Rail Structure Interaction Verification as per UIC 774-3 - Part 1

midasBridge TeamMay 24, 2024

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.

MIDAS Connector: Revolutionizing Data Exchange with MIDAS CIVIL NX

midasBridge TeamMay 17, 2024

Introduction to MIDAS Connector

The newly to be released MIDAS CIVIL NX has an API feature installed. API stands for Application Programming Interface, which is a language used for communication between the operating system and applications. In other words, a communication environment has been set up where you can send or receive data from MIDAS CIVIL NX through the API. However, to utilize the API, you need to know how to code using a development language. It feels like there's more to do because you need to know how to code.

Prestress Tension Loss Verification as per EN 1992

midasBridge TeamMay 10, 2024

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.

Empowering Future Engineers: MIDAS IT's Academic Software Initiative!

midasBridge TeamMay 2, 2024

The Reality: Difficulty in Integrating Classroom Learning into Practical Design

Recent surveys indicate that 78% of civil engineering graduates in the United States felt that what they learned in school didn't translate well into practical application. Why is there such a disparity between academia and real-world practice? The primary reason is that while universities predominantly focus on 2D-based mechanics, practical design involves considering various load combinations and complex structures.

[Free Download] Time-Dependent Material Properties Calculation Sheet

midasBridge TeamApril 25, 2024

👉🏻 Check out our previous post

The Impact of Differential Shrinkage

midasBridge TeamApril 25, 2024

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.

The Role of Eurocode and BS Code in Structural Engineering

midasBridge TeamApril 19, 2024

Eurocode VS BS code

 

[API] Temperature Gradient Self-Equilibrating Stress Calculator

midasBridge TeamApril 11, 2024

1. Why do bridge engineers consider Non-linear Temperature Gradients?

Temperature loads threaten bridge safety, especially for long-span bridges. If the bridge is located with a big temperature difference, A structural engineer analyzes and designs a bridge based on the beam theory. The temperature gradient should be considered with the beam theory. The beam theory assumes the beam deforms primarily in one direction, the material behaves linearly elastic, and the beam has a uniform cross-section. It means even if the beam cross-section gets a different thermal expansion depending on the depth, the cross-section does not change, and it is also possible to substitute thermal stress as a self-equilibrating stress in restraint conditions.

[Free Download] Excel for Data Processing with Practice Examples

midasBridge TeamApril 5, 2024

👉🏻 Check out previous post

The Impact of Tendon Profile Choices on Curved Bridge Structures

midasBridge TeamApril 4, 2024

A. Introduction

I'd like to share my old experience with the Tendon Profile.

The Easiest Way to Create Load Combinations

midasBridge TeamMarch 27, 2024

1. Plug-in for Creating Load Combinations Using Only Basic Loads

To design structures, we must necessarily create load combinations. These combinations change depending on the state of the loads affecting the structure, and the coefficients considered for these loads vary according to standards. Therefore, while automatically generated load combinations are used for convenience in creating various load combinations, it is difficult to generate combinations that satisfy all conditions.

Spine and Grillage Models in Curved Bridge Design

midasBridge TeamMarch 22, 2024

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,

Introduction to IS Codes

midasBridge TeamMarch 20, 2024

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.

Optimizing Workflow with MIDAS OpenAPI and Plug-ins

midasBridge TeamMarch 13, 2024

1. MIDAS OpenAPI

   I would like to introduce the basic and advanced information about MIDAS API. I was surprised that many users wanted to use MIDAS API and asked when we could start to use it. Users have contacted us worldwide regardless of specific regions, company size, and areas.

[Part 3. Damping method] Initial Load Optimization in Nonlinear Time History Analysis

midasBridge TeamMarch 7, 2024

📢 To check the entire series, click here

 

 

A. Damping Method

1. Modal & Direct Integration Analysis Method

   In this section, we will discuss the damping method applied to Nonlinear Boundary Time History Analysis.

   There are four types of damping methods.

  • Modal,
  • Mass & Stiffness Proportional,
  • Strain Energy Proportional,
  • Element Mass & Stiffness Proportional

 

Time History Load Cases - Damping Method

 

   The four damping methods are categorized for analysis purposes as follows.

 

 

   The method of applying damping varies depending on whether you want to apply the same damping to all elements of the structure or not.

   The options you choose also depend on whether you use the Modal or Direct Integration methods. The two methods differ in how they account for damping, which can lead to much longer analysis times depending on the selected damping method.

   Depending on the analysis method, the recommended damping method is as follows

  • For the Modal method, the damping is usually applied as "Modal".
  • For direct integration, the damping is generally set to "Mass & Stiffness Proportional".

 

2. Mass & Stiffness Proportional method

   The Mass & Stiffness Proportional method is Rayleigh Damping, which assumes that the damping matrix can be constructed as a linear sum of the mass and stiffness matrices, expressed by the equation below.

 

 

   Here, a and b are the damping coefficients, which can be represented by the natural frequency (w) and damping ratio (h) of the two modes.

 

 

I   n MIDAS CIVIL, enter the natural frequency (or period) and damping ratio (typically 0.05) for the two modes.

 

 

   A common question we get is what values should be entered for Mode 1 and Mode 2. (Is it enough to enter the period values for Mode 1 and Mode 2, or what period values should be entered?)

Let's take a look at a quick overview of Rayleigh Damping to get a better understanding.

 

 

 

   The graph above is for Rayleigh Damping (Mass - Stiffness Proportional Damping).
With two natural frequencies (or periods) and a damping ratio, the coefficients a and b can be calculated, and thus the damping ratio at any frequency can be calculated.
We typically apply a damping ratio of 0.05. However, the determination of two natural frequencies (W1 and W2) with a damping ratio of 0.05 requires engineering judgment.

 

 

 

You can check more of these details in the download file.

 

The remaining contents of 2. Mass & Stiffness Proportional method

B. Conclusion

[Part 2. Direct Integration method] Initial Load Optimization in Nonlinear Time History Analysis

midasBridge TeamFebruary 28, 2024

📢 To check the entire series, click here

 

   So when the Direct Integration method is used, how should we define the initial load?

   In this content, we will discuss the initial load of an analysis using the Nonlinear Direct Integration Method.

 

A. Definition of initial load for Direct Integration method.

   Defining the initial loading conditions is comparatively easier for nonlinear time history analysis using Direct Integration than for the Modal method.

   Let's take a look at the same example from Part 1 and see how the initial load is defined for the time history analysis using direct integration.

 

 

   The Analysis Method is selected as Direct Integration, and the End Time, Time Increment, and Step Number Increment for Output are the same as the Modal method in Part 1. (The "Order In Sequential loading" option can be considered for initial load consideration in Part 1, and selecting ST (static load case) is an inappropriate method for this option).

   In this content, we will see how to consider the initial load using Initial Load (Global Control) in the Nonlinear - Direct Integration method.

 

Initial Load (Global Control)

  • Active only for Nonlinear - Direct Integration analysis is a method for selecting load cases within Global Control and considering them as initial loads.
  • This option allows selecting multiple static Load cases, unlike Time-varying Static Loads where only one load can be selected.
  • It is the same as if you used the Time-Varying Static Loads option to perform a Nonlinear - Static analysis on a static load.

 

Figure 2. Time History Load Cases - Nonlinear(Analysis Type), Static(Analysis Method)

 

B. Initial Load (Global Control)

   Let's have a look at these options in a little more detail.

 

1. Time History Global Control

   In the Nonlinear-Direct Integration method, the initial load using Global Control is defined as follows.

 

Figure 3. Load > Dynamic Loads > Global Control

 

  1. Select "Perform Nonlinear Static Analysis for Initial Load",

  2. Select the static load cases to be considered as initial loads.

 

   With this setting, a nonlinear static analysis of the selected loads is performed. The results are used as initial conditions for the time history analysis.


 

2. Time History Load Cases

   After selecting Initial Load in Time History Global Control, select "Initial Load (Global Control)" in Time History Load Case as follows.

 

Figure 4. Nonlinear - Direct Integration with Initial Load(Global Control)

 

   The initial load applied in Global Control is considered as the constantly acting initial load. Therefore, "Keep Final Step Loads Constant" is always "Checked On".

 

"Cumulate D/V/A Results" is an option to select whether to combine the results of the time history analysis with the results of the initial load analysis.

 

   A detailed description of both options is explained in Part 1.

 

 

You can check more of these details in the download file.

 

3. Global Control (Initial load) / Nonlinear - Static method results comparison

C. Conclusions

[Part 1. Modal method] Initial Load Optimization in Nonlinear Time History Analysis

midasBridge TeamFebruary 23, 2024

📢 To check the entire series, click here

 

In MIDAS CIVIL, elements with nonlinear properties such as seismic isolation, vibration control bearings, and dampers can be represented in the analysis model with the General Link option.

Introduction to AASHTO Bridge Design Specification

midasBridge TeamFebruary 20, 2024

1. Why do we need design codes?

   Numerous impressive structures were created before the formulation of standardized design codes, but challenges existed. The shift to modern design codes introduced a systematic and scientific approach to bridge engineering, enhancing safety, consistency, and reliability in design and construction. Design codes also play an important role in protecting bridge engineers by providing a framework for legal compliance, standardization, risk mitigation, and professional accountability.

Non-linear Temperature Gradient Part 4. Effects on Bridges

midasBridge TeamFebruary 15, 2024

📢 To check the entire series, click here

 

4. Nonlinear Temperature Effects on PSC Box Section

   The above example is difficult to consider in terms of practical use. Therefore, to make a calculation that can be applied to an arbitrary cross-section, we will go over one-by-one through the formulas and calculations that are needed.

 

(1) Section Information

   The example cross-section is a PSC box shape as shown below, and the input of the cross-section is in the form of consecutive coordinates. When using the calculation program, the input should be in a general coordinate system, but for the convenience of the calculation in the example, the following coordinate system is used where the upper right corner is the origin (0,0) and the lower left direction is positive.

 

Figure 1. Example of a PSC box cross-section

 

(2) Section Property

   Sectional properties are calculated using Green's theorem from the input coordinate data. The required section properties for the calculation are the area, second moment of area, and distance from the section's top edge to its centroid.

 

Figure 2. Cross-Sectional Properties

 

(3) Differential Temperature Load

   AASHTO LRFD Heating case - Zone 3 is considered.

Figure 3. Differential Temperature load

 

(4) Section Coordinates and Temperature Gradient Load

   To ensure the accuracy of the calculation, the change point of the temperature gradient load must be included. Therefore, the change point of the temperature gradient load was added to the cross-sectional coordinates, and the temperature gradient load was applied to each node.

 

Figure 4. Temperature gradient load at Each node

 

(5) Restraint force

   The restraint force can be calculated using the equation derived in section 3, but since the temperature and width vary linearly on the z-axis and y-axis, respectively, we can write linear equations in terms of z for temperature (t) and y for width (b) and substitute them into the equation. Therefore, the equation can be expressed as follows:

 

Figure 5. Equation of a straight line based on changes in width and temperature

 

Figure 6. The formula for calculating restraint force

 

   Now, if we apply the formula for calculating restraint force that has been determined to each straight line and calculate it, we can obtain the following restraint force.

 

Figure 7. Restraint force

 

(6) Residual Stress

   Using the calculated acceleration and temperature gradient load, the residual stress at each node is determined as follows.

 

Figure 8. The equation for Residual Stress

 

Figure 9. Residual Stress

 

(7) Calculation and Verification

   This is an Excel spreadsheet designed using VBA based on the formulas introduced above. It allows users to input the loads examined in Part 1/Part 2, calculates the residual stress accordingly, and generates a graph.

 

Figure 10. Sample Calculation

 

   Now, let's verify the created spreadsheet. First, we will use the same cross-section as in the example, and the loads are defined as follows, and the results are shown in the spreadsheet accordingly.

 

Figure 11. Calculation example for verification 1

 

Figure 12. Calculation example for verification 2

 

Figure 13. Calculation example for verification 3

 

   The verification was performed using MIDAS CIVIL. The four simple spans with the same cross-section are created as shown in below the example and analysis is performed by applying the loads according to each design standard.

 

Figure 14. MIDAS CIVIL model for verification

 

The results are as follows.

 

Figure 15. Top Stress - MIDAS CIVIL

 

Figure 16. Bottom Stress - MIDAS CIVIL

 

   As expected, the results show a 99% match with the values obtained from the spreadsheet.

 

Figure 17. Values obtained from the spreadsheet

 

(8) Conclusion

   We have examined the effect of temperature gradient loads on beams according to each design standard. Hopefully, this has provided a basic understanding of temperature gradient loads.

We can take this one step further by using these results to calculate axial strain and bending moment, which can then be converted into equivalent linear temperature loads. By doing so, we can predict the impact of temperature gradient loads in indeterminate structures.

   In design, temperature loads are often included in most load combinations, and if the design is done within the range that does not allow tensile stress, the impact of temperature loads can be significant and cannot be ignored. I hope that the following article will be helpful in design.

 

#Temperature Gradient #Non-linear Temperature #Temperature Gradient #Temperature difference # Design Calculation #BS EN # AASHTO LRFD #BS 5400 #NCHRP #DMRB #CS 454

 

GOODNO, Barry J.; GERE, James M. Mechanics of materials. Cengage learning, 2020.HAMBLY, Edmund C. Bridge deck behaviour. CRC Press, 1991.

 

Would you like to use the Excel Spreadsheet in the content?

Submit the form below right away, and receive the file for calculating temperature gradient loads.

 

(Note! This spreadsheet requires access to the MIDAS CIVIL API for utilization.
If you have any inquiries regarding the CIVIL API, please feel free to leave a comment.)

MIDAS API Plug-in: Inertial Forces Controller

midasBridge TeamFebruary 13, 2024

1. The usual method for calculating inertial force

   For curved and skew bridges, when the overall coordinate system (Global Coordinate System) and the diagonals/orthogonals of the piers are not parallel in the analysis, users need to consider the seismic inertial forces in the horizontal direction acting on the entire pier in the "most unfavorable direction.”

Non-linear Temperature Gradient Part 3. Effects on Beams

midasBridge TeamFebruary 8, 2024

📢 To check the entire series, click here

 

Nonlinear Temperature Effects on Beams

(1) Basic Concept

   Through Part 1 & 2, we looked at how the temperature gradient load of a bridge is calculated based on the design criteria. Now, let's examine how the calculated load affects the bridge deck.