• Geomechanics and Engineering
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• v.18 no.1
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• pp.41-48
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• 2019

Bending moments in the raft of a pile raft system is affected by pile-pile interaction and pile-raft interaction, amongst other factors. Three-Dimensional finite element program has to be used to evaluate these bending moments. Winkler type analysis is easy to use but it however ignores these interactions. This paper proposes a very simplified and novel method for finding bending moments in raft of a piled raft based on Winkler type where raft is supported on bed of springs considering pile-pile and pile-raft interaction entitled as "Winkler model for piled raft (WMPR)" The pile and raft spring stiffness are based on load share between pile and raft and average pile raft settlement proposed by Randolph (1994). To verify the results of WMPR, raft bending moments are compared with those obtained from PLAXIS 3D software. A total of sixty analysis have Performed varying different parameters. It is found that raft bending moments obtained from WMPR closely match with bending moments obtained from PLAXIS 3D. A comparison of bending moments ignoring any interaction in Winkler model is also made with PLAXIS-3D, which results in large difference of bending moments. Finally, bending moment results from eight different methods are compared with WMPR for a case study. The WMPR, though, a simple method yielded comparable raft bending moments with the most accurate analysis.

• Steel and Composite Structures
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• v.9 no.4
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• pp.303-323
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• 2009

Charts for the bending moments in the closed rib orthotropic deck plate are derived, based on the method originally introduced by Pelikan and Esslinger. New charts are done for EN 1991-2 traffic load distribution schemes. The governing Huber plate equation is solved utilizing Fourier series for various bridge deck plate boundary conditions. Bending moments are given as a function of deck plate rigidities and span length between cross beams. Old diagrams according to DIN 1072, the new ones according to EN 1991-2 and FE analyses results are compared. For typical bridge orthotropic deck plates, it can be concluded that the new EN 1991-2 traffic loads produce larger mid-span bending moments when two lane schemes are used, then those of DIN 1072. For support moments, DIN 1072 gives larger values for any number of lanes, especially under span lengths of 5m. The relevant differences are up to 25%.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.36 no.4
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• pp.595-604
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• 2016

This paper proposed the design bending moments of cantilever slabs with KL-510 load according to span length of long span decks. Their span length range is from 6.0 to 12.0 meter, and length of cantilever slabs is from 30 to 50 percent of their span length. The effects of orthotropic concrete decks, stiffness of steel girders and multiple lane loading factors (MLLF) were reflected in the design bending moments. The proposed design bending moments of cantilever slabs were compared to the design bending moments with DB-24 load.

• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.3-13
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• 1996

An extensive research programme has been aimed at the effct of ship weight distribution on the ship responses applying ship hydroelasticity theory. In the previous works, consistent tendencies of the still-water and the wave bending moments. respectively, were found as the weight distribution was varied systematically. The paper is therefore concerned mainly with any correlation between still-water and wave bending moments with the variations of weight distribution. Although these bending moments share different features with each other, such a comparison of tendencies was plausible and informative. These and other matters for the future are discussed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.36 no.3
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• pp.375-384
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• 2016

In the current Korea highway bridge design code (KHBDC), the criteria of concrete bridge decks are mainly based on short span decks of steel plate girder bridge, there are very little the specific criteria of long span decks in the twin steel plate girder bridge. Therefore, to put more rational and practical design criteria of the long span decks on the code, the complements of the related criteria are required in the current design code. This paper proposed the design bending moments of decks with 6.0~12.0m span for KL-510 load in direction to bridge (longitudinal direction) and perpendicular direction to bridge (transverse direction). The effects of orthotropic concrete decks, stiffness of steel girders and multiple lane loading factors (MLLF) were reflected in the design bending moments. The proposed design bending moments were compared to the design bending moments with DB-24 load.

• Geomechanics and Engineering
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• v.34 no.6
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• pp.611-621
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• 2023

This paper presents the results of a numerical investigation of the effect of geotextile reinforcement on underlying buried pipe behavior using PLAXIS 3D. In this study, variable parameters such as the in-plane stiffness of the geotextile, the pipe stiffness, the soil stiffness, the footing width, the geotextile width, and the location of the geotextile reinforcement layer are investigated. Deflections and bending moments acting on the pipe are evaluated for different combinations of variables and are presented graphically. It is observed that with an increase in the in-plane stiffness of the geotextile reinforcement, there is a tendency for a decrease in both deflections in the pipe and bending moments acting on the pipe. Conversely, with an increase in the pipe stiffness, geotextile reinforcement efficiency decreases. In the investigated region of soil stiffness, for the given pipe and geotextile stiffness, an optimum efficiency of geotextile is observed in medium dense soils. Further, it is shown that relative lengths of geotextile and footing has an important role on geotextile efficiency. Lastly, it is also demonstrated that relative location of geotextile layer with respect to the buried pipe plays an important role on the geotextile efficiency in reducing the bending moments acting on the pipe and deflections in the pipe. In general, geotextiles are more efficient in reducing the bending moments as opposed to reducing deflections of the pipe. Numerical validation is done with an experimental study from the literature to observe the applicability of the numerical model used.

• Structural Engineering and Mechanics
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• v.9 no.5
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• pp.469-482
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• 2000

A numerical study using nonlinear finite element analysis is performed to investigate the behavior of isolated reinforced concrete walls subjected to combined axial force and in-plane and out-of-plane bending moments. For a nonlinear finite element analysis, a computer program addressing material and geometric nonlinearities was developed. Through numerical studies, the internal force distribution in the cross-section is idealized, and then a new design method, different from the existing methods based on the plane section hypothesis was developed. According to the proposed method, variations in the interaction curve of the in-plane bending moment and axial force depends on the range of the permissible axial force per unit length, that is determined by a given amount of out-of-plane bending moment. As the out-of-plane bending moment increases, the interaction curve shrinks, indicating a decrease in the ultimate strength. The proposed method is then compared with an existing method, using the plane section hypothesis. Compared with the proposed method, the existing method overestimates the ultimate strength for the walls subjected to low out-of-plane bending moments, while it underestimates the ultimate strength for walls subject to high out-of-plane bending moments. The proposed method can address the out-of-plane local behavior of the individual wall segments that may govern the ultimate strength of the entire wall.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.187-195
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• 2020

In this paper, we investigate the vectorial moments of Bäcklund transformations of a space curve in 𝔼³. Firstly, it is obtained the vectorial moments which named α𝓖 dual curve, β𝓖 dual curve, and γ𝓖 dual curve of Bäcklund transformations. Then we give the Euler elastic bending energies of these curves. Finally, we provide some examples of α𝓖 dual, β𝓖 dual, and γ𝓖 dual, and their Euler elastic bending energies.

• Steel and Composite Structures
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• v.23 no.5
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• pp.597-610
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• 2017

This paper presents a mathematical model for fixed-end moments of I-sections with straight haunches for the general case (symmetrical and/or non-symmetrical) subjected to a concentrated load localized anywhere on beam taking into account the bending deformations and shear, which is the novelty of this research. The properties of the cross section of the beam vary along its axis "x", i.e., the flange width "b", the flange thickness "t", the web thickness "e" are constant and the height "d" varies along of the beam, this variation is linear type. The compatibility equations and equilibrium are used to solve such problems, and the deformations anywhere of beam are found by the virtual work principle through exact integrations using the software "Derive" to obtain some results. The traditional model takes into account only bending deformations, and others authors present tables considering the bending deformations and shear, but are restricted. A comparison between the traditional model and the proposed model is made to observe differences, and an example of structural analysis of a continuous highway bridge under live load is resolved. Besides the effectiveness and accuracy of the developed models, a significant advantage is that fixed-end moments are calculated for any cross section of the beam "I" using the mathematical formulas.

• Computers and Concrete
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• v.18 no.6
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• pp.1113-1134
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• 2016

A methodology using neural networks has been proposed for rapid prediction of inelastic bending moments in reinforced concrete continuous beams subjected to service load. The closed form expressions obtained from the trained neural networks take into account cracking in concrete at in-span and at near the internal supports and tension stiffening effect. The expressions predict the inelastic moments (considering the concrete cracking) from the elastic moments (neglecting the concrete cracking) at supports. Three separate neural networks are trained since these have been postulated to represent all the beams having any number of spans. The training, validating, and testing data sets for the neural networks are generated using an analytical-numerical procedure of analysis. The proposed expressions are verified for example beams of different number of spans and cross-section properties and the errors are found to be small. The proposed expressions, at minimal input data and computation effort, yield results that are close to FEM results. The expressions can be used in preliminary every day design as they enable a rapid prediction of inelastic moments and require a computational effort that is a fraction of that required for the available methods in literature.