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.
Eurocode Bridge Tips & Tutorials MOTIVE Tool Field_Bridge Category_How-to Category_Industry Structure Type_Bridge Structure Type_Retaining Design Code_Eurocode
Calculations based on EN 1997-1 with Graph Tracer
How uncomfortable and nervous are you? When do you find values manually using a provided 2-D graph? I feel you. I always doubt myself if I guess or choose the correct value. This doubt made me apply more conservative values, and as a result, I got ineffective and uneconomic design results.
I rolled out a Graph Tracer to solve the above issues. The user only needs to input several inputs into this tool and can use the results on their report or calculation sheets. The vague values were calculated elaborately using the spline interpolation method, and the user can find the exact value in a short time.
With the Graph Tracer, I could more easily focus on the essential parts of the design because it helped me escape iterations and a confused workflow. The Graph Tracer will be released in a series, which means it will expand to provide various functions. It will simplify the work process and amplify your design professionalism. Try it now!
Graph Tracer is starting to convert conventional manual work processes to digitalization. Its main purpose is to support engineers in working effectively and accurately. It began with Eurocodes; however, it will soon add international codes!
Accuracy: Calculate trusted value by using linear and spline interpolations
Effective: Find exact value promptly with several inputs and remove iterations
User-friendly: Easy to use with an intuitive interface
Applying Graph Tracer to your project will allow you to experience easy but exact ways to calculate design factors in your work process.
The first series of the Graph Tracer: Earth Pressure Coefficient tool focuses on finding the active/passive soil coefficient exactly, which is the essential factor for reviewing the stability of retaining structures(e.g., gravity walls, embedded walls, composite retaining structures, etc.).
Stability review is an essential part of the structure design and construction design process, especially soil pressure, which is considered the most important external force applied to structures. Active and passive soil pressure changes depending on the characteristics of the soil and wall movement conditions, and finding the exact value is crucial for the stability and economics of the structure.
Annex C of EN 1997-1 provides a table of earth pressure coefficients for calculating the mobilized passive earth pressure in soils based on the log spiral theory proposed by Kerisel and Absi (1990). Kerisel and Absi assumed a log spiral failure surface to provide a more realistic description of the soil resistance mechanism and to complement the limitations of the conventional Coulomb theory due to the assumption of a straight failure surface.
This graph is designed to represent the characteristics of soil and wall traits and provide the earth pressure coefficient under various conditions. Through this graph, engineers can access the coefficient intuitively and get high accuracy simultaneously. Kerisel and Absi's EN 1997-1 Annex C coefficient graph enables the fast and exact calculation of the earth pressure coefficient in the practical design process.
EN 1997-1 Annex C coefficient graph gives high accuracy values; however, it is limited in finding exact values because it does not provide equations.
In particular, the coefficient values are expressed in a logarithmic scale, requiring complex interpretation. For inclined surfaces (β > 0), only limited charts of δ/ϕ′=0, 0.66, and 1 are provided, making it more difficult to estimate intermediate values. This may negatively impact design reliability and efficiency.
Graph Tracer is the fastest and most exact find tool to determine Active(Ka) and Passive(Kp) coefficients based on EN 1997-1 Annex C. The users only need to input β, ϕ', δ values and then find trusted results. Graph Tracer eliminates estimation, ensuring design efficiency and accuracy simultaneously.
Horizontal Active Earth Pressure Coefficient
EN 1997-1, Annex C, figure C.1.1 (β = 0)
EN 1997-1, Annex C, figure C.1.2, C.1.3, C.1.4 (δ/ϕ conditionally different values)
Horizontal Passive Earth Pressure Coefficient
EN 1997-1, Annex C, figure C.2.1 (β = 0)
EN 1997-1, Annex C, figure C.2.2, C.2.3, C.2.4 (δ/ϕ conditionally different values)
1. Input your project parameters
Input parameters: Slope angle of the ground behind the wall(β), Angle of shearing resistance(ϕ'), Angle of shearing resistance between ground and wall (δ).
Input parameters
2. Calculate the coefficient and check the graphs
Execute calculate after input parameters by clicking the "Calculate" button.
3. Check results
Result graphs and tables draw immediately including Horizontal Active(Ka)/ Passive(Kp) Earth Pressure Coefficient. Able to find coefficient depending on β condition and δ/ϕ' values.
4. Zoom-in graph and export results
The user can find detailed values using the zoom-in function. It is possible to download the file as a PNG file or attach it to the report.
Following these straightforward steps, users can quickly and accurately determine the Earth Pressure Coefficient in EN 1997-1 Annex C.
Graph Tracer is a design efficiency and accuracy tool. The user can get reliable results with simple parameters. Even in complex non-linear relationships, this tool finds the accurate coefficient using an automated interpolation method.
This tool allows engineers to focus on more engineering work, not a repeated and ambiguous process. It is helpful to export calculated results easily and comfortably to apply your project. The Graph Tracer suggests a new paradigm to find the earth pressure coefficient.
As a result, engineers can improve design quality and save time. Experience shifts your design work for yourself over the simple calculator.
Click the link below to access MIDAS Tools for free.
Eurocode Bridge Tips & Tutorials MOTIVE Tool Field_Bridge Category_How-to Category_Industry Structure Type_Bridge Design Code_Eurocode
Understanding Eurocode 1:
Actions on Structures and the Role of Basic Wind Velocity Data
Whenever I applied wind loads during structural design, I’d find myself hauling out a hefty tome standard manual that could double as a doorstop and squinting at tiny, barely readable maps, trying to pinpoint my project location. For familiar regions, this was manageable, but for less familiar places, it often turned into a frustrating guessing game, especially when manuals offered nothing but pages of cryptic tables instead of clear maps. I’d waste valuable time double-checking, second-guessing, and wondering if I had the right data. That’s why we created the Basic Wind Velocity Map—a digital tool designed to make retrieving wind speed values quick, intuitive, and frustration-free. No more flipping through outdated manuals or wrestling with static maps; this tool ensures you can instantly access accurate wind data, focus on what matters most, and design confidently. 🚀
With the Basic Wind Velocity Map, finding essential wind data has never been easier. Click on your desired location to instantly retrieve the Fundamental Basic Wind Velocity (vb,0) needed for wind load calculations. Alternatively, you can enter your project address directly into the tool for precise, location-specific results.
Pair this data with our Design Guide, and you'll effortlessly calculate wind pressures and forces tailored to your structural design needs. This streamlined process guarantees efficiency and accuracy, allowing you to focus on designing safer and more reliable structures.
The Basic Wind Velocity Map redefines how engineers access wind speed data. Built with an intuitive interface and the seamless functionality of modern mapping tools, it eliminates the need for tedious manual analysis of static maps or dense tables.
Effortless Navigation: Instantly retrieve any location's wind velocity data (vb,0).
Improved Accuracy: Access precise data that is critical for reliable wind load calculations.
Time-Saving Efficiency: Skip manual interpretation and focus on designing safer structures.
1. Find the Tool: Find the tool for “Wind Velocity Maps” (Link)
2. Input Your Project Location: Type in your project's address or click directly on the map.
3. View Velocity Data: Instantly retrieve your location's wind velocity(vb,0).
By using the Basic Wind Velocity Map, engineers can eliminate inefficiencies, streamline their workflows, and focus on delivering safe, innovative designs without unnecessary delays.
1. Select Standards:
Choose from supported countries and their respective standards:
|
Country |
Standards |
|---|---|
|
Belgium |
bel-en-1991-1-4 |
|
Cyprus |
cyp-en-1991-1-4 |
|
Denmark |
dnk-en-1991-1-4 |
|
France |
fra-en-1991-1-4 |
|
Germany |
deu-en-1991-1-4 |
|
Italy |
ita-en-1991-1-4 |
|
Poland |
pol-en-1991-1-4 |
|
Moldova |
mda-en-1991-1-4 |
|
Romania |
rou-en-1991-1-4 |
|
Spain |
esp-en-1991-1-4 |
|
United Kingdom |
gbr-en-1991-1-4 |
2. Get Results:
Enter your location or click on the map to retrieve data.3: Check the fundamental basic wind velocity values.
3. Check the Values:
Review the fundamental wind velocity values (vb,0).
The fundamental basic wind speed values (vb,0) can be applied to various design calculations. Here are a couple of examples:
Peak Velocity Pressure Calculation at Height (🔗Link)
Engineers can calculate peak velocity pressure at specific heights using the tool's wind velocity data (vb,0). This data is essential for determining wind pressure and enabling accurate assessments of external forces on structures.
Wind Force Calculation (🔗 Rectangular Piers, 🔗Circular Piers)
With the wind velocity values, you can calculate wind loads on structures like rectangular or circular bridge piers. This data can be directly applied in simulations and structural designs for enhanced accuracy.
By directly applying this data, engineers can achieve more accurate designs, reduce errors, and improve overall structural safety.
The Basic Wind Velocity Map has revolutionized how European designers access basic wind speed data. Gone are the days of wasting time searching through country-specific maps for relevant information. This tool is fast, intuitive, and provides essential data for wind load calculations.
If you want to enhance structural safety and streamline your design process, it’s time to experience the Basic Wind Velocity Map. You can achieve more intelligent and efficient designs with just a few clicks.
Add innovation to your design journey and unlock smarter, more efficient workflows with just a few clicks.
Click the link below to access MIDAS Tools for free.
Eurocode Bridge Tips & Tutorials MOTIVE Tool Field_Bridge Category_How-to Category_Industry Structure Type_Bridge Design Code_Eurocode
We usually rely on the response spectrum data generated by our software. However, you'll manually open Excel to create a custom spectrum when a project has specific requirements. The reference peak ground acceleration (PGA) didn't match standard values, or additional factors must be applied for uncommon site conditions or design scenarios.
I've been there, too. Even when the project does not explicitly require it, I often encourage my team to draw a response spectrum manually. For seismic design engineers, understanding the relationship between a structure's natural period and ground acceleration isn't just helpful—it's essential. Whether you're analyzing general structures or ground models using EN1998-1 or designing bridges according to EN1998-2, mastering this concept is the foundation of effectively working with Eurocode 8.
Say goodbye to tedious and repetitive tasks! We created the Response Spectrum Generator to simplify seismic design. This tool complies with 🔗Eurocode 8 and delivers quick, accurate results for both elastic and design conditions. It allows you to visualize horizontal and vertical elastic spectrum data on a single graph, making comparisons and insights much clearer.
However, creating a response spectrum isn’t just about setting the reference PGA—factors like ground type and importance must also be carefully considered. The Response Spectrum Generator simplifies these complexities, delivering precise results quickly and effortlessly.
Why use it? Every project has unique demands. This tool removes the burden of manual calculations, helping you focus on critical design decisions while streamlining your workflow for accurate and efficient results.
With the Response Spectrum Generator, seismic design has never been this intuitive or efficient. Discover a tool every engineer needs—try it today!
The Response Spectrum Generator is a practical tool designed to reduce repetitive tasks, allowing engineers to concentrate on the core aspects of their designs. Engineers no longer have to spend hours manually generating and comparing graphs. This tool improves design efficiency in several key ways:
Focus on Design: Shift your efforts from repetitive tasks to innovation and decision-making.
Enhance Accuracy: Instantly compare Elastic and Design spectra to identify key differences.
Save Time: Generate all necessary spectra with just a few clicks.
1. 👀 Everything at a Glance
View Horizontal and Vertical Elastic and Design spectra simultaneously. Say hello to cleaner comparisons and more precise insights.
2. 🛠️ Interactive Features
Easily zoom, pinpoint critical data points, and export graphs as PNG files—ready to drop into your reports.
3. ⚙️ Flexible Input
Define parameters like Ground Type, PGA, Spectrum Direction, and Damping Ratio with an intuitive interface.
4. 📈 Real-Time Results
Get instant spectra generation, no matter the seismicity levels. Faster insights mean smarter, data-driven decisions every time.
The Response Spectrum Generator transforms seismic data analysis with accuracy, speed, and an intuitive interface, making Response Spectrum generation effortless.
1. Input Your Project Parameters
Click the "Inputs" button and fill out the form with seismic parameters such as Ground Type, PGA, Importance Factor, and Behavior Factor.
2. Set Spectrum Preferences
Choose the Spectrum Direction (Horizontal or Vertical) and Spectrum Shape (Elastic or Design).
Instantly view all four spectra in a unified graph and table. Compare Elastic and Design Spectra across directions in real-time.
3. Export the Results
Zoom in for clarity or download the graph as a PNG file for documentation and further analysis.
1. Ground Type
Classified as A, B, C, D, or E based on the site's stratigraphic profile (refer to EN1998-1 Table 3.1).
2. Spectrum Type
3. Verify Structural Stability
The PGA value is obtained from the Seismic Hazard Map provided in the National Annex.
4. Importance Factor (γ)
5. Viscous Damping Ratio (ξ)
6. Behavior Factor (q)
7. Lower Bound Factor (β)
A horizontal design spectrum parameter with a recommended value of β = 0.2 (see National Annex).
Building upon the Recommended Standards of EN1998-1, we plan to develop an enhanced Response Spectrum Generator incorporating National Annex guidelines for each European country. This advanced tool will be seamlessly integrated with🔗Seismic Hazard Maps, enabling comprehensive European seismic assessments.
The upcoming RS Generator will provide:
Country-Specific Response Spectra based on National Annex requirements.
Direct Integration with Seismic Hazard Maps for site-specific PGA values.
This tool will empower engineers to conduct accurate, reliable, and streamlined seismic assessments, ensuring safety and compliance for European structures by aligning with Eurocode 8 and National Annex guidelines.
The Response Spectrum Generator eliminates the traditional inefficiencies of seismic analysis and empowers engineers to work faster and wiser. This tool enhances precision, efficiency, and overall design workflow by generating and comparing all spectra in real time. For projects requiring compliance with Eurocode 8, the RS Generator is an essential innovation that brings modern technology into seismic design practices.
Say goodbye to outdated methods and embrace a streamlined, more intelligent approach to Eurocode 8 compliance.
Design faster. Analyze smarter. Build safer.
Click the link below to access MIDAS Tools for free.
Eurocode Bridge Tips & Tutorials MOTIVE Tool Field_Bridge Category_Knowledge Category_Industry Structure Type_Bridge Design Code_Eurocode Design Code_AASHTO Design Code_ACI
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.
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.
1. Select Graph
2. Select Standard Code
3. Put values
4. Click the calculation button
1. Select Graph type
2. View a result as a table
3. Check additional information
4. Graph tool (save, zoom in and out, move, restore)
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.
Click the link below to access MIDAS Tools for free.
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.
Eurocode Bridge Tips & Tutorials MOTIVE Tool Field_Bridge Category_How-to Category_Industry Structure Type_Bridge Design Code_Eurocode
Understanding Eurocode 1: Actions on Structures and the Role of Temperature Data
I still vividly remember the first time I had to determine the maximum and minimum air shade temperatures using the UK National Annex. My project site was situated between London and Brighton, and I turned to the isothermal maps for guidance. However, finding the exact location on the map turned out to be a surprisingly daunting task. The maps, embedded in a PDF file, lacked the precision and interactivity we've come to expect in the 21st century.
To my disbelief, this antiquated process had remained unchanged for decades. Pinpointing a project's location on a static 2D map was inefficient and error-prone. Like many engineers, I felt frustrated by the lack of modern tools to streamline this essential part of the design process. This frustration ultimately led me to develop a solution: the Maps of Isotherms tool, a more accurate, convenient, and intelligent way to handle temperature data.
Now, we are focusing on our new Tool. For engineers working with Eurocode, every provision and note holds significance. Among the codes, 🔗Eurocode 1: Actions on Structures is essential for load assessment and is fundamental to structural design. This code enhances design efficiency by allowing engineers to apply its parts based on specific project needs selectively.
One essential aspect of Eurocode is the 🔗National Annex. Engineers must project the National Annex for localized guidelines depending on the project's location. While the annex provides sufficient information for design purposes, extracting precise details can be time-consuming. A case in point is the Map series. Through this blog, MIDAS will introduce three Map series. The first is "Maps of Isotherms,” the second is "🔗Seismic Hazard Map," and the last is the "Fundamental Basic Wind Velocity Map." We'll talk about the "Maps of Isotherms" in EN 1991-1-5, which addresses thermal actions in this blog. These maps are crucial for evaluating temperature data for structural design but often require meticulous interpretation.
The Maps of Isotherms tool is a modern solution that simplifies temperature data extraction. Designed to feel as intuitive as everyday map applications, it revolutionizes how engineers interact with isothermal maps.
1. Input Your Project Location: Type in your project's address or click directly on the map.
2. View Temperature Data: Instantly retrieve your location's maximum and minimum shade air temperatures.
3. Visualize Isothermal Areas: The tool provides a color-coded visualization of isothermal zones, making it easy to interpret temperature gradient tools.
With this Tool, engineers can bypass the cumbersome task of manually analyzing static maps, saving time and effort.
1. Search methods: a. Select the map directly, b: Enter the address
2. Select Standards: currently provides Belgium, Czech Republic, Finland, Greece, Ireland, and United Kingdom National Annex.
3. Convert the maximum and minimum temperature contour maps.
4. Check the maximum and minimum values.
When do engineers use temperature data? Temperature plays a crucial role in the design of fixed-supported structures, 🔗long-span bridges, high-rise buildings, and more. Here's a brief overview of how temperature data is used in the design process:
1. Collect Temperature Data
Gather climate data for the design area, including maximum and minimum temperatures. This information serves as the foundation for thermal load calculations.
2. Calculate Thermal Stress
Calculate the thermal stress acting on the structure using temperature changes and the material's coefficient of thermal expansion. This step ensures that the structure can handle temperature-induced deformations.
3. Verify Structural Stability
Analyze the deformation and stress caused by thermal loads to confirm the structure's stability. This evaluation ensures the design meets safety and performance standards.
With technological advancements, engineers no longer need to rely on outdated methods for temperature data analysis. Modern tools simplify the data collection process and provide additional capabilities for subsequent steps in the design process.
A 🔗Uniform Temperature Load in Structure and 🔗Temperature Gradient Calculation Toolwill soon be available. This Tool will:
By integrating these tools into their workflow, engineers can focus on innovation and design rather than time-consuming manual calculations.
Eurocode 1991-1-5 provides the essential framework for structural design, and temperature data is a vital part of this process. While traditional methods of working with isothermal maps have been cumbersome, tools like the Maps of Isotherms and the upcoming load calculator transform how engineers approach thermal analysis.
These tools empower engineers to access precise data, streamline calculations, and ensure their designs are both safe and efficient. We can take a significant step forward in modernizing structural engineering practices by embracing these advancements.
Click the link below to access MIDAS Tools for free.
Bridge Insight Rail Structure Interaction UIC 774-3 Field_Bridge Category_Knowledge Category_How-to Structure Type_Bridge Design Code_Eurocode
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 CIVIL Bridge Insight verification Prestress Loss Field_Bridge Category_Knowledge Category_How-to Structure Type_Bridge Design Code_Eurocode
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.
Bridge Insight Composite Section Shrinkage Field_Bridge Category_Industry Structure Type_Bridge Design Code_Eurocode
Bridge Insight Composite Section Shrinkage Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_Eurocode
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.
Eurocode Bridge Insight Structural Design BS Code Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_Eurocode Design Code_BS
MIDAS CIVIL Tips & Tutorials Temperature Gradient Thermodynamics Self-Equilibrating Field_Bridge Category_How-to Category_Industry Structure Type_Bridge Design Code_Eurocode Design Code_BS Design Code_AASHTO
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.
Bridge Insight Temperature Gradient Non-Linear Elements Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_Eurocode Design Code_BS Design Code_AASHTO
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.
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
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
AASHTO LRFD Heating case - Zone 3 is considered.
Figure 3. Differential Temperature 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
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
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
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
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.)
Eurocode Bridge Insight Temperature Gradient BS Code AASHTO Classification Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_Eurocode Design Code_BS Design Code_AASHTO
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.
Eurocode Bridge Insight Temperature Gradient BS Code Field_Bridge Category_Knowledge Structure Type_Bridge Design Code_Eurocode Design Code_BS
In BS EN, the temperature gradient load for bridges is described in section 6.1.4.2, "Vertical temperature components with non-linear effects (Approach 2)," of BS EN 1991-1-5. The load is specified differently depending on the type of bridge deck, which can be steel, composite, or concrete.
In addition to these rules, the magnitude of the temperature gradient load also varies depending on the thickness of the pavement and the height of the structure. This information is provided in Appendix B of BS EN.
BS EN 1991-1-5 Annex B
It should be noted that the temperature gradient load provided in BS EN is inherently more complex than that of AASHTO LRFD, and there are several errors and incomplete parts, making it difficult to calculate the load.
Therefore, let's look at BS 5400-2:2006 together, and determine the correction and load calculation method for it.
For reference, the latest information on this load can be found in CS 454 - Assessment of highway bridges and Structures provided by DMRB (Design Manual Road Bridge).
The steel deck provides 4 types of load depending on the girder shape and temperature. The temperature based on thickness is divided into three categories: unsurfaced, 20mm, and 40mm.
In the case of 1b, the temperature according to the surfacing thickness is not provided.
In BS 5400-2, 1b is separated into group 2, and a table showing temperature changes according to surfacing thickness is provided, so it should be applied accordingly.
BS EN 1991-1-5 Figure 6.2a & Annex B Table B.1
BS 5400-2 Figure 9 & Annex C Table C.1a & C.1b
The composite deck has a total of four different temperature gradient load categories which are divided based on Normal/Simplified procedures and temperature effects. Additionally, ten sets of temperature gradient loads are provided taking into account the variation of surfacing thickness according to the height of the slab.
In "Heating", it is expressed as "h2" and is applied across the entire cross-section.
In Cooling, the lengths for h1 and h2 are missing.
Regarding T2, although the diagram shows 4℃/-8℃ for a 100mm surfacing, no table is provided for other conditions.
There is no table provided for slab depth and pavement thickness in the Simplified Procedure.
Heating insets are replaced with those of BS 5400-2.
The length is applied in the same way as heating.
T2 uses 4℃/-8℃ as a fixed value.
It is not used in the case of the simplified procedure.
BS EN 1991-1-5 Figure 6.2b & Annex B Table B.2
BS 5400-2 Figure 9 & Annex C Table C.2
Loads are provided in two types according to temperature, but 36 sets of temperature gradient loads are provided according to the section height and pavement thickness, so several linear interpolations are required to apply them.
In Heating, when h is more than 0.8, it is indicated as 13.0℃, but in Annex Table B.3, it is indicated as 13.5℃.
In Cooling, the range notation of h3 is incorrect.
In cooling, h2/h3 is set to be larger than 0.20m.
In B.3 Table, although Cooling T1 is indicated as 4.3 for a slab depth of 1.0m and surfacing thickness of 200mm, it should be interpolated to the intermediate value for the depth of 0.8/1.5.
It is applied in accordance with BS 5400-2, as 13.5°C.
Range notation follows BS5400-2.
In Cooling, h2/h3 is set to be less than 0.20m.
It is revised to 4.8 instead of 4.3.
BS EN 1991-1-5 Figure 6.2c & Annex B Table B.3
BS 5400-2 Figure 9 & Annex C Table C.3
There are no guidelines other than the specified slab height and surface thickness. However, based on experience, linear interpolation within the range is acceptable. linear interpolation is performed within the range and the closest value is taken for the value exceeding or less than this.
BS EN 1991-1-5 Annex B. Table B1 to B3
Conceptually, the temperature load on the top surface of a slab decreases as the thickness of the surface increases.
In the case of Type 2 & 3, when the thickness is unsurfaced, i.e., zero, the value is calculated to be smaller than when there is thickness. Then, in the case of types 2 & 3, should the unsurfaced and 50mm be interpolated for the surface thickness of less than 50mm? A question may arise.
This can be seen by referring to BS 5400-2, which specifies that the surfaced thickness includes waterproofing thickness. This means that Types 2 & 3 can be divided into two types of surfaces: one with waterproofing and another without any surfacing.
Therefore, for sections with a surfacing thickness of 50mm or less, it is necessary to interpolate the value between waterproofing thickness and 50mm, and CS454 provides accurate information on this.
BS 5400-2:2006 Annex C
CS 454 Appendix D2.3
In the load combination of BS EN, the uniform temperature and temperature difference are not separately dealt with, but expressed as one “Thermal action”.
BS EN 1991-1-5 6.1.5
Based on the above, the calculation sheet for determining the temperature gradient load can be prepared as follows:
Calculation Example by Deck Type
BS EN 1991-1-5 covers a wide variety of applications for temperature gradient loads based on the shape and variation of temperature. However, it has inherent errors that can be confusing for engineers encountering the standard for the first time. Therefore, it is necessary to compare it with BS 5400-2:2006 to understand it better.
If possible, It is recommended to apply the latest information contained in DMRB CS454 as much as possible.
Imbsen, Roy A., et al. Thermal effects in concrete bridge superstructures. National Cooperative Highway Research Program, 1985.Shushkewich, Kenneth W. "Design of segmental bridges for thermal gradient." PCI journal 43.4 (1998): 120-137.AASHTO, LRFD Bridge Design Specification, Ninth Edition, American Association of State Highway and Transportation Officials, Washington, D.C., 2020.AASHTO, LRFD Bridge Design Specification, SI Units, Fourth Edition, American Association of State Highway and Transportation Officials, Washington, D.C., 2007.BSI, BS EN 1991-1-5, Eurocode 1 : Actions on structures - Part 1-5: General actions - Thermal actions, British Standard Insititution, London, 2003.BSI, BS 5400-2, Steel, concrete and composite bridges - Part 2: Specification for loads, British Standard Insititution, London, 1978.BSI, BS 5400-2, Steel, concrete and composite bridges - Part 2: Specification for loads, British Standard Insititution, London, 2006.England, Highways, CS 454 Assessment of highway bridges and structures, The National Archives, Kew, London, 2022.Emerson, Mary. Temperature differences in bridges: basis of design requirements. No. TRRL Lab Report 765. 1977.
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