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This paper introduces a probabilistic assessment of steel column damage caused by blast loads, utilizing simulation reliability methods and gene expression programming. The research focuses on an H-section steel column and incorporates uncertainties associated with input loads (axial and blast loads) and geometric factors (i.e., maximum slenderness) under various boundary conditions (pinned and fixed supports). The reliability analysis employs three different methods: the point estimate method (PEM), the Monte Carlo simulation (MCS) method, and the Monte Carlo simulation with Latin hypercube sampling method (MCS-LHS). To perform the reliability analysis, formulas derived from a previous study conducted by the authors using gene expression programming (GEP) were employed. Damage assessment was carried out based on a damage index criterion, considering the post-blast residual axial load-bearing capacity of the steel column. The research results are presented in terms of damage probability, considering the different reliability analysis methods and boundary conditions. The findings demonstrate that the PEM effectively estimates the probabilistic response of the steel column with acceptable accuracy and less effort compared with the MCS and MCS-LHS. Furthermore, the MCS-LHS demonstrates higher accuracy in estimating the probability distribution function by utilizing the Latin hypercube sampling (LHS) method, as compared to the MCS. These findings emphasize the importance of considering uncertainties in calculating the column response under extreme dynamic blast loading. [ABSTRACT FROM AUTHOR]

The solution of the motion equation for a structural system under prescribed loading and the prediction of the induced accelerations, velocities, and displacements is of special importance in structural engineering applications. In most cases, however, it is impossible to propose an exact analytical solution, as in the case of systems subjected to stochastic input motions or forces. This is also the case of non-linear systems, where numerical approaches shall be taken into account to handle the governing differential equations. The Legendre–Galerkin matrix (LGM) method, in this regard, is one of the basic approaches to solving systems of differential equations. As a spectral method, it estimates the system response as a set of polynomials. Using Legendre's orthogonal basis and considering Galerkin's method, this approach transforms the governing differential equation of a system into algebraic polynomials and then solves the acquired equations which eventually yield the problem solution. In this paper, the LGM method is used to solve the motion equations of single-degree (SDOF) and multi-degree-of-freedom (MDOF) structural systems. The obtained outputs are compared with methods of exact solution (when available), or with the numerical step-by-step linear Newmark-β method. The presented results show that the LGM method offers outstanding accuracy. [ABSTRACT FROM AUTHOR]

Damage to building load-bearing members (especially columns) under explosions and impact are critical issues for structures, given that they may cause a progressive collapse and remarkably increase the number of potential victims. One of the best ways to deal with this issue is to provide values of safe protective distance (SPD) for the structural members to verify, so that the amount of damage (probability of exceedance low damage) cannot exceed a specified target. Such an approach takes the form of the so-called safe scaled distance (SSD), which can be calculated for general structural members but requires dedicated and expensive studies. This paper presents an improved calculation method, based on structural reliability analysis, to evaluate the minimum SSD for steel columns under dynamic blast loads. An explicit finite element (FE) approach is used with the Monte Carlo simulation (MCS) method to obtain the SSD, as a result of damage probability. The uncertainties associated with blast and material properties are considered using statistical distributions. A parametric study is thus carried out to obtain curves of probability of low damage for a range of H-shaped steel columns with different size and boundaries. Finally, SSD values are detected and used as an extensive databank to propose a practical empirical formulation for evaluating the SSD of blast loaded steel columns with good level of accuracy and high calculation efficiency. [ABSTRACT FROM AUTHOR]