Georgios P. Balomenos

Finite element reliability and sensitivity analysis of structures using the multiplicative dimensional reduction method

Abstract Finite element reliability analysis (FERA) has been used to evaluate the reliability of structures. In FERA, approximate methods are commonly used to estimate the mean and variance of the structural response, while its probability distribution is primarily derived based on the Monte Carlo simulation (MCS) method. This paper advances FERA by combining it with the multiplicative dimensional reduction method (M-DRM). The proposed M-DRM allows fairly accurate estimation of the statistical moments, as well as the probability distribution of the structural response. The distribution of the response is obtained using fractional moments, which are calculated from the M-DRM, along with the maximum entropy principle. The variance of the response, based on global sensitivity measures, is obtained as a by-product of the analysis. The proposed approach is integrated with the OpenSees software and is illustrated through examples of nonlinear finite element analyses of reinforced concrete and steel frames. The paper shows that the proposed approach is an accurate and efficient alternative for FERA.

Reliability Analysis of a Reinforced Concrete Slab-Column Connection without Shear Reinforcement

Punching shear design is a topic of international interest because it is critical for reinforced concrete slab-column connections, based on the fact that this type of connection can fail in a brittle way and without warning. Punching shear strength depends on many variables which may have some degree of uncertainty due to geometry, material properties, manufacturing processes, etc. In this study, reliability analysis will be performed by applying Monte Carlo Simulation due to random input parameters for current design codes (ACI 318-11, EC2-2004) and for an analytical punching shear model, such as Critical Shear Crack Theory, which was incorporated in the new fib Model Code (2010), so as to be compared and useful conclusions to be derived. For sensitivity analysis, valuable results will be derived on how specific parameters influence the output response (i.e., punching shear resistance). The sensitivity analysis will show how the uncertainty associated with the models input parameters impacts the resultant uncertainty of its output, and which input parameters affect (most and least) the punching shear strength. Moreover, simulation results will give us an idea on which parameters are most important and which are the consequences of changing these parameters, regarding the punching shear strength of a slab-column connection, so as to improve punching shear design.

Computationally efficient estimation of the probability density function for the load bearing capacity of concrete columns exposed to fire

Concrete columns are critical for the stability of structures in case of fire. In order to allow for a true Performance Based Design, the design should be based on considerations of risk and reliability. Consequently, the probability density function (PDF) which describes the load-bearing capacity of concrete columns during fire exposure has to be assessed. As second order effects can be very significant for columns, traditional probabilistic methods to determine the PDF become very computationally expensive. More precisely, for most current numerical calculation tools (e.g. Finite Element), the computational requirements are so high that traditional Monte Carlo simulations become infeasible for any practical application. In order to tackle this, a computationally very efficient method is presented and applied in this paper. The method combines the Maximum Entropy Principle together with the Multiplicative Dimensional Reduction Method, and Gaussian Interpolation, resulting in an estimation of the full PDF requiring only a very limited number of numerical calculations. Although the result is necessarily an approximation, it gives very good assessment of the PDF and it is a significant step forward towards true risk- and reliability-based structural fire safety.

Probabilistic evaluation of concrete strains for assessing prestressing loss in nuclear containment segments

The main function of the nuclear containment structure is to prevent any radioactive leakage to the environment. The Canadian Standard Association (CSA) provides guidelines for the periodic inspection of the containment prestressed system. However, these inspections are not possible to assess directly the condition of the bonded tendons. Thus, the main objective of this research is to investigate if concrete strain measurements, obtained during inspections, can be used for evaluating the prestressing loss of these bonded systems. First, the fracture energy approach is applied for modelling the tensile strength of the concrete, using the concrete damage plasticity model. The finite element analysis (FEA) results are in good agreement compared to the test results, indicating the accuracy of the adopted modeling approach. Then, probabilistic analysis is applied, since the measured concrete strains are expected to have a distribution due to several uncertainties. The results indicate that the prestressing loss of bonded tendons seems to affect the concrete strain distribution. The proposed probabilistic framework can be used as an approach for estimating the magnitude of the prestressing loss, during periodic inspections.

Finite element reliability analysis of structures using the dimensional reduction method

Finite Element Reliability Analysis (FERA) has been used to evaluate the reliability of structures. Mean and variance of the structural response is often estimated with the use of approximate methods, while structural response distribution is approximated based on Monte Carlo simulation (MCS). In this paper, FERA is applied in an efficient manner with the use of a Multiplicative form of Dimensional Reduction Method (M-DRM), which can estimate accurately the statistical moments and the probability distribution of the structural response, e.g., drift of a structure. The proposed approach is combined with OpenSees FE software and illustrated through the nonlinear pushover and nonlinear dynamic analysis of a steel frame. MCS is also performed for comparison of the proposed method.