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Keywords = axial, bending and shearing load

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19 pages, 7907 KB  
Article
Experimental Study on Axial Compressive Behavior of the BFRP-Confined Timber Columns with and Without Knots
by Ya Ou, Chenghu Tang, Le Yan, Yunlei Fan and Hao Zhou
Buildings 2026, 16(2), 457; https://doi.org/10.3390/buildings16020457 - 22 Jan 2026
Viewed by 29
Abstract
Timber has gained popularity in the construction industry in recent years due to its low carbon footprint, favorable seismic performance, and esthetic appeal. However, due to the size limit and inevitable natural defects such as knots in the lumber, the axial capacity of [...] Read more.
Timber has gained popularity in the construction industry in recent years due to its low carbon footprint, favorable seismic performance, and esthetic appeal. However, due to the size limit and inevitable natural defects such as knots in the lumber, the axial capacity of timber columns might be insufficient. Therefore, wrapping the timber column with basalt fiber-reinforced polymers (BFRPs), which is an environmentally sustainable material, to improve the load-carrying capacity has been a promising technology. While existing research mostly focuses on defect-free specimens, this study investigates the effects of knots on the structural performance of timber columns wrapped by BFRP. Axial compressive tests were carried out on timber columns, i.e., Douglas fir (knot-free) and camphor pine (with knots), wrapped by BFRP. The results showed that the load-carrying capacity, stiffness, and ductility can be significantly enhanced by the BFRP wrapping. The failure mode of the Douglas fir specimens transitioned from timber crushing failure to shear failure, while the camphor pine specimens failed around the knot area, and the failure mode changed from overall bending to BFRP rupture when the three layers of BFRP were employed. Furthermore, compared to knot-free columns, those specimens containing knots exhibited greater variability in load capacity and recorded a higher percentage increase in strength after reinforcement by BFRP. Based on the test results, three prediction models of the compressive strength of the BFRP-wrapped Douglas fir and camphor pine columns are presented. Full article
(This article belongs to the Special Issue Seismic Performance of Seismic-Resilient Structures)
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19 pages, 7019 KB  
Article
Multiparametric Cost–CO2 Optimization of Bored Reinforced-Concrete Piles Under Combined Loading in Cohesive Soils
by Primož Jelušič
Buildings 2025, 15(24), 4519; https://doi.org/10.3390/buildings15244519 - 14 Dec 2025
Viewed by 301
Abstract
Laterally loaded slender piles present a classic soil–structure interaction problem where pile displacements and flexural demands are governed by the mobilized lateral resistance of the surrounding soil and the axial-bending capacity of the reinforced concrete section. In response to increasing pressure to reduce [...] Read more.
Laterally loaded slender piles present a classic soil–structure interaction problem where pile displacements and flexural demands are governed by the mobilized lateral resistance of the surrounding soil and the axial-bending capacity of the reinforced concrete section. In response to increasing pressure to reduce embodied emissions, this study develops LAVERCO, an optimization framework for cost- and CO2-efficient design of bored reinforced-concrete piles in cohesive soils subjected to combined lateral and axial actions. The framework integrates Eurocode-based geotechnical checks with full NM section verification of the RC pile and applies a genetic algorithm over a multi-parametric grid of lateral load, vertical load, and undrained shear strength, using economic cost and embodied CO2 as alternative single objectives. Rank-based (Spearman) sensitivity analysis quantifies how actions, soil strength, and design variables influence the optimal solutions. The results reveal two consistent geometry regimes: CO2-optimal piles are systematically longer and slimmer, while COST-optimal piles are shorter and thicker. In both cases, the objective is dominated by pile length and is reduced by higher undrained shear strength; vertical load has a moderate direct effect, while horizontal load contributes mainly through deflection and bending checks. Feasibility improves significantly in stronger clays, and CO2-optimal geometries generally incur higher costs, clarifying the trade-off between economic and environmental performance. The framework provides explicit geometry-level guidance for selecting bored pile designs that balance cost and embodied CO2 across a wide range of soil and loading conditions and can be directly applied in both preliminary and detailed designs. Full article
(This article belongs to the Section Building Structures)
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24 pages, 23700 KB  
Article
Design Interaction Diagrams for Shear Adequacy Using MCFT-Based Strength of AS 5100.5—Advantages of Using Monte Carlo Simulation
by Koon Wan Wong and Vanissorn Vimonsatit
J. Exp. Theor. Anal. 2025, 3(4), 41; https://doi.org/10.3390/jeta3040041 - 5 Dec 2025
Viewed by 365
Abstract
This paper presents three different approaches for generating points along the interaction diagram corresponding to design load effects—shear, bending moment, and axial force—to achieve optimal shear strength adequacy with the Australian bridge design standard AS 5100.5. The methodology targets the optimal shear condition [...] Read more.
This paper presents three different approaches for generating points along the interaction diagram corresponding to design load effects—shear, bending moment, and axial force—to achieve optimal shear strength adequacy with the Australian bridge design standard AS 5100.5. The methodology targets the optimal shear condition by matching the design shear V* with the capacity ϕVu, which represents achieving a load rating factor of unity within the specified tolerance limits. The first typical approach for generating points for two load effects is by increasing the moment–shear ratio ηm in small increments from zero to a large value (theoretically infinity), and for each increment, to goal-seek the condition. The other approaches investigated are the use of increasing factored moment M* and the use of Monte Carlo simulation. A pretensioned bridge I-girder section reported in the literature was used in the study. The Monte Carlo simulation method was found to be the simplest to program. It allows an interaction surface for the influence of three load effects for optimal shear adequacy to be obtained with minimal program coding and outperforms the goal–seeking approaches for multi-variable interactions. It can create 2-D interaction lines for various levels of shear adequacy for the interaction of M* and V*, and 3-D interaction surfaces for M*, V*, and N*. The potential use of interaction diagrams was explored, and the advantages and limitations of using each method are presented. The interaction curves of two typical pretensioned concrete sections of a plank girder, one next to an end support and the other close to mid-span, were created to show the distinguishing features resulting from their reinforcement. Full article
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19 pages, 4513 KB  
Article
Shear Analysis of “Concrete-to-Concrete” Contact as an Important Parameter for Strengthening Concrete Structures
by Matúš Farbák, Martin Vavruš, Peter Koteš and Anna Adamczak-Bugno
Buildings 2025, 15(21), 3889; https://doi.org/10.3390/buildings15213889 - 28 Oct 2025
Cited by 2 | Viewed by 654
Abstract
The need to strengthen existing load-bearing elements (slabs, girders, columns, etc.) is often encountered in practice mainly because existing reinforced concrete structures were previously designed according to provisions and standards that were valid decades ago and no longer comply with currently valid Eurocodes, [...] Read more.
The need to strengthen existing load-bearing elements (slabs, girders, columns, etc.) is often encountered in practice mainly because existing reinforced concrete structures were previously designed according to provisions and standards that were valid decades ago and no longer comply with currently valid Eurocodes, which provide new load levels and cross-section resistance calculations and, thus, a new level of reliability. Another reason is that the purpose behind the use of existing structures is changing, with these structures often now needing to withstand greater loads than were considered during the design. Many methods of strengthening elements stressed by axial force (pressure, tension), bending, shear, and their combination exist, with a common one being the addition of a new, more load-bearing layer of concrete, fibreconcrete, or ultra-high-performance concrete (UHPC). This experimental study focuses on the point of contact between two concrete surfaces and their modification to increase the bearing capacity of the bonded concrete-to-concrete cross-section. To strengthen the cross-section of the reinforced concrete (RC), a decisive condition is contact between individual layers, which is dependent on the resistance of the new, strengthened member. Connection occurs at the cross-section when the elements placed on top of each other are prevented by any suitable method from moving at the level of their contact surface. In this study, experimental tests were carried out to determine shear resistance using beams with dimensions of 100 × 100 × 300 mm, which consisted of two parts connected diagonally at an angle of 30°. To compare the increase in bearing capacity, the modifications of the contact surfaces and the characteristics of the material used for individual added layers were taken into account. The contact surfaces were either untreated, such as stamping from formwork, or smooth surfaces soaked in water for 48 h. For the modified surfaces, modifications included notches, indents, the use of an adhesive layer, and modifications of surface roughness using a steel brush. All base layers were concreted with the same class of concrete and processed according to the mentioned modifications. Different recipes were used for the upper (over-concreted) layer (part). The most effective processing methods were determined from the obtained results, and the coefficient of cohesion was determined through reverse calculation for individual surface treatments and subsequently compared with the Eurocode values. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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28 pages, 7823 KB  
Article
Numerical Investigation of Seismic Soil–Structure–Excavation Interaction in Sand
by Tarek N. Salem, Mahmoud S. Elmahdy, Dušan Katunský, Erika Dolníková and Ahmed Abu El Ela
Buildings 2025, 15(20), 3732; https://doi.org/10.3390/buildings15203732 - 16 Oct 2025
Cited by 1 | Viewed by 1082
Abstract
The dynamic loads affecting earth-retaining structures may increase in seismically active regions. Therefore, studying the soil–structure interaction among the soil, shoring systems, and adjacent structures is crucial. However, there is limited research on this important topic. This study investigates the seismic performance of [...] Read more.
The dynamic loads affecting earth-retaining structures may increase in seismically active regions. Therefore, studying the soil–structure interaction among the soil, shoring systems, and adjacent structures is crucial. However, there is limited research on this important topic. This study investigates the seismic performance of a deep braced excavation and a nearby 10-story building in sandy soil formation. The main focus of this study is the consideration of the influence of varying foundation depths of adjacent structures on the seismic response of the shoring system and the performance of the shoring system and adjacent structure under different earthquake records. PLAXIS 2D software (Version 22.02) was used to carry out the numerical analysis. Sandy soil was modeled using the Hardening Soil with small-strain stiffness model (HS-small). Back analysis of observation data extracted from a real case study of a deep braced excavation in the central district of Kaohsiung City, adjacent to the O7 Station on the Orange Line of the Kaohsiung MRT system in Taiwan, was used to validate the numerical analysis. Beyond model validation, a parametric study was conducted to address the effect of the foundation level of the building adjacent to the excavation on both the seismic behavior of the shoring system and the structure itself, using the Loma-Prieta (1989) earthquake record. The parametric study was further extended to assess the responses of the shoring system and the adjacent structure under the influence of the earthquake records of Loma-Prieta (1989), Northridge (1994), and El-Centro (1940). The results show that the maximum lateral displacement of the diaphragm wall occurred at the top of the wall in all studied cases. The maximum dynamic bending moment in the retaining structure was more than three times the static one on average. In contrast, the dynamic shear force was more than 2.85 times the static one on average. In addition, the dynamic axial force of the first and second struts was 1.38 and 3.17 times the static forces, respectively. The results also reveal large differences in the behavior of the shoring system and the adjacent structure between the different earthquake records. Full article
(This article belongs to the Special Issue Constructions in Europe: Current Issues and Future Challenges)
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25 pages, 6701 KB  
Article
Experimental Study on Bearing Characteristics of Pile-Anchor Foundations for Floating Offshore Wind Turbines Under Inclined Loading
by Yuxuan Wang, Pingyu Liu, Bo Liu, Jiaqing Shu, Huiyuan Deng, Mingxing Zhu, Xiaojuan Li, Jie Chen and Haoran Ouyang
J. Mar. Sci. Eng. 2025, 13(10), 1890; https://doi.org/10.3390/jmse13101890 - 2 Oct 2025
Cited by 1 | Viewed by 627
Abstract
Pile-anchor foundations, serving as one of the anchoring solutions to ensure the safety and stability of floating offshore wind turbines, are primarily subjected to inclined loading induced by anchor chain forces, resulting in significantly different bearing behavior compared to conventional vertically loaded pile [...] Read more.
Pile-anchor foundations, serving as one of the anchoring solutions to ensure the safety and stability of floating offshore wind turbines, are primarily subjected to inclined loading induced by anchor chain forces, resulting in significantly different bearing behavior compared to conventional vertically loaded pile foundations. However, experimental research on the inclined pullout performance of anchor piles remains insufficient. To address this gap, this study employs a self-developed servo-controlled loading system to investigate the pullout bearing characteristics of anchor piles in dry and saturated sand, considering factors such as pullout angle and loading point depth. The research results show that from the load–displacement curve of the model pile, it can be found that with the increase in displacement, the load it bears first gradually increases to the peak, then decreases, and then gradually stabilizes. The loading angle has a significant impact on the bearing performance of pile-anchor foundations. As the loading angle increases, the failure mode shows pullout failure. When the loading angle increases from 30° to 60°, the bearing performance of the pile foundation decreases by approximately 63%. When the depth of the loading point increases from 0.22 times the pile length to 0.78 times the pile length, the diagonal anchor tensile bearing capacity of the model pile increases by approximately 45%. When the depth of the loading point is the same, the distribution patterns of bending moment and shear force are basically similar. However, the smaller the loading angle, the larger the value. This is because the horizontal load component plays a dominant role. The compression of the piles above and below the loading point, as well as the bending moment, shear force and axial force under saturated sand conditions, are similar to those in dry sand, but their values are reduced by about 50%. It can be seen that the soil conditions have an influence on the bearing characteristics of pile foundations. Full article
(This article belongs to the Section Coastal Engineering)
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18 pages, 4746 KB  
Article
An Analytical Solution for Short Thin-Walled Beams with Monosymmetric Open Sections Subjected to Eccentric Axial Loading
by Branka Bužančić Primorac, Marko Vukasović, Radoslav Pavazza and Frane Vlak
Appl. Mech. 2025, 6(3), 68; https://doi.org/10.3390/applmech6030068 - 5 Sep 2025
Viewed by 1187
Abstract
A simple analytic procedure for the linear static analysis of short thin-walled beams with monosymmetric open cross-sections subjected to eccentric axial loading is presented. Under eccentric compressive loading, the beam is subjected to compression/extension, to torsion with influence of shear with respect to [...] Read more.
A simple analytic procedure for the linear static analysis of short thin-walled beams with monosymmetric open cross-sections subjected to eccentric axial loading is presented. Under eccentric compressive loading, the beam is subjected to compression/extension, to torsion with influence of shear with respect to the principal pole and to bending with influence of shear in two principal planes. The approximate closed-form solutions for displacements consist of the general Vlasov’s solutions and additional displacements due to shear according to the theory of torsion with the influence of shear, as well as the theory of bending with the influence of shear. The internal forces and displacements for beams clamped at one end and simply supported on the other end, where eccentric loading is acting, are calculated using the method of initial parameters. The shear coefficients for the monosymmetric cross-sections introduced in these equations are provided. Solutions for normal stress and total displacements according to Vlasov’s general thin-walled beam theory, and those obtained with the proposed method taking shear influence into account, are compared with shell finite element solutions analyzing isotropic and orthotropic I-section beams. According to the results for normal stress relative differences, and Euclidean norm for displacements, it has been demonstrated that shear effects must be accounted for in the analysis of such structural problems. Full article
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23 pages, 8814 KB  
Article
Study on the Anchored Bearing Characteristics of Mooring Pile Foundations in Sandy Soil for Floating Wind Turbines
by Pengpeng Wang, Jinqiong Xian, Bo Liu, Huiyuan Deng, Xiaoqing Gu, Mingxing Zhu, Xiaojuan Li and Guoliang Dai
J. Mar. Sci. Eng. 2025, 13(9), 1631; https://doi.org/10.3390/jmse13091631 - 26 Aug 2025
Viewed by 877
Abstract
As one of the mooring foundation types for floating wind turbine platforms, research on the anchor pullout bearing characteristics of mooring pile foundations remains insufficient, and the underlying mechanism of anchor pullout bearing capacity needs further investigation and clarification. This paper conducts a [...] Read more.
As one of the mooring foundation types for floating wind turbine platforms, research on the anchor pullout bearing characteristics of mooring pile foundations remains insufficient, and the underlying mechanism of anchor pullout bearing capacity needs further investigation and clarification. This paper conducts a numerical study on the bearing characteristics of mooring pile foundations under tensile anchoring forces with loading angles ranging from 0° to 90° and loading point depths of 0.2L, 0.4L, 0.6L, and 0.8L (where L is the pile length). The research findings indicate that the anchor pullout bearing capacity decreases as the loading angle increases from 0° to 90°, and exhibits a trend of first increasing and then decreasing with the increase in loading point depth. For rigid pile-anchors, the maximum anchor pullout bearing capacity occurs at a loading point depth of 0.6–0.8L, while for flexible piles, it appears at 0.4–0.6L. Both the bending moment and shear force of the pile shaft show abrupt changes at the loading point, where their maximum values also occur. This implies that the structural design at the loading point of the mooring pile foundation requires reinforcement. Meanwhile, the bending moment and shear force of the pile shaft gradually decrease with the increase in the loading angle, which is attributed to the gradual reduction of the horizontal load component. The axial force of the pile shaft also undergoes an abrupt change at the loading point, presenting characteristics where the upper section of the pile is under compression, the lower section is in tension, and both the pile top and pile tip are subjected to zero axial force. The depth of the loading point significantly influences the movement mode of the pile shaft. Shallow loading (0.2–0.4L) induces clockwise rotation, and the soil pressure around the pile is concentrated in the counterclockwise direction (90–270°). In the case of deep loading, counterclockwise rotation or pure translation of the pile shaft results in a more uniform stress distribution in the surrounding foundation soil, with the maximum soil pressure concentrated near the loading point. Full article
(This article belongs to the Section Coastal Engineering)
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41 pages, 3195 KB  
Article
A Stress Analysis of a Thin-Walled, Open-Section, Beam Structure: The Combined Flexural Shear, Bending and Torsion of a Cantilever Channel Beam
by David W. A. Rees
Appl. Sci. 2025, 15(15), 8470; https://doi.org/10.3390/app15158470 - 30 Jul 2025
Cited by 1 | Viewed by 2500
Abstract
Channels with three standard symmetrical sections and one asymmetric section are mounted as cantilever beams with the web oriented vertically. A classical solution to the analysis of stress in each thin-walled cantilever channel is provided using the principle of wall shear flow superposition. [...] Read more.
Channels with three standard symmetrical sections and one asymmetric section are mounted as cantilever beams with the web oriented vertically. A classical solution to the analysis of stress in each thin-walled cantilever channel is provided using the principle of wall shear flow superposition. The latter is coupled with a further superposition between axial stress arising from bending and from the constraint placed on free warping imposed at the fixed end. Closed solutions for design are tabulated for the net shear stress and the net axial stress at points around any section within the length. Stress distributions thus derived serve as a benchmark structure for alternative numerical solutions and for experimental investigations. The conversion of the transverse free end-loading applied to a thin-walled cantilever channel into the shear and axial stress that it must bear is outlined. It is shown that the point at which this loading is applied within the cross-section is crucial to this stress conversion. When a single force is applied to an arbitrary point at the free-end section, three loading effects arise generally: bending, flexural shear and torsion. The analysis of each effect requires that this force’s components are resolved to align with the section’s principal axes. These forces are then considered in reference to its centroid and to its shear centre. This shows that axial stress arises directly from bending and from the constraint imposed on free warping at the fixed end. Shear stress arises from flexural shear and also from torsion with a load offset from the shear centre. When the three actions are combined, the net stresses of each action are considered within the ability of the structure to resist collapse from plasticity and buckling. The novelty herein refers to the presentation of the shear flow calculations within a thin wall as they arise from an end load offset from the shear centre. It is shown how the principle of superposition can be applied to individual shear flow and axial stress distributions arising from flexural bending, shear and torsion. Therein, the new concept of a ‘trans-moment’ appears from the transfer in moments from their axes through centroid G to parallel axes through shear centre E. The trans-moment complements the static equilibrium condition, in which a shift in transverse force components from G to E is accompanied by torsion and bending about the flexural axis through E. Full article
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34 pages, 12831 KB  
Article
Behavior of Large-Diameter Circular Deep Excavation Under Asymmetric Surface Surcharge
by Ping Zhao, Youqiang Qiu, Feng Liu, Zhanqi Wang and Panpan Guo
Symmetry 2025, 17(8), 1194; https://doi.org/10.3390/sym17081194 - 25 Jul 2025
Cited by 2 | Viewed by 868
Abstract
Circular deep excavations, characterized by their symmetrical geometry, are commonly employed in constructing foundations for large-span suspension bridges and as launching shafts for shield tunneling. However, the mechanical behavior of such excavations under asymmetric surface surcharge remains inadequately understood due to a paucity [...] Read more.
Circular deep excavations, characterized by their symmetrical geometry, are commonly employed in constructing foundations for large-span suspension bridges and as launching shafts for shield tunneling. However, the mechanical behavior of such excavations under asymmetric surface surcharge remains inadequately understood due to a paucity of relevant investigations. This study addresses this knowledge gap by establishing a three-dimensional finite element model (3D-FEA) based on the anchor deep excavation project of a specific bridge. The model is utilized to investigate the influence of asymmetric surcharge on the forces and deformations within the supporting structure. The results show that both the internal force and displacement cloud diagrams of the support structure exhibit asymmetric characteristics. The distribution of displacement and internal forces has spatial effects, and the maximum values all occur in the areas where asymmetric loads are applied. The maximum values of the displacement, axial force, and shear force of underground continuous walls increase with the increase in the excavation depth. The total displacement curves all show the feature of a “bulging belly”. The maximum displacement is 13.3 mm. The axial force is mainly compression, with a maximum value of −9514 kN/m. The maximum positive and negative values of the shear force are 333 kN/m and −705 kN/m, respectively. The bending moment diagram of different monitoring points shows the characteristics of “bow knot”. The maximum values of the positive bending moment and negative bending moment are 1509.4 kN·m/m and −2394.3 kN·m/m, respectively. The axial force of the ring beam is mainly compression, with a maximum value of −5360 kN, which occurs in ring beams 3, 4, and 5. The displacement cloud diagram of the support structure under symmetrical loads shows symmetrical characteristics. Under different load conditions, the displacement curve of the diaphragm wall shows the characteristics of “bulge belly”. The forms of loads with displacements from largest to smallest at the same position are as follows: asymmetric loads, symmetrical loads, and no loads. These findings provide valuable insights for optimizing the structural design of similar deep excavation projects and contribute to promoting sustainable urban underground development. Full article
(This article belongs to the Special Issue Symmetry, Asymmetry and Nonlinearity in Geomechanics)
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18 pages, 33781 KB  
Article
New Experimental Single-Axis Excitation Set-Up for Multi-Axial Random Fatigue Assessments
by Luca Campello, Vivien Denis, Raffaella Sesana, Cristiana Delprete and Roger Serra
Machines 2025, 13(7), 539; https://doi.org/10.3390/machines13070539 - 20 Jun 2025
Cited by 1 | Viewed by 550
Abstract
Fatigue failure, generated by local multi-axial random state stress, frequently occurs in many engineering fields. Therefore, it is customary to perform experimental vibration tests for a structural durability assessment. Over the years, a number of testing methodologies, which differ in terms of the [...] Read more.
Fatigue failure, generated by local multi-axial random state stress, frequently occurs in many engineering fields. Therefore, it is customary to perform experimental vibration tests for a structural durability assessment. Over the years, a number of testing methodologies, which differ in terms of the testing machines, specimen geometry, and type of excitation, have been proposed. The aim of this paper is to describe a new testing procedure for random multi-axial fatigue testing. In particular, the paper presents the experimental set-up, the testing procedure, and the data analysis procedure to obtain the multi-axial random fatigue life estimation. The originality of the proposed methodology consists in the experimental set-up, which allows performing multi-axial fatigue tests with different normal-to-shear stress ratios, by choosing the proper frequency range, using a single-axis exciter. The system is composed of a special designed specimen, clamped on a uni-axial shaker. On the specimen tip, a T-shaped mass is placed, which generates a tunable multi-axial stress state. Furthermore, by means of a finite element model, the system dynamic response and the stress on the notched specimen section are estimated. The model is validated through a harmonic acceleration base test. The experimental tests validate the numerical simulations and confirm the presence of bending–torsion coupled loading. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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22 pages, 9093 KB  
Article
Numerical Investigation of the Pull-Out and Shear Mechanical Characteristics and Support Effectiveness of Yielding Bolt in a Soft Rock Tunnel
by Yan Zhu, Mingbo Chi, Yanyan Tan, Ersheng Zha and Yuwei Zhang
Appl. Sci. 2025, 15(12), 6933; https://doi.org/10.3390/app15126933 - 19 Jun 2025
Viewed by 1065
Abstract
Conventional bolts frequently fail under large deformations due to stress concentration in soft rock tunnels. In contrast, yielding bolts incorporate energy-absorbing mechanisms to sustain controlled plastic deformation. This study employed FLAC3D to numerically investigate the pull-out, shear, and bending behaviors of yielding bolts, [...] Read more.
Conventional bolts frequently fail under large deformations due to stress concentration in soft rock tunnels. In contrast, yielding bolts incorporate energy-absorbing mechanisms to sustain controlled plastic deformation. This study employed FLAC3D to numerically investigate the pull-out, shear, and bending behaviors of yielding bolts, evaluating their support effectiveness in soft rock tunnels. Three-dimensional finite difference models incorporating nonlinear coupling springs and the Mohr–Coulomb criterion were developed to simulate bolt–rock interactions under multifactorial loading. Validation against experimental pull-out tests and field measurements confirmed the model accuracy. Under pull-out loading, the axial forces in yielding bolts decreased more rapidly along the bolt length, reducing stress concentration at the head. The central position of the maximum load-bearing capacity in conventional bolts fractured under tension, resulting in an hourglass-shaped axial force distribution. Conversely, the yielding bolts maintained yield strength for an extended period after reaching it, exhibiting a spindle-shaped axial force distribution. Parametric analyses reveal that bolt spacing exerts a greater influence on support effectiveness than length. This study bridges critical gaps in understanding yielding bolt behavior under combined loading and provides a validated framework for optimizing energy-absorbing support systems in soft rock tunnels. Full article
(This article belongs to the Special Issue Recent Advances in Rock Mass Engineering)
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20 pages, 1500 KB  
Article
Mathematical Calculations for the Design of Elliptical Isolated Foundations with Optimal Cost
by Eyran Roberto Diaz-Gurrola, Arnulfo Luévanos-Rojas, Griselda Santiago-Hurtado, Victor Manuel Moreno-Landeros and Aldo Emelio Landa-Gómez
Mathematics 2025, 13(11), 1777; https://doi.org/10.3390/math13111777 - 27 May 2025
Cited by 1 | Viewed by 883
Abstract
This paper presents an optimal model for the design of elliptical isolated footings subjected to biaxial bending under the minimum cost criterion, assuming that the footing rests on elastic soils and that the soil pressure distribution is linear. The methodology is developed in [...] Read more.
This paper presents an optimal model for the design of elliptical isolated footings subjected to biaxial bending under the minimum cost criterion, assuming that the footing rests on elastic soils and that the soil pressure distribution is linear. The methodology is developed in two parts. The first is used to obtain the minimum area, and the second is used to determine the minimum cost. Some authors show the equations for circular and elliptical footings for moments, bending shear, and punching shear. However, they do not present the minimum cost, and the numerical examples are presented only for circular footings and not for elliptical footings. Two numerical problems are given (each problem presents five variants), and the optimal cost design for elliptical isolated footings subjected to biaxial bending are shown. Problem 1: Modifying the moment on the Y axis. Problem 2: Modifying the axial load. In addition, a comparison is made between elliptical footings and circular footings. The results show that the minimum area is smaller for elliptical footings than for circular footings, and the minimum cost appears in elliptical footings when the footing dimensions are governed by the minimum pressure. Therefore, the new model for elliptical footings will be of great help to foundation engineering specialists. Full article
(This article belongs to the Special Issue Mathematical Models in Mechanics and Engineering)
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28 pages, 17234 KB  
Article
Three-Dimensional Seismic Analysis of Symmetrical Double-O-Tube Shield Tunnel
by Chia-Feng Hsu, Chih-Hsiung Huang, Yeou-Fong Li, Shong-Loong Chen and Cheng-Der Wang
Symmetry 2025, 17(5), 719; https://doi.org/10.3390/sym17050719 - 8 May 2025
Viewed by 1106
Abstract
The symmetrical Double-O-Tube (DOT) shield tunneling method, first developed in Japan in the 1980s, offers advantages in optimizing cross-sectional area and reducing construction space. While past studies have primarily focused on construction-induced settlement or empirical modeling, this study presents the first comprehensive three-dimensional [...] Read more.
The symmetrical Double-O-Tube (DOT) shield tunneling method, first developed in Japan in the 1980s, offers advantages in optimizing cross-sectional area and reducing construction space. While past studies have primarily focused on construction-induced settlement or empirical modeling, this study presents the first comprehensive three-dimensional seismic analysis of Taiwan’s first DOT shield tunnel, part of the CA450A contract of the Taoyuan International Airport MRT. A detailed numerical simulation is conducted using PLAXIS 3D 2024 with the Hardening Soil model, capturing both static and dynamic responses under earthquake loading. Notably, the analysis incorporates full-direction seismic input (3D) using Arias intensity-based filtering and scaling to assess the tunnel’s mechanical behavior under varying seismic intensities. Key structural responses such as displacement, axial force, shear force, and bending moment are evaluated. The findings reveal critical deformation patterns and stress concentrations in the central support structure, offering novel insights for the seismic design of complex multi-cell shield tunnels in high-risk seismic zones. Full article
(This article belongs to the Special Issue Symmetry in Finite Element Modeling and Mechanics)
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21 pages, 13953 KB  
Article
The Mechanical Properties of Reinforced Concrete Columns with Longitudinal Pre-Embedded Holes
by Junzheng Zhang, Weisheng Xu, Jianjun Ye and Xuexi Liu
Appl. Sci. 2025, 15(9), 5010; https://doi.org/10.3390/app15095010 - 30 Apr 2025
Viewed by 1685
Abstract
While the longitudinal pre-embedded holes in a reinforced concrete column have a variety of beneficial functions during the whole life of the building, they have certain negative influences on the mechanical properties of the column. To investigate the influences of longitudinally pre-embedded holes [...] Read more.
While the longitudinal pre-embedded holes in a reinforced concrete column have a variety of beneficial functions during the whole life of the building, they have certain negative influences on the mechanical properties of the column. To investigate the influences of longitudinally pre-embedded holes on the mechanical properties of reinforced concrete (RC) columns, numerical simulations were conducted using the finite element software ABAQUS 2021 to analyze the effects of various parameters, including hole diameter, concrete strength, stirrup ratio, and slenderness ratio, on the mechanical behavior of RC columns under axial pressure. The results show that the presence of longitudinally pre-embedded holes reduces the load-bearing capacity of the columns. Furthermore, when the hole diameter exceeds 75 mm and the concrete strength is over C35, the failure mode of the columns shifts from axial compression failure to shear failure at the bending section of the pre-embedded hole. Increasing the stirrup ratio effectively enhances the ductility and load-bearing capacity and avoids brittle failure, whereas the influence of slenderness ratio variations on the column’s bearing capacity is negligible. These results provide a theoretical basis for the safe design of longitudinally pre-embedded hole columns in green buildings, effectively balancing the requirements between structural lightweight design and load-bearing performance. Full article
(This article belongs to the Section Civil Engineering)
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