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There are a couple of ways to analyze suspension bridges. As previously discussed (Uniqueness and Difficulties of Suspension Bridge Analysis), the deflection theory proposed by Melan and solved by Moisseiff is one of the first. The second one may be trigonometric methods proposed by Timoshenko (Theory of suspension bridges, Journal of the Franklin Institute, Volume 235, Issue 4, April 1943, Pages 327-349). In this article, a brief explanation of trigonometric methods and related excel, and the example bridge dimensions will be provided.

**What is the Equilibrium Equation for Dynamic Problems? **

The equilibrium equation for any dynamic problem can be expressed as Eq (1). Eq (1) is just an extension of a more familiar equilibrium equation for a static problem. In Eq (2), F is the applied force, k is the stiffness, and y is the displacement. We know F and K, so we can calculate y. In other words, we have only one unknown y, so we can calculate y.

**How to Perform Time-dependent Analysis?**

Mainly there are two ways to perform the time-dependent analysis. One is the time-step analysis and the other is the age-adjusted method. The age-adjusted method is a simplified one and can consider the long-term effects with only a one-step analysis. Of course, this is an approximate way to consider..

In the blog article intro to Time-dependent Analysis for Concrete Structures, we have touched upon the importance of construction stage analysis for concrete structures. The material time function can be plotted and inputted into analysis software like midas Civil to simulate their changing material behavior in various stages of the construction. This article will go over the process of calculating various parameters that contribute to the shape and location of the material's time functions.

Before starting the rigorous discussion about time-dependent analysis, let's start a simple structural analysis problem.

What is the reaction R1 for the blow fixed end beam?

It is easy to obtain the result from bridge finite element analysis, but to get more accurate results requires extra efforts. Even the most robust finite element analysis solvers adopts the method that approximates the structural behavior, by minimizing the associated error function compared with the complex function that represents the realistic structural behavior.

**Why is cable-stayed bridge difficult to analyze? **

Cable-stayed bridges, including so-called Extradosed bridges, do not have any classical solutions. Computer based displacement method is the only way to analyze cable-stayed bridges and it is hard to check the output. Also, in the cable-stayed bridge analysis, the following three nonlinearities should be considered.

From the previous tip geometric nonlinearity explained, Dr. Seungwoo Lee compared various approaches to approximate geometric nonlinearity by showing examples of how they varied the structural effects of the studied cantilever beam. One of the easier and more accurate approaches was through linearized finite displacement analysis in midas Civil, which was then compared with the hand calculation that considered stiffness...

From the previous tip basic nonlinear analysis explained, Dr. Seungwoo Lee talked about some fundamental differences between linear and nonlinear analysis in structural engineering. In a linear analysis, the relationship between the stress and strain of a model is held constantly, and the stiffness matrix of the model stays the same throughout the analysis. For a nonlinear analysis, there can be various factors that contributes to its nonlinearities, for example, material yielding, nonlin,,,

Generally a load rating is the bridge's ability to carry the live load for design and allowable legal vehicles, overloads, and determine weight postings. But how to perform the load rating of Curved and Complex Geometry Composite Steel Bridges in Midas Civil? Tom Less will expand the knowledge of Two-Dimensional/Grillage Modeling and Three-Dimensional Modeling and show how he sets up the inputs like rating design code, rating parameters, unbraced length, fatigue parameter, etc., for bridge rating design.

A linear analysis is when a linear relationship is held constantly for the stress and strain of a model, meaning that the stiffness matrix of the model stays the same throughout the analysis. However, when can an analysis be called non-linear? What are the types of non-linear analysis? Seungwoo Lee, Ph.D., senior supervising engineer at WSP USA is here with us to talk about some basic types of non-linear analysis.