Solid Beam Research Articles

Numerical and Experimental Evaluation of the Mechanical Behavior of FRP-Strengthened Solid and Glulam Timber Beams

Numerical and Experimental Evaluation of the Mechanical Behavior of FRP-Strengthened Solid and Glulam Timber Beams

LTB analysis of pre-stressed steel beams using mono-symmetric thin-walled beam and spatially inclined un-bonded cable elements

A FE procedure is proposed for spatial buckling analysis of thin-walled steel beams that are pre-stressed (PS) by spatially inclined cables. Here, the beams are simply supported, and their cross section can be bi/mono-symmetric. Also, the pre-stressing cables are connected to several deviators under bonded/un-bonded conditions. For lateral–torsional buckling (LTB) analysis of the PS beams, a thin-walled beam element for the steel beam and solid beam elements for the deviator members are firstly formulated using total potential energies. After that, the potential energies of two-node bonded and multi-node un-bonded cable elements are rigorously derived, and the corresponding elastic and geometric stiffness matrices are explicitly presented. Finally, the validity and accuracy of the present FE formulation are demonstrated through numerical examples, and a set of parametric studies is conducted to investigate the effects of initial tension, multi-deviators, vertical and lateral eccentricities, and flexible deviators on the LTB of the PS beams.

Structure-property relationships of velar bone tissue from the energy absorbing horncore of bighorn sheep rams.

Velar bone is the material that fills the horncore of bighorn sheep rams. The architectural dimensions of velar bone are orders of magnitude larger than trabecular bone, and velae are more sail-like compared to strut-like trabeculae. Velar bone is important for energy absorption and reduction of brain cavity accelerations during high energy head impacts, but velar bone material properties were previously unknown. It was hypothesized that velar bone tissue would have properties that are beneficial for increased energy absorption at the material level. Solid velar bone beams were tested using dynamic mechanical analysis and three-point bending to quantify mechanical properties. Additionally, the porosity, osteon population density, and mineral content of the solid velar sails were quantified. The velar bone damping factor (∼0.03 - 0.06) and modulus of toughness (3.9 ± 0.4 MJ/m3) were lower than other mammalian cortical bone tissues. The solid bony sails have a bending modulus (8.6 ± 0.5 GPa) that lies within the range of bending moduli values previously reported for individual trabecular struts and cortical bone tissue. The solid velar bone sails had porosity (6.7 ± 0.9 %) and bone mineral content (66 ± 1 %) in the range of cortical bone values. Interestingly, velar sails contained osteons, which are rarely found in trabecular struts. The velar bone osteon population density (5.8 ± 0.9 osteons/mm2) is in the low end of the range of values reported for cortical bone in other mammals. STATEMENT OF SIGNIFICANCE: Bighorn sheep rams sustain high energy head impacts during intraspecific combat without overt signs of brain injury. Previous studies have shown that the bony horncore plays a critical role in energy absorption and reduction of brain cavity accelerations post impact, which has implications for concussion prevention in humans. However, the material properties of the horncore velar bone were previously unknown. This study quantified the material properties and structure-property relationships of the horncore velar bone at the tissue level. Results from this study will improve our understanding of how bighorn sheep mitigate brain injury during head-to-head impacts and may inspire the design of novel materials for energy absorption applications (i.e., helmets materials that reduce concussion occurrence in humans).

High-Data-Rate and Wide-Steering-Range Optical Wireless Communication via Nonuniform-Space Optical Phased Array

The silicon photonic optical phased array (OPA) featured by high integration and agile beam steering exhibits greatly potential application in optical wireless communication (OWC). In this paper, we demonstrate high-data-rate and long-range OWC using an integrated Silicon-Silicon Nitride OPA chip with 12 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> large aperture. The OPA chip constituted by 128 waveguide grating antennas at nonuniform spacing is employed for wide-steering and small-divergence solid beam steering. In the experiment, we demonstrated 100° wide range communications in horizontal direction via antenna phase tuning. To our best knowledge, 100° is the widest cover range in the reported OPA-based OWC systems. Moreover, the OPA chip is also utilized to achieve up to 32 Gb/s low BER transmission of non-return-to-zero (NRZ) signal over 54 m free space distance. In addition, we also successfully demonstrated more than 50 Gb/s PAM4 signal transmission by measuring clear eye diagrams at the horizontal direction of 0° and 50° over 10 m. Thanks to agile beam steering of the OPA, switching time among arbitrary positions in multi-targets communication can be less than 27 μs. By virtue of tiny beam divergence 0.021° × 0.029° emitted from the OPA, data transmission switching between two targets spaced at 3.5 cm over 20 m can be achieved accurately. The experimental measurement shows the sidelobe crosstalk from the adjacent target channel is less than -25.2 dB. Our demonstrations validate the feasible implementation of the silicon-based OPA in the high-data-rate and wide-steering-range OWC system.

Strengthening of solid beam with fiber reinforced polymers

Timber, concrete and steel are among the traditional building materials used in the construction of buildings. Since concrete is a durable material, it is a building material used in buildings, highways, dams, sidewalks and many other areas. Wood is one of the oldest building materials, and the use of wood and wood-based materials for structural purposes continues to increase. The deterioration of existing wooden structures may result from fatigue and biological attack over time. The cost of replacing the damaged wooden elements is very high, so it seems more appropriate to repair and strengthen the damaged elements. In this study, 20x20x360 mm solid wood beam is reinforced with fiber reinforced polymers and the effect of fiber reinforced polymers on the bending properties of the beam was investigated. In order to determine the bending properties, three-point bending test was applied to the wood beams. As a result of this study, it was determined that the bending properties of wood beam reinforced with fiber reinforced polymer composites were better than the reference samples.

Numerical Simulation of Train-Induced Structural Vibration

Train-induced structural vibration caused more and more attentions nowadays, and the present paper developed a numerical approach of train-induced structural vibration simulation with ANSYS software. The finite element model is composed by buildings, rail, sleepers, ballast and several layers of soil, and the moving load is represented by wheel-rail coupling forces, and both solid element, shell element and beam element are used in the finite element model. Acceleration time history and vibration levels of the key point on the buildings are given, and effect of different wheel-rail coupling forces and the dynamic response of the building are also numerically investigated. Comparisons of free boundary, symmetric boundary, fixed boundary and transmitting boundary conditions on the dynamic responses are also illustrated. Numerical results show that, both boundary condition and load type could affect the dynamic response of the structures near the train tracks, and validation test should be performed firstly to determine the proper boundary condition and load amplitude and frequency. The proposed numerical method provides a powerful technic tool for numerically predicting the dynamic response of train-induce structural vibration, and could also be employed to evaluate the vibration control results of different approaches.

Billion-design-variable-scale topology optimization of vehicle frame structure in multiple-load case

In topology optimization, sufficient resolution and a constraint volume of less than 1% are required to obtain a practical vehicle body structure without solid circular-section frames. To meet the requirement for sufficient resolution, the authors are developing voxel topology optimization software, including a finite element solver that utilizes the building cube method framework available in massively parallel environments. The authors have performed a topology optimization of billions of elements intended for a vehicle frame using 35,000–66,000 processors and measured its parallel performance. In addition, four different methods to treat multiple-load cases required for vehicle performance into single objective functions are examined. As a result, normalizing compliance with the appropriate target energy obtained by the original body-in-white frame balances the optimization performance across cases. In the single-load case, thick solid beams are generated through optimization. In contrast, such solid frames are suppressed in multiple-load cases, resulting in a structure similar to a practical body-in-white frame.

Structural Behavior of Reinforced Concrete Hollow Beams under Partial Uniformly Distributed Load

A Longitudinal opening is used to construct hollow core beam is a cast in site or precast or pre stressed concrete member with continuous voids provided to reduce weight, cost and, as a side benefit, to use for concealed electrical or mechanical runs. Primarily is used as floor beams or roof deck systems. This study investigate the behavior of six beams (solid or with opening) of dimension (length 1000 x height 180 x width120mm) simply support under partial uniformly distributed load, four of these beam contain long opening of varied section (40x40mm) or (80x40mm). The effect of vertical steel reinforcing, opening size and orientations are investigated to evaluate the response of beams. The experimental behavior based on load-deflection measured at central and quarter of tension zones. The experimental test result shows the presence of Hollow decrease the load carrying capacity by about (37.14% to 58.33%) and increased the deflections by about (71.6% for (Hollow ratio 7.4%) to 75.5% for (Hollow ratio 14.8%)) for same applied loadcompared with solid beams with the same properties. The increase shear steel reinforcing will decrease all the deformations at all stages of loading, but particularly after initial cracking and give enhancement in ultimate load capacity of beams by about 31.5% with increasing the amount of shear steel reinforcing by about 50%. Finally, ductility is increased in all cases under partial uniformly distributed load when hollow ratio decreased by about 50% or increased in shear steel reinforcing by about 50%

Numerical modeling of fluid–structure–piezoelectric interaction for energy harvesting

In the present work, we propose a numerical coupling scheme combining the corotational Finite Element Method (FEM) for solid beams, the regularized Lattice Boltzmann Method (LBM) for fluid flows and a PiezoElectric Model (PEM) for energy harvesting module. The proposed coupling method can be employed to numerically solve Fluid–Structure–PiezoElectric Interaction (FSPEI) multiphysics problems which are the fundamental phenomena in the considered energy harvesting applications. In the proposed coupling method, the FEM and LBM are strongly coupled through the implicit Immersed Boundary Method (IBM) ensuring exactly the no-slip condition. Comparing with volumetric FEMs, the adopted corotational beam formulation can not only allow for large structural displacements, but also help improve the computational efficiency, as the solid structures for energy harvesting devices are usually slender under large motion. The piezoelectric effects are incorporated into the corotational beam dynamics with the help of the virtual work principle. The FEM, LBM and PEM are coupled together in a strong way in the sense that the time integrations are carried out without staggered communications. The proposed coupling scheme is assessed by a series of validation test-cases with increasing complexity, in which a good agreement is obtained with references.

Enhancing the Shear Capacity of RC Beams with Web Openings in Shear Zones Using Pre-Stressed Fe-SMA Bars: Numerical Study

Openings in the shear span can significantly affect the structural behavior of reinforced concrete (RC) beams, particularly in terms of shear capacity and crack propagation. This paper aims to investigate the feasibility of strengthening the web opening in the shear zone of RC beams by using iron-based shape memory alloy (Fe-SMA) bars, providing valuable insights for structural engineers and researchers. Numerical analysis with ABAQUS/CAE 2020 software was employed in the current study. The research was divided into six groups of beams with web openings of different lengths (150, 300, and 450 mm), prestressing levels (0%, 30%, and 60%), and reinforcement diameters (14, 18, and 22 mm) of Fe-SMA bars. The results show that the presence of web openings can cause a significant reduction in the cracking and ultimate loads of the beams, with reductions ranging from 11% to 50% and 36% to 48%, respectively. However, by adding pre-stressed Fe-SMA bars around small web openings (100 × 150 mm), the shear capacity of the beam is restored, and the beam exhibits behavior similar to solid beams. Additionally, activating the Fe-SMA bars by 30% and 60% resulted in almost similar cracking loads but improved load-carrying capacity of the beam with small openings by 12% and 9%, respectively, compared to the solid beam. The technique proposed for enhancing shear strength is most effective for beams with small (100 × 150 mm) and medium (100 × 300 mm) web openings as it can restore both the beam’s shear strength and stiffness. However, for beams with larger web openings (100 × 450 mm), the use of activated Fe-SMA beams can recover almost 90% of the solid beam’s shear capacity. Furthermore, reinforcing small openings with Fe-SMA bars of different diameters enhances beam shear capacity and stiffness, while for larger openings, higher Fe-SMA reinforcement ratios could potentially restore the beam’s full strength and stiffness. This study emphasizes the importance of strengthening web openings in RC beams, particularly in shear zones, and provides significant insights into how to strengthen beams with web openings, thereby contributing to developing safer structures. However, further laboratory experiments are recommended to validate, complement and extend the findings of this numerical study.

Load-Bearing Performance of Non-Prismatic RC Beams Wrapped with Carbon FRP Composites

This study investigated the influence of CFRP composite wrapping techniques on the load–deflection and strain relationships of non-prismatic RC beams. A total of twelve non-prismatic beams with and without openings were tested in the present study. The length of the non-prismatic section was also varied to assess the effect on the behavior and load capacity of non-prismatic beams. The strengthening of beams was performed by using carbon fiber-reinforced polymer (CFRP) composites in the form of individual strips or full wraps. The linear variable differential transducers and strain gauges were installed at the steel bars to observe the load–deflection and strain responses of non-prismatic RC beams, respectively. The cracking behavior of unstrengthened beams was accompanied by excessive flexural and shear cracks. The influence of CFRP strips and full wraps was primarily observed in solid section beams without shear cracks, resulting in enhanced performance. In contrast, hollow section strengthened beams exhibited minor shear cracks alongside the primary flexural cracks within the constant moment region. The absence of shear cracks was reflected in the load–deflection curves of strengthened beams, which demonstrated a ductile behavior. The strengthened beams demonstrated 40% to 70% higher peak loads than control beams, whereas the ultimate deflection was increased up to 524.87% compared to that of the control beams. The improvement in the peak load was more prominent as the length of the non-prismatic section increased. A better improvement in ductility was achieved for the case of CFRP strips in the case of short non-prismatic lengths, whereas the efficiency of CFRP strips was reduced as the length of the non-prismatic section increased. Moreover, the load–strain capacity of CFRP-strengthened non-prismatic RC beams was higher than the control beams.

Nonlinear Analysis on Torsional Strengthening Of Rc Beams Using Cfrp Laminates

This research is devoted to investigate the behavior and performance of reinforced concrete beams strengthened with externally bonded Carbon Fiber Reinforced Polymer (CFRP) laminates under the effect of torsion. In this study a theoretical analysis has been conducted using finite element code ANSYS. Six previously tested beams are used to investigate reinforced concrete beams behaviorunder torsion, two of them are solid and the rest are box-section beams. Also, two beams are without CFRP reinforcement, which are used as control beams for the strengthened one, and the other four beams are strengthened with CFRP laminates with different number of layers and spacing. Numerical investigation is conducted on these beams, and comparisons between the available experimental results for these beams and numerical results from the current study are made. Conclusions from these comparisons are presented and discussed. An increase of about 15.6% in the ultimate torque for the solid beam and of about 9.8% in the ultimate torque for the box-section beam is observed after using the CFRP strips. A parametric study is carried out to study the torsional behavior of RC beams having different number of CFRP layers and concrete compressive strength; also U-wrap for the CFRP configuration is investigated.

Flexural strength and drift ratio of reinforced concrete beams with longitudinal square hole

The main aim of this investigation was to study the flexural strength and drift ratio of simply supported rectangular RC hollow beams (with a longitudinal square hole) subjected to gradually increased and symmetrically applied one-point load. Each hollow beam had a 300 mm2 and 900 mm2-area of a square, and the position of the center of the hole was 80 mm from the top. The cross-section of the beam, the amount of longitudinal steel, and the stirrups of the beam was kept constant. The flexural strength and deflection of these hollow beams were compared with that of a solid RC beam that had the same outer dimensions and steel reinforcements. A comparison of experimental results shows that specimens with square holes 10 x 30 achieve higher peak load, MOE, and MOR. On other hands, solid beam specimens achieve a larger drift ratio.

Dynamics modeling and stress response solution for liquid-filled pipe system considering both fluid velocity and pressure fluctuations

Dynamics modeling and stress response solution of the liquid-filled pipe system (LFPS) are necessary to predict the reliability of the pipe. However, the existing methods still need further research to solve the stress response of pipe system, and the influence of fluid velocity and pressure (FVAP) fluctuations on the vibration response is not considered. Based on this, a dynamics modeling method named FEM-TMM is proposed to solve the natural characteristics and stress response of the LFPS based on the combination of the finite element method (FEM) and transfer matrix method (TMM), which can consider the fluctuations of FVAP. The incompatible solid (Solid-NC) and virtual beam (VBeam) elements are constructed to establish the finite element models of the solid and fluid domains respectively, and the coupling elements are introduced to couple the solid and fluid domains. TMM is used to solve the FVAP fluctuations of the LFPS under external excitation, and the steady-state resonant frequency and vibration mode are obtained based on the iteration method. The virtual force iteration and stress smoothing methods are adopted to solve the stress response of the LFPS, then the dynamics modeling method FEM-TMM is obtained, and the rationality of the modeling method is verified by experiments. Finally, the analysis results show that the influence of velocity fluctuation on resonance frequency and stress response can be ignored. The critical pressures of resonant frequencies are less than or equal to those of resonant frequencies without considering pressure fluctuation. There are multiple stress barriers and valleys in the different-order stress responses of the LFPS, and the pressure fluctuation will change the distribution laws and maximum peak values of the stress barriers.

Enhanced electron radiation shielding composite developed by well dispersed fillers in PDMS polymer

This study reports a novel shielding material against high energy electron beam, where bismuth oxide (Bi2O3) and multiwalled carbon nanotube (MWCNT) nanoparticles added in a polymer matrix can solid electron beam radiation several times more efficient than aluminum with the same areal density. The polymer nanocomposites were prepared by dispersing nanoparticles in polydimethylsiloxane (PDMS) with a simple one-step fabrication process, in five areal densities (0.5, 1, 1.5, 3, and 5 g/cm2). All the samples were irradiated by 9, 12, 16, and 20 MeV electron beam. The prepared PDMS/CNT/BiO (CNT and BiO are the shorten name of fillers for coding the samples) showed better electron shielding ability than aluminum (Al) for any areal density. The weight advantageous of nanocomposite over aluminum was calculated up to 36 wt% for same attenuation efficiency. The thermal stability of nanocomposites up to 415 °C, as well as the tensile strength of up to 4.7 MPa, exhibited the high potential of developed samples for high energy electron beam shielding in medical and aerospace applications.

Behaviour of cellular steel beams at ambient and high-temperature conditions

New developments in building construction have been observed to attain sustainable design criteria and the efficient use of raw materials, as steel is an example. This led to an increase in recent research on the optimization of geometric configurations of web-opening steel sections to meet cost-effectiveness in structural design. Improvement of the design method for perforated unrestrained steel beams to assess their behaviour under lateral torsional buckling (LTB) is still an ongoing issue for scientists and designers alike. In this article, cellular beams bound to instability were studied analytically by Eurocode and numerically by the finite element method to investigate their behaviour at ambient and elevated temperatures due to fire. The analysis encompasses the effect of the coupling and the endplates' thickness on the cellular beams' collapse strength considering the initial geometric imperfections and material nonlinearities. A parametric study including changing temperature, cross-section geometry, and web aperture configurations was done for beams subjected to uniform bending and distributed load. The analyses depicted the following failure modes: LTB and LTB+ plastification of the two T-section (P-2 T) for end moment load and yielding of top tee section's flange (B-1 T), P-2 T, web post-buckling (WPB), Vierendeel mechanism (VM) and LTB for a distributed load. Combined failure modes such as LTB + WPB, LTB + VM and LTB + VM + WPB have also been observed. Buckling curves for cellular beams were assessed by comparing FE reduction factors with those of the buckling curve recommended by Eurocode 3 for equivalent solid steel beams. A new proposed formula for the plateau length of the LTB curves was obtained, based on the mean squared error method (MSE) between the numerical results and Eurocode formulae. The comparison between the numerical and the simplified design method predicted results shows that the proposed formulae have reduced the discrepancy and improved the LTB curve to better assess the cellular beams behaviour.

Dynamics modeling and vibration transmission visualization of fluid-conveying series pipe system based on FEM-TMM

The fluid-conveying series pipe system (FCSPS) is an important part of the pipe system, and its stress response solution and vibration transmission analysis are of great significance to life prediction and defect analysis. In this paper, the finite element method (FEM) and transfer matrix method (TMM) are combined. The dynamics modeling method named FEM-TMM is proposed to solve the stress response of the FCSPS, and the structural intensity method (SIM) is used to perform vibration transmission visualization. The incompatible solid (Solid-NC) and virtual beam (VBeam) elements are constructed to establish the finite element model of the solid and fluid domains respectively. The zero-thickness (Z-T) and coupling elements are created to simulate the contact of the pipe joint and fluid-solid coupling. TMM is used to solve the responses of fluid velocity and pressure (FVAP) in the frequency domain, then FEM-TMM for the pipe system is obtained and verified by experiments. Furthermore, the stress smoothing method and SIM are introduced to solve the stress response and perform vibration transmission visualization. The results show that the SIM can visualize the vibration transmission of the pipe system, and the pipe joint plays the role of transmission, conversion, and redistribution of vibration energy.

Shear capacity of UHPFRC deep beams with web openings

The shear capacity of Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) deep beams with web openings located between the provided stirrups was investigated experimentally. All the tested beams were constructed from the same UHPFRC mix containing steel fibers volume fraction of 1.5 %. The test program included eight simply supported deep beams with the same cross-section and same longitudinal reinforcement. The principal studied parameters were opening height, width, location, and the stirrups ratio ρv %. The provided stirrups spacing sv was considerably more than the maximum stirrups spacing sv,max required by ACI 318 code for normal reinforced concrete, while sv,max required by the Egyptian code (ECP 203) were more or equal to sv. The equations used by French recommendations (AFGC) and Korea Concrete Institute (KCI) for the shear design of UHPFRC deep beams have been examined. The experimental results indicated that the shear capacity of UHPFRC deep beams is mainly controlled by opening height, width, and location. Square opening with a height of 20 % of the beam's overall height located at the natural load pass caused reduction of shear capacity by 43 % compared with the reference solid beam. Increasing the opening width by 75 % symmetrically around the natural load pass reduced the shear capacity of the UHPFRC beam by about 21 % while increasing the opening width by 125 % from one side out of the load pass caused a reduction by only 5 %. Increasing the stirrups ratio by 80 % for beams of similar opening size and location, increased the shear capacity by 17.1 %. Predicting the ultimate shear strength of the tested UHPFRC deep beams with openings of height 20 % and 40 % of the beam's total height using the equations of AFGC was just safe if these equations were calculated by deducting the height of opening from the beam effective depth. The equations used by KCI were also safe with a factor of safety about 6 % more than that of AFGC.

Radially polarized beams' phase filtering focal properties based on path integral analysis.

This paper introduces the path integral (PI) to the analysis of radially polarized (RP) beams' tight focusing problem. The PI makes the contribution of each incident ray on the focal region visible and then makes it possible to choose the filter's parameters more intuitively and precisely. Based on the PI, a zero point construction (ZPC) phase filtering method is realized intuitively. With ZPC, the focal properties of RP solid and annular beams before and after filtering were analyzed. The results show that the combination of a large NA annular beam and phase filtering can result in superior focus properties.

Behavior of hollow self-compacted concrete beams reinforced with aluminum sections

This paper presents a study on improving the flexural performance of self-compacting hollow concrete beams with embedded aluminum sections, both experimentally and numerically. The experimental program involved testing three specimens to illustrate the impact of the bare and aluminum-reinforced voids on the mechanical properties of the hollow beams relative to the solid reference beam. A three-dimensional (3D) non-linear finite element model (FEM) was initially developed using ABAQUS software and validated against experimental results. The validated model examined the effects of void area (16–49% of the beam cross-section), void configuration (square or circular), longitudinal tensile reinforcement ratio (0.41–1.19%), and shear reinforcement ratio (0–0.56%) on the failure patterns and load–displacement relationships of hollow reinforced concrete (RC) beams with or without reinforced internal aluminum sections. Results showed that the embedded aluminum reinforcement promoted a more uniform distribution of flexural cracks along the effective length of the hollow RC beams and delayed the formation of shear cracks compared to the bare specimens. Furthermore, the embedded aluminum reinforcement effectively restored the ultimate capacity of the hollow beams with a void area ranging from 16 to 36% of the beam cross-section. Despite having the same area, the ultimate load-carrying capacity of both bare and reinforced beams featuring circular voids was higher than those with square voids.