Beam Length Research Articles

A Parametric Study on the Behavior of Arch Composite Beams Prestressed with External Tendons

Arch beams are widely used in bridge construction due to their ability to withstand much greater loads than horizontal beams. The utilization of composite construction has also increased due to its tendency to optimize the utilization of construction materials, leading to significant savings in steel costs. In this research, a detailed experiment work on a simply supported arch composite beam under a positive moment was presented; then, a numerical model was created using ABAQUS to simulate its nonlinear behavior. The beams were formed from a concrete slab attached to steel beams by means of perfobond shear connectors (PSCs). A good agreement between the model and experiment was obtained. A parametric study was developed to identify the influence of the initial prestressing, rise to span ratio, and beam length on the behavior of the arch composite beam. It was found that the presence of tendons enhances the serviceability behavior, increases the ultimate load by 40% compared to the control beam, and equilibrates the horizontal thrust of the arch, even in the absence of initial prestressing. In addition, the beam exhibits a clear tied arch behavior due to the large eccentricity as the rise-to-depth ratio increases. Furthermore, the prestress force was found to be more effective in the longer span and the incremental stress in tendons more remarkable.

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 FLEXURAL PERFORMANCE OF BUILT-UP STEEL BEAMS WITH DIFFERENT WEB OPENINGS

Recently, the usage of Structural Steel Beams with Opening in the Web has spread extensively in all over the world, in various types of buildings such as high-rise buildings and industrial buildings. There are several advantages in using openings in beams. There for, an analytical investigation was carried out on fourSteel Beams with Opening (SBWO) models by using a powerful nonlinear simulation software ABAQUS. The initiative was to study the overall flexural behaviour of (SBWO’s) and to establish the maximum load carrying capacity, and deflection. Only vertical loads have been considered in the (SBWO’s) performance investigation. The Built-Up sections were tested up to failure. The simulated models were considered to be under simply supported condition at their edges and a uniform distributed load were applied over the upper flange of the beam along all beam's length. The flexural behaviour of beams with different opening shapes were tested and compared. The test results proved to be very useful in selecting the opening shape.

Shear capacity of corrugated web steel beams strengthened with CFRP strips

In recent years, there has been significant advancement in strengthening techniques for steel structures using carbon-fiber reinforced polymer (CFRP). While numerous studies have focused on CFRP strengthening of steel beams with flat webs, similar investigations on corrugated web steel beams (CWSBs) remain limited despite their increasing application in various steel structures. This study presents numerical and analytical investigations aimed at evaluating the effectiveness of CFRP strengthening for CWSBs and developing a design procedure to predict the shear buckling capacity of strengthened CWSBs. The research employs a finite element (FE) model developed using ANSYS software, validated against previous experimental work by the same authors, which accurately reflects the overall behavior of CWSBs. A parametric study is conducted on 105 CWSBs using the validated FE model to assess the impact of various geometrical parameters, including beam web slenderness ratio, length and thickness of CFRP strips, and different CFRP strip schemes. Results demonstrate that CFRP strengthening can enhance the shear capacity of CWSBs by up to 74.50%. The study identifies the arrangement of CFRP strips on both sides of the web as the most effective parameter for controlling the efficiency of the CFRP strengthening technique. Conversely, changes in CFRP strips up to 70% of web height have minimal effect. A proposed design procedure for predicting the design shear buckling strength of CFRP-strengthened CWSBs shows good consistency with FE model results.

Analysis of Supports Displacements Induced Delamination in Multilayered Indeterminate Beam Structures

This theoretical paper is focussed on the problem of delamination in a multilayered beam loadcarrying structure that is statically indeterminate. The beam is supported by three supports. The middle support represents a vertical spring. There is no external mechanical loading on the beam. Instead of this, the beam is under vertical displacement of the left-hand support. The main goal of the paper is to investigate the delamination due to the displacement of the left-hand support. Another issue that is under consideration is the effect of the vertical spring. The beam has non-linear elastic mechanical behaviour. The parameters of the nonlinear constitutive law that is applied for treating the beam mechanical behaviour vary continuously along the beam length since the beam layers are made of engineering materials that are continuously inhomogeneous in the length direction. Equations for determination of the curvatures and coordinates of the neutral axis in the portions of the beam are constituted. The strain energy release rate (SERR) induced by the support displacement is derived and checked-up by the integral J.

Deflections of Cantilever Beams Subjected to A Point Load At the Free End

In this study, the displacements of cantilever beams for various slenderness ratios under point load are analyzed using Timoshenko and Bernoulli-Euler beam theories. The variation of the slenderness ratio is achieved only by changing the beam length. The results from these theories are compared with those from SolidWorks, which is considered a reliable simulation software. With this comparison, the % difference rates between the simulation and theoretical results are determined. This study explains under which conditions the Timoshenko and Bernoulli-Euler beam theories should be applied and evaluates the accuracy of the simulation software. Detailed research is carried out to examine its compatibility with these two theories. Some numerical results are presented to demonstrate their validity and sensitivity.

Study on Error Influence Analysis of an Annular Cable Bearing-Grid Structure

Manufacturing errors of cable length, external node coordinates and tension force by the passive tension method are inevitable, which will inevitably affect the prestressing of cable bearing-grid structures, while existing studies lack the error analysis of error influences in this area. This paper proposes a method for analyzing random errors in constructing annular cable bearing-grid structures. An error control index and a normal distribution-based random error model, considering the impact of cable and ring beam length errors on cable force, were established afterwards. Taking the roof of the Qatar Education City Stadium as an example, the influence of the length errors of the radial cable, ring cable, and outer pressure ring beam on the structural cable force and stress level was analyzed, and the coupling error effect analysis was carried out. The results show that ring cable force and radial cable force are less affected by the length error of each other’s cables, while they are more affected by the length error of the outer ring beam. Stress levels exhibit greater sensitivity to outer ring beam errors compared to cable length errors. As the error limits of outer ring beam increase, radial and ring cable error ratios and outer ring beam stress errors also rise.

Bending performance of RC beams reinforced with UHPFRC strips with different geometry and positions

AbstractUltra‐high‐performance fiber‐reinforced concrete (UHPFRC) is one of the most favorable materials for strengthening RC beams. Studies on UHPFRC strengthening of RC beams mainly address flexural behavior. Further research is needed on key factors, such as UHPFRC‐to‐beam bond and system cost linked to strip geometry. This research studies experimentally and theoretically the possibility of strengthening the RC beams by combining a strip of UHPFRC to the bottom surface of some specimens or the bottom and top surfaces together for others. The study focused on three key variables to assess the effectiveness of UHPFRC strengthening strips: placement (bottom side only or both sides), length of the bottom strip relative to the total beam length (0.50, 0.60, and 0.80 L), and presence or absence of concrete cover on the bottom side before casting the UHPFRC strip. The results for a load‐deflection response, crack propagation, stiffness, and energy dissipation were used to compare other strengthened specimens. Eight strengthened specimens, divided into three series, were tested through a 4‐point loading regime to consider the effects of different parameters. Results revealed that strengthened beams on the bottom and top sides showed remarkably enhanced ultimate load, stiffness, and energy dissipation. UHPFRC strip length and removal of concrete cover were the most significant parameters. Moreover, extending the strip length from 1000 to 1200 mm shifted failure from shear to bending, increasing stiffness by 29% and load capacity by 23%, while deflection and energy dissipation were less affected. Further increasing the strip length to 1600 mm boosted load capacity and stiffness by 38% and 75%, while deflection and energy dissipation dropped by 21% and 31%. Finally, a numerical analysis was presented to investigate the influence of numerous parameters that might influence the bending performance of strengthened RC beams.

A straight-arch-straight beam tandem quasi-zero stiffness structure

Extremely low dynamic stiffness is essential for the successful utilization of quasi-zero stiffness (QZS) structures for vibration isolation, energy harvesting, and micromechanical sensing. However, most conventional QZS structures are based on a parallel connection of positive and negative stiffness mechanisms, which poses challenges for stiffness matching, structure design, and fabrication. We propose a QZS structure based on a straight-arch-straight (SAS) tandem connection, in which the integrated design of the structure overcomes the problem of stiffness matching, and more importantly, the simple design of the structure greatly reduces the difficulty of fabrication and enables the design of a wide range of load-carrying capacity by only adjust the ratio of the length of the straight beam to the arch and the ratio of the height of the arch to the thickness. The symmetric deformation of the SAS structure extends the working range of the QZS structure, which can be further extended several times or divided into several different QZS intervals by connecting several identical or different SAS units in parallel. The experimental results show that the SAS structure has excellent vibration isolation performance in the low-frequency region, and more importantly, the low preload requirement also provides an important reference for structural design in the field of micromechanical sensing.

Bending Behavior of RC Beams with Regular Web Openings and Non-corroding GFRP Reinforcement

The present study pertains to the flexural behavior of RC beams with openings and non-metallic (GFRP) reinforcement. The main goal of preferring GFRP reinforcement over the conventional steel reinforcement was to safeguard the beams against the reinforcement corrosion. The presence of multiple regular transverse openings throughout the beam length increases the susceptibility of reinforcing bars to corrosion as the larger contact area in these beams with the outside environment increases the ingress of corrosive agents. Within the scope of the study, a total of 8 RC beams, including two reference beams without web openings, were tested under four-point bending. The test parameters were the flexural reinforcement ratio, the presence of short stirrups in the chords, and the presence of diagonal reinforcement spiraling around the openings. Since GFRP stirrups are difficult to bend, each stirrups was formed by connecting four individual FRP bars around the longitudinal bars. The opening circular geometry was adopted to avoid stress concentrations around the sharp corners of opening and to facilitate the placement and fixing of different schemes of reinforcement in the beams. The present tests depicted that the diagonal reinforcement around the openings have considerable contribution to the flexural behavior of RC beams with GFRP reinforcement and with multiple regular transverse openings. The RC beams with openings were able to approach their analytical flexural capacities in the presence of diagonal reinforcement for both moderately and heavily reinforced beam groups. The analytical deflection predictions of GFRP-RC beams with openings showed a good agreement with experimental data.

Numerical analysis of fixed-end hollow rectangular beam under uniformly distributed load

The purpose of using opening in the reinforced concrete (RC) rectangular beam is the reduction of self-weight, cost, displacement, and strain. Therefore, this research performs linear elastic finite element analysis by using ETABS for fixed-ended RC hollow and solid rectangular beams under uniformly distributed loadings with variable beam lengths, compressive strengths, and opening sizes.The solid and hollow beams are considered to be a 2-nodded line element for the numerical analysis. The maximum range of validation result in case of hollow beam is found to be (3.9 to 7.9) %, which may indicate good accuracy of numerical analysis. The 50 × 50 mm opening size is suitable for 300 × 300 mm RC rectangular beam because of showing the positive normalized deflection of (0–1.45) % and lower strain rates (i.e. 0.13 % and 0.17 %) to compare the solid beam. This research may help professional engineers to use suitable opening size for design and construction works. Although, there is a scope to enhance this research in future by performing nonlinear analysis.

Approximate fundamental frequency formula for cantilevers with weakly non-uniform sections and verification with experiments and other studies in the literature

The vibrational frequencies of beams with uniform cross-sections are easily derived from the analytical solutions of the Euler-Bernoulli equation (EBE). However, for beams with non-uniform cross-sections, complex and time-consuming numerical solutions are typically required for each cross-sectional geometry. This paper presents a formula that accurately predicts the vibrational frequencies in the presence of weak heterogeneities, regardless of how the cross-sectional shape varies along the beam's length. Experimental verification and comparisons with literature confirm that the formula reliably predicts frequency shifts in cases where a thin heterogeneous film is coated on a uniform beam, thin heterogeneous layers are removed from a uniform beam, and when a moving point load affects the vibrational frequency. The average absolute percentage error between the experimentally measured and calculated frequencies was <0.17 %. As such, this formula serves as a practical tool for various engineering applications involving weakly heterogeneous beams.

Dynamic of composite nanobeams resting on an elastic substrate with variable stiffness

This study introduces a novel approach by combining finite simulation and an enhanced shear deformation theory to analyze the dynamic behavior of multi-layer composite nanobeams supported by an elastic foundation. The calculation formulae are derived from nonlocal theory in order to account for the impact of size effect. An intriguing aspect of this research is the presence of intricate curved profiles in the two material layers of the beam. The elastic foundation exhibits varying stiffness throughout the beam's length, accounting for many imperfections in the beam and including the drag parameter of the material. These elements contribute to the steady evolution of the issue model towards more realistic structures. Nevertheless, the computation gets intricate and impedes the precise approach. However, our work has successfully resolved this difficult and significant difficulty using the two-node element. This research demonstrates the temporal evolution of the dynamic reactions of the point with the greatest displacement and velocity, as dictated by the law of change. Simultaneously, it also presents visual representations of every point on the beam as it undergoes temporal variations. These conclusions possess both scientific and practical value, establishing a foundation for real-world implementations.

Study on seismic performance and bearing capacity calculation of post-earthquake repairable high-strength steel joints with weakened-angle

This paper combines common steel and high-strength steel to design a post-earthquake, repairable joint, considering post-earthquake function repairable and seismic performance comprehensively. To prevent early plastic deformation of the joint during the initial loading, slot holes are cut in the web and obround holes are cut in the flange of the angle. This is done to enhance the joint's seismic performance and its capacity for repair. Carrying out the proposed pseudo-static test and finite element parameter expansion analysis on the designed joints to compare and analyze the post-earthquake function repairable capacity of the joint. According to the different failure mechanisms, the calculation method of the bearing capacity and the design method of the joints are proposed. The weakened angle joints have low bearing capacity but the damage is completely concentrated in the damage element, and shows excellent ductility and seismic performance. The damage element was replaced when the story-drift was reached at 0.04 rad, and the peak bearing capacity before and after replacement errored by only 7.1 %. The maximum residual deformation of the joint is 0.48 %, which is lower than the threshold value for residual deformation of the post-earthquake function repairable structure, indicating excellent post-earthquake function repairable capacity. Based on the parameter and theoretical analysis, it is recommended that the thickness of damage element is not greater than the thickness of the beam, the length of the cantilever beam takes the value range of 0.18–0.25 times the total length of the beam, the bolts spacing of angle flange should be in the range of 30 times the thickness of the angle, and the reducing rate of the flange cover plate is about 0.7. According to the full-section plasticity theory, the peak bearing capacity can be calculated. The experimental and simulated values have an error within the range of 10 %.

Self-Oscillations of Submerged Liquid Crystal Elastomer Beams Driven by Light and Self-Shadowing

Liquid Crystal Elastomers (LCEs) are responsive materials that undergo significant, reversible deformations when exposed to external stimuli such as light, heat, and humidity. Light actuation, in particular, offers versatile control over LCE properties, enabling complex deformations. A notable phenomenon in LCEs is self-oscillation under constant illumination. Understanding the physics underlying this dynamic response, and especially the role of interactions with a surrounding fluid medium, is still crucial for optimizing the performance of LCEs. In this study, we have developed a multi-physics fluid-structure interaction model to explore the self-oscillation phenomenon of immersed LCE beams exposed to light. We consider a beam clamped at one end, originally vertical, and exposed to horizontal light rays of constant intensity focused near the fixed edge. Illumination causes the beam to bend towards the light due to a temperature gradient. As the free end of the beam surpasses the horizontal line through the clamp, self-shadowing induces cooling, initiating the self-oscillation phenomenon. The negative feedback resulting from self-shadowing injects energy into the system, with sustained self-oscillations in spite of the energy dissipation in the surrounding fluid. Our investigation involves parametric studies exploring the impact of beam length and light intensity on the amplitude, frequency, and mode of oscillation. Our findings indicate that the self-oscillation initiates above a certain critical light intensity, which is length-dependent. Also, shorter lengths induce oscillations in the beam with the first mode of vibration, while increasing the length changes the elasticity property of the beam and triggers the second mode. Additionally, applying higher light intensity may trigger composite complex modes, while the frequency of oscillation increases with the intensity of the light if the mode of oscillation remains constant.

Damage detection in composite and plastic thin-wall beams by operational modal analysis: An experimental assessment

The detection and localization of different damage features in thin-wall beam composite and plastic beams using Operational Modal Analysis (OMA) has been demonstrated experimentally. The detection of small damage features using modal analysis techniques is an emerging field, with few experimental OMA-based assessments having been reported so far. The proposed method is based on OMA combined with Stochastic Subspace Identification (SSI) and the enhancement of damage features by Continuous Wavelet Transforms (CWT). A composite thin-wall beam (CTWB) structure in two measurement configurations and a PVC tube in a free-free configuration have been tested. Damage features detected include extra masses attached to the beam, with a range from 9.5 % to 14.0 % of the beam mass, and small cracks perpendicular to the beam axis with lengths of about 4 % of the perimeter of the cross section. Calibration curves relating the strength of the damage signal with the weight of the attached masses have been constructed. Two simultaneous cracks or two masses could be detected as well. The quantification and localization of damage feature along the beam was possible through the use of Gaussian fit surface applied to damage maps obtained with the CWT technique. The width of the Gaussian fit curve was of the order of the distance between accelerometers, but the accuracy, estimated to be around 3 % of the beam length, was found to have sub-grid resolution. The proposed method was shown to work reliably with a relatively coarse measurement grid, potentially allowing for cost-effective Structural Health Monitoring (SHM) approaches.

Flexural reliability of corroded RC beams strengthened with CFRP sheets considering longitudinal corrosion non-uniformity of steel bars

The corrosion of steel bars in RC beams along the longitudinal direction is usually non-uniform, thereby increasing the variabilities of failure mode and flexural behavior of corroded RC beams strengthened by CFRP sheets. This paper analyzed the flexural reliabilities of CFRP sheet-strengthened corroded RC beams, which considered the corrosion non-uniformities of longitudinal steel bars along the beam length. Based on the failure mode-based calculation method and Monte-Carlo simulation, the beams were discretized into a series of units along the beam length and the failure probabilities of the beams were considered as the failure probabilities of the serial units. Meanwhile, the occurrence probabilities of failure modes at bending failure were also studied. Parametric analysis results showed that the occurrence probabilities of failure modes were affected by steel reinforcement corrosion degrees, CFRP strengthening ratios and initial strains at concrete tensile edge. Meanwhile, the longitudinal corrosion non-uniformity could significantly affect the occurrence probabilities of different failure modes and degrade the flexural reliabilities; e.g., for RC beams under third-point bending, when the corrosion degree is 0.3, the predicted reliability index with considering longitudinal corrosion non-uniformity can be 28.3 % lower than that without. The proposed reliability calculation method could accurately assess the impacts of longitudinal corrosion non-uniformity on flexural reliabilities and lay a solid foundation for calibrating design factors used in CFRP sheet-based strengthening designs, thereby contributing to both evaluating the safety of existing CFRP sheet-strengthened corroded RC beams and designing the strengthening CFRP sheets for existing corroded RC beams, which improve the safety and maintenance of existing RC structures in corrosive environments.

Secondary Resonances of Asymmetric Gyroscopic Spinning Composite Box Beams

A comprehensive theoretical investigation on the occurrence of secondary resonances in parametrically excited unbalanced spinning composite beams under the stretching effects is conducted numerically and analytically. Based on an optimal stacking sequence and Rayleigh’s beam theory, the governing equations of the system are derived using extended Hamilton’s principle. The system’s partial differential equations are then discretized using the Galerkin method. Numerical (Runge–Kutta technique) and analytical (multiple scales method) approaches are exploited to solve the reduced-order equations, and their results are compared and verified accordingly. Comparison and convergence investigations are performed to guarantee the validity of the outcomes. Stability and bifurcation analyses are accomplished, and resonance effects are thoroughly studied utilizing frequency-response diagrams, phase portraits, Poincaré maps and time-history responses. It is observed that among the various types of secondary resonance, only a combination resonance can be observed in the system dynamics. The outputs reveal that, in this resonance, the gyroscopic coupling results in the steady-state time response consisting of three main frequencies. By examining the effects of damping, eccentricity, and beam length, it is exhibited that this resonance does not occur in the system’s dynamics for any combination of these parameters. Therefore, these parameters can be adjusted in the design of asymmetric beams to prevent this type of resonance.

Parameter effects on performance of piezoelectric wind energy harvesters based on the interaction between vortex-induced vibration and galloping

Our previous research experimentally validated that the interaction between vortex-induced vibration and galloping is an effective method for enhancing the performance of piezoelectric wind energy harvesters under low wind speed conditions. We proposed a distributed-parameter electromechanical coupling model as well. This study aims to investigate the effects of various parameters and optimize the performance of VIV-galloping interactive piezoelectric wind energy harvesters. Initially, we assessed the applicability of the model under different circuit and aerodynamic force conditions and discussed boundary and convergence conditions by replicating previous results. Further, simulations were performed to analyze the effects of the structural parameters of the bluff body and piezoelectric beam. The width or depth of the bluff body significantly influenced the low critical wind speed, interactive occurrence, and electrical output. To achieve a balance between material cost and electrical benefit, we recommend positioning the electrode length from the fixed end with a coverage ratio of at least 60%. Additionally, the output power is highly sensitive to the piezoelectric beam length, but reducing it results in a higher natural frequency and critical wind speed. We fabricated and tested four prototypes, which have demonstrated significantly higher power densities compared with previously reported values at the same wind speed.

An experimental and numerical effort on the vibration behavior of additively manufactured recycled polyethylene terephthalate glycol components

AbstractThe importance of recycling engineering components and thus obtaining low‐cost production solutions has become prominent in today's world. In this study, the mechanical and dynamic behaviors of three‐dimensional‐printed recycled polyethylene terephthalate glycol (RePET‐G) beams were investigated numerically and experimentally for the first time in the literature. Initially, the governing equations of the beams were determined according to the Bernoulli–Euler beam theory, and these equations were numerically solved using the differential quadrature method and ANSYS program. Subsequently, to validate the accuracy of the numerical models, the obtained natural frequencies were compared with experimental results. It was observed that the numerical results showed good agreement with the experimental results. Finally, the effects of beam length, infill rate, and building direction on the natural frequencies of RePET‐G beams were investigated. The outcomes showed that as the beam length changed, natural frequencies were significantly affected. Increasing the infill rate, especially for beams with vertical building direction, from 20% to 100% led to a slight decrease in the natural frequency values of the structure. Moreover, it was found that for beams with an infill rate of 100%, the natural frequency values obtained in the horizontal building direction were higher than those obtained in the vertical building direction.Highlights Printable recycled filaments have great potential for vibration applications. Sample length affects the first natural frequency value of RePETG parts. Differential quadrature and ANSYS methods can be utilized for the vibration. For the 3D‐printed samples, rising infill rate causes a natural frequency drop.