Rectangular Section Research Articles

Twisted-tape inserts of rectangular and triangular sections in turbulent flow of CMC/CuO non-Newtonian nanofluid into an oval tube

Purpose This paper aims to study numerically the non-Newtonian solution of carboxymethyl cellulose in water along with copper oxide nanoparticles, which flow turbulently through twisted smooth and finned tubes. Design/methodology/approach The twisted-tape inserts of rectangular and triangular sections are investigated under constant wall heat flux and the nanoparticle concentration varies between 0% and 1.5%. Computational fluid dynamics simulation is first validated by experimental information from two test cases, showing that the numerical results are in good agreement with previous studies. Here, the impact of nanoparticle concentration, tube twist and fins shape on the heat transfer and pressure loss of the system is measured. It is accomplished using longitudinal rectangular and triangular fins in a wide range of prominent parameters. Findings The results show that first, both the Nusselt number and friction factor increase with the rise in the concentration of nanoparticles and twist of the tube. Second, the trend is repeated by adding fins, but it is more intense in the triangular cases. The tube twist increases the Nusselt number up to 9%, 20% and 46% corresponding to smooth tube, rectangular and triangular fins, respectively. The most twisted tube with triangular fins and the highest value of concentration acquires the largest performance evaluation criterion at 1.3, 30% more efficient than the plain tube with 0% nanoparticle concentration. Originality/value This study explores an innovative approach to enhancing heat transfer in a non-Newtonian nanofluid flowing through an oval tube. The use of twisted-tape inserts with rectangular and triangular sections in this specific configuration represents a novel method to improve fluid flow characteristics and heat transfer efficiency. This study stands out for its originality in combining non-Newtonian fluid dynamics, nanofluid properties and geometric considerations to optimize heat transfer performance. The results of this work can be dramatically considered in advanced heat exchange applications.

Instability of porous FGM rectangular hollow section (RHS) beam element in a thermal environment.

Instability of porous FGM rectangular hollow section (RHS) beam element in a thermal environment.

Qualitative Analysis of the Heat Transfer in a Package of Square Steel Sections

During the heat treatment of square or rectangular steel sections, a heated charge, arranged in regular packages, is placed inside a furnace. This type of charge forms a porous medium through which a complex heat flow occurs during heating. Several heat transfer mechanisms act simultaneously within this medium: conduction through the section walls, conduction and natural convection within the gas, thermal radiation between the section walls, and complex heat transfer (mainly contact conduction) at the joints between the adjacent sections. This article presents a qualitative analysis of heat transfer, aiming to determine the contribution of individual heat transfer mechanisms to the overall process. For this purpose, an analytical model of complex heat transfer within the package was employed, based on the thermo-electric analogy. The results from experimental studies were used to calculate the natural convection and heat transfer at the joints. It was assumed that the material of the sections was low-carbon steel, and the gas was air. Calculations were performed for the temperature range of 25 °C to 700 °C, considering three different geometrical configurations of the sections. It was shown that the effective thermal conductivity (ETC) of the package for the considered geometrical cases varies between 2.2 and 10.6 W/(m·K), which is an order of magnitude lower than the thermal conductivity of the individual sections. This parameter increased dynamically with the temperature. Moreover, the heat transfer intensity within the package of sections was nearly an order of magnitude lower than the heat conduction observed in a solid steel charge. Additionally, it was shown that the primary heat transfer mechanisms governing the heating process were thermal conduction (in the lower temperature range—up to approximately 350 °C) and thermal radiation (in the higher temperature range—above 350 °C). The gas convection inside the sections had a minimal impact on the heating process of the package. The primary parameters influencing the quality of the results were the joint resistance between the adjacent sections and the emissivity of the sections. The presented model can be used for the optimization of heat treatment processes for the considered charge.

Free vibration of flexible two links manipulator with variable cross-sectional areas

This paper demonstrated the free vibration of a planar two-link flexible manipulator with harmonic drivers and non-uniformity in the cross-section of links. A dynamic model has been developed that incorporates flexibilities in both link and joint experiencing harmonic vibration, with joint flexibility modeled as torsional spring-inertia components combination. Two links were modeled based on Von Karman’s nonlinear strain relations and theory of the Euler-Bernoulli beam. The nonlinear governing equations were derived using the extended Hamilton’s principle for planar two-link flexible manipulators with variable cross-sections for each link. The coefficients of the obtained partial differential equations were as a function of spatial coordinates and were reduced to the ordinary differential equations for a family of cross-section geometries with exponentially varying widths of rectangular sections of each link. The frequency equation was obtained and analytical solutions of the vibration were achieved for different exponential shapes of each link (widening and narrowing beam for each link). Natural frequencies and mode shapes were presented for varying cross-section areas of the links. The effects of the end masses, payload, beam mass density, flexural rigidity ratio, and joint frequency were investigated on the mode shapes and natural frequencies when the power of the exponential function of the cross-sectional areas of two links was varied. The numerical results were verified with experimental results.

A superb axe-head of G-type flint from the vicinity of Bronocice as a reason to consider the production of macrolithic four-sided tools in the Eneolithic of Lesser Poland

This article presents the study of a unique artefact in the form of a very large trapezoidal axe-head with rectangular section from Słupów, Lesser Poland, against the background of Eneolithic phenomena occurring in the area. The specimen is in the collection of the Archaeological Museum in Kraków since 1929, but has not been discussed until now. It was made by local communities from flint of the G variety, a raw material exploited by Eneolithic groups in western Lesser Poland. The axe-head from Słupów is one of the largest flint axes to have been discovered on Polish lands. This find provokes a broader discussion of the role of local production of macrolithicfour-sided forms against a wider background.

Cyclic axial loading tests on mortar-filled rectangular tube with various connection details

Although a mortar-filled rectangular hollow structural section (RHS) under monotonic loading has achieved large tensile capacity using various connection details and buckling capacity of RHS members, the structural capacity of the mortar-filled RHS tubes has not been investigated under cyclic loading. In this study, the seismic performances of newly developed mortar-filled RHS tubes with various connection details were evaluated under cyclic axial loading. The major test parameters included the end connection type, the thicknesses of the RHS tube, cap plate, and cleat plate, as well as the length of the RHS tube. The test results showed that the RHS tube in all specimens failed by tensile fracture before axial compression failure. The seismic performance of the embedded shear plate end connection with penetrating rebar was superior to that of a conventional welded T-end connection. The test results were compared with the current design code to evaluate the seismic capacity of the RHS tube according to the connection details. Design considerations for the connections of the mortar-filled rectangular tubes were also provided.

A Simple Method to Evaluate the Bearing Capacity of Concrete-Filled Steel Tubes with Rectangular and Circular Sections: Beams, Columns, and Beam–Columns

This study investigates the behavior and capacity of concrete-filled steel tubes (CFTs) with rectangular and circular sections under various loading conditions: axial loads, pure-bending, and combined axial load-bending moments. A finite element-based numerical model is developed and validated against existing experimental data. Using an extensive databank generated from finite element analysis, this research proposes analytical empirical relations for determining the bearing capacity of rectangular and circular composite beams, columns, and beam–columns. These relations provide a direct, concise, and efficient method for calculating the ultimate strength of CFT members, making them valuable for engineering design. Comparisons between the proposed analytical results and previous experimental studies demonstrate the high accuracy of this method in analyzing rectangular and circular CFT member behavior. The findings contribute to a better understanding of CFT structural performance and offer practical tools for designers working with these composite elements.

Estimation of viscoelastic properties in ribbon-shaped homogeneous waveguides by wavenumber analysis and model reduction

Wavenumber based procedures applied to 1D waveguides provide a rigorous framework with an exact signal model that allows for a proper identification of both storage and loss properties independently from the boundary conditions. However, the associated inverse problem is either computationally intense if using a reference solution (e.g. SAFE) or limited to a specific frequency range that depends on the reduced beam model. We propose here to apply the wavenumber-based estimation of isotropic viscoelastic properties to ribbon-shaped homogeneous waveguides, characterized by a rectangular section with slender height-to-width aspect ratio. We show theoretically that considering the ribbon as a thick plate by assuming a model reduction in the height dimension, drastically reduces the wave propagation problem (hence its inverse counterpart) while providing a sufficiently good approximation on the low height-to-wavelength regime. In addition, full-field measurements are performed on an Aluminium and a PVC homogeneous ribbon-shaped waveguide. The experimental dispersive branches (bending and torsion modes) are identified on an ultra-wide frequency range (1 kHz - 1 MHz) using High Resolution Wave Analysis. For both materials, an excellent agreement is observed with the thick plate reduced model, paving the way for wide-band viscoelastic properties identification of ribbon-shaped waveguide.

Hysteretic behavior of eccentric RHS beam-to-column joints under cyclic in-plane bending

This paper conducted experimental and numerical studies on the hysteretic behavior of eccentric rectangular hollow section (RHS) beam-to-column joints under cyclic in-plane bending. The study began with the design of both stiffened and unstiffened joints, followed by hysteresis tests that revealed failure modes like web weld tearing and stiffener fracture. The seismic performance of the joints was evaluated using hysteresis curves, skeleton curves, ductility coefficients, strength degradation coefficients, and energy dissipation coefficients. Compared to unstiffened joints, the stiffened joints exhibited a 30 % increase in peak load and a 18 % improvement in maximum energy dissipation coefficient. Subsequently, finite element (FE) analysis was performed, and the influence of key parameters on the hysteretic behavior was studied using validated FE models. The results indicated that the hysteretic behavior was positively correlated with the flange width ratio of beam to column, the ratio of beam section height to column flange width, and the thickness ratio of beam to column, while it was negatively correlated with the width-to-thickness ratio of the column. Finally, a mathematical model for the hysteretic behavior of both stiffened and unstiffened joints was developed and validated through experimental and FE comparison, offering practical applicability in engineering design.

Experimental testing and plastic strain analysis of high strength steel longitudinal plate to tubular X joints

Applying high strength steels to tubular joints can increase the propensity to fracture failure due to their lower ductility. However, to simulate the fracture behavior in the finite element (FE) analysis, sophisticated material damage model with rigorous fracture criteria should be incorporated. Recently, the latest draft of ISO 14346 has advocated the use of 5% strain limit in FE analysis of tubular joints. The strain limit concept has been further developed by the authors’ previous work, for its use as a practical alternative to the complicated material damage model. Specifically, a lowered limit of 2.5% was recommended for longitudinal plate to circular hollow section (CHS) joints subjected to in-plane bending. This study extends the strain limit investigation to longitudinal plate to tubular X joints subjected to tensile loads. An experimental program is first presented which included both CHS and rectangular hollow section (RHS) chord members fabricated from two high strength steels with nominal yield stresses of 460 MPa and 700 MPa. Based on test-validated supplemental numerical analyses, it is suggested that the joint load corresponding to 2.5% strain limit can be taken as the load-bearing capacity to suppress occurrence of a fracture failure for the tubular joint configurations considered in this study.

Comparative analysis of the influence of different shapes of shaft sections on dust transportation

Large amounts of dust are generated during digging operations in underground mines, and the transportation of dust is affected by the shape of the roadway section. In order to know the dust transportation law of different cross-section shapes when digging. Fluent software was used to simulate the distribution of wind flow field, dust transportation trajectory, and dust quality concentration in roadways with semicircular arch, three-centered arch, rectangle and trapezium, and then analyze and compare the influence of four cross-section shapes on dust transportation, and use gray correlation analysis to investigate the correlation between the time needed to reduce the dust quality concentration of the roadway to the safe value and the ventilation air volume and air supply distance. The results of the study show that the wind speed in the roadway is in the following order from high to low: rectangle > trapezium > three-centered arch > semicircular arch. Dust particles of each size rubbed each other after blasting, and there were fewer dust particles with larger sizes in the three-centered arch roadway. Both the air supply distance and ventilation air volume impact the dust removal effect; when the air supply distances are 5 m and 10 m, the three-centered arch has a better dust removal effect; when the air supply distances are 15 m and 20 m, the effect is better in the rectangular roadway and trapezoidal roadway; and when the ventilation air volume is increased, it is the three-centered arch. Through the gray correlation analysis, it can be seen that in order to improve the construction environment in the roadway after blasting, the rectangular section can be chosen when considering the air supply distance, and the three-centered arch can be chosen when considering the ventilation air volume.

Stability of hot-finished and cold-formed steel hollow section columns: A comparative study

A comparative study into the buckling behaviour of hot-finished and cold-formed steel hollow section members subjected to axial compression is presented in this paper. The main differences between hot-finished and cold-formed hollow sections are initially discussed. An experimental programme conducted to investigate the local, global and local-global interactive buckling of hollow section columns is then described. Three S355 normalised hot-finished and three S355/S420 (dual certified) cold-formed profiles, covering circular, square and rectangular hollow sections (CHS, SHS and RHS respectively), were studied. The stress-strain characteristics of the examined materials were obtained through tensile coupon tests. 3D laser scanning was utilised to determine the distribution of geometric imperfections in selected SHS test specimens and a consistent approach to characterise different forms of geometric imperfections from the scan data is put forward. A stub column test was carried out on each cross-section to examine its local buckling behaviour, and a series of long column tests were performed on all test profiles. In total, 21 tensile coupon tests, six stub column tests and 40 long column tests were conducted in this programme. Finite element models were also developed, validated and used for parametric studies to generate supplementary numerical datasets. The obtained test and numerical data, along with the existing experimental results collected from the literature, were used to evaluate the accuracy and reliability of the Eurocode 3 (EC3) stability design provisions for hot-finished and cold-formed hollow section columns; aspects requiring improvements are highlighted to guide future studies.

Study of Alternatives to Manufacturing of Long Pipes with Many Holes

Abstract In industrial manufacturing, certain long, thin-walled pipe-type parts that have many holes arranged along their longitudinal axis are required. In the automotive industry, such thin-walled long pipe parts are needed for body frames, for heavier component supports, for protection bars, etc. Frequent cases are encountered, for example, in the manufacture of modular shelves for storage. In these cases, long pipes, up to 6 meters long, with thin walls are used. Such long thin-walled pipes, which have many holes arranged along them, sometimes even equally spaced between them, are frequently made with a manufacturing technology that has several characteristic steps: 1) making holes in sheet metal strips, 2) bending the strips and welding them lengthwise, resulting in perforated pipes having a rectangular or square section. In this paper, two variants of obtaining pipes with holes arranged along the length of the pipe, but which are obtained from laminated pipes with thin walls of rectangular section, are proposed and analyzed. The characteristics of obtaining holes in these pipes are presented and the advantages and disadvantages of the proposed solutions are analyzed. The finite element method was also used for the analysis using SolidWorks software.

Effect of web holes on web crippling capacity of rectangular hollow steel sections under two flange loadings

This paper presents experimental and numerical investigations on web crippling behavior of hot rolled rectangular hollow section (RHS) with web holes. A total of 20 rectangular hollow sections, subjected to interior-two-flange (ITF) and end-two-flange (ETF) loading conditions undergoing web crippling, were experimentally tested. The experimental program was designed to obtain web crippling of specimen having slenderness (h/t) value of 21.32, by varying size and offset distance of web holes under two flange loading conditions. Finite element models of experimentally tested beams were developed, and results of finite element analysis showed good agreement with experimental results. A parametric study was then conducted using finite element analysis on different cross section sizes, to demonstrate the effect of size and position of web holes on web crippling capacity of rectangular hollow sections. It was demonstrated that ratio of diameter of web hole to the depth of flat portion of web (a/h) and ratio of offset distance of web hole to the flat portion of web (x/h) are the primary parameters affecting the web crippling strength. Design recommendations in the form of reduction factors for both loading conditions are proposed, that are conservative to both experimental and finite element results. To assess the reliability level of design recommendations, reliability analyses were undertaken.

БАГАТОШАРОВІ ІНДУКТОРИ ДЛЯ УСТАНОВКИ ІНДУКЦІЙНОЇ ТЕРМООБРОБКИ АЛЮМІНІЄВИХ ЗЛИВКІВ ПРИ ПРЕСУВАННІ КАТАНКИ ДЛЯ СИЛОВИХ КАБЕЛІВ

On the basis of the developed mathematical model, computer (numerical) modeling of electrothermal processes in a multi-layer inductor installation, which is used for heating cylindrical aluminum ingots (blanks) before pressing the wire rod, as a basis for obtaining current-conducting cores of power cables from it, was carried out. Single-phase and three-phase multilayer inductors of the galette type were studied, as a result of which it was shown that the maximum value of the electrical efficiency of such an installation for both inductors is provided by their three-layer winding with a water-cooled copper tube of rectangular section. For both inductors, distributions along the radius and length of the aluminum blanks of the volumetric specific power and the specific linear power of heat release from the eddy currents induced in the blanks were obtained. For a three-phase inductor, such distributions were obtained when feeding it with voltages with phase shift angles of 120 and 60 degrees. The losses in the turns of the inductors and their distribution along the length and layers of both inductors were also studied. Ref. 8, fig. 7, tables 2.

Experimental study on flexural behavior of corroded post-tensioned T- shaped beam

A comprehensive literature review on pre-stressed concrete beams subjected to corrosion reveals that most experimental studies are on rectangular sections even though T-shaped and box sections are more widely used in engineering practice with post-tensioned prestress, in particular for heavy structures like bridges. In this paper, five post-tensioned T-shaped beams were prepared, four of which were subjected to accelerated corrosion, and then all the beams were subjected to the four-point bending test. Special attention was directed to the cracking propagation and failure patterns, load-deflection, load-strain of concrete and steel strand, ductility and flexural capacity of the test beams. The experimental results show that the flexural behavior of the test beams deteriorates with the corrosion degree of prestressed strands, especially when the corrosion degree exceeds 2 %. When the corrosion degree is 8.42 %, the failure pattern of crushing of compressed concrete is changed to the rupture of the wires. The corrosion effects on the load-strain of steel strands depend on corrosion loss, strand position and loading stress state. Corrosion of steel strands reduces the compressive strain of concrete at the same compression position and the ultimate strain of the prestressed strands at the position of beam end. Finally, a numerical model is proposed, which can provide accurate and effective predictions of the failure pattern and flexural capacity of the corroded post-tensioned T-shaped beam.

Design of a Trailer Adapted for Accommodation and Transport of Beehives

There is relevant interest concerning beehives, taking into account climate change and its influence on bees’ behavior. A part of the industrial engineering sector is focusing on beekeeping applications. More specifically, the present study aims to develop a trailer for the transport of beehives adapted to be placed or fixed to a tractor or a vehicle trailer, with the objective of transporting the beehives safely and stably during transhumance. The proposed novel design relates to a trailer that incorporates a device for housing a rectangular section of the beehives, which can be adapted for fixing or housing in a vehicle or in a vehicle trailer. The device comprises a lower support structure, adapted to support a plurality of rectangular sections of beehives stacked horizontally on the lower structure, an upper frame adapted to house the beehives inside, and two or more connecting elements between the lower structure and the upper frame. The connection of the trailer with the device facilitates the loading and unloading of the beehives by mechanical means. The different parts have been designed as individual pieces and then assembly is carried out to achieve the complete design. This method of implementation is because the simulation of individual components is simpler and easier, since if it is carried out through assembly, the type of joint, such as welding, and the length of the weld would have to be indicated at each point of contact between components, along with its thickness and all the necessary parameters. Therefore, in those welding points, fixed fastenings are indicated and so will simplify it. In accordance with the individual creation of each part, its own load simulation has been carried out. Static analyses are performed taking into account structural elements of this proposed design, with restrictions and loads being established. The analysis, including upper bars and supports, has been completed with several situations. Based on stress values, deformations have been determined and calculations evaluated. The trays have been manufactured using flat steel bars and angled bars for the legs and support of the hives.

Numerical analysis of seismic response of a circular tunnel-rectangular underpass system in liquefiable soil

Earthquake-induced liquefaction can lead to uplift displacements of underground structures. While the behaviour of a single underground structure has been extensively studied, the coupled response of a shallow buried circular tunnel adjacent to an underpass with a rectangular section in liquefiable ground remains unclear. In this study, the finite difference method based on the fully coupled effective stress is employed to analyse the seismic response of two adjacent underground structures. Firstly, comprehensive parameters of Hostun sand for P2Psand constitutive model was calibrated. The accuracy of the numerical method is verified through a centrifuge test. Subsequently, comparisons are made between the seismic response of the tunnel-soil-underpass interaction and other cases: free field, tunnel, and underpass. The tunnel-soil-underpass interaction in liquefiable ground is analysed, with a special emphasis on the development of excess pore pressure, acceleration response of the soil, displacement and deformation of the structures. A section deformation coefficient was proposed to depict the tunnel deformation. Finally, horizontal spacing, buried depth of tunnel and underpass are discussed to clarify the interaction of two structures. The optimal relative position of two structures is suggested, providing valuable insights for the spatial design of underground structures in liquefiable ground.

In-plane flexural behavior of eccentric rectangular hollow section (ERHS) X-joints: Experimental, numerical and analytical study

This paper investigates the in-plane flexural behavior of an eccentric rectangular hollow section (ERHS) X-joint, where the two braces are continuous at one side and the inner face is aligned with a chord sidewall. The presented X-joints are full lateral offset RHS joints. In this study, laboratory static testing is implemented on two ERHS X-joint specimens and one traditional RHS X-joint specimen under in-plane bending moment (IPBM), and the corresponding numerical simulation is conducted. The results show that the ultimate flexural strength and initial stiffness of the ERHS X-joints with a medium brace-to-chord width ratio (β) are larger than those of the RHS X-joints. The initial stiffness and strength of ERHS X-joints increase with the growth of β. Based on the load transferring mechanism, two analytical models and the relevant formulae are proposed to predict the strength of the ERHS X-joints with β ≤ 0.925 and β = 1.0, and the strength of joints with 0.925 <β < 1.0 can be determined by linear interpolation. The proposed analytical models are validated against experimental data and finite element results.

Modeling a poiseuille flow through a rectangular pipe in a floor slab (PSD)

This study was devoted to the modeling of a laminar fluid flow in a pipe of the rectangular section located in a floor slab. This theme was raised because of its relevance in the large business sector as well as in the areas of energy saving and storage at the residential scale. The equations of motion quantity and heat transport are the classical equations of forced convection. However, to describe the movement amount within the heating slab pipeline, Prandtl simplified model was most appropriate. In addition, this model retains the most important terms for a laminar regime flow. In addition, the modeling of fluid flow conservation in the pipeline was taken into account in the equation system. To achieve the above-mentioned objective, a numerical resolution was made for the system resolution of the Navier-Stokes equations that govern this fluid flow. These equations were discretized by an implicit finite difference method. The system of algebraic equations as well as obtained was solved by the algorithm of Gauss and the algorithm of Thomas. The results obtained such as: the evolution of the fluid velocity profile within the slab according to pipeline to the Reynolds number variation, the fluid temperature have clearly demonstrated the Poiseuille effect on fluid flow. Moreover, the stabilization of the Gauss algorithm and the Thomas algorithm in this numerical modeling was well verified against the tricks that were taken into consideration. The result of this study was that Thomas algorithm and Gauss algorithm are the best in this type of numerical modeling.