Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 7

reliability index Related Abstracts

7 Simple Procedure for Probability Calculation of Tensile Crack Occurring in Rigid Pavement: A Case Study

Authors: Ales Florian, Lenka Ševelová, Jaroslav Žák


Formation of tensile cracks in concrete slabs of rigid pavement can be (among others) the initiation point of the other, more serious failures which can ultimately lead to complete degradation of the concrete slab and thus the whole pavement. Two measures can be used for reliability assessment of this phenomenon - the probability of failure and/or the reliability index. Different methods can be used for their calculation. The simple ones are called moment methods and simulation techniques. Two methods - FOSM Method and Simple Random Sampling Method - are verified and their comparison is performed. The influence of information about the probability distribution and the statistical parameters of input variables as well as of the limit state function on the calculated reliability index and failure probability are studied in three points on the lower surface of concrete slabs of the older type of rigid pavement formerly used in the Czech Republic.

Keywords: Simulation, Probability, Pavement, Failure, reliability index, tensile crack

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6 Influence of Deficient Materials on the Reliability of Reinforced Concrete Members

Authors: Sami W. Tabsh


The strength of reinforced concrete depends on the member dimensions and material properties. The properties of concrete and steel materials are not constant but random variables. The variability of concrete strength is due to batching errors, variations in mixing, cement quality uncertainties, differences in the degree of compaction and disparity in curing. Similarly, the variability of steel strength is attributed to the manufacturing process, rolling conditions, characteristics of base material, uncertainties in chemical composition, and the microstructure-property relationships. To account for such uncertainties, codes of practice for reinforced concrete design impose resistance factors to ensure structural reliability over the useful life of the structure. In this investigation, the effects of reductions in concrete and reinforcing steel strengths from the nominal values, beyond those accounted for in the structural design codes, on the structural reliability are assessed. The considered limit states are flexure, shear and axial compression based on the ACI 318-11 structural concrete building code. Structural safety is measured in terms of a reliability index. Probabilistic resistance and load models are compiled from the available literature. The study showed that there is a wide variation in the reliability index for reinforced concrete members designed for flexure, shear or axial compression, especially when the live-to-dead load ratio is low. Furthermore, variations in concrete strength have minor effect on the reliability of beams in flexure, moderate effect on the reliability of beams in shear, and sever effect on the reliability of columns in axial compression. On the other hand, changes in steel yield strength have great effect on the reliability of beams in flexure, moderate effect on the reliability of beams in shear, and mild effect on the reliability of columns in axial compression. Based on the outcome, it can be concluded that the reliability of beams is sensitive to changes in the yield strength of the steel reinforcement, whereas the reliability of columns is sensitive to variations in the concrete strength. Since the embedded target reliability in structural design codes results in lower structural safety in beams than in columns, large reductions in material strengths compromise the structural safety of beams much more than they affect columns.

Keywords: Reliability, Code, structural safety, Random variables, Reinforced Concrete, shear, reliability index, flexure, limit states

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5 Reliability Analysis of Steel Columns under Buckling Load in Second-Order Theory

Authors: Hamed Abshari, M. Reza Emami Azadi, Madjid Sadegh Azar


For studying the overall instability of members of steel structures, there are several methods in which overall buckling and geometrical imperfection effects are considered in analysis. In first section, these methods are compared and ability of software to apply these methods is studied. Buckling loads determined from theoretical methods and software is compared for 2D one bay, one and two stories steel frames. To consider actual condition, buckling loads of three steel frames that have various dimensions are calculated and compared. Also, uncertainties that exist in loading and modeling of structures such as geometrical imperfection, yield stress, and modulus of elasticity in buckling load of 2D framed steel structures have been studied. By performing these uncertainties to each reliability analysis procedures (first-order, second-order, and simulation methods of reliability), one index of reliability from each procedure is determined. These values are studied and compared.

Keywords: buckling, reliability index, second-order theory, steel columns

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4 Structural Reliability Analysis Using Extreme Learning Machine

Authors: Mehul Srivastava, Sharma Tushar Ravikant, Mridul Krishn Mishra


In structural design, the evaluation of safety and probability failure of structure is of significant importance, mainly when the variables are random. On real structures, structural reliability can be evaluated obtaining an implicit limit state function. The structural reliability limit state function is obtained depending upon the statistically independent variables. In the analysis of reliability, we considered the statistically independent random variables to be the load intensity applied and the depth or height of the beam member considered. There are many approaches for structural reliability problems. In this paper Extreme Learning Machine technique and First Order Second Moment Method is used to determine the reliability indices for the same set of variables. The reliability index obtained using ELM is compared with the reliability index obtained using FOSM. Higher the reliability index, more feasible is the method to determine the reliability.

Keywords: Reliability, reliability index, statistically independent, extreme learning machine

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3 Reliability Analysis of Dam under Quicksand Condition

Authors: Manthan Patel, Vinit Ahlawat, Anshh Singh Claire, Pijush Samui


This paper focuses on the analysis of quicksand condition for a dam foundation. The quicksand condition occurs in cohesion less soil when effective stress of soil becomes zero. In a dam, the saturated sediment may appear quite solid until a sudden change in pressure or shock initiates liquefaction. This causes the sand to form a suspension and lose strength hence resulting in failure of dam. A soil profile shows different properties at different points and the values obtained are uncertain thus reliability analysis is performed. The reliability is defined as probability of safety of a system in a given environment and loading condition and it is assessed as Reliability Index. The reliability analysis of dams under quicksand condition is carried by Gaussian Process Regression (GPR). Reliability index and factor of safety relating to liquefaction of soil is analysed using GPR. The results of reliability analysis by GPR is compared to that of conventional method and it is demonstrated that on applying GPR the probabilistic analysis reduces the computational time and efforts.

Keywords: Quicksand, factor of safety, reliability index, GPR

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2 Sensitivity and Reliability Analysis of Masonry Infilled Frames

Authors: Avadhoot Bhosale, Robin Davis P., Pradip Sarkar


The seismic performance of buildings with irregular distribution of mass, stiffness and strength along the height may be significantly different from that of regular buildings with masonry infill. Masonry infilled reinforced concrete (RC) frames are very common structural forms used for multi-storey building construction. These structures are found to perform better in past earthquakes owing to additional strength, stiffness and energy dissipation in the infill walls. The seismic performance of a building depends on the variation of material, structural and geometrical properties. The sensitivity of these properties affects the seismic response of the building. The main objective of the sensitivity analysis is to found out the most sensitive parameter that affects the response of the building. This paper presents a sensitivity analysis by considering 5% and 95% probability value of random variable in the infills characteristics, trying to obtain a reasonable range of results representing a wide number of possible situations that can be met in practice by using pushover analysis. The results show that the strength-related variation values of concrete and masonry, with the exception of tensile strength of the concrete, have shown a significant effect on the structural performance and that this effect increases with the progress of damage condition for the concrete. The seismic risk assessments of the selected frames are expressed in terms of reliability index.

Keywords: Sensitivity Analysis, reliability index, RC frames, fragility curve

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1 Effect of Correlation of Random Variables on Structural Reliability Index

Authors: Agnieszka Dudzik


The problem of correlation between random variables in the structural reliability analysis has been extensively discussed in literature on the subject. The cases taken under consideration were usually related to correlation between random variables from one side of ultimate limit state: correlation between particular loads applied on structure or correlation between resistance of particular members of a structure as a system. It has been proved that positive correlation between these random variables reduces the reliability of structure and increases the probability of failure. In the paper, the problem of correlation between random variables from both side of the limit state equation will be taken under consideration. The simplest case where these random variables are of the normal distributions will be concerned. The case when a degree of that correlation is described by the covariance or the coefficient of correlation will be used. Special attention will be paid on questions: how much that correlation changes the reliability level and can it be ignored. In reliability analysis will be used well-known methods for assessment of the failure probability: based on the Hasofer-Lind reliability index and Monte Carlo method adapted to the problem of correlation. The main purpose of this work will be a presentation how correlation of random variables influence on reliability index of steel bar structures. Structural design parameters will be defined as deterministic values and random variables. The latter will be correlated. The criterion of structural failure will be expressed by limit functions related to the ultimate and serviceability limit state. In the description of random variables will be used only for the normal distribution. Sensitivity of reliability index to the random variables will be defined. If the reliability index sensitivity due to the random variable X will be low when compared with other variables, it can be stated that the impact of this variable on failure probability is small. Therefore, in successive computations, it can be treated as a deterministic parameter. Sensitivity analysis leads to simplify the description of the mathematical model, determine the new limit functions and values of the Hasofer-Lind reliability index. In the examples, the NUMPRESS software will be used in the reliability analysis.

Keywords: Steel Structure, reliability index, correlation of random variables, sensitivity of reliability index

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