Motives for better Engineering
Explore horizontal earth pressure,
Coulomb's theory, and its applications.
Compare geotechnical results and
understand the trial wedge method's nuances.
Explore the technical content on vessel collision
to calculate the annual frequency of bridge component collapse.
Introducing the concept of seismic isolation design.
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It is easy to obtain the result from bridge finite element analysis, but to get more accurate results requires extra effort. Even the most robust finite element analysis solvers adopt the method that approximates the structural behavior, by minimizing the associated error function compared with the complex function that represents the realistic structural behavior.
Concrete Construction Stage Analysis Cantilever Bridge Nonlinear Analysis moment redistribution America Shrinkage Creep Coefficient
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.
With the help of Tarcisio Barreto Celestino and Antonio Bobet, our MIDAS Expert Osvaldo Paiva Magalhães Vitali took on a new approach using midas GTS NX on tunnels with complex ground and loading conditions. In their recent publication in the Soils and Rocks Journal, we can see how they used the features in midas GTS NX to impose body forces to the 3D finite elements; this is done by providing components of the Cauchy stress tensor.
Soil Structure Interaction Finite Element Analysis MIDAS GTS NX Construction Stage Analysis Nonlinear Analysis America
Believe it or not, once upon a time, there were no computers available for us, bridge engineers. At that time, we had to perform every calculation by hand using calculators or even slide-rules. It was quite dull and time-consuming. Now all we have cutting-edge computers, which is way better than those we used when we landed at the Moon. Everything looks nice, and life seems beautiful, doesn't it?
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.
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.
Iteration is just a repeated calculation.
If we want to solve an equation x + 1 = 5 , we can assume x and check whether x + 1 = 5 or not. If not, we can try another value of x and repeat this calculation until x + 1 = 5.
In this simple equation, we can solve x = 5 - 1 = 4 easily. But some engineering problems are more complicated and iteration is more efficient and/or sometimes iteration is the only way to find the solution.
If we want to solve another equation xy = 5, this is rather complicated because there are infinite combinations of x and y’s. However, if we can add some “constraints” like we want to minimize x + y, we can find the solution and this is called the “optimization problem”.
(If another condition is something like, x + y = 4, this is not an optimization problem because there is only one set of solutions.)
In our pile cap problems, there are many combinations of pile cap dimensions that satisfy all requirements. In this case, we can try to find the pile cap dimensions that satisfy all requirements and corresponds to the minimum volume, and this is a good example of both “Iteration” and “Optimization”.
(There can be an argument that the minimum volume can not be optimum. Someone can insist that the optimum shall be minimum cost and we have to consider reinforcements, forwork, etc. The author has no objection to this, but still believes minimum volume is a good choice as the target.)
“Optimization” does need “Iteration” and the purpose of “Iteration” is “Optimization”, so these two terminologies are somewhat mixed and have different meanings for each engineer. It is not a universal/correct definition, but the author accepts “Iteration” as checks for all possible scenarios, and “Optimization” as finding only the optimum in the fastest way.
Think about a two-span continuous bridge, as shown in Fig 1. Let's calculate the secondary creep moments. Detailed dimensions and creep factors, etc., are not important, and the MIDAS file "Creep 2ndary Check"is attached for the reader's reference.