Four-point Bending Research Articles

Research on Fatigue Characteristics and Prediction of Large-Particle Asphalt Mixtures Based on Four-Point Bending Tests

Research on Fatigue Characteristics and Prediction of Large-Particle Asphalt Mixtures Based on Four-Point Bending Tests

Flexural behaviour of built-up I-shaped bamboo scrimber beams: experimental tests and design method

ABSTRACT This paper presents the flexural behaviour of built-up I-shaped bamboo scrimber beams under four-point bending. Ten bamboo scrimber beams were tested, employing different types of connections between the web and flanges. The load-deflection relationship, failure mode and load-slip relationship of beams were obtained through experimental tests. Besides, the measured strains of bamboo scrimber in various regions were used to analyse the flexural mechanisms of I-shaped beams. Test results showed that the beam with a glued connection exhibited debonding at the web-flange interface, hindering the development of flexural capacity of the beam. By using self-tapping screws or bolted steel angles to strengthen the connection, the slip between the web and flanges was considerably reduced, resulting in the increased flexural capacity of beams. The rupture of the bottom flange near the concentrated point load led to the final failure of strengthened beams. The design method for mechanical fastened glulam beams in Eurocode 5 was adopted to assess the flexural capacity of bamboo scrimber beams. Comparisons between experimental results and calculated results per Eurocode 5 indicate that the method is capable of predicting the flexural resistances of I-shaped bamboo scrimber beams with reasonably good accuracy.

Investigating the efficiency and reliability of different lap-splice configurations in NSM BFRP rods for strengthening RC beams

The use of near-surface mounted (NSM) fiber-reinforced polymer (FRP) reinforcement has shown great promise for flexural and shear strengthening of reinforced concrete (RC) members. However, the continuity of NSM FRP rods is often interrupted due to length constraints, necessitating lap splices to transfer forces between spliced rods. The performance of lap splices depends on design configuration factors, including anchorage shape, splice length, and connection method. This research describes an experimental investigation into the bond behaviour and failure mechanisms of various lap splice designs for NSM basalt FRP (BFRP) rods in RC beams. The parameters investigated were end anchorage shape (straight or Embedded Through-Section (ETS) anchors), and connection type (overlay rods or face-to-face with FRP sheet wrap). A total of 8 simply supported RC beams strengthened with different NSM BFRP lap splice configurations were tested under four-point bending. The load-deflection response, strain distribution, and failure modes were evaluated. Test results showed that beams with NSM FRP rods with ETS anchors exhibited higher bond strength and ductility than face-to-face connections. The outcomes of this study can help optimize lap splice design and detail provisions for NSM FRP systems in future strengthening applications.

Manufacture and structural performance of modular hybrid FRP–timber thin-walled beams

Developed to fulfil the rising societal demand for sustainable constructions, Modular Hybrid Fibre-reinforced polymer-Timber (MHFT) thin-walled sections are lightweight timber-based composite structures manufactured through a modular assembly method. Motivated by prior research on MHFT columns characterized by efficient load-carrying capacity, this paper conducted a thorough investigation into the manufacture and structural performance of MHFT beams. Experimental, analytical and numerical studies were conducted for beams subjected to four-point bending load, with parametric analyses of four distinct beam types to investigate design parameter influence on flexural performance. The experimental study demonstrated the structural efficacy of MHFT beams, as evidenced by increased moment of inertia and enhanced resistance to edge split failures, as compared to previously studied folded HFT beams. MHFT beams also exhibited a comparable strength-to-weight ratio compared to their structural steel counterparts. Both numerical and analytical methods provided acceptable predictions for flexural strength and material failure modes of MHFT beams, with strength predictions varying by less than 22% compared to experimental averages. The numerical method reliably predicted flexural stiffness and load–displacement responses, with discrepancies within 12%. The parametric analyses further revealed that the thickness of glass fibre-reinforced polymer (GFRP) layers and cross-sectional geometric profile were most strongly influenced beam parameters. Specifically, the use of 3-layer GFRP material resulted in a strength increase of over 17% and a stiffness increase of over 19% compared to 1-layer material, effectively mitigating the occurrence of local buckling and edge split failures.

Investigation of Variability of Flaw Strength Distributions on Brittle SiC Ceramic

The present paper investigates flaw strength distributions established using various flexural tests on batches of SiC bar test specimens, namely four-point bending as well as three-point bending tests with different span lengths. Flaw strength is provided by the elemental stress operating on the critical flaw at the fracture of a test specimen. Fracture-inducing flaws and their locations are identified using fractography. A single population of pores was found to dominate the fracture. The construction of diagrams of p-quantile vs. elemental strengths was aimed at assessing the Gaussian nature of flaw strengths. Then, empirical cumulative distributions of strengths were constructed using the normal distribution function. The Weibull distributions of strengths are then compared to the normal reference distributions. The parameters of the Weibull cumulative probability distributions are estimated using maximum likelihood and moment methods. The cumulative distributions of flexural strengths for the different bending tests are predicted from the flaw strength density function using the elemental strength model, and from the cumulative distribution of flexural strength using the Weibull function. Flaw strength distributions that include the weaker flaws that are potentially present in larger test pieces are extrapolated using the p-quantile diagrams. Implications are discussed regarding the pertinence of an intrinsically representative flaw strength distribution, considering failure predictions. Finally, the influence of the characteristics of fracture-inducing flaw populations expressed in terms of flaw strength interval, size, dispersion, heterogeneity, and reproducibility with volume change is examined.

Experimental study on the flexural performance of FRP grid-reinforced ultra-high-performance concrete I-beams with different steel fiber contents

To adapt to harsh engineering environments, the use of structural components with fiber-reinforced polymer (FRP) grid-reinforced ultra-high-performance concrete (UHPC) is considered a new development trend. Twelve FRP grid-reinforced UHPC I-beams are fabricated to investigate the effects of the thicknesses of FRP grids (0 mm, 1 mm, 3 mm, and 5 mm) and the steel fiber contents of UHPC (0%, 1%, and 2%) on their flexural performance. Four-point bending tests are conducted to obtain the failure modes, load-deflection characteristics, and strain responses of each testing beam, and a simplified calculation method for cracking loading and flexural bearing capacity is proposed. The results reveal that the increase in FRP grid thickness, the ultimate load bearing capacity of FRP grid-reinforced UHPC structural beams increases and the ductility also can be enhanced. The presence of steel fiber effectively inhibits the cracking and increases the first cracking load of the beam during the test process, although its influence on the ultimate bearing capacity is limited. Besides, until to the cracking stage, there is no noticeable change in the tensile strain of the FRP grids as the applied load increases. It has been used to simplify theoretical calculations, which shows good agreement with the experimental results.

Age-dependent deflection analysis of high-volume fly ash RC beams: experimental and artificial neural network modelling

This research examines the influence of high-volume fly ash (HVFA) on reinforced concrete (RC) beam deflections over 180 days of continuous loading. The study comprises eight fly ash-based concrete mixes with varying fly ash ratios (0–60%). Experimental assessments were conducted on two load levels, corresponding to 25% and 50% of the initial cracking load. Thirty-two full-scale RC beams, each measuring 100 × 150 × 1800 mm, were fabricated for both load levels. Long-term deflections were monitored for all concrete mixes through sustained four-point bending tests at ages ranging from 1 to 180 days. A comparative analysis of the overall mid-span deflection between conventional and fly ash concrete RC beams was carried out against established design codes. It was determined that high-volume fly ash RC beams exhibited less creep and shrinkage deflection compared with conventional RC beams. Moreover, artificial neural network (ANN) modelling was also carried out to propose a significant model helpful in predicting the total deflection of RC beams containing any fly ash content and at any age of concrete. The present study offers valuable insights for engineers and designers, facilitating the evaluation of age-dependent deflection patterns in RC beams constructed with reinforced high-volume fly ash concrete.

Flexural strength of novel glass infiltrated monochrome and multilayer high yttrium oxide containing zirconia upon various sintered cooling rates.

The sintering technique and cooling strategy influence the strength of zirconia. This study examined the impact of altering the cooling rate of glass-infiltrated monolayer and multilayer 5 mol% yttria-partially stabilized zirconia (5Y-PSZ) on their strength. One-hundred eighty (180) specimens (width×length×thickness = 10×20×2mm) were prepared using monolayer (Mo: Cercon-xt) and multilayer (Mu: Cercon-xt ML) 5Y-PSZ. Randomly distributed specimens (n = 15/group) were sintered with traditional (T) versus glass infiltrated (G) technique and cooled down with different cooling rates: slow (S: 5°C/min), normal (N: 35°C/min), and fast (F: 70°C/min). Four-point bending test was used to measure flexural strength (σ). Microstructures were investigated by scanning electron microscope (SEM), energy dispersive spectroscopy (EDS), and X-ray diffraction (XRD). Three-way ANOVA and Tamhane comparisons were determined for a significant difference of σ (p<0.05). Weibull analysis was determined for Weibull modulus (m). The highest σ (MPa) was seen for GMuS (696.8 ± 69.8). Mo-PSZ and Mu-PSZ showed no significant difference in σ. G-sintering presented significantly higher σ (659.9 ± 79.3) than T-sintering (426.0 ± 63.7). S-cooling (560.9 ± 126.1) had the highest σ. The highest m-value was observed in GMuN (12.1 ± 3.8). A significant difference in σ was indicated due to cooling rates and sintering techniques (p<0.05). Glass infiltration significantly enhanced strength through elastic gradience. F-cooling reduced grain size, impaired grain boundary integration, and increased the tetragonal to monoclinic phase transition, significantly decreasing flexural strength in traditional sintering. Nevertheless, F-cooling was recommended for glass-infiltrated 5Y-PSZ to enhance strength while reducing processing time.

Effect of Composition Characteristics on Mechanical Properties of UHPMC Based on Response Surface Methodology and Acoustic Emission Monitoring.

Manufactured sand (MS) is a promising alternative aggregate to quartz sand (QS) in ultra-high-performance concrete (UHPC) in the preparation of ultra-high-performance manufactured sand concrete (UHPMC), which possesses the characteristics of high strength, low cost, and environmental friendliness. In this study, the effects of variable compositional characteristics including the water-binder ratio, the stone powder (SP) content, and the MS replacement ratio on the mechanical and flexural strength of UHPMC were compared and analyzed based on response surface methodology (RSM). Meanwhile, the damage characteristics of UHPMC during compressive and flexural stress were monitored and evaluated using acoustic emission (AE) technology. The results reveal that the compressive and flexural strengths of UHPMC are both negatively correlated with the water-binder ratio, while they are positively correlated with the MS replacement rate. They tend to firstly increase and subsequently decrease with the increase in the stone powder content. In the load-displacement curve of concrete with a high MS replacement ratio and a low water-binder ratio, the slope in the elastic stage is steeper, the stiffness is higher, and the bending toughness and ductility are also better. The specimens with a 10% to 0% stone powder content present a steeper elastic phase slope, a slightly higher stiffness, and superior ductility. The specimens with a low MS replacement ratio and a high water-binder ratio display earlier cracking and weaker resistance, and the destruction process is complex and very unstable. The damage mode analysis based on RA-AF shows that an increase in the MS replacement ratio and a decrease in the water-binder ratio can both reduce the tensile cracking of UHPMC specimens under a four-point bending test. Although 10% stone powder can marginally slow down crack growth, the failure mode is not significantly affected.

Study on flexural property of glass fiber-reinforced polymer reinforced wood–plastic composite panels

ABSTRACT Fiber-reinforced polymers (FRPs) and wood–plastic composites (WPCs) have broad application prospects with the advantages of recyclability, lightweight, and corrosion resistance. However, WPCs cannot be used for bearing structures because of their poor mechanical properties. In order to improve the mechanical properties of WPCs, this study proposed a glass fiber-reinforced polymer (GFRP) to reinforce the tensile zone of WPCs. The failure mode, ultimate bearing capacity, and deformation of the panels were studied by four-point bending tests and finite-element simulations. The results showed that the failure modes of the panels were a mainly flexural failure, flexural shear failure, and interface debonding, and the optimal thickness of GFRP improved the ultimate bearing capacity of the WPC panel by 205% and the deflection by 55%. Finite-element simulations of WPC reinforced with GFRP were carried out, and the densities of WPC and the angles of glass fiber layup were considered. The results showed that the higher the density of WPC, the better the strengthening effect of the structure, and the fiber layup angles had less effect.

Monitoring of static and vibration responses of laminated composite materials using integrated carbon nanotube fibers

Carbon nanotube fibers or yarns (CNTYs) are lightweight, stiff, strong, electrically, and thermally conductive fiber-like materials that exhibit a piezoresistive response and could be integrated in glass-fiber/epoxy laminated composite materials to measure strain and to detect damage. Aiming at extending the scope of previous studies, this work is about the piezoresistive response of CNTY sensors integrated in composite laminates of industrial interest, accounting for interactions between the CNTY and the typical heterogeneous, anisotropic surrounding media, including the effects induced by the curing process of the composite matrix. This study reports experimental results on the mechanical response of laminated composite materials under quasi-static and vibration loading monitored using integrated CNTY sensors. A combination of CNTY sensor configurations and experimental setups were used to monitor the deformation and strains among the various layers of the laminated composites. As the laminated composites were mechanically loaded under quasi-static four-point bending, the CNTY sensors captured instantaneously the deformation as demonstrated by the change in their electrical resistance. Also, as the laminated composites were subjected to sinusoidal loading at specific frequencies, the integrated CNTY sensors were able to capture the loading cycles exactly including durations and peaks. Integrated sensing using CNTYs may offer a highly adaptive, practical, and sensitive structural monitoring method for a variety of applications.

Identification of defects in underground structures using machine learning aided distributed fiber optic sensing

Despite the extensive use of distributed fiber optic sensing (DFOS) in monitoring underground structures, its potential in detecting structural anomalies, such as cracks and cavities, is still not fully understood. To contribute to the identification of defects in underground structures, this study conducted a four-point bending test of a reinforced concrete (RC) beam and uniaxial loading tests of an RC specimen with local cavities. The experimental results revealed the disparity in DFOS strain spike profiles between these two structural anomalies. The effectiveness of DFOS in the quantification of crack opening displacement (COD) was also demonstrated, even in cases where perfect bonding was not achievable between the cable and structures. In addition, DFOS strain spikes observed in two diaphragm wall panels of a twin circular shaft were also reported. The most probable cause of those spikes was identified as the mechanical behavior associated with local concrete contamination. With the utilization of the strain profiles obtained from laboratory tests and field monitoring, three types of multi-classifiers, based on support vector machine (SVM), random forest (RF), and backpropagation neural network (BP), were employed to classify strain profiles, including crack-induced spikes, non-crack-induced spikes, and non-spike strain profiles. Among these classifiers, the SVM-based classifier exhibited superior performance in terms of accuracy and model robustness. This finding suggests that the SVM-based classifier holds promise as a potential solution for the automatic detection and classification of defects in underground structures during long-term monitoring.

To Monitor Fracture Behaviors in Four-Point Cyclic Bending Tests of Low-Activated High Alumina Concrete and Standard Concrete RC Beams Using Acoustic Emission Technique

In this study, acoustic emission monitory (AE) was used to observe and evaluate the mechanical behavior of two kinds of RC beam members, made of low-activation concrete and normal concrete, by general four-point bending test and cyclic four-point bending test. During the loading, acoustic emissions due to cracking, shearing, rubbing, de-bonding or interlocking could be monitored and recorded using a real-time high sampling rate DAQ system and proper sensors; besides, beam displacement, cracking situation and loading were also measured simultaneously. The experiment goals included: (1) to observe the damage mechanisms of the beams under bending test and their corresponding AE performance; and (2) to observe the material fracture and corresponding AE in the beams under the cyclic bending test of 0.5Hz (periodic dynamic condition). After experiments, the fracture history of the beam under general loading test could be revealed through the comparison for the chronicled AE signal density and load/strain data. The damage on beam under the cyclic test could be analysed through the chronological comparison for the cumulative sum of AE signal counts obtained for different test periods and stages. Both the irreversibility on fracture mechanism (affected by the Kaiser effect) and the “remainder toughness” could be discussed through the quantitative analysis on AE characteristics for two different beams. They might relate to the durability and toughness of material for beam.

Bending performance of 3D printed ultra high-performance concrete composite beams

The integrated optimization of materials, processes, and structural performance is the development trend for 3D concrete printing. Composite beam reinforced by 3D printed ultra high-performance concrete (3DP-UHPC) was proposed, i.e., 3DP-UHPC was applied as the strengthen skeleton for the entire composite beam. In this study, three 3DP-UHPC skeleton optimized forms were derived through topology optimization design. Four-point bending tests were conducted on 3DP-UHPC skeleton composite reinforced concrete beams (CRC), rebars locally reinforced CRC beams (R-CRC), and rebars locally reinforced 3D printed concrete beams (R-PC). Additionally, conventionally reinforced concrete beam (RC) was produced for comparison. The results showed that the of CRC and R-PC perform 1/4 and 1/2 flexural capacity of RC, respectively. Their limited flexural capacity led to sudden failures, failing to meet structural load requirements. In contrast, R-CRC exhibited superior stiffness and strength, demonstrating exceptional bending performance for 3D printed concrete beams without the reinforcement of reinforcement cages. This approach significantly enhances the structural load capacity of 3D printed structures while preserving flexibility and reducing reliance on reinforcement cages. The study provides valuable experimental data and methodological guidance for the application of 3D printed concrete structures in structural load-bearing engineering.

Relation between edge stress, bending strength, surface stress and fracture pattern of thermally toughened glass

Thermally toughened safety glass must meet safety requirements in the building industry. Here, destructive tests are defined in the product standards, which must be carried out on small, standardized format (360 mm × 1100 mm) glass elements to determine the fracture pattern and bending strength. This is costly and not in the interests of sustainability. As part of the quality control of optical anisotropy effects in thermally toughened glass, isochromatic scans that can provide information on the edge stress are acquired. The evaluation of the isochromatics and retardations at the edge with deduction of the edge stress and transfer to bending strength and fracture pattern could provide essential findings for assuring the safety requirements of thermally toughened glass. In this experimental investigation, the surface and edge stress were measured on standardized format thermally toughened safety glass, with different edge processing and glass thicknesses from three different suppliers. Afterwards, the fracture pattern is controlled, or the bending strength is analyzed in a destructive four-point bending test. Conclusively, the results from the photoelastic and destructive tests are compared to determine whether the photoelastic measurement methods used to measure surface and edge stress can be employed as quality control.

Experimental investigation on flexural performance of steel-UHPC composite beams with steel shear keys

Test results of steel-ultra high performance concrete (UHPC) composite beams with welded steel shear keys (SSKs) under four-point bending are presented in this paper. The objective of the investigation is to reduce the self-weight and manufacturing cost of large-span structures. The study investigates the effects of strength of concrete slab, type, spacing and size of SSK, and concrete slab height and width on flexural behavior of composite beams. The experimental results demonstrate that enhancing concrete strength, reducing SSK spacing, increasing concrete slab size, and using large-size SSK can all significantly enhance the flexural performance. The composite beams with welded SSK exhibit a maximum relative slip of less than 4 mm, while the counterpart with welded bolts has a maximum relative slip greater than 4 mm. The study shows that the welded SSK is more effective than welded bolts in improving the interface shear performance of composite beams and improving the stiffness and load capacity. Additionally, the study defines four failure modes of steel-UHPC composite beams, and the formulae for flexural capacity is developed based on the reasonable basic assumptions. The calculated results fit well with the tested results. The research findings can be provided as a technical support for the design and application of steel-UHPC composite beams.

Constant-curvature bending response of thin glass: Analytical, numerical and experimental study of “clamp-bending” tests

New generation thin, lightweight and damage-resistant glass, having impressively impact resistance and ability to be bent up to small radii, appears to be the optimal material for extremely deformable structural elements. Its structural use and design require an accurate evaluation of its mechanical properties. However, standard methods to test the glass strength, as the Four-Point Bending and the Coaxial Double Ring test, cannot be used for thin glass, due to its high deformability. Here, an innovative test is proposed, consisting into deforming a thin element into a costant-curvature shape, by prescribing a rotation on two opposite edges of a rectangular plate, while allowing the adjustment of the distance between the supporting hinges. This produces a deformation into an arch of a circle and to a constant stress distribution, allowing to determine the thin glass strength with very simple formulas. An innovative experimental setup, recently proposed for twisting tests on thin glass, has been adapted for constant-curvature bending tests, based on the results of both analytical modelling and numerical analyses. This has been used to perform an experimental campaign, comprising 15 destructive tests on chemically tempered thin glass.

Optimization and fatigue assessment of girders with large-dimension corrugated steel webs

In recent years, large-dimension Corrugated Steel Webs (CSW) has increasingly become an available solution for long-span bridges to reduce deadweight and improve prestressing efficiency. Compared to conventional CSW used in small-span bridge girders, girders with large-dimension CSW in long-span bridges are more susceptible to fatigue cracking under repetitive traffic loads. However, the specifications aimed for small-dimension CSW may resulted in unsafe fatigue detail categories. This paper investigated the fatigue performance of large-dimension CSW girders for bridges. The reasonable corrugation angles of girders with CSW were obtained using Grey Relational analysis. The fatigue detail category corresponding to optimized corrugation angles was suggested based on the Theory of Critical Distance (TCD). The Finite Element Analysis (FEA) results indicate that the hot spot stress concentration factor (Ks) on the web-flange weld toe increases with the corrugation angle and decreases with the bend radius. When the corrugation angle and the bend radius are fixed, Ks increases with the corrugation wavelength. By developing a balanced fatigue and shear buckling performance scheme, the optimized corrugation angles of wavelength 1000 ∼ 2000 mm are between 30° and 45°. There is a negative correlation between the fatigue detail categories of CSW girders and corrugation wavelengths. In general, the fatigue detail category of wavelength 1600 ∼ 2000 mm under four-point bending can be classified into a range between 50 and 71 for Eurocode 3, Category D and Category E′ design curves for AASHTO, FAT 50 and FAT 71 for IIW respectively.

Restraining geometrically-necessary dislocations to the active slip systems in a crystal plasticity-based finite element framework

Strain gradients have been cast in the form of geometrically-necessary dislocations (GND) to relate the length-scale dependence of strength and to determine potential sites for failure initiation. The literature contains various different incompatibility measures, the main ones being: the total form (∇×Fp), the rate form for large displacements (∇×γ̇anaFp), and the slip gradient form (∇γ̇a). Here, these different approaches are compared rigorously for the first time. Obtaining GND densities when using the total form is a rank-deficit linear problem, solved by singular value decomposition (SVD) known as the Least Squares Minimization (L2 method). Alternative methods for finding GND densities such as Karush–Kuhn–Tucker (KKT) optimization are also investigated. Both L2 and KKT methods predict unrealistic GND densities on inactive slip systems leading to excessive strain hardening; even for a single crystal single slip case. Therefore, the restriction of GNDs to the active slip systems by using a threshold based on the total slip is proposed. This restriction reveals relatively consistent results for various single crystal single slip cases including: simple shear, uniaxial tension, and four-point bending. In addition, the small numerical differences in the slip leads to large discrepancies in the flow stress due to error accumulation, even for strain-gradient-free uniaxial tension, hence a threshold for the GND density increment (2×102 m−2) is used in all models to avoid formation of erroneous GND densities. Finally, the proposed method is applied to the evolution of the GND density for a grain inside a polycrystal aggregate that posses a complex stress state. The lowest incompatibility error is obtained by both of the total forms that use the curl of the plastic deformation gradient with the active slip system restriction suggesting them to be the most reliable GND measures.

Effect of slope of grain on mechanical properties of some tropical wood species

ABSTRACT The aim of this work was to study the relationship between the mechanical properties of Cameroonian tropical woods and the slope of grain. The forests of the Cameroonian part of the Congo Basin abound in species that are highly solicited for structural applications. However, little information is available on the influence of the slope of a grain of these wood species. Clear wood specimens of ayous (Triplochiton scleroxylon), azobe (Lophira alata), fraké (Terminalia superbe), okan (Cylicodiscus gabunensis), padouk (Pterocarpus soyauxii), and sapelli (Entandrophragma cylindricum) were prepared. The specimens have a cross section of 20 × 30 mm and a length of 300 mm. These specimens were subjected to a four-point bending test and a double cantilever beam test. Modulus of elasticity (MOE), modulus of rupture (MOR), work at maximum load (WML) and fracture toughness (GIC) were determined. These mechanical properties were calculated for specimens with slopes of grain 0°,15°, 30°,45°,60°, 75° and 90°. The results showed that the slope of grain had significant effects on all the mechanical properties measured on clear wood specimens. MOE, MOR, WML, and GIC decreased with increasing grain slope. On the other hand, azobe and okan absorb much more of the energy that causes microcracking than the other species.