Bending Moment Research Articles

Seismic response of column‐supported silos considering granular–structure interaction

AbstractTo predict the seismic response of column‐supported silos (CSSs), the granular–structure interaction (GSI) analysis method is proposed with considering the combined effect of the friction between the particles–particles and the particles–silo wall. Using free‐body dynamic equilibrium equations, we reconstruct the mutual interactions between different grain portions and between the grains and the silo wall to develop the ideal calculation model of the CSS structure. Based on the analysis model, additional dynamic overpressure and the effective mass caused by the stored content interacting with the silo wall is obtained with different slenderness ratios and peak accelerations. The additional bending moment caused by the friction between the particles and silo wall is further quantified. To verify the reliability of the proposed method, we discuss some applicative examples by comparing the GSI method with other theories, Eurocode 8, and experimental results. Moreover, the along‐the‐height acceleration profiles of the silo wall and the ensiled content are analyzed according to the shaking‐table tests. The results show that the GSI method can match Janssen's theory well in the case of static pressure at slenderness ratios exceeding 1.0. The overpressure profiles along the height of the silo wall follow a nonlinear distribution, different from Eurocode 8. The bending moment obtained by predictive formulas agrees well with the experimental results for the CSS, indicating that the GSI method is reasonable. Some design and construction recommendations, including the maximum overpressure position, the reference range of the dynamic overpressure coefficient, and the reduction factors of the ensiled content mass, are proposed to facilitate the engineering applications of CSSs, considering different slenderness ratios.

Experimental investigations on the behaviour of structural-sized wood-CFRP composite beams in local fire

AbstractThe study involved combustion of 24 structural-sized beams under three-point bending subjected to substantial loading prior to ignition, reaching 90% of characteristic load-carrying capacity. A localised fire exposure zone was established proximal to the region experiencing the highest bending moment. The specimens were categorised into two groups: the first consisted of tituted by glued-laminated timber (B), and the second comprised wood-CFRP (carbon fibre reinforced polymer) composite (BW). Initial measurements encompassed pre-ignition static deflection and load. Subsequently, the specimens underwent controlled combustion, during which parameters including burning duration and deflection up to failure, were documented. Following cooling with sand, two cross-sectional slices were extracted from each fractured beam, enabling to find vector-based contours of the remaining cross-section. The charring rate and the approximate heat flux density for each test were determined, enabling a direct comparison of the results. A statistically significant number of specimens was examined, facilitating a comparative analysis between reinforced and unreinforced beams concerning failure time and form. Incorporating CFRP tapes among wooden constituents was found to increase the fire resistance of the structure, however, the thickness of the wooden material enveloping the CFRP composite emerges as a pivotal determinant. This issue needs thorough testing under standard fire in the future. Nevertheless, the fact is that adding CFRP tapes engenders a distinct form of beam collapse, transitioning from instantaneous cracking in B-beams to ductile failure in BW-beams.

Cyclic test and analysis of UHTCC‐enhanced buckling‐restrained steel plate shear walls

AbstractThe ultra‐high toughness cementitious composite (UHTCC) has the tensile strain‐hardening characteristic and an excellent ability to prevent tensile cracking. To enhance the seismic and durability performance of the conventional buckling‐restrained steel plate shear wall (BRSPSW), UHTCC‐enhanced BRSPSW (UBRSPSW) was proposed in this paper as a new type of lateral bearing system. The buckling of the inner steel plate is restrained by UHTCC‐normal concrete (NC) functionally graded panels, where the panels are composed of UHTCC and NC layers. In this study, experimental and numerical research was carried out on the UBRSPSWs. Six specimens were tested to investigate the seismic behavior of the UBRSPSW. Parameters including the number of stiffeners, the thickness of UHTCC‐NC functionally graded panels, the material of restraining panels, and the gap between the inner steel plate and restraining panels were considered in the test design. Mechanical response and failure modes of the structures under cyclic loads were analyzed. The obtained hysteretic curves and corresponding skeleton curves indicated that the proposed design had excellent seismic performance. Compared to the steel plate shear wall (SPSW), the load‐bearing capacity of UBRSPSW was improved by 13%, respectively. The appearance of macrocracks was delayed by a drift angle of 1.2%. In addition, a refined finite element (FE) model was developed and validated by the results obtained from experiments. The development and distribution of bending moments in the restraining panels were extracted based on the FE method. Then, the loading capacity design method of restraining panels and a theoretical model for controlling the crack width of restraining panels were proposed. The research results of this paper can provide useful suggestions for the seismic design of UBRSPSWs.

An analytical method for out-of-plane stability assessment of network arch bridges

Network arch bridges typically feature inclined cables with a net configuration to support the bridge deck, therefore, improving the bridge's stiffness and reducing bending moments along the arch elements. Given their relatively slender cross-sections and large compression stresses, properly evaluating stability safety is crucial to the integrity of network arch bridges. However, because of the unique design of cable configuration, current design specifications mostly do not provide specific methods for such stability assessments. To address this gap, the study proposes a new analytical methodology that elucidates the mechanical relationship between basic design parameters and the stability performance of network arch bridges. A numerical example is conducted using finite element analysis to validate the performance of the proposed method. In addition, the influence of several design parameters on the stability factor and buckling length factor is investigated. This research further proposes a practical expression for the buckling length factor of arch ribs with nonlinear regression analysis. The results exhibit that the proposed method can efficiently and accurately evaluate the buckling stability performance of network arch bridges, and the established practical expression can facilitate designers in easily estimating the critical buckling load during the design process.

Research on Monitoring Technology for Frame Piers of Continuous Box-Girder Bridges Constructed by the Cantilever Method

This paper focuses on the analysis of the stress state of a large-span frame pier-continuous box girder bridge with pier crossbeams anchored by pier crossbeams on the main pier of the Guangfo-Zhao Expressway. The bridge is constructed by the cantilever method, and a refined finite element model of the entire bridge is established using the finite element software Midas/FEA to analyze the stress state of the frame pier during the cantilever construction process. It is found that under the possible combined action of an unbalanced load during construction, the torsional resistance of the frame pier crossbeam does not meet the requirements of the design code. In order to eliminate the torsion of the frame piers, counterweights were used to monitor the frame piers during the construction of the box girders. In this paper, the theoretical calculation formula of the inclination angle of the end section of the frame pier crossbeam with the change of unbalanced bending moment, the calculation formula of the relationship between the horizontal displacement of the frame pier and the unbalanced bending moment, and the calculation formula corresponding to the relationship with the water tank counterweight are derived using the structural mechanics method. Two monitoring methods for the frame pier are proposed. In the construction monitoring of the bridge, the numerical fitting formula obtained by finite element numerical analysis calculation is compared with the calculated formula obtained by substituting the design parameters of the frame pier into the theoretical formula. The basic constants in both formulas are basically equal, verifying the correctness of the monitoring calculation formula proposed in this paper for the torsional resistance of the frame pier crossbeam. The applicability of the two monitoring methods is also compared and analyzed. This paper takes the main pier of Chaoyang overpass’s mainline bridge as the engineering background, which adopts the framework pier with a large-span prestressed concrete continuous box girder bridge. It analyzes the torsional state of the beam of the framework pier during the bridge construction process and conducts research on the construction monitoring of the framework pier crossbeam, providing valuable references for the construction monitoring of framework pier crossbeams in the construction of large-span framework pier continuous bridges in the future. The research results of this paper can provide assistance for the construction monitoring of similar projects. This paper’s innovation primarily resides in employing structural mechanics methods to compute the torsion of frame piers. On this basis, a simplified beam torsion calculation formula is proposed to strengthen its practical application in construction monitoring. The findings of this paper can help in the construction monitoring of similar projects.

A Numerical Study of Reinforcement Structure in Shaft Construction Using Vertical Shaft Sinking Machine (VSM)

Using the Vertical Shaft Sinking Machine (VSM) for shaft construction is an emerging modern technology, which is also currently one of the most advanced techniques in the field of shaft sinking. Current research on VSM technology primarily focuses on mechanical and technical issues, neglecting the impact of the construction on the surrounding soil and the structure itself. This oversight leaves structural design lacking a reliable foundation. Additionally, there is insufficient information on the role of reinforcement design during construction in soft soils. These engineering challenges have hindered the widespread implementation of this new technology. Therefore, a series of numerical models were used to analyse the mechanical behaviour of shaft and soil during or after the sinking process, with the aim of addressing these gaps by investigating the influence of shafts constructed using VSM technology, and providing a scientific basis for reinforcement design in soft soil. The case study shows that increasing the soil-cement strength does not have a significant effect on the overall deformation of the soil surrounding the shaft, but leads to a notable reduction in the plastic zone volume, subsequently enhancing the overall stability of the neighbouring soil. The ring bottom beam design effectively reduces convergence deformation by about 50%, while also improving the horizontal internal force distribution near the cutting edge. However, this approach significantly escalates local vertical bending moments, necessitating thorough consideration in the design stage.

Effect of Flexible Tank Wall on Seismic Response of Horizontal Storage Tank

Horizontal storage tanks are integral to the petrochemical industry but pose significant risks during earthquakes, potentially causing severe secondary disasters. Current seismic designs predominantly assume rigid tank walls, which can lead to an underestimation of seismic responses. This study introduces a novel analysis method for assessing the dynamic response of flexible-walled horizontal storage tanks. By separating the liquid velocity potential into convective and impulsive components and integrating these with beam vibration theory, we developed a simplified mechanical model. A parameter analysis and dynamic response research were conducted using numerical methods. Results indicate that flexible tank walls amplify seismic responses, including liquid dynamic pressure peaks, base shear, and overturning bending moments, compared to rigid walls. Additionally, the impact of flexible walls is more pronounced in tanks with larger radii, aspect ratios, diameter–thickness ratios, and H/R ratios. These findings highlight the necessity for revised seismic design approaches that consider wall flexibility to enhance the safety and resilience of horizontal storage tanks.

Characterization of damage to steel bridge girders subjected to over-height vehicle collision

Bridge structures that span roads and highways are often at the risk of over-height vehicle collision. Such collisions can cause structural damage to bridge girders, adversely affecting the bridge's safety and functionality, while posing an immediate hazard to traveling motorists. To ensure the structural integrity of the bridge girders, it is imperative to evaluate them in response to the loading demand induced by over-height collisions. However, current specifications and codes do not have the details necessary to predict the impact forces that steel bridge girders can experience during such collisions. To address this gap, a comprehensive investigation was conducted in this study to (i) determine impact force characteristics, (ii) evaluate various impact-induced structural response measures, and (iii) identify design parameters in need of attention to minimize the extent of impact-induced damage to steel girders. For this purpose, nonlinear finite-element models were developed and validated with experimental tests and field surveys. The structural performance of the steel bridge girders was then investigated, in terms of damage patterns, girder displacements and rotations, shear forces and bending moments, and impact forces, during a range of over-height collision scenarios. Based on the obtained results, predictive equations were developed to estimate the mean impact force. This was to facilitate the impact-resistant design of steel girders commonly used in bridge structures.

Does high-intensity running to fatigue influence lower limb injury risk?

ObjectivesThe aim of this study was to quantify changes in peak bending moments at the distal tibia, peak patellofemoral joint contact forces and peak Achilles tendon forces during a high-intensity run to fatigue at middle-distance speed. DesignObservational study. Methods16 high-level runners (7 female) ran on a treadmill at the final speed achieved during a preceding maximum oxygen uptake test until failure (~3 min). Three-dimensional kinetics and kinematics were used to derive and compare tibial bending moments, patellofemoral joint contact forces and Achilles tendon forces at the start, 33 %, 67 % and the end of the run. ResultsAverage running speed was 5.7 (0.4) m·s−1. There was a decrease in peak tibial bending moments (−6.8 %, p = 0.004) from the start to the end of the run, driven by a decrease in peak bending moments due to muscular forces (−6.5 %, p = 0.001), whilst there was no difference in peak bending moments due to joint reaction forces. There was an increase in peak patellofemoral joint forces (+8.9 %, p = 0.026) from the start to the end of the run, but a decrease in peak Achilles tendon forces (−9.1 %, p < 0.001). ConclusionsRunning at a fixed, high-intensity speed to failure led to reduced tibial bending moments and Achilles tendon forces, and increased patellofemoral joint forces. Thus, the altered neuromechanics of high-intensity running to fatigue may increase patellofemoral joint injury risk, but may not be a mechanism for tibial or Achilles tendon overuse injury development.

Thermo‒mechanical behavior of energy pile group in dry sand subjected to a horizontal load

The energy pile is an innovative structure element designed to utilize geothermal energy while simultaneously supporting building loads by means of integrating heat exchange tubes into the pile foundation. Despite the intricate thermodynamic characteristics of energy pile groups, research on them remains limited. This study investigated the horizontal load transfer mechanism of an energy pile group in dry sand by conducting a model test on a 2 × 2 energy pile group subjected to horizontal loads. Specifically, the impact of heating or cooling a single pile within the energy pile group was examined. The results showed that the bending moment was significantly larger on a single pile subjected to a thermal load than that of the other piles, with the majority of this variation occurring in its upper part. Additionally, the horizontal load had a strong influence on the rotational angle and horizontal displacement of the energy pile group. The rotational angle and horizontal displacement decreased with increasing depth. With rising temperature, the interaction between the pile and the soil intensified, and the soil pressure on the upper part of the pile increased while that in the lower part decreased.

Horizontal bearing capacity of post-expanded arm grouting pile foundations

In order to effectively improve the horizontal bearing capacity of pile foundations, this study proposes post-expanded arm grouting technology and associated pile foundations. The horizontal bearing characteristic of the post-expanded arm grouting pile was explored through model tests. The test results indicate that the post-expanded arm grouting pile can increase the contact area between the pile and soil, and can improve the strength of the soil. The horizontal bearing capacity of the post-expanded arm grouting pile was approximately 3 times that of the conventional pile. It also shows that the larger the plate diameter ratio or grouting volume, the higher the horizontal bearing capacity of the post-expanded arm grouting pile. The maximum bending moment of the post-expanded arm grouting pile was located at the pile plate, and the displacement zero point of the new pile was higher than that of the conventional pile. The soil resistance at the pile plate was significantly higher than that of conventional piles, indicating that the pile plate effectively enhances the soil resistance. The improved p-y curve model and horizontal bearing capacity calculation method for the post-expanded arm grouting pile were proposed by considering the pile plate diameter factor. This method was finally verified by experimental results. The results of this study can provide a reference for calculating the horizontal bearing capacity of the post-expanded arm grouting pile.

Behavior of GFRP-Reinforced Concrete Members under Combined Bending Moment and Low Axial Load

Behavior of GFRP-Reinforced Concrete Members under Combined Bending Moment and Low Axial Load

Experimental analysis of extreme wave loads on a containership

Model-scale experiments were conducted to investigate the non-linearities associated with the Vertical Bending Moment (VBM) of a rigid container vessel in irregular waves. Long-duration runs ( ≃ 25 hours of data in full scale) were performed to allow the calculation of statistically meaningful extreme values of hogging and sagging on five different sea-states (from Hs = 6 m up to Hs = 17 m).The model tests are presented in detail, and sampling errors are estimated. It is found that the ratio between linear and non-linear VBM (the so-called non-linear factor) can be modeled as a function of the linear value only. For a given linear value, the non-linear correction is the same, whatever the sea state. This observation, new in the fully non-linear case, is very valuable as it opens the door to efficient design assessment methodologies such as increased design sea state or design waves.

Microstructural and fatigue characterization of 316L stainless steel subjected to flow drilling and tapping: comparison with machined threads

Despite extensive research on the plastic deformation of materials to enhance their fatigue resistance, the influence of the flow tapping process on the fatigue resistance of drilled and tapped bars remains poorly understood. Herein, the fatigue performance of flow-drilled (friction-drilled) and flow-tapped 316L stainless steel bars was experimentally analyzed and compared with that of conventional material-shearing-based drilling and tapping operations. The effect of flow processes on the material properties was evaluated via microhardness tests and microstructural analyses. The results indicated that the hardness near the holes produced via flow forming was 62 % higher than that of the base metal. Moreover, grain refinement and plastic deformation were observed beneath the thread surfaces. Metallographic observations revealed the occurrence of craters and folds at the crest of the flow-formed threads. Following the ASTM F382-17 standard, four-point bending fatigue tests were performed at three stress amplitudes with a stress ratio of 0.1. No noteworthy differences were observed when the maximum bending moments applied were at 75 % and 60 % of the bending moment at yield. However, when the maximum bending moment applied was limited to 50 % of the bending moment at yield, the average fatigue life of the specimens with machined threads was longer than that of their flow-formed counterparts. Fractographic observations were used to identify the crack initiation regions and elucidate the underlying fracture mechanisms. For both types of specimens, failure originated at the crest of the first thread, beneath the surface of the maximum tensile stress. The flow-processed specimens exhibited secondary cracks at the root of the threads, where grain refinement also occurred. This study provides robust empirical evidence that using flow-forming processes to thread 316L stainless steel does not systematically improve the fatigue resistance of the material surrounding the holes. Furthermore, by optimizing the flow process and eliminating discontinuities, the threading process proposed herein could help improve the fatigue resistance of orthopedic implants.

Effect of scour remediation by solidified soil on lateral response of monopile supporting offshore wind turbines using numerical model

Offshore wind turbines supported by monopiles are inevitably influenced by scour, which will weaken the support provided by soils around and reduce the lateral capacity of the foundations, potentially leading to structure failures. In response, solidified soil is recognized as a promising solution for scour remediation, not only effectively filling the scour holes but also increasing the overall bearing capacity of the monopile. Nevertheless, the mechanism for scour remediation of solidified soil to increase the bearing capacity of the monopile is still unclear. Therefore, this paper mainly investigates the impact of solidified soil on the lateral bearing capacity of monopiles under various scour conditions and compares the effectiveness of different scour remediation methods (i.e., inverted conical remediation to half or all of scour hole and cylindrical remediation to half or all of scour hole). Firstly, the effect of solidified soil on lateral responses of monopile was investigated numerically. The overall load-displacement behavior, profile of bending moment and deflection versus depth of monopile under different scour stages and scour remediation conditions have been fully studied, in addition to the displacement field and failure mode of soil around monopile. It was found that solidified soil can greatly improve the lateral capacity and initial stiffness of monopile, and the cylindrical remediation to all of scour hole scenario showing the greatest improvement. After remediated by solidified soil, the resistance of soil around the monopile is greatly improved, and the rotation center position of monopile is moved up. Furthermore, a series of supplementary sensitivity analyses were conducted to study the effects of remediation parameters (i.e., elastic modulus and strength of solidified soil) and original soil parameter on lateral capacity of monopile.

Model Test and Numerical Simulation of Two Typical Close-Fitting Pile–Wall Integrated Structures in Deep Excavation

Compared to conventional support methods, the close-fitting pile–wall integration technique features a minimized construction spacing between the retaining pile and the basement retaining wall. This approach leverages the pile stiffness to minimize the wall thickness and enhance underground space utilization. However, it currently lacks significant discussions and measured data about the interaction laws between the pile and the wall. The model test and finite element method (FEM) are employed to study the deformation and internal force interaction laws of two typical close-fitting pile–wall integrated structures, and a comparison with conventional design is conducted. Furthermore, this study separately investigates the impact of sensitivity factors, specifically the pile–wall stiffness ratio and floor plate stiffness, on both structures during the basement construction and serviceability stages. The test results can closely match the numerical simulation. The study results reveal that the wall impacts the bending moment of the pile to some extent. The internal force in the wall is significantly influenced by the lateral deformation of the pile and the floor plate. Compared to conventional designs, this structure significantly reduces the bending moment of the wall, particularly in the composite structure. Additionally, the analysis of sensitivity factors reveals their considerable influence on the pile–wall interaction.

Hysteretic behavior optimization of hollow laminated viscoelastomer-filled steel tube damper

This study proposes a shape optimization approach for designing hollow laminated viscoelastomer-filled steel tube dampers (HLVSTDs), aiming to reduce stress concentration, enhance energy dissipation capacity, and improve low-cycle fatigue performance. The shape optimization curve is obtained based on the definition of stress contours for HLVSTD bending moments and shear forces, with the assumption that points on the same contour yield simultaneously. Cyclic loading experiments were conducted on four HLVSTDs. Numerical models were established and validated to further investigate the mechanical properties, energy dissipation capacity, and seismic performance of the shape-optimized HLVSTDs. The results demonstrate that the shape-optimized HLVSTDs specimen exhibits excellent energy dissipation capacity and improved low-cycle fatigue performance. The calculated initial stiffness and yield force closely align with experimental values. Compared to non-optimized HLVSTDs, the shape-optimized HLVSTDs exhibit more uniform stress and equivalent plastic strain distributions, effectively reducing the concentration of plastic strains. Additionally, structures equipped with shape-optimized HLVSTDs demonstrate superior seismic performance.

Classification of equivalent static wind loads: Comparisons and applications

This paper reviews the basic ideas, developments, and codification practices of different calculation methods for equivalent static wind load (ESWL) in the past about sixty years. From the landmark work of Davenport's Gust Loading Factor (GLF), Kasperski's Load-Response-Correlation (LRC), and Katsumura, Tamura's Universal-ESWL (U-ESWL), the development thread of ESWL is clarified. The ESWLs are classified based on the number of target load effects (Single-target or Multiple-target) and on actuality (Realistic or Unrealistic). GLF is representative as a “Single-target Unrealistic” ESWL, which has been adopted in many international codes and standards for building design and is extended into many approaches considering different targets (e.g. base bending moment), and different components (along-wind, crosswind, torsional). The LRC method identifies a realistic wind load distribution that causes one target maximum/minimum load effect, is a representative of “Single-target Realistic” ESWL, is well adopted as a background component ESWL, and is further developed to consider the dynamic resonant effect. The U-ESWL simultaneously reproduces maximum/minimum load effects in multiple structural members with only two sets of load distributions, is a “Multiple-target Unrealistic” ESWL, and has also been developed and employed in a wind load code for roof structures.

ALEM-FEM-BEM coupling for response analysis of pile group in laminated fluid-saturated geomaterials induced by tunnel excavation

This paper proposes a two-stage analytical methodology for predicting the response of pile groups in layered fluid-saturated soils induced by tunnel excavation. The Loganathan analytical approach is adopted for estimating the free-field response induced by tunneling. At the second phase, the solution to the surrounding soil of pile groups is employed as the kernel function based on the analytical layer-element method (ALEM). Subsequently, the analysis of soil-structure interaction is presented using the boundary element method (BEM). The Timoshenko-beam model is utilized to simulate each monopile combined with finite element method (FEM). Finally, the responses of adjacent pile groups are derived by the coordination conditions and coupling of BEM and FEM. Comparisons are made between the presented analytical solutions and existing experimental and numerical results. Parametric analyses are performed to evaluate the influence of soil permeability, material stratification, tunnel-pile distance, tunnel buried depth, and pile slenderness ratio on the mechanical behavior of grouped piles. The results show that the pile group in hard top and soft bottom saturated soils demonstrates better load-bearing capacity than that in soft upper and hard lower soils. Then, with the increment of tunnel-pile distance, the displacement and bending moment are reduced by 22.2 %-50 % and 41.2 %-66.7 %, respectively, and the increased rate of mechanical response over time slows down. Moreover, increasing the burial depth reduces the displacement by 8.6 %-33.3 % and the bending moment by 33.4 %-50 %, respectively, and the locations of peak responses increase from 0.6 times the pile length to 0.8 times the pile length.

Damage analysis in welded steel pipe elbow under strong cyclic loading

According to cyclic loading modes, highly pressurized tubular elements, such as those in elbows, differ from other straight tubular structures in their modes of stress and damage. This work aims to perform a numerical prediction of a tubular structure. It consists of an X52 steel elbow welded to X65 grade ends by straight tubular sections. This pressurized structure is subjected to strong cyclic loading in bending moment applied until damage occurs. The bending moment is combined with different orientations between the closing or opening moment and the out-of-plane moment, presenting a possible but rarely analyzed situation. This cyclic loading mode is taken as an evaluative parameter in its various amplitudes, orientations, and patterns. The cyclic hardening of the elbow and straight tubular sections, including those of the welded joints, are all formulated by the combined isotropic and kinematic model introduced in the ABAQUS calculation code with parameters calibrated according to the Voce model and experimental results, using plasticity by the Von Mises equivalent stress flow theory. The appropriate XFEM (Extended Finite Element Method) technique is used in conjunction with the hardening model to overcome numerical calculation difficulties and predict damage in traction laws, separation by crack initiation and propagation. The results, in the form of hysteresis curves in cyclic bending moment and angular displacement, have shown a strong dependency that conditions the structure’s response as well as the level of its damage.