Mid-span Load Research Articles

Simulation and Experiment Study on the Bridge Deflection Measuring Method Based on Secant Inclination

Deflection is the most direct indicator that reflects the bearing capacity of the bridge and the overall stiffness. There are many ways to measure the deflection of Bridges, and the inclination angle method is the most commonly used indirect method, but the existing theory of inclination angle method is relatively complicated. Based on the facts of the bridge small inclination, this article proposes the method of obtaining the bridge deflection by the inclination of the secant line constructed from the adjacent measurement points. Firstly, according to the bending deformation curve of general simply supported beam, the deflection calculation formula of each measuring point is derived based on the assumption of small deformation and the inclination Angle of measuring point. Secondly, a large commercial finite element software ANSYS 10.0 is used to carry out numerical simulation on the simply-supported beam under concentrated load in mid-span, and the deflection results of the numerical simulation are compared and verified with the theoretical results of the proposed method. Finally, the measured deflection results of the simply-supported beam model under mid-span load are compared with the theoretical results of the proposed method. The verification results show that if the actual model is consistent with the theoretical model, the proposed method has good accuracy.

Web buckling mechanism of pultruded GFRP bridge deck profiles subjected to concentrated load

The web’s local buckling is a major failure type of pultruded glass fiber-reinforced polymer (GFRP) bridge deck subjected to concentrated wheel loads. Three kinds of external actions-that is, in-plane shear force, local compressive force and bending moment-are coupled at web. Besides, the couple ratio of those three external actions is changed due to varied wheel’s loading position, resulting in a more complicated web buckling mechanism. Hence, a study of the web buckling behavior was firstly conducted through two experiments with different concentrated loading cases, namely mid-span loading and quarter-span loading. After then, parametric analysis of FE model with detailed simulated web-flange junctions (WFJ) were performed to reveal a more comprehensive understanding. The experimental results showed that both specimens went through buckling failure of middle web, post-buckling strengthening owing to structural redundancy, and final failure caused by crack propagation on the top flange. The parametric analysis showed that the compression buckling and shear buckling coupled together, and that the compression buckling is dominant. In addition, as the shear-span ratio decreased, the principal compressive stress and the shear buckling became more pronounced, and consequently the GFRP bridge deck’s bearing capacity reduced.

Behavior of Reinforced Concrete Beams Strengthened By GFRP Composites Subjected to Combined Bending and Torsion – Experimental Study

This paper presents an experimental investigation on the behavior of reinforced concrete beams subjected to combined bending and torsion, strengthened by using externally bonded glass fiber reinforced polymer (GFRP). The experimental work includes an investigation of three RC beams tested under combined bending and torsion. One beam is kept without strengthening as a control specimen, while the other two beams are strengthened using GFRP wrapping with different configurations. All RC beams have the same concrete grade and steel reinforcement. The strengthened beams in the experimental study include full wrapping with continuous GFRP sheets and discrete GFRP strips with the same GFRP reinforcement ratio. The load-mid span deflection curves and the torsional moment-twist angle curves were recorded to failure. The crack patterns and failure modes of the RC beams were also indicated. The Experimental results reveal that strengthening by using GFRP wrapping helped effectively in improving the overall performance of the strengthened beams.

Ductility of simply supported rubberized concrete beams

Dispose of waste rubberized tires become a dangerous problem around the world, represented a big serious risk to the sur-rounded environment. Many studies show that over 1000 million tires reach their expired date yearly and this figure is anticipated to be 5000 million tires by reaching 2030. A minor part of them is employed as recycled materials and the residual amount is stockpiled or buried. This paper aimed to successfully utilize the vast amounts of tire rubber waste existing currently in landfills. This paper represents a practical investigation of the ductility performance of the reinforced rubberized concrete beams. Thirteen reinforced concrete beams simply supported, with waste rubber tires mixtures vary from 0 to 8 percentage as aggregates replacements, were tested by mid-span load. Therefore, to examine the ductility performance of reinforced rubberized concrete beams, three sets of samples were made. In the first group, coarse aggregates in the concrete mix were replaced by different percentages of the waste rubber partials, while for the second group, crumb rubber was replaced for the fine aggregates, and for the third one, a mix of waste and crumbed rubber were replaced for both types of aggregates. Experimental results of rubberized specimens were also compared with that of the reference beam (without rubber replacement), the comparison results declare that concrete contains rubber particles is less ductile than conventional concrete.

Flexural Behavior of Simply Supported Beams Consisting of Gradient Concrete and GFRP Bars

In order to study the flexural behavior of simply supported beams consisting of gradient concrete and GFRP bars, 28 simply supported beams were designed. The main parameters included the strength grades of high-strength concrete (HSC), GFRP reinforcement ratio, and sectional height of HSC. Based on nonlinear constitutive models of materials, meanwhile, considering the bond slip between concrete and GFRP bars, five simply supported beams with gradient concrete and five simply supported beams with GFRP bars were simulated, respectively. Then the mid-span load–displacement curves of beams were obtained. By comparing with the experimental data, the rationality of material constitutive models and finite element modeling was verified. Based on this, the parameter analysis of the beams with GFRP bars and gradient concrete was carried out, and the failure modes of the beams were obtained through investigation. The results show that the failure process of the beams can be divided into two stages: elastic stage and working stage with cracks. With the increase of GFRP reinforcement ratio, the flexural bearing capacity of the beams does not change significantly, while their stiffness increases gradually. The flexural bearing capacity of the beams can be significantly improved by appropriately increasing the strength and sectional height of HSC. The ultimate bearing capacity of the beams is 40% higher than that of the GFRP concrete beams. Finally, based on the plane-section assumption, the calculation formula of normal-section flexural bearing capacity of this kind of beams is proposed through statistical regression method.

Aerodynamics of Boundary Layer Ingesting Fuselage Fans

Abstract Boundary layer ingestion (BLI) potentially offers significant reductions in fuel burn and pollutant emissions. The propulsive fuselage concept features a fan at the back of the airframe that ingests the 360 deg fuselage boundary layer. Consequently, the distortion at the fan face during cruise is close to radial. This article aims to devise and test a fan design philosophy that is tuned to this inflow distortion. Initially, a free-vortex fan design matched to clean inflow is presented. The effects of BLI on the aerodynamics of this fan are investigated. A series of design steps are then presented to develop the baseline fan into a new design matched to fuselage BLI inflow. Both fan designs have been tested within a low-speed rig. The impact of the fan design changes on the aerodynamics and the performance with BLI are evaluated using the test results. This article presents the successful application of a unique experimental facility for the analysis of BLI fuselage fans. It shows that it is possible to design a fan that accepts the radial distortion caused by fuselage BLI with a modified profile of work input. The new fan design was found to increase the work input by 4.9% and to improve the efficiency by 2.75% relative to a fan designed for clean flow. This new fan design has reduced loading near the hub to account for the incoming distortion and increased mid span loading and negative incidence toward the tip for tolerance to circumferential distortion off-design.

Numerical study and strength model of concrete-filled high-strength tubular flange beam under mid-span load

High-strength steels (HSS) have been increasingly used in building and bridges due to their advantages, such as lightening the self-weight and reducing the carbon emissions. However, these benefits cannot be fully utilised for long-span flexural members because of lateral–torsional buckling (LTB). For an improved buckling resistance, a new concrete-filled high-strength tubular flange beam (HS-CFTFB) is formed, and its strength is theoretically and numerically studied. Theoretical models of the HS-CFTFB are derived to estimate the full plastic strength and the elastic LTB strength. The finite-element models are then built to determine the buckling factor in the inelastic LTB strength model. The FE models are validated and found to be in good agreement experimental results. With these verified numerical models, a comprehensive parametric study is conducted to investigate the effect of geometric and material properties of HS-CFTFBs. Finally, the design formula of HS-CFTFBs and its scope of application are determined on the basis of a parametric study.

Crack Width and Propagation in Recycled Coarse Aggregate Concrete Beams Reinforced with Steel Fibres

Reducing the crack width is a vital feature for protecting rebars from corrosion. In this investigation, the impact of steel fibres (SFs) on the cracking of recycled coarse aggregate reinforced concrete (RCARC) beams was investigated. Twenty-seven reinforced concrete (RC) experimental samples (150 mm × 200 mm × 1500 mm) were manufactured. Shear rebars were considered with different spacings. Specimens were tested under a four-point flexural setup. Recycled coarse aggregate (RCA) from a destroyed building was employed at 0%, 50% and 100% by weight. SFs were added at three contents (0%, 1% and 2%) in order to reduce the crack width. The mid-span load–displacement relationship and the crack propagation and width were measured during the tests. Therefore, this study intended to assess the impact of utilising RCA and natural coarse aggregate on cracks’ spacing and propagation in RC beams when SFs were employed. The obtained outcomes were compared with the requirements of CSA S474, NS 3473E, EC2-04, CEB-FIP and ACI 224R-01. It was found that enough shear rebars should be provided through the beams to control the crack width and propagation, but that SFs enhanced the bending performance of RCARC with no shear rebars.

Structural Performance Under Monotonic Static Loading of Reinforced Concrete Gable Roof Beams with Multiple Web Openings

In the present study, an attempt has been made to experimentally investigate the flexural performance of ten simply supported reinforced concrete gable roof beams, including solid control specimen (i.e., without openings) and nine beams with web openings of different dimensions and configurations. The nine beams with openings have identical reinforcement details. All beams were monotonically loaded to failure under mid-span loading. The main variables were the number of the created openings, the total area of the created openings, and the inclination angle of the posts between openings. Of interest is the load-carrying capacity, cracking resistance and propagation, deformability, failure mode, and strain development that represent the behavior of reinforced concrete gable beams. Test results showed that the total concrete weight consumed for the tested gable beams with openings was lower than the solid gable beam by (14.9–26%). This reduction in weight led to a reduction in the flexural stiffness and, in turn. in the load-carrying capacity by (6.2–17.9%). The percentage of the decrease in the concrete consumption to the reduction in the load-carrying capacity for the tested beams with openings attained (140–240%). It was recorded that the maximum crack width depended on the total area of the created openings rather than the number of these openings.

Lateral-torsional buckling behaviour of concrete-filled high-strength steel tubular flange beams under mid-span load

Lateral-torsional buckling (LTB) behaviour of concrete-filled high-strength steel tubular flange beams (HS-CFTFBs) is experimentally and numerically investigated. Six specimens are tested in simple support with a lateral unrestrained concentrated load in mid-span. Among them, two are failure controlled through flexural yielding (FY), whereas the remaining specimens are controlled through LTB. Finite-element (FE) models are then constructed and the comparison with the experimental results indicates that they could reliably and accurately evaluate failure modes, load–displacement relationship and ultimate capacities of HS-CFTFBs. These verified FE models are consequently used to investigate the effect of flange depth, concrete and steel with various span lengths. Results suggest that the ultimate moment capacity evidently decreases as the span length increased, particularly for the high-strength steel beams. The increasing flange depth remarkably improved the LTB strength but merely slightly increased the amount of steel. The infilled concrete could improve the resistance to flange distortion and thus increase the ultimate capacity. However, the strength of concrete exhibits a slight influence on ultimate capacity. Increasing fy could improve the LTB capacity when the span length is relatively small, but the improvements decrease with increasing span length. When the failure mode is elastic LTB, increased fy could substantially improve post-buckling stiffness and ductility

Experimental investigation on the flexural behavior of steel cold-formed I-beam with strengthened hollow tubular flanges

This research presents an experimental study to examine the flexural behavior of steel cold-formed I-beam with strengthened hollow tubular flanges. Nineteen of cold-formed steel I-beam with hollow tubular flanges were prepared and experimentally tested on four-point bending tests. One of these specimens was not strengthened, which used as a control specimen, and eighteen specimens were strengthened with filling the tubular flanges by different materials. Twelve specimens were strengthened at the compression hollow tubular flanges only, with and without shear connectors. Finally, six specimens were strengthened at the compression and tension hollow tubular flanges. The strengthened materials used are different types of wood wastes (Particleboard Wood- Sawdust with cement mortar- Sawdust with epoxy- Sawdust with polyester), light weight concrete, and polymer-mortar. All specimens were loaded by two vertical loads to failure. Specimens’ mode of failure and vertical displacements were recorded. Vertical load-deflection at mid-span relationships have been analyzed to study the effect of strengthened materials. It was observed that maximum capacity was achieved by using polymer-mortar rather than the other materials. Using shear studs and strengthened compression and tension flanges did not show an obvious effect on the ultimate load of the tested specimens compared to those that were strengthened the compression flanges only. For all the strengthened specimens, improving in the load-mid span deflection relationships were achieved compared with the control specimen. The bending moment capacities were compared with the expected values using the Egyptian Code of Practice for Steel Construction (LRFD), which indicates that the design method of this code is conservative in comparison to the experimental test results, but it is not conservative in expected the moment capacities of strengthened specimens that used the Sawdust with cement mortar and light weight concrete materials.

Numerical study of cold-formed steel channel sections under combined web crippling and bending action

Cold-formed steel sections used in floor systems are vulnerable to web crippling, and with increasing span lengths, they are likely to fail under combined web crippling and bending action. A numerical study was therefore undertaken to investigate the combined web crippling-bending interaction behaviour of unlipped channel sections used as bearers in floor systems with fastened supports. Web crippling finite element models developed and validated by the authors in a recent study were extended to investigate the behaviour of unlipped channels under combined action of web crippling and bending while new finite element models were developed for bending and validated using available experimental results. All three types of finite element models were used in a detailed parametric study to obtain the capacities of 12 unlipped channel sections made of G250 and G450 steels under pure and combined web crippling and bending actions. Comparison of the combined web crippling and bending capacities obtained from finite element analyses with the interaction equations in three cold-formed steel design standards, AISI S100, AS/NZS 4600 and Eurocode 3 Part 1.3, showed that the current design equations are accurate for 50 mm bearing length. However, they can also be used to predict the combined web crippling-bending capacities conservatively for bearing lengths of 100 and 150 mm. A new design equation with a suitable capacity reduction factor was then proposed to improve the accuracy of predicting the mid-span load capacity of channel sections subject to combined web crippling and bending actions. • Investigated the behaviour of unlipped channels with fastened supports under pure and combined web crippling and bending. • Developed and validated finite element models for web crippling and bending actions. • Recommended ABAQUS quasi-static analysis based on explicit conditions instead of general static method. • Current web crippling and bending interaction equations were shown to be conservative. • Proposed new equations to predict the mid-span load capacity under combined web crippling and bending action.

Numerical Study on The Structural Behavior of RC Beams after Exposure to Elevated Temperature

This paper presents a numerical simulation of the structural response of reinforced concrete (RC) beams under elevated temperature using the commercial finite element package ABAQUS. A numerical model is firstly suggested by selecting the appropriate geometrical and material properties of the RC beam model at elevated temperature. Thereafter, the suggested numerical model was validated against the experimental tests conducted in this study. The validation results in terms of temperatures- time histories; load-mid span deflection of the RC beams have confirmed the accuracy of the suggested numerical model. The validated numerical model was implemented in conducting a parametric study to investigate the effects of two important parameters on the behavior and failure of RC beams under elevated temperature. These parameters are the effect of the high ranges of elevated temperatures; and the effect of heating rate. The parametric study results have revealed that the failure load and the ductility of RC beams under elevated temperature are not considerably influenced by changing the heating rate. It has also been concluded that the ultimate load capacities of RC beams have considerably decreased by 55.49%, 74.72%, and 81.31% comparing with the control RC beam when they exposed to temperature values of 600 ºC, 700 ºC, and 800ºC respectively. These conclusions may be used in the design of RC beams subjected to fire induced temperature.
 Numerical model

Numerical study of RC beams under various loading rates with LS-DYNA

Having an accurate understanding of concrete behavior under effects of high strain rate loading with the aim of reducing incurred damages is of great importance. Due to complexities and high costs of experimental research, numerical studies can be an appropriate alternative for experimental methods. Therefore, in this research capability of the finite element method for predicting concrete behavior at various loading conditions is evaluated by LS-DYNA software. First, the proposed method is presented and then is validated in three stages under different conditions. Results of load—midspan displacement showed good agreement between experimental and finite element results. Capability of finite element method in analyses of beams under various rates of loading was also validated by low error of the results. In addition, the proposed method has reasonable ability to evaluate reinforced concrete beams under various loading rates and different conditions.

Retrofitting of shear strength self-compacting reinforced concrete deep beams with FRP

Experimental program were carried out to investigate the behavior of self-compacting reinforced concrete deep beams retrofitting with carbon fiber reinforced polymer (CFRP). Six simply supported deep beams were tested under symmetrically two point loads, three beams were tested up to failure without strengthening as a control beams with different shear span to effective depth ratio (a/d) while the other two beams were loaded up to 60% from the ultimate load of control beams for each a/d ratio and then retrofitted by the same configuration of CFRP to study the effect of a/d ratio on the properties of deep beams retrofitted. a/d for tested beams were (0.8, 1, 1.2). Study was focused on determining failure loads, cracking loads, failure modes, load midspan deflection. All the beams had the same compressive strength, overall dimensions and flexural and shear reinforcement. It was concluded that using this retrofitted method is very efficient and a gain in the ultimate load capacity of the deep beams was obtained also the results showed that when a/d ratio increase from 0.8 to 1.2, the ultimate load was decrease by 25% and midspan deflection was increased approximately at all load stages for control and retrofitted beams.

Research on the fatigue whole life of asphalt mixture based on the nonlinear damage theory

The analytical solution of the fatigue crack forming life based on the nonlinear cumulative damage model was deduced by using the simply supported beam with mid-span loads as the study model. Then the fatigue whole life model by the Paris formula with the crack length factor was established. Flexural-tensile strength test and fatigue test were made by using the trabecular specimen at different temperatures. By the contrast of the asphalt mixture fatigue life at different temperatures and stress ratios, it was found that as increasing of temperature, the fatigue life of the trabecular specimen will reduce. When it is at the same temperature, the fatigue life will reduce as the stress ratio increasing. The fatigue developing life of the asphalt pavement will occupy a higher ratio of the whole fatigue life when the temperature is higher. The fatigue developing life is shorter when the temperature is lower. The values of the fatigue damage parameter a∗ and p were obtained by the regression of the test data. The expressions of the functional relation between a∗ and p with temperature T were deduced. The change law between the crack developing speed and the stress intensity factor amplitude was studied to determine the parameters A and n in the formula Paris under different stress ratio. The established model in this paper was verified effectively by contrast of the calculation values of the fatigue whole life model and the test values.

Effect of end connections on mid-span load capacity of laminated particleboard bookshelves

ABSTRACTThe purpose of the study was to determine the effect of joints on the mid-span load capacity of bookshelves made from laminated particleboard. Twenty types of joints were selected based on their popularity in the cabinet-making industry. Results showed that highest mid-span load capacities were obtained with glued groove joints that included glued wooden dowels. Overall, highest mid-span load capacities were obtained with fixed shelf-joint constructions, whereas lower capacities were obtained with adjustable constructions. Based on its high-load capacity and ease of construction, the spline joint appears best-suited for use by most craftsmen. Statistical lower tolerance limits were used to take capacity variability into account for design purposes. The 75% confidence|75% proportion limits for the glued wood spline and glued fiberboard spline joints were 94% and 93% of average, respectively.

Shear behaviour and design of Lipped Channel Beams with non-circular web openings

Cold-formed steel Lipped Channel Beams (LCB) with web openings are commonly used as floor joists and bearers in building structures. Their shear behaviour is influenced by the presence of web openings and the shear capacities are considerably reduced. However, the shear behaviour and capacity of LCBs with non-circular web openings (square, rectangular and elliptical web openings) has not been investigated adequately. Hence a detailed numerical study was conducted to investigate the shear behaviour and capacity of LCBs with non-circular web openings. Finite element models of simply supported LCBs under a mid-span load with aspect ratios of 1.0 and 1.5 were developed and validated by using the available shear test results. They were then used in a detailed parametric study to investigate the effects of various influential parameters. Numerical results showed that the current shear design equations in cold-formed steel structures design standards are conservative or unsafe. New shear design equations were therefore proposed for the accurate prediction of the shear capacity of LCBs with non-circular web openings. This paper presents the details of finite element modelling of LCBs with unreinforced non-circular web openings and the development of new shear design rules. The proposed shear design equations in this paper can be considered for inclusion in the future versions of cold-formed steel design standards. Suitable design equations were also developed under the direct strength method.

Experimental investigation on continuous reinforced SCC deep beams and Comparisons with Code provisions and models

The test results on eight two-span deep beams made of self-compacting concrete (SCC) are presented and discussed in this paper. The main parameters investigated were the shear span-to-depth ratio, and the amount and configuration of steel reinforcement. All beams failed due to a major diagonal crack formed between the applied mid-span load and the intermediate support separating the beam into two blocks: the first one rotated around the end support leaving the other block resting on the other two supports. Both concrete compressive strength and web reinforcement had a major effect in controlling the shear capacity of the beams tested. For the shear span-to-depth ratio considered, the vertical web reinforcement had more influence on the shear capacity of the specimens than the horizontal web reinforcement. The shear provisions of the ACI 318M-11 are unconservative for most of the beams tested. Comparisons of test results with the strut-and-tie model (STM) suggested by ACI 318M-11, EC2 and CSA23.4-04 showed that the predictions are reasonable for continuous deep beams made with low and medium compressive strength. Although the equation suggested by ACI 318M-11 is very simple, its prediction is more accurate than the STM suggested by different design codes.

Modeling of the structural behavior of multilayer laminated glass beams: Flexural and torsional stiffness and lateral-torsional buckling

In recent years several investigations were performed about the behavior of laminated structural glass elements, namely in terms of their flexural and torsional stiffness, with the lateral-torsional buckling of beams being one of the most relevant and complex topics. Various analytical formulations were proposed to describe the equivalent stiffness of laminated elements; however, none covers more than three layers of glass in a comprehensive and unified manner, and those that exist are not consensual. This work proposes a new formulation, based on sandwich theory, which provides equivalent results to previous formulations in a limited set of conditions, but that is also able to characterize the behavior of simply supported laminated glass columns and beams up to five layers, subjected to compressive axial loads, mid-span loads, uniformly distributed loads, four-point bending, pure bending or torsion. The fundamentals of the formulation presented in this paper allow it to be extended to a larger number of layers and to different load and support conditions. The proposed formulation is assessed by means of a parametric study based on the comparison with numerical results retrieved from finite element simulations, in order to assess the range of validity of each expression. Two analytical approaches for the lateral-torsional buckling problem are studied in detail, with their fundamentals being explained. Another formulation, proposed in Australian Standard AS 1288, is also addressed. An experimental assessment of the work developed is achieved by comparing the results from flexural tests available in the literature with analytical and numerical predictions.