• Structural Engineering and Mechanics
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• v.80 no.6
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• pp.645-655
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• 2021

Performance-based reliability analysis is a practical approach to investigate the seismic performance and stochastic nonlinear response of structures considering a random process. This is significant due to the uncertainties involved in every aspect of the analysis. Therefore, the present study aims to evaluate the performance-based reliability within a stochastic finite element (FE) framework for reinforced concrete (RC) shear walls that are considered as one of the most essential elements of structures. To accomplish this purpose, deterministic FE analyses are conducted for both squat and slender shear walls to validate numerical models through experimental results. The presented numerical analysis is performed by using the ABAQUS FE program. Afterwards, a random-effects investigation is carried out to consider the influence of different random variables on the lateral load-top displacement behavior of RC members. Using these results and through utilizing the Monte-Carlo simulation method, stochastic nonlinear analyses are also performed to generate random FE models based on input parameters and their probabilistic distributions. In order to evaluate the reliability of RC walls, failure probabilities and corresponding reliability indices are calculated at life safety and collapse prevention levels of performance as suggested by FEMA 356. Moreover, based on reliability indices, capacity reduction factors are determined subjected to shear for all specimens that are designed according to the ACI 318 Building Code. Obtained results show that the lateral load and the compressive strength of concrete have the highest effects on load-displacement responses compared to those of other random variables. It is also found that the probability of shear failure for the squat wall is slightly lower than that for slender walls. This implies that 𝛽 values are higher in a non-ductile mode of failure. Besides, the reliability of both squat and slender shear walls does not change significantly in the case of varying capacity reduction factors.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.5
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• pp.29-37
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• 1993

The extension of the weighted integral method in the area of stochastic finite element analysis is presented. The use of weighted integral method in numerical analysis was extended to CST(constant strain triangle) element by Deodatis to calculate the response variability of 2D stochastic systems. In this paper, the extension of the weighted integral method for general plane-elements is represented. It has been shown that the same mesh used in the deterministic FE analysis can be used in the stochastic FE analysis. Furthermore, because the CST element is a special case which has constant strain-displacement matrix the mingling of CST elements with the other quadrilateral elements in the analysis may also be possible.

• Computational Structural Engineering
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• v.8 no.1
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• pp.127-136
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• 1995

In this paper the stochastic FE analysis considering the material and geometrical property of the plate structure is performed by the weighted integral method. To consider the stochasity of the material and geometrical property, the stochastic field is assumed respectively. The mean value of the stochastic field is 0 and the value of variance is assumed as 0.1. The characteristics of the assumed stochastic field is represented by auto-correlation function. This auto-correlation function is used in evaluating the response variability of the plate structure. In this study a new auto-correlation function is derived to concern the uncertainty of the plate thickness. The newly derived auto-correlation function is a function of auto-correlation function and coefficient of variation of the assumed stochastic field. The two results, obtained by proposed Weighted Integral method and Monte Carlo Simulation method, are coincided with each other and these results are almost equal to the theoretical result that is derived in this study. In the case of considering the variability of plate thickness, the obtained result is well coincide with those of Lawrence and Monte Carlo simulation.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.11-18
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• 1998

In this paper the stochastic analysis of semi-infinite domain is presented using the weighted integral method, which is expanded to include the infinite finite elements. The semi-infinite domain can be thought as to have more uncertainties than the ordinary finite domain in material constants, which shows the needs of and the importance of the stochastic finite element analysis. The Bettess's infinite element is adopted with the theoretical decomposition of the strain matrix to calculate the deviatoric stiffness of the semi-infinite domains. The calculated value of mean and the covariance of the displacement are revealed to be larger than those given by the finite domain assumptions giving the rational results which should be considered in the design of structures on semi-infinite domains.

• Computers and Concrete
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• v.15 no.2
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• pp.259-277
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• 2015

The lack of experimental studies on the mechanical behavior of reinforced concrete (RC) haunched beams leads to difficulties in statistical and reliability analyses. This study performs stochastic and reliability analyses of the ultimate shear capacity of RC haunched beams based on nonlinear finite element analysis. The main aim of this study is to investigate the influence of uncertainty in material properties and geometry parameters on the mechanical performance and shear capacity of RC haunched beams. Firstly, 65 experimentally tested RC haunched beams and prismatic beams are analyzed via deterministic nonlinear finite element method by a special program (ATENA) to verify the efficiency of utilized numerical models, the shear capacity and the crack pattern. The accuracy of nonlinear finite element analyses is verified by comparing the results of nonlinear finite element and experiments and both results are found to be in a good agreement. Afterwards, stochastic analyses are performed for each beam where the RC material properties and geometry parameters are assigned to take probabilistic values using an advanced simulating procedure. As a result of stochastic analysis, statistical parameters are determined. The statistical parameters are obtained for resistance bias factor and the coefficient of variation which were found to be equal to 1.053 and 0.137 respectively. Finally, reliability analyses are accomplished using the limit state functions of ACI-318 and ASCE-7 depending on the calculated statistical parameters. The results show that the RC haunched beams have higher sensitivity and riskiness than the RC prismatic beams.

• Structural Engineering and Mechanics
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• v.32 no.1
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• pp.1-20
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• 2009

The present contribution addresses uncertainty quantification and uncertainty propagation in structural mechanics using stochastic analysis. Presently available procedures to describe uncertainties in load and resistance within a suitable mathematical framework are shortly addressed. Monte Carlo methods are proposed for studying the variability in the structural properties and for their propagation to the response. The general applicability and versatility of Monte Carlo Simulation is demonstrated in the context with computational models that have been developed for deterministic structural analysis. After discussing Direct Monte Carlo Simulation for the assessment of the response variability, some recently developed advanced Monte Carlo methods applied for reliability assessment are described, such as Importance Sampling for linear uncertain structures subjected to Gaussian loading, Line Sampling in linear dynamics and Subset simulation. The numerical example demonstrates the applicability of Line Sampling to general linear uncertain FE systems under Gaussian distributed excitation.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Structural Engineering and Mechanics
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• v.32 no.1
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• pp.95-126
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• 2009

The present contribution addresses the parallelization of advanced simulation methods for structural reliability analysis, which have recently been developed for large-scale structures with a high number of uncertain parameters. In particular, the Line Sampling method and the Subset Simulation method are considered. The proposed parallel algorithms exploit the parallelism associated with the possibility to simultaneously perform independent FE analyses. For the Line Sampling method a parallelization scheme is proposed both for the actual sampling process, and for the statistical gradient estimation method used to identify the so-called important direction of the Line Sampling scheme. Two parallelization strategies are investigated for the Subset Simulation method: the first one consists in the embarrassingly parallel advancement of distinct Markov chains; in this case the speedup is bounded by the number of chains advanced simultaneously. The second parallel Subset Simulation algorithm utilizes the concept of speculative computing. Speedup measurements in context with the FE model of a multistory building (24,000 DOFs) show the reduction of the wall-clock time to a very viable amount (<10 minutes for Line Sampling and ${\approx}$ 1 hour for Subset Simulation). The measurements, conducted on clusters of multi-core nodes, also indicate a strong sensitivity of the parallel performance to the load level of the nodes, in terms of the number of simultaneously used cores. This performance degradation is related to memory bottlenecks during the modal analysis required during each FE analysis.

• Earthquakes and Structures
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• v.2 no.2
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• pp.189-206
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• 2011

In this study, the subspace stochastic realization theories (SSR model I and SSR model II) have been applied to a real bridge for estimating its dynamic characteristics (natural frequencies, damping constants, and vibration modes) under ambient vibration. A numerical simulation is carried out for an arch-type steel truss bridge using a white noise excitation. The estimates obtained from this simulation are compared with those obtained from the Finite Element (FE) analysis, demonstrating good agreement and clarifying the excellent performance of this method in estimating the structural dynamic characteristics. Subsequently, these methods are applied to the vibration induced by both strong and weak winds as obtained by remote monitoring of the Kabashima bridge (an arch-type steel truss bridge of length 136 m, and situated in Nagasaki city). The results obtained with this experimental data reveal that more accurate estimates are obtained when strong wind vibration data is used. In contrast, the vibration data obtained from weak wind provides accurate estimates at lower frequencies, and inaccurate accuracy for higher modes of vibration that do not get excited by the wind of lower intensity. On the basis of the identified results obtained using both simulated data and monitored data from a real bridge, it is determined that the SSR model II realizes more accurate results than the SSR model I. In general, the approach investigated in this study is found to provide acceptable estimates of the dynamic characteristics of highway bridges as well as for the vibration monitoring of bridges.

• Smart Structures and Systems
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• v.11 no.5
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• pp.533-553
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• 2013

In this paper, system identification of a cable-stayed bridge in Korea, the Hwamyung Bridge, is performed using vibration responses measured by a wireless sensor system. First, an acceleration based-wireless sensor system is employed for the structural health monitoring of the bridge, and wireless sensor nodes are deployed on a deck, a pylon and several selected cables. Second, modal parameters of the bridge are obtained both from measured vibration responses and finite element (FE) analysis. Frequency domain decomposition and stochastic subspace identification methods are used to obtain the modal parameters from the measured vibration responses. The FE model of the bridge is established using commercial FE software package. Third, structural properties of the bridge are updated using a modal sensitivity-based method. The updating work improves the accuracy of the FE model so that structural behaviors of the bridge can be represented better using the updated FE model. Finally, cable forces of the selected cables are also identified and compared with both design and lift-off test values.