보도육교의 해외 설계사례 (트러스교)

21. 4. 19 오후 7:59

This case study covers the following aspects:

 

1. Introduction

2. Footbridge Design Specifics and Challenges

3. Eurocode Requirements

4. Case Study - Warren Truss Footbridge

 


 

1.Introduction

 

 

A footbridge or a pedestrian bridge has mainly a purpose that allows people to walk over the bridge. The aesthetic considering harmony with the surrounding environment is an important factor in this type of bridges. Since that, the shape of the bridge is getting slender and aesthetic. And also the footbridge generally has a narrow carriageway and lightweight itself. Those characteristics make a high possibility to happen the vibration on the bridge. Especially, if the frequency of walking is equal to the natural frequency of the bridge, it makes resonance phenomena. Resonance phenomena causes a higher amplitude of vibration, which can influence safety for pedestrians.

 

 
 
Figure 1: Bob Kerrey Pedestrian Bridge
 
Figure 1: Bob Kerrey Pedestrian Bridge
 
 
 
 
Figure 2: Insertion point & Offset insertion point
 
Figure 2: Insertion point & Offset insertion point
 
 

 


 

2. Footbridge Design Specifics and Challenges

 

Let’s have a look at what makes footbridge design different from a road and rail bridge and what challenges the designer might have to face when designing a footbridge. In the footbridge design, aesthetics and structure robustness could be one of the key points. At the same time, the designer needs to pay attention to the stability and the vibration of the bridge. It doesn’t mean unique to footbridges but those specific points can be encountered frequently when designers design a footbridge.

 

 

Figure 3: The aesthetic factor of the footbridges

Figure 3: The aesthetic factor of the footbridges
 
 

The aesthetic structure design of the footbridge is quite often developed in close cooperation with an architect. Architects have their ideas about the appearance and the visual impact of the bridge. Therefore, the shape of bridges might involve unusual or complicated geometry. The footbridge design allows for various selections of materials. So designers need to understand the properties and behavior of these materials such as timber, aluminum, or glass.

 

 

Figure 4: Slender airy footbridgesFigure 4: Slender airy footbridges
 
 
  

In terms of structure robustness, when designers design a footbridge, probably they want a footbridge to be lightweight. So, a footbridge is often designed as a slender airy structure. At the same time, we have to ensure that they have sufficient stiffness and strength to maintain their stability including wind effects and accidental situations. Therefore, a critical load combination may be different from those common at road bridges.

The stability is also related to a dynamic response and vibration. It is not a main issue for a majority of short and medium span road bridges. But it is an important factor in the footbridge design. Because if the structure has a low natural frequency, it might lead to unstable lateral response and the loss of stability. Also it might lead to the vibration which may cause discomfort to users.

 


 

3. Footbridge Design Specifics and Challenges

 

Eurocode proposes various requirements regarding footbridge design. Requirements for the footbridge design can be found in:

 

  • Loading Requirements
    • EN 1991-2:2003, Section 5
    • EN 1991-1-4, Section 8.2
    • EN 1991-1-7, Section 4.3
  • Structural Design
    • EN 1992 (Concrete)
    • EN 1993 (Steel)
    • EN 1994 (Composite)
    • EN 1996 (Timber)

Footbridges are subjected to different type of live load. Same limit state principles apply to footbridges.

Static load models for the footbridges are made up from four elementary components called uniformly distributed load, concentrated load, service vehicle, and horizontal forces. These loads are combined into groups of loads. It is similar concept as with the road traffic.

 
 
Figure 5: Static load models and groups 
Figure 5: Static load models and groups

 

 

The accidental loads are covered partially in the traffic loading code, EN 1991-2 and it also is covered partially in the accidental actions, EN 1991-1-7. Since accidental loads can have fatal consequences, and strengthening the structure to resist them would be uneconomical so we need to take measures to avoid them. Therefore, collision forces on piers of footbridges are reduced because the piers are usually protected by a barrier. Collision forces on the deck, we can avoid application of this accident load if we provide sufficient clearance which is in the UK and Ireland 5.7 meters. And for the accidental presence of a vehicle on the bridge, it can be avoided if a permanent barrier is installed which prevents access of vehicles on the bridge.

 

 

Figure 6: Equivalent static design force due to the impact
Figure 6: Equivalent static design force due to the impact

  

Dynamic Loads can be found in section 5.7, EN 1991-2. Now, we will look at what differentiates footbridges most from normal road bridges of short and medium span bridge that has the application of dynamic loads. There are two key points which we need to pay attention.

 

The first key point is the natural frequency of the structure. Because if any of the natural frequency are identical to the frequency due to dynamic forces applied to the structure, there is a risk of resonance which may lead to unacceptable vibration or even loss of stability.

 

The second key point is to pay attention to the vibration. The vibration from normal pedestrian traffic should not cause discomfort to users so that is why the code specifies a limit defined as an acceleration limit. Dynamic effects of walking pedestrians can be represented by a periodic force and this force will have a typical frequency of between one and three hertz. In the horizontal direction, the effects of walking pedestrians would have a frequency between 0.5 and 1.5 hertz. And if there’s a group of joggers crossing a bridge, that may induce forces with a frequency about three hertz so we can see that this range say from 0.5 to 3 hertz would be a critical spectrum. And if any of the natural frequencies of the structure is within this spectrum there is a risk of issues related to the vibration or stability so specific models and detail criteria how to fulfill it and how to achieve that the structure is stable. They are defined in a nation annex or other national application document.

 

 

Figure 7: Equivalent static design force due to the impact
Figure 7: Equivalent static design force due to the impact (click here to zoom)

 

And for the UK and Ireland, the Eurocode 1 specifies the maximum vertical deck acceleration which has a limiting service element serviceability value in the range between 0.5 and 2 m/s2. The exact limit value is calculated based on formula in the code and it depends of the site usage route redundancy and structure height. Single pedestrian or a pedestrian group load are represented by the application of vertical pulsating force which moves across the span of the bridge. The pulsating force can be calculated via the formula shown in the figure 7. The formula has various parameters.

 

 

Figure 8: Classes of the footbridges in Eurocode
Figure 8: Classes of the footbridges in Eurocode
 
 
 

The footbridges for the purpose of dynamic loading are split into four classes depending on the location and usage. And then, the dynamic force is applied. Also we should know that the pedestrian speed crossing. It is also defined which helps us to define the duration of dynamic loading.

 

 

Figure 9: A formula for a vertical pulsating distributed load
Figure 9: A formula for a vertical pulsating distributed load

 

 

The other aspect of dynamic loading would be loading crowded conditions so if a bridge is located in the city center or close to a stadium, it may get into the crowded state instead of using a point single force pulsating and moving across the bridge. The dynamic loading is modeled by a vertical pulsating distributed load.

 

 

Figure 10: Evaluation the stability of a pedestrian bridge 
 
Figure 10: Evaluation the stability of a pedestrian bridge 
 
 
 
 

That helps us to assess the possible vibration issue and the other requirement regarding the natural frequencies. If there are no significant lateral modes with frequencies below 1.5 hertz. We may assume that the structure is stable. It means there are no risk of lateral instability. If any of the critical frequencies is lower than 1.5 hertz then there are additional checks to perform or to introduce some dumping devices or we may redesign the structure.

Apart from dynamic effects of pedestrians, in certain situations, we may need to investigate the dynamic effects of wind loading. The Eurocode dealing with the wind loading also provides general guidance. It says that dynamic magnification effects due to vertical response can be ignored if fundamental frequencies in bending and torsion are greater than 1 hertz or we may need to fulfill alternative conditions but taking into account that generally we want to avoid frequencies below 1.5 or even 3 hertz. It means that for most bridges where we fulfill the condition for the pedestrian dynamic load. We are fulfilling the condition for the wind loading as well. But for the long span or special structures, it is something which needs to be taken into account.

 

 


 

4. Case Study – Warren Truss Footbridge

 

 

Figure 11: Warren truss footbridge
 
Figure 11: Warren truss footbridge

 

 

The bridge of the case study has a span of 50 meters, a clear internal width of 3 meters, and the maximum structure depth in the mid span was 4.2 meters. Both top and bottom cords of the truss are curved in the gentle radius to improve the appearance although in this particle case the aesthetics wasn’t governing factor for the design because the bridges in rural location with a low flow of pedestrian. The design of this footbridge was actually developed as a result of a value engineering exercise or a value engineering proposal because the original structure was a two spans slab beam bridge. We proposed a single span structure to avoid placing support in the center median of the motorway.

 

And the truss works well for this arrangement. We can focus on how this particle structure or generally truss can be generated in midas Civil. How we can generate a model in relation to what we discussed in the Eurocode requirements for dynamic response and natural frequencies. We will look into stability and dynamic response and again how this can be performed in midas Civil. Then global static analysis member verification and the generation of the design report.

 

 

4.1 Model generation – Geometry

A model can be defined by using functions related to modeling manually. midas Civil provides various options to model. The user can use ‘Truss Wizard’ function to model truss shape elements directly. If there is a CAD file, it can be imported to midas Civil.

 

 

Figure 12: Truss Wizard function and CAD import
 
Figure 12: Truss Wizard function and CAD import

 

 

4.2 Model generation – Structure’s properties

The member sections and material properties are selected in the database of midas Civil. The user doesn’t need to define additional properties if there is desired property in the database. The bearings of the bridge are modelled via Elastic Links function.

 

 

Figure 13: Structure’s properties 
 
Figure 13: Structure’s properties 

 

In the bridge model, dummy beam elements are created to apply of pedestrian dynamic load. In order to perform the dynamic analysis in midas Civil, the user needs to set some options regarding the mass of a structure. Those options are called ‘Convert Self-weight into Masses’ and ‘Loads to Masses’.

 

 

  Figure 14: Structure type and Loads to Masses functions
 
Figure 14: Structure type and Loads to Masses functions
 
 
 

4.3 Stability and Dynamic Response

There are two key parts. The one is the analysis to obtain a natural frequency and the other is the dynamic analysis to obtain dynamic response. To investigate the natural frequencies of the structure in midas Civil, the user need to turn ‘Eigenvalue Analysis Control’ function. Here, we can select the analysis type, the number of frequencies, and so on. 

 

 

Figure 15: Eigenvalue Analysis Control function
 
Figure 15: Eigenvalue Analysis Control function
 
 
 
 

The output from the eigenvalue analysis can be either numerical like in this example. For each mode, we can see the actual frequency. For example, the mode 1 in the figure has a frequency of 1.68 which is actually close to 1.5 hertz but we can notice that it is vibrating in the longitudinal axis of the bridge for the modal participation masses. So it is not critical. The second mode has a frequency of 2.53 hertz and it’s vibrating in the y-axis so it is a lateral transverse vibration. And the third mode has 3.47 in the z-axis so it is an actual vertical vibration.

 

 

 

Figure 16: Result table of the eigenvalue analysis

Figure 16: Result table of the eigenvalue analysis

 
 
 
 

For the assessment of the dynamic response, we want to prove that the vertical deck acceleration is within the limits set in the code so that any vibration is not causing any discomfort to the users. The general principles are to calculate values of pulsating force at defined time increments and to apply the force onto series of nodes along the bridge span. midas Civil provides several functions regarding the time history analysis. The procedure to apply the time history load case in midas Civil:

 

1. Create a time history load case.

2. Generate a time history function.

3. Apply dynamic nodal loads on the structure.

 

 

  • Figure 17: Time History Analysis Data
  •  
  •  Figure 17: Time History Analysis Data

 



In the time history load case function, the user can specify duration of the load, time increments, and damping. And to define a time history function, the user can input values directly. In this case bridge designed, walking load is only applied because it’s in the rural condition and there wasn’t requirement for joggers. If we have a structure in urban environment or a specific requirement, we might need to define two load functions for walking and jogging.

 

 

Figure 18: Time History Load Case and Functions 

 

 

Figure 18: Time History Load Case and Functions 


And then, this pulsating force defined in the time history function is applied on selected nodes on the structures via Dynamic Nodal Loads function.

 

 

 

 

Figure 19: Time History Load Case and Functions
 
Figure 19: Time History Load Case and Functions
 
 
 
 

After the analysis, we can review the acceleration, forces, or displacements at any point in graphical form or numerical form. But the problem is if our time increments are hundreds per second. It means a lot of numbers to review. So it is not practical to look at results in this way. There is a function in midas Civil to allow the user to create an envelope of results for any selected point on the structure. The figure shows the dynamic acceleration results of the warren truss footbridge. The peak acceleration is 0.036 m/s2 is much smaller than limiting value in the code, 0.5 m/s2. It is due to the low pedestrian loading. The peak acceleration are close to the middle of the time period. It says that the maximum acceleration would be at time 16 seconds and the minimum acceleration would be 14 seconds. It makes sense because the pedestrian is right in the middle of the bridge so it has a greatest effect on the vibration.  

 

 

Figure 20: Time History Graph function 
 
Figure 20: Time History Graph function 

 

 

4.4 Global Static Analysis

The global static analysis is performed the same way as any other structure. Deformation, reactions, stress results, and force diagrams have been checked. Review of deformation is usually first step after analysis to verify correct behavior of the model. And we can decide whether pre-camber is necessary or not through checking deflection from permanent loads.

 

 

Figure 21: Displacement results
 
Figure 21: Displacement results

 

 

Figure 22: Reaction force results
 
 
Figure 22: Reaction force results

 

 

Figure 23: Member stress results
 

Figure 23: Member stress results

 

 

Figure 24: Member force results
 
 
Figure 24: Member force results

 

 

4.5 Member Verification

The member verification is defined a set of checks and it is the most time consuming. Even in-house prepared design spreadsheets save time but we still need to identify critical members and manually transfer results from the structural model. midas Civil has a set of member design features to simplify this task.

 

midas Civil provides steel design features for Eurocode 3, section 6. There are 3 ways to obtain verification results. Results table as shown the figure 25 shows the design results for the selected members. These results can be checked as a graphic view or text format.

 

 

 

Figure 25: Member force results
 

Figure 25: Member force results

 

 

Figure 26: Member force results
 
 

Figure 26: Member force results

 
 

 

 

Watch the full webinar video

 

 

CIM 뉴스레터 구독

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Martin Bosak | Senior Engineer | Barry Transportation (UK)

- 15 Years experience in structural bridge design
- Specialization in concrete bridges

 

Participated in the design at major infrastructure projects across Europe
- Czech Republic (D3 Motorway, R48 Expressway, I/11)
- Slovakia (D3 Motorway)
- UK (A5 Northern Ireland, A737 Scotland)

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