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Journal articles on the topic 'Trapezoidal section'
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1
Easa, Said M., and Yan-Cheng Han. "New Compound Open Channel Section with Polynomial Sides: Improving Cost and Aesthetics." Water 11, no. 8 (2019): 1545. http://dx.doi.org/10.3390/w11081545.
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Previous research on compound trapezoidal cross sections has mainly focused on improving the prediction of the discharge (flow rate) because of its inherent challenges. This paper focuses on two other important aspects: Section shape and optimal construction cost. First, the paper proposes a new compound section with third-degree polynomial sides of main channel with horizontal bottom (HB) that allows its top corners to be smooth, called herein compound polynomial section. The special cases of this versatile section include the simple polynomial section, polygonal section, trapezoidal-rectangular section, two-segment linear-side section, and parabolic bottom-trapezoidal section. The simple polynomial section, which is the bank-full part of the compound polynomial section, can further produce parabolic (with or without HB), trapezoidal, rectangular, and triangular sections. Second, an optimization model that minimizes construction cost (excavation and lining) of the compound (or simple) polynomial section is developed. The model includes discharge and physical constraints. Theoretical and empirical methods of discharge prediction were used in the model. The results show that the simple polynomial section was more economical than the popular parabolic section by up to 8.6% when the side slopes were restricted. The new polynomial-based sections not only reduced construction cost, but also improved maintenance and aesthetics. As such, the new sections should be of interest to researchers and practitioners in hydraulic engineering.
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Ma, Bin, Zhengxiang Huang, Yongzhong Wu, Yuting Wang, Xin Jia, and Guangyue Gao. "Research on the Formation Characteristics of the Shaped Charge Jet from the Shaped Charge with a Trapezoid Cross-Section." Materials 15, no. 23 (2022): 8663. http://dx.doi.org/10.3390/ma15238663.
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The formation characteristics of the shaped charge jet (SCJ) from the shaped charge with a trapezoid cross-section is analyzed in this work. A theoretical model was developed to analyze the collapsing mechanism of the liner driven by the charge with a trapezoid cross-section. Based on the theoretical model, the axial and radial velocities of the SCJ from different trapezoid cross-section charges. The pressure model was employed to calculate the velocity for the subcaliber shaped charge, which was verified through numerical simulation. The results show that the influence of the angle of the trapezoidal charge (acute angle) on the axial velocity of the SCJ is not distinct, whereas the variation of the radial velocity of the shaped charge jet is obvious as the change in the angle of the trapezoidal charge. In addition, the related X-ray experiments were conducted to verify the theory. The theoretical results correlate with the experimental results reasonably well.
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Fan, Gui Jie. "Optimization of Trapezoidal Runner in Plastic Molding Based on MATLAB." Applied Mechanics and Materials 552 (June 2014): 66–69. http://dx.doi.org/10.4028/www.scientific.net/amm.552.66.
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The runner design is an important parts in plastic molding design. Its shape and dimensions have special effects on the molten plastic’s pressure, hot loss, injection speed, etc. At present, trapezoidal runner is used widely for better fluidity and lower assembly precision relatively compared with the circular runner. This paper uses the Fminsearch function of MATLAB and constructs an objective function based on the minimum length of the perimeter of the trapezoidal runner to optimize the trapezoidal runner section. The conclusion of this paper is that the perimeter of the trapezoidal runner is the shortest one when a equals c (shown as Fig.1), as well as the obtuse angle between a and c equals 120o. At this conditions, the volume of the molten plastic that flows through the runner section is maximum when the trapezoidal runner section area is given. The optimization results in the plastic mould design can used as the size or the constraints to drive the runner section in 3D CAD/CAM software, which can help the designer to get the trapezoidal runner section easily and quickly.
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Wang, Yijia. "Technical Research on Optimization of Irrigation Canal System Considering Genetic Algorithm." Mobile Information Systems 2022 (August 8, 2022): 1–9. http://dx.doi.org/10.1155/2022/8687532.
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In order to solve the lack of optimization and comparison of the previous schemes in the irrigation and water conservancy project reconstruction, the engineering design and planning are difficult to reach the best state, resulting in water resource waste and other problems. In this paper, genetic algorithm optimization technology of the irrigation canal system is studied, in-depth learning technology of image processing is elaborated, the rectangular optimization model is established, and the optimal nonlinear design of trapezoidal and U-shaped sections of irrigation channel is verified by engineering examples. According to the geographical location, water source, irrigation area, irrigation area, and designer’s experience, two possible irrigation scheme layouts have been determined, and the trapezoidal section has been optimized. The results show that the value of the objective function decreases rapidly with the increase of iteration time. Scheme 1 has stabilized for about 19 generations. Scheme 2 tends to be stable for about 25 generations. The optimization results of the U-shaped section show that scheme 1 is stable for about 43 generations, while scheme 2 tends to be stable for about 60 generations. By comparing the optimal schemes of the trapezoidal section and the U-section, it can be found that the water supply cost of the U-section is low. Therefore, under the condition of layout scheme 2, the U-shaped section is the best scheme. The calculation shows that under the same conditions, the trapezoidal section area is about 45% larger than the U-shaped section area. Although the trapezoidal section is adopted in the original project, the U-shaped section is recommended when construction conditions permit. The optimization method can quickly determine the overall optimization scheme of irrigation channels. The water supply cost depends on the final optimized objective function value, which is used as the reference basis for formulating the water supply price. The optimal design scheme should not only meet the provisions of engineering practice but also meet the requirements of the lowest water supply cost.
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Hao, Hongwei, Mengdong Chen, Wei Kang, Zhanfeng Deng, and Hangyin Mao. "Effect of flow channel cross-section shape on the performance of proton exchange membrane electrolysis cell." Journal of Physics: Conference Series 2728, no. 1 (2024): 012028. http://dx.doi.org/10.1088/1742-6596/2728/1/012028.
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Abstract To study the thermal and mass distribution in proton exchange membrane electrolytic cells (PEMEC), a two-phase numerical model of a single-channel electrolytic cell was established. The polarization performance and gas-heat distribution in a single-channel electrolytic cell under five different flow channel cross-sections (rectangle, trapezoid, inverted trapezoid, triangle, and circle) were studied. The findings indicate that the inverted trapezoidal flow channel’s gas buildup effect is rather severe in both the catalytic and diffusion layers. In the trapezoidal flow channel, the temperature of the proton exchange membrane region is lower, and the electrochemical performance of the rectangular flow channel electrolytic cell is the best, with an improvement rate of up to 11.47%. The electrochemical performance of the triangular and circular flow channels is the worst.
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Obernikhin, D., and A. Nikulin. "CRACKING WIDTH OF REINFORCED CONCRETE BEAMS TRAPEZOIDAL CROSS SECTION." Bulletin of Belgorod State Technological University named after. V. G. Shukhov 7, no. 4 (2022): 68–74. http://dx.doi.org/10.34031/2071-7318-2021-7-4-68-74.
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The article discusses experimental studies of the values of the crack opening width at various stages of loading the investigated trapezoidal beams. For comparison, reference samples of rectangular and tee cross-sections with the same overall dimensions are also considered. The use of trapezoidal beams in construction practice can significantly reduce the consumption of concrete in comparison with rectangular beams. It should be noted that when constructing trapezoidal beams, complete disassembly of the formwork is not required in comparison with beams of T-shaped and rectangular profiles. The paper compares the values of the loads of the appearance of the first cracks in beams with different transverse outlines. The values of the loads corresponding to the achievement of the normative limiting value of the crack opening width have been determined. In the course of the study, it was found that cracks in trapezoidal beams reach the maximum opening width at a higher loading level than cracks in rectangular and tee beams due to a greater number of cracks along the length of the element. An analysis of both absolute and relative characteristics was carried out, taking into account the consumption of concrete over the section of the elements. The main advantages and disadvantages of bending reinforced concrete elements of trapezoidal cross-section in comparison with reference samples are highlighted
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Li, Xiaofeng, Junfeng Xiao, Feng Wang, Wei Wang, and Mengqi Hu. "Research on the influence of different obstacle structures on the energy distribution characteristics of pulse detonation gas." Thermal Science, no. 00 (2021): 194. http://dx.doi.org/10.2298/tsci201026194l.
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In order to improve the gas energy conversion efficiency at the outlet of the pulse detonation combustor, numerical calculation methods were used to study the influence of three different cross-section obstacle structures of square, circle and trapezoid on the distribution characteristics of gas pressure potential energy, kinetic energy and internal energy in a single cycle at the outlet of pulse detonation combustor. The results show that: the expansion of pulse detonation gas mainly includes three stages: primary expansion, secondary expansion, and over-expansion. Gas pressure potential energy, kinetic energy and internal energy increase during the primary and secondary expansion stages, and decrease during the over-expansion stage; Pulse detonation combustor with trapezoidal cross-section obstacle structure has the smallest proportion of gas energy at the outlet of the combustor during the over-expansion stage and the highest proportion during the secondary expansion stage; compared with square and circle cross-section obstacle structures, the gas energy distribution at the outlet of the pulse detonation combustor with trapezoidal cross-section obstacle structure is the easiest for turbomachinery to convert the gas energy.
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Mihandoust, Asma, Sajad Razavi Bazaz, Nahid Maleki-Jirsaraei, Majid Alizadeh, Robert A. Taylor, and Majid Ebrahimi Warkiani. "High-Throughput Particle Concentration Using Complex Cross-Section Microchannels." Micromachines 11, no. 4 (2020): 440. http://dx.doi.org/10.3390/mi11040440.
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High throughput particle/cell concentration is crucial for a wide variety of biomedical, clinical, and environmental applications. In this work, we have proposed a passive spiral microfluidic concentrator with a complex cross-sectional shape, i.e., a combination of rectangle and trapezoid, for high separation efficiency and a confinement ratio less than 0.07. Particle focusing in our microfluidic system was observed in a single, tight focusing line, in which higher particle concentration is possible, as compared with simple rectangular or trapezoidal cross-sections with similar flow area. The sharper focusing stems from the confinement of Dean vortices in the trapezoidal region of the complex cross-section. To quantify this effect, we introduce a new parameter, complex focusing number or CFN, which is indicative of the enhancement of inertial focusing of particles in these channels. Three spiral microchannels with various widths of 400 µm, 500 µm, and 600 µm, with the corresponding CFNs of 4.3, 4.5, and 6, respectively, were used. The device with the total width of 600 µm was shown to have a separation efficiency of ~98%, and by recirculating, the output concentration of the sample was 500 times higher than the initial input. Finally, the investigation of results showed that the magnitude of CFN relies entirely on the microchannel geometry, and it is independent of the overall width of the channel cross-section. We envision that this concept of particle focusing through complex cross-sections will prove useful in paving the way towards more efficient inertial microfluidic devices.
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SHAPOVAL, V. H., O. V. SKOBENKO, O. V. NESTEROVA, and S. M. GAPIEIEV. "VERTICAL STRESS DISTRIBUTION AT THE BASE OF SOIL DAMS WITH A TRAPEZOIDAL CROSS SECTION." Ukrainian Journal of Civil Engineering and Architecture, no. 2 (August 23, 2021): 131–37. http://dx.doi.org/10.30838/j.bpsacea.2312.270421.131.760.
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Problem statement. The research materials outlined in this work make it possible to construct the design profile of dams from soil materials, taking into account the strong compressibility of the soil and check the strength of the foundation of soil dams in depth. In addition, the results obtained by us can be used to determine the lower boundary of the compressible thickness of the bases, to the upper boundary of which a distributed load of either a triangular or trapezoidal shape is applied. Methods. Theoretical studies of geomechanical processes using analytical and numerical mathematical methods. Analysis and generalization of the results of theoretical research. Results. In the course of writing this article, we obtained analytical dependences of stresses at the base of earth dams on the coordinates and applied to the upper boundary of the base of the trapezoidal external load and showed the methods of accounting. Scientific novelty. Analytical dependences of vertical normal at the base of a soil dam with a trapezoidal profile have been obtained. The profiles of the dam in the form of isosceles and non-isosceles trapezoids are considered. Practical significance. The research materials outlined in this work make it possible to construct the design profile of dams from soil materials, taking into account the strong compressibility of the soil and check the strength of the foundation of soil dams in depth. In addition, our results can be used to determine the lower boundary of the compressible strata of the bases, to the upper boundary of which a distributed load of either a triangular or trapezoidal shape is applied.
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Lu, Tianbo, Yuqiang Li, Jianxin Zhang, Pingfan Ning, and Pingjuan Niu. "Cooling and Mechanical Performance Analysis of a Trapezoidal Thermoelectric Cooler with Variable Cross-Section." Energies 13, no. 22 (2020): 6070. http://dx.doi.org/10.3390/en13226070.
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In this study, a full-scale three-dimensional trapezoidal thermoelectric cooler model is constructed to study its cooling performance and mechanical reliability using finite element simulation. Temperature dependent material properties are considered in this work. The boundary conditions similar to those in a real experimental environment are applied. The effects of the input electrical current and geometry of the thermoelectric leg on the cooling performance and reliability of a trapezoidal thermoelectric cooler are analyzed, and a comparison is made with a rectangular thermoelectric cooler. The results indicate that increasing the leg height and the variable cross-sectional design of the leg can improve the cooling performance of the trapezoidal thermoelectric cooler. Compared to the original rectangular thermoelectric cooler, the minimum chip temperature was reduced by 0.87% under the trapezoidal thermoelectric cooler with optimized geometry. Furthermore, increasing the leg height enhances the mechanical reliability of the trapezoidal thermoelectric cooler, while the trapezoidal design of the leg reduces its mechanical reliability. The maximum von Mises stress of the leg for the trapezoidal thermoelectric cooler with optimal cooling performance increased by 40.1%. The results of this work provide useful guidance for the structural design of trapezoidal thermoelectric coolers.
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Hashim, Ahmed A., Khalil I. Mahmoud, and Hussein M. Ridha. "Geometry and shape optimization of piezoelectric cantilever energy harvester using COMSOL multiphysics software." International Review of Applied Sciences and Engineering 12, no. 2 (2021): 103–10. http://dx.doi.org/10.1556/1848.2021.00170.
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AbstractIn embedded systems that necessarily require a steady source of power and (or) attaches to a sensor(s), there are opportunities to mix small batteries to supply such power. The aim of this research is to optimize the geometry and shape of piezoelectric cantilevers to harvest more power. Several piezoelectric cantilever geometries with various shapes (rectangular, triangular, circular, and trapezoidal cross section) are tested in COMSOL multiphysics simulator to find the best geometry that provides the highest accomplishable power. The most efficient geometry was found to be conferred by the trapezoidal, cross section cantilever. Next, another improvement method was applied to maximize the harvested power of the cantilever by modifying the shape of the trapezoidal cantilever structure through increasing the number of its faces. The results demonstrated that the highest output power (36 mW) was produced by the four faces, trapezoidal cross section design of cantilever.
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Norlin, Bert, and Torsten Höglund. "Bearing Length on Cold-Formed Sections." Key Engineering Materials 710 (September 2016): 421–26. http://dx.doi.org/10.4028/www.scientific.net/kem.710.421.
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The effective bearing length of trapezoidal sheeting on cold formed sections at inner supports is 10 mm according to EN 1999-1-4 (aluminium) and EN 1993-1-3 (steel). In the original design provisions the effective bearing length on Z-sections was the actual width of the loaded flange. In order to find out the appropriate effective bearing length, FEM calculations were made on simply supported beams with C-, Z-and Sigma-cross-section. Contact elements between the trough of the trapezoidal sheeting and the loaded flange of the beam made it possible to evaluate the contact area. This area and the stresses in the trapezoidal sheeting show that the effective bearing length is very small for C-sections. For Z-sections and for Sigma sections with large folds in the web the contact area is the flange width, unless the flange width versus profile height is large and the plate thickness is small.
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Han, Yan-Cheng, and Said M. Easa. "New and improved three and one-third parabolic channel and most efficient hydraulic section." Canadian Journal of Civil Engineering 44, no. 5 (2017): 387–91. http://dx.doi.org/10.1139/cjce-2016-0535.
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Several parabolic-shaped open channel sections are available in the literature, including quadratic and semi-cubic parabolic sections. This paper presents a three and one-third parabolic cross-section that has superior characteristics compared to those of previous parabolic-shaped sections. The section characteristics, including two approximate formulas for the wetted perimeter and a simple iterative formula for the normal water depth are presented. The exact solution for the most efficient hydraulic section is derived. The results show the width–depth ratio for the most efficient hydraulic section is 2.1273. Practical applications of the proposed most efficient hydraulic section are presented, including direct formulas for the discharge and explicit formulas of normal and critical depths. The results show that the proposed section improves the hydraulic characteristics compared with other parabolic sections and trapezoidal section.
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Flodr, Jakub, Martin Krejsa, David Mikolášek, Oldrich Sucharda, and Libor Žídek. "Mathematical Modelling of Thin-Walled Cold-Rolled Cross-Section." Applied Mechanics and Materials 617 (August 2014): 171–74. http://dx.doi.org/10.4028/www.scientific.net/amm.617.171.
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The purpose of the paper is to perform a static analysis of a thin-wall cold-rolled steel cross-section of a trapezoidal sheet by means of a mathematical model developed in ANSYS, commercially available software applications. The trapezoidal sheets are used typically as an external cladding which covers the structures of steel halls. Investigating into behaviour of the trapezoidal sheets subjected to extreme loads represents an urgent issue in wind engineering. A physical tension test has been performed in order to verify and confirm the mathematical model. Experiments have been performed to prove results of the static analysis into the behaviour of a load-carrying structure formed by a thin-wall cross-section.
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DUMITRIU, DAN, MARIUS IONESCU, and CRISTIAN RUGINA. "Hook crane shape design improvement for reducing the maximum stress." Romanian Journal of Technical Sciences - Applied Mechanics 68, no. 1 (2023): 21–44. http://dx.doi.org/10.59277/rjts-am.2023.1.02.
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The stress analysis of a hook crane submitted to some vertical static force is a simple FEM problem, approached here using SolidWorks Simulation software. Our purpose was to simulate different possibilities to slightly modify the shape of the hook crane, without adding too much material, in order to reduce the maximum stress induced in the hook. The shape design concerned here both the shape of the (transversal) cross-section and the shape of the hook longitudinal profile. The stress distribution is strongly depending on the shape of the hook crane, but it is almost independent on the hook material, since the bending mechanical stress, which is dominant in this combined bending and elongation case study, is not depending on the elastic modulus of the hook material. Obviously, the material choice is crucial from the point of view of the yield strength, usually hardened steels with increased yield strength are preferred. In what concerns the shape design improvement from the point of view of the cross-section (of equal area), our study confirmed that the trapezoidal section proposed generally in the literature corresponds to a reduced maximum induced stress. As a new result, a T-shape hook crane cross-section seems to prove better results that the trapezoidal section. To avoid stress concentrators, a combination between the trapezoidal and T-shape cross-sections has been also considered. The idea is to avoid as much as possible the discontinuity points on the outer contour of hook cross-section, since these discontinuity points are usually mechanical stress concentrators. A shape design improvement has been performed also in what concerns the longitudinal section/profile of the hook crane.
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SAYAN, Yunus. "INVESTIGATION OF THE EFFECT OF A DIFFERENT TRAPEZOIDAL INCLINATION ANGLE IN A REVERSE TRAPEZOIDAL CROSS-SECTION FLOW CHANNEL ON THE PERFORMANCE OF THE PEM FUEL CELL WITH THE COMPUTATIONAL FLUID DYNAMIC (CFD) METHOD." Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi 26, no. 2 (2023): 408–23. http://dx.doi.org/10.17780/ksujes.1180483.
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In this work, a reverse trapezoidal cross-section channel shape for a single flow channel PEM fuel cell was examined with computational fluid dynamic (CFD) method. ANSYS Fluent was applied to solve electrochemical reactions, potential fields, mass, species, and energy transport equations. Species mass ratio, temperature distribution and relative humidity were obtained for the cell as well as the i-V and power density plots. The results were compared to two reference geometries with the commonly used square section shape for the channel. One reference geometry has the same channel width and height with the reverse trapezoidal cross-section channel while the other has the same cross-section area. The results indicate that the cell with reverse trapezoidal cross sectional flow channel shape has more than 32% higher power density than the cell with square cross-sectional flow channel shapes, but poor water management.
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Hameed, Ayman T. "Optimal Design of Round Bottomed Triangle Channels." Tikrit Journal of Engineering Sciences 17, no. 3 (2010): 31–43. http://dx.doi.org/10.25130/tjes.17.3.04.
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In optimal design concept, the geometric dimensions of a channel cross-section are determined in a manner to minimize the total construction costs. The Direct search optimization method by using MATALAB is used to solve the resulting channel optimization models for a specified flow rate, roughness coefficient and longitudinal slope. The developed optimization models are applied to design the round bottomed triangle channel and trapezoidal channels to convey a given design flow considering various design scenarios However, it also can be extended to other shapes of channels. This method optimizes the total construction cost by minimizing the cross-sectional area and wetted perimeter per unit length of the channel. In the present study, it is shown that for all values of side slope, the total construction cost in the round bottomed triangle cross-section are less than those of trapezoidal cross-section for the same values of discharge. This indicates that less excavation and a lining are involved and therefore implies that the round bottomed triangle cross-section is more economical than trapezoidal cross-section.
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., Ankur. "Cost Aanalysis and Comparison of Rectangular and Trapezoidal Box Girder Section." International Journal for Research in Applied Science and Engineering Technology 9, no. VI (2021): 1325–33. http://dx.doi.org/10.22214/ijraset.2021.35249.
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The present study aims at design, analysis and parametric comparison of two different cross section of box girder deck system. Objectives of this study are to compare the stresses at important location like top slab and bottom slab using analysis tool MIDAS-2016. And design and estimates different sizes of rectangular and trapezoidal box girder section using hand calculation. Keywords: Box Girder, Rectangular box girder, Trapezoidal box girder and MIDAS-2016
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Froehlich, David C. "Width and Depth‐Constrained Best Trapezoidal Section." Journal of Irrigation and Drainage Engineering 120, no. 4 (1994): 828–35. http://dx.doi.org/10.1061/(asce)0733-9437(1994)120:4(828).
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Schaumann, Peter, Florian Tabeling, and Waldemar Weisheim. "Numerical simulation of the heating behaviour of steel profiles with intumescent coating adjacent to trapezoidal steel sheets in fire." Journal of Structural Fire Engineering 7, no. 2 (2016): 158–67. http://dx.doi.org/10.1108/jsfe-06-2016-012.
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Purpose This paper aims to present numerical investigations regarding the heating behaviour of steel elements protected by an intumescent coating with an adjacent trapezoidal steel sheet. Design/methodology/approach For this purpose, a three-dimensional numerical model of a coated I-section profile is developed in Abaqus taking into account the restrained foaming process of the intumescent coating due to the adjacent member explicitly. Findings After the validation of the numerical model against own fire tests, the steel temperatures of a coated I-section profile with and without an adjacent trapezoidal steel sheet, resulting from fire exposure according to ISO-834, are compared to demonstrate the influence of the steel sheet in detail. Originality/value The main objective is to evaluate the influence of an unprotected trapezoidal steel sheet on the temperatures of coated I-section profiles.
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Nawar, Mahmoud T., Ola A. Silem, Ishac Ibrahim, Hassan M. Maaly, and Yasser E. Ibrahim. "Enhancing the Toughness of Composite Cold-Formed Steel Beams with ECC and Different Stiffener Arrangements and Shapes." Journal of Composites Science 9, no. 1 (2025): 24. https://doi.org/10.3390/jcs9010024.
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This study investigates the toughness and load capacity of various innovative beam configurations of cold-formed steel beams (CFSB) using both ordinary concrete slabs and engineered cementitious composite (ECC) slabs. A finite element analysis with ABAQUS 20 was conducted on double-channel, sigma, G, and omega sections, both with and without inverted lips, as well as the effects of L, channel, and trapezoidal stiffeners and length-to-depth ratios. The double-omega section with ordinary concrete achieved the highest first peak load of 365.2 kN and a toughness increase of 181.1%. Inverted lips enhanced toughness in the double-G and sigma sections, with increases of 156.9% and 158.3%, respectively. Among ECC configurations, the double-omega section with ECC3 slab reached 387.4 kN and a toughness increase of 199.5%. Thinner ordinary concrete sections (70 mm and 90 mm) negatively impacted toughness, emphasizing the need for adequate thickness. Trapezoidal stiffeners also improved toughness. These findings highlight the importance of geometrical design and material selection in optimizing CFSB performance, offering valuable insights for future design practices.
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Jaferian, Vahid, Davood Toghraie, Farzad Pourfattah, Omid Ali Akbari, and Pouyan Talebizadehsardari. "Numerical investigation of the effect of water/Al2O3 nanofluid on heat transfer in trapezoidal, sinusoidal and stepped microchannels." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 5 (2019): 2439–65. http://dx.doi.org/10.1108/hff-05-2019-0377.
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Purpose The purpose of this study is three-dimensional flow and heat transfer investigation of water/Al2O3 nanofluid inside a microchannel with different cross-sections in two-phase mode. Design/methodology/approach The effect of microchannel walls geometry (trapezoidal, sinusoidal and stepped microchannels) on flow characteristics and also changing circular cross section to trapezoidal cross section in laminar flow at Reynolds numbers of 50, 100, 300 and 600 were investigated. In this study, two-phase water/Al2O3 nanofluid is simulated by the mixture model, and the effect of volume fraction of nanoparticles on performance evaluation criterion (PEC) is studied. The accuracy of obtained results was compared with the experimental and numerical results of other similar papers. Findings Results show that in flow at lower Reynolds numbers, sinusoidal walls create a pressure drop in pure water flow which improves heat transfer to obtain PEC < 1. However, in sinusoidal and stepped microchannel with higher Reynolds numbers, PEC > 1. Results showed that the stepped microchannel had higher pressure drop, better thermal performance and higher PEC than other microchannels. Originality/value Review of previous studies showed that existing papers have not compared and investigated nanofluid in a two-phase mode in inhomogeneous circular, stepped and sinusoidal cross and trapezoidal cross-sections by considering the effect of changing channel shape, which is the aim of the present paper.
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M. Md. Tahir, A. Sulaiman, and A Saggaff. "Structural Behaviour of Trapezoidal Web Profiled Steel Beam Section using Partial Strength Connection." Electronic Journal of Structural Engineering 8 (June 1, 2008): 55–66. http://dx.doi.org/10.56748/ejse.8100.
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Connections are usually designed as pinned which associated with simple construction or rigid which is associated with continuous construction. However, the actual behaviour falls between these two extreme cases. The use of partial strength or semi-rigid connections has been encouraged by EC3 code and studies on hot-rolled steel sections on semi-continuous construction for braced steel frames have proven that substantial savings in steel weight and the overall construction cost. The objective of this paper is to present the performance of full scale testing of sub-assemblage steel beam and isolated beam-to-cloumn with partial strength connections for Trapezoid Web Profiled (TWP) steel sections. The TWP steel section is a built up section where the flange is of S355 steel section and the corrugated web of S275 steel section. Two full scales testing with beam set-up as sub-assemblage and beam-to-column connection have been carried out for flush and extended end-plate connections as partial strength connections. It was concluded that the use of extended end-plate connection has contributed to significant reduction to the deflection and significant increase to the moment resistance of the beam than flush end-plate connection.
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Natsheh, Sufian H., and Craig C. Menzemer. "Built-Up Closed-Rib Steel Orthotropic Bridge Decks." CivilEng 3, no. 4 (2022): 960–78. http://dx.doi.org/10.3390/civileng3040054.
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A new built-up closed-rib section is proposed that may improve the installation, performance, and durability of orthotropic steel bridge decks. The rib is composed of two partial or whole standard hot-rolled steel sections which are connected by a steel plate. The concept is used to design a built-up closed-rib replacement for the Benjamin Franklin Bridge deck. In addition, section performance was compared with the actual bulb section as well as a typical trapezoidal section through finite element simulations. The analyses indicate that the built-up section has smaller stress concentration values as compared with the other sections, and hence, improved fatigue resistance is expected. Finally, it is concluded that the built-up rib has potential to be considered in future orthotropic steel deck designs.
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Mansur, Abdalla, Muhammad Shoaib, Iharka Szücs-Csillik, Daniel Offin, and Jack Brimberg. "Action minimizing orbits in the trapezoidal four body problem." AIMS Mathematics 8, no. 8 (2023): 17650–65. http://dx.doi.org/10.3934/math.2023901.
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<abstract><p>In this paper, we study the minimizing property for the isosceles trapezoid solutions of the four-body problem. We prove that the minimizers of the action functional restricted to homographic solutions are the Keplerian elliptical solutions, and this functional has a minimum equal to $ \frac{3}{2}(2\pi)^{2/3}T^{1/3}\left(\frac{\xi (a, b)}{\eta (a, b)}\right) ^{2/3} $. Further, we investigate the dynamical behavior in the trapezoidal four-body problem using the Poincaré surface of section method.</p></abstract>
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Patel, Chetankumar M., Kartik D. Kothari, and Ghanshyam D. Acharya. "Deflection Analysis of Non Prismatic Beam with Trapezoidal Sectorial Section with Uniformly Perpendicular Loading Condition." International Journal of Engineering Research in Africa 26 (October 2016): 1–10. http://dx.doi.org/10.4028/www.scientific.net/jera.26.1.
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Non-prismatic beams are extensively used for many engineering application. Due to varying section, deflection analysis becomes very complex. Loading condition also makes the whole theory complex. This paper shows analytical analysis for the deflection of trapezoidal sectorial section with uniformly perpendicular loading condition. The method illustrated is comparatively easy and can be applied for the similar other sections as well. Analytical method is validated using Finite Element Analysis using Creo Simulation which shows good amount of match with analytical result.
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Thote, Shrikant Arunrao, and Netra Pal Singh. "Variation in the enhancement of heat transfer with different fluids using twisted tape inserts." IOP Conference Series: Materials Science and Engineering 1259, no. 1 (2022): 012005. http://dx.doi.org/10.1088/1757-899x/1259/1/012005.
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Abstract This research intends to look into the transformation of heat, factors affecting the friction, and characteristics of the efficacy ratio for the ratio of twist as 3.0, 4.4, and 6.0, independently of a concentric pipe heat exchanger with and without trapezoidal section twisted tape insert. For different Reynold’s Number (Re) ranges of 200-2000, 800-2000, and 2000-12000, experimentation was accomplished to find the transformation of heat energy and aspect of factors of the friction of coaxial tubes. The investigated data from the tube without an insert were compared to the conventional correspondence to assure that the investigation output was valid. The findings of the trapezoidal section twisted tape tube has been in contrast to the simple tube’s results. The consequences reveal that the trapezoidal section twisted tape appreciably improves heat transmission along with friction coefficient. The Trapezoidal section twisted tape enhancement transmission of heat was once additionally judged to be practical because the realized output ratio is maximum than unity. The twisted tape has a greater Nusselt Number (Nu), frictional influence, and overall efficacy attainment than a plain tube, by the research. According to the tapes that have been tested, the tapes with the lowest twist ratio 3.0 are greater fine than the tapes with the other ratio of twist, as a consequence of the fact that the tape with the lowest ratio of twist is the most environmentally friendly at supplying heat augmentation.
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Li, Song, Jiangbo Wu, Xiaoze Du, Haonan Dong, and Zhibin Yu. "Study on heat transfer characteristics of supercritical co2 printed circuit heat exchangers with different shape channels." Thermal Science, no. 00 (2024): 157. http://dx.doi.org/10.2298/tsci240110157l.
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Printed circuit heat exchanger (PCHE) is a microchannel heat exchanger. Because of its high efficiency, high pressure and high temperature resistance, it has been widely used in photovoltaic power generation, nuclear energy and other fields. In particular, the research on the cross section shape of heat exchanger channel has been widely concerned by researchers. In this paper, the PCHE performance of semi-circular, square and trapezoidal channels with the same inlet and outlet area is compared under the pressure of 8MPa. The heat transfer performance of the mass flow rate in the range of 500-2000 kg /(m2) under three cross section shapes was investigated. The results show that the heat transfer effect of fluid in the trapezoidal channel is obviously better than the other two channels. This is mainly because the heat exchange contact area of cold and hot fluids in the trapezoidal channel is large, resulting in an increase in heat exchange between cold and hot fluids. When the inlet velocity is the same, the Reynolds number of the fluid in the trapezoidal channel is larger. The outlet temperature of the cold fluid in the trapezoidal channel is 7.9% higher than that in the semi-circular channel and 4.1% higher than that in the rectangular channel. The outlet temperature of the hot fluid in the trapezoidal channel is 6.28% lower than that in the semi-circular interface channel and 3.4% lower than that in the square channel. The trapezoidal channel has better PCHE heat transfer effect and better heat transfer performance.
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Vipin, V. P., and P. A. Krishnan Dr. "A FINITE ELEMENT STUDY ON THE PERFORMANCE OF CORRUGATED STEEL SECTIONS UNDER COMPRESSION." International Journal of Emerging Technologies and Innovative Research Volume 4, Issue 5 May-2017 eISSN: 2349-5162 (2017): 249–51. https://doi.org/10.5281/zenodo.583727.
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Corrugated steel sections are having a wide variety of applications in engineering fields like civil, mechanical, aviation, etc. The unique properties of corrugated steel sections make them a better option compared to the conventional thin steel sections. In the current study behaviour of thin steel shells with corrugations made of mild steel plates under compression is investigated using finite element software ABAQUS. The corrugated sections and the conventional sections under study are having the same area of cross section. For the corrugated sections, trapezoidal profile was used with corrugation angle ranging from 30 degree to 90 degree. Influence of corrugation height on the characteristics of corrugated section is also studied. In axial compression, corrugated steel section exhibited 1.5 to 2 times the load carrying capacity of conventional steel section. The load carrying capacity was found to be increasing with increasing corrugation angle as well as with increasing corrugation height. It has been also observed that slender members are more sensitive to changes in corrugation profile.
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Dmitrieva, Tatiana, and Khukhuudei Ulambaya. "TO THE QUESTION OF THE DETERMINATION OF GEOMETRIC CHARACTERISTICS OF THE SECTION OF CORRUGATED BEAMS WITH TRAPEZOIDAL WEBS BASED ON THE SIMULATION RESULTS." International Journal for Computational Civil and Structural Engineering 15, no. 1 (2019): 29–40. http://dx.doi.org/10.22337/2587-9618-2019-15-1-29-40.
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An algorithm for calculating the geometric characteristics of steel I-beams with plate corrugated webs of arbitrary type is proposed. The algorithm is implemented using the I-beam with plate trapezoid webs as an example. The determination of reduced area and moments of inertia in the axes of the cross section of the trapezoidal profile based on the finite element modeling of the beam with shell elements in calculations for bending and axial compression in the “ANSYS 14.5” software package is described. The verification procedure has been performed for a shell finite element model using the example of an I-beam with a standard flat web. A table has been compiled of geometric characteristics of rod corrugated elements of a trapezoidal profile in order to realize their finite element calculation using a rod diagram. An example of the calculation of a flat frame with a horizontal corrugated element, made in software package “LIRA-SAPR” using a flat rod diagram is given.
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Inzhutov, Ivan, Sergey Amelchugov, Rashit Nazirov, Marina Perkova, Christina Rudyak, and Ada Baltinate. "Energy efficiency of timber construction joint with wooden screw." E3S Web of Conferences 110 (2019): 01022. http://dx.doi.org/10.1051/e3sconf/201911001022.
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The topicality of studied subject is based on inappropriate usage of different materials in wooden structures, since using metal joint in wooden construction leads to reduction of construction working life cycle. In this regard, a study of several options for wooden screw carving was conducted in order to determine the most appropriate one (screw). There are several different types of carving, such as: trapezoidal, triangular, rectangular, etc. The most appropriate ones are trapezoidal and triangular-section threads for wooden screws. The effectiveness of a wooden screw thread was determined from the conditions (capacity) of shear fracture and bearing stress. After analyzing the results of calculations of the specific capacity for shear fracture and bearing stress, it can be concluded that the value of specific bearing capacity for shear fracture is less than the value of bearing stress by 1.3%. Therefore, a further comparison of the trapezoidal thread and the triangular cross-section will proceed from the spalling conditions. It has been found that the most effective thread is a triangular cross-section. Based on the results of calculations, a mathematical model has been established that describes the dependence of the carrying capacity on the screw diameter.
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Tu, Yi, and Yu Zeng. "Comparative Study on Thermos-Hydraulic Performance of Different Cross Section Shapes of Microchannels with Supercritical CO2 Fluid." Journal of Chemistry 2021 (August 5, 2021): 1–13. http://dx.doi.org/10.1155/2021/5525235.
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The influence of the cross section shape of microchannels on the thermos-hydraulic performance of the supercritical CO2 fluid is an important issue in the design of industrial compact heat exchangers, but few studies have been conducted about this issue. In this paper, comparative studies of the flow and heat transfer performance of SCO2 fluid in horizontal microchannels with circular, semicircular, rectangle, and trapezoidal cross sections were conducted numerically. The comparison is based on the same hydraulic diameter and length for all channel types and is carried out under the same mass flux, outlet pressure, and wall heat flux. The fluid bulk temperature in this analysis ranges from 285 K to 375 K, which covers the pseudocritical point of SCO2. The results show that the circular channel has the highest average heat convection coefficient, while the trapezoidal channel has the worst convective heat transfer performance under the same hydraulic diameter and boundary conditions. The results also indicate that the effect of cross section shape on the heat convection coefficient is significantly greater than that on the channel pressure drop, and the existence of the corner region in the cross section, especially the acute angle, will weaken the heat transfer performance.
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Kumari, Emarti. "Research Article Mathematical Modelling and Bending Analysis of Beams." Journal of Mechanical and Construction Engineering (JMCE) 4, no. 2 (2024): 1–12. https://doi.org/10.54060/a2zjournals.jmce.62.
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In this communication finite element formulation of Euler-Bernoulli beam is done considering Hermites shape functions and illustrated the calculation of stiffness matrix, mass matrix and force vector in detail. Here, considered the various cross-section of beams such as trapezoidal, rectangular, circular, triangular, etc under various loading and boundary conditions to investigate the effect of transverse deflection, shear force and bending moment with change in cross-section of beams by using finite element method based commercial software ANSYS 18.1. Here, present numerical results are validated with analytical results of beams with different cross-sections, loading and boundary conations.
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Vardakostas, Spyros, Stavros Kementsetsidis, and Evangelos Keramaris. "Saline Gravity Currents with Large Density Difference with Fresh Water in a Valley of Trapezoidal Shape." Environmental Sciences Proceedings 2, no. 1 (2020): 64. http://dx.doi.org/10.3390/environsciproc2020002064.
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In this study, lock-exchange experiments in a tank of rectangular upper cross section and a lower valley of trapezoidal shape are performed. This is a realistic model of the valleys, which occur in nature. The experiments are performed for equal depths of heavy and light fluid on both sides of the lock gate. Density difference between salt water and clear water is varied between 0.5% and 0.9%. This density difference exists in liquid waste whose spreading is an environmental problem. The release of pollutants into rivers, oil spills in the ocean and the outflow of desalinations plants are examples of man-made gravity currents that cause negative environmental impacts. The aim of this study is to contribute to a better understanding of the propagation and process of mixing of a gravity current with large density difference with water. The movement of the gravity current is monitored with a digital video of high definition, the front velocity is measured and the height of the front is captured. Twenty experiments were performed, ten inside the trapezoidal section (H = 5 or 10 cm) and ten over the trapezoidal section (H = 17.5 or 25 cm). Results are compared with those of gravity currents in lock-exchange experiments, which were performed by other researchers.
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Song, Hui, Shuangxiu Fan, and Dayi Qu. "Experimental Study on Flow and Heat Transfer Characteristics in the Circular-Arc-Shaped Flow Channel." Applied Sciences 12, no. 1 (2021): 376. http://dx.doi.org/10.3390/app12010376.
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Different parameters of the circular-arc, trapezoidal and equal cross-section-shaped flow channels were analyzed, and the core volume goodness factor was used for the comparison of the three different types of flow channels. During the experiment, the Reynolds number (Re) on the air side ranged from 1200 to 5100. The results showed that the overall heat transfer performance of the three channels in this paper are circular-arc, trapezoidal and equal cross-section in order from good to bad. The overall heat transfer enhancement performance of the circular-arc flow channel is the best, which is 9–26.2% and 3.6–11.8% higher than that of the equal and trapezoidal cross-section flow channels, respectively. This showed that although the divergent flow channel structure reduces the fluid velocity in the flow process, it weakens the convective heat transfer performance in the flow channel. However, this gradually decreasing cross-sectional area improves the downstream heat transfer area and reduces the pressure drop in the flow process, thus promoting the overall heat transfer performance. With the increase in the circular radius (R), both the j and f factors increase, and the highest overall heat transfer performance is obtained at R = 300 mm. The convective heat transfer coefficient increases with the decrease in the inlet height.
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Muhsun, Sadiq. "Characteristics of the Hydraulic Jump in Trapezoidal Channel Section." Journal of Environmental Studies 9, no. 1 (2012): 53–63. http://dx.doi.org/10.21608/jesj.2012.191531.
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Lu, Zonghuan, David M. Frey, Thomas Merkh, Robert Lord, Morris A. Washington, and Toh-Ming Lu. "Resistivity of epitaxial copper nanolines with trapezoidal cross-section." Thin Solid Films 599 (January 2016): 187–93. http://dx.doi.org/10.1016/j.tsf.2015.12.063.
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Peng, Wen-qiang, Yu-lie Wu, Yong Liu, and Zhi-qiang Yin. "Scattering loss in optical waveguide with trapezoidal cross section." Journal of Central South University 19, no. 5 (2012): 1317–21. http://dx.doi.org/10.1007/s11771-012-1144-9.
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Prodan, V. D., G. V. Bozhko, and P. N. Boiko. "Gland Seals with Soft Gasket with Trapezoidal Cross-Section." Chemical and Petroleum Engineering 51, no. 7-8 (2015): 476–80. http://dx.doi.org/10.1007/s10556-015-0072-6.
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Han, Yan-Cheng, Zheng-He Xu, Said M. Easa, Shuai Wang, and Lin Fu. "Optimal Hydraulic Section of Ice-Covered Open Trapezoidal Channel." Journal of Cold Regions Engineering 31, no. 3 (2017): 06017001. http://dx.doi.org/10.1061/(asce)cr.1943-5495.0000128.
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MORALES, F., and J. HEIRAS. "EFFECT OF A STEP AT AN INTERFACE ON TUNNELLING BARRIER PARAMETERS." Modern Physics Letters B 02, no. 11n12 (1988): 1289–95. http://dx.doi.org/10.1142/s0217984988001260.
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The problem of penetration by a conducting slab in tunnel junction metal-oxide interfaces is treated using a step model for the barrier. The dynamical conductance of a junction having a composed barrier (two sections with different widths but the same barrier heights) is calculated using a trapezoidal barrier model for each section. An unexpected increment of the barrier height is found when a very thin conducting slab penetrates the barrier of a junction.
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Haga, Toshio, Kohei Tuchitani, Hisaki Warari, and Shinichi Nishida. "Casting of Bar Using a Twin Wheel Caster." Key Engineering Materials 831 (February 2020): 46–51. http://dx.doi.org/10.4028/www.scientific.net/kem.831.46.
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A simple twin-wheel caster is proposed for casting thin bars. The lower wheel of this caster has a trapezoidal groove with an area of 25 mm2. A 1070 pure aluminum bar with a convex, not concave and trapezoidal, cross section could be cast at speeds ranging from 3 to 4 m/min. The area of the bar was 38 mm2 when the wheel speed was 3 m/min. The area decreased with increasing wheel speed.
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Feng, Jiajia, Chengye Yang, Chongyang Bu, Yangyang Xia, and Gen Zhang. "Effect of Topographic Condition of Drainage Channel on the Interaction Between Granular Flow and Slit Dams." Sustainability 17, no. 4 (2025): 1649. https://doi.org/10.3390/su17041649.
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One of the most dangerous geological disaster risks in mountainous areas is granular flow. Slit dams, which might partially block the granular flow and let downstream flow at a slower speed, have been crucial in reducing the geohazards associated with granular flow. In this work, the discrete element method (DEM) was used to explore the effect of the topographic condition of drainage channels, including slope angle and cross-section types, on the interaction between granular flows and slit dams. The interactions dynamic process between the dry granular flows and slit dams with different drainage channel cross-section types has been investigated. And the simulation results demonstrate the significance of taking drainage channel cross-section types into account when designing barriers, particularly slit dams. The flow process, particularly in channels with V-shaped and trapezoidal sections, is characterized by a more rapid movement and larger final accumulation length, potentially resulting in increased impact force on the downstream slit dams. Moreover, the cross-section types and slope angles jointly influence the regulation function and impact force. The dry granular flow in the drainage channel with a V-shaped cross-section leads to a smaller normal impact force and retention efficiency. Taking into account the complexity of construction, retention efficiency, and impact force, it can be concluded that a trapezoid shape is the most appropriate option from an engineering perspective. This research may add to the understanding of the relationship between granular flow and slit dams and help the engineering design of slit dams with scientific evidence.
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Wang, Zhiqiang, Chao Wu, Jianqiao Luo, Wenyu Lv, Lei Shi, and Peng Wang. "Research on Stress Analysis and Control of Surrounding Rock of Trapezoidal Roadways Based on Complex Variable Theory." Shock and Vibration 2021 (August 3, 2021): 1–14. http://dx.doi.org/10.1155/2021/6381785.
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Aiming at the problem of the serious deformation of the mining roadways in the trapezoidal section of the coal mine, the method of combining theoretical analysis and field application is used to study the surrounding rock control method of the trapezoidal roadways. The conformal mapping function of the trapezoidal roadways is calculated by the theory of complex change, and then from the analytical solution of the tangential stress distributed in the surrounding rock of trapezoidal roadways which is under the influence of the bidirectional unequal pressure, homogeneous, isotropic, and elastic rock mass is obtained. Research studies show that the roof-stress distribution of the trapezoidal roadways is uniform and the confining pressure is small, while the two sidewalls and the floor are opposite. The stress distribution of the two sidewalls and the floor varies greatly, and the stress concentration factor is large. The top corner of the trapezoidal roadways is basically not affected by stress concentration, but the stress concentration coefficient at the bottom corner is relatively large, and reinforcement measures are required in the roadway support. Based on the aforementioned research results, the multisupport scheme of “bolting with wire mesh and anchor cable + W-type steel belt + joist steel shed support + anchor cable grouting” was proposed to the surrounding rock of trapezoidal roadways with large stress caused by mining influence, thus solving the actual mining problem.
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Botis, Marius Florin, and Camelia Cerbu. "Design Solutions for Slender Bars with Variable Cross-Sections to Increase the Critical Buckling Force." Materials 15, no. 17 (2022): 6094. http://dx.doi.org/10.3390/ma15176094.
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In large metal civil constructions (stadium roofs, bridges), slender bars can lose their stability under compression loading. There is a lack in the literature regarding design solutions and methods for increasing the critical buckling force of bars with variable cross-sections. The aim of this research is to present a numerical model with finite elements used for a comparative analysis of increasing the critical force of stability loss in cases of (i) bars with stepwise variation in the cross-sections and (ii) bars with continuous variation in the moment of inertia along the bar axis (parabolic, sinusoidal, triangular, and trapezoidal variation). Considering the large-scale applications in civil engineering, bars that were pin-connected at one end and simple-supported at the other end were analyzed. Firstly, the analytical model was described to compute the critical buckling force for bars with stepwise variation in the cross-sections. Then, a finite element model for a slender bar and the assumptions considered were presented. The results were computed using the MATLAB program based on the numerical model proposed and were validated with the analytical model for stepwise variable cross-sections of the bars. The numerical model was adapted for bars with continuous variation in the moment of inertia along the bar axis. It was shown that, by trapezoidal variation in the second moment of inertia along the axis of a bar, i.e., as buckling occurred in the elastic field, the critical buckling force could be increased by 3.556 times compared to a bar with a constant section. It was shown that there was certain bar with stepwise variation in the cross-section for which the critical buckling force was approximately equal to the one obtained for the bar with sinusoidal variation in the moment of inertia (increased by 3.427 times compared to a bar with a constant section).
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Hrebennikov, Mykhailo M., Oleksandr H. Dibir, and Anatolii O. Kyrpikin. "Discretization of Thin-Walled Sections with Variable Wall Thickness." Journal of Mechanical Engineering 27, no. 3 (2024): 34–41. http://dx.doi.org/10.15407/pmach2024.03.034.
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At the stage of designing thin-walled aircraft structures, to simplify calculations, their cross sections are idealized. To do this, the section with the skin and the longitudinal elements reinforcing it is replaced (when determining normal stresses) by a discrete one, consisting of concentrated areas at characteristic points. In this case, the equality of the moments of inertia of the initial and discrete sections is preserved. Such idealization is used in the calculation of thin-walled rods for normal and shear stresses (Wagner model). For sections consisting of a system of rectangular strips of constant thickness, discretization allows to set approximate values of normal and shear stresses and accurately find the locations of the singular points of the bending center (in an open contour) and the center of rigidity (in a closed one). The discrete model of a strip consists of three lumped areas: two at the edges and one in the center. The paper proposes to extend the discrete model to sections in which the skin thickness changes according to a linear law. In addition to the rectangular strip, it is possible to use elongated triangles and trapezoids, replaced by three and four concentrated areas, respectively. The possibility of using a discrete model for calculating some thin-walled sections of open and closed contours is considered. The section of an open contour is studied - the problem of transverse bending without torsion of a channel having flanges with a linearly variable thickness. Differences in the flows of tangential forces calculated from the exact and discrete models are shown. The coincidence of the results in determining the position of the bending center according to two models was established. When studying the application of a discrete model to a closed contour, its simplified option is proposed. The problem of transverse bending without torsion and finding the center of rigidity in a section with a contour line in the form of a trapezoid with front and rear walls of constant thickness and upper and lower skins and a similar section with a contour in the form of a rectangle was considered. Differences in the flows of tangential forces calculated by exact and discrete models are established. For a closed section in the form of a rectangle, the decrease in the moment of inertia for torsion due to the redistribution of material in the cross section was studied separately. It has been established that when finding the position of the center of rigidity, the discrepancy between the results of the exact and discrete models in sections with geometric parameters close to real ones was less than 1% for a rectangular contour, and 4% for a trapezoidal contour. The results indicate the possibility of extending the application of the discrete model of thin-walled cross section to the design calculations of thin-walled rods with variable skin thickness, representing practical structures.
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Nikulina, Y. "DETERMINATION OF CRACK RESISTANCE OF PRESTRESSED REINFORCED CONCRETE BEAMS OF TRAPEZOIDAL CROSS-SECTION." Bulletin of Belgorod State Technological University named after. V. G. Shukhov 6, no. 11 (2021): 41–48. http://dx.doi.org/10.34031/2071-7318-2021-6-11-41-48.
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Beams of a trapezoidal cross-section with a wide upper edge with prestressed reinforcement combine positive qualities in terms of strength, crack resistance, deformability and resource saving, which allows them to cover significant spans of multi-storey buildings. 
 To develop a method for calculating the moment of cracking in these structures, a nonlinear deformation model was adopted, which includes equilibrium equations, conditions for the linear distribution of relative deformations along the height of the element section, and refined deformation diagrams of concrete and reinforcement. Concrete state diagrams are assumed to be nonlinear without a falling branch. To describe the deformation diagrams of high-strength and conventional reinforcement, a universal dependence is adopted, consisting of one linear and two nonlinear equations, in which the calculation of individual parameters is performed using different formulas. For the initial stage of the crack formation process, a design scheme is presented, in accordance with which the necessary equations and ratios are drawn up in relation to the considered prestressed reinforced concrete beam of a trapezoidal cross-section. 
 The purpose of the study, in addition to developing a calculation methodology, was also the development of an algorithm and a computer calculation program. To obtain and analyze the results, a numerical experiment was carried out, the results of which are presented in tabular form. Due to the fact that the calculation method was built without involving empirical dependencies, the possibility of its application to determine the crack resistance of prestressed reinforced concrete beams of trapezoidal cross-section for any class of concrete and reinforcement was confirmed.
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Tian, Yu, Yongye Li, and Xihuan Sun. "Study on the Hydraulic Characteristics of the Trapezoidal Energy Dissipation Baffle Block-Step Combination Energy Dissipator." Water 14, no. 14 (2022): 2239. http://dx.doi.org/10.3390/w14142239.
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The step-type energy dissipator is widely used to construct small- and medium-sized reservoirs with its high energy dissipation rate. In order to further improve its air entrainment characteristics and energy dissipation, and reduce the influence of cavitation, in this paper, we added a trapezoidal energy dissipation baffle block at the convex corner of the traditional step to form a trapezoidal energy dissipation baffle block-step combination energy dissipator. We used a combination of hydraulic model experiments and numerical simulation to study the hydraulic characteristics. The results showed that the trapezoidal energy dissipation baffle block-step combination energy dissipator initial entrainment point, with the increase in flow rate, gradually moved backward. A step horizontal surface pressure change in the cavity recirculation area showed a prominent “V” shape; in front of the trapezoidal energy dissipation baffle block, there was a rising trend, and in the energy dissipation baffle block gap, there was a declining trend. The step vertical surface pressure showed a decreasing trend, and negative pressure appeared near the convex angle. The cross-section velocity distribution presented a trend of being small at the bottom and large at the surface, with a large velocity gradient in the longitudinal section of the energy dissipation baffle block and a small velocity gradient in the longitudinal section of the nonenergy dissipation baffle block. The energy dissipation rate reached more than 70% within the test range, and the energy dissipation rate gradually decreased with the increase in the flow rate. The combined energy dissipator is conducive to reducing the cavitation hazard and improving the energy dissipation effect, providing a reference for engineering design and existing step energy dissipators to remove risks and reinforcement.
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Sada, Majid Jafar, and Sa'ad Fahad Resan. "Structural behavior of hybrid reinforced concrete beams of trapezoidal section." Materials Today: Proceedings 42 (2021): 2733–41. http://dx.doi.org/10.1016/j.matpr.2020.12.713.
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Sada, Majid Jafar, and Sa’ad Fahad Resan. "Shear Performance of Hybrid Concrete Deep Beams of Trapezoidal Section." IOP Conference Series: Materials Science and Engineering 1067, no. 1 (2021): 012015. http://dx.doi.org/10.1088/1757-899x/1067/1/012015.
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