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.

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.

An advanced evaluation technique, helpful in the fire resistance assessment of a simple steel structure exposed to fire is presented and discussed in detail on the example of an unrestrained and uniformly heated steel beam. The proposed design methodology deals with the generalised probability-based approach in which the most probable failure point is formally identified. The random nature of all variables considered in the detailed analysis is taken into account. The critical temperature of the steel from which the considered beam is made of is accepted here as the authoritative safety measure. This temperature value is associated with the fire resistance limit state defined for the maximum acceptable value of failure probability. When forecasting the failure probability, not only the risk of a potential fire being initiated but also not being effectively extinguished is included in the calculation. Various levels of the target failure probability may be assumed in such the analysis, depending on the selected reliability class. They are specified in general by setting an appropriate value of the required reliability index β fire req. In the presented design algorithm no representative values of the considered random variables are specified. The critical temperature estimates obtained from these calculations are always less restrictive in comparison with the corresponding solutions computed after applying the conventional standard procedure.

In the paper, the Hasofer-Lind index is applied for determining the probability of stability loss oftruss structure under random load. In 1974 Hasofer-Lind proposed a modified reliability index thatdid not exhibit the invariance problem. The “correction” is the evaluation the limit state functionat a point known as the “design point”, instead of the mean values. The design point is generallynot known a priori, an iteration technique must be used to find out the reliability index. The papershows how the reliability index changes under the influence of different variables mean value,standard deviation, and probability density function.