• Title/Summary/Keyword: Rectangular distribution

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Theoretical analysis of stress-strain behavior of multi-layer RC beams under flexure

  • Ertekin Oztekin
    • Structural Engineering and Mechanics
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    • v.90 no.5
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    • pp.505-515
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    • 2024
  • In this study, obtaining theoretical stress-strain curves and determining the parameters defining the equivalent rectangular stress block were aimed for 3 and 4-layered rectangular Reinforced Concrete (RC) cross-sections subjected to flexure. For these aims, the analytical stress-strain model proposed by Hognestad was chosen for the concrete grades (20 MPa≤fck≤60 MPa) used in this study. The tensile strength of the concrete was neglected and the thickness of the concrete layers in the compression zone of the concrete cross-section was taken as equal. In addition, while concrete strength was kept constant within each layer, concrete strengths belonging to separate layers were increased from the neutral axis towards the outer face of the compression zone of the concrete cross-section. After the equivalent rectangular stress block parameters were determined by numerical iterations, variations of these parameters depending on concrete strength in layers and layer numbers were obtained. Finally, some analytical equations have been proposed to predict the equivalent stress block parameters for the 3 and 4-layered RC cross-sections and validities of these proposed equations were shown by different metrics in this study.

Formability of Sheet Metal in Noncircular Cup Drawing(I) (for Rectangular Cross Section) (비원형 단면에 대한 판재 성형성(I) (직사각형 단면에 대하여))

  • Shin, J.H.;Kim, M.S.;Seo, D.K.
    • Transactions of the Korean Society of Automotive Engineers
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    • v.2 no.1
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    • pp.84-95
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    • 1994
  • The effects of punch and blank shapes in the rectangular cup drawing process are examined experimentally to improve the formabilities. For this purpose, three blank shapes which are h-bl., G-bl., and T-bl., and five punch shape factors which are the ratios of two adjacent side lengths in rectangular cross section are adopted. The constructing methods of the three blank shapes are as follows. The h-bl. is designed by slip-line theory, and the G-bl. is selected for the similar shape to the punch. The T-bl. is obtained by the drawing method which is introduced in the technical references. The five punch shape factors are selected for length/width=1, 1.25, 1.5, 1.75 and 2. The experimental procedures are performed for all the above forming conditions to investigate and compare the formabilities. As a result, it is verified experimentally that the rectangular cups drawn by the h-bl. are more ideal than those drawn by G-bl. and T-bl.. They have not only higher limiting drawing ratio, more uniformity in drawn cup heights and more ideal thickness distributions, but also need relatively less maximum drawing forces.

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Seismic tests of RC shear walls confined with high-strength rectangular spiral reinforcement

  • Zhao, Huajing;Li, Qingning;Song, Can;Jiang, Haotian;Zhao, Jun
    • Steel and Composite Structures
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    • v.24 no.1
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    • pp.1-13
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    • 2017
  • In order to improve the deformation capacity of the high-strength concrete shear wall, five high-strength concrete shear wall specimens confined with high-strength rectangular spiral reinforcement (HRSR) possessing different parameters, were designed in this paper. One specimen was only adopted high-strength rectangular spiral hoops in embedded columns, the rest of the four specimens were used high-strength rectangular spiral hoops in embedded columns, and high-strength spiral horizontal distribution reinforcement were used in the wall body. Pseudo-static test were carried out on high-strength concrete shear wall specimens confined with HRSR, to study the influence of the factors of longitudinal reinforcement ratio, hoop reinforcement form and the spiral stirrups outer the wall on the failure modes, failure mechanism, ductility, hysteresis characteristics, stiffness degradation and energy dissipation capacity of the shear wall. Results showed that using HRSR as hoops and transverse reinforcements could restrain concrete, slow load carrying capacity degeneration, improve the load carrying capacity and ductility of shear walls; under the vertical force, seismic performance of the RC shear wall with high axial compression ratio can be significantly improved through plastic hinge area or the whole body of the shear wall equipped with outer HRSR.

Process Design and Finite Element Analysis of Rectangular Cup used for Ni-MH Battery with High Aspect Ratio (니켈-수소 2차 전지용 고세장비의 직사각 컵에 대한 성형공정 설계 및 유한요소해석)

  • Ku, T.W.;Kim, H.Y.;Song, W.J.;Kang, B.S.
    • Transactions of Materials Processing
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    • v.17 no.3
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    • pp.170-181
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    • 2008
  • The shape of rectangular cup used for Ni-MH(Nickel-coated Metal Hydrogen) battery for hybrid car looks quite simple, but the forming process of extruding and setting up process design are highly difficult. Furthermore, there are few concrete reports on the rectangular deep drawn cup as part of hybrid vehicles till now. In this study, process design for rectangular cup in the multi-stage deep drawing process is carried out, and FE analysis is also preformed based on the result of the process design. From the simulation result, some unexpected problems such as earing, wrinkling and excessive thickness changes of the intermediate blank occurred. To overcome these failures, a series of modification for punch shape in the forming process design are completed and applied. Considering the modified punch shape in the multi-stage deep drawing process, additional FE analysis is also carried out and the simulation result is verified in view of the deformed shape, thickness change and effective strain distribution. The result of FE analysis with the improved process design confirmed not only reducing thinning of wall and possibilities of failure but also improving the quality of drawing product through the modification of punch shape.

Vibration analysis of FG porous rectangular plates reinforced by graphene platelets

  • Zhou, Changlin;Zhang, Zhongxian;Zhang, Ji;Fang, Yuan;Tahouneh, Vahid
    • Steel and Composite Structures
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    • v.34 no.2
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    • pp.215-226
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    • 2020
  • The aim of this study is to investigate free vibration of functionally graded porous nanocomposite rectangular plates where the internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The GPL-reinforced plate is modeled using a semi-analytic approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. New results reveal the importance of porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, geometrical and boundary conditions on vibration behavior of porous nanocomposite plates. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution.

Two-Phase Flow Regimes for Counter-Current Air-Water Flows in Narrow Rectangular Channels

  • Kim, Byong-Joo;Sohn, Byung-Hu;Siyoung Jeong
    • Journal of Mechanical Science and Technology
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    • v.15 no.7
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    • pp.941-950
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    • 2001
  • A study of counter-current two-phase flow in narrow rectangular channels has been performed. Two-phase flow regimes were experimentally investigated in a 760mm long and 100mm wide test section with 2.0 and 5.0mm gap widths. The resulting flow regime maps were compared with the existing transition criteria. The experimental data and the transition criteria of the models showed relatively good agreement. However, the discrepancies between the experimental data and the model predictions of the flow regime transition become pronounced as the gap width increased. As the gap width increased the transition gas superficial velocities increased. The critical void fraction for the bubbly-to-slug transition was observed to be about 0.25. The two-phase distribution parameter for the slug flow was larger for the narrower channel. The uncertainties in the distribution parameter could lead to a disagreement in slug-to-churn transition between the experimental findings and the transition criteria. For the transition from churn to annular flow the effect of liquid superficial velocity was found to be insignificant.

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Effective Longitudinal Shear Modulus of Continuous Fiber-Reinforced 3-Phase Composites (연속섬유가 보강된 3상 복합재료의 종방향 전단계수 해석)

  • Jeong, Tae-Heon;Lee, Dong-Joo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.9
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    • pp.2782-2791
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    • 1996
  • The effective longitudinal shear modulus(LSM) of continuous composites is studied theoretically and numerically using 3-phase unit cell model. Circular, hexagonal and rectangular shapes of reinforced fiber are considered to predict the shear modulus as a function of elastic modulus of each phase and volume fraction of interphase and reinforced fiber. It is found that rectangular fiber shape in low fiber volume fraction($v_f$<30%) and circular fiber shape in high volume fraction($v_f$>40%) shows the higher longitudinal shear modulus. Also the obtained values of LSM for rectangular array and by numerical analysis are higher than those of hexagonal array and by theoretical analysis respectively. The reinforcing effects of interphase are more significant in cases of higher fiber volume fraction and circular fiber shape. Not only the spatial distribution and shape of reinforcing fiber but also the volume of interphase have a pronounced effects on the overall LSM. It is also found that the tangent moduous of 2-and 3-phase polymer matrix composites is insensitive to the shape and distribution of reinforcing fibers.

Rectangular prism pressure coherence by modified Morlet continuous wavelet transform

  • Le, Thai-Hoa;Caracoglia, Luca
    • Wind and Structures
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    • v.20 no.5
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    • pp.661-682
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    • 2015
  • This study investigates the use of time-frequency coherence analysis for detecting and evaluating coherent "structures" of surface pressures and wind turbulence components, simultaneously on the time-frequency plane. The continuous wavelet transform-based coherence is employed in this time-frequency examination since it enables multi-resolution analysis of non-stationary signals. The wavelet coherence quantity is used to identify highly coherent "events" and the "coherent structure" of both wind turbulence components and surface pressures on rectangular prisms, which are measured experimentally. The study also examines, by proposing a "modified" complex Morlet wavelet function, the influence of the time-frequency resolution and wavelet parameters (i.e., central frequency and bandwidth) on the wavelet coherence of the surface pressures. It is found that the time-frequency resolution may significantly affect the accuracy of the time-frequency coherence; the selection of the central frequency in the modified complex Morlet wavelet is the key parameter for the time-frequency resolution analysis. Furthermore, the concepts of time-averaged wavelet coherence and wavelet coherence ridge are used to better investigate the time-frequency coherence, the coherently dominant events and the time-varying coherence distribution. Experimental data derived from physical measurements of turbulent flow and surface pressures on rectangular prisms with slenderness ratios B/D=1:1 and B/D=5:1, are analyzed.

Optimum Air-Gap Flux Distribution with Third Harmonic Rotor Flux Orientation Adjustment for Five-Phase Induction Motor

  • Kang, Min;Yu, Wenjuan;Wang, Zhengyu;Kong, Wubin;Xiao, Ye
    • Journal of Electrical Engineering and Technology
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    • v.13 no.1
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    • pp.315-325
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    • 2018
  • This paper investigates optimum air-gap flux distribution with third harmonic rotor flux orientation adjustment for five-phase induction motor. The technique of objective is to generate a nearly rectangular air-gap flux, and it improves iron utilization under variation loading conditions. The proportional relations between third harmonic and fundamental plane currents is usually adopted in the conventional method. However, misalignment between fundamental and third harmonic component occurs with variation loading. The iron of stator teeth is saturated due to this misalignment. This problem is solved by third harmonic rotor flux orientation adjustment simultaneously, and direction and amplitude are changed with mechanical load variation. The proposed method ensures that the air-gap flux density is near rectangular for a maximum value from no load to rated load. It is confirmed that the proposed method guarantees complete both planes decoupling with third harmonic flux orientation adjustment. The effectiveness of the proposed technique is validated experimentally.

Sway Added Mass of a Rectangular Cylinder in a Restricted Water

  • Hwang, J.H.;Rhee, K.P.;Kang, C.K.
    • Bulletin of the Society of Naval Architects of Korea
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    • v.19 no.1
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    • pp.3-14
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    • 1982
  • In this paper, the sway added mass of a rectangular cylinder in a restricted water is considered by applying Hamilton's principle as the frequency tends to zero. The present method is an extension of Isshiki's method proposed in 1978. In the present method, it is assumed that the fluid velocity distribution in each subdomain of the fluid can be represented by higher order polynomials while Isshiki assumed linear velocity distribution. The fluid flow is assumed as a rotational motion in the present analysis. However, the results obtained from the present method show good agreement with Bai's numerical results for the case of large clearances between a canal wall and a cylinder. From Kelvin's minimum energy theorem, we can see that the value of sway added mass obtained from the present method approaches the upper bound. The approximate formula obtained in the present study takes a simple form which consists of the dimensions of the canal and the cylinder. The present formulae are derived for the cases of a rectangular cylinder swaying at the center of a narrow or wide canal relative to a cylinder, at off-center location in a canal, and in the restricted water with a single wall. From the results of numerical calculation, it is concluded that the sway added mass in restricted waters is more affected by water depth than clearance between a wall and a cylinder.

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