Straight Beam Research Articles

Structural performance of perforated arched self-compacted reinforced concrete beams under concentrated static loading

Arched reinforced concrete (RC) beams are a viable solution for use as the main supporting system for large-span halls. This is because of the developed normal force owing to the curvature, which approaches the line of pressure under loading, leading to a balance of the resulting bending moment. Therefore, the curved beam can sustain more applied loads than the ordinary straight beam for the same span. However, providing web openings along the entire span of the arched beam can compromise the ultimate capacity. Thus, the behavior of two-hinged perforated arched RC beams made of self-compacting concrete was investigated experimentally and numerically. The experimental program consisted of 11 RC beams, one straight and 10 arched beams, divided into five groups to study the effects of arching, perforation shape and size, and reinforcement configuration around the perforations. In addition, a parametric numerical study using the ABAQUS program was conducted to investigate the relevant parameters in detail. It was found that the arched beam exhibited remarkable ultimate capacity compared to that of the straight beam; however, the strength gains due to the arching effect reduced significantly due to providing web openings. In addition, it was found that providing additional web reinforcement in both the circular and cross-bar configurations around the perforations significantly enhanced the overall behavior. Furthermore, it was found that the best rise-to-span ratio of arched beams was 0.18 for both solid and perforated ones.

Beneficial effects of the precritical nonlinearities on the lateral buckling of extremely flexible beams

The lateral buckling of extremely flexible beams, uniformly or non-uniformly bent in a principal inertia plane, is studied. An exact polar continuum model of an internally constrained 1D straight beam, immersed in the 3D space, is formulated. The model is linearized in the out-of-plane displacement only, so that it is able to capture: (i) the exact planar non-trivial fundamental path, and (ii) the exact critical point along it, at which the beam experiences out-of-plane flexural–torsional buckling. It is proven that the precritical deflections increase the critical load with respect to that evaluated by the classic theory, in which a trivial fundamental path is assumed, thus playing a beneficial role. Moreover, when the beam is extremely flexible, bifurcation disappears, similar to what discussed in literature for axially soft compressed beams, although via a different mechanism of the eigenvalues.

A new exhaustive semi-analytical method to calculate stress distribution on the surface of a curved beam with circular cross section, with an application to helical compression springs

In mechanical and in civil engineering, stressed curved beams are found in many applications involving failure and fatigue analysis. However, stress formulas of straight beams cannot be applied to curved beams with any reasonable degree of accuracy. Hence, curved beam theory is yet to be properly defined and is only established for particular sets of loads, particular applications, and particular cross-section geometries. This work proposes the first exhaustive solution of stress field calculation on the surface of a curved beam with a circular cross section, computed with an open-access databank preliminary built with FE simulations and considering every kind of static mechanical load applied and any curvatures. Such data are an important prerequisite for probabilistic fatigue life analysis. A numerical campaign was executed with different relative curvatures and was gathered in an open-access stress coefficient databank to facilitate data use. For any given curvature and wire diameter, the method can obtain the distribution of each stress on the surface of the circular curved beam, calculated with any combination of forces and momenta applied on its centroidal line. This calculation method was successfully verified with an application to a cylindrical compression spring. As a result, the present semi-analytical model has a 99.9% accuracy on the maximal Tresca stress calculation, being more than 43,000 times faster than the most realistic FE model. This is a significant breakthrough for researchers and engineers looking to save industrial time, optimization process or fatigue estimations.

Vibrational analysis of a coupled damaged Timoshenko beam-arch mechanical system with von Kármán nonlinearities and layer discontinuity

The present study investigates vibrations in the nonlinear regime of a partially elastically connected beam with damage and either a curved or straight beam, focusing on the time domain. The mechanical system under consideration consists of two beams with varying discontinuities: one in an elastic layer and the other in a narrow cross-section area of the beam. To analyze the vibrations in this coupled system, a p-version finite element method is employed. This method allows for the examination of shear deformable beam-beam or beam-arch systems with small or large discontinuities in the elastic layer and cross-section area of the beam. The main contribution of this work lies in the dynamic analysis of a novel coupled geometrically nonlinear mechanical system. It has been discovered that in specific cases of combinations of discontinuities in the upper beam and elastic layer, a different energy transmission occurs, caused by geometrically nonlinear couplings of the nonlinearity of the elastic layer, to the lower arch, resulting in multiple cycles of oscillations executed by the system in the steady-state regime of vibrations. The analysis considers various scenarios, including the effects of the discontinuity in the viscoelastic connection layer, beam damage, and the varying curvature of the lower arch. General mode shapes are determined, and forced damped vibrations in the time domain are analyzed using the Newmark method. The findings from this dynamic analysis have broad applications in engineering and technical practice.

A novel view on the canonical ‘stretching-due-to-bending’ nonlinear effect: A slighly curved beam

The analysis of nonlinear coupling between flexural and longitudinal vibrations of ideally straight elastic beams is a classical topic in vibration theory. The boundary conditions usually applied in this analysis are formulated as immobile hinges, which generate the canonical ‘stretching-due-to-bending’ nonlinear effect. The key assumption in formulation of this model is neglecting the longitudinal inertia, which may be referred to as ‘static condensation’. The aims of this work are, first, to re-consider this problem from the viewpoint of a nonlinear theory of curved beams, and, second, employ alternative type of boundary conditions, known as class-consistent ones. A paradoxical difference in nonlinear parts of Duffing equations obtained in the limit of vanishing curvature of an initially curved beam and in the case of an ideally straight beam is demonstrated and explained.

Flexural vibration of elastic composite beams using a third-order deformation kinematics

The present study introduces a one-dimensional finite element (FE) model that utilizes third-order deformation kinematics to analyze the flexural vibration of two-layered composite beams with partial shear slip. The proposed model incorporates a three-node straight beam element, utilizing the field-consistent approach and full numerical integration of the stiffness matrix. This approach is adopted to effectively address stress oscillation and shear locking issues, ensuring accurate and reliable results. The analysis focuses on the third-order deformation kinematics of longitudinal displacement within the beam depth, examining each of the two layers individually. The interface between the two material layers is joined using deformable shear connectors, which are represented as dispersed shear springs over the length of the beam. This study focuses on conducting a flexural vibration analysis of two-layered composite beams. The analysis includes the examination of both free vibration and forced vibration responses while considering or omitting the influence of damping under various loading conditions. The validity of the proposed FE model is assessed by the utilization of a two-dimensional model developed within the ABAQUS software. Additionally, the suggested model is evaluated through the process of verification by comparing it with previously published results.

An experimental and statistical study on the characteristics of non-metallic inclusions that serve as hydrogen-induced crack nucleation sites in pipeline steel

This study consists of a statistical study to identify spatial distribution parameters of non-metallic inclusions (NMIs) at hydrogen-induced cracking (HIC) nucleation sites in both low-strength and high-strength steel pipes. The electrochemical cathodic charging method was used to induce HIC in pipeline steel plates, and the nucleation of the HIC was monitored using straight beam ultrasonic testing. Optical microscopy (OM) and scanning electron microscopy (SEM) were used to evaluate the shape, size, area fraction, and separation distance of NMIs. The hydrogen microprint technique (HMT), electron backscattered diffraction (EBSD) analysis, and finite element (FE) stress analysis were performed to characterize HIC nucleation sites. The findings showed that cubical and spinal NMIs, characterized by strong hydrogen trapping capacity due to high misfit strain and von Mises stress, are favored sites for HIC nucleation. The main finding of this study is that the shape and sharpness of NMIs are the factors that determine when NMIs will be a HIC nucleation site, rather than size, as generally accepted.

Modelling of a general lumped-compliance beam for compliant mechanisms

Compliant mechanisms are crucial in a wide range of applications, and straight flexure beams with uniform thickness serve as their fundamental building blocks. While techniques and methods exist to estimate the sophisticated load-displacement behavior of these beams, dealing with the nonlinear large deformation and parametric design of complex compliant mechanisms using these beams remains a significant challenge. To address this challenge, an analytical model has been developed to integrate six independent geometric parameters into a general lumped-compliance beam, known as the general lumped-compliance beam model (GLBM). This approach enables the determinate synthesis of force-displacement characteristics in compliant mechanisms that feature any two flexure beams connected in series, such as the conventional lumped-compliance beam, distributed beam, inverted beam, and folded beam. The closed-form beam constraint model (BCM) is utilized to derive the GLBM that accurately captures geometric nonlinearity and load-dependent effects. To demonstrate the effectiveness of this modeling technique, we verified five specific configurations of the GLBM using nonlinear finite element analysis (FEA). In addition, we selected two representative compliant mechanisms, a revolute joint and a bistable mechanism, for nonlinear analysis and experimental validation, which further showcases the efficacy of this proposed GLBM.

Experimental observations of nucleation and crack growth paths of hydrogen-induced cracking in pipeline steel

The microstructural features that favor hydrogen-induced cracking (HIC) in internal, middle, and external layers of pipeline steels were investigated. The electrochemical cathodic charging was used to induce HIC, and straight beam ultrasonic inspection was identified in which steel layers HIC nucleate and grow. The cracked plates were examined by optical microscope and scanning electron microscope (SEM). The hydrogen microprint technique (HMT) was used to visualize the site of high hydrogen concentrations. Electron backscatter diffraction (EBSD) was used to analyze the role of crystallographic texture in HIC pathways. The results revealed that HIC nucleation and growth are influenced by the segregation degree and inclusion contents, which are higher in the internal surface layer of our studied steels but not consistently so in the middle thickness layer. Further, HIC nucleated in cuboidal and spinal inclusions and propagated along ferrite/pearlite bands with high misorientations. The HMT results showed that hydrogen is present in pearlite colonies, grain boundaries, and non-metallic inclusions. The results indicated that HIC is not solely controlled by the crack geometry.

A practical strategy to identify appropriate application patterns for adhesively bonded joints

AbstractThis paper presents a simple experimental validation of a method for finding optimal application patterns in adhesive bonding, as previously introduced by Flaig et al. (2023). The study uses two examples to demonstrate that the patterns found in theory effectively fill the target gaps after pressing in practice. The results confirm that the identified application patterns fill the target gaps almost perfectly, ensuring excellent joint integrity after the pressing process. In particular, the applicability of the star pattern to fill square gaps is experimentally validated. In addition, the method of creating a rectangle by pressing a cut star connected by a straight beam is also effective. While the theoretical results in Flaig et al. (2023) were already promising, this research now provides experimental evidence of their practical applicability.

Sound delivery to listening point using tangent line method.

In personal audio systems, sounds should propagate toward the listening point and attenuate beyond the listening point. This study deals with controlling directivity and distance attenuation using loudspeaker arrays. The array signal processing is based on tangent line method (TLM), which can generate acoustic beams following arbitrary convex trajectories. A curvilinear acoustic beam is produced as an envelope of tangent lines, i.e., straight acoustic beams. Specifying the envelope length enables controlling distance attenuation while enhancing directivity. In this study, the TLM for arbitrary circular trajectories is formulated. Optimization algorithm is applied to identify the trajectory maximizing acoustic contrast.

Vision-Assisted Millimeter-Wave Beam Management for Next-Generation Wireless Systems: Concepts, Solutions, and Open Challenges

Beamforming techniques have been widely used in the millimeter-wave (mm-wave) bands to mitigate the path loss of mm-wave radio links as narrow straight beams by directionally concentrating the signal energy. However, traditional mm-wave beam management algorithms usually require excessive channel state information (CSI) overhead, leading to extremely high computational and communication costs. This hinders the widespread deployment of mm-wave communications. By contrast, the revolutionary vision-assisted beam management system concept employed at base stations (BSs) can select the optimal beam for the target user equipment (UE), based on location information determined by machine learning (ML) algorithms applied to visual data, without requiring channel information. In this article, we present a comprehensive framework for a vision-assisted mm-wave beam management system, its typical deployment scenarios, and the specifics of the framework. Then, some of the challenges faced by this system and their efficient solutions are discussed from the perspective of ML. Next, a new simulation platform is conceived to provide both visual and wireless data for model validation and performance evaluation. Our simulation results indicate that vision-assisted beam management is indeed attractive for next-generation wireless systems.

Onsite Load Bearing Capacity of Curved-up versus Straigt Beams

Straight and curved-up beams are cast as part of the frame models. The models are made as single-span, double-span, and triple-span models. Experimental investigation is conducted to predict load capacity of curved-up beams compared to straight beams. Six models: single-span, double-span and triple-span are presented. Onsite, masonry blocks and bricks, steel pipes and gravel are used to load the beams uniformly. Load is applied gradually until failure mechanism. Enhancement to load capacity is observed in the range between 8.67% to 14.12%. The average enhancement ratio can be taken as 11% due to curved-up effect. Load capacity of interior curved-up beam/span will enhance by 120.3% and 131.3% for both straight and curved-up beams.

Virtual Coriolis-Force-Based Mode-Matching Micromachine-Optimized Tuning Fork Gyroscope without a Quadrature-Nulling Loop.

A VCF-based mode-matching micromachine-optimized tuning fork gyroscope is proposed to not only maximize the scale factor of the device, but also avoid use of an additional quadrature-nulling loop to prevent structure complexity, pick-up electrode occupation, and coupling with a mode-matching loop. In detail, a mode-matching, closed-loop system without a quadrature-nulling loop is established, and the corresponding convergence and matching error are quantitatively analyzed. The optimal straight beam of the gyro structure is then modeled to significantly reduce the quadrature coupling. The test results show that the frequency split is narrowed from 20 Hz to 0.014 Hz. The scale factor is improved 20.6 times and the bias instability (BI) is suppressed 3.28 times. The observed matching accuracy demonstrates that a mode matching system without a quadrature suppression loop is feasible and that the proposed device represents a competitive design for a mode-matching gyroscope.

Research of Properties and Rational Composition of Ecosafe Building Materials with Ash-and-Slag Waste from Masute Fuel and Coal Combustion

The study evaluates the method for determination of the rational technical and economic indicators, namely the rational composition and flexural strength, of building materials containing ash-and-slag obtained from heat-and-electric power plant as waste from the combustion of masute and coal. Results of method application were obtained. The study is aimed on reduction of the negative technogenic impact on the lithosphere by developing an appropriate environmental protection technology for utilization of the mentioned above waste as a replacement of sand in building materials made of cement-sand mixture. The rational composition of the building materials containing ash-and-slag waste granules was selected basing on the results of two stages of experimental research – mechanical bending tests of straight two-support beams on a rupture machine. It was proposed to provide a complex index for assessment of the efficiency of ash-and-slag waste disposal in the building materials, which refers to relation of the strength limit to the density of the material per unit value. The results of calculation of the index magnitudes were obtained.

Taking inspiration from medieval architecture: Using catenary arches in place of straight beam as the building block into bending-dominated lattice structures

Regular bending-dominated lattice structures use straight strut elements as the building blocks in their unit cell which is easier to deform under compression. To improve their performance, replacing the straight elements with the curved members of catenary arch geometry is proposed. Two representative cases – body centered cubic and simple cubic are designed, manufactured using AlSi10Mg alloy and tested experimentally in this study with their struts replaced by catenary arches. Numerical simulations were also conducted at the unit cell level to understand the stress development and regions of high stress concentrations. The effect of different heat treatment procedures was also investigated for both test cases. It was observed that the use of catenary elements had opposing effects on the strength of the BCC and SCC lattice structures when compared to their straight element counterparts. The higher nodal connectivity adversely affected the strength and the lattice failure depended highly on the same. The residual stress release heat treatment improved the mechanical properties of the lattice structures while the solution treatment and aging reduced the strength and modulus but substantially increased the compressibility of the lattice structures.

On Isospectral Composite Beams

We consider a composite system consisting of two identical straight elastic beams under longitudinal vibration connected by an elastic interface capable of counteracting the relative vibration of the two beams with its shearing stiffness. We construct examples of isospectral composite beams, i.e., countable one-parameter families of beams having different shearing stiffness but exactly the same eigenvalues under a given set of boundary conditions. The construction is explicit and is based on the reduction to a one-dimensional Sturm–Liouville eigenvalue problem and the application of a Darboux’s lemma.

A novel procedure to determine the hoop mechanical properties of pipe materials using ring elongation testing technique

In this study, experiments including axial tensile tests and ring elongation tests, as well as analytical analyses were developed to determine the mechanical properties of ASTM A106 Grade B seamless carbon steel (A106-B) pipe material. Ring elongation tests were performed on the ring specimens to determine the mechanical properties of the A106-B pipe material in the hoop direction. Whereas axial tensile tests were carried out on standard axial tensile specimens to determine the axial stress-strain behavior of the A106-B pipe material. The axial stress-strain curve of the A106-B pipe material was used as a reference to validate the ring elongation test results. Besides, Analytical analyses using curved and straight beam formulas were developed. Directly from the ring elongation tests experimental results, both the curved and straight beam formulas accurately predicted the young's modulus and hoop yield strength of the A106-B pipe material. Moreover, the A106-B pipe material's plastic stress-strain behavior in the hoop direction was also successfully determined directly from the ring elongation test results with high accuracy.

A New Method for Analyzing Dynamic Characteristics of Generalized Planar Frame Structures Under Complex Conditions

This paper presents a novel method for analyzing the vibration characteristics of planar frame structure composed of straight beams with arbitrary shapes. The method is based on the first-order shear theory, which takes into account the shear deformation and cross-sectional rotational inertia of the beams. On the one hand, an improved Fourier series method (IFSM) is employed to approximate the displacement function of the straight beam, and the displacements are determined by using the Rayleigh–Ritz method. On the other hand, the displacements of the curved beam are obtained by using the finite element method (FEM), which are then combined with the IFSM for the analysis of coupled nodes of straight and curved beams. This results in a computational method for calculating the vibration characteristics of complex planar frame structures with concentrated masses, straight and curved beams, arbitrary boundary conditions, and any connection form of nodes. The applicability of the proposed method is demonstrated through numerical examples, including planar frame structure with arbitrary shapes composed of straight beams, different cross-sectional shapes, and combinations of beam with various cross-sectional shapes, as well as planar frame structures with straight and curved beams. The results of the proposed method are validated by comparing them with those obtained from literature or finite element software ABAQUS. The numerical examples show that the proposed method combining the IFSM with FEM has the advantages of high accuracy, good convergence, and strong applicability for calculating the vibration characteristics of planar frame structures.

A hybrid shell-beam element for straight thin-walled tubular structures

A novel beam model is proposed in order to consider deformations of its cross-section in the context of straight thin-walled tubes. For this purpose, the straight beam kinematics is enriched by addition of orthogonal shell-type displacement field of the tube section. Linear strain in terms of displacement is considered in conjunction with the non-linear coupling between local deformation of the section and its global rotation. Both Euler–Bernoulli and Love-Kirchhoff hypotheses for beam and shell kinematics, respectively, are adopted as well as the thin-walled assumption. First-order shear deformation for the radial variable and Fourier expansion in terms of the circumferential variable are also considered for the mid-surface displacement field. Then, the stress tensor is obtained under plane stress conditions. The virtual power principle is finally used to obtain the equations of motion satisfied by the corresponding generalized forces. Afterwards, an explicit updated Lagrangian Finite-Element approach using a lumped mass matrix is proposed for solving the tube governing equations and the stability condition of the time integration is given. Test-cases are then chosen to assess the present tube finite-element. Both static and dynamic problems are considered. First, the proposed model is compared to analytical solutions. Finally, a tube subjected to a distributed patch loading is studied. The influence of the number of Fourier modes, of warping and coupling terms is examined. The proposed model makes it possible to retrieve classical shell solution of the cross-section deformation with significant computational savings.