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.

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A. Introduction

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

📢 To check the entire series, click here

• [Part 1. Modal method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

• [Part 2. Direct Integration method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

• [Part 3. Damping method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

 

 

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.

 

 

📢 To check the entire series, click here

• [Part 1. Modal method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

• [Part 2. Direct Integration method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

• [Part 3. Damping method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

 

   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.

 

📢 To check the entire series, click here

• [Part 1. Modal method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

• [Part 2. Direct Integration method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

• [Part 3. Damping method] Easy Guide to Considering Initial Load in Boundary Nonlinear Time History Analysis

 

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.

Hello civil engineers . This is Connor and Ben!! 👬

   In railway or highway design projects, structure engineers always receive decided alignment from the project manager. Highway or Railway alignment usually changes slightly because of many external factors while working on a project. Sometimes, slightly changed alignment can have potential critical issues to construction or other project steps, serviceability, and even a legal issue. For example, a transition curve is related to drivability and driving safety. If so, structural engineers must recognize and consider that minor change. Let's look into how structure engineers change alignment during their projects.

Hello civil engineers . This is Connor and Ben!! 👬

Happy New years 🌞 civil engineers . This is CoBen!! 👬

It's time for a review, as usual. Do you remember Offset function in CIVIL NX?

Let me reiterate. You cannot apply a Beam End Offset at the same time when a Section Offset is in place. It is not possible to apply Offsets simultaneously.

For more details, you can click on 'Offset function in CIVIL NX' to check it out!

Stability Check for Spread Footing

Hello everyone, Welcome back 🎉. This is CoBen!! 👬

Do you remember the content we shared last week?

For those who may have missed the previous content or are a bit unclear, let me briefly summarize it. 🤓

Last week, we shared a method for simultaneously checking multiple loads.

Click on the Display menu in the View tab, and in the Load tab, check on specific loads or load combinations you want to represent. This will display all selected loads on the model.

For more details, you can click on 'Displaying Multiple Loads Simultaneously' to check it out!

 

Hello everyone, CoBen here! 🎉

Construction Stage Modeling and Analysis of PSC BOX Girder Bridge

Evaluating Tendons Through Simulation in Civil Engineering

 

Please fill out the Download Section (Click here) below the Comment Section to download the Complete Guide to Seismic Anlalysis

 

Please fill out the Download Section (Click here) below the Comment Section to download the Complete Guide to Seismic Anlalysis