Bridge Seismic Analysis Seismic Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_AASHTO
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Field_Bridge Category_Knowledge Category_How-to Structure Type_Bridge Design Code_Eurocode Design Code_CSA Design Code_AASHTO
Pushover is a nonlinear static procedure that incrementally applies lateral loads to a bridge model, typically until a target displacement is reached or the structure reaches global instability. The analysis is instrumental in identifying inelastic behavior, hinge formation, redistribution of internal forces, and the progression of failure mechanisms.
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What is Rail Structure Interaction?
Rail structure interaction studies the interaction between railway tracks and concrete bridge structures. Differential stresses are generated in the rail and the deck of a railway bridge due to temperature, braking, traction, and the train's weight. Let's take two cases here. One interacts with rail and ground, and the other shows an interaction of rail and bridge. So, the area of interest is the second case, not the first one.
The need for RSI in the modern world
Rail structure interaction (RSI) remains crucial in the rail transportation era and with the recent development of high-speed trains globally, playing a vital role in estimating the impact of rail on the bridge and the optimum design of the bridge system for the safe passage of trains without disturbing the passenger's riding comfort. Most of the modern-day railways use CWR. Fish plate joints were used in which the length of each rail was around 20-40 m, but in the case of CWR, the length of rails is up to a few hundred meters. The fish plates allow certain deflections, releasing the stresses in the rails, while accumulation of stress occurs in CWR.
Let's take two scenarios: rails over an embankment and a bridge.
Figure 1:a) Fish Plate Joint b) Welded Rail Joint
Case 1: Rails on the ground
Let’s take a scenario and study the stresses in railway tracks when there is no bridge, and increase the temperature. We know that the ground won’t react to this change in temperature, but the railway track tends to expand. In the central zone, we can observe that there will not be any net force acting, and the stress profile is constant here.
- Stress = E x alpha x T
- Alpha - coefficient thermal expansion
- T - temperature rise
Figure 2: Central zone
But in the end zone, there is some net force which will result in some net displacement. This displacement will release the stresses and it tends to be zero.
Figure 3: End zone (Expansion zone)
Case 2: Rails on bridge deck
Let us take the same case, but the bridge deck is connected monolithically with the track plinth, and the track plinth connects to the rail track using rail fasteners. But the rail fasters are not rigid and have a bilinear behavior. Due to this differential temperature, there will be thermal stresses in the deck and rail. These thermal stresses will tend to expand the deck and vice versa.
Figure 4: Differential stresses develop due to temperature
Code and guidelines for RSI
The guidelines and specifications are mentioned in the mother code of rail structure interaction
- UIC 774 3R.
Loads to be considered.
- Thermal Loads
- Braking and acceleration forces
- Vertical loads of the train
Effects that need to be considered while performing RSI.
- Additional stresses in Rail
As per the code UIC 774 3r:
Maximum Permissible Additional Compressive Stress: 72 MPa
Maximum Permissible Additional Tensile Stress: 92 MPa
Figure 5: Example of a curve showing rail stresses due to temperature variation in bridge deck
- Absolute and relative displacement of the rails and deck
So, as per the code guidelines, there are displacement norms the analysis needs to fulfill. These are as follows:
- Maximum Permissible displacement between rail and deck or embankment under braking and acceleration forces is 4 mm.
- The maximum absolute horizontal displacement of the deck is 5 mm.
- In the case of CWR on a ballasted track with an expansion device, the maximum permissible horizontal displacement of the deck under the same load is 30 mm.
Figure 6: Limits to relative longitudinal displacement
- End rotation of the deck
Due to the vertical bending of the deck, the deck's end will rotate, and the permissible displacement between the top of the deck and the embankment between the two consecutive deck end due to vertical bending is 8 mm. - Figure 7: Limits to end rotation of the deck
- Bilinear behavior of the track
We have already discussed the bilinear behavior of fasteners earlier. Now, in the case of
tracks, the code has segregated them into ballast and ballastless tracks and has categorically
provided a curve defining the resistance - “k” for the longitudinal displacement of the rails.
The ballast has different stiffness in loaded and unloaded conditions, adding to the
nonlinearity of the analysis.
- Figure 8: Resistance k of the track per unit length as a function of the longitudinal displacement u of the rails
-
Types of RSI Analysis
You might be wondering how to combine the results for temperature, braking, and vertical loads,
considering the nonlinearity of the bed. The superpositioning principle is invalid, making RSI analysis too complex. But don’t worry. UIC guidelines suggest two types of analysis to simplify our lives: The simplified Separate Analysis Method and the Complete Analysis Method. All the loads like thermal loading, braking, and traction loading are separately considered in a simplified separate analysis, whereas these loadings are concurrently considered in the case of complete analysis.
Simplified Separate Analysis
This is the simplest method for analyzing rail structure interaction. The thermal variation, braking/
acceleration forces, and vertical deflection are analyzed separately, and the results are combined,
assuming the principle of superposition. Since separate analysis is carried out for each load case, the assumption of zero initial stress and strain in the structure before train loading is considered.
Case 1
A model with temperature loads and resistance of ballast as per unloaded condition.
Case 2
A model with vertical train load, acceleration, and braking forces, which have different ballast resistance (loaded/ unloaded condition) depending on the presence of train loads.
Figure 9: Longitudinal resistance of the ballast for separate analysis
Complete Analysis Method
In Complete Analysis, the simultaneous effect of the thermal variation, braking/ acceleration force, and vertical deflection is considered, where the temperature load is applied first before the application of the vehicle load. The initial displacement due to temperature load is considered for the Analysis when the moving load is applied.
Figure 10: Longitudinal resistance of the ballast for a Complete Analysis
So, in short, we tend to overestimate the stresses in the case of simplified separate analysis as we linearly add the stresses in both the loadings, which we cannot do as the principle of superposition is not applicable for nonlinear (bilinear in this case) structures. But still, a simplified separate analysis is practiced in the industry as it is more conservative. The complete analysis would give more accurate and realistic results, but it depends on the designer which method to adopt.
Steps in Rail Structure Interaction
Figure 11: Flowchart for RSI
What Makes Midas the Global Choice for RSI?
MIDAS has become the global choice for RSI analysis due to its robust capabilities, user-friendly interface, track record of success, and commitment to innovation.
Midas Civil RSI wizard
Like the other Midas wizards, the RSI wizard is the most exciting feature most engineers working in the railway sector crave. Rail Track Analysis Model Wizard is provided to account for additional stresses and displacements due to an interaction between decks and rails.
The wizard facilitates Separate and Complete analysis considering the nonlinear properties of the ballast. Analysis is performed to find the location of the maximum additional stress by moving the train forward. When the train is moved forward, models that reflect the changes in boundary conditions are automatically created. Detailed reports are generated.
Figure 12: Rail Track Analysis Model Wizard
Figure 13: Boundary conditions simulating loaded and unloaded stiffness of the ballast
Aside from the wizards, analysis results are periodically validated and widely trusted. According to UIC 774-3 (1.7), computer programs for track-bridge interaction analysis must undergo validation for test cases outlined in Appendix D. Validation is achieved when errors for both individual and overall effects are below 10%. UIC 774-3 permits a higher 20% tolerance if it leads to safer results.
As a test case, our engineers have validated the RSI analysis results for the following bridge configuration.
Table 1: The bridge configuration is as follows as per UIC 774-3 A1-3 test case
From the above results, we can conclude that the results obtained from Midas Civil match well with the UIC 774-3 results and have an error within the permissible limit of the code, which is 10%.
What’s next?
As the rail industry evolves, so will the challenges and opportunities related to RSI. Engineers and researchers will continue to push boundaries, developing innovative solutions that enhance rail transportation in our ever-connected world.
As we journey into the future of rail engineering, MIDAS will continue to evolve, adapting to new challenges and innovations in the industry.
Its role in shaping the world of rail structure interaction remains pivotal, promising a safer, more efficient, and sustainable future for rail transportation.
The upcoming blog will discuss the Rail Structure Interaction in curved railway bridges. Stay tuned.
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Eurocode Bridge Tips & Tutorials MOTIVE Tool Field_Bridge Category_Knowledge Category_Industry Structure Type_Bridge Design Code_Eurocode Design Code_AASHTO Design Code_ACI
🕖 Surviving in times of change
I felt one thing while working as a structural engineer who designs concrete bridges(RC/PSC) according to various countries' design standards: A profound understanding of ACI318(AASHTO) and EN2 is essential to successfully working on bridge projects. Most countries' standards are developed based on those standards. (Of course, it is my personal opinion.) Personally, I believe that my design career was successful because I recognized these facts.
Reviewing the ACI318 and EN once is not enough because design standards change over time. Revision is an indispensable process, and I expect two things before the new edition is released.
First, to be precise, the existing vague parts; the other is simplifying the calculating equations to apply the practical design process. Fundamentally, those are relevant problems. Complexity usually brings unclear parts.
Unfortunately, the newly updated 2G:Eurocode 2 did not meet these expectations. Standards are more convoluted than before, and this has indeed led to an increase in unclear areas.
Now, the moment has come to prepare for the future.
⚙️ Introduction to Our New Tool
Now, let's talk about tools.
The primary function of this tool is to easily output stress-strain curve graphs, which are strength characteristics of concrete, and graphs of time-dependent characteristics such as creep and drying shrinkage.
Notably, by providing the existing EN1992-1-1 and the new 2G:EN1992-1-1 together, the user can compare those results and experience the calculating processes. I believe it would be a handy tool to validate that new standards align with user understanding before implementing them in practice.
❓How to use it?
🔢 Input values
1. Select Graph
- Concrete Properties (Stress-strain diagrams)
- Time-Dependent Behavior
2. Select Standard Code
- 2G:EN 1992-1-1
- EN 1992-1-1
3. Put values
4. Click the calculation button
📈 Review a result
1. Select Graph type
- A. Concrete Properties
- Non-linear
- Parabola rectangle
- Bi-linear (Not include 2G:EN 1992-1-1)
- B. Time-Dependent Behavior
- Creep coefficient
- Shrinkage strain
- Elastic modulus
- Mean compressive strength
- Mean tensile strength
2. View a result as a table
3. Check additional information
4. Graph tool (save, zoom in and out, move, restore)
😜 Conclusion
The 2nd Generation Eurocode is continually being released and is targeted to start use in 2028. In line with this, MIDAS provides tools to compare the modifications between the 1st and 2nd generations. This work will only be possible with the support of ongoing research and constant user interest. We ask for your interest and anticipation for the upcoming tools.
Are you curious about this tool?
Click the link below to access MIDAS Tools for free.
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Eurocode Bridge Tips & Tutorials Field_Bridge Category_Knowledge Category_Industry Structure Type_Bridge Design Code_Eurocode
Some people have already heard about the second generation of Eurocodes. It’s not too early to figure out what changes are in the second generation and what civil and architecture engineers need to know. This blog does not handle the specifications; however, it would be helpful for those who want to know the overall changes. I will give you a quick summary for busy people.
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Bridge Insight Rail Structure Interaction RSI Field_Bridge Category_Knowledge Category_Industry Structure Type_Bridge
What is Application Programming Interface (API)?
The first thought that will come into your mind is exactly what is this API? and why a civil engineer like me needs to know about this techno-sounding topic.
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Defining Suspension Bridges: An Engineering Marvel
Suspension bridges are remarkable structures supported by massive main cables stretched between two or more towers. This design is the preferred choice for expansive spans where conventional bridge types prove impractical. The main cables, anchored at both ends of the bridge, are under tension and bear the weight of the bridge deck along with dynamic loads from vehicles and pedestrians. Typically, the deck hangs below these main cables, secured by smaller vertical cables or rods.
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Beam Bridges: An Essential Element in Transportation Infrastructure
Beam bridges, commonly referred to as girder bridges, represent one of the most prevalent and fundamental bridge types globally. Despite their apparent simplicity, these structures play a pivotal role in our transportation systems, ensuring the safe passage of vehicles and pedestrians across various terrains such as rivers, valleys, and highways. This article delves into the design, construction, and essential features of beam bridges, highlighting the science behind their stability and strength.
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Bridge Insight Rail Structure Interaction UIC 774-3 Field_Bridge Category_Knowledge Category_How-to Structure Type_Bridge
1. Introduction
When performing the Rail-Structure Interaction (RSI), It is often found that the stress limits are exceeding the permissible values. So there are some countermeasures to ensure safety. Let’s look at how we can implement these control measures which affect the stresses in rails when performing rail structure interaction.
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Bridge Insight Rail Structure Interaction UIC 774-3 Field_Bridge Category_Knowledge Category_How-to Structure Type_Bridge Design Code_Eurocode
1. Introduction
With the recent development of high-speed trains globally, structural interaction plays an important role in estimating the impact of rail on the bridge and the optimum design of the bridge system for the safe passage of trains without disturbing the passengers' riding comfort. The UIC 774-3, Eurocode in 1991-2, RDSO, Korean code, ACI, and various codes and standards provide methodologies for considering rail-bridge interaction problems in the design and analysis of railway bridges. These guidelines take into account the dynamic interactions between trains and bridges, which can affect the stress, displacement, and stability of the rail during train passage. Based on experimental and numerical studies, these guidelines provide limiting values for stress, displacement, and stability of the rail to ensure railway bridges' safe and reliable performance. These limiting values are derived to prevent excessive deformations and stress in the rail that could lead to failure of the rail or other bridge components.
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MIDAS CIVIL Bridge Insight verification Prestress Loss Field_Bridge Category_Knowledge Category_How-to Structure Type_Bridge Design Code_Eurocode
1. Introduction
In Prestressed concrete structures, the prestressing force is a crucial variable type. The behaviors of pre-stressed concrete structures depend on the effective prestress because it provides compressive stresses to counteract the tensile stresses that develop in the concrete due to loads. However, the prestressing force does not remain constant over time due to various factors that cause prestress losses. These losses can occur during the transfer of prestress from the tendons to the concrete member or over the service life of the structure.
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Bridge Insight Composite Section Shrinkage Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_Eurocode
A. Introduction:
Differential shrinkage is a phenomenon that occurs in composite sections, which are made up of different materials or different grades of concrete, as the different materials will experience a different rate of shrinkage (i.e., PSC composite I Girder). In this article, we will focus on differential shrinkage due to the different time-dependent effects for the composite section consisting of the same material with different grades of concrete for the deck slab and the girder. Differential shrinkage is an important concept to consider when designing composite sections even when the same material is used for both the girder and deck, the age difference will cause the differential shrinkage effects. This will induce different time-dependent effects on both since both the parts are integrally connected internal stress will be generated to reduce the differential effect.
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Eurocode Bridge Insight Structural Design BS Code Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_Eurocode Design Code_BS
Eurocode VS BS code
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MIDAS CIVIL Bridge Insight Tendon Profile Tendon Loss Field_Bridge Category_Knowledge Structure Type_Bridge
A. Introduction
I'd like to share my old experience with the Tendon Profile.
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Bridge Insight Grillage Models Curved Bridges Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_AASHTO
A. Introduction
Designing a curved bridge was a challenge for me in every aspect. The tendon profile in MIDAS Civil, which we covered before, it’s a very well-known issue,
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1. Introduction
In India, the IS codes, or Indian Standards codes, play a crucial role in ensuring the quality, safety, and reliability of structures in India. It serves as an essential benchmarks to guide the design, construction, modification, and upkeep of structures. These codes are formulated by the Bureau of Indian Standards (BIS), a national body that develops and publishes standards to promote quality and consistency across various industries. These codes are reviewed from time to time and updated to reflect the latest developments in industries.
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