Beam Length Research Articles

Hybrid machine learning model for prediction of vertical deflection of composite bridges

A novel hybrid model, based on machine learning technique, for quick and accurate prediction of the vertical deflection of steel–concrete composite bridges was developed. The model is a combination of a bagging (B) ensemble and an instance-based k-nearest neighbours (IBk), hence called the B-IBk. In the models, five easily determined input parameters (cross-sectional shape, concrete beam length, age of the bridge, height of main girder and distance between main girders) are used to obtain the output parameter (maximum vertical deflection). To develop the models, direct measurement data from 83 steel–concrete composite bridges located at different places in Vietnam were collected and used as input and output parameters. Standard statistical evaluation indicators (mean absolute error, correlation coefficient (R) and root mean square error) were used to validate and compare the models’ performance. The results showed that the performance of the novel hybrid model (B-IBk) for predicting the maximum vertical deflection (Y) of steel–concrete composite bridges was very good (R = 0.908) and better than that of the single IBk model (R = 0.875) on the testing dataset. The developed novel model is thus a promising tool for accurate prediction of the Y of steel–concrete composite bridges.

Torsional behavior of FRP-strengthened reinforced concrete members considering various wrapping configurations: Theoretical analysis and modeling

Reinforced concrete (RC) structural members such as spandrel, flanged and curved beams, slab beams, and bridge girders may be subjected to significant torsional loading. Despite extensive research on the strengthening of RC members, very little is known about the torsional behavior of RC members strengthened with fiber-reinforced polymer (FRP) sheets. Therefore, very limited guidelines apply to the design of externally bonded FRP systems for torsional strengthening, and no design provisions exist for the U-wrapped and 2-sided strengthening systems in torsion. This study aims to contribute to this growing area of research by developing a new analytical model to predict the full torsional response of strengthened RC members with many conventional configurations such as spiral, transverse and longitudinal FRP, continuous and intermittent strips along the beam length, side bonded, and full-wrapped systems. Moreover, this study provided an analytical model accurately predicting the contribution, efficiency, and failure mode of side-bonded strengthening systems. Additionally, the influence of various parameters such as FRP stiffness and transverse steel reinforcement ratio is taken into account in the constitutive law of concrete and internal reinforcement for the first time. The good agreement between the test results of 32 collected FRP-strengthened RC beams from the literature and the theoretical ones, which were predicted through programming proves the validity and accuracy of the presented theory.

Investigation on the Coaxial-Annulus-Argon-Assisted Water-Jet-Guided Laser Machining of Hard-to-Process Materials.

In this study, the novel coaxial-annulus-argon-assisted (CAAA) atmosphere is proposed to enhance the machining capacity of the water-jet-guided laser (WJGL) when dealing with hard-to-process materials, including ceramic matrix composites (CMCs) and chemical-vapor-deposition (CVD) diamond. A theoretical model was developed to describe the two-phase flow of argon and the water jet. Simulations and experiments were conducted to analyze the influence of argon pressure on the working length of the WJGL beam, drainage circle size, and extreme scribing depth on ceramic matrix composite (CMC) substrates. A comparative experiment involving coaxial annulus and helical atmospheres revealed that the coaxial annulus atmosphere disrupts the water jet proactively, while effectively maintaining the core velocity within the confined working length and enhancing the processing capability of the WJGL beam. Single-point percussion drilling experiments were performed on a CMC substrate to evaluate the impact of machining parameters on hole morphology. The maximum depth-to-width ratio of the groove and depth-to-diameter ratio of the hole reached up to 41.2 and 40.7, respectively. The thorough holes produced by the CAAAWJGL demonstrate superior roundness and minimal thermal damage, such as fiber drawing and delamination. The average tensile strength and fatigue life of the CMCs specimens obtained through CAAAWJGL machining reached 212.6 MPa and 89,463.8 s, exhibiting higher machining efficiency and better mechanical properties compared to femtosecond (194.2 MPa; 72,680.2 s) and picosecond laser (198.6 MPa; 80,451.4 s) machining. Moreover, groove arrays with a depth-to-width ratio of 11.5, good perpendicularity, and minimal defects on a CVD diamond were fabricated to highlight the feasibility of the proposed machining technology.

Dynamic Stability of an Asymmetric Sandwich Beam Resting on a Paternak Foundation

The parametric dynamic stability of a pinned-pinned asymmetric sandwich beam resting on a Pasternak foundation with viscoelastic core, subjected to an axial pulsating load is investigated. The effects of thickness ratio of two elastic layers (h31), elastic modulus ratio(E3/E1), the ratio of modulus of the shear layer of Pasternak foundation to the Youngs modulus of elastic layer (Gs/E1), the ratio of length of the beam to the thickness of the elastic layer (lh1), the ratio of in phase shear modulus of the viscoelastic core to the Youngs modulus of the elastic layer (G2/E1), the ratio of thickness of Pasternak foundation to the length of beam (δ/l), coreloss factor (η) the ratio of thickness of viscoelastic layer to that of elastic layer (h21) on the non-dimensional static buckling load are considered. In addition to these the effects of the above parameters on the regions of parametric instability have been studied.

Optimizing the Flexural Behavior of Bamboo Reinforced Concrete Beams Containing Cassava Peel Ash using Response Surface Methodology

The growing concern to reduce global warming has necessitated the use of more eco-friendly materials in construction. The study is focused on the utilization of cassava peel ash as supplementary cementitious material and bamboo as reinforcement in concrete beams. The response surface methodology approach was explored to determine the effect of simultaneously varying the cassava peel ash content, bamboo size, beam length, and beam depth on the flexural strength and strain of beams. An analysis of variance was carried out on experimentally obtained results to determine the accuracy of the obtained models and the contributions made by the linear interaction and quadratic terms on flexural strength and flexural strain. The coefficient of determination obtained for RSM models showed a good correlation between all predicted and experimentally obtained results. The optimum conditions obtained for bamboo-reinforced concrete containing cassava peel ash were 3% cassava peel ash, 16 mm bamboo diameter, 500 mm beam length, and 150 mm beam depth. The predicted flexural strengths were 11.85, 14.34, and 14.95 N/mm2 and flexural strains of 0.64, 0.67, and 0.91 for 28 days, 56 days, and 90 days, respectively. To validate the model prediction, a laboratory experiment was conducted using the optimum mix design proportion. From the results obtained, it was observed that the experimental results were close to those predicted by the models. These models can be efficiently used for simulating the flexural behavior of bamboo-reinforced concrete beams. Doi: 10.28991/CEJ-2023-09-08-011 Full Text: PDF

Experimental study of moment redistribution before yielding in precast prestressed concrete beams made continuous

AbstractThe bending stiffness distribution of beams composed of simple‐span precast prestressed beams, which are made continuous by deck reinforcement at intermediate supports, is not constant. As the structure undergoes loading, the deck slab at the intermediate support cracks earlier than the prestressed span soffit and due to that the bending stiffness distribution changes along the beam length. The effect of nonconstant bending stiffness distribution on the moment redistribution of the structure before the yielding is studied experimentally and analytically. Two continuous beams with spans of 10 m + 10 m were manufactured, loaded to failure, and studied. It was concluded that the studied structure undergoes considerable moment redistribution before yielding although it would be designed for zero redistribution at the ultimate limit state. If this elastic redistribution is neglected in the structural analysis, the service limit state sagging moment at midspan may end up on the unconservative side. Elastic redistribution can be predicted quite accurately with the help of nonlinear analysis or roughly with simplified idealization as proposed in this article.

Sub-wavelength effects in a free electron laser oscillator.

Previous simulation studies of cavity based free electron lasers (FELs) have utilised models which average the optical field in the FEL interaction over an integer number of radiation wavelengths. In this paper, two unaveraged simulation codes, OPC and Puffin, are combined to enable modelling, for the first time, of a cavity based FEL at the sub-wavelength scale. This enables modelling of effects such as coherent spontaneous emission from the electron beam and sub-wavelength cavity length detuning. A cavity FEL operating in the mid-infrared is modelled and it is shown that, for small sub-wavelength cavity detunings, the FEL can preferentially lase at the third harmonic of the fundamental FEL wavelength. This novel result suggests other modes of operation may be possible and opens up cavity-based FEL operation to investigation of further, potentially useful, modes of operation.

Structural Analysis and material selection for biocompatible cantilever beam in soft robotic nanomanipulator

This paper investigates the selection of appropriate materials for cantilever beams in surgical robotic nanomanipulators. Cantilever beams play a crucial role in soft robotic surgery. Biocompatible materials, which have minimal adverse effects on biological systems, are commonly used for these beams. Using SOLIDWORKS software simulation, the study assesses the flexibility of cantilever beams made from different biocompatible materials. The analysis involves varying the applied force (0.001 µN to 0.004 µN), beam length (80 µm, 120 µm, and 160 µm), and beam thickness (0.4 µm, 0.6 µm, and 0.8 µm). Four materials—Alumina, Poly-Ether-Ether-Ketone (PEEK), Polyurethane (PUR), and Ti-6Al-4V—are evaluated. Simulation results highlight Polyurethane (PUR) as a suitable material for cantilever beams in nanomanipulators due to its favorable properties. These findings provide valuable insights for the design and advancement of efficient and reliable robotic nanomanipulators, advancing the field of soft robotic surgery.

Mechanical performance of prefabricated concrete beam-column joints with double-grouted sleeve connectors: A numerical and theoretical study

This paper presents a systematic numerical study on the structural performance of a newly developed quick-buildable beam-column joint with double-grouted sleeves considering its surface-to-surface contact behaviour between the prefabricated concrete and grouting mortar and strain penetration of the transition rebar. Theoretical analysis is also conducted to predict the load-bearing capacity of the proposed connection. After validation with experimental data, the finite element model is employed to investigate the effects of different factors including protruding beam length and grouting mortar thickness on the structural behaviour of the joint. Results indicate that the maximum stress of the reinforcing bars in the joint with no protruding beam is approximately 15.0% greater than that with a protruding beam, while the maximum stress of the joint anchorage bars decreases by around 87.0% when the short sleeves are placed completely in the joint core area. As the protruding beam length increases, the maximum crack width drops rapidly first and then slowly with a turning point of 1.36 times the short sleeve length, and the highest load-bearing capacity is achieved when the protruding beam length and short sleeve length equal. With the rising grouting mortar thickness, the maximum stress of the transition rebar reduces rapidly first and then slowly with an inflexion point of 50 mm. The change in eccentricity of the transition rebar leads to an around 3% change in the load-bearing capacity of the joint without a projecting beam. The theoretical predictions are in satisfactory agreement with numerical results and can be adopted for practical engineering design.

Enhancing fiber-coupling efficiency of beam-to-fiber links in turbulence by spatial non-uniform coherence engineering.

We present a general formula for the fiber-coupling efficiency of various types of non-uniformly correlated beams propagating in a turbulent atmosphere. With it, we calculate the fiber-coupling efficiency of a specific type of non-uniformly correlated beams, Laguerre non-uniformly correlated (LNUC) beams, to investigate how the non-uniform correlation structure plays a role in enhancing the fiber-coupling efficiency. Compared with conventional Gaussian Schell-model beams, the LNUC beams possess better coupling behavior, and the initial coherence length and beam order of such beams can be adjusted to further improve the fiber-coupling efficiency in turbulence. Our results demonstrate how non-uniformly correlated beams can be used for fiber-coupling applications, and demonstrate their intriguing potential for free-space optical communications.

Stability control of overburden and coal pillars in the gob-side entry under dynamic pressure

To improve the recovery ratio of coal resources and stress environment of the roadway, gob-side entries have been widely implemented to numerous coal mines in China. Traditional gob-side entry is generally excavated after the gob of the adjacent longwall face is stabilized. To achieve a balance between the seam mining and roadway excavation, numerous mine coals use the method of driving a roadway along the next gob, which heads adjacent to the advancing coal face, and maintaining a narrow coal pillar. Consequently, the dynamic pressure occurs at the gob-side entry; accordingly, the difficulty of roadway maintenance is increased. However, the traditional gob-side entry stability analysis is not applicable to a gob-side entry under dynamic pressure. In this study, the overburden structural model and coal pillar stress model of a gob-side entry under dynamic pressure were established considering the compression load of the immediate roof and gangue and influence law of the cantilever beam length of main roof. Subsequently, thickness, hardness, and deformation of the immediate roof on the stability of the gob-side entry were studied, and the theoretical criterion for the stability of “voussoir beam” structure and coal pillar of the gob-side entry under dynamic pressure were proposed. Based on the geological conditions in tailgate # 110505 of the Yushuling coal mine, reasonable measures were taken considering the aspects of roof cutting and pressure relief, coal pillar design, and surrounding rock reinforcement. After applying the proposed measures, the width of the coal pillar was reduced from 15 m to 4 m. Meanwhile, the grouting cable beam was used to strengthen the roof, and the narrow coal pillar was reinforced by a bidirectional grouting anchor cable was developed. As a result, after the roadway was stabilized, the roof-to-floor convergence and two-side convergence were 268 mm and 105 mm, respectively. Moreover, the stress concentration factor of the coal pillar was 1.20. The stability characteristics of the overburden and coal pillar of the gob-side entry under dynamic pressure were effectively controlled, and remarkable economic benefits were obtained in this coal mine. The techniques proposed for maintaining the stability of the 4 m wide coal pillar and ensuring the bidirectional grouting reinforcement have been successfully applied in a coal mine for the first time, which have high innovation and application values. This study provides a reference for the design and maintenance of the gob-side entry under dynamic pressure.

A Comparison of Load Distribution Methods at the Node and Internal Force Analysis of the Lattice Beam Based on the Winkler Foundation Model

As a new type of retaining structure, lattice beams with tie-back anchor cables have been increasingly used in slope reinforcement and have achieved improved prevention effects. However, the simplified load distribution method (SLDM) at the node, which is the theoretical basis of internal force analysis for lattice beams, is not perfect at present. An alternative new load distribution method (NLDM) at the node based on the force method for the lattice beam was therefore introduced in this paper. Taking into account the loads acting on other nodes of the beams in both directions and according to the static equilibrium condition and deformation compatibility condition at the nodes, NLDM assigns the loads acting on the nodes to the cross beams and vertical beams, respectively, by constructing and solving a system of linear equations. In order to verify the superiority of NLDM, a case of slope reinforced by a lattice beam was introduced in this paper, and the load distribution of the nodes under the design condition was carried out based on both methods. Then, the deflections at the nodes of the lattice beam resting on the Winkler foundation, loaded with the known loads, were analyzed by the superposition method. The results of the deformation analysis showed that the deflections at the same nodes of the beams in both directions based on NLDM were almost equal, thus demonstrating the superiority of NLDM in terms of deformation compatibility. In addition, a comparative analysis of the theoretical bending moments of the lattice beam under the design and the actual working conditions based on both methods was also carried out. The results of the bending moment analysis showed that the bending moments of the cross beam differed significantly in the middle third of the beam length, while the bending moments of the vertical beams differed significantly at the beam sections where the maximum bending moments are located, and the theoretical bending moments under the actual working condition were in relatively good agreement with the measured values. Consequently, NLDM for the lattice beam was self-consistent in terms of the deformation compatibility at the node, and therefore the introduction of this new method provides an important theoretical basis for the accurate internal force analysis of lattice beams.

Intelligent Knife Switch Contact Status Monitoring Based on Special-Shaped Beam Fiber Bragg Grating Electromechanical Sensor

To ensure the safety of people’s lives and property, the accurate measurement of various small vibrations is of great significance. Using gratings as sensitive components to make optical fiber sensors is a kind of electromechanical vibration measurement device with rapid development. In this study, a special-shaped beam Fiber Bragg Grating (FBG) electromechanical vibration sensor with sensitized grooves is proposed based on equal-strength cantilever beams. The composition and implementation principle of FBG sensing system are expounded, and how to realize the signal induction of FBG under vibration conditions is further analyzed. According to the intrinsic relationship between sensitivity coefficient and natural frequency in vibration sensor, the sensor head structure composed of structural parameters, such as equal-strength beam length of 73 mm, bottom width of 14 mm, and thickness of 5 mm, is finally selected. With the help of ANSYS software to calculate the natural frequency of the sensing head as a theoretical reference value, and SS304 stainless steel is selected as the cantilever beam to obtain a good vibration sensing effect. In the test, the acceleration is set to 0.35 G, and the pulse generates a sinusoidal signal of 0–10000 Hz. The natural frequency of the sensing head is 182 Hz, and the sensitivity is 100 mV/G, which is only small error with the theoretical analysis value calculated by ANSYS. The acceleration of the sensing head is changed, and different degrees of vibration are generated. The results show that the change of output center wavelength has a linear relationship with the acceleration change. The introduction of sensitized grooved special-shaped beams helps to improve the sensitivity of the device to perceive vibration. It is used for the monitoring of the contact status of the intelligent knife switch. The results show that the designed photoelectric grating electromechanical sensor measurement has good repeatability, and the wavelength of the reflection interrogator will suddenly increase and decrease rapidly with obvious regularity.

Nondiffracting beam length adjustment by using 3-bit coding metasurfaces

In this paper, a nondiffracting beamforming scheme employing 3-bit coding metasurfaces to adjust the beam lengths is proposed. The 3-bit coding is implemented with a four-layer phase control unit whose phase can be adjusted by tuning the side length of the metal square. Simulation and measured results show that the electric field distributions generated by the metasurface is independent of the polarization of the incident wave due to the central symmetry of the structure. Experimental results are provided which verifies the feasibility of the proposed scheme in adjusting the nondiffracting beam lengths. A relative error as small as 6.0% in the beam lengths is observed, and all results prove the proposed 3-bit coding metasurfaces can be applied to generate different nondiffracting beam lengths.

Use of the Airy beam to extend the micro-hole measurement range of an OCT system

Optical coherence tomography (OCT) has the advantage of high precision in measuring micrometre-scale precision structures, but its measurement range is limited by the correlation with Rayleigh length of Gaussian beam. Therefore, this study used the Airy beam to extend the focal depth of the OCT system. The system’s coupled power was increased by 7.34 times when the sample position was at an optical defocus of 3 mm. Measurements of the resolution plate and silicon wafer sample showed that Airy beam OCT had a lateral resolution of 7.4 μm and the focal depth was >6 mm. While the focal depth of the Gaussian beam OCT with the equivalent lateral resolution was less than 1 mm. This improved OCT system demonstrates significant potential for sample measurements at large aspect ratios in the industrial surface detection field.

Dynamic Volumetric Imaging of Mouse Cerebral Blood Vessels In Vivo with an Ultralong Anti-Diffracting Beam.

Volumetric imaging of a mouse brain in vivo with one-photon and two-photon ultralong anti-diffracting (UAD) beam illumination was performed. The three-dimensional (3D) structure of blood vessels in the mouse brain were mapped to a two-dimensional (2D) image. The speed of volumetric imaging was significantly improved due to the long focal length of the UAD beam. Comparing one-photon and two-photon UAD beam volumetric imaging, we found that the imaging depth of two-photon volumetric imaging (80 μm) is better than that of one-photon volumetric imaging (60 μm), and the signal-to-background ratio (SBR) of two-photon volumetric imaging is two times that of one-photon volumetric imaging. Therefore, we used two-photon UAD volumetric imaging to perform dynamic volumetric imaging of mouse brain blood vessels in vivo, and obtained the blood flow velocity.

Novel graph for an appropriate cross section and length for cantilever RC beams

Abstract Whether the design is done manually or by software, the designer will have difficulty choosing the economic and strength cross section. The designer, in this case, either relies on their experience or resorts to the method of trial and error. Especially for Cantilever beams with a long span as a result of risk deflections, it is exposed. The current theoretical study was performed on rectangular concrete cross sections of different dimensions and subjected to uniformly distributed loads. Based on a previous study, the sections are reinforced with a specific reinforcement ratio. Through an algorithm, Python 3.4 software, and an output file, the permissible deflections for each cross section were calculated according to the ACI 318M-19. Finally, the authors could draw a graph to choose the appropriate cross section for each required beam length in less time and effort.

Theoretical thermal damping vibration analysis of functionally graded viscoelastic Timoshenko microbeam with integral nonlocal strain gradient model

In this work, nonlocal strain gradient integral model is applied to investigate the free damping vibration analysis of functionally graded (FG) viscoelastic Timoshenko microbeam with immovable boundary conditions in thermal environment. The microbeam is assumed to be viscoelastic and modeled by Kelvin–Voigt model. The differential governing equations and corresponding boundary conditions are derived with the Hamilton’s principle. Combining nonlocal strain gradient integral model and Kelvin–Voigt viscoelastic model, the integral constitutive equations of nonlocal stress with thermal effect are derived and then converted into differential form plus constitutive constraints. The size-dependent axial force due to thermal expansion is explicitly derived through the immovable boundary conditions. The bending deflection and moment, cross-sectional rotation as well as shear force are explicitly derived with Laplace transformation for linear thermo-elastic vibration. Taking into account the boundary conditions as well as constitutive constraints, one gets a nonlinear equation with complex coefficients, from which one can determine the complex characteristic frequency. A two-step numerical method is proposed to solve the elastic vibration frequency and damping ratio. The influence of length scale parameters, viscos coefficient, FG index, thermal effect, vibration order and ratio between beam length and thickness on the vibration frequencies and damping ratio is investigated numerically for FG viscoelastic Timoshenko microbeams under different immovable boundary conditions.

Thermal vibration of perforated nanobeams with deformable boundary conditions via nonlocal strain gradient theory

Abstract Due to nonlocal and strain gradient effects with rigid and deformable boundary conditions, the thermal vibration behavior of perforated nanobeams resting on a Winkler elastic foundation (WEF) is examined in this paper. The Stokes transformation and Fourier series have been used to achieve this goal and to determine the thermal vibration behavior under various boundary conditions, including deformable and non-deformable ones. The perforated nanobeams’ boundary conditions are considered deformable, and the nonlocal strain gradient theory accounts for the size dependency. The problem is modeled as an eigenvalue problem. The effect of parameters such as the number of holes, elastic foundation, nonlocal and strain gradient, deformable boundaries and size on the solution is considered. The effects of various parameters, such as the length of the perforated beam, number of holes, filling ratio, thermal effect parameter, small-scale parameters and foundation parameter, on the thermal vibration behavior of the perforated nanobeam, are then illustrated using a set of numerical examples. As a result of the analysis, it was determined that the vibration frequency of the nanobeam was most affected by the changes in the dimensionless WEF parameter in the first mode and the changes in the internal length parameter when all modes were considered.

Evaluation of transfer length of CFRP tendon in pretensioned concrete beam using embedded FBG sensors

This study aimed to determine the transfer length of pretensioned concrete beams strengthened with carbon fiber-reinforced polymer (CFRP) using a fiber Bragg grating (FBG) sensor. The transfer length is the distance along the tendon that is critical to ensuring effective prestressing force and structural capacity of the concrete beam. Typically, electric strain gauges are used to measure the transfer length, but they can produce measurement errors due to installation errors and data noise. In this study, an FBG sensor was embedded in a CFRP tendon instead of a strain gauge, enabling accurate measurements of tendon strain and transfer length.