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.
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.
The concept of fire safety covers an extremely vast scope of issues. To ensure an adequate fire safety level, it is necessary to combine research and actions in several fields, such as the mathematical, physical, or numerical modelling of a fire phenomenon. Another problem is to design different types of fire protection, including alarm systems, sprinkler systems, and also roads and evacuation systems, in a manner that ensures maximum safety for the building’s users. A vital issue is the analysis of the static-strength response of the structure under fire conditions. This study, concerned with such analyses, is limited to steel truss structures. In technical approvals, manufacturers of fire-proofing materials do not account for the character of the performance of individual structural members. The components in compression need thicker insulation than those in tension. This phenomenon is related to the fact that under fire conditions, the flexural buckling coefficient in compressed members is abruptly reduced with an increase in temperature. In turn, this increase in temperature leads to a fast reduction in resistance. In addition, members in tension have much higher resistance than those in compression in the basic design situation, i.e., at the instant of t = 0 min. Consequently, even a considerable decrease in the resistance of tension members is not as dangerous as that of compression members. Therefore, due to the nature of the performance of individual elements, fire-proofing insulation of every steel structure should be computationally verified. Additionally, in this paper, the influence of the type of fire insulation on the mechanical response of the structure was investigated. Calculations were carried out for different types of sprayed-on insulation, and also for contour and box insulation panels. The graphs show the behaviour of the elastic modulus, the yield point, and the resistance of the elements in the successive minutes of the fire for the different methods of fire protection used. The best results were obtained for vermiculite and gypsum spray.
This paper focuses on the new method of searching cut-sets, which enables us to conduct the system reliability analysis for plane trusses. As the result of such, the analysis of the reliability index for the whole structure is obtained, not only for the single elements. In the case of truss structures, the huge number of cut-sets could be generated if only the geometry of the structure is taken into account. Considering also the effects of actions and the load capacity, it is possible to reduce the number of cut-sets: what makes the whole analysis faster and more effective. The structures were considered not only in persistent design situations, but also in accidental-under-fire influence. The effect of action in individual elements was computed using the Robot Structural Analysis program. The temperature of the elements under fire load and the load-bearing capacity of the elements were calculated according to the Eurocode procedure in the Mathematica script. The proposed method allows to reduce the number of cut-sets, what makes the whole procedure of system reliability analysis much more efficient. All cut-sets were found by using a C++ console application prepared by author.
This article focuses on the reliability analysis of the plane steel truss under fire conditions. The safety of the structure was estimated by system reliability analysis combined with First Order Reliability Method (FORM). The authors created the C++ code, which enables us to prepare the advanced probabilistic model for bearing capacity in the selected time of fire duration. Searching cut-sets for system analysis was performed in the C++ code, where stiffness matrix spectral analysis was employed. It was found that a probabilistic model has significant influence on the reliability indices. The research showed that depending on the probabilistic model, the sensitivity of the reliability index to individual variables is different.
Abstract. The paper presents a proposal for the assessment of the reliability of statically determinate steel truss in the persistent and accidental (fire) design situation. The steel truss was modelled as series system from the reliability standpoint. The global Hasofer-Lind reliability index was employed, computed in successive time steps for the whole structure, not for individual elements. Fire analysis was carried out according to three different time-temperature curves-standard, hydrocarbon and external. 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.
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