Defining Suspension Bridges: An Engineering Marvel

Suspension bridges are remarkable structures supported by massive main cables stretched between two or more towers. This design is the preferred choice for expansive spans where conventional bridge types prove impractical. The main cables, anchored at both ends of the bridge, are under tension and bear the weight of the bridge deck along with dynamic loads from vehicles and pedestrians. Typically, the deck hangs below these main cables, secured by smaller vertical cables or rods.

 

Beam Bridges: An Essential Element in Transportation Infrastructure

Beam bridges, commonly referred to as girder bridges, represent one of the most prevalent and fundamental bridge types globally. Despite their apparent simplicity, these structures play a pivotal role in our transportation systems, ensuring the safe passage of vehicles and pedestrians across various terrains such as rivers, valleys, and highways. This article delves into the design, construction, and essential features of beam bridges, highlighting the science behind their stability and strength.

 

1. Introduction

When performing the Rail-Structure Interaction (RSI), It is often found that the stress limits are exceeding the permissible values. So there are some countermeasures to ensure safety. Let’s look at how we can implement these control measures which affect the stresses in rails when performing rail structure interaction.

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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.

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.

 

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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.

Eurocode VS BS code

 

A. Introduction

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

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,

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.

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• [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.