Reliability Analysis of a Prestressed Concrete Beam
Reliability Analysis of a Prestressed Concrete Beam
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Abstract on Reliability Analysis of a Prestressed Concrete Beam
The Reliability Analysis of a Prestressed Concrete Beam (PCB) was presented using First Order Reliability Method and Eurocode 2 procedures to carry out the analysis. The results show that the safety of the PCBin bending decreasedfrom 2.9 to 1.0 and 3.1 to 2.6 as prestress force and the depth from the extreme compressive fiber to the neutral axis of the beam increased from 20kN to 100kN and 150mm to 350mm respectively, therefore the PCB is safer at low prestress force and depth to the bottom layer of the beam. The safety of the PCB increased from 1.52 to 2.5, 1.52 to 2.5 and 0.1 to 2.0 respectively as depth to the neutral axis, area of the compressive reinforcement and eccentricity increased from 150mm to 350mm, 800mm2 to 1200mm2 and 100mm to 300mm respectively. The safety of the prestressed concrete beam remained constant at 0.1 with eccentricity of 100mm, 0.8 with eccentricity of 150mm, 1.3 with eccentricity of 200mm, 1.7 with eccentricity of 250mm and 1.95 with eccentricity of 300mmas effective widths and load ratios of the beam increased from 100mm to 300mm and 0.2 to 1.0 respectively in shear. Increase in dead load and span resulted to a corresponding increase in the safety of the beam in deflection. The best value of eccentricity for a reliable prestressed beam is within the range of 200mm to 300mm. It was also observed that the variation of depth to the bottom layer and prestressing force of the prestressed beam in bending are at equilibrium at 60kN and the safety index is 1.83. Also, the target safety indices considering bending, shear and deflection failure criteria of the prestressed beam were obtained to be 2.01, 1.526 and 4.716 respectively.
Chapter One of Reliability Analysis of a Prestressed Concrete Beam
INTRODUCTION
PREAMBLE
Prestressed concrete beam is one of the most widely used construction element in bridge projects around the world. It has rent itself to an enormous array of structural applications, including buildings, bridges, nuclear power vessels, Television towers and offshore drilling platform (Antonie,2004).
Prestressing involves inducing compressive stresses in the zone which will tend to become tensile under external loads. Thesecompressive stresses neutralize the tensile stresses so that no resultant tension exists (or in only very small values). Cracking is therefore eliminated under working load and all of the concrete may be assumed effective in carrying load. Therefore lighter sections may be used to carry a given bending moment and over much longer spans than reinforced concrete.
The prestressing force also reduces the magnitude of principal tensile stress in the web so that thin webbed I sections may be used without the risk of diagonal tension failures and with further savings in self weight. The prestressing force has to be produced by high tensile steel and it is necessary to use high quality concrete to resist the higher compressive stresses that are developed(Mosley and Bungey, 2002).
In the design and construction of the prestressed concrete, there are many sources of uncertainties which are put into consideration during the construction in order for the structure to serve its intended purpose. Consequently, structures must be designed to serve their functions with a finite probability of failure (Nowak and Colins, 2002).
In order to treat these uncertainties in the construction processes of the prestressed concrete, reliability analysis comes into play. Reliability is the probability that the structure will perform its required function without failure under a specified limit state during a specified reference period (Thoft-Christensen and Baker, 1982). The probability of structural failure from all possible causes is inevitable. However, the uncertainties and their significance on the structural safety and performance can be analyzed systematically only through methods of probability.
The development of structural reliability methods during the last three to four decades have provided a more rational basis for the design of structures in the sense that the method facilitate a consistent basis of comparison between the reliability of a well-tested structural design and the reliability of new types of structures. For this reason the methods of structural reliability have been applied increasingly in connection with the development of new design codes (Sorenson et,al., 2002). In recent years design codes have been continuously revised to include limit states based on probabilistic methods. In fact the limit state design approach has been used nearly in all the recent advances in codified design (Ellingwood, 1996). The use of structural reliability methods for design can lead to structures that have a more consistent level of risk (Zimmerman et, al., 1992). Therefore, to account for the system effect in structural assessment and design, the safety importance of structural members must be quantified (Gharaibeh, et, al., 2001)
PROBLEM STATEMENT AND JUSTIFICATION OF STUDY
The way in which civil engineering systems fail, the occurrence and frequency of failure, its economics and social consequences, demonstrate considerable differences between hypothetical and actual systems. Induced loading, site characterization, material properties, developed formulations and procedures and adequacy of predicted sizes and shapes of the system and its elements are far from certain. All these factors are subject to complex inter relationships, materials defects, structural deficiencies, human errors and hence to varying degrees of randomness. Reliability analysis of structures is required as a result of these problems. Failure of a system is assessed by its inability to perform its intended function adequately on demand for a period of time and under specified condition, while its antithesis, the measure of success, is called reliability (Milton 1987).
AIM AND OBJECTIVES
Aim
The aim of this research is to carry out a reliability analysisof a prestressed concrete beam using First Order Reliability Method (FORM) and Eurocode 2 (2004) design procedure.
Objectives
The objectives of this research are to:
- identify the various modes of failure due to ultimate limit state of a prestressed concrete beam.
- compute the probabilities of failure associated with the various modes of failure of theprestressed concrete beam.
- determine the implied safety indices related to the probabilities of failure.
- compute the mean safety index for each mode of failure.
- establish a target safety indices associated with the modes of failure of the Prestressed concrete beam.
- design a typical Prestressed concrete beam to meet a target safety level.
SCOPE OF RESEARCH
The scope of this research was limited to the reliability analysis of a simply supported Prestressed concrete beam in accordance with the recommendation of Eurocode 2 (2004).
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