# Industrial Applications

DOI: 10.4018/978-1-4666-6379-4.ch013

## Abstract

The application of structural analysis techniques to solve real engineering problems is an entirely independent discipline by itself that cannot be properly presented in a book of structural mechanics. However, it is important to give an overview of how mathematical models can help make engineering decisions. This is the subject of the current chapter. The context of the presentation is that of earthquake safety assessment. Of course, this is not the only industrial application of the fracture and damage mechanics of frames, but it is a very representative one and a good example of it. The chapter is organized as follows. First, the problem is presented and a protocol to solve it is described in Section 13.1. Then, an academic software that can be accessed via Internet is described in Section 13.2. This program is used to solve some examples of real structures in the last section of the chapter.
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## 13.1 Analysis And Diagnosis Of Vulnerable Structures

Any structure, for instance a building, can be evaluated using static or dynamic analyses. Besides, any of these studies may be performed considering linear or nonlinear behavior. The models, based on Damage and Fracture Mechanics, described in the former chapter may be used with any of the currently established nonlinear procedures for seismic structural assessment.

This chapter presents some industrial applications using nonlinear dynamic analysis. For this purpose, a mathematical model of a structure is subjected to an earthquake shaking represented by ground motion time histories corresponding to an earthquake hazard. Commonly seismic hazard is assessed from instrumental, historical and geological records. It varies from place to place because depends on the magnitudes of likely earthquakes, how often they occur and the properties of the soil through which the earthquake waves travel. In this chapter, three hazard levels are stated (see Table 1). They are defined through the probability of exceeding a certain amount of ground shaking in 50 years, how often they occurs (Mean Return Period) and a corresponding peak ground acceleration (PGA) that is defined as the maximum acceleration experienced by a particle during the course of the earthquake motion. PGA is expressed as a percentage of the acceleration of gravity (g). The greater an earthquake magnitude, stronger is the ground motion it generates.

Table 1.
Earthquake Hazard Levels
 Earthquake Probability of Exceedance (50 Years) Mean Return Period (Years) Percentage of Peak Ground Acceleration (% PGA) Frequent 50% 72 0.4 Severe 20% 225 0.8 Rare 10% 474 1.0

Since the calculated response can be highly sensitive to the characteristic of the ground motion, it is recommendable the use of several ground motion records trying to cover all the potential shaking movements in the zone. When several real ground motions are not available, simulated time history data can be used. These records should have an equivalent duration and a spectral content corresponding to the zone where the structure is placed. These simulated time history data can be obtained from the general response spectrum, that is a plot of the peak acceleration, velocity or displacement of a series of oscillators of different natural frequency that are forced to move by the same base vibration. The description of the procedure for the calculation of simulated ground motions is out of the scope of this book but it can be easily found related information in the technical literature, some of them are cited in the references of this chapter. The analyses presented in the next sections were performed using only one simulated time history data.

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