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Figure 2 presents the flow chart for SRM.
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Two examples analyzed by Haldar and Mahadevan, were used to compare with the methodology developed in the previous section. It should be noted that the validation of the SRM was done by comparing it with data provided by Agostini and Freitas, and Haldar and Mahadevan, The first structure that was analyzed is represented in Figure 3. Statistical properties of random variables considered in the analysis of that structure are described in Table 1. As regards the present example, structural reliability analysis was carried out considering the geometric nonlinearity and the presence of semi-rigid connections in the joints between columns and beam.
The limit state in question refers to the horizontal displacement of Node 2, limited to 0. As for the portal frame in Example 1, represented by the structure shown in Figure 3 , three different connecting behaviors were simultaneously analyzed for Nodes 2 and 3. These analyses took into account the nonlinear behavior of the connection using the Richard and Abbott, mathematical model.
The model comprises the following parameters: initial stiffness k , strain-hardening stiffness k p , reference moment M 0 , and a parameter defining the shape of the curve n. Figure 4 shows the values of the four parameters for all three analyzed cases; the values were inserted into the analysis as non-random.
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Haldar and Mahadevan, analyzed the reliability considering also the random behavior of the parameters that make up the Richard and Abbott, model. Table 2 presents, for curves 1 to 3, the results from Agostini on the reliability analysis carried out considering the presence of semi-rigid connections in the structure. The second example, shown in Figure 5 , consists of a frame with an asymmetric arrangement of its elements.
For the actual example, the presence of semi-rigid connections was not taken into account.
The horizontal displacement of Node 1 was limited to 0. Table 5 presents the results of the reliability analysis carried out for the structure in Example 2, based both on linear and nonlinear analysis. Comparing the results of Example 1 - presented in Tables 2 and 3 - it can be seen that the presence of semi-rigid connections resulted in a decrease in the reliability index, when the behavior of semi-rigid connections of nodes 2 and 3 goes from more stiff to less stiff.
These authors considered the idealization of connections as perfectly pinned or stiff as inadequate and suggested a careful investigation, even for the serviceability limit state, in frames modelled with semi-rigid connections.
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Hadianfard and Razani, stated that to achieve more reliable results, it is necessary to consider the semi-rigid behavior of connections in the reliability analysis. By comparing the results in Example 2, shown in Table 6 , with those determined by Haldar and Mahadevan, , one is able to notice an agreement between values.
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Results shown in Tables 5 and 6 indicate mainly that the consideration of the geometric nonlinearity did not result in great differences in the reliability index, sensitivity indices or final values of the variables. One noted that, for the incident loading, the properties of the material and the geometric characteristics of the structure in Example 2 show only small manifestations of the effects of geometric nonlinearity in the limit state under study.
This study was carried out to understand the influence of the effects of geometric nonlinearity and of semi-rigid connections on the reliability of steel plane frames. The results indicate the efficiency of the proposed implementation. These results suggest the need to take the semi-rigid behavior of connections into account when carrying out reliability analyses of steel plane frames.
Tese de Doutorado em Engenharia Civil. Ouro Preto. Effects of semi-rigid behavior of connections in the reliability of steel frames. Structural Safety, v. Reliability assessment using stochastic finite element analysis.
An exact and invariant first-order reliability format. Journal of Engineering Mechanics, v. Santa Clara, c Installing and using the IMSL libraries. Access in: 6 sep. Table of Contents. Previous article Next article. Article Abstract PDF Metrics Show article metrics. Services Same authors - Google Scholar.
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