (see here for one of such research papers).

 

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Andrea Caristo | Principal Engineer | AECOM(UK)

  • Over 5 years of experience in Bridge Engineering & The modeling and design of cable-supported structures.

  •  

    - 4th Manama Crossing cable stayed bridge (detailed design)

    - Msikaba cable stayed bridge (erection engineering services)

    - River Irwell Bridge (Cat. 3 Check)

    - London Millennium Bridge cable retensioning preliminary modeling

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