This study concerns the safety factor and the reliability calculation for structural codes. The Eurocodes are used as a reference. Safety factor calculation is a demanding task which necessitates using an appropriate root-solving algorithm with a sufficient numerical accuracy. This article introduces a simple algorithm to calculate the safety factors directly, as previously there has been no means to control the accuracy. Presently, the safety factors are defined indirectly through the reliability index. The basic safety factor calculation is presented here in six different equations with the same outcome but differences regarding the numerical calculation, which provides a method to check the accuracy and select a proper equation for the root solver. The safety factor calculation for the permanent and the variable load in the Eurocodes is based on the independent, i.e., random, load combination and single load pairs. The current approach of safety factor calculation applied in the Eurocodes is disclosed here. Simple analytical equations based on the convolution equation are presented. Those can be used instead of the computer programs applied currently.
This paper concentrates on the combination of permanent and variable loads in the structural probability theory and its implementation in codes. In the current codes, the permanent and variable loads are sometimes combined independently, and sometimes they are combined dependently. We propose that, for the safest outcome in the standardized load estimation, the actual permanent and variable loads should be combined dependently without any load reduction. The load reduction arising from the independent combination leads to an unsafe design. For example, when the permanent and variable loads are both equal to 1, the combination load is 2 if the dependent combination is applied. However, the value predicted by the model for independent load combination is only ca 1.8. Although the load formation processes are independent, the dependent combination is applied since the load formation and the load combination are different processes. To support our view, we present arguments and examples based on probability theory, physics and statics and relate them with the current codes.
The reliability of load-bearing structures is normally secured through codes, a competent structural design and proper execution inspection. Alternatively, the reliability can be obtained via skilled test loading, which is a feasible technique both in the construction of new structures and in the load-bearing verification of existing ones. Although the current codes lack instructions for test loading, they are, however, used in special cases; for example, when the reliability of the structures is doubtful due to a defect, or when the structure is suspected to have especially high resistance variability. Test loading involves significant research questions that need to be addressed, including: What is the test load in comparison with the expected maximum service time load or the characteristic load? How can the instantaneous test load be compared with the actual long-term service-time load? Does the test loading harm the structure, and what is the target reliability in the test loading calculation? In this paper, we approach these questions from a theoretical point of view and propose how a suitable test load can be chosen in practice using an approximate and a precise approach.
Lightweight structures, especially trusses, have attracted a tremendous attention due to their extensive applications in the construction of infrastructures. Optimizing the shape and cross-sectional topology of truss members is essential since the truss systems are widely used in engineering routines. These systems form the framework of structures like bridges, steel halls for industry and trade, and towers. For the scope of this research, genetic algorithms were used for weight optimization of truss structures. This paper aims to optimize truss structures for finding optimal cross-sectional area. To optimize the cross-sectional area, all members were selected as design variables, with the structure’s weight being the objective function. The restrictions related to the change of the location of the nodes and the tension in the members were the looked-upon problems, the permissible values of which were determined under the circumstances of the problem. In addition, the resulting optimized model which masses for sizing, shape, and topology or their combinations, were compared.
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