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.

What is the Support of Excavation System?

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.

How to Design Bridge Footing and Its Pile Spacing?

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.

Iteration and Optimization

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.
 

Example

Creep Analysis 6

Creep Analysis 7

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.

Creep Analysis 1 

Unsymmetric Section Analysis

Overview

Sometimes we need tiresome calculations, even though they are not critical nor difficult, but they are essential, and they take time if we do not have proper tools. One of these is the moment of inertia calculation for cracked, circular concrete sections. We need this calculation when we perform service stress checks for flexure and deflection checks.