Beam Displacement Research Articles

Seismic response study of multi-span continuous beam bridges near faults considering permanent displacement attenuation effects

The fling-step effect caused by near-fault ground motion induces a step-like permanent displacement of the ground surface, which decays sharply with increasing fault distance, leading to varying degrees of ground motion at each supporting point of the bridge structure. In this context, multi-span long-span bridges exhibit echelon displacement of the main beam and a more complex internal force response compared to ordinary bridges. To investigate the seismic response characteristics of multi-span long-span continuous girder bridges under near-fault ground motion, this study is based on the permanent displacement attenuation model. The main bridge of the Hongyazi Yellow River Bridge in Shizuishan City, consisting of 16 spans, is taken as the research object. Using OpenSees software, a finite element model for the dynamic analysis of the multi-span long-span continuous girder bridge was established, and its structural dynamic characteristics were compared with the natural vibration test of the actual bridge. Based on simulated ground motions that consider the permanent displacement attenuation effect and spatial variability, the seismic response of the key components of the near-fault multi-span long-span continuous beam bridge is examined. The results indicate that under near-fault ground motion considering the attenuation effect of permanent displacement, the main girder of multi-span long-span bridges frequently deviates from the axis in different directions, ultimately resulting in residual deformation of the main girder post-earthquake. The permanent displacement attenuation effect increases the maximum bending moment response at the pier bottom and causes uneven internal force distribution in the bridge. Ignoring this effect can lead to overestimation of bearing deformation.

Influence of velocity pulse directivity on seismic response of cross-fault bridges

Pulse-type ground motions have special destructive effects on structures, and directivity is one of the fundamental characteristics of velocity pulses. In this paper, the impact of the velocity pulse directivity of seismic motions on both sides of the fault on the seismic response of fault-crossing bridges was quantified using the original records from the Chi-Chi earthquake in Taiwan. First, an automatic baseline correction method was applied to restore the permanent ground displacement, and the direction corresponding to the strongest pulse energy on both sides of the fault was identified based on continuous wavelet transformation. On this basis, the variability of the peak intensity of ground motions on the hanging wall and footwall in different directions, as well as the differences in pulse characteristics between the strongest pulse component and the two initial horizontal components, were analysed. Finally, a typical 5 × 30 m continuous girder bridge was considered as the research object to reveal the influence of the velocity pulse directivity on the seismic response of key parts on both sides of the fault. The results showed that the variability in the peak ground-motion intensity on the hanging wall of the fault was higher than that on the footwall. The displacement variability was up to 863 %, velocity was 262 %, and acceleration was 124 %. The pulse characteristics of the strongest pulse component were stronger than those of the parallel and vertical fault components, and its acceleration, velocity, and displacement response spectra were larger. The amplification effects of the velocity pulse directivity on the transverse bending moment, longitudinal bending moment, and torque of the pier bottom reached 1.3, 1.1, and 1.6, respectively. However, the amplification effect of the velocity pulse directivity on the relative displacement of the pier top, displacement of the main beam, and displacement of the bearing was more than 1.6 times, which was more significant than the internal force of the pier bottom.

Dynamic Modeling and Analysis of Multi-Span Timoshenko Beams Under Moving Loads

Dynamic response analysis of multi-span beams is one of the important topics in the field of highway and railway engineering, which provides valuable guidance for the design, operation and maintenance of multi-span bridges. It is worth considering how to calculate the dynamic characteristics of multi-span beams quickly and conveniently. In this study, an effective analytical method is developed for the dynamic modeling and investigations of multi-span Timoshenko beams under moving loads by employing the assumed mode method (AMM). Based on Hamilton’s principle, the equation of motion of the Timoshenko multi-span beam subjected to moving loads is formulated and the natural frequencies are calculated. A comprehensive investigation is conducted on the dynamic responses of the multi-span Timoshenko beam considering different factors, including the length-to-thickness ratio, disorder degree, arrangement order, number of spans and related parameters of moving loads. In addition, the influence of the interval and velocity of the moving load series on the dynamic responses, including displacement, velocity and acceleration of the multi-span beam, are analyzed in detail. The theoretical calculation results of multi-span Timoshenko beams under moving loads are compared with numerical results obtained from ANSYS software, and the results are in good agreement. This demonstrates that the developed method, which utilizes the AMM to analyze the dynamic characteristics of multi-span beams subjected to moving loads, significantly simplifies the calculations and is well-suited for practical engineering applications.

Design, fabrication, and characterization of a deformation-restricted piezoelectric vibration energy harvester triggered by a stopper

Vibration energy harvesting based on piezoelectric effect is emerging as a promising sustainable energy solution for micro-electromechanical systems and wireless sensor networks. Whereas, reliability issues stemming from excessive deformation-induced damage to piezoelectric materials have hindered the progress of piezoelectric vibration energy harvester development. Herein, an indirect triggering method involving a stopper has been implemented to design the deformation-restricted piezoelectric vibration energy harvester (D-RPVEH). This device utilizes the stopper to limit the maximum deformation of the piezoelectric beam, facilitating unidirectional deformation. Consequently, the D-RPVEH delivers enhanced reliability even under unexpected excessive impacts. The feasibility of the proposed principle and design are proved by finite element simulation and experimental test. Most importantly, the research results are found that the simulated end displacement and experimental voltage of PZT beam declined with the decrease of stopper height difference. Moreover, the efficacy of limiting the piezoelectric beam's maximum deformation by implementing the stopper structure is supported by both simulation and experimental findings. The D-RPVEH device can achieve a peak power output of 2.58 mW at frequencies as low as 5.5 Hz, utilizing an optimal load resistance of 30 kΩ. Furthermore, it can illuminate a minimum of 60 blue commercial LEDs connected in series. Therefore, the D-RPVEH not only has good power generation performance but also has high reliability. This design will provide a reference for the research on improving the reliability of PVEH.

Prediction of dynamic shear and maximum displacement of clamped reinforced concrete beams subjected to impact loading

This paper presents a novel approach for predicting the dynamic shear forces and the maximum displacement of clamped reinforced concrete (RC) beams subjected to impact loading. By integrating wave propagation effects, membrane actions and the time-dependent acceleration distribution into the analysis, the study presents an improved approach based on single-degree-of-freedom (SDOF) analysis and overcomes the limitations of conventional SDOF method. The proposed model is validated against experimental data and finite-element simulations, demonstrating its reliability and accuracy in predicting dynamic response. Based on the validated model, a series of design charts are generated facilitating quick predictions of the maximum shear force at support and the maximum displacement of RC beams under impact, offering practical tools for engineers to enhance the safety and resilience of RC beams against impact loading.

Numerical analysis of fractional‐order Euler–Bernoulli beam model under composite model

The primary objective of this study is to develop a new constitutive model by combining a fractional‐order Kelvin–Voigt model with an Abel dashpot element in parallel. Subsequently, this new model will be incorporated into the Euler–Bernoulli beam's governing equation, utilizing shifted Legendre polynomials as basis functions, a classical orthogonal polynomial system, to solve the fractional‐order partial differential equations. By comparing the numerical solutions with the analytical solutions, we aim to evaluate the applicability of shifted Legendre polynomials in solving such problems and the accuracy of the obtained numerical solutions. Furthermore, we will investigate the performance of viscoelastic HDPE beams under different loading conditions and conduct a comparative analysis of the displacements of HDPE beams under the new constitutive model and the traditional fractional‐order Kelvin–Voigt model. Through this research, we hope to gain a deeper understanding of the characteristics of fractional‐order phenomena and provide more accurate and efficient numerical simulation and analysis methods for the field of structural mechanics, promoting the development of related engineering applications.

Identification of Structural Damage by Rate of Change of Non-Dimensional Displacement of Beams Subject to Moving Loads

Identification of Structural Damage by Rate of Change of Non-Dimensional Displacement of Beams Subject to Moving Loads

A Method for Determining the Fundamental Site Period and the Average Shear Wave Velocity

The soil–structure interaction plays a crucial role in determining the displacement and internal forces of multi-story buildings subjected to strong ground motion. One of the critical dynamic characteristics influencing soil–structure interaction is the fundamental site period and the average shear wave velocity associated with it. This study introduces an original equation to determine these parameters. In addition, for the first time in the literature, the version of the Rayleigh method used for finding the fundamental periods of buildings is used to find the fundamental site period. The soil is modeled as an equivalent shear beam to obtain the proposed equation. The peak displacement is obtained by acting the soil mass as an external load on the equivalent shear beam. For single-layer soil, the fundamental site period is proportional to the square root of the peak displacement of the equivalent shear beam. The least squares method generalizes the proposed relation for single-layer soils to multi-layer soil profiles. Modified Finite element Transfer matrix method is used for calibration in the least squares method. The equations used in the literature and earthquake codes for determining the fundamental site period and average shear velocity are tested on various examples, and it is shown that the method proposed in this study, along with the Rayleigh method, gives better results than these equations. The performances of these two methods and the five commonly used equations are tested and compared on different soil profiles. Transfer functions, Finite Element Method (SAP200) and Modified Finite Element Transfer Matrix Method are used for verification. For all soil profiles, the results obtained from the transfer function, Finite Element Method (SAP200) and Modified Finite Element Transfer Matrix Method are found to be in agreement. The true percent relative error found in the results obtained with the proposed method is 4.47%.

Photonic spin Hall effect on the surface of two-dimensional black arsenic

Two-dimensional (2D) materials have attracted considerable research interest due to their potential optoelectronics applications. Black arsenic (B-As), a cousin of black phosphorus, has exceptionally high anisotropy in physical properties. In this study, we report the photonic spin Hall effect on the surface of two-dimensional B-As, manifesting in both transverse and in-plane beam shifts. By applying the beam propagation model near the surface of anisotropic 2D materials, we demonstrate that B-As exhibits higher or comparable photonic spin Hall shifts due to its extreme anisotropy. Moreover, a substantial spin-dependent beam displacement is observed when the incidence conditions meet the Brewster angle. These findings hold potential for novel scientific research and device applications involving anisotropic two-dimensional atomic crystals.

LVI analysis on the beams with nonuniform cross-sectional area using exponential shear–strain function

Purpose The study aims to investigate the low-velocity impact (LVI) on the surface of a beam with a changeable cross-sectional area. In the study “LVI on a beam with a changeable cross-sectional area and clamped-free boundary conditions”, the effect of changes in the cross-section are on the contact force, the beam displacement, the impactor displacement and the impactor velocity are investigated. Design/methodology/approach To obtain the motion equations, first, a field of displacements of the beam is written using third-order shear deformation of beams, including the exponential shear–strain function, and then the energy method is used. By combining Hamilton’s approaches and Ritz’s method, finally, the equations of motion are extracted. Using ABAQUS finite element code, validation of the theoretical approach is carried out. In this study, the beam with changeable cross-sectional area is considered in such a way that the height of the beam is constant, but the width of the beam changes linearly. Findings The results show that assuming the width of the beam in the clamped support is constant, an increase in the width of the beam in the free support leads to an increase in the peak contact force and the residual velocity of the impactor, also, the peak displacement of the beam and the impactor are decreased. Originality/value It can be shown from the analysis of LVI on beams with nonuniform cross-sectional area that the important influence on the contact force, impactor residual velocity, beam displacement and impactor displacement is achieved.

Maximum displacement prediction model for steel beams with hexagonal web openings under impact loading based on artificial neural networks

The estimation of the maximum displacement of steel beams with hexagonal web openings under impact loads is crucial for the anti-impact design of structures. The dynamic characteristics are complex, and the maximum displacement can be obtained experimentally, although the time cost, and expense of such experiments are high. In this context, a 6-5-1 artificial neural network model based on the Levenberg-Marquardt backpropagation algorithm was developed, incorporating 5-fold cross-validation techniques. Due to limited experimental data, 324 high-precision finite element models were created in bulk using Python-based ABAQUS software scripts to provide additional numerical data, and 26 specimens were designed for drop hammer tests to validate the finite element models. The artificial neural network model on the test data yielded a mean squared error of 0.0268, a mean absolute error of 0.0014, and a coefficient of determination value of 0.9806, with samples having an error of less than 10% comprising 77.16% of the total samples. Using Garson’s algorithm, the contribution of input features was estimated, and a full parameter analysis of the proposed model was conducted. The results indicate that the most significant factor is the impact mass, which accounts for 37.58%. When the impact mass increased from 530 kg to 630 kg, the maximum displacement of Q235 surged by 93.75%. The factor with the least impact is the opening spacing, accounting for 2%, with an average increase in maximum displacement of only 3.45%. Finally, ANN-based equations that can be used as design tools are established.

Polarizing beam splitter for vacuum ultraviolet to x-ray radiation.

We present a v-groove grating functioning as a polarizing beam splitter. The grating works in the off-plane or conical diffraction geometry. In order to guarantee polarization selectivity and efficiency, the v-groove is designed to split the incoming radiation with a single reflection at the Brewster angle of the grating coating. This geometry is conceptually the same as the one reported by Caretta etal. [Struct. Dyn. 8, 034304 (2021)], but it reduces the noise on the splitting ratio introduced by beam-shape variations or beam displacements. We calculate the groove size to simultaneously perform polarization and spectral analysis.

Asymmetric electrostatic dodecapole: compact bandpass filter with low aberrations for momentum microscopy.

Imaging energy filters in photoelectron microscopes and momentum microscopes use spherical fields with deflection angles of 90°, 180° and even 2 × 180°. These instruments are optimized for high energy resolution, and exhibit image aberrations when operated in high transmission mode at medium energy resolution. Here, a new approach is presented for bandpass-filtered imaging in real or reciprocal space using an electrostatic dodecapole with an asymmetric electrode array. In addition to energy-dispersive beam deflection, this multipole allows aberration correction up to the third order. Here, its use is described as a bandpass prefilter in a time-of-flight momentum microscope at the hard X-ray beamline P22 of PETRA III. The entire instrument is housed in a straight vacuum tube because the deflection angle is only 4° and the beam displacement in the filter is only ∼8 mm. The multipole is framed by transfer lenses in the entrance and exit branches. Two sets of 16 different-sized entrance and exit apertures on piezomotor-driven mounts allow selection of the desired bandpass. For pass energies between 100 and 1400 eV and slit widths between 0.5 and 4 mm, the transmitted kinetic energy intervals are between 10 eV and a few hundred electronvolts (full width at half-maximum). The filter eliminates all higher or lower energy signals outside the selected bandpass, significantly improving the signal-to-background ratio in the time-of-flight analyzer.

Mid-span displacement and damage degree predictions of RC beams under blast loading using machine learning-based models

Civil engineering has extensively employed RC beams in various applications. However, these beams are susceptible to damage and failure under blast loading. Assessing damage of RC beams from blasts requires real measurement data and time-intensive numerical simulation, making rapid evaluation a significant challenge. In this study, machine learning (ML) models were developed to swiftly evaluate the damage degree and predict the mid-span displacement of RC beams, comprising three models for each problem. To compensate for the lack of real experiment data, a total of 1041 data points are generated through numerical simulation using ABAQUS to create the training dataset. Additionally, for displacement prediction models, 39 collected measurement data was integrated. Initially, the ML models were established to predict the peak mid-span displacement of RC beams under explosion, with inputs including twelve RC beam structural parameters and two blast load parameters, and the output being the maximum min-span displacement of the beam. Subsequently, the ML models were developed using the same fourteen parameters as inputs, with the output being the beam’s damage degree and failure mode. These models achieved adequate performance, demonstrated by evaluation metrics such as R2, RMSE, MAE, MAPE, with values of 0.95, 5.468 mm, 3.16 mm, 17.7 %, respectively, for regression problem. For the classification problem, metrics such as accuracy, precision, recall, and f1-score were employed, with an overall value of 0.837 for the best model. The results show that the developed ML models can precisely and rapidly assess the damage degree, failure mode and predict the mid-span displacement of the RC beam under blast load, which provides a good method for the anti-explosive protection design of RC beams. The graphical user interface tool was also established for ease of use.

Enhancing photonic spin Hall effect in the long-range surface plasmon resonance structure with antimonene.

In this paper, a long-range surface plasmon resonance (LRSPR) structure with antimonene is proposed to enhance the photonic spin Hall effect (PSHE). By exploiting the LRSPR with antimonene, the maximum transverse displacement of the incident beam with a wavelength of 633 nm can reach 121.4λ (76.9 µm), which is much larger than the previously reported value in the insulator-metal LRSPR structure. Given the high sensitivity of spin splitting to alterations in the refractive index of the sensing layer, PSHE finds application in sensors. Remarkably, the LRSPR structure featuring antimonene demonstrates a sensitivity of 7 × 104 µm/RIU, an order of magnitude higher than that of conventional SPR structures. These results present a promising avenue for integrating PSHE into biosensing applications.

Study on the Closing Sequence of Asymmetric High Pier Multi-Span Continuous Rigid Frame Bridge

In order to study the influence of different closing schemes on the non-symmetrical high-pier multi-span continuous rigid frame bridge, this paper uses Midas/Civil finite element software to simulate the vertical displacement of main beam, stress of main beam, horizontal displacement of pier top and bending moment of pier bottom under four different closing schemes. The results show that the vertical displacement of the main beam is small when scheme 3 is adopted. The stress of the main beam and the bending moment of the bottom of the pier are smaller after adopting the scheme 4 closing scheme. The maximum horizontal displacement of the top pier is smaller after the closure of scheme 1 and Scheme 3. After comprehensive consideration, it is suggested that the closure of Hegou Bridge should be carried out in scheme 4.

To Monitor Fracture Behaviors in Four-Point Cyclic Bending Tests of Low-Activated High Alumina Concrete and Standard Concrete RC Beams Using Acoustic Emission Technique

In this study, acoustic emission monitory (AE) was used to observe and evaluate the mechanical behavior of two kinds of RC beam members, made of low-activation concrete and normal concrete, by general four-point bending test and cyclic four-point bending test. During the loading, acoustic emissions due to cracking, shearing, rubbing, de-bonding or interlocking could be monitored and recorded using a real-time high sampling rate DAQ system and proper sensors; besides, beam displacement, cracking situation and loading were also measured simultaneously. The experiment goals included: (1) to observe the damage mechanisms of the beams under bending test and their corresponding AE performance; and (2) to observe the material fracture and corresponding AE in the beams under the cyclic bending test of 0.5Hz (periodic dynamic condition). After experiments, the fracture history of the beam under general loading test could be revealed through the comparison for the chronicled AE signal density and load/strain data. The damage on beam under the cyclic test could be analysed through the chronological comparison for the cumulative sum of AE signal counts obtained for different test periods and stages. Both the irreversibility on fracture mechanism (affected by the Kaiser effect) and the “remainder toughness” could be discussed through the quantitative analysis on AE characteristics for two different beams. They might relate to the durability and toughness of material for beam.

Optimization analysis for bolted steel I-beam: Considering various sizes of beam web with a focus on sustainability design

Abstract Steel structural construction has consistently held a pivotal role in modern construction practices. Presently, a substantial portion of research efforts has been directed towards the examination of bolted connections, while the optimization of steel beam usage has not garnered equivalent attention. This research initiative is focused on determining the ideal dimensions for the beam web through the utilization of finite element analysis (FEA). This analysis specifically investigates bolted steel I-beams featuring varying beam web sizes under concentrated loads. To achieve this, a three-dimensional (3D) simulation model of a bolted beam-to-column structure has been meticulously constructed and executed within the ABAQUS software to derive optimization insights. The beam web sizes considered span a range from 200 mm, representing a smaller size, to 400 mm, signifying a medium size, and up to 600 mm, which represents a larger beam web size. Following the simulation, the results pertaining to beam displacement and bending stress have been tabulated and compared against manually calculated values to validate the accuracy of the simulation. Remarkably, the percentage disparity between the FEA and manual calculations remained below 5 %, signifying a high level of acceptability. From the post hoc test, the efficiency rate of the 400 mm beam web size stood at 76.67 %, rendering it the most favourable choice in terms of cost-effectiveness and sustainability among the three considered sizes.

Seismic design optimization of space steel frame buildings equipped with triple friction pendulum base isolators

To increase the seismic resilience of structures, it is necessary to utilize seismic isolation to increase structural periods and reduce story drifts. When seismic isolation is implemented, structures are capable of deforming by remaining within safe limits. Thus, more seismically resilient designs are achieved compared to conventional fixed-based structures since lighter structural design weights are attained. The principal aim of this study is to achieve the comparative design optimization of space steel frame buildings equipped with seismic base isolation and to examine the effect of seismic base isolation on optimum structural design weight by comparing the same structures with conventional rigid-based ones. For seismic base isolation, triple friction pendulums are implemented into steel frame buildings. For this aim, four different space steel frame buildings with 4-, 6-, 8-, and 10-story are treated as design examples. A novel design optimization algorithm is encoded, which includes nature-inspired metaheuristic artificial bee colony, crow search, and Archimedes optimization algorithms to achieve design optimizations of triple friction pendulums equipped with seismic-isolated space steel frame buildings. The practice code provisions of load and resistance factor design specification for structural steel buildings have been applied to control the structural design constraints of inter-story drift, top-story drift, strength, displacement, and connections geometry of beams and columns. Eventually, it has been remarked that seismic base isolation significantly reduces the structural optimal design weight of space steel frame buildings.

Analysis of bending vibrations of a three-layered pre-twisted sandwich beam with an exact dynamic stiffness matrix

This paper presents the novel development of the dynamic stiffness matrix for a three-layered symmetric pre-twisted sandwich beam (PTSB), aiming to investigate its free vibration characteristics. The outer layers of the beam are modeled using the Euler–Bernoulli theory, while the core is assumed to deform solely in shear. The boundary conditions and governing partial differential equations of motion are derived based on Hamilton's principle. By applying harmonic variations of displacements, the governing equations of motion are expressed as a tenth-order equation, which is solved to obtain the desired dynamic stiffness matrix. To compute the natural frequencies of in-plane and out-of-plane free vibration for both uniform and PTSBs, the Wittrick–Williams algorithm is employed. The computed frequencies are compared with the results obtained by other authors as well as those obtained from ABAQUS simulations. Various vibration modes of uniform and twisted sandwich beams are plotted and thoroughly discussed. Interestingly, contrary to straight symmetric sandwich beams, the results indicate that flexural displacements in pre-twisted symmetric sandwich beams exhibit coupling in two planes. Additionally, although there are minor changes in vibration frequencies, the mode shapes undergo significant transformations as the pre-twist angle is altered.