Rectangular Beam Research Articles

Effect of interfacial thermal history on bonding mechanism of laser assisted joining of QP980-CFRTP with adjustable flat-top rectangular laser beam

Carbon fiber reinforced thermoplastic composite (CFRTP) - metal hybrid structures, which have been increasingly used in the industry, can significantly reduce structure weight and energy consumption. In this paper, an adjustable flat-top rectangular diode laser beam was used as a heat source to join the quenched and portioned QP980 steel and CFRTP in a lap joint configuration. Compared to conventional laser beam scanning process in the literatures, the rectangular laser beam provides a relatively uniform temperature distribution at interface. The relationship between interfacial thermal history and the joint performance was explored. Experimental results showed that thermal history had a significant impact on interfacial chemical compositions and the formation of joint defects via affecting the resin state, resulting in change of the joint fracture behaviors. Furthermore, higher interfacial temperature and sufficient heating/holding time contributed to the complete melting and diffusing of resin matrix on QP980 surface, filling the micro pores of the interface, and promoting the chemical bonding between QP980 and CFRTP. On this basis, a novel strategy to achieve excellent interfacial bonding via adjusting the interfacial thermal history was proposed to produce a high-quality joint with the peak load higher than 10 kN and the shear strength of 22 MPa.

Structural behaviour of LDSS tubular beams with web perforation under three-point bending

The paper deals with the numerical study of Lean Duplex Stainless Steel (LDSS) rectangular tubular beams with circular and rectangular web perforation under three-point bending to assess the shear and moment response employing FE software package Abaqus. Various parameters such as cross-section slenderness, perforation depth, perforation length and shape were considered in the study. The results of the FE analysis are then compared to the revised European stainless-steel design regulations. A modification of the currently available European design specification was also proposed based on the numerical study conducted.

Theoretical study on the bending collapse of multi-cell thin-walled rectangular beams

Multi-cell thin-walled beams possess excellent energy absorption capacity and efficiency under bending collapse. Unfortunately, there are still no systematic theoretical methods to predict their bending response under three-point bending. In this work, the constituent element method is proposed to predict the bending response of multi-cell rectangular beams. Theoretical models are established for two types of constituent elements: E-shaped and ▪-shaped elements. The bending process of the constituent elements is divided into two stages: the elastic–plastic bending stage and the buckling stage. Theoretical solutions are derived individually for these two stages. Multi-cell beams with 2 × 2 and 2 × 3 cell sections are then analyzed and employed to validate the feasibility and accuracy of the proposed theories. The theoretical predictions show good agreement with the numerical results. The present work provides an effective approach to predict the bending moment response and energy absorption of multi-cell beams under three-point bending.

Electromechanical response of boron nitride nanosheet reinforced nanocomposite beam: A finite element study

The objective of the present study is to investigate the electromechanical response of a piezoelectric boron nitride nanosheet reinforced nanobeam accounting for the surface and the flexoelectric effects using finite element analysis. The finite element model was developed by using the size-based Euler–Bernoulli beam model, modified piezoelectricity theory, and Galerkin's weighted residual method. The boron nitride nanosheet-reinforced nanobeam was loaded with uniformly distributed load and point-loading conditions. Three common boundary conditions for beams such as clamped-free, simply supported, and clamped-clamped have been considered here. The electromechanical behavior of the boron nitride nanosheet reinforced nanobeam has been studied under the pure surface, pure flexoelectric, as well as combined surface and flexoelectric effects. It is observed that the integrated surface and flexoelectric effects are mainly responsible for enhancing the electromechanical performance of the nanobeam. For the thickness H = 20 nm, the maximum deflection of the nanobeam was reduced by ∼50% when both the flexoelectricity and surface effects are combined together for all the support conditions. Moreover, the circular cross-section beam becomes ∼30% stiffer than the rectangular cross-section beam under the integrated effect of surface and flexoelectricity under all loading conditions. Hence, the highly size-dependent surface and flexoelectricity must be explored in the accurate electromechanical behavior of the nanostructure. Furthermore, beam stiffness is highly influenced by the flexoelectric effect irrespective of the beam boundary conditions whereas the surface effect is largely reliant on the beam boundary conditions. This research work provides a methodology to design efficient boron nitride nanosheet reinforced nanostructures that may potentially be applied in the design and development of several nanoelectromechanical systems such as force and pressure-based nanosensors and actuators.

Free vibration and buckling of functional graded box beams and the effect of the cross-sectional warping shape

Box beams have been used widely in engineering fields. This paper proposes a higher-order shear deformation beam theory to investigate the transverse vibration and stability of box beams in pure bending, especially free vibration and buckling of functionally graded box beams. A warping shape function is constructed for the first time to take shear deformation and rotary inertia of the hollow-core rectangular cross section into account simultaneously during bending. The governing equation and boundary conditions are derived. The frequency equations for typical end supports are given. The characteristic equations for buckling and critical loads are determined. Numerical results are evaluated. Besides its simplicity and easy-to-implement, the proposed theory has sufficient accuracy on the mechanical behavior of the box beams. By comparing the obtained results with the simulation results based on three-dimensional finite element method, the accuracy of the numerical results obtained is verified. The effects of parameters such as aspect ratio, gradient index, and wall thickness on the natural frequencies and critical loads are explored in detail. When box beams become rectangular beams, our model reduces to the well-known Levinson beam model.

Experimental and numerical investigations on three-point bending collapse of thin-walled beams

Multi-cell thin-walled beams showed excellent energy absorption efficiency under various load conditions. However, the theoretical prediction of their bending resistance is quite a challenging task. In this work, the three-point bending collapse of thin-walled rectangular beams with single-, double-, and triple-cell sections is investigated experimentally and numerically. Two finite element schemes: the shell element scheme and the solid element scheme, are employed to simulate the experimental tests, and the features of the two schemes are compared. The influence of friction coefficients on the force response and deformation mode of the beams is analyzed. Finally, a constituent element method is proposed to predict the bending responses of multi-cell beams, and the feasibility of the method is demonstrated.

Flexural Strength of Damaged RC Beams Repaired with Carbon Fiber-Reinforced Polymer (CFRP) Using Different Techniques

In this study, an experimental program was developed to investigate the flexural behavior of pre-damaged reinforced concrete (RC) beams that had been repaired and strengthened using carbon fiber-reinforced polymer (CFRP) laminates under a monotonic load. Two techniques were used: externally bonded reinforcement (EBR) and near-surface-mounted (NSM) reinforcement, to repair and strengthen the tested beams. The experimental program involved casting and testing nine simply supported RC rectangular beams; one beam was considered as the reference beam and did not undergo additional strengthening, and the remaining beams were strengthened using CFRP laminates. These eight beams were divided into two main groups for the purposes of strengthening: beams for which the EBR technique was used, and beams for which the NSM technique was used. The primary variables observed in the EBR and NSM groups included four damage percentages obtained according to the preload (20, 40, 60, and 80%) from the ultimate load carried by the reference beam. The experimental results show that decreasing the damage percentage leads to an increase in ultimate strength from about 3.6% to 17.2% for the beams repaired using the EBR technique and from 27.6% to 57% for the beams repaired using the NSM technique; additionally, the NSM method was more effective than the EBR method in terms of the flexural strength and mode of failure. However, using CFRP laminates enhances the flexure capacity of strengthened RC beams.

High-speed hot-wire laser brazing technology for steel/aluminum alloy dissimilar joint using twin beam irradiation

The demand for steel/aluminum alloy dissimilar joints has increased for light-weighting the automobile body. However, it is well known that joining both metals by conventional welding methods, the brittle intermetallic compound (IMC) is generated at the interface, and it significantly deteriorates the joint strength. In this paper, the hot-wire laser brazing process using the twin-spot irradiation was proposed and its conditions were optimized to achieve the high brazing speed and the high joint strength on a lap-fillet joint of the steel/aluminum alloy dissimilar combination. The twin spots of a circle (ϕ5) and rectangular (5 × 11) laser beams aligned at spot ends achieved the high brazing speed up to 6 m/min, stable brazing phenomena and sound bead appearance. The joints fabricated using the optimized conditions realized the very thin IMC thickness under 2 μm and high joint strength over the yield strength of the base steel sheet.

Fire resistance of austenitic stainless steel beams with rectangular hollow sections

AbstractThis paper presents a study on the structural behaviour of stainless steel profiles under fire conditions. An experimental campaign of three‐point bending tests on rectangular hollow section beams of the grade 1.4301 (also known as 304) were conducted, considering both steady‐state and transient state conditions. Prior to those tests, the mechanical characterization of the stainless steel was investigated. The constitutive laws obtained by tensile tests at high temperatures are compared with those recommended in Eurocode 3, whose respective material models were recently proposed for modifications, still requiring complete validation. In addition, numerical modelling of the bending tests has been performed afterwards achieving close approximation to the observed experimental results. Finally, analytical methods to predict the load‐deflection behaviour are also presented. Good agreement between the considered methodologies was attained validating their application on the prediction of the fire behaviour of stainless steel beams.

Finite Element Based Static and Dynamic Vibration Analysis of a Beam with Axial Variation of Material Properties

Abstract: The study examines the vibration analysis of a damped cantilever beam with nonuniform variation in material properties using finite element methods. With power modification of material parameters in the axial direction, the static and dynamic response of a prismatic rectangular beam with damping has been examined. For the finite element approach, two noded beam elements with two degrees of freedom at each node were evaluated. The power law variation of material properties was used throughout the investigation. This research investigated the effects of proportional damping on displacement, velocity, and acceleration responses. The proposed beam's mass, stiffness, and damping matrices were calculated using Hamilton's concept. In the temporal domain, the Newmark Method has been utilized

Evaluation of experimental techniques for performance estimation of post-tensioned concrete beams

Structural health monitoring (SHM) techniques have become a significant subject in structural evaluation due to the development of non-destructive methods used to monitor and assess the integrity of structures. This paper aims to investigate the effect of damage on the flexural performance indicators and dynamic characteristics of post-tensioned concrete (PC) beams, using both static and vibration tests. The beams were tested at several load levels to reproduce different load stages of a PC member: pre-cracking, during and after the formation of initial cracks, and finally, during and after the formation of larger significant cracks. The performance of the elements is evaluated based on static data, energy calculations, and the three criteria of ACI 437 recommendations. Data from the vibration tests were used to identify the changes in modal parameters after different load levels. Acoustic emission data analysis and results were used to classify the level of damage. Experimental bending stiffness and crack length determination via visual inspection was used as control parameters to assess the deterioration levels of the beams. The outcomes of this study show the relationship level among the different experimental responses obtained: flexural performances, the presence of damage in the beams, and natural frequencies. By considering the relationships of the SHM techniques and their individual findings, the evaluation of performance indicators or damage classification in rectangular concrete prestressed beams reveals that the main limitation is the required knowledge about the previous response of the system.

Nearly Perfect Transmission of Lamé Modes in a Rectangular Beam with Part and Through-Thickness Vertical Cracks.

The guided waves in the uniform waveguide of rectangular cross-section exhibit complicated propagation and scattering characteristics due to the diversity of vibration modes. This paper focuses on the mode conversion of the lowest Lamé mode at a part-through or through-thickness crack. Firstly, the Floquet periodicity boundary condition is applied to derive the dispersion curves in the rectangular beam, which relates the axial wavenumber to the frequency. On this basis, the frequency domain analysis is conducted to investigate the interaction between the fundamental longitudinal mode in the vicinity of the first Lamé frequency and a part-through or through-thickness vertical or inclined crack. Finally, the nearly perfect transmission frequency is evaluated by extracting displacement and stress harmonic fields throughout the cross-section. It is shown that this frequency originates from the first Lamé frequency, increases with the crack depth, and decreases with the crack width. Between them, the crack depth plays a major role in the frequency variation. In addition, the nearly perfect transmission frequency is negligibly affected by the beam thickness, and such a phenomenon is not observed for inclined cracks. The nearly perfect transmission may have potential applications in the quantitative evaluation of crack size.

Energy harvesting using PZT4 based beam type structural element

Piezoelectric materials are mainly used for the development of sensors and actuators. However, they are also used to develop structures to harvest electricity. This study uses the most utilized piezoelectric material, lead zirconate titanate (PZT4), as a structural element. The structural element is modeled in the form of a rectangular beam. The material properties of PZT4 such as dielectric constant, elastic orthotropic, piezoelectric, and density are used to model the rectangular beam. To analyze the piezoelectric effect, the potential difference at the bottom surface of the beam is kept at zero. Then, the compressive load, or pressure, is applied at the top and bottom surfaces of the beam. As a result of finite element analysis, it is observed that the electric potential increases with the increasing load. A maximum electric potential of 977 V is obtained under 20 kPa of compressive load. The results of this study can be used as a basis for the development of energy harvesting devices based on piezoelectric materials. In the future, FEA can be used to analyze the inverse piezoelectric effect for the development of actuators.

Flexural strength and drift ratio of reinforced concrete beams with longitudinal square hole

The main aim of this investigation was to study the flexural strength and drift ratio of simply supported rectangular RC hollow beams (with a longitudinal square hole) subjected to gradually increased and symmetrically applied one-point load. Each hollow beam had a 300 mm2 and 900 mm2-area of a square, and the position of the center of the hole was 80 mm from the top. The cross-section of the beam, the amount of longitudinal steel, and the stirrups of the beam was kept constant. The flexural strength and deflection of these hollow beams were compared with that of a solid RC beam that had the same outer dimensions and steel reinforcements. A comparison of experimental results shows that specimens with square holes 10 x 30 achieve higher peak load, MOE, and MOR. On other hands, solid beam specimens achieve a larger drift ratio.

Comparison of Bursting Forces in Concrete Post-Tensioned Beam using Two Modeling Approaches

A case study on a rectangular post-tensioned concrete beam end block with 3-dimensional analysis is presented in this paper. ANSYS software is used to model the end-block of a post-tensioned concrete specimen i.e., beam. An actual anchorage plate, widely used in construction is modeled with two different approaches, and a concentrated jacking force is applied to the same anchorage area. A case study is performed in which two different modeling approaches are used to model the end plate. For both modeled plates, the results are obtained and findings are compared in terms of stresses, its location and bursting force. Different equations from various design manuals are used to compare the calculated bursting tensile force.

Experimental investigation on shear behaviours of textile reinforced concrete beams

An experimental study on eight concrete beams reinforced by combining GFRP bars for moment and glass textile sheets for shear resistances is conducted to examine the use of these non-corrosive reinforced materials in creating the structural concrete beams. Rectangular cross-section beams with two different aspect ratios, 1.1 and 1.7, are investigated. For each group, there are two control beams with and without GFRP bars for shear reinforcements. The other two beams in each group are reinforced with one and two glass textile grids for shear resistance. Fine-grained high-strength concrete with a similar grade is used for all tested beams. Three-point bending tests are employed to examine the shear performances of these specimens, including the load–deflection curves, cracking patterns, failure modes and strains in reinforcements. The experimental results indicate that the crushing failure is recorded in all tested short-span beams reinforced with shear reinforcements. Increasing the number of textile layers improves the shear capacities of the specimens. The shear strengths of the tested beams are significantly affected by the aspect ratio. Finally, the ratios of the effective experimental strength over the compressive strength of concrete are compared with the existing guidelines.

Suggestions for repairing various defects in the NSM strengthening mechanism with hybrid rebars for RC beams: Experimental and numerical study

NSM bars enhance flexural strength of RC components but degrade ductility and transform the failure mechanism from ductile flexure to brittle shear. Failure due to debonding and other causes still has an impact on the strengthening system's efficiency. The focus of this research will be on how successful hybrid steel-CFRP/GFRP rebar strengthening is in enhancing the overall behaviour of reinforced concrete (RC) beams under flexure. Six rectangular RC beams were cast and strengthened using various semi-NSM procedures (120 mm width by 300 mm depth by 3000 mm length), then tested to failure in four-point bending tests. The beams were classified into four categories: (I) control beam, (II) strengthening with mild steel bar, (III) strengthening with mild steel-CFRP/GFRP hybrid rebars, and (IV) strengthening with high tensile steel-CFRP/GFRP hybrid rebars. To enhance the overall behaviour of RC beams, particularly beam ductility, and to avoid corrosion, FRP confinement was utilized in association with steel bars. End anchoring with strengthening rebars aims to limit unexpected de-bonding of NSM bars at higher loads, resulting in superior flexural performance of the RC members. In compared to the others, strengthening with mild steel-GFRP rebars enhances ductility and beam stiffness. This study also suggests and validates a 3D numerical model to simulate the performance and failure of NSM Strengthening mechanism with hybrid rebars for RC beams using the finite element (FE) software “ANSYS”. Regarding the behaviour of load-deflection, moment-curvature, load-crack width, and mode of failure, the FE results were accurate representations of the experimental results. An additional FEM specimen was examined to corroborate the effect of the experimental parameters.

Compact E-Band Sheet Beam Folded Waveguide Traveling Wave Tube for High Data Rate Communication

The design of a compact <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{E}$</tex-math> </inline-formula> -band (71–76 GHz) sheet beam (SB) folded waveguide (FWG) traveling wave tube (TWT) for high data rate communications is presented in this article. The round beam tunnel for a pencil FWG slow wave structure (SWS) has been redesigned with a rectangular beam tunnel to be suitable for the SB with increased beam current. A novel periodic permanent magnet (PPM)–periodic quadrupolar magnet (PQM) focusing system has been developed to reduce the beam ripple and improve the transmission ratio. A multistep side-out coupler is designed to import and extract the RF power from the SWSs and be compatible with the planar periodic magnetic focusing system. Particle-in-cell (PIC) simulations are employed to evaluate the performance of the high-frequency circuit. Driven by a 1 W signal, the 30-period circuit is estimated to produce more than 100 W power and achieve a 21 dB gain with a less than 0.4 dB variation over 71–76 GHz. Moreover, phase and linearity analysis show a less than 6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> in-band phase distortion and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim$</tex-math> </inline-formula> 30 dB third-order intermodulation distortion (C/3IM) at 30 W of output power, meeting the requirements of a communications-focused TWT. Over 5% circuit efficiency and 40% overall efficiency when equipped with a single-stage collector can be achieved by the compact TWT over the target band.

Flexural and compressive performance of BFRP-reinforced geopolymer sea-sand concrete beams and columns: Experimental and analytical investigation

The combination of geopolymer sea-sand concrete (GSSC) and basalt fiber reinforced polymer (BFRP) reinforcement has the potential to optimally exploit the advantages of both materials, resulting in superior structural durability and environmental friendliness. The resulting structure is called a BFRP-reinforced GSSC structure, which has broad application prospects in marine engineering construction. This paper presents a recent experimental and analytical investigation into the flexural and compressive performance of BFRP-reinforced GSSC structures to verify the expected benefits of such a material combination. In particular, a type of GSSC that uses MgO as an expansion agent to reduce concrete shrinkage was used in this study. The results of four-point bending tests on nine rectangular beams, where longitudinal reinforcement ratios and reinforcement types were key parameters, and monotonic axial compression tests on seven columns, where concrete types and transverse reinforcement ratios were key parameters, are reported in this paper. The test results initially confirmed the advantages of using GSSC in combination with BFRP reinforcement and showed that: (1) the ultimate carrying capacity of BFRP-reinforced GSSC beams and columns was higher than that of conventional steel-reinforced counterparts for the same reinforcement configurations; (2) the flexural and compressive capacity of BFRP-reinforced concrete beams and columns could be enhanced by an appropriate increase in reinforcement ratio and the addition of expansion agents. Finally, this paper presents design equations for the flexural and compressive capacity of BFRP-reinforced GSSC structures.

Machine learning models for predicting concrete beams shear strength externally bonded with FRP

This paper focuses on preparing a database that covers a wide range of experimental data encompassing all the variations in concrete design and fiber reinforced polymer (FRP) composition in reinforced concrete (RC) beams. Artificial intelligence technique is applied to develop 10 machine learning models for estimating the shear capacity of RC beams strengthened in shear using FRP. This study is unique in the sense that it covers the largest data regarding T-beams available in literature so far and is not limited to a particular beam cross section or FRP composition. A comparison among several design guidelines is done to evaluate the efficiency of the guidelines as well as the models developed in shear capacity estimation of FRP retrofitted RC beams. The results reveal that the ensemble learning models developed in this paper namely, random forest, CatBoost and XGBoost give the highest precision in estimating shear capacity of the FRP retrofitted RC beams. For rectangular beams the R2 and MAE values from CatBoost are 0.871 and 0.214 kN, respectively whereas those for XGBoost are 0.870 and 0.202 kN, respectively. The R2 and MAE values for T-beams using random forest are 0.897 and 0.128 kN, respectively and those using CatBoost are found to be 0.899 and 0.127 kN, respectively. The most significant input feature by Shapley Additive exPlanations is found to be the effective depth for the rectangular beams whereas height of FRP layers in the case of T-beams. The proposed ensemble models in this paper are proved to be superior to the existing mechanics-driven models currently being used for design practices.