General Nonlinear Method Research Articles

Reliability of slender concrete columns designed according to the Eurocodes

For compressed structural elements that are likely to lose stability, the second-order theory has to be incorporated into the design process. In Eurocode 2 (EN 1992-1-1, 2004), there are three methods for calculating the effects of the second-order theory, and there are some doubts as to whether the General nonlinear method has a sufficient degree of reliability. For this reason, six specimens of slender columns were designed, fabricated, and tested. All of the column specimens failed due to the loss of stability inside their design interaction diagram, which allows for an analysis of the reliability of the design method in Eurocode 2. As a part of an experimental campaign, prediction of the experimental behaviour of the specimens was carried out. Based on a numerical model, the safety factor for the tested columns was observed, and the likelihood of a possibly unsafe design is explained and presented.

Experimental Verification of Slender Reinforced Concrete Columns Design

The columns have been part of the constructions since the beginning of the buildings and have retained their design and construction importance to the present. The advantage of using more slender elements are less material consumption and more usable space in the interiors. The continuous improvement of the building materials and the use of hybrid structural elements leads to the downsizing of the structural elements. The aim of this article is the nonlinear analysis of the slender rein-forced concrete columns and the loss of stability verified by the experimental tests. Nonlinear calculations can be considered as the most accurate calculation option for the load bearing structural elements. On the other hand, the effect of the “black box” has been, and will be the cause of a large number of building defects. In the Eurocode 2 in chapter 5.8.6 of the European Concrete Design Standard, there is a possibility of using the general nonlinear method in practice, even for the com-pressed elements. In the design of the slender structures, the influence of second-order theory is a very important part of the design. In this publication are described theoretical and experimental analyses of the slender columns, that failed due to loss of stability inside of their design interaction diagram - much sooner than the critical cross-sections reached its resistance. As a part of the experimental preparations, reinforced concrete columns were designed, based on numerous numerical analyses. Later, the chosen columns were tested in the laboratories of TU Wien in Vienna. Experimental verification is one of the main parts of my dissertation thesis.

Reliability analysis of very slender columns subjected to creep

A mechanical model was developed to evaluate the reliability of very slender columns subject to creep, employing the nonlinear moment-curvature relationship. Second-order effects were considered by the finite difference method. Numerical tests were carried out on 432 columns with a slenderness index between 100 and 200. The general nonlinear method was adopted to determine the design load, applying the displacement of the stress-strain diagram for consideration of creep. The reliability index was calculated using the Monte Carlo method and the First Order Reliability Method. Among the results obtained, it was observed that it is important to review the safety criterion of the Brazilian Standard NBR 6118 about the very slender columns (90 < λ ≤ 200) by performing the calibration of the additional coefficient γn1. In addition, it was observed that an increase in the reinforcement ratio commonly produces a reduction in the reliability index; an increase in the first-order relative eccentricity promotes a decrease in reliability, among other evaluated factors.

Nonlinear Analysis and Comparison of Design Methods for Slender Concrete Columns with their Impact on Economy and Reliability

The subject of this article is a comparison of the calculation methods for slender reinforced concrete columns, which are likely to lose stability, and therefore it is necessary to take into account the influence of the second order theory. The columns were calculated by the nominal curvature method [1] Chap.5.8.8 and the general nonlinear method [1] Chap.5.8.6 (3). Our comparison was aimed on the reliability of the design of the columns and the cost of the column. The analysis was made for the columns we selected from the halls built in practice. For this reason, we have asked for co-operation with Statika Čížek s.r.o.. This company has designed lot of hall objects during numerous years of its practise. In this study, we proposed a selected column located in a particular hall object. Parameters of the selected column have been slightly modified against the practical design. Reinforcement of selected column was designed using the curvature method. This proposal was then subjected to "optimization", where the task was to minimize the amount of concrete and minimize the amount of reinforcement with usage of a general nonlinear method. Then we compared the results of this analysis in terms of reliability and cost of production. This article aims to alert authorized engineers to be careful with usage of the general non-linear method in practice. It is questionable, whether saving money on the cost of building structure is worthwhile to design columns with significantly lower reliability. Sometimes even with the risk of a loss of stability that belongs to the category - brittle failures

Failure of Slender Concrete Columns Due to a Loss of Stability

Abstract The European standard for the design of concrete structures that are likely to lose stability requires taking into account the effects of second order theory. This effect increases the impact of a bending moment due to member deformation and additional eccentricity. Slender members can be calculated by the use of a non-linear method. This approach shows a deficit in global reliability for cases where the concrete columns fail due to the loss of stability before reaching the design resistance in the critical cross-sections. Buckling is a brittle failure which occurs without any warning, and the probability of its formation is markedly influenced by the slenderness of the column. Here, the calculation results are presented and compared with the results from an experiment which was carried out in cooperation with STRABAG Bratislava LTD at the Central Laboratory of the Faculty of Civil Engineering SUT in Bratislava. The columns were designed according to the methods stated in STN EN 1992-1-1, namely, a general non-linear method. The focus of this study is to compare multiple approaches based on codes used in Germany (DIN 1045-1, 2001) and Austria (ÖNORM B 4700, 2001) with the present European code mentioned above. The paper aims to compare the global reliability of slender concrete columns with variable slendernesses of 90 and 160.

Bearing Capacity of Slender Concrete Columns

Abstract The European standard for the design of concrete structures using nonlinear methods contains a deficit in global reliability for cases when concrete columns fail due to a loss of stability before reaching the design resistance in the critical cross-sections. A buckling failure is a brittle failure which occurs without warning, and the probability of its formation is markedly influenced by the slenderness of the column. The calculation results presented herein are compared with the results from experimental data. The paper aims to compare the global reliability of slender concrete columns with a slenderness of 90 and higher. The columns are designed according to the methods stated in EN 1992-1-1, namely, a general nonlinear method and methods based on nominal stiffness and nominal curvature. The mentioned experiments also served, on the one hand, as a basis for the deterministic nonlinear modeling of the columns and, subsequently, for the probabilistic evaluation of the variability of the structural response. Finally, the results may be utilized as thresholds for the loading of the structural elements produced. The paper aims at presenting a probabilistic design that is less conservative than the classic partial safety factor-based design and alternative ECOV method.

Extracting unstable periodic orbits from chaotic time series data

A general nonlinear method to extract unstable periodic orbits from chaotic time series is proposed. By utilizing the estimated local dynamics along a trajectory, we devise a transformation of the time series data such that the transformed data are concentrated on the periodic orbits. Thus, one can extract unstable periodic orbits from a chaotic time series by simply looking for peaks in a finite grid approximation of the distribution function of the transformed data. Our method is demonstrated using data from both numerical and experimental examples, including neuronal ensemble data from mammalian brain slices. The statistical significance of the results in the presence of noise is assessed using surrogate data.

Constrained nonlinear least squares: an exact penalty approach with projected structured quasi-Newton updates

This paper is concerned with the development, numerical implementation, and testing of an algorithm for solving constrained nonlinear least squares problems. The algorithm is an adaptation of the least squares case of an exact penalty method for solving nonlinearly constrained optimization problems due to Coleman and Conn. It also uses the ideas of Nocedal and Overton for handling quasi-Newton updates of projected Hessians, those of Dennis, Gay, and Welsch for approaching the structure of nonlinear least squares Hessians, and those of Murray and Overton for performing line searches. This method has been tested on a selection of problems listed in the collection of Hock and Schittkowski. The results indicate that the approach taken here is a viable alternative for least squares problems to the general nonlinear methods studied by Hock and Schittkowski.

Robust kriging?A proposal

Geological data frequently have a heavy-tailed normal-in-the-middle distribution, which gives rise to grade distributions that appear to be normal except for the occurrence of a few outliers. This same situation also applies to log-transformed data to which lognormal kriging is to be applied. For such data, linear kriging is nonrobust in that (1)kriged estimates tend to infinity as the outliers do, and (2)it is also not minimum mean squared error. The more general nonlinear method of disjunctive kriging is even more nonrobust, computationally more laborious, and in the end need not produce better practical answers. We propose a robust kriging method for such nearly normal data based on linear kriging of an editing of the data. It is little more laborious than conventional linear kriging and, used in conjunction with a robust estimator of the variogram, provides good protection against the effects of data outliers. The method is also applicable to time series analysis.