Bending Moment Research Articles

The Influences of Selected Factors on Bending Moment Capacity of Case Furniture Joints

This study experimentally investigated the effects of selected factors on the bending moment capacity (BMC) of case furniture joints. The main aim was to explore mixed applications of wood-based materials and fasteners in manufacturing case furniture to reduce material costs. The study examined the effects of the face member material—particle board (PB), plywood (PL), and block board (BB)—edge member material (PB, PL, and BB), and joint shape (T-shape and L-shape) on BMC. Additionally, the study evaluated the effects of joint type (two eccentrics (TE), two dowels (TD), and one eccentric and one dowel (ED)), and material type (PB, PL, and BB) on BMC for L-shaped joints. The results showed that joint shape and face member material significantly affected the BMC of case furniture joint. The BMCs of T-shaped joints were significantly greater than those of L-shaped joints, regardless of the material of the face and edge members, except when the face member was made of PL. For L-shaped joints with PL face members, the BMCs were significantly higher compared to others. Joints constructed with TE exhibited significantly higher BMC compared to ED and TD for the same material type. For PB, TE joints exhibited an increase of approximately 3.0 Nm and 2.0 Nm compared to TD and ED, respectively. For PL, TE showed an increase of 9.1 Nm and 4.1 Nm compared to ED and TD, respectively. For BB, the increases were 7.0 Nm and 6.6 Nm compared to ED and TD. The BMC of joints made with PL and constructed with TE and ED was significantly greater than those of BB, followed by PB. However, for joints assembled with TD, there was no significant difference among the three materials. The ratios of BMC for joints constructed with ED compared to the half-sum of TE and TD were 0.73, 1.04, and 0.79 for PB, PL, and BB, respectively. These results suggest that the face member material predominantly influences the BMC of case furniture joints, indicating the potential to reduce costs by combining different materials and joint types.

Parameter Study and Optimization of Static Performance for a Hybrid Cable-Stayed Suspension Bridge

The hybrid cable-stayed and suspension (HCSS) bridge is known for its stability and cost-effectiveness, with significant application potential. This study examined the static performance of an HCSS bridge with a 1440 m main span. A finite element model (FEM) was developed to assess key parameters, such as the span-to-rise ratio, cable-to-hanger ratio, pylon stiffness, steel–concrete interface, and cable stiffness. Through FEM analysis and parameter optimization using the zero-order and first-order optimization methods in an ANSYS module, key design variables were optimized. The results show that an inappropriate span-to-rise ratio negatively impacts mid-span girder forces, while increasing the cable-stayed area enhances the overall stiffness. Main cable stiffness plays a crucial role in load-bearing and deformation control. Significant force differences were observed between stay and hanger cables, with axial force in the main girder increasing from the side span to the pylon under dead load. Bending moments in the transition region varied widely under combined loads. Optimizing parameters, such as the span-to-rise and cable-to-hanger ratios, significantly improved the mechanical performance of HCSS bridges, offering valuable insights for future designs.

Effects of transverse loading on the ultimate strength prediction of stiffened panels under biaxial loads: Potential improvements to the IACS rule formulation

The current International Association of Classification Societies (IACS) rule for designing stiffened panels was found in Wang et al. (2024) to conservatively predict the ultimate strength of panels when transverse loads predominate. This conservatism arises from the overestimation of bending moments acting on stiffeners by directly applying the beam analogy in both longitudinal and transverse directions in the rule formulation when evaluating stiffener yielding.To address this issue, this paper applies the orthotropic plate theory to calculate bending moments experienced by the stiffeners of panels under biaxial loads. Orthotropic properties are derived from equivalent sectional areas and moments of inertia. The predicted bending moments are validated through comparisons with numerical simulations. The effects of boundary conditions and deflection patterns with varying numbers of half-waves are discussed. Based on the analytical results, a modification of the IACS rule formulation is proposed by introducing a correction factor to account for transverse loading effects in the bending moment calculations. The factor is a function of the ratio between longitudinal and transverse loading.The modified IACS rule formulation is verified through numerical simulations of aluminium panels using ABAQUS and comparisons with results from existing literature on steel stiffened panels under various biaxial loading conditions. The modified rule formulation shows improved accuracy in predicting the ultimate strength of stiffened panels, particularly in cases with dominating transverse loads. The modified IACS rule formulation can be useful for more reliable and cost-effective design of ships and offshore structures.

Ship-shaped vessel hydroelastic numerically supported analysis in a narrow ultra-reduced model tank with full scale extrapolation

Although the rigid body hypothesis is broadly used when studying floating bodies dynamics, it is known that a ship-shaped vessel will have hydroelastic responses. Considering a conventional closed main deck hull in which the ship's length is considerably greater than its breadth, it is expected that the vertical bending moments can represent an important load that must be considered to guarantee structural integrity. Numerical models can be developed to assess the hydroelastic response, but the validation process is necessary. Model tests can be performed to validate the numerical model and require specific considerations to properly represent hydroelastic phenomena, such as having equivalent bending stiffness when compared to the full-scale body. Many experimental facilities that can be used to perform such experiments consist of narrow wave channels, in which the wall effect will influence the model's dynamics. This work implements a Tank Green Function (TGF) to a numerical model developed in Capytaine to represent the wall effect on the body's response. The numerical results were then compared to experimental data from tests in a narrow wave channel and good adherence was found. The validated numerical model can then be used to simulate open-water conditions, so the results can be extrapolated to full scale without the need to perform model tests in an ocean tank in which the wall effect would not be relevant.

Research on the influence of out-of-plane loads on the fatigue life of metal structures

Abstract For civil aircraft structures, in-plane tensile, compressive, shear, and their combined forms of loads are the usual loads on plate and shell structures, while bending moments, torsion, and other forms of loads are mainly borne by assemblies consisting of multiple parts. However, some plate and shell structures are subjected to in-plane loads while also being affected by out-of-plane loads. In order to study the difference between the fatigue performance of plate and shell structures under the influence of out-of-plane load and the fatigue performance under the effect of pure in-plane load, the axial tensile fatigue test considering the out-of-plane load is carried out, which demonstrates the negative effect of the out-of-plane load on the axial tensile fatigue strength of the structure. At the same time, a new structural fatigue life prediction method considering out-of-plane loads is established by combining finite element analysis, which can more accurately predict the structural fatigue life under the influence of out-of-plane loads and provide support for metal structure fatigue analysis.

Finite Tube Method for buckling analysis of tubular members using Fourier-approximation for the displacements

In this paper an efficient numerical method for the static analysis of cylindrical tubes is introduced. The method is designed for the linear buckling analysis of wind turbine support towers which are, most typically, built up from conical and/or cylindrical cans. Accordingly, the developed method uses cylindrical tube segments as elementary building blocks, along with specialized shape functions, and is named the Finite Tube Method. Within a tube segment the displacements are approximated by two-dimensional Fourier series. The curved nature of the surface is directly considered in the kinematic equations. The segments are joined and/or supported to the ground by constraint equations or by elastic links. In the current implementation internal stresses are determined in a simplified way: the circumferential stress distributions are calculated from the internal forces/moment by classic strength of material formulae, while the longitudinal distribution within each segment is quadratic. The considered internal forces/moments are: normal force, shear force, bending moment, and torsional moment. The internal forces can be arbitrarily combined. In the paper the underlying derivations are briefly summarized, then the method is demonstrated and validated by numerical examples, comparing the results to analytical and alternative numerical solutions. The authors are actively developing the method and will provide future work on utilization of the method for buckling mode identification and decomposition, as well as practical advancements to make the method a useful tool in the engineering design and analysis of wind turbine support towers.

A refined nonlinear theoretical model for mechanical analysis of tunnels subjected to strike-slip faulting with multiple fault planes

During strike-slip fault dislocation, multiple fault planes are commonly observed. The resulting permanent ground deformation can lead to profound structural damage to tunnels. However, existing analytical models do not consider multiple fault planes. Instead, they concentrate the entire fault displacement onto a single fault plane for analysis, thereby giving rise to notable errors in the calculated results. To address this issue, a refined nonlinear theoretical model was established to analyze the mechanical responses of the tunnels subjected to multiple strike-slip fault dislocations. The analytical model considers the number of fault planes, nonlinear soil‒tunnel interactions, geometric nonlinearity, and fault zone width, leading to a significant improvement in its range of applicability and calculation accuracy. The results of the analytical model are in agreement, both qualitatively and quantitatively, with the model test and numerical results. Then, based on the proposed theoretical model, a sensitivity analysis of parameters was conducted, focusing on the variables such as the number of fault planes, fault plane distance (d), fault displacement ratio (η), burial depth (C), crossing angle (β), tunnel diameter (D), fault zone width (Wf), and strike-slip fault displacement (Δfs). The results show that the peak shear force (Vmax), bending moment (Mmax), and axial force (Nmax) decrease with increasing d. The Vmax of the tunnel is found at the fault plane with the largest fault displacement. C, D, and Δfs contribute to the increases in Vmax, Mmax, and Nmax. Additionally, increasing the number of fault planes reduces Vmax and Mmax, whereas the variation in Nmax remains minimal.

Experimental and numerical study on behavior of UHPC-filled circular stainless steel tube stub columns under eccentric compression

Ultra-high performance concrete (UHPC) filled stainless steel tube (UFSST) is a newly proposed composite structure specifically designed to withstand harsh natural environments. To study the behavior of the UFSST column, 3 axial compression and 9 eccentric compression UFSST stub columns were tested respectively. And a comprehensive parametric analysis was conducted by employing a refine finite element model validated by the test data. The results show that the thickness (t) of stainless steel tubes is a key parameter affecting the eccentric compression performance of UFSST stub column. The increase in t can significantly improve the performance of UFSST stub columns, including the ultimate bearing capacity (Nu), ultimate bending moment (Mu), and ductility (DI). Finally, a modified computational model for the bearing capacity of UFST and UFSST stub columns under eccentric compression was proposed and showed a higher prediction accuracy. For UFST and UFSST stub columns, the prediction model yielded mean values of 0.99 and 1.00 for the ratio of predicted to experimental results, with standard deviations of 0.06 and 0.08, respectively.

An experimental and numerical study on chloride transport in concrete under single bending load and coastal soft soil environment

This paper presents an experimental and numerical simulation study on the corrosion of chloride ions in concrete components, using a single pre-applied bending load to represent an additional bending moment caused by an external one-off disturbance. Besides, a novel correlation testing method, the Pearson-Mutual Information (PMI) method, is proposed based on Pearson correlation coefficients and mutual information theory. The findings indicate that a significant effect on chloride ion transport is only observed when the ratio of the applied bending load to the ultimate bending load (λ) exceeds 0.3. There is a distinctly positive and nonlinear relationship between λ and free chloride concentration (CCl), the apparent chloride diffusion coefficient (Da), as well as apparent surface chloride concentration (Cs). The bivariate time-varying model developed in this study demonstrates high fitting accuracy, with simulation results that closely correspond to actual measured data, achieving a coefficient of determination (R²) of 0.98 or higher. Furthermore, a sensitivity analysis of the model input parameters indicates that Cs is more sensitive than Da, and λ is identified as the key parameter. The impacts of the interfacial transition zone (ITZ) and its diffusion coefficient (Ditz) were found to be minimal on the output of the model.

Determination of the moment–rotation relation of continuous timber–concrete composite floors based on the component method

Timber–concrete composite (TCC) combines the advantages of timber and reinforced concrete construction. In multi-storey buildings, the design of TCC floors is often governed by the deformation serviceability requirements. One way to improve deformation serviceability is through the design of continuous floor systems. However, the current practice of TCC slab systems is often limited to load-carrying as single-span beams. This paper presents an analytical model based on the component method for determining the moment–rotation relation of continuous TCC slabs in the range with negative bending moments. The investigations involve the development of load–displacement curves for the individual force-transmitting components, including timber and reinforced concrete, followed by their assembly into a component model. The model has been verified using finite element calculations and the results demonstrate that the moment–rotation relation of continuous TCC systems can be accurately captured. As the variability of the material properties strongly influences the stiffness of the joint and therefore the deformation and stresses in the TCC slab, a probabilistic analysis of the material parameters was performed using the Monte Carlo method. The probabilistic investigations show that the variability of the input parameters has a significant impact on the joint stiffness, with notable scattering observed in the moment–rotation relation, especially in the range of the cracking phase of the concrete. The results from the probabilistic investigations enable initial statements about the joint stiffness of continuous timber–concrete composite slabs in ranges with negative bending moments.

Web shear buckling of steel-concrete composite girders – advanced numerical analysis

Load-bearing capacity of plate girders, often used in design of bridges and high-rise buildings, is limited by the shear capacity of connected slender plate elements subjected to shear buckling. To quantify this, experimental investigations on five large-scale steel and steel-concrete composite plate girders loaded solely in shear, with a minimal influence of bending moments, have been conducted and evaluated. In this paper, the phenomenon of web shear buckling is investigated within the numerical analysis using the ABAQUS Software. An advanced numerical model has been developed and results validated against existing experimental findings. One of the focal points of this study represents the methodology of developing such a comprehensive numerical model, implementation of suitable analysis procedures, material models, boundary conditions, finite elements and interactions, in order to correctly replicate the observed response in the tests. In addition, case studies tackling the influence of web slenderness, aspect ratio, initial imperfections, shear connection and concrete classes on the structural-mechanical behavior of steel-concrete composite girders in shear as well as the applicability and suitability of the existing analytical model are also presented and analyzed.

Full-Scale Load Testing for Evaluating Crack Performance in Precast Prestressed Concrete Communication Towers with Annular Sections

Tall prestressed concrete poles with annular cross-sections are increasingly used as communication towers. The annular section subjected to bending moments has a smaller extreme tension area, resulting in higher stress increments in the materials within this region. As slender concrete structures, their bending behavior and crack resistance performance need to be critically examined. However, large-scale tower structures have rarely been experimentally investigated. Moreover, current code-specified crack width calculation methods are designed for square sections, so their applicability to concrete members with annular sections requires further investigation. To address these issues, this study conducted full-scale static loading tests on two 30-meter-high tower structures made of prestressed high-strength concrete and evaluated the accuracy of code methods for estimating the maximum crack width. During the static loading tests, displacement, cracking moments, crack widths, and crack spacings were meticulously recorded, and a theoretical methodology for calculating the stress in the extreme tension bars was developed. Four calculation methods specified in structural codes were compared: the Concrete Design Code of China (GB50010), Eurocode 2, ACI 224R, and the Concrete Design Guideline of Japan (JGC2007). The experimental results showed that diameter significantly affects the stiffness and displacement of the structure, with reloading stiffness of the full-scale tower reducing by up to 11% after exceeding the serviceability limit state. Regarding crack width prediction, substantial deviations were observed among the results of the four methods. On average, GB50010 underestimated crack widths, while JSCE, Eurocode 2, and ACI 224R overestimated them. Eurocode 2 and ACI 224R provided relatively conservative and accurate predictions. These findings highlight the need for improved and tailored code provisions for annular sections. It is also noted that the comparison was limited to crack widths less than 0.1 mm and a relatively small amount of data. Future research should focus on developing prediction methods specifically for prestressed concrete tower structures with annular sections.

Prestressed steel wires impact on axial bearing capacity of ultra-large section jacking prestressed concrete cylinder pipe (JPCCP): Field experiment and simulation

Jacking prestressed concrete cylinder pipe (JPCCP) represents an innovative composite structure for pipe jacking applications. As a critical component of the JPCCP, the stress levels and stress loss of the prestressed steel wires significantly influence the axial bearing capacity during the jacking process, subsequently impacting the long-term safety and durability of the pipeline. This study presents a field loading experiment conducted with China’s largest JPCCP project. The results reveal tension and relaxation phenomena in the prestressed wires at various positions throughout the jacking process, and the wires’ deformation in the pipe’s central section was greater than that at the bell-spigot end. Following the initial jacking, the stress loss of the prestressed wires was the highest, with significantly reduced deformation in subsequent jacking stages, culminating in a maximum stress loss of 29.0 MPa. Utilizing ABAQUS, a numerical model of the JPCCP incorporating multiple interlayer relationships was developed and validated against experiment data. The study further analyzes the effects of steel wire spacing, prestress level, and prestress loss across different concrete layers, and examines the damage to key areas of the pipe under ultimate compression jacking. The findings indicate that the inner concrete at the spigot end is more prone to damage and yielding, predominantly due to cross-sectional mutations, additional bending moments, and tensile stresses. Based on these findings, specific design and construction proposals are proposed. This study provides an in-depth analysis of the impact of prestressed steel wires on the axial bearing capacity of ultra-large section JPCCP, offering valuable insights into its design and construction.

Study on the Ratio and Model Test of Similar Materials of Heavily Weathered Granite.

To study the bearing characteristics of rock-socketed single piles on the southeast coast of Fujian Province, we conducted similar material ratio tests and single pile model tests. Initially, based on the mechanical parameters of strongly weathered granite, 10 groups of similar material samples were prepared using iron concentrate powder, barite powder, and quartz sand as aggregates, with rosin and alcohol as the cementing agents and gypsum as the modulating agent. Through triaxial testing and range and variance analysis, it was determined that the binder concentration has the most significant impact on the material properties. Consequently, Specimen 1 was selected as the simulation material. In the model test, the strongly weathered granite stratum was simulated using the ratio of Specimen 1. A horizontal load was applied using a pulley weight system, and the displacement at the top of the pile was measured with a laser displacement meter, resulting in a horizontal load-displacement curve. The results indicated that the pile foundation remained in an elastic state until a displacement of 2.5 mm. Measurements of the horizontal displacement and bending moment of the pile revealed that the model pile behaves as a flexible pile; the bending moment initially increases along the pile length and then decreases, approaching zero at the pile's bottom. The vertical load test analyzed the relationship between vertical load and settlement of the single pile, as well as its variation patterns. This study provides an experimental basis for the design of single pile foundations in weathered granite formations on the southeast coast of Fujian Province and aids in optimizing offshore wind power engineering practices.

Moment Curvature and P-M Interaction Analysis of Steel and GFRP Reinforced Concrete Column

This research explores the use of Glass Fiber Reinforced Polymer (GFRP) bars and GFRP circular sections as longitudinal reinforcement in Reinforced Concrete (RC) columns, specifically to mitigate corrosion issues in harsh coastal environments. Twelve concrete specimens were prepared and tested under various loading conditions to evaluate the performance of GFRP as a substitute for conventional steel reinforcement. The experimental findings indicated that GFRP-RC columns displayed slightly lower axial load and bending moment capacities compared to steel-RC columns, though the ductility of both types was found to be similar. The study also highlights the significance of considering the role of GFRP bars in compression, supported by experimental results. This research offers valuable insights into the behavior and performance of both steel and GFRP-reinforced concrete columns, particularly in environments vulnerable to corrosion, with assessments conducted at 28 and 60-day intervals. A comparison of the outcomes from these timeframes reveals the effectiveness of GFRP as a reinforcement option in corrosive conditions

Investigation of higher-order springing of a ship in regular waves by experimental analysis and two-way CFD-FEA coupled method

In this paper, the higher-order springing phenomenon is addressed for a segmented barge ship model through experimental and numerical measures. An efficient in-house two-way coupled numerical solver between Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) is developed and validated against experimental results. The coupling method is based on a domain-separated approach and necessitates the resolution of individual boundary value problems in distinct domains. To ensure convergence within these individual domains, an implicit numerical scheme is employed and further facilitated exchange of variables for coupling. The current approach emphasizes the overall convergence between two solvers, maintaining a strongly coupled setup to comprehensively address fluid-structure interaction phenomena, including added mass and damping effects. A series of tank tests were conducted first to measure the wave-induced sectional loads and motions, during which the springing responses to very high-order harmonics of wave load were observed. By comparing the numerical prediction with the tank test results for rigid body motion and flexible vertical bending moment (VBM), the proposed numerical method demonstrated agreement with experimental results, affirming its validity and robustness. Finally, the springing response up to 14th order harmonics is discussed and investigated.

Flexural behavior of reinforced concrete arch ribs

For many years, arch bridges have been celebrated for their striking appearance and structural effectiveness. However, the response of arch bridges to dynamic loadings, particularly during earthquakes, remains poorly understood, and reliable seismic design guidelines are lacking. Previous research has suggested that reinforced concrete (RC) arch ribs may experience flexural yielding at their springings due to the interaction of axial force and bending moment under earthquake loading. To assess the ductile behavior and ensure the adequate performance of RC arch ribs, a comprehensive investigation combining experimental and analytical approaches was conducted in this study, taking into account the influence of high axial load and the hollow section configuration present in RC arch ribs. The test results revealed that all RC arch ribs exhibited a typical flexural failure mode. As the axial load increased, the lateral load bearing capacity also increased, but the displacement ductility decreased significantly. Comparing different section configurations, the RC arch rib specimen with a double-cell boxed section demonstrated higher lateral load bearing capacity but lower displacement ductility compared to the single-cell boxed section, while the energy dissipation capacity was approximately similar for both section configurations.

Analysis of Strengthening Beam Structure Case Study on Food Court Building of Ruang Terbuka Hijau (RTH) Project at Alun-Alun Kota Kediri

The Green Open Space (RTH) construction in Kediri City includes a food court building utilizing reinforced concrete structures. During construction, cracking issues occurred in several beam structures due to the inability to bear the design loads effectively, necessitating a strengthening approach. This study aims to develop and evaluate a strengthening method for cracked beam structures by employing concrete jacketing. The specific objective is to improve the structural integrity and load-bearing capacity of these beams to ensure the durability and safety of the building. A concrete jacketing technique was used to reinforce the cracked beams, utilizing K-300 ready-mix concrete and additional reinforcing steel. The study involved structural analysis to assess the load-bearing capacity before and after jacketing, and on-site evaluation was conducted to monitor the method's effectiveness. The findings indicate that the jacketing method significantly increased the beams' bending moment capacity and overall structural strength, successfully addressing the cracks and enhancing the beams' ability to bear the intended loads. The reinforced beams showed improved load distribution and structural resilience performance. Concrete jacketing proved to be an effective method for strengthening the cracked beam structures in the Green Open Space project. The study provides valuable insights for similar future construction projects, suggesting that concrete jacketing can be a reliable reinforcement technique to enhance the durability and safety of building structures.

Seismic Response Characteristics of a Utility Tunnel Crossing a River Considering Hydrodynamic Pressure Effects

As a long lifeline system of buried structures, the utility tunnel (UT) is vulnerable to earthquake invasion. For utility tunnels with inverted siphon arrangements crossing rivers, the seismic response is more complex due to the basin effect of acceleration in the topography and the influence of fluctuating hydrodynamic pressure, but there is currently a gap in targeted seismic response analyses and references. Based on a UT project in Haikou, this paper studied seismic responses of a cast-in-place UT considering the coupled model of water–soil–tunnel structure on ABAQUS software. Herein, the dynamic fluctuation of hydrodynamic pressure is simulated using an acoustic–solid interaction model. A viscoelastic artificial boundary was used to simulate the soil boundary effect, and seismic loads were equivalent to nodal forces. Considering seismic invading direction and varying water elevation, this paper investigates the dynamic response characteristics and damage mechanisms of river-crossing utility tunnels. This study shows that the basin effect causes the soil acceleration around the UT to show variability in different sections, and the amplification factor of the peak acceleration at the central location is almost doubled. The damage and dynamic water pressure of the UT are intensified under bidirectional seismic excitation, and the damage location is concentrated at the junction of the horizontal section and the vertical section. Bending moments and axial forces are the main mechanical behaviors along the axial direction. Changes in river levels have a certain positive effect on the UT peak MISES, DAMAGEC, and SDEG, and it exhibits a certain degree of energy dissipation and seismic damping effect. For the aseismic design of cross-river cast-in-place utility tunnels, bidirectional seismic calculations should be performed, and the influence of river hydrodynamic pressure should not be neglected.

Guidance for structural integrity assessment of smooth pipe elbows containing defects using R6

Recently, guidance for fracture assessment of defective elbows using the R6 failure assessment diagram (FAD) method has been included in R6 Revision 4 Amendment 13 (2023). This paper provides an overview of the new guidance and supporting validation. The guidance is validated using 75 cases of 3-D finite element (FE) elastic-plastic J results of smooth pipe elbows of various geometries with axial/circumferential internal/external semi-elliptical/extended/fully-circumferential surface cracks under internal pressure, in-plane/out-of-plane bending moment, torsion and various load combinations, by comparing the FE-based Option 3 failure assessment curves (FAC) with the R6 Option 2 FAC. The results show that, for 74 out of 75 cases, the FE-based Option 3 data points are above the R6 Option 2 FAC with reasonable conservatism when the guidance for evaluating the elbow stress intensity factor and limit load is followed. In other words, following the new guidance can lead to reasonably conservative assessment results.