• Wind and Structures
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• v.14 no.4
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• pp.359-381
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• 2011

This paper deals with the flutter instability problem of flexible bridge decks in the framework of bimodal-coupled aeroelastic bridge system analysis. Based on the analysis of coefficients of the polynomials deduced from the singularity conditions of an integral wind-structure impedance matrix, a set of simplified formulations for calculating the critical wind velocity and coupled frequency are presented. Several case studies are discussed and comparisons with available approximated approaches are made and presented, along with a conventional complex eigenvalue analysis and numerical results. From the results, it is found that the formulas that are presented in this study are applicable to a variety of bridge cross sections that are not only prone to coupled-mode but also to single-mode-dominated flutter.

• Structural Engineering and Mechanics
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• v.8 no.1
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• pp.1-18
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• 1999

Procedures are investigated by which nonlinear finite element shell analysis algorithms can be simplified to provide more cost effective approximate analyses of orthogonally-reinforced concrete flat plate structures. Two alternative effective stiffness formulations, and an unbalanced force formulation, are described. These are then implemented into a nonlinear shell analysis algorithm. Nonlinear geometry, three-dimensional layered stress analyses, and other general formulations are bypassed to reduce the computational burden. In application to standard patch test problems, these simplified approximate analysis procedures are shown to provide reasonable accuracy while significantly reducing the computational effort. Corroboration studies using various simple and complex test specimens provide an indication of the relative accuracy of the constitutive models utilized. The studies also point to the limitations of the approximate formulations, and identify situations where one should revert back to full nonlinear shell analyses.

• Nuclear Engineering and Technology
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• v.53 no.12
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• pp.3861-3878
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• 2021

The steady-state simplified spherical harmonics equations (SP_N equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SP_N equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.

• Safety and Health at Work
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• v.15 no.1
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• pp.59-65
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• 2024

Background: Different job strain formulations based on the Job Demand-Control model have been developed. This study evaluated longitudinal associations between job strain and psychological distress and whether associations were influenced by six formulations of job strain, including quadrant (original and simplified), subtraction, quotient, logarithm quotient, and quartile based on quotient, in randomly selected Japanese workers. Methods: Data were from waves I and II of the Survey of Midlife in Japan (MIDJA), with a 4-year followup period. The study sample consisted of 412 participants working at baseline and had complete data on variables of interest. Associations between job strain at baseline and psychological distress at follow-up were assessed via multivariable linear regression, and results were expressed as β coefficients and 95% confidence intervals including R² and Akaike information criterion (AIC) evaluation. Results: Crude models revealed that job strain formulations explained 6.93-10.30% of variance. The AIC ranged from 1475.87 to 1489.12. After accounting for sociodemographic and behavioral factors and psychological distress at baseline, fully-adjusted models indicated significant associations between all job strain formulations at baseline and psychological distress at follow-up: original quadrant (β: 1.16, 95% CI: 0.12, 2.21), simplified quadrant (β: 1.01, 95% CI: 0.18, 1.85), subtraction (β: 0.39, 95% CI: 0.09, 0.70), quotient (β: 0.37, 95% CI: 0.08, 0.67), logarithm quotient (β: 0.42, 95% CI: 0.12, 0.72), and quartile based on quotient (β: 1.22, 95% CI: 0.36, 2.08). Conclusion: Six job strain formulations showed robust predictive power regarding psychological distress over 4 years among Japanese workers.

• Wind and Structures
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• v.17 no.3
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• pp.275-298
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• 2013

This paper presents a number of approximated analytical formulations for the flutter analysis of long-span bridges using the so-called uncoupled flutter derivatives. The formulae have been developed from the simplified framework of a bimodal coupled flutter problem. As a result, the proposed method represents an extension of Selberg's empirical formula to generic bridge sections, which may be prone to one of the aeroelastic instability such as coupled-mode or single-mode (either dominated by torsion or heaving mode) flutter. Two approximated expressions for the flutter derivatives are required so that only the experimental flutter derivatives of ($H_1^*$, $A_2^*$) are measured to calculate the onset flutter. Based on asymptotic expansions of the flutter derivatives, a further simplified formula was derived to predict the critical wind speed of the cross section, which is prone to the coupled-mode flutter at large reduced wind speeds. The numerical results produced by the proposed formulas have been compared with results obtained by complex eigenvalue analysis and available approximated methods show that they seem to give satisfactory results for a wide range of study cases. Thus, these formulas can be used in the assessment of bridge flutter performance at the preliminary design stage.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.419-426
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• 2003

Simplified modeling approach for the seismic behavior of a reinforced concrete bridge is investigated in this paper. For this purpose, a hysteretic axial-flexure interaction model was developed and implemented into a nonlinear finite element analysis program. Thus, the seismic response of reinforced concrete bridge piers was evaluated by the simplified point hinge representations. Comparative studies for reinforced concrete bridge piers indicated that the analytical predictions obtained with the new formulations showed a good correlation with experimental results. In addition, seismic response analysis of a reinforced concrete bridge utilizing the simplified point hinge model revealed the adequacy and applicability of the present development.

• Proceedings of the Optical Society of Korea Conference
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• 1989.02a
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• pp.225-229
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• 1989

Taking the normal mode transmission direction perpendicular to the substrate, an alternative equivalent network formulation is developed for the analysis of optical strip waveguides. All kinds of mode couplings between the normal modes are included in this formulation. Compared to the previous equivalent network formulations, the calculations are simplified especially when the thickness of the uniform slab is thin enough such that no well guided modes are available along the uniform slab waveguide.

• Earthquakes and Structures
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• v.15 no.4
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• pp.419-429
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• 2018

The seismic vulnerability analysis of multi-span bridges can be based on the response of the piers, provided that deck, bearings and foundations remain elastic. The lateral response of an RC bridge pier can be affected by different mechanisms (i.e., flexure, shear, lap-splice or buckling of the longitudinal reinforcement bars, second order effects). In the literature, simplified formulations are available for mechanisms different from the flexure. On the other hand, the flexural response is usually calculated with a numerically-based Moment-Curvature diagram of the base section and equivalent plastic hinge length. The goal of this paper is to propose a simplified analytical solution to obtain the Moment-Curvature relationship for hollow circular RC sections. This based on calibrated polynomials, fitted against a database comprising 720 numerical Moment-Curvature analyses. The section capacity curve is defined through the position of 6 characteristic points and they are based on four input parameters: void ratio of the hollow section, axial force ratio, longitudinal reinforcement ratio, transversal reinforcement ratio. A case study RC bridge pier is assessed with the proposed solution and the results are compared to a refined numerical FEM analysis, showing good match.

• Computers and Concrete
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• v.3 no.2_3
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• pp.123-144
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• 2006

Reinforced concrete corbels are structural elements widely used in practical engineering. The complex response of these elements is described in design codes in a simplified manner. These formulations are not sufficient to show the real behavior, which, however, is an essential prerequisite for the manufacturing of numerous elements. Therefore, a deterministic and probabilistic study has been performed, which is described in this contribution. Real complex structures have been modeled by means of the finite element method supported primarily by experimental works. The main objective of this study was the detection of uncertainties effects and safety margins not captured by traditional codes. This aim could be fulfilled by statistical considerations applied to the investigated structures. The probabilistic study is based on advanced Monte Carlo simulation techniques and sophisticated nonlinear finite element formulations.

• Earthquakes and Structures
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• v.9 no.3
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• pp.455-480
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• 2015

In the last decade, displacement-based (DB) methods have become established design procedures for reinforced concrete (RC) structures. They use strain and displacement measures as seismic performance control parameters. As for other simplified seismic design methods, it is of great interest to prove if they are usually conservative in respect to more refined, nonlinear, time history analyses, and can estimate design parameters with acceptable accuracy. In this paper, the current Direct Displacement-Based Design (DDBD) procedure is evaluated for designing simple single degree of freedom (SDOF) systems with specific reference to simply supported RC bridge piers. Using different formulations proposed in literature for the equivalent viscous damping and spectrum reduction factor, a parametric study is carried out on a comprehensive set of SDOF systems, and an average error chart of the method is derived allowing prediction of the expected error for an ample range of design cases. Following the chart, it can be observed that, for the design of actual RC bridge piers, underestimation errors of the DDBD method are very low, while the overestimation range of the simplified displacement-based procedure is strongly dependent on design ductility.