Statistical conformity criteria for the compressive strength of concrete are a matter of debate. The criteria can have prejudicial effects on construction quality and reliability. Hence, the usefulness of statistical criteria for the small sample size n=3 is questioned. These defects can cause a reduction in the quality of produced concrete and, consequently, too much risk for the recipient (investor). For this reason, the influence of conformity control on the value of the reliability index of concrete and reinforced concrete has been determined. The authors limited their consideration to the recommended standards PN-EN 206-1, PN-EN 1992 and ISO 2394 method of reliability index, which belongs to the analytical methods FORM (First Order Reliability Method). It assumes that the random variables are defined by two parameters of the normal distribution or an equivalent normal: the mean and the standard deviation. The impact of conformity control for n=3 for concrete structures, designed according to the Eurocode 1992, for which the compressive strength of concrete is the capacity dominant parameter (sensitivity factor of dominating resistance parameter according to the FORM is 0.8), has been determined by evaluation of the reliability index.
The study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.
Methods of Reliability Index Determination Concerning Municipal Water Quality
Two - parametric method was used for evaluating a reliability of Water Treatment Plant, making use of an availability - K and the Mean Down Time - T. It has been developed a method of defininitioning the reliability indexes for drinking water in an aspect of its physical and chemical quality.
The paper presents a proposal for the assessment of the reliability of steel truss (both statically determinate and indeterminate) in the persistent and accidental design situation. In the analysis, a probabilistic approach was used. The global Hasofer-Lind reliability index was employed, computed in successive time steps for the whole structure, not for individual elements. The statically determinate truss was modelled as a serial system from the reliability standpoint. For the statically indeterminate truss, kinematically admissible failure mechanisms were determined by means of the examination of the singularity of the stiffness matrix of the structure, converting the truss into a geometrically variable system. For the problem thus formulated, a serial-parallel reliability model was constructed. Monitoring the reliability index in the successive minutes of the fire makes it possible to estimate the probability of the structure failure, and to decide whether the required safety level is maintained.
In the paper, the Hasofer-Lind index is applied for determining the probability of stability loss of truss structure under random load. In 1974 Hasofer-Lind proposed a modified reliability index that did not exhibit the invariance problem. The “correction” is the evaluation the limit state function at a point known as the “design point”, instead of the mean values. The design point is generally not known a priori, an iteration technique must be used to find out the reliability index. The paper shows how the reliability index changes under the influence of different variables mean value, standard deviation, and probability density function
The paper demonstrates how the reliability methods can be utilised in order to evaluate safety in geotechnics. Special attention is paid to the so-called reliability based design that can play a useful and complementary role to Eurocode 7. In the first part, a brief review of first- and second-order reliability methods is given. Next, two examples of reliability-based design are demonstrated. The first one is focussed on bearing capacity calculation and is dedicated to comparison with EC7 requirements. The second one analyses a rigid pile subjected to lateral load and is oriented towards working stress design method. In the second part, applications of random field to safety evaluations in geotechnics are addressed. After a short review of the theory a Random Finite Element algorithm to reliability based design of shallow strip foundation is given. Finally, two illustrative examples for cohesive and cohesionless soils are demonstrated.
Presently the new generation of Eurocodes is under development. It is expected that the basis of structural design given in current EN 1990 will be considerably revised including the format for load combinations in the Ultimate Limit States and new categorisation of consequence classes for construction works. It is expected that the partial factors for self-weight of structural members could be reduced and factors for variable loads more differentiated. Calibration of partial factors should be performed for actions and materials including also structural glass and FRP polymers.
We compared the method of least squares (LS), Pope’s iterative data snooping (IDS) and Huber’s M-estimator (HU) in realistic leveling networks, for which the heights or the vertical displacements of points are known. The study was conducted using the Monte Carlo simulation, in which one repeatedly generates sets of observations related to the measurement data, then calculates values of the estimators and, finally, assesses it with respect to the real coordinates. To simulate outliers we used popular mixture models with two or more normal distributions. It is shown that for small, strong networks robust methods IDS and HU are more accurate than LS, but for large, weak networks occurring in practice there is no significant difference between the considered methods in the accuracy of the solution.
The assessment of existing components of power producing facilities is based on probabilistic methods of the theory of reliability provided in Eurocodes and ISO standards. An example of quickclosing valves in a selected hydroelectric power plant indicates the assessment of reliability and the prediction of the remaining working life of a structural component for the considered model of corrosion.
The paper concerns reliability analysis of steel trusses under fire conditions with taking into account randomness of buckling coefficient, modulus of elasticity’s and yield strength’s reduction factors. To assess the reliability system analysis was employed. The calculations of appropriate standard deviations of random variables were realized in Mathematica program. Two types of trusses were analysed: statically determinate and indeterminate, so respectively serial and mixed system were used. The results, gotten for different levels of coefficients of variation of reduction factors were presented.