Sensitivity analysis of the design portal frames of steel industrial buildings

This study presents aims at investigate and apply the sensitivity and reliability analysis methods to assess the reliability of a structural design according to the Vietnam standards design TCVN 5575:2012. Specifically, the sensitivity and reliability analysis of horizontal steel frame in one-story industrial building with crane is considered. The random factors that may occur during the design, fabrication, erection, and utilization stages are taken into account as much as possible. Then, the problem of number of results is analysed in order to obtain the reasonable design solution.


Introduction
Local sensitivity analysis aims at calculate the partial derivatives of the target function with respect to each variable. The simplest method is One At a Time (OAT), which was presented in numerous literatures [1,11,15]. A popular method using this kind of sensitivity index is that of Morris [12], which was applied in [8,15].
Global sensitivity consists of individual sensitivity of each variable and its interaction with other variables. Sobol's sensitivity index was proposed and then widely applied [4,9,14,16,17].
The steel structure often presents high durability and includes slender components. Therefore, sensitivity and reliability analysis for steel structures was interested by many researchers [2, 3, 4, 6, 7 ,13, 18].
In this research, the author presented the global sensitivity of the input design parameters on the output parameters of the random model for horizontal steel frame, including parameters in the design, fabrication and exploitation stages. From the results of this quantitative analysis, the research assessed the overall contribution of each input parameter to the output parameters and eliminated the randomness of some parameters that exhibited small global sensitivity to all the output parameters.
A first order Sobol' index is determined by: A second order Sobol' index is determined by: Total order Sobol' index is then determined by: The Sobol indices are often estimated using Monte Carlo method and the computation program is written using Python language and is validated by comparing its results with Ishigami funtions.

Deterministic design problem of horizontal frame
The procedure for the deterministic design problem of horizontal frame in industrial building is detailed in the literature [19], which consists of the following steps according to TCVN 5575:2012.
Analyze the frame to determine the internal forces at 6 sections (4 column sections and 2 beam sections) and determine the horizontal displacement at the top of column i Output parameters for column sections: Output parameters for beam sections: Output parameters for displacements at the top of columns:

Sensitivity analysis program
The sensitivity analysis program for design of steel frame is proposed based on the algorithm of the global sensitivity analysis program using the Sobol Sensitivity Index (GSAP) and stochastic model of steel frame design problem, as illustrated in Fig. 3.

Sensitivity and reliability analysis of the design problem of horizontal steel frame in industrial buildings
In this sections, the program developed in sections 3 will be used to assess the sensitivity and reliability of a design of steel frame which is designed according to the standard TCVN 5575:2012 and solve the economic-technical problem associated with reliability. Input random variables are assumed to be independent probability and uniformly distributed, as detailed in Table 2. The variations of each variable are assumed to be in the range around 10%  of the deterministic values in order to show the influences of the variables.

Sensitivity of the input parameters on theto output parameters
The first-order and Global total order sensitivity analysis indices results of the design parameters onto the output parameters are shown in Figs. 5-13. It is observableseen from these figures that the obtained results are consistent with the qualitative analysis results. The input paprameters , and that that present aexhibit small global sensitivity onto all the output parameters, will be assumed to be deterministic parameters in reliability analysis.

Conclusion
This research investigates the algorithm and develops a Global Sensitivity analysis program using the Sobol 'sensitivity index and Monte Carlo simulation method. The program is written using Python language and demonstrated to be accurate by comparing its results with Ishigami funtions and research investigates the algorithm and develops a reliability analysis program using Monte Carlo simulation method. The computation program is written using Python language and applied to the reliability analysis of planar frame structure using the stable condition to illustrate the method.
The research develops a process for assessing the sensitivity and reliability of building structures using the proposed sensitivity and reliability analysis programs. This process is then applied to analyze the sensitivity and reliability of a horizontal frame in single-storied industrial building with crane to illustrate the method.