📢 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.

 

Please fill out the Download Section (Click here) below the Comment Section to download the Full Webinar PDF File 

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In June 2020,  we hosted a webinar, “How I Design Bridge : Load Rating of Steel U-Through Bridge" by Abdullah Zaid, Senior Engineer/SMEC.

Please fill out the Download Section (Click here) below the Comment Section to download the Full Webinar PDF File

 

 

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Load Rating of Steel U-Through Bridge

 

 

Please fill out the Download Section (Click here) below the Comment Section to download the Full Webinar PDF File.

 

To watch the full webinar video, click here.

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Table of Contents 

*Click the content to move to the section

 

1. Introduction

2. When to go for Dynamic analysis?

3. Case Study

4. Conclusion

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High-speed rail is becoming increasingly popular worldwide. Many countries are investing in high-speed rail as a way to reduce travel times, improve transportation efficiency, and reduce dependence on automobiles and air travel. The growth of high-speed rail has been driven by factors such as increasing urbanization, population growth, and the need to reduce carbon emissions from transportation.

Please fill out the Download Section (Click here) below the Comment Section to download the Full Webinar PDF File 

 

The fatigue analysis is one of the assessment methods of bridges. Time History Analysis can be used to calculate the fatigue stresses. In this course, we tried to broaden your understanding of functions that are for time history analysis in midas Civil. In addition, we walked through in detail the process of time history analysis. It will be helpful to most of the bridge engineers who handle the time history analysis.

Please fill out the Download Section (Click here) below the Comment Section to download the Full Webinar PDF File 

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Steel composite footbridge Morava project is presented in this session. The structure is described with interesting remarks from the assembly. Practical experience on how to design footbridges that are sensitive to the load imposed by pedestrians is shared. After this session, bridge engineers will understand more deeply how to deal effectively with dynamically loaded bridges.