Literature Review Chapter: Factors Leading to Failure

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[. . .] The programs (QC/QA) are organizational practices that ensure the expectations of the bridge under construction are met. The program assures the quality of the materials being used and ensures the right implementations of the proposed procedures are followed to the latter during the construction. For instance, the designing phase of the project will require the designers to confirm that their calculations are done with accuracy and are well programmed to avoid bridge failure. The program is therefore implemented to ensure that there is reduced instance of committing errors and omitting some major elements when designing the bridge (Federal Highway Administration, 2011, p 6).

The structural system of the cable stayed bridge

Figure 1.1

Fig. 1: The structural system of the cable strayed bridge (Wolff & Starossek, 2009, p.18).

The cable-stayed bridge shown in the figure 1 is the bridge under consideration, constructed in the arrangement of a fan using 80 cables on each of the vertical planes. The cables used have a cross-sectional area of about 40-117 cm2 and the usual pretension is in a manner that will support the bridge with permanent weights. In most cases, the pylons are constructed using compressed concrete. Cross grinders and steel decks make up the stiffening grinder, which is restrained by the use of cables. Beam elements are used to model the grinders and the pylon, whereas the truss elements are used when modeling the cables (Wolff & Starossek, 2008, p 2).

The Tree diagram-showing the top categories of default and failure

Figure 2: symbols used in fault tree diagrams

Symbol

Case

Usage

Events

Is used to represent the topmost and intermediate events

Basic Events

Represents the basic events which is usually the lowest resolution level of the tree

Or Gate

The Or Gate exists only in case one input event also exists

And Gate

The And Gate exits in cases where the all connected events (input) also exist in a simultaneous manner

When utilizing the tree diagram, modeling of bridges are used in determining the most critical paths that lead to failures of a bridge, in this case the cable stayed bridge. Structural elements of interaction, actions like corrosion/fatigue, environmental effects like floods, redundancy and many causes of failure are indicated, with the intention of assisting designers improve the quality and conditions of the bridges, or curb the issues resulting to bridge failures. Most of the illustrations of the fault tree diagrams cater for the qualitative analysis of the bridge, however in some instances; the data could be used for quantitative analysis, in determining the probability of different failures of bridges. There is always the provision for evaluation of the bridge design, hence improving the entire quality of the bridge.

The tree diagram for the cable stayed bridges

The general frame of the fault tree diagram comprises of four major components, the operation (design), the construction, fabrication and lastly the inspection categories. In most cases the design categories indicates and appreciates the fact that the collapse of fatal defects of the cable-stayed bridge may occur during the servicing of the bridge. The inspection category relates to the issues dealing with the frequency of bridge inspection, due to designs, which hardly consider the inspection components of the bridge. Failure of the bridge could also be because of the process of construction, especially of the girder of the bridge (usually made of steel). The delay in construction could also lead to failures. The fabrication of the steel is a process that is to be given consideration, as it may also lead to the collapse of the bridge. An illustration of the cable stayed bridge diagram is shown in figure 3 for more elaborations.

The Cable Stayed Bridge FailureFigure 3: The cable stayed bridge fault tree diagram

Design/Operations

Construction

Inspection

Fabrication

Failure events of the cable stayed bridge

Dynamic Amplification Factor (DAF)

The analysis of the nonlinear dynamic or the approaches of quasi-statistics are used in the calculations of the response of sudden losses of cables in the bridge. For most systems, the dynamic amplification factor is usually 2.0. The value has been recommended by PTI. However, the complexity of the system matters. In the cable stayed bridge case, other values other than the 2.0 are possible and expected. The recommendations for the PTI clearly stipulate that the value could be limited to 1.5. The DAF is most likely calculated to the variables of all elements of the structure (Walther, 1999, p. 131).

The influence of cable modeling

If there is loss of a cable in sudden circumstances, the act always leads to the immediate redistribution of the load to the other structural components, which are in most cases adjacent. The next cables undergo great displacement in the end nodes. Because the cables will always sag, there is a non-linear relationship between the corresponding forces of the cables and the forces of the displacements. The displacements of the cables will also experience vibrations that cause drastic cable vibrations. To avoid failures, the inclined cables of the bridges have to be stiff in horizontal paths relating to the upper nodes, and in vertical direction in the case of lower nodes, so as to be able to sustain or rather absorb the forces in case of large displacements (Wolff & Starossek, 2009, p.19).

The damping influence of the cables

Most of the case scenarios where there are enormous displacements of huge cables are caused by the low damping values of the specified cables and the effects of corrosion of the cables. The use of secondary cables is advised, which are used to connect the other main cables, with the aim of enhancing stability and stiffness (Emmerich, 2001, p. 126). The span of the Kessock Bridge in Scotland, which was about 240 meters in length, experienced massive oscillations just after it had been opened, due to the winds that were at high speeds of about 22 m/s. After the incident, there was fresh installation of dampers (the tuned mass type) as the solution. Years later greater and more adverse oscillations occurred. After analyzing of the structure, then it was evident that the dampers used had undergone stronger vibrations than they could hold. There is therefore need to ensure proper installation of the required quality of dampers (Emmerich, 2001, P. 127).

Progressive collapse of the bridges

Non-linear dynamics are used in most cases to track the progress of a collapsing structure. The behavior of a grinder and the cables is always assumed as elastoplastic, in case the bridge is undergoing progressive collapse, then the stress caused by the cables will be higher compared to its initial state. Nonetheless, there is the possibility of the slacking. Cable sagging and frequent vibrations also lead to the progressive collapse of the bridges. In most cases though, especially in the cable stayed bridges, the failing of a single cable hardly leads to progressive collapse. The only effect is plastification and raptures at the points of anchorage in the cables. Most of the bridges tolerate the loss of cables. In fact only the loss of three or more cables might result to the compete collapsing of the bridge (Wolff & Starossek, 2008, p. 5). The progression is characterized mainly by the factors responsible for the girders stability, the lack of lead bracings to maximize deflections and the high stress effects affecting longitudinal girders. The event of one has the effects on the other, making it a progressive sequence.

Overview of failures

In reality, there is dependent classification of failure or vulnerabilities. Identification of the vulnerabilities using the redundant approach has been approved to be the best criteria for the analysis of possibilities that might have led to the failure of the cable-stayed bridge. A good instance is the case of the state of New York, where procedures for screening vulnerabilities have been established. The vulnerabilities include the details of the concrete, the issues of collision, overloading the bridge, hydraulics and many others.

Extreme failures in most cases are caused when two vulnerabilities occur at the same time. Mostly issues concerned with construction, design and maintenance are some of the elements that have led to disasters, with regards to the preceding incidences. The elements mentioned before are crucial in determining the lifespan of the bridge. Choice of the components is mandatory for acquiring the best structures because of the nature of the bridge such as one constructed with many structural equipments-decks, towers and stays (Ren, 1999, p. 31).

The deficiencies that occur during the process of engineering and management are what have led to the most of the failures experienced. Currently, most of the programs overseeing the safety of bridges are recommending competence in the engineers, especially when designing the bridge and during the construction phases too. The issue of economy is also important, and the management concerned should lay strategies that are economic friendly. Management of the structuring process is therefore to be analyzed and prioritized in the project, for fruitful endings. Safety of the bridges is important, as the failures have led… [END OF PREVIEW]

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