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Keywords = stiffness calculation

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23 pages, 18768 KB  
Article
Deflection Analysis of Steel Truss Web–Concrete Composite Beams Based on Zigzag Beam Theory
by Ningning Zhou, Feng Gao, Rongqiao Xu and Yang Zhao
Buildings 2026, 16(6), 1183; https://doi.org/10.3390/buildings16061183 - 17 Mar 2026
Viewed by 130
Abstract
To address the inherent inaccuracies of the classical beam theory (which overestimates the flexural stiffness) and the “quasi-plane section method” (which neglects the shear deformation) in the deflection analysis of steel truss web–concrete composite beams, this study homogenizes discrete steel truss web members [...] Read more.
To address the inherent inaccuracies of the classical beam theory (which overestimates the flexural stiffness) and the “quasi-plane section method” (which neglects the shear deformation) in the deflection analysis of steel truss web–concrete composite beams, this study homogenizes discrete steel truss web members into a continuous steel web with equivalent thickness based on the strain energy equivalence principle. This homogenization is conducted under the assumption of fixed-end constraints for web members, thus establishing a sandwich laminated beam model. Incorporating the assumptions of zigzag axial displacement and layer-wise quadratic parabolic transverse shear stress, this study adopts the governing equations for static bending of composite beams derived via Hamilton’s mixed energy variational principle—this theory eliminates the need for an artificial shear correction factor, as the transverse shear stress naturally satisfies the zero boundary conditions at the upper and lower surfaces and the continuity condition at the interlayers. Analytical solutions for bending deflection under uniformly distributed loads are derived and validated against three-dimensional (3D) finite element (FE) models. The analysis results of a 45-meter-span beam demonstrate that the relative error in the maximum deflection of both simply supported beams and cantilever beams calculated by the proposed method is approximately 5%, which is significantly superior to the classical beam theory; the deflection induced by the zigzag effect at the mid-span of simply supported beams accounts for 15% of the total deflection, making it an indispensable key component in structural design. This method enables accurate deflection prediction and provides reliable technical guidance for the preliminary design of steel truss web–concrete composite beam bridges. Full article
(This article belongs to the Section Building Structures)
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15 pages, 4598 KB  
Article
Performance Analysis of a Novel Shallow Oil Chamber Hybrid Journal Bearing with Adjustable Depth
by Haidong Hu, Youmin Rong, Hailong Cui, Hanwen Zhang, Yu Huang and Guojun Zhang
Lubricants 2026, 14(3), 129; https://doi.org/10.3390/lubricants14030129 - 17 Mar 2026
Viewed by 106
Abstract
A novel shallow oil chamber hybrid journal bearing with adjustable oil chamber depth was designed based on piezoelectric ceramics, inspired by conventional shallow oil chamber bearing structures. The computational fluid dynamics method is used to analyze the bearing characteristics of shallow oil chamber [...] Read more.
A novel shallow oil chamber hybrid journal bearing with adjustable oil chamber depth was designed based on piezoelectric ceramics, inspired by conventional shallow oil chamber bearing structures. The computational fluid dynamics method is used to analyze the bearing characteristics of shallow oil chamber bearings, including the volume flow, the seal oil pressure, load capacity and stiffness. An experimental platform equipped with signal acquisition device and piezoelectric ceramic control device was developed. The eddy current sensors collected the displacement signal at the shaft end. The required voltage was calculated by the displacement signal. The piezoelectric ceramics elongated or shortened, causing a displacement of the same magnitude in the depth of the oil chamber, thereby controlling the radial displacement of the shaft. The adjustment effect of this bearing was verified by experiment for no-load and 500 N load at 200–1000 rpm, with a baseline initial oil chamber depth of 20 and an oil supply pressure of 2 MPa. The results showed that compared with the case without adjustment, the accuracy in Y direction has increased from 8.9 μm to 1.9 μm (max. 78.4%) after adjustment. Under the above load conditions, the displacement can be controlled below 2 μm, indicating a significant improvement in shaft vibration resistance. Full article
(This article belongs to the Special Issue Hydrostatic and Hydrodynamic Bearings)
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15 pages, 3660 KB  
Article
Dynamic Stiffness Characteristics of Bearings Under Combined Loads with Rotor Excitation
by Wei Dou, Shengdi Sun, Xinjie Zang, Xi Kuang and Zhilei Jin
Lubricants 2026, 14(3), 128; https://doi.org/10.3390/lubricants14030128 - 17 Mar 2026
Viewed by 175
Abstract
The unbalanced excitation of a rotor has a significant impact on the dynamic stiffness of the bearing. Traditional unbalanced excitation force models for the calculation of bearing stiffness are usually simplified as single-directional excitation models, which cannot fully reflect the impact of unbalanced [...] Read more.
The unbalanced excitation of a rotor has a significant impact on the dynamic stiffness of the bearing. Traditional unbalanced excitation force models for the calculation of bearing stiffness are usually simplified as single-directional excitation models, which cannot fully reflect the impact of unbalanced excitation of the rotor on the dynamic stiffness of the bearing. A bidirectional excitation model based on orthogonal decomposition is used in this paper and is introduced into the finite element model of the bearing based on ABAQUS. The proposed bearing mechanics model is verified through numerical software and a bearing rotor system test rig. The effects of single/bidirectional excitation models on the dynamic stiffness of bearings were compared. The variation in bearing dynamic stiffness characteristics under rotor excitation and axial load were discussed. The results show that the presented model has good consistency with experimental results (the proposed model yields a maximum stress deviation of only 2.42% compared to MESYS numerical results and a maximum dynamic stiffness difference of 9.12% against experimental data). The traditional unidirectional excitation force model can only consider the influence of excitation frequency on the dynamic stiffness of bearings. However, the unbalanced excitation force model considering bidirectional excitation can further take into account the influence of excitation amplitude on the dynamic stiffness of bearings. Under the combined effect of excitation frequency and excitation amplitude, the radial dynamic stiffness of bearings shows a quadratic nonlinear hardening trend with rotational speed. As the rotational speed increases, the contribution of axial load to the radial stiffness significantly enhances: in the low-speed zone, its influence is only approximately 8%, while in the high-speed zone, it increases to 34%. Although the modeling method formed in this paper does not take into account the thermal–fluid dynamic coupling effect of the lubricating oil film, the obtained laws can provide a basis for the dynamic design of rotor systems of actual liquid rocket engines and have certain engineering application value. Full article
(This article belongs to the Special Issue Low Viscosity Medium-Lubricated Bearing)
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18 pages, 1672 KB  
Article
Theoretical Research on Eccentrically Braced Composite Frames with Vertical Shear Links
by Yan-Kai Huang, Liang-Dong Zhuang, Hong-Yu Wang, Yan Li and Li-Long Fan
Buildings 2026, 16(6), 1166; https://doi.org/10.3390/buildings16061166 - 16 Mar 2026
Viewed by 89
Abstract
This paper presents a theoretical study on the seismic behavior and working mechanisms of eccentrically braced composite frames with vertical shear links. A theoretical model is established based on structural mechanics principles to analyze the internal force distribution and deformation patterns under lateral [...] Read more.
This paper presents a theoretical study on the seismic behavior and working mechanisms of eccentrically braced composite frames with vertical shear links. A theoretical model is established based on structural mechanics principles to analyze the internal force distribution and deformation patterns under lateral loading. Formulas for the lateral stiffness, bending moments in beams and columns, and joint rotations are derived. A multi-stage theoretical skeleton curve model is proposed, identifying key points such as cracking, yielding, peak strength, and failure, along with corresponding methods for calculating load and displacement values. The theoretical results show good agreement with experimental data, effectively predicting the structural stiffness, load-bearing capacity, and deformation behavior. Key design parameters affecting structural performance are identified, including the beam–column linear stiffness ratio, geometric properties of the shear link, and brace stiffness. The study provides a theoretical basis and practical methodology for the seismic design of such structures. Full article
(This article belongs to the Section Building Structures)
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22 pages, 6025 KB  
Article
Interface Force Transfer Mechanism of Internal Prestressing and Section Enlargement Composite Reinforcement in PC Box Girder Bridges
by Qu Wang, Xiangyu Han, Ziming Fang, Qingxiong Wu, Qingwei Huang, Kangming Chen and Yi Xie
Buildings 2026, 16(6), 1159; https://doi.org/10.3390/buildings16061159 - 16 Mar 2026
Viewed by 196
Abstract
To address issues such as web and bottom plate cracking and insufficient bending capacity in in-service prestressed concrete box girder bridges, this study proposes internal prestressing and section enlargement composite reinforcement. Firstly, taking a bridge of Shenhai Expressway as the background project, the [...] Read more.
To address issues such as web and bottom plate cracking and insufficient bending capacity in in-service prestressed concrete box girder bridges, this study proposes internal prestressing and section enlargement composite reinforcement. Firstly, taking a bridge of Shenhai Expressway as the background project, the combined reinforcement method is designed and the reinforcement effect is analyzed by MIDAS/Civil. Secondly, through numerical analysis, the influence of the bond shrinkage of self-compacting concrete with different mix ratios on the stress of the web of the original box girder is analyzed, and the interface between the new and old concrete is carried out. The analysis of the loss of the new prestress on the bonding surface of the new and old concrete is carried out by parameters such as the interface planting rate, the interface shear stiffness and the reinforcement structure. Furthermore, the theoretical calculation method of prestress loss rate of new and old concrete bonding interface is obtained. The results show that the flexural capacity of the normal section of the main beam is significantly improved after reinforcement, and the surplus coefficient is 1.18, which meets the requirements of the secondary safety level, and the mid-span deflection is improved by 34.28%, which verifies the effectiveness and feasibility of the combined reinforcement method. When the content of fly ash is 54%, the bond shrinkage strain and shrinkage stress of self-compacting concrete are reduced to the lowest level, which has the least influence on the existing box girder structure. It is suggested that the reinforcement ratio between the new and old concrete interface is 0.6%, and the interface roughness is 0.9 mm, which can increase the shear resistance of the new and old concrete interface and effectively reduce the transfer loss of prestress at the interface. Error analysis shows that the proposed semi-empirical calculation method has high accuracy with a deviation of less than 10%. Full article
(This article belongs to the Special Issue Urban Renewal: Protection and Restoration of Existing Buildings)
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17 pages, 1032 KB  
Article
Dynamic Analysis of Bi-Stable Galloping Energy Harvesters Under Random Excitation
by Ying Zhang, Ruobing Qin, Kaixin Zheng and Jingwen Zhang
Micromachines 2026, 17(3), 358; https://doi.org/10.3390/mi17030358 - 15 Mar 2026
Viewed by 127
Abstract
The flow-induced vibration energy harvester provides a solution to the power supply problem for low-power sensors. However, in practical engineering applications, flow-induced vibration energy harvesters often operate in complex environments and are inevitably affected by random external disturbances. Therefore, it is necessary to [...] Read more.
The flow-induced vibration energy harvester provides a solution to the power supply problem for low-power sensors. However, in practical engineering applications, flow-induced vibration energy harvesters often operate in complex environments and are inevitably affected by random external disturbances. Therefore, it is necessary to study the dynamic response of flow-induced vibration energy harvesters under random excitations. In this paper, a bi-stable galloping piezoelectric energy harvesting system is transformed into an equivalent decoupled system through variable transformation. The stochastic averaging method (SAM) of an energy envelope is used to calculate the energy harvester response under random excitation. The validity of the proposed theoretical framework is further confirmed through Monte Carlo (MC) simulations, followed by a systematic analysis of the effects of key parameters on the mean-square voltage output. The results show that noise intensity, aerodynamic coefficient, stiffness coefficient, and wind speed have significant effects on the dynamic response of the system. Full article
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25 pages, 3675 KB  
Article
Natural Motion Design for Energy-Efficient Pick-and-Place Scenarios
by Juan Pablo Mora, Carlos F. Rodriguez and Burkhard Corves
Machines 2026, 14(3), 330; https://doi.org/10.3390/machines14030330 - 14 Mar 2026
Viewed by 160
Abstract
Reducing the energy consumption of industrial robots performing pick-and-place tasks is required to increase profitability while reducing carbon footprint. Natural motion stands out as a mixed-energy-reduction strategy, especially useful for cyclical tasks. An optimization approach is proposed for calculating the elastic parameters, namely [...] Read more.
Reducing the energy consumption of industrial robots performing pick-and-place tasks is required to increase profitability while reducing carbon footprint. Natural motion stands out as a mixed-energy-reduction strategy, especially useful for cyclical tasks. An optimization approach is proposed for calculating the elastic parameters, namely the stiffness and equilibrium position, of constant-stiffness springs parallel to the actuators of parallel robots. Three typical trajectory-dependent methods for calculating these parameters are presented: free-vibration response, optimized, and predefined trajectory. As the set of springs and the task specification are strongly coupled, deviations from the nominal task would require replacing or removing the springs. Therefore, two adjustment strategies, one based on trajectory optimization and the other on equilibrium position update, are proposed to further exploit the natural motion. All optimization problems are solved and compared in a case study of a five-bar linkage performing a nominal pick-and-place task. Then, a palletizing pick-and-place scenario is introduced to perform the proposed trajectory and equilibrium adjustments. It is shown that using nominal springs reduces energy consumption near the nominal task, and implementing the proposed adjustments reduces energy over a wider region. Full article
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21 pages, 10044 KB  
Article
Axial Compressive Behavior of SCS Composite Wall Members for Wind Turbine Towers: Numerical Investigation and Performance Evaluation
by Shuchen Zhang, Yong Yang, Longkang Xu, Shiqiang Feng, Gejia Liu and Samuel Elias Hernandez Gadea
Buildings 2026, 16(6), 1139; https://doi.org/10.3390/buildings16061139 - 13 Mar 2026
Viewed by 193
Abstract
The rapid development of multimegawatt wind turbines presents greater demands on the structural safety and stability of tower structures. In response, this study investigates the axial compressive behavior of steel–concrete–steel (SCS) composite towers with a low steel ratio and enhanced shear connection. The [...] Read more.
The rapid development of multimegawatt wind turbines presents greater demands on the structural safety and stability of tower structures. In response, this study investigates the axial compressive behavior of steel–concrete–steel (SCS) composite towers with a low steel ratio and enhanced shear connection. The two steel plates are integrated by bolt connectors to ensure overall stiffness and effective composite action. Axial compression tests are conducted on curved tower wall members representing a 1/16 segment of the tower cross-section. Previous experimental results indicate that failure is dominated by local buckling of steel plates between adjacent connectors, highlighting the critical role of connector-induced confinement in controlling instability. Numerical models of curved composite walls are established and validated against previously published experimental results, showing good agreement in both failure modes and bearing capacity. Parametric analysis indicates that increasing the bolt diameter from 16 mm to 20 mm and 24 mm enhances the ultimate load by 3.09% and 6.58%, respectively. For the full-section tower model, reducing bolt spacing to 500 mm, 300 mm, and 250 mm increases the ultimate load by 16.33%, 20.05%, and 21.79%, respectively, compared to the bolt-free model. These results confirm that reducing connector spacing substantially enhances bearing capacity through improved confinement and delayed local buckling. A calculation method for evaluating the axial bearing capacity of SCS composite towers incorporating confinement effects is proposed, showing good consistency with both experimental and numerical data. Full article
(This article belongs to the Section Building Structures)
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24 pages, 8480 KB  
Protocol
Evaluating Microclimate Modification and Acute Cardiovascular Stress Responses to a Dense Urban Microforest: The Green Oasis (GRO) Protocol
by Rachel Keith, Sean Willis, Natalie Christian, Farzaneh Khayat, Jackie Gallagher, William Scott Gunter, Julia Kachanova, Andrew Mehring, Rachel Pigg, Doris Proctor, Allison E. Smith, Cameron K. Stopforth, Patrick Piuma, Ted Smith and Aruni Bhatnagar
Int. J. Environ. Res. Public Health 2026, 23(3), 365; https://doi.org/10.3390/ijerph23030365 - 13 Mar 2026
Viewed by 229
Abstract
The Green Oasis (GRO) Project is a targeted urban greening intervention designed to evaluate the environmental and health impacts of compact, high-density plantings in dense built environments. Initiated in downtown Louisville, the project transformed Founders Square, a 0.64-acre sparsely planted park, into a [...] Read more.
The Green Oasis (GRO) Project is a targeted urban greening intervention designed to evaluate the environmental and health impacts of compact, high-density plantings in dense built environments. Initiated in downtown Louisville, the project transformed Founders Square, a 0.64-acre sparsely planted park, into a microforest (“Trager Microforest”), a multilayered planting of 119 trees and more than 200 shrubs. The impact of this intervention is being assessed through a randomized crossover study in which participants walk in the microforest and a nearby impervious parking lot. Physiological outcomes include heart rate, heart rate variability, arterial stiffness, and stress biomarkers measured in saliva, urine, and sweat. Environmental conditions are continuously monitored by fixed and mobile weather stations, air pollution sensors, and biodiversity surveys. Baseline assessments were conducted in 2023 and 2024, with post-planting evaluations now underway (2025–). Power calculations indicate adequate sensitivity (n ≈ 40–50) to detect changes in cardiovascular stress responses in participants. Complementary ecological measurements include soil microbiome composition, greenhouse gas fluxes, and avian diversity. This study addresses critical gaps in understanding how small-scale, high-density greening interventions affect cardiovascular resilience, stress physiology, and microclimatic regulation. By integrating environmental, biological, and human health data, GRO establishes a comprehensive framework for evaluating the efficacy of urban microforests as nature-based solutions. The results are expected to inform urban planning, public health strategies, and climate adaptation policies, demonstrating how compact greening interventions can simultaneously mitigate heat, reduce pollution, enhance biodiversity, and promote human wellbeing in dense urban cores. Full article
(This article belongs to the Section Environmental Health)
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34 pages, 5641 KB  
Article
Flexural Failure Characteristics and Fracture Evolution Law of Layered Composite Rock Mass
by Ping Yi, Zhaohui Qiu, Yue Song, Binyang Duan, Lei Wang and Yanwei Duan
Processes 2026, 14(6), 888; https://doi.org/10.3390/pr14060888 - 10 Mar 2026
Viewed by 176
Abstract
To address the engineering challenges of frequent flexural deformation and instability of composite roadway roofs and the difficulty in accurately controlling the support strength range during deep coal mining, this study takes the soft–hard interbedded composite roof of the working face in the [...] Read more.
To address the engineering challenges of frequent flexural deformation and instability of composite roadway roofs and the difficulty in accurately controlling the support strength range during deep coal mining, this study takes the soft–hard interbedded composite roof of the working face in the West No. 1 Mining Area of Shuangyang Coal Mine in Shuangyashan as the engineering background. Typical fine sandstone (hard rock) and tuff (soft rock) from the on-site roof were selected to prepare layered composite specimens, and indoor four-point bending tests were conducted. Combined with theoretical calculations, strain monitoring, and acoustic emission (AE) real-time localization technology, the regulatory mechanisms of three key factors—lithological combination, loading rate, and span—on the flexural mechanical properties, deformation and failure modes, and fracture evolution laws of layered composite rock masses were systematically investigated. The research results show the following: (1) The flexural performance of layered composite rock masses is dominated by the interlayer interface effect. Their flexural strength is 46.7% and 41.1% lower than that of single hard rock and soft rock specimens, respectively, and the competitive mechanism between interface slip and delamination fracture is the core inducement of strength deterioration. (2) The strength and deformation characteristics of layered composite rock masses exhibit a significant loading rate effect. When the loading rate increases from 0.002 mm/s to 0.02 mm/s, the flexural strength decreases by 51.8% and the mid-span deformation deflection reduces by 50.1%. High loading rates will exacerbate the deformation mismatch between soft and hard rock layers, trigger premature failure of interface bonding, and inhibit the full development of structural plastic deformation. (3) Increasing the span significantly optimizes the flexural bearing performance of layered composite rock masses. When the span increases from 170 mm to 190 mm, the flexural strength increases by 65.7% and the mid-span deformation deflection synchronously increases by 65.7%. A large span can extend the flexural deformation path, promote the coordinated deformation of rock layers, and suppress local stress concentration. (4) The flexural failure of layered composite rock masses is dominated by Mode II shear cracks, while single-lithology specimens are mainly dominated by Mode I tensile cracks. Loading rate and span significantly change the crack propagation mode and energy release law. This study establishes a calculation method for the equivalent flexural stiffness of layered composite rock masses and reveals the mesoscopic mechanism of flexural failure of heterogeneous layered rock masses. The research results can provide a theoretical basis and experimental support for the optimization of support schemes and the prevention and control of roof collapse hazards for composite roofs of deep coal mine roadways. Full article
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17 pages, 2682 KB  
Article
Evaluation of Cone-Penetration Test as a Rheology Quality-Control Field-Oriented Test for 3D Printing Cement-Based Systems
by Enrique Gomez, Hugo Varela and Gonzalo Barluenga
Materials 2026, 19(5), 1029; https://doi.org/10.3390/ma19051029 - 7 Mar 2026
Viewed by 244
Abstract
3D printing (3DP) of cement-based systems (CBSs) is a highly demanded technology in the construction field. Material requirements include specific rheological conditions for proper extrusion, followed by fast stiffening and strength gain to allow the construction process to continue, taking into account variable [...] Read more.
3D printing (3DP) of cement-based systems (CBSs) is a highly demanded technology in the construction field. Material requirements include specific rheological conditions for proper extrusion, followed by fast stiffening and strength gain to allow the construction process to continue, taking into account variable environmental conditions if the construction is on-site. To guarantee quality control of the process, it is essential to define field-oriented testing methodologies that allow real-time monitoring of mechanical properties’ evolution of the printed material, which will govern construction speed. This study evaluates the cone penetration test (CPT) method as a field-oriented test method to estimate the mechanical properties of 3DP CBSs over time. CPT penetration depth measurements were used to calculate shear yield stress and fresh compressive strength over time for 90 min. The experimental results were compared to two widely used laboratory tests: the fresh compressive strength test (squeeze test—SQT) and DSR test (vane test—VT). CBS pastes with and without fly ash and with three inorganic modifiers (nanoclays) and two types of organic rheology-modifying admixtures were considered. The results showed that CPT is highly conditioned by the stiffness of the paste, measured by the compressive Young Modulus (E), overestimating CBSs’ strength. The increase in E over time showed an inflection point at 130 kPa, corresponding to the evolution from plastic to pseudo-rigid behavior in the pastes. The corresponding time was used to define a linear adjustment for the average strength calculated using the CPT regarding both the fresh compressive SQT and shear yield stress VT. Full article
(This article belongs to the Special Issue 3D Printing Materials in Civil Engineering)
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21 pages, 4437 KB  
Article
Flexural Behavior of Steel Grating–UHPC Composite Bridge Decks
by Pengfei Ren, Hanshan Ding and Sumei Liu
Eng 2026, 7(3), 123; https://doi.org/10.3390/eng7030123 - 5 Mar 2026
Viewed by 267
Abstract
Through static bending tests on two full-scale specimens of a new steel grating–UHPC (ultra-high-performance concrete) composite bridge deck, the load–displacement curves, crack propagation, strain distribution, and failure characteristics were analyzed. According to the experimental results, a numerical model was established using ABAQUS software [...] Read more.
Through static bending tests on two full-scale specimens of a new steel grating–UHPC (ultra-high-performance concrete) composite bridge deck, the load–displacement curves, crack propagation, strain distribution, and failure characteristics were analyzed. According to the experimental results, a numerical model was established using ABAQUS software 2021, in which two contact methods were employed to simulate the interfacial connection between UHPC and steel. The results indicate that the surface-to-surface contact method provides better agreement with the experimental data. Subsequently, conducted parameter studies using this model to investigate the impact of key geometric parameters, including section height, flange width, flange thickness, steel bottom plate thickness, and steel web plate thickness, on the flexural performance of the structure. The results demonstrated that the section height and the steel bottom plate thickness had a significant effect on the load-bearing capacity and overall stiffness of the component, while the influence of other parameters was comparatively minor. Finally, based on both experimental and numerical results, a formula for calculating the flexural bearing capacity of steel grating–UHPC composite bridge slabs was proposed, providing a reference for the structural design and promotion of the new composite bridge deck. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
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12 pages, 1038 KB  
Article
Load-Dependent Non-Uniform Bending Stiffness and Curvature-Based Deflection Calculation in Timber–Concrete Composite Beams
by Yuchen Jiang and Xiamin Hu
Buildings 2026, 16(5), 989; https://doi.org/10.3390/buildings16050989 - 3 Mar 2026
Viewed by 237
Abstract
The effective bending stiffness formula for cross-sections of timber–concrete composite (TCC) beams was derived under semi-sinusoidal loading condition in Eurocode 5; however, this formula does not account for the non-uniform distribution of bending stiffness along the span. This limitation prevents it from characterizing [...] Read more.
The effective bending stiffness formula for cross-sections of timber–concrete composite (TCC) beams was derived under semi-sinusoidal loading condition in Eurocode 5; however, this formula does not account for the non-uniform distribution of bending stiffness along the span. This limitation prevents it from characterizing the mechanical behavior under real loading conditions, which could potentially compromise the safety and serviceability of the structural design. To investigate the distribution pattern of bending stiffness, differential segment analysis was conducted, incorporating interfacial slip effects. A governing differential equation for curvature was established, and the resulting curvature distribution was used to compute deflections by means of the conjugate beam method. The results demonstrate that the bending stiffness distribution depends critically on shear connector arrangement and loading conditions. Under third-point loading, the bending stiffness monotonically decreases from the mid-span to the load application points and increases toward the supports. Under uniform loads, bending stiffness peaks at the mid-span and declines gradually toward the supports. Reducing shear connector spacing enhances composite action while amplifying bending stiffness non-uniformity. Experimental validation confirms that both the conjugate beam method (using analytical curvature solutions) and the simplified approach in Eurocode 5 achieve 99% average accuracy in predicting the mid-span deflection of TCC beams. In addition, careful attention must be paid to the deflection values at loading points, particularly when the loading position is close to the supports. Full article
(This article belongs to the Section Building Structures)
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17 pages, 3617 KB  
Article
Geomechanical Substantiation of Soil Stability During Tunnel Construction by Shield Tunneling Complexes in Layered Massifs
by Anatoly Protosenya and Vsevolod Kumov
Eng 2026, 7(3), 108; https://doi.org/10.3390/eng7030108 - 1 Mar 2026
Viewed by 215
Abstract
This paper presents the development and results of an analytical method for calculating the stability coefficient of a rock mass that is capable of adjusting the face support pressure required for face stability depending on changes in the mass structure at the tunnel [...] Read more.
This paper presents the development and results of an analytical method for calculating the stability coefficient of a rock mass that is capable of adjusting the face support pressure required for face stability depending on changes in the mass structure at the tunnel face. The analytical relationships presented in this work are based on the simulation of 225 three-dimensional finite element numerical models. The influence of the mass structure at the tunnel face was examined by varying the thickness and position of the layer at the tunnel face, as well as its stiffness and strength parameters. The maximum difference in the values of the main monitored criteria exceeded 85% for such indicators as the area of the surface settlement trough, the area of the zone of negative vertical deformations, the width of the settlement trough, and the maximum value of vertical settlements. This study proposes a practical implementation of the developed analytical method—a stability coefficient of the soil mass was developed to adjust existing analytical relationships when a soil layer with mechanical characteristics differing from the host mass is present at the tunnel face. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
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22 pages, 6118 KB  
Article
Response Model and Experimental Analysis of a Walnut Vibration Harvesting System
by Yu Ru, Xiao Zhang, Yang Zhang, Fengxiang Liu, Yuquan Sun, Linyun Xu, Hongping Zhou and Haifeng Zhang
Agriculture 2026, 16(5), 551; https://doi.org/10.3390/agriculture16050551 - 28 Feb 2026
Viewed by 203
Abstract
This study investigates the vibration response and energy transfer characteristics of walnut trees in mechanical vibration harvesting, aiming to improve fruit detachment efficiency and reduce structural damage. Three walnut tree architectures were classified based on branching height, trunk stiffness, canopy size, and geometric [...] Read more.
This study investigates the vibration response and energy transfer characteristics of walnut trees in mechanical vibration harvesting, aiming to improve fruit detachment efficiency and reduce structural damage. Three walnut tree architectures were classified based on branching height, trunk stiffness, canopy size, and geometric regularity. A dynamic model of the trunk was established, modeled as an equivalent conical beam with Rayleigh damping, and the clamping point was simplified to a single-degree-of-freedom system. To quantify energy transfer, three indicators were introduced: energy transfer coefficient, energy attenuation rate, and trunk overload index (OLI). Sweep-frequency experiments (9–17 Hz) were conducted at a clamping height of 80 cm. Triaxial acceleration responses were measured, and branch kinetic energy was calculated. The model-predicted natural frequencies matched the experimental acceleration peaks well, identifying a frequency-sensitive band between 15 and 17 Hz. Significant differences in energy distribution were observed among the three tree architectures. Tree 1 exhibits intense energy concentration near the trunk, with rapid energy decay along branches and the highest canopy vibration index (OLI: 6.13), indicating the highest trunk overload risk. Tree 2 demonstrates whole-tree coordinated vibration and the lowest OLI value (2.10). Tree 3 possesses two sensitive frequency bands with relatively uniform energy distribution and an OLI of 2.89. Trunk stiffness, branching height, canopy structure, and geometric irregularities collectively determine energy distribution within resonance bands and overload risk. The proposed energy metrics and OLI provide quantitative guidance for selecting excitation frequencies and controlling operational duration during walnut vibration harvesting. Full article
(This article belongs to the Section Agricultural Technology)
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