• Steel and Composite Structures
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• v.38 no.4
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• pp.415-430
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• 2021

The effective flange width was usually introduced into elementary beam theory to consider the shear lag effect in steel-concrete composite beams. Previous studies have primarily focused on the effective width under positive moments and elastic loading, whereas it is still not clear for negative moment cases in the normal service stages. To account for this problem, this paper proposed simplified formulas for the effective flange width and reinforcement stress of composite beams under negative moments in service stages. First, a 10-degree-of-freedom (DOF) fiber beam element considering the shear lag effect and interfacial slip effect was proposed, and a computational procedure was developed in the OpenSees software. The accuracy and applicability of the proposed model were verified through comparisons with experimental results. Second, a method was proposed for determining the effective width of composite beams under negative moments based on reinforcement stress. Employing the proposed model, the simplified formulas were proposed via numerical fitting for cases under uniform loading and centralized loading at the mid-span. Finally, based on the proposed formulas, a simplified calculation method for the reinforcement stress in service stages was established. Comparisons were made between the proposed formulas and design code. The results showed that the design code method greatly underestimated the contribution of concrete under negative moments, leading to notable overestimations in the reinforcement stress and crack width.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.523-529
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• 2010

In this paper, we obtain some recurrence relations for the quotient moments of the lower record values from the generalized extereme value(GEV) distribution. We also deduce some recurrence relations for the negative moments from the GEV distribution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.55-72
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• 2009

A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = c + 1 are misclassified as x = c with probability $\alpha$, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and sizebiased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.

• Journal of the Korea Concrete Institute
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• v.23 no.6
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• pp.731-740
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• 2011

Provisions for the redistribution of negative moments in KCI 2007 and ACI 318-08 use a method for continuous flexural members subjected to uniformly-distributed gravity load. Moment redistributions and plastic rotations in beams of reinforced concrete moment frames subjected to lateral load differ from those in continuous flexural members due to gravity load. In the present study, a quantitative relationship between the moment redistribution and plastic rotation is established for beams subjected to both lateral and gravity loads. Based on the relationship, a design method for the redistribution of negative moments is proposed based on a plastic rotation capacity. The percentage change in negative moments in the beam was defined as a function of the tensile strain of re-bars at the section of maximum negative moment, which is determined by a section analysis at an ultimate state using KCI 2007 and ACI 318-08. Span, reinforcement ratio, cracked section stiffness, and strain-hardening behavior substantially affected the moment redistribution. Design guidelines and examples for the redistribution of the factored negative moments determined by elastic theory for beams under lateral load are presented.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.505-513
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• 2011

In this paper, we obtain the derivations of moments of discrete probability distributions by using the backward difference operators. Also, we presents such derivations for several well-known distributions; they are the binomial, Poisson, geometric, hypergeometric and negative hypergeometric distributions.

• Steel and Composite Structures
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• v.20 no.1
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• pp.57-70
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• 2016

The predominant type of buckling that I-steel concrete composite beams experience in the negative moment area is distortional buckling. The key factors that affect distortional buckling are the torsional and lateral restraints by the bottom flange. This study thoroughly investigates the equivalent lateral and torsional restraint stiffnesses of the bottom flange of an I-steel concrete composite beam under negative moments. The results show a coupling effect between the applied forces and the lateral and torsional restraint stiffnesses of the bottom flange. A formula is proposed to calculate the critical buckling stress of the I-steel concrete composite beams under negative moments by considering the lateral and torsional restraint stiffnesses of the bottom flange. The proposed method is shown to better predict the critical bending moment of the I-steel composite beams. This article introduces an improved method to calculate the elastic foundation beams, which takes into account the lateral and torsional restraint stiffnesses of the bottom flange and considers the coupling effect between them. The results show a close match in results from the calculation method proposed in this paper and the ANSYS finite element method, which validates the proposed calculation method. The proposed calculation method provides a theoretical basis for further research on distortional buckling and the ultimate resistance of I-steel concrete composite beams under a variable axial force.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.396-403
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• 2002

To eliminate deck joints, continuous span bridges are becoming an attractive option. Defferent continuty methods and construction sequences have different time-dependent effects on the behavior of the bridge system. This paper is carried out to evaluate the restraint moments generated at interior span of bridges constructed with full-span prestessed concrete bridge. Especially, effects of creep and shrinkage between ACI209-95 and Eurocode 2 are compared in this paper. Time-dependent effects in prestressed concrete bridges include creep and shrinkage of concrete. Creep due to prestress makes the girders camber up and cause positive restraint moments. The most significant effect of shrinkage in continuous bridges is the differential shrinkage that occurs because of the difference in type and age of girder and deck concrete. Differential shrinkage between the precast girder and the deck typically causes negative res03int moments.

• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.629-651
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• 2003

Current design specifications prescribe that the upper and lower reinforcement mat is required in the same amount to resist negative and positive moment in bridge decks. This design concept is primarily based on the unrealistic assumption that the girder plays a role of rigid support against deck deflection. In reality, however, girders are flexible and the deflection of girders affect the behavior of deck slabs. In the present study, an analytical method was developed to take the effect of the girder flexibility on the deck behavior into account. The method was formulated based on the slope-deflection equations of plates and harmonic analysis. Unlike the conventional finite element analysis, the input and output schemes are simple and convenient. The validity of the presented study was verified by a series of comparative studies with finite element analyses and experimental tests. It was shown from the analyses that the negative transverse moments of decks were significantly reduced in many cases when the girder flexibility were appropriately taken into consideration whereas the positive moments tend to increase. This poses a strong need to improve the conventional design concept of decks on rigid girders to those on flexible girders.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.2
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• pp.81-95
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• 2008

In this paper, the negative Polya-Eggenberger distribution has been introduced by compounding negative binomial distribution with beta distribution of I-kind which generates a number of univariate contagious or compound (or mixture of) distributions as its particular cases. The distribution is unimode, over dispersed and all of its positive and negative integer moments exist. The difference equation of the proposed model shows that it is a member of the Ord's family of distribution. Some of its interesting properties have been explored besides different methods of estimation been discussed. Finally, the parameters of the proposed model have been estimated by using a computer programme in R-software. Application of the proposed model to some data, available in the literature, has been given and its goodness of fit demonstrated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.153-160
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• 2008

A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.