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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.
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.
I'd like to share my old experience with the Tendon Profile.
In this section, we will discuss the damping method applied to Nonlinear Boundary Time History Analysis.
There are four types of damping methods.
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
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.
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.
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)
Figure 2. Time History Load Cases - Nonlinear(Analysis Type), Static(Analysis Method)
Let's have a look at these options in a little more detail.
In the Nonlinear-Direct Integration method, the initial load using Global Control is defined as follows.
Figure 3. Load > Dynamic Loads > Global Control
Select "Perform Nonlinear Static Analysis for Initial Load",
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.
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.
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!
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! 🎉
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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