Solid Beam Research Articles

Equivalent pin-forces or equivalent moments for the modelling of piezoelectric patches: a parametric study

Many piezoelectric (PZ) actuation or sensing systems consist of PZ patches bonded on elastic beams or blades. In order to optimise the design of such systems, Finite Element Analysis (FEA) can be used. However, this option is relatively time consuming and not necessarily appropriate to the first steps of the design process. The replacement of FEA by simple analytical tools is desirable in the early design stages in order to explore the optimal configurations for the device (beam dimensions, patch position and properties). Two main modelling approaches can be found in the literature, based on the Solid Mechanics beam theory. The first approach consists in replacing the PZ patch by two opposite forces positioned at the surface of the beam, each at one extremity of the PZ patch. The second approach consists in replacing the PZ patch by two opposite moments positioned at the neutral axis of the beam, each at one extremity of the PZ patch. The object of this paper is to detail these options, and to evaluate their range of validity. For this purpose, a parametric study is conducted on a cantilever beam structure to compare the different approaches for standard dimensions and material properties. The results of corresponding FEA simulations are taken as reference. It is shown that the validity of analytical models is restricted to a narrow range of material properties and dimensions. This range is chosen when the error between the normalised displacements obtained analytically and those obtained by numerical calculation does not exceed 6%. Within this range, the two-moment model is revealed a more precise choice than two pin-forces. As a consequence, its validity range is larger compared to other analytical approaches. This is due to the introduction of the flexural stiffness of the PZ patch and of a realistic strain profile across the section of the structure. These results can be used to obtain analytical expressions of stress and strains in PZ actuation and sensing devices.

Effect of Web Post Width on Strength Capacity of Steel Beams with Web Openings: Experimental and Analytical Investigation

Day by day, technology has been changing progressively because of the remarkable hastening of research and development activities. Perforated beams are one such example of advancement in construction technology. Steel beams with web openings are those that have regularly spaced web openings along the length of the beam. The web openings are created in various ways such as wire cutting and welding. Castellated and cellular beams differ in the creation of web openings. Studies addressing the effect of web post width of steel beams with web openings on the strength capacity of beams are rare. Therefore, the objective of the present work was to examine the influence of web post width on the strength capacity of beams with web openings. First, experimental tests were carried out on three full-scale specimens of a steel beam with oval-shaped web openings, cellular beam, and solid web beam. The same beam was modeled using finite-element software ANSYS and the behavior was compared in terms of load–displacement curve and failure modes. Later, a detailed parametric study was carried out to study the behavior of beams with web openings having variation in web post width using nonlinear finite-element analysis. The simply supported steel beams with web openings subjected to midspan concentrated load with varying web post width and shape of openings were modeled and analyzed. From the analysis results, it was found that the shape of web openings and the web post width play an important role in the strength capacity of the perforated beams. The maximum strength reduction capacity was found to be 51.78% for hexagonal openings of depth 150 mm and having a web post width of 50 mm. The minimum strength reduction capacity was found to be 8.93% for hexagonal openings of depth 100 mm having a web post width of 500 mm. Web post width plays a significant role in the ultimate strength capacity of beams. Web post buckling is a predominant failure mode in steel beams with web openings and it can be prevented by maintaining sufficient web post width.

Strengthening of Reinforced Concrete Beams with Circular Opening at Flexure Zone by Various Types of Fiber Reinforced Polymer

This paper aims to investigate the flexural behaviour of reinforced concrete (RC) beams containing circular opening at mid-beam span and strengthened using externally bonded Textile Reinforced Concrete (TRC) sheets, Carbon Fibre Reinforced Polymer (CFRP) sheets and Carbon Fibre Reinforced Polymer (CFRP) plates. The flexural behaviour including ultimate load, deflection, crack pattern as well as failure mode was investigated. Five RC beams with the dimensions of 1700 mm length and cross section of 200 mm x 250 mm with design concrete strength of 64 N/mm2 were tested under 4-points loading. The tested RC beams consists of solid beam as a control beam, unstrengthened RC beam with circular opening and strengthened RC beams with circular opening. The circular opening with ratio of 0.32 is classified as small opening with diameter of 80 mm was kept constant for all beam specimens. The inclusions of circular opening at the middle of beam span slightly decreased the ultimate load of beam about 6.2% compared to control beam. The reduction of stiffness was also experienced in RC beam with opening. The application of strengthening in beams with circular openings manages to regain the beam capacity about 17.5 to 22.6% higher than the unstrengthened RC beams with opening.

Experimental Study of RC Hollow Beams with Embedded PVC Pipes

This study investigated the behaviour of reinforced concrete (RC) hollow beams under incremental static loads. Polyvinyl Chloride (PVC) pipes were used to create longitudinal voids in hollow beams. The parameters studied included the size (25 mm, 50 mm and 75 mm diameter) and location (39 mm and 139 mm from beam soffit) of the PVC pipes in the beam. Nine specimens were tested under the four-point load test setup. The loads were progressively increased until the specimens failed. The specimens were analysed based on the failure modes, load-displacement responses and mechanical properties. The hollow beams gave a 2% to 36% lower strength than the solid beams. In terms of the strength per unit concrete, the hollow beams were less efficient than the solid beams. The efficiency ratio of hollow beams ranged from 0.67 to 1.0. For that, none of the proposed hollow beams was recommended.

Numerical Modeling of Concrete Deep Beams Made with Recycled Aggregates and Steel Fibers

A bilinear tensile softening law that can describe the post-cracking behavior of concrete made with recycled concrete aggregates (RCAs) and steel fibers was developed based on an inverse analysis of characterization test data. Numerical simulation models were developed for large-scale concrete deep beams. The tensile softening laws along with characterization test results were used as input data in the analysis. The numerical deep beam models were validated through a comparative analysis with published experimental results. A parametric study was conducted to investigate the effect of varying the shear span-to-depth (a/h) ratio, steel fiber volume fraction (vf), and the presence of a web opening on the shear response. Results of the parametric study indicated that the shear strength gain caused by the addition of steel fibers at vf of 1 and 2% was higher in the deep beam models with a lower a/h of 0.8, relative to that of their counterparts with a/h of 1.6. The effect of a/h on the shear strength gain of the solid deep beam models diminished at the higher vf of 3%. The solid deep beam models with a/h of 0.8 exhibited a shear strength gain of 78 to 108% due to the addition of steel fibers, whereas their counterparts with the web opening experienced a reduced shear strength gain of 45 to 70%.

Structural behavior of hollow-core reinforced self-compacting concrete beams

This paper presents an experimental investigation on the structural performance of hollow-core reinforced self-compacting concrete beams and performs an optimization analysis to select the optimum hollow-core beam section, as well as perform a sustainability analysis. The experimental program includes constructing and testing five beams with different longitudinal hollow-core diameters created by using recycled plastic pipes, as well as a solid beam, used as a reference specimen. The results show that it can reduce the concrete from self-compacting concrete beams with percentages from 5.4 to 14.2 with a decrease in the first crack load from 9.1 to 22.7% and the ultimate strength from 2.3 to 10.5% respectively compared to the reference solid beam. The optimization analysis shows that the beam of 46 mm diameter hollow-core is the optimum selection in the concrete volume reduction of 11.1%, cracking load, and ultimate load reduction of 13.6% and 9.3% respectively among all the other beam specimens. While the sustainability analysis reveals that, using longitudinal voids of diameters from 32 to 52 mm leads to a decrease in the embodied energy with percentages from 5.4 to 14.2% and carbon dioxide emission with percentages from 5.4 to 14.1% respectively. Increasing the longitudinal void diameter makes hollow-core self-compacting concrete beams more ductile and exhibits large deflections before failure occurrences.Article HighlightsTests on hollow-core reinforced self-compacting concrete beams are conducted.Recycled plastic pipes are used to create hollow-core in the beams and to reduce ineffective concrete.Reducing ineffective concrete contributes to sustainability with maintaining a good ratio of beam strength.

Elliptical and circular annular solid electron beam for excitation of hybrid modes in the plasma combined circular and elliptical waveguides

For two new configurations presented and by considering annular solid electron beam with background plasma the growth rates of the hybrid modes and the dispersion relation of electromagnetic waves propagating are studied. The interaction of elliptical and circular annular solid electron beams with plasma is investigated that it occurs microwave radiation generation dependent of configuration dimensions. The structures are including metallic elliptical(circular) waveguide with elliptical(circular) dielectric cladding and a core having a circular(elliptical) dielectric rod in center that it is surround by circular(elliptical)annular plasma and a circular(elliptical)annular relativistic electron beam is injected in to plasma. The electromagnetic fields components in each of regions in the considered configurations are calculated. By applying the boundary conditions dispersion relation and operating frequency are obtained. Furthermore for another case that it is applied an infinite magnetic field to considered structures,the problem is investigated. Numerical computations are made and results are graphically presented.

Large Scale Hydrodynamically Coupled Brownian Dynamics Simulations of Polymer Solutions Flowing through Porous Media.

Large scale simulations of polymer flow through porous media provide an important tool for solving problems in enhanced oil recovery, polymer processing and biological applications. In order to include the effects of a wide range of velocity and density fluctuations, we base our work on a coarse-grain particle-based model consisting of polymers following Brownian dynamics coupled to a background fluid flow through momentum conserving interactions. The polymers are represented as Finitely Extensible Non-Linear Elastic (FENE) dumbbells with interactions including slowly decaying transient forces to properly describe dynamic effects of the eliminated degrees of freedom. Model porous media are constructed from arrays of parallel solid beams with circular or square cross-sections, arranged periodically in the plane perpendicular to their axis. No-slip boundary conditions at the solid–fluid interfaces are imposed through interactions with artificial particles embedded within the solid part of the system. We compare the results of our simulations with those of standard Smoothed Particle Hydrodynamics simulations for Newtonian flow through the same porous media. We observe that in all cases the concentration of polymers at steady state is not uniform even though we start the simulations with a uniform polymer concentration, which is indicative of shear-induced cross-flow migration. Furthermore, we see the characteristic flattening of the velocity profile experimentally observed for shear-thinning polymer solutions flowing through channels as opposed to the parabolic Poiseuille flow profile for Newtonian fluids.

An open source code for two-phase rarefied flows: rarefiedMultiphaseFoam

This paper presents the development and benchmarking tests of an open source code for providing solutions of two-phase rarefied flows. The solver is named in rarefiedMultiphaseFoam and it is developed in OpenFOAM, based on dsmcFoamPlus, which is used for the rarefied gas phase. The solver can produce both steady and transient results for arbitrary 2D/3D two-phase rarefied flows and includes a phase change model for materials that experience melting and solidification processes. The benchmarking tests include momentum and heat exchange between gas phase and solid phases, particle phase change, a converging nozzle that creates a solid particle beam, and transport of solid particles. The tests yield good agreement with analytical and experimental data where available, and are compared to previous numerical results from the literature. Program summaryProgram Title: rarefiedMulitphaseFoamCPC Library link to program files:https://doi.org/10.17632/8vxrc5gsb8.1Licensing provisions: GNU General Public License 3Programming language: C++Nature of problem: rarefiedMultiphaseFoam has been developed to help investigate multiphase problems with rarefied gas and solid phases. The rarefied gas phase is simulated with the direct simulation Monte Carlo (DSMC) method, with both one and two way coupling models available to simulate the momentum and heat transfer between the phases. It provides an easily extended, parallelised, environment.Solution method: rarefiedMultiphaseFoam implements an explicit time-stepping solver with stochastic molecular collisions appropriate for studying rarefied gas flow problems and uses a Green's function model to calculate the energy transfers between phases.

Bending Behaviour of Different Types of Timber I-Joist

Engineered wood I-joist is a structural system that comprises of flanges and web elements, and utilised as beams in buildings. Both elements must work together as a structural system to fit and meet the strength behaviour of a solid wood beam. The main objective of the study was to determine the bending strength behaviour of I-joist which produced from three types of jointed technique (finger, L-butt and nail plate) of oriented strand board (OSB) web element with two types of flange element (Keruing solid wood and laminated veneer lumber (LVL)). A total of 18 specimens of I-joist were tested to determine the bending behaviour, especially the modulus of elasticity (E) and modulus of rupture (MR). From the result of testing, LVL flanges specimen were obtained almost as strong as the specimens with solid wood flanges. Additionally, either solid wood or LVL flange was shown non-significant variances in bending strength behaviour because the MR values of the I-joist were insignificantly affected by flange element material. The I-joist specimen with finger jointed web was observed to be the strongest specimen when compared with other joints. Furthermore, the weakest joint among the three types of joints were fabricated with nail plate jointed web. The failures mode of the I-joist specimens were observed to fail due to tension or compression.

Shear behavior of reinforced concrete beams with web opening near supports

Deterioration of reinforced concrete beam capacity might occur due to introducing web openings to accommodate essential services such as air conditioning, and electricity. These openings might be near supporting columns at locations of maximum shear forces. In this paper, the influence of utilizing web openings near the supports on the behavior of RC beams was experimentally investigated. The enhancement in these beams ‘behavior due to strengthening the openings with external Carbon Fibre Reinforced Polymer (CFRP) sheets was estimated. Six RC beams with different opening sizes located near the supports were cast and tested under four-point loading. Crack pattern, deflections, and strains of the six beams were compared to those of a reference solid RC beam without an opening. Experimental load–deflection and shear strength of the tested beams were compared to those predicted from analytical and code equations. The experimental results revealed that introducing large openings reduced the shear capacity of RC beams by up to 35% compared to that of a solid beam. Also, it was concluded that strengthening the web opening with CFRP sheets increased the shear capacity by 21% ∼ 28% compared to similar beams without CFRP.

General electron conductance expression of the multi-gap extended interaction cavity

To predict the stability of a multi-gap extended interaction cavity used in the klystrons, a general electron conductance expression has been rigorously derived from the small-signal space charge wave theory, where the field shape at the gap edge is described by a uniform distribution or a hyperbolic cosine function. Moreover, it is also pointed out that a simplified expression is acceptable in applications. This formula can be readily applied to the solid and annular beams, and its validity has been demonstrated through the stability analysis of a triple-gap extended interaction cavity, where the effect of adopting different gap field shapes is presented. This general expression is very useful for the parameter choice during the cavity design of extended interaction klystrons.

Optimizing the Load-Bearing Capacity of Cross Timber Beams Using Different Types of Timber

This article examines the operation of structures made of solid wooden beams and composite glued beams of two types, consisting of different types of wood. The object of the study was a beam structure, which is a homogeneous slab resting along a contour of constant stiffness under the action of an external load. The calculation of structures made of glued beams of rectangular cross-section has been performed. The calculation is based on the finite element method, analysis of the main methods and approaches for the optimal design of spatial structural structures/The main unknowns are the displacements and rotations of the nodes of the design scheme, based on this, the idealization of the structure is embodied in a form adapted to the use of this method: this system is presented in the form of a certain set of bodies of a standard type, which is attached to the nodes.

Assessment of Bending Strength of Afara Glued Laminated Timber using Polyurethane (PUR) Adhesive

Timber has long been a popular building material, with benefits such as low energy consumption and the ability to create an in-built atmosphere that helps to mitigate the effects of global warming. Afara (Terminalia Superba) is a well-known timber species with high demand in Nigeria. The objective of this paper is to assess the physical and mechanical properties of Afara (Terminalia Superba) wood, as well as the flexural strength in flatwise bending of its glued laminated timber beam using polyurethane (PUR) adhesive, to determine its viability for structural construction. The research specimens were made using MS758:2001, EN408, and ASTM D198:2013 standards for the physical and mechanical properties tests. By MS758:2001, a shear test for glue line integrity was conducted to assess the bond performance of the glulam. In the laboratory, bending tests were performed on five glulam beams and five solid beams. Glulam beams were glued together with polyurethane (PUR) adhesive. The bending strength of solid wood was higher than that of glue-laminated wood. Solid Afara (Terminalia Superba) beams have a bending strength of 40.09 N/mm<sup>2</sup>, whereas glued laminated timber has a bending strength of 19.18 N/mm<sup>2</sup>. The preliminary investigation of the timber under BS 5268 (structural use of timber) revealed that glue-laminated beams can be used as structural members in a flatwise orientation, despite their strength being lesser than that of solid beams. Also, the polyurethane adhesive strength has an inverse relationship with the moisture content of the specimens at room temperature.

Multidimensional Vibrations of Cable-Harnessed Beam Structures with Periodic Pattern: Modeling and Experiment

The dynamics of space structures is significantly impacted by the presence of power and electronic cables. Robust physical model is essential to investigate how the host structure dynamics is influenced by cable harnessing. All the developed models only considered the decoupled bending motion. Initial studies by authors point out the importance of coordinate coupling in structures with straight longitudinal cable patterns. In this article, an experimentally validated mathematical model is developed to analyze the fully coupled dynamics of beam with a more complex cable wrapping pattern which is periodic in nature. The effects of cable wrapping pattern and geometry on the system dynamics are investigated through the proposed coupled model. Homogenization-based mathematical modeling is developed to obtain an analogous solid beam that represents the cable wrapped system. The energy expressions obtained for fundamental repeating segment are transferred into the global coordinates consisting of several periodic elements. The coupled partial differential equations (PDE) are obtained for an analogous solid structure. The advantage of the proposed analytical model over the existing models to analyze the vibratory motion of beam with complex cable wrapping pattern has been shown through experimental validation.

Residual post fire strength of non-prismatic perforated beams

The main aim of this study is to assess the performance and residual strength of post-fire non-prismatic reinforced concrete beams (NPRC) with and without openings. To do this, nine beams were cast and divided into three major groupings. These groups were classified based on the degrees of heating exposure temperature chosen (ambient, 400, and 700°C), with each group containing three non-prismatic beams (solid, 8 trapezoidal openings, and 8 circular openings). Experimentally, given the same beam geometry, increasing burning temperature caused degradation in NPRC beams, which was reflected in increased mid-span deflection throughout the fire exposure period and also residual deflection after cooling. But on the other hand, the issue with existing openings was exacerbated. The burned NPRC beams were then gradually cooled down by leaving them at ambient temperature in the laboratory, and the beams were loaded until failure to examine the effect of burning temperature degree on the residual ultimate load-carrying capacity of each beam by comparing them to unburned reference beams. It was found, increasing the exposure temperature leads to a reduction in ultimate strength about (5.7 and 10.84%) for solid NPRC beams exposed to 400 and 700°C, respectively related to unburned one, (21.13 -32.8) % for NPRC beams with eight trapezoidal openings, and (10.5 - 12.8) % for those having 8 circular openings. At higher loading stage the longitudinal compressive strain of Group ambient in mid-span of solid beams reach 2700 με, while the others with openings exhibit divergent strain higher than that, it’s about 3300 με meanwhile, the lower chord main reinforcements have been pass beyond yielding stress. Exposure to high temperatures reduces rafters’ stiffness causing a reduction in load carrying capacity, companion with premature failure consequently reduce the strain at the ultimate stage.

Formation of band gaps in periodic composite beams by finite element analysis

It is known that a filtering phenomenon, called a band gap, occurs in structures in which materials or structures with different properties are repeated, and vibration propagation is suppressed in the band gap frequency. This study intends to realize the band gap phenomena using composite beams consisting of metallic materials. First, the wave finite element analysis (WFEM) is applied to derive a dispersion curve, which indicated the conditions for the formation of a band gap. Next, by comparing the results of frequency response analysis using Ansys, the formation of band gaps is confirmed by showing no resonant peaks exist in the frequency bands where band gaps are predicted. By evaluating several periodic composite beams, it was found that the condition for widening the frequency band in which the band gap is formed is a large difference between the EI/ρA values of the two phases. Furthermore, by replacing the hollow beams with solid beams with ρA and EI set to be equivalent, it was shown that it is possible to predict the formation of a band gap by dispersion analysis using WFEM for beams with a complex structure.

Serviceability of Post-fire RC Rafters with Openings of Different Sizes and Shapes

This study deals with the serviceability of reinforced concrete solid and perforated rafters with openings of different shapes and sizes based on an experimental study that includes 12 post-fire non-prismatic reinforced concrete beams (solid and perforated). Three groups were formed based on heating temperature (room temperature, 400 °C, and 700 °C), each group consisting of four rafters (solid, rafters with 6 and 8 trapezoidal openings, and rafter with eight circular openings) under static loading. A developed unified calculation technique for deflection and crack widths under static loading at the service stage has been provided, which comprises non-prismatic beams with or without opening exposed to flexure concentrated force. Two approaches were used to compute the deflection: The first attempt was conducted by using the moment of inertia for solid non-prismatic beam and reduced for those with openings by the ratio of residual rafter self-weight. The second was performed by using the moment of inertia of transformed cracked sections depending on the segmental rafter method. The crack width was determined using the ACI code's equation. The analytical and experimental results were evaluated and found to be in good agreement.

Fast dual-beam alignment method for stimulated emission depletion microscopy using aggregation-induced emission dye resin

A stimulated emission depletion is capable of breaking the diffraction limit by exciting fluorescent molecules with a solid Gaussian beam and quenching the excited molecules with another donut beam through stimulated emission. The coincidence degree of these two beams in three dimensions will significantly influence the spatial resolution of the microscope. However, the conventional alignment approach based on raster scanning of gold nanoparticles by the two laser beams separately suffers from a mismatch between fluorescence and scattering modes. To circumvent the above problems, we demonstrate a fast alignment design by scanning the second beam over the fabricated sample, which is made of aggregation-induced emission (AIE) dye resin. The relative positions of solid and donut laser beams can be represented by the fluorescent AIE from the labeled spots in the dye resin. This design achieves ultra-high resolutions of 22 nm in the x/y relative displacement and 27 nm in the z relative displacement for fast spatial matching of the two laser beams. This study has potential applications in scenarios that require the spatial matching of multiple laser beams, and the field of views of different objectives, for example, in a microscope with high precision.

Investigations for Development of Structures for Control of Fog Contaminations

Characterization of fogs is an important problem that does not have a good solution in real conditions. To investigate this problem, we chose the electromagnetic echo effect (EMEE) because it offers several advantages measurements are fast, accurate and can be contactless. Various concepts for the detection of impurities in the composition of fogs by implementing the EMEE were considered. An overview was made of the advantages and disadvantages of the proposed methods. An experimental setup was designed to conduct studies regarding the development of sensors for the control of fog contaminations. It has been experimentally proven that a change in the generated EMEE signal is observed when a change in the composition of the fog is present. The signal is also influenced by various conditions, e.g. solid interaction efficiency and laser beam intensity, modulation frequency, etc. Those parameters were optimized properly to achieve high sensitivity and accuracy. Research results indicate the possibility to use them for the detection of CBRN agents.