Beam Height Research Articles

Critical lateral‐torsional buckling loads of porous orthotropic rectangular beams containing warping effects

AbstractDue to their elemental porosity, porous materials display individual mechanical properties, rendering them essential components in various engineering applications. So, this study investigates the lateral‐torsional buckling (LTB) sensitivity of porous orthotropic rectangular beams subjected to a concentrated load, including the warping effects. Porosity‐dependent material properties vary along the beam's height via four different porosity distribution patterns. The constitutive equations are obtained using the principle of virtual work based on the classical beam theory containing the warping effect, and the governing equations are solved by performing the Ritz method to obtain the critical LTB load. The porous orthotropic beams and the warping effects add complexity to the analysis. So, the influence of some parameters, such as porosity coefficients, porosity distribution patterns, orthotropy, height‐to‐width ratio, slenderness ratio, and warping coefficients, on the LTB characteristics of porous orthotropic rectangular beams are investigated in detail. The novelty of this study lies in its comprehensive LTB analysis of orthotropic rectangular beams under specific effects, such as porosity and warping factors. The findings offer valuable insights into the LTB characteristics of orthotropic porous beams, contributing to an improved comprehension of their structural behavior and facilitating the design of engineering structures. This study contributes to the composite materials and structural stability analysis, offering potential applications in many engineering domains.

Progressive collapse of beam-to-upright subassemblies of steel storage racks under a column removal scenario

This paper presents an experimental investigation into progressive collapse behaviour of steel storage pallet racks under a column removal scenario. The double-half-span substructure is applied in experimental tests. A total of eight substructures are tested, considering two types of beam-to-upright connections, i.e., boltless and bolted connections, commonly used in pallet racks. Different upright profiles and thicknesses, varied beam heights, and the number of tabs are carefully considered in the tests, and their effects on progressive collapse behaviour of pallet racks are thus evaluated. In particular, the influence of pallet loads is carefully evaluated in this paper. Detailed experimental results of all specimens are provided, including the full-range force-displacement curves and the failure modes. The dominated failure modes observed in the tests are the combination of tab crack and bolt bearing failure leading to tearing of beam-end-connector (T+B), the combination of tab crack and bolt bearing failure leading to tearing of upright wall (T+C), and tab crack (T). The test results revealed that the presence of pallet loads greatly influences structural progressive collapse behaviour and thus should be considered in further studies. Moreover, in bolted connections, smaller beam heights and thinner column thicknesses exhibit better resistance against progressive collapse. Whereas in boltless connections, increasing the number of tabs enhances the resistance against progressive collapse. Generally, the bolted connections are proven to have better resistance against progressive collapse than boltless connections and can be used in storage racks to improve structural robustness.

Seismic performance of square concrete-filled steel tubular column-composite beam single-side bolted joints: An experimental and numerical study

The seismic behavior of square concrete-filled steel tubular (SCFST) column-composite beam single-side bolted joints has not been fully investigated. To address this gap, both experimental and numerical studies were conducted, focusing on the impact of various parameters. This research entailed constructing and testing nine prototypes of SCFST column-composite beam single-side bolted joints, scaled to a 1/2 zoom ratio, under conditions simulating seismic loads. Variables considered in these tests included the presence of stiffener ribs, bidirectional stirrups, the section height of the steel beam, and the axial compression ratio. A finite element model was developed and its accuracy was affirmed through comparison with the experimental outcomes. The analysis encompassed several aspects: the hysteretic response, skeleton curves, strain, ductility, stiffness degradation, and energy dissipation. The findings revealed that the design of bidirectional stirrups is crucial, especially under high axial compression ratios (n = 0.8), in preventing compression-flexure failures at the column ends. The hysteresis curves of the specimens manifested in two distinct shapes: spindle-shaped with bidirectional stirrups and bow-shaped without them. Enhancements such as the addition of stiffener ribs or an increase in the steel beam’s height resulted in a more comprehensive hysteresis curve, and improvements in the initial rotational stiffness, flexural bearing capacity, and energy dissipation capability of the specimens were observed. Notably, even when the beam-column bending capacity ratio in the SCFST column-composite beam single-side bolted joint reached 1.5, the joint’s energy absorption was predominantly governed by the beam’s energy dissipation.

Subsidence Prediction Method Based on Elastic Foundation Beam and Equivalent Mining Height Theory and Its Application

Grouting technology in overburden separation is recognized as an effective method to prevent surface subsidence and reuse solid waste. This study used mechanical analysis to explore deflection characteristics of key strata and accurately predict and control surface subsidence. Conceptualizing the coal–rock mass beneath the key strata as an elastic foundation, we developed a method to calculate the elastic foundation coefficients for various regions and established an equation for key strata deflection, validated through discrete element numerical simulations. This simulation also examined subsidence behavior under different grout injection–extraction ratios. Additionally, combining the equivalent mining height theory with the probability integral method, we formulated a predictive model for surface subsidence during grouting. Applied to the 8006 working face of the Wuyang Coal Mine, this model was supported by numerical simulations and field data, which showed a maximum surface subsidence of 546 mm at a 33% injection–extraction ratio, closely matching the theoretical value of 557 mm and demonstrating a nominal error of 2%. Post-grouting, the surface tilt was reduced to below 3 mm/m, meeting regulatory standards and eliminating the need for ongoing surface structure maintenance. These results confirm the model’s effectiveness in forecasting and controlling surface subsidence with grouting. The study can provide a basis for determining the grouting injection–extraction ratios and evaluating the effectiveness of surface subsidence control in grouting into overburden separation projects.

Convolution Neural Network Development for Identifying Damage in Vibrating Pylons with Mass Attachments.

A convolution neural network (CNN) is developed in this work to detect damage in pylons by measuring their vibratory response. More specifically, damage detection through testing relies on the development of damage-sensitive indicators, which are then used to reach a decision regarding the existence/absence of damage, provided they have been retrieved from at least two distinct structural states. Damage indicators, however, exhibit a relatively low sensitivity regarding the onset of structural damage, further exacerbated by the low amplitude response to a variety of environmentally induced loads. To this end, a mathematical model is developed to interpret the experimental data recovered from a fixed-base pylon with a top mass attachment to transverse motion. Damage is introduced in the mathematical model in the form of springs corresponding to the cracking of the beam's lower end. Families of numerically generated acceleration records are produced at select stations along the beam's height, which are then used for training a CNN. Once trained, it is used to identify damage from acceleration records produced from a series of experiments. Difficulties faced by CNN in correctly identifying the presence/absence of damage in the pylon are discussed, and steps taken to improve the quality of the results are proposed.

Proposal and parametric investigations of square steel tubes as post-tensioned connectors for linear-shaped precast concrete elements

Given the pivotal role of connections in the progress of the precast building industry, issues such as costs, chain collapse, and low robustness in all degrees of freedom are critical considerations. This study draws inspiration from Concrete Filled Steel Tube Elements to design and investigate using simple steel tubes as joints for precast linear-shaped elements. The study proposes and examines uncomplicated joints where two precast reinforced concrete beams are positioned within the tube. The encompassment of the beams by the tube, combined with the application of post-tensioning forces, creates a sturdy integrity between the beams, resembling a head-to-head joint. Through 48 experimental tests, various connection parameters such as beam and tube cross-section height, re-bar quantity, tube thickness, and length were systematically investigated. The experimental setup utilized a three-point bending-shear testing configuration, and the results were compared with monolithic references. The findings demonstrate that these adaptive and ductile connections rapidly exhibit a capacity similar to that of monolithic exact beams. All studied parameters exhibited their influences on the capacity of the connection; however, the primary determinant is the length of the tube. Within the discussed range, the tube length should be at least twice as long as the height of the beam. Failing to meet this criterion would prevent the complete manifestation of the desired failure mechanism.

Performance analysis and design method of strengthening beam-column welded connections against progressive collapse

To address the insufficient collapse resistance of the beam-column welded connection (BWC), this study proposes a strengthening beam-column welded connection with truss elements (BWCTE). A static test on a BWCTE specimen with a composite slab was conducted to investigate its failure pattern, final deflection, and the evolution of axial force, bending moment, and collapse resistance. The results indicate that the addition of truss elements increases the peak load and corresponding deformation of BWCTE by 108.6 % and 27.3 %, respectively, compared to BWC. Moreover, the axial force in the composite beam of the BWCTE specimen achieved the yield axial force, facilitating the complete development of catenary action and optimizing beam performance. Subsequently, primary parameters of the truss element were analyzed using refined numerical models. It is recommended that the projected length of the inside leaning limb is within 0.5 to 0.7 times the height of the steel beam, and the thickness of each limb is within 0.6 to 1.2 times the thickness of the beam flange. Then, the working mechanism of BWCTE was explored through theoretical analysis. The resistance process of BWCTE can be divided into elastic, elastic-plastic, plastic, transition, and catenary stages. The loading and deformation synergies between truss elements and composite beams enable the formation of double plastic zones and double strengthening zones at the beam root, effectively delaying the rupture of the stretched beam flange. Finally, a design method for BWCTE is proposed according to theoretical and numerical analysis.

Design Parameters Affecting Rill Swell Events for Block Caving Applications

Rill swell (RS) events are outflows of dry, fine-grained material mainly observed at drawpoints in cave mining. These events can negatively affect production and have fatal consequences. Unfortunately, comprehensive studies analyzing these events are lacking. This paper uses the discrete element method to study RS events. With this method, a numerical model was constructed and calibrated based on an RS event recorded in Ridgeway Deeps Block Cave. Drawpoint geometries, material properties, and the initial mass of the fine material were then analyzed. The results show that both the brow beam height and drawpoint width had a noticeable influence on the RS magnitude, mainly on the tonnage of the flow and the distance reached by coarse particles dragged into the extraction drift. While the mass of fine material is crucial to the magnitude of RS events, results suggest that narrowing drawpoint width and/or increasing brow beam height can mitigate the impact of RS events.

Numerical characterisation of reaction forces’ contribution to initial stiffness in speed-lock beam-to-upright connections

This article presents a detailed numerical model of speed-lock (boltless) beam-to-upright connections in steel storage pallet rack systems. The model is capable of predicting initial stiffness and characterising the reaction forces of connector-to-upright interactions. The study examines nine configurations, combining three types of uprights and three types of beams with a common connector. Initially, experimental tests were conducted using the monotonic cantilever test method according to EN 15512 standard, with initial stiffness calculated using a standardised version of the initial stiffness method. Subsequently, a numerical analysis was developed through a finite element model based on the experimental setup. The model introduces new geometric details, evaluating each impact on behaviour, particularly on initial stiffness. Results show that numerical accuracy improves with detailed components such as inclined tabs, more detailed perforations, and 3D weld modelling. The contribution of reaction forces of connector-to-upright interactions to initial stiffness was analysed, considering the impact of the rotation centre’s position. It was found that a lower rotation centre position reduces the connector-to-upright lateral contact contribution while increasing tab-to-slot interaction contributions. The impact of beam height and beam weld position on initial stiffness was also analysed, with results showing that increasing these variables consistently led to increased initial stiffness. Finally, the rotation centre’s position was shown to evolve throughout the test, redefining the contribution of interactions. It clarified that connector-to-upright lateral interaction and tab1-to-slot1 and tab2-to-slot2 interactions have the highest contributions. This information is valuable for rack manufacturers to improve, optimise, and ensure the safety of their designs.

Research on Train-Induced Vibration of High-Speed Railway Station with Different Structural Forms.

Elevated stations are integral components of urban rail transit systems, significantly impacting passengers' travel experience and the operational efficiency of the transportation system. However, current elevated station designs often do not sufficiently consider the structural dynamic response under various operating conditions. This oversight can limit the operational efficiency of the stations and pose potential safety hazards. Addressing this issue, this study establishes a vehicle-bridge-station spatial coupling vibration simulation model utilizing the self-developed software GSAP V1.0, focusing on integrated station-bridge and combined station-bridge elevated station designs. The simulation results are meticulously compared with field data to ensure the fidelity of the model. Analyzing the dynamic response of the station in relation to train parameters reveals significant insights. Notably, under similar travel conditions, integrated stations exhibit lower vertical acceleration in the rail-bearing layer compared to combined stations, while the vertical acceleration patterns at the platform and hall layers demonstrate contrasting behaviors. At lower speeds, the vertical acceleration at the station concourse level is comparable for both station types, yet integrated stations exhibit notably higher platform-level acceleration. Conversely, under high-speed conditions, integrated stations show increased vertical acceleration at the platform and hall levels compared to combined stations, particularly under unloaded double-line working conditions, indicating a superior dynamic performance of combined stations in complex operational scenarios. However, challenges such as increased station height due to bridge box girder maintenance, track layer waterproofing, and track girder support maintenance exist for combined stations, warranting comprehensive evaluation for station selection. Further analysis of integrated station-bridge structures reveals that adjustments in the floor slab thickness at the rail-bearing and platform levels significantly reduce dynamic responses, whereas increasing the rail beam height notably diminishes displacement responses. Conversely, alterations in the waiting hall floor slab thickness and frame column cross-sections exhibit a minimal impact on the station dynamics. Overall, optimizing structural dimensions can effectively mitigate dynamic responses, offering valuable insights for station design and operation.

Numerical analysis of the seismic performance of existing steel frames with rigid connection with truss-beam-segments

Addressing the insufficient research on fully welded connection with truss-beam-segments (FWCT), this study conducts a comprehensive investigation into the seismic performance of FWCT and its associated steel frame. Primary parameters influencing the seismic performance of FWCT are examined through numerical analysis, and a design method for FWCT is provided. Subsequently, a time-history analysis of composite frames with FWCTs is proposed to investigate the effect of adding truss-beam-segments during rare earthquakes on the seismic performance of the structure as a whole, along with reinforcement recommendations. The study results show that the width of the truss-beam-segment (TS) should ideally be equal to the width of the beam flange, with a thickness equal to that of the beam flange. The net height should be less than or equal to 0.17 times the clear height of the steel beam. The horizontal angle of the external diagonal leg should be less than or equal to 40°, and the length of the horizontal short leg should be greater than the plastic deformation region length at the beam root. The axial compression ratio for the column should be less than 0.7 to prevent local buckling of the column. As the thickness of the composite slab increases, the initial stiffness and load-bearing capacity of the positive moment region gradually increase, while those of the negative moment region remain relatively constant. Time-history analysis indicates that the maximum story displacement and inter-story displacement of the composite frame with TSs are reduced by 4.7 %–5.3 % and 2.5 %–5.8 %, respectively, compared to the composite frame without TSs under seismic wave action. This implies an enhanced capacity of the composite frame with TSs to withstand lateral deformation. For a mid-to high-rise composite frame with n stories, the addition of TSs was recommended primarily for the first (n/2 + 1) floors where plastic regions occur, aiming for a more economically efficient retrofit design and enhanced seismic performance.

Seismic performance of high-strength steel octagonal double-sided plate joints in wall-type concrete-filled steel tubular columns connected to steel beams

This study explores the use of a novel octagonal double-sided plate joint made from high-strength steel for connecting steel beams to wall-type concrete-filled steel tubular (WCFST) columns, which is a new solution to the problem of traditional side plate extending from the wall and interfering with wall panel installation. Two full-scale test specimens were developed and assessed under cyclic loading. The results illustrate that the joint specimens exhibit considerable energy dissipation capacities. After experimental verification, a reliable finite element model was obtained and used for a parametric analysis of side plate dimensions. The results suggest that the height, thickness, and strength grade of the side plate should be 1.2 times the beam height, 1.0 times the beam flange thickness, and Q460C, respectively. Hence, the well-designed proposed joint can be employed with less steel and is superior to previous joints in terms of load capacity and energy consumption.

Wave-inspired piezoelectric bistable energy harvester considering stress distribution: Design, simulation and experimental investigation

The rapid development of IoT technology has spurred the need for self-driven and low-power sensors. Numerous research studies focused on exploring the efficiency of energy harvesting as a means of powering miniaturized sensors, but the issue of the fatigue life of these energy harvesters has been largely overlooked. Inspired by wave motion, this study proposes a novel bistable piezoelectric energy harvester. The host structure of the harvester is made of a 301 stainless steel sheet preformed to a W-shaped beam, with PVDF piezoelectric films on its upper and lower surfaces. The results show that the proposed wave-inspired beam can significantly improve stress distribution, and the peak stress is 27.5 % lower than that of the arch beam. Experimental results show that the peak open-circuit output voltage can reach 11.8 V, when the pre-deformation height of the wave-inspired beam is 5 mm, the mass of the proof mass is 20 g and the frequency range is 13.6 Hz-18.9 Hz. When the excitation frequency is 13 Hz, the maximum root-mean-square voltage of the PVDF piezoelectric film and output power can reach 4.64 V and 16.25μW (single piece), respectively.

Introduction and application of a drive-by damage detection methodology for bridges using variational mode decomposition

In this research, the variational mode decomposition (VMD) method is used for the drive-by health monitoring of bridges. Firstly, the problem of a half-trailer tractor moving over a bridge is formulated. Next, a Finite Element (FE) code is developed and verified against modal analysis results where complete agreement is found. The vehicle's output signals are decomposed through VMD and then analyzed to identify and precisely locate damage in the bridge structure. The range of applicability of this technique is examined from different perspectives by including various road classes, damage severity and location, and noise. The results prove the robustness and reliability of using VMD for drive-by damage detection. The method outcomes indicate that through the VMD method, cracks with a depth of 10% to 20% of the beam height can be detected even in the case of a rough road profile. A comparison of the results of the VMD and the well-known empirical mode decomposition (EMD) method has also been conducted. This comparison reveals that by implementing the VMD, precise damage locations can be determined, whereas the EMD fails to detect any damage under the conditions considered in this study. The effects of noise and moving vehicle speed are also investigated in the research, and it is found that processing the output signals using VMD can yield reliable estimates of the damage location(s).

Long-Term Monitoring of RC Beams under Different Partial Alkali–Silica Reactions: Experimental Results and Restraint Mechanisms

The alkali–silica reaction significantly impacts the durability of reinforced concrete structures. This paper aims to investigate the structural expansion properties of reinforced concrete beams under different partial alkali–silica reactions. Alkali–silica reaction tests were conducted on four reinforced concrete beams, focusing on immersion depth and NaOH solution position as key parameters. Subsequently, the spatial and temporal distribution characteristics of the beam expansion rate were analyzed. Results indicate notable variations in the expansion’s initiation, rate, and final magnitude at different measurement points on the concrete beam, depending on the soaking positions and depths used. The expansion rate was higher in areas directly immersed in the NaOH solution, decreasing near the reinforcement regions. However, strain distribution, along with beam height, satisfied plane-section assumption in the reinforced beam section. Finally, a regional expansion index was established to quantitatively assess the non-uniform damage by alkali aggregates in beams, and the uniaxial restraint mechanism in reinforced concrete structures was also described.

Nonlinear coupled vibration of an arch-beam structural system

Nonlinear dynamic analysis of a shallow arch coupled with a cantilever beam (resting on Winkler foundation) is investigated by direct perturbation method. Two key parameters, (beam over arch) density ratio and height of beam, recharacterize coupling intensity between arch and beam. Nonlinear dynamic responses of arch-beam coupled model are predicted by asymptotic analysis, which include hardening and softening cases. After numerical verification of arch-beam coupled model, the uncoupled model (i.e., skipping beam-arch coupling) is also investigated for comparison. Besides, two more related but degenerately coupled models, e.g., arch-oscillator coupled model [1] and arch-rigid body coupled model [2] are both compared with the current arch-beam coupled model, revealing one key coupling characteristic of elastic support/foundation, which is however overlooked in previous models, e.g., only partial mass is involved with dynamic coupling.

Numerical Analysis of Corrugated Castellated Beam with and Without Openings

The construction industry is constantly seeking innovative solutions to optimize the performance and efficiency of structural elements. Castellated beams with corrugated webs have emerged as a promising option in this pursuit. Their unique geometry, including web holes, makes estimating shear load capacity different from traditional beams with solid webs. These beams are becoming increasingly popular in engineering and economics due to their advantages. The openings in the web can take various shapes, as detailed in the research paper, which compares the load versus deflection for castellated beams with rectangular and hexagonal openings, analyzed using the software ABAQUS® CAE. The trapezoidal corrugated web configuration notably augments the beam's resistance to buckling failure and furnishes superior resistance to buckling compared to a plain web beam. Predominant factors impacting the efficacy of castellated-corrugated web beams encompass the overall beam height and the size of the web opening. The study conducts a comparative analysis of the ultimate load-bearing capability of these beams about both plain and corrugated web beams. Moreover, the manuscript advances an original technological proposal entailing the integration of a trapezoidal-shaped web into a castellated beam. The load-bearing capacity of castellated beams with various web opening shapes, such as rectangles and hexagons, was contrasted with that of the I beam. Among these shapes, hexagon web opening TWHC has higher Material savings with an increase of 13 % compared to the I beam. The results detail that the corrugated web rectangular castellated beams have less weight and more strength than the corrugated web hexagon castellated beam.

Research on Work Performance of Monolithic Precast Concrete Shear Walls with Post-Cast Epoxy Resin Concrete

Precast concrete structures are popular in the building industry because of their high efficiency and environmental friendliness. In this paper, the U-type reinforcement ferrule connection technique was applied to study the seismic performance of precast concrete shear walls. Five shear wall finite element models and four shear wall specimens were prepared. Both experiments and finite element analysis were conducted to explore the impact of parameters on the work performance of precast reinforced concrete shear walls, such as the variety of post-cast concrete, the form of horizontal joints, and the buckle length of U-type reinforcements. On this basis, the mechanism of failure as well as the characteristics of hysteresis, ductility, and energy dissipation capacity were analyzed. According to the analytical results, the cast in situ reinforced concrete shear wall is inferior to the precast shear wall with post-cast epoxy resin concrete in terms of seismic performance. In addition, the specimen with a keyway on the horizontal joint interface outperforms the specimen without a keyway. With an increase in the buckle length of the U-type reinforcement, there is a rise in the sectional height and stiffness of the hidden beam at the bottom of the wall, while the horizontal load-bearing capacity of the wall is improved. However, its ductility and energy dissipation capacity are decreased. As revealed by a thorough analysis, the construction scheme most suitable for precast shear wall horizontal joints adopts epoxy resin concrete as the post-cast material, the buckle length of U-type reinforcements is approximately one-third the height of the horizontal joint, and there is a keyway at the interface of the joint.

Prediction of shear wall residential beam height based on machine learning

The beam height is an important design parameter that influences structural properties such as load-bearing capacity and stability of beams. In the early stages of structural design, the existing methods for determining beam height mainly include empirical formulae. However, empirical methods are highly subjective, lack accuracy, and are poorly adapted to complex conditions. This paper establishes a beam height prediction model for shear wall residential structures. Using structural design data from projects built by a real estate company across various regions in China, a large dataset of beam heights was collected. The Permutation Feature Importance (PFI) method and six unique machine learning (ML) models were used to rank the importance of input variables. The Gradient Boosting (GB) model, consistent with the feature ranking obtained from PFI, was selected. The model evaluation method was then used to select the number of input features for the GB model, and grid search and K-fold cross-validation were employed to optimize the GB prediction model. This model was compared with a prediction model obtained from a Back Propagation Neural Network (BPNN). Finally, the SHAP method was used to interpret the "black box" machine learning model. The results show that the GB model has higher accuracy compared to the BPNN model, and the input features of the proposed GB model contribute to the beam height in accordance with mechanical laws, demonstrating the model's rationality. The research findings can provide a reference for initial beam height design.

Experimental Investigation on Shear Behavior of Non-Stirrup UHPC Beams under Larger Shear Span–Depth Ratios

Due to the extraordinary mechanical properties of ultra-high-performance concrete (UHPC), the shear stirrups in UHPC beams could potentially be eliminated. This study aimed to determine the effect of beam height and steel fiber volume content on the shear behavior of non-stirrup UHPC beams under a larger shear span–depth ratio (up to 2.8). Eight beams were designed and fabricated including six non-stirrup UHPC beams and two comparing stirrup-reinforced normal concrete (NC) beams. The experimental results demonstrated that the steel fiber volume content could be a crucial factor affecting the ductility, cracking strength, and shear capacity of non-stirrup UHPC beams and altering their failure modes. Additionally, the height of the beam had a considerable effect on its shear resistance. French standard formulae were more accurate for the UHPC beams with larger shear span–depth ratios, PCI-2021 formulae greatly overestimated the shear capacity of UHPC beams with larger shear span–depth ratios, and Xu’s formulae were more accurate for the steel fiber-reinforced UHPC beams with larger shear span–depth ratios. In summary, French standard formulae were the most suitable formulae for predicting the shear capacity of UHPC beams in this paper.