Beam Loading Research Articles

Разрушение хрупких балок при антисимметричном четырехточечном изгибе

The nucleation of cracks in structural elements during their service life is due to the degradation of the material or the presence of hidden defects. The structure therefore loses its original load-bearing capacity and fails under significantly lower external loads. As a rule, the fracture of structures due to crack growth occurs under mixed loading. In this paper, an eccentric beam of rectangular cross-section with an edge crack subjected to antisymmetric four-point loading is considered. By changing the position of the crack relative to the center of the beam, it is possible to obtain the entire range of mixed fracture modes: I+II, pure I and pure II modes. Using the finite element method, stress intensity coefficients for modes I and II of failure, as well as T-stresses, were obtained for different geometric parameters of the beam and different loading conditions. The length of the crack, its position relative to the beam center, and the length of the short span were varied. The methods commonly used for calculating T-stresses were analyzed. In the element closest to the crack tip, strong displacement oscillations, not mentioned in the literature, are observed, therefore to determine T-stresses with the highest possible accuracy it is suggested to calculate them from displacements, cutting off the 3-4 nodes closest to the crack tip. Experimental studies of the fracture toughness of ebonite in a mixed mode were carried out. For each type of loading and geometry, 3-5 identical specimens were tested. The tests were carried out under static load until the specimens were completely destroyed. In all experiments, the crack initiation angle and critical load were recorded. Six failure criteria were used to predict both failure direction and critical load: the generalized maximum tangential stress criterion, the extended maximum tangential strain criterion, the generalized strain energy density criterion, the generalized maximum averaged stress criterion, the maximum elastic energy release rate criterion and the generalized maximum elastic energy release rate criterion. The results obtained demonstrate good agreement between the experimental values of critical loads and the numerical calculations. The error in determining the crack initiation angle does not exceed 5%. Considering that the experimental results agree with the predictions of failure criteria for the beam subjected to antisymmetric four-point bend loading, this type of a beam specimen can be used to study mixed-type fracture in the elements manufactured from engineering materials, such as, for example, plexiglass, ebonite, and getinax.

Expansion Characteristics and Shear Behavior of Reinforced Concrete Beams Under Non-Uniform Expansion Induced by Alkali-Silica Reaction.

Alkali-silica reaction (ASR) is an important factor that seriously affects the durability of reinforced concrete (RC) structures. The current research on alkali-aggregate mainly focuses on the deterioration mechanism of materials and the mechanical properties of standard specimens. However, there is a gap in the field of research on the effect of alkali-aggregate damage on the level of RC structures. In this study, five RC beams were tested, and the depth and location of alkali solution immersion were used as the test variables, with the aim of investigating how the steel reinforcement suppresses the expansion caused by ASR and evaluating the shear behavior of RC beams after non-uniform ASR damage. The results of the study showed that immersion in an alkali solution and an increase in immersion depth accelerated the rate of expansion development, while steel reinforcement inhibited the rate of expansion development. Compared with undamaged RC beams, ASR initially generates expansion stresses within the concrete, which increase the cracking and yield loads of RC beams and delay the cracking of RC beams, and ASR reduces the ultimate load-carrying capacity and ductility of RC beams due to the disruption of the concrete microstructure. Finally, a chemo-mechanical analysis method is proposed based on experimental results, which incorporate an ASR expansion model and a pore mechanics model. The efficacy and precision of this model are validated through comparison with experimental results.

A geometrical morphology-enhanced computer vision approach for structural health assessment

Images contain abundant valuable information about the health state of the photographed infrastructures. However, local defects are mostly detected in vision-based structural health monitoring (SHM), while global safety and risk at a larger scale are rarely assessed. To fill up this gap, a geometrical morphology-based image analysis framework is developed for structural global health assessment. A structured random forest edge detector is adopted to extract the edges in an image, and the morphological operations are subsequently used to highlight the edge skeleton, from which the continuous line segments are estimated by the Hough transform. Via these operations, the intrinsic geometrical features of different structures can be extracted and highlighted in an unsupervised manner and at a real-time speed. A global health indicator, line-to-edge ratio, is finally calculated to assess the structural state according to the fact that the deterioration of material will introduce abundant irregular edges in an image and break the lines at the structure boundaries. A destructive beam loading test video and a set of images from different bridge piers are analyzed for verification. The images are taken from arbitrary, uncontrolled, and backlighting views. The results show that the proposed framework can correctly quantify the health condition and detect the occurrence of damage for the in-field infrastructures.

Study of the Impact of Loads on the Deformation of Building Structures using Differential Equations

The paper investigates the influence of different types of loads on the deformation of building structures, particularly beams, using second-order differential equations that allow modeling deformation processes. For this purpose, we considered two beam deflection equations under concentrated and distributed loads. Several experiments were conducted under different geometrical conditions (variable parameters of the beam cross-section, length, and loads). The solutions were studied using graph-analytical methods: constructing a graph of solutions reflecting the system's behaviour, a hodograph allowing tracking of additional nuances of the studied process, and amplitude and phase-frequency characteristics. The influence of conditions on the nature of system behavior is determined. The study's results can be used to optimise design solutions in construction.

Numerical Investigation on Improving Shear Strength of RC Beams with Various Web Opening Shapes Using Pre-Stressed Fe-SMA Bars

The presence of web openings in the shear span significantly impacts the structural behavior of reinforced concrete (RC) beams, affecting both shear capacity and crack propagation. This study explores the feasibility of strengthening web openings in the shear zone of RC beams using iron-based shape memory alloy (Fe-SMA) bars through numerical analysis with ABAQUS software. The investigation considered various web opening shapes; diamond, circular, and square strengthened with pre-stressed Fe-SMA bars. Results showed that web openings notably decrease the ultimate loads of beams by 53%, 44%, and 39% for square, circular, and diamond shapes, respectively. However, pre-stressed Fe-SMA bars enhanced the shear capacity of beams with unstrengthened web openings by approximately 60%, making their behavior comparable to solid beams. The proposed strengthening technique was most effective for diamond web openings, nearly restoring both shear strength and stiffness, while circular openings recovered nearly 90% of shear capacity and square openings about 75%. Additionally, Fe-SMA bars effectively controlled cracking at the corners of the openings. This study highlights the importance of strengthening web openings in RC beams, especially in shear zones, and provides significant insights into enhancing such beams, contributing to safer structural designs. Further laboratory experiments are recommended to validate and extend these numerical findings.

Flexural Behavior of BFRP Bar-Recycled Tire Steel Fiber-Reinforced Concrete Beams.

This research advocates for the use of basalt fiber-reinforced polymer (BFRP) bars and recycled tire steel fibers to reinforce concrete beams. Six concrete beams were constructed using different volume contents of recycled tire steel fibers (0, 0.5%, 1.0%, 1.5%) and BFRP reinforcement ratios (0.48%, 0.75%, 1.08%). Mechanical properties tests were conducted to investigate the flexural characteristics and failure modes of beams utilizing the non-contact full-field strain displacement measuring technology-digital image (3D-DIC) technology. The recycled tire steel fiber (RTSF) improves flexural performance, which contributes to inhibiting crack propagation, reducing flexural deformation, and improving the first cracking and ultimate loading capacities. Under the same reinforcement ratio, in comparison to ordinary BFRP beams, the cracking load of BFRP-RTSF beams increased by 17.73%, 23.76%, and 42.94%, respectively, and the ultimate bearing capacity increased by 4.03%, 5.85%, and 13.21%, respectively. In addition, a modified calculation model of bearing capacity considering RTSF tensile strength is proposed. The predicted values of BFRP-RTSF beams match well with the experimental values.

Response of the beam-base system to a sudden change in the modulus of elasticity of the beam material

A mathematical model of the dynamic process excited in a statically loaded beam-base system by a sudden change in the beam's bending rigidity is constructed. It is assumed that either the beam material's elastic modulus or the beam's cross-sectional axial moment of inertia changes when it is rotated by 90 degrees relative to the beam's longitudinal axis while maintaining the load direction. Forced vibrations are investigated by decomposing the load and static deflection of the initial beam into rows according to the beam's natural vibration modes with changed parameters. Natural frequencies and corresponding displacement and bending moment modes are determined by the initial parameter method using a vector-matrix representation of the states of arbitrary beam sections. Numerical results are provided to demonstrate the capabilities of the approach.

Experimental investigation and analytical model for the shear behavior of composite beams with prefabricated U‐shaped RPC permanent formworks

AbstractThis study aimed to investigate the shear performance of composite beams with prefabricated U‐shaped reactive powder concrete (RPC) permanent formworks with normal strength concrete poured inside. Three‐point bending tests were performed on eight composite beams with prefabricated U‐shaped RPC‐reinforced formworks and one reinforce concrete beam. Additional parameters, such as the stirrup spacing, shear span ratio, and inner core concrete strength, were evaluated. The test results indicated that the prefabricated U‐shaped RPC permanent formworks increased the shear capacity of the composite beams. Under the same configuration, the bending cracking load, stirrup yield load, and peak load of the composite beams increased by 51.54%, 88.02%, and 78.38%, respectively. An analytical model was proposed to predict the shear strength of composite beams with prefabricated U‐shaped RPC formwork and validated using the experimental results.

Flexural Behavior of Zero Coarse Aggregate Concrete Beams reinforced with Glass Fibers: An Experimental Comparative Study

In recent decades, engineers have focused on finding solutions to reduce the weight of concrete structures. Undoubtedly, the coarse aggregate weight in concrete is important. This study examined the flexural behavior of zero coarse aggregate concrete with Glass Fiber (GF) added to the steel reinforcement. Also, normal-weight fine aggregate was substituted with autoclaved aerated concrete (Thermostone) by 50% and 75% by weight. The process involved comparison of the test results of two groups. The first group comprised normal reinforcement Lightweight Aggregate Concrete (LWAC), while the second group comprised fiber-reinforced LWAC and a specimen of Lightweight (LW) mortar. Fiber addition boosts energy absorption and slows down the rapid development of crack formation. GFs by 1.5% of concrete weight were added. The results revealed a decrease in the failure load of beams reinforced with GF compared to those reinforced with steel bars. The decrease amounted to 54%, 50%, and 59% for aggregate replacement percentages of 0%, 50%, and 75%, respectively. Replacing steel reinforcement with GF reduced the ultimate load by almost half. All beams with steel reinforcement experienced flexural failure, while the beams with GF reinforcement underwent shear failure.

Flexural behavior of steel/GFRP reinforced concrete beams having layered sections integrated with normal and rubberized concrete

Rubberized concrete (RuC) is one of the possible sustainable solutions to the problem of quickly disposing of old tires. This study introduced a new coating material (metakaolin, MK) for crumb rubber (CR) at a controlled temperature to avoid decreasing the RuC mechanical properties. Additionally, to prevent the possible reduction in the RuC strength on the RC beam behavior, the functionally graded material (FGM) approach was applied (layered beam section with RuC at 67 % of the beam section and normal concrete (NC) at the top one). The influence of RC beams on the tensile reinforcement (glass fiber-reinforced polymer (GFRP) instead of steel) was also examined. The experimental investigation comprised several concrete combinations: conventional concrete and RuC integrated uncoated and MK-coated CR replacing sand with percentages (0 %, 5 %, 15 %, and 25 %). The mechanical characteristics of concrete mixtures under compression and splitting tension tests were examined. Moreover, fourteen RC beams were experimentally loaded in flexural to investigate the impact of proposed parameters on the beam response. Following that, Finite Element (FE) modeling was carried out to examine the influence of the additional parameters on the RC beams' performance. The results demonstrate a notable improvement in the compressive strength of concrete by 17.4 % and a 25.4 % rise in split tensile strength due to the use of MK-coated CR compared to the uncoated CR. The impact of MK-created CR was more prominent in increasing the GFRP RC beam loads than the steel RC ones. In addition, using the FGM approach could eliminate the CR effect and exhibit nearly the same NC beam load.

Flexural behavior of GFRP and steel bars reinforced lightweight ultra-high performance fiber-reinforced concrete beams with various reinforcement ratios

The synergistic operating mode of the concrete matrix and the reinforcing bar determines the dependability of a structure in complicated environments. The objective of this research has been to provide a comprehensive analysis of the flexural behavior exhibited by lightweight ultra-high performance fiber-reinforced concrete (LUHPC) beams that have been reinforced with high-strength steel bars (HRB500) and glass fiber-reinforced plastic (GFRP) bars. LUHPC was used as the matrix material with a compressive strength of 120 MPa and a density of 2050 kg/m3. This study focused on examining the impact of different reinforcement ratios (0.59 %, 1.27 %, and 1.94 %) and reinforcement types (GFRP and HRB500 bars) about the flexural performance of LUHPC beams under four-point bend loading. As demonstrated by the results of experiments, GFRP-reinforced LUHPC (G-LUHPC) beams with higher reinforcement ratios have higher peak loads, flexural stiffness, and cracking loads but lower ductility. Compared with steel-reinforced LUHPC (S-LUHPC) beams, the bending strength of G-LUHPC beams was reduced by 18.2 %, 24.2 %, and 6.7 %, the peak deflection was increased by 166.5 %, 24.8 %, and 56.9 %, and stiffness degradation and crack development were rapid. After comparing the test results with the current commonly used specifications, it was seen that the codes could better predict the cracking moments and the deflections under service loads of G-LUHPC beams. However, it was noted that both the ultimate moments and the corresponding mid-span deflections were greatly underestimated.

Investigation of The Effect of Radius of Curvature on Buckling Load in Thin-Walled Beams

This study examines the effect of curvature radius on the buckling behavior of thin-walled beams, which are commonly used in aerospace, automotive, and structural engineering due to their high strength-to-weight ratios. The buckling phenomenon, which represents a critical failure mode for thin-walled hat-shaped structures, was investigated under axial loading through the utilization of numerical methods. A nonlinear analysis was conducted using ANSYS Workbench to model three distinct geometries with varying curvature angles and identical dimensions. The models were subjected to analysis in order to ascertain the critical buckling loads and reaction forces at a displacement of 1 mm, with a particular focus on both nonlinear and post-buckling behavior. Given its importance in structural applications, Aluminum Alloy NL was selected as the material. The eigenvalue buckling analysis identified the critical loads for the first ten modes, revealing that models with higher curvature angles demonstrated more stable buckling characteristics, whereas those with smaller angles were more prone to local deformation. A post-buckling analysis was conducted to ascertain the nonlinear load-bearing capacities of these structures.

Flexural Behavior of Innovative Glass Fiber-Reinforced Composite Beams Reinforced with Gypsum-Based Composites.

Glass Fiber-Reinforced Composite (GFRP) has found widespread use in engineering structures due to its lightweight construction, high strength, and design flexibility. However, pure GFRP beams exhibit weaknesses in terms of stiffness, stability, and local compressive strength, which compromise their bending properties. In addressing these limitations, this study introduces innovative square GFRP beams infused with gypsum-based composites (GBIGCs). Comprehensive experiments and theoretical analyses have been conducted to explore their manufacturing process and bending characteristics. Initially, four types of GBIGC-namely, hollow GFRP beams, pure gypsum, steel-reinforced gypsum, and fiber-mixed gypsum-infused beams-were designed and fabricated for comparative analysis. Material tests were conducted to assess the coagulation characteristics of gypsum and its mechanical performance influenced by polyvinyl acetate fibers (PVAs). Subsequently, eight GFRP square beams (length: 1.5 m, section size: 150 mm × 150 mm) infused with different gypsum-based composites underwent four-point bending tests to determine their ultimate bending capacity and deflection patterns. The findings revealed that a 0.12% dosage of protein retarder effectively extends the coagulation time of gypsum, making it suitable for specimen preparation, with initial and final setting times of 113 min and 135 min, respectively. The ultimate bending load of PVA-mixed gypsum-infused GFRP beams is 203.84% higher than that of hollow beams, followed by pure gypsum and steel-reinforced gypsum, with increased values of 136.97% and 186.91%, respectively. The ultimate load values from the theoretical and experimental results showed good agreement, with an error within 7.68%. These three types of GBIGCs with significantly enhanced flexural performance can be filled with different materials to meet specific load-bearing requirements for various scenarios. Their improved flexural strength and lightweight characteristics make GBIGCs well suited for applications such as repairing roof beams, light prefabricated frames, coastal and offshore buildings.

Assessment of impaired reinforced concrete dapped‐end beams: An analytical approach

AbstractReinforced concrete dapped‐end beams (DEBs) represent a unique structural type with the presence of recessed ends. The beam configuration is ideal for structural connections. However, the recessed area is structurally a disturbed region, and is vulnerable to embedded reinforcement deterioration. This study explored the potential of strength assessment of impaired DEBs via an analytical approach. A kinematics based model (KBM) was opted, and it was subjected to significant modifications to account to suit with distinct structural defects that were common to DEBs. The extended model (EKBM) was validated using experimental results available for eight beams. Both the load and failure mode predictions from the EKBM were found to be more accurate than those from the KBM, where the EKBM prediction offset was within a fair range of −23% to 15%. Furthermore, a parametric analysis was carried out to investigate the sensitivity of shear reinforcement deficiency and of reinforcement corrosion in the joint region on the beam load capacity. It revealed that the first two shear links were the most critical links. The load reduction was linearly proportional to the area reduction of reinforcement due to corrosion, however, the trend deviated from that at some combined deficiencies. The corroded reinforcement length was rather insensitive to the resulting beam strength.

New operation analysis method for vacuum tube driving a tuned cavity

The rf system of China Spallation Neutron Source (CSNS) Rapid Cycling Synchrotron (RCS) utilizes vacuum tubes to drive the ferrite-loaded cavities. Ensuring stable tube operation in the rf system is crucial for the acceleration of high-intensity beams, as any instability may impede further increases in beam power. Therefore, the operation of the vacuum tube under heavy beam loading has attracted significant attention, particularly in the case of CSNS-II RCS, where the circulating beam current is expected to reach up to 15.25 A, imposing a substantial burden on the vacuum tube for beam loading compensation. Thus, a comprehensive analysis of tube operation is imperative. However, current methods for the tube operation analysis are developed based on wideband rf cavities, which are inadequate when the load of the tube is a narrowband ferrite-loaded cavity equipped with a tuning system. The presence of a tuning system renders the modeling method for wideband rf cavities inapplicable for ferrite-loaded cavities. Therefore, the development of a new method is necessary. This paper introduces a novel method for analyzing operation of vacuum tube driving a tuned cavity. The effectiveness of the method is validated by comparing the analysis results with measurements under beam loading conditions. Furthermore, an estimation of tube operation under 500 kW beam loading for CSNS-II is provided. Published by the American Physical Society 2024

Research on ultrasonic synchronous detection method for material residual stress and thickness

Being limited to the different transmission and reception modes and detection signals of the critical refracted longitudinal wave method for stress measurement and the perpendicular incident echo method for thickness measurement, it is necessary to use different probes and equipments when simultaneously measuring stress and thickness. For this difficulty, the acquisition frequency and the number of bits are taken as the research object to realize the optimization of the echo signal. By combining FEM simulations with Comsol software with experimental research, the effects of probe incidence angle, probe spacing, and temperature on ultrasonic waves are investigated, and the relationship between probe spacing and the stress coefficient of measured component (K) is analyzed. A novel ultrasonic synchronous detection method for residual stress and thickness is proposed. This method is based on an integrated transmit-receive probe with oblique incidence, utilizing critical refracted longitudinal wave (LCR wave) for stress detection and synchronously generated transverse waves for thickness measurement. For the first time, a formula for ultrasonic thickness measurement based on inclined incidence is derived. Using self-developed equipment, ultrasonic testing experiments on step test block and cantilever beam loading device were conducted to verify the accuracy and precision of the proposed synchronous detection method for stress and thickness. This method has significant application prospects in the inspection or online monitoring of pressure vessels concerned with fatigue and corrosion performance.

A simple but accurate FEM for lateral-torsional buckling loads of mono-symmetric thin-walled beams considering pre-buckling effects

This study intends to present a simple but accurate FE buckling analysis procedure in order to determine lateral-torsional buckling (LTB) loads of mono-symmetric steel beams considering pre-buckling effects. For this, a nonlinear co-rotational FEM for lateral-torsional post-buckling of a thin-walled beam system with non-symmetric cross sections is summarized in which all displacement parameters are defined at centroid. After that, an iterative LTB analysis method is newly proposed with consideration of in-plane deformations due to external loads. Through numerical examples, it is demonstrated that buckling solutions by this method are very well matched with those by lateral post-buckling analysis of the steel beam with lateral imperfections. Finally, numerical results on LTB of simple/cantilever beams under conservative moments, simple beams under gradient moments, simple beams under eccentric compression, a cantilever beam with an un-symmetric channel section, and a cantilever right-angle frame with I-section are presented using conventional LTB, iterative LTB, and post-buckling analysis methods.

Experimental, analytical, and numerical investigation on flexural behavior of the gradient UHPC-NC composite beams

To enhance the deformation resistance of concrete beams, the flexural behavior of eight gradient ultra-high performance concrete (UHPC)-normal concrete (NC) composite beams was experimentally studied. The effects of different gradients and fiber types on the deflection of the gradient UHPC-NC composite beams were investigated, and a deflection calculation method for the composite beams was proposed. Finally, numerical simulations were conducted on the basis of the cohesion models. Results indicate that the gradient UHPC design significantly improves both the loading-bearing and deformation capacity of the composite beams. The cracking load of the gradient composite beams with steel fiber-UHPC at the bottom layer is much higher than that of the beams with basalt fiber-UHPC, and the number of cracks in the pure bending section of the beams with steel fiber-UHPC at the bottom layer is remarkably less than that of the beams with basalt fiber-UHPC at the bottom layer. However, their ultimate capacities were comparable, indicating that steel fibers can effectively improve the fracture toughness of UHPC. The predicted deflection of the gradient UHPC-NC composite beams agrees well with the test results, indicating the accuracy of the proposed deflection model. The bearing capacity and deflection obtained from the numerical simulation also align well with the test results.

Study on Dynamic Factors of Damped Beam Members Under Exponential Attenuation Loading

Blast loading is characterized as an impact loading with exponential attenuation, while damping serves as an intrinsic parameter that affects the vibration effect of beam members. The linear attenuation for simplified blast loading and undamped situation for beam members is often adopted by most scholars or codes for the calculation of dynamic factors. These assumptions that do not conform to the actual situation can lead to deviations in the results of the dynamic factor. In this study, the implicit solutions for the dynamic factors of both flexible and rigid beam members were derived by the exponential attenuation loading and damping of beam members. The dynamic response verification of an H-shaped steel beam blast test was completed using LS-DYNA software. The comparison calculation of the theoretical solutions of dynamic factors in this paper with the Chinese blast-resistant design code and finite element simulation was carried out. The results show that the dynamic factor will be higher when the blast loading is simplified to linear attenuation loading for undamped beams. The shape parameter of the exponential attenuation loading and the damping ratio of beam members both reduce the effect of the dynamic factor, with the damping ratio having a more significant effect.

Relativistic beam loading, recoil-reduction, and residual-wake acceleration with a covariant retarded-potential integrator

An algorithm is demonstrated that performs first-principles tracking of relativistic charged-particles. A covariant approach is used which relies on retarded vector potentials for trajectory integration instead of performing electromagnetic field calculations. When accounting for retardation effects, the peak vector potential and corresponding Lorentz force in the direction of travel increase asymptotically for high-β particles. This produces a very strong field distribution at small angles from the particle’s direction of travel, which can result in considerable change in momentum when approaching a conducting or charged object. We study these dynamics using protons and electrons at relativistic energies passing through apertures in conducting surfaces, where substantial energy shifts are observed for particles passing within roughly 10μm of the aperture boundary.We also simulate breaking a test particle’s line of sight with a conductor or other charged body. After this instant, the test particle continues to accelerate due to residual fields, but no longer produces an opposing force on any charged or conducting object; thus any recoil on the enclosing structure is effectively reduced. In this test, a 1% energy gain is observed for an 85 MeV electron traversing its reflected wake after having conducting plate in its path screened by a dielectric object.We then incorporate a micro-scale dielectric laser acceleration (DLA) device into our simulations. Compared with a 2 mm DLA on its own, we find a factor of two increase in energy gain when adding a series of conducting-surface choppers.