Bending Moment Research Articles

Stability of arches with internal hinge

The in-plane stability of internally hinged, end-fixed shallow arches is in the spotlight. The non-linear model accounts for the coupled effect of the bending moment and axial force on the membrane strain. The model itself can handle homogeneous or non-homogeneous material distributions along the thickness of the uniform arch. Analytical findings reveal how the typical geometrical data, like arch length, radius of gyration, and arch angle, affect the lowest buckling loads. The typical non-linear behaviour of arches is also assessed including the equilibrium path and the internal force system.

The effect of temperature difference on bending of external panel walls

One of the most common structural systems of buildings intended for various purposes is a prefabricated panel system of factory-made elements assembled on-site. Single-layer structures made of lightweight concrete are widely used as envelopes of these buildings. In buildings operated under various climatic conditions, exterior wall panels, as well as other envelopes, are exposed to thermal deformations and, accordingly, changes in the stress-strain state. As the temperature changes, corresponding stresses and deformations occur across the thickness of the exterior panels. To analyze their values, the bending moments and support reactions of single-layer lightweight concrete panels of different length and thickness in the range of temperature differences from 0 °С to 65 °С have been calculated. It was found that the bending moments and support reactions of 1,500 mm long panels decrease as the thickness of the panels increases over the entire temperature gradient. The values of bending moments and support reactions of panels with length of 3,000, 4,500 and 6,000 mm decrease only when the temperature rises from 0 to 10 °С, in the rest of the range 15–65 °С – increase as the thickness of the panel increases due to the bending stiffness.

Investigation of Concrete Damage on a Prefabricated Steel Spring Floating Slab Track by Finite Element Modelling

AbstractTo investigate the concrete damage of prefabricated steel spring floating slab tracks (SSFST), a three-slab prefabricated SSFST system was established using the ABAQUS finite element software. Full trainload conditions and fatigue load conditions of a train passage were successively applied to the system. Plastic damage and fatigue damage of the floating slab were simulated based on concrete damage plasticity theory and model code, respectively. For comparison, a simulation of the fatigue experiment was conducted. Parametric analyses of the concrete strength and isolator stiffness were also performed. The results show that the maximum positive and negative bending moments of the floating slab throughout the loading stage are close in value. The positive bending moment causes stress concentration on the top slab surface which leads to plastic damage and low-cycle fatigue damage, while the negative bending moment causes middle-level elastic tensile stress on the bottom slab surface which leads to high-cycle fatigue damage. Under experimental conditions, damage on the bottom surface is much more severe, while the upper part is undamaged. Improving the concrete strength can reduce both kinds of damage, while increasing the isolator stiffness can only mitigate the high-cycle fatigue damage. Accordingly, recommendations are provided for improving fatigue experiments and structural design of prefabricated floating slabs.This study can inform the design and maintenance of the prefabricated SSFST system, ultimately enhancing their safety and longevity.

Plastic behavior and shakedown limit of defected pressurized pipe under cyclic bending moment

Pipelines subjected to thermal or mechanical loads may fail due to plastic strain accumulation which leads to ratcheting. In this research, cyclic plastic behavior and shakedown limit are investigated experimentally and numerically for a defected pressurized pipe under cyclic bending moment. In the numerical model, the combined isotropic/kinematic hardening model based on the Chaboche model is adopted to represent the cyclic plastic flow of the material. The hardening parameters are determined experimentally and used in the finite element (FE) model. A four-point bending test rig is manufactured to test a pressurized API 5L steel pipe under cyclic bending. An elliptical defect is created by machining to depict corrosion pits in pipes. The plastic strains are measured experimentally and the results are used to tune the parameters of the FE model. The shakedown limit of the defected pipe is determined numerically by tracking the critical points behavior and the results are verified experimentally. Furthermore, the plastic work dissipated energy (PWD) is estimated within the defective structure to study the behavior of the pipe. By running this compatible model, it is found that the yield and the shakedown limits are lowered by mean values of 55% and 25% respectively due to the presence of metal loss defect occupying almost half of the pipe thickness.

A Comparative Study on Load Assessment Methods for Offshore Wind Turbines Using a Simplified Method and OpenFAST Simulations

Simplified methods are often used for load estimations during the initial design of the foundations of offshore wind turbines (OWTs). However, the reliability of simplified methods for designing different OWTs needs to be studied. This paper provides a comparative study to evaluate the reliability of simplified approaches. The foundation loads are calculated for OWTs at the mudline level using a simplified approach and OpenFAST simulations and compared. Three OWTs, NREL 5 MW, DTU 10 MW, and IEA 15 MW, are used as reference models. An Extreme Turbulence Model wind load at a rated wind speed, combined with a 50-year Extreme Wave Height (EWH) and Extreme Operating Gust (EOG) wind load and a 1-year maximum wave height are used as the load combinations in this study. In addition, the extreme loads are calculated using both approaches for various metocean data from five different wind farms. Further, the pile penetration lengths calculated using the mudline loads via two methods are compared. The results show that the simplified method provides conservative results for the estimated loads compared to the OpenFAST results, where the extent of conservativism is studied. For example, the bending moment and shear force at the mudline using the simplified approach are 23% to 69% and 32% to 53% higher compared to the OpenFAST results, respectively. In addition, the results show that the simplified approach can be effectively used during the initial phases of monopile foundation design by using factors such as 1.5 and 2 for the shear force and bending moment, respectively.

Enhancing fatigue reliability prediction of offshore wind turbine jacket joints through individual uncertainties for each degree of freedom of stress concentration factor

This paper presents the fatigue reliability prediction for welded planar tubular joints of offshore fixed jacket support structures. A coupled model is employed to calculate the dynamic response of the jacket support structure under wind and wave loads. Stress concentration factors (SCFs) are evaluated using Efthymiou parametric equations, and the hot-spot stresses at eight locations on the chord and brace of the tubular joints are derived by summing the stress components from axial, in-plane, and out-of-plane actions. The stress distribution is determined using the rainflow counting method, fatigue damage from an S–N curve, and Miner’s rule. Uncertainties associated with the fatigue lifetime evaluation procedure are identified, quantified, and modeled. The focus is specifically given to modeling the uncertainty related to the SCFs, and a framework is proposed to evaluate the fatigue reliability of the joint by incorporating individual uncertainties for each degree of freedom of the SCFs (i.e., axial load crown, axial load saddle, in-plane bending moment, and out-of-plane bending moment). The results reveal that assuming the same uncertainty level (Coefficient of Variation of 0.2) as recommended by DNV-RP-C210 for each degree of freedom of the SCFs and including the uncertainty after obtaining the stress distribution from rainflow counting does not consistently yield conservative reliability index values, as it depends on the critical hot spot. It is essential to note that the simplified assumptions derived from the oil and gas sector may not directly translate to the offshore wind industry due to differences in loading conditions. A reduction of up to approximately 24% in the reliability index is observed for one critical hot spot, while an increase of up to 20% was observed for another. Overall, this paper provides valuable insights into the complex interplay of factors affecting the reliability of joints in offshore fixed jacket support structures, shedding light on the need for tailored approaches to address uncertainties in the specific context of the offshore wind industry.

Horizontal Tail Flight Load Prediction Method for Large UAVs based on Machine Learning

In today’s rapidly developing large UAVs field, flight safety and reliability are essential considerations. Flight load is one of the important factors affecting the load capacity of large UAVs, so the research on load prediction technology can improve flight safety and the reliability of air transportation. This paper first introduces the collection and processing method of flight load data, then uses the machine learning method-BP neural network to predict flight load, establishes the BP neural network model to predict flight load with flight parameters, and optimizes the model according to error analysis. Finally, the accuracy and practicability of the model are verified by analysing the fitting of the training set and the test set, and the error distribution of the true value of shear, bending moment, torque and the absolute percentage of the predicted value, and the model is evaluated.

ALTERNATIVE LOAD PATH AVOIDING BRIDGE COLLAPSE AFTER DEMOLITION OF A PIER BY COLLISION

Present codes require structures to be designed sufficiently robust, either by creating alternative load paths, or by increasing resistance of members. In the case of collision of column piers, alternative load paths seem to be an unworkable solution, since the loss of an essential support cannot be replaced by some other column or bracing. If all the columns of the same pier are destroyed, the adjacent beams of a concrete bridge are no longer in equilibrium, unless they become continuous and thus a corresponding bending moment can arise. The latter can be delivered by a couple of forces. The compressive force on top of the beams is provided by the bridge slab itself. The tensile force can be provided by a steel plate, below the bearings of the adjacent beams. Once the damaged condition comes about, there is a slight further shift of the bearings and the steel plate acts as a tensile element. A small-scale test has allowed us to confirm this principle experimentally. This idea has been tested for two cases of concrete bridges. A standard road bridge of multiple 34 m span of 39 precast prestressed hollow core girders and a 22.5 m span with classical I-section girders. Dummy cables are necessary to compensate the effect that bonded tendons are inactive at the ends of the PC-beams. Other details are still to be worked out, yet the general idea appears to be working and could meet the requirement for robustness.

ALTERNATIVE LOAD PATH AVOIDING BRIDGE COLLAPSE AFTER DEMOLITION OF A PIER BY COLLISION

Present codes require structures to be designed sufficiently robust, either by creating alternative load paths, or by increasing resistance of members. In the case of collision of column piers, alternative load paths seem to be an unworkable solution, since the loss of an essential support cannot be replaced by some other column or bracing. If all the columns of the same pier are destroyed, the adjacent beams of a concrete bridge are no longer in equilibrium, unless they become continuous and thus a corresponding bending moment can arise. The latter can be delivered by a couple of forces. The compressive force on top of the beams is provided by the bridge slab itself. The tensile force can be provided by a steel plate, below the bearings of the adjacent beams. Once the damaged condition comes about, there is a slight further shift of the bearings and the steel plate acts as a tensile element. A small-scale test has allowed us to confirm this principle experimentally. This idea has been tested for two cases of concrete bridges. A standard road bridge of multiple 34 m span of 39 precast prestressed hollow core girders and a 22.5 m span with classical I-section girders. Dummy cables are necessary to compensate the effect that bonded tendons are inactive at the ends of the PC-beams. Other details are still to be worked out, yet the general idea appears to be working and could meet the requirement for robustness.

Experimental study on the stability of dike reinforced by steel sheet pile under storm surge

Over recent decades, upgrading dikes that defend against storm surges increasing in both intensity and frequency resulting from global warming, face challenges such as environmental impact and susceptibility to brittle failure. To address this issue, the steel sheet pile can be employed to improve the dike stability due to its resilience in withstanding substantial deformation. To investigate the reinforcement mechanism of the steel sheet pile, this study conducted three wave flume tests including the dike without configuration, the dike with single sheet pile, and the dike with double sheet pile. The dike stability and pile bending moment were analyzed based on the monitoring data. The experimental results showed that the single pile significantly improved the dike stability by reducing the seepage. The maximum bending moment for the single sheet pile occurred at approximately 1/3 of the pile depth, primarily due to its proximity to the wave impact area on the dike. The double pile further enhanced the dike stability primarily through the reduction of wave scour. The maximum bending moment for the double pile occurred at a lower position (2/3 of the pile depth) and was smaller due to the external force distribution and tie rod limitation.

Structure-Structure Interaction in the Reinforced Concrete Frames-Wall

Abstract Reinforced concrete frame-wall (RC frame-Wall) structures are generally solved in a global manner by modeling the entire structure by assembling the RC frame and wall stiffness matrices into a global matrix. The bar-wall element interface is modeled at the mean line of the beam-column element, according to RPA 99, which limits the interaction to the axial and transverse components of the forces (mechanical and kinematic) thus neglecting the effects of section rotations. In order to take into account, the rotational components of the mechanical behavior of the beams (section rotation and bending moment), the interaction between the RC frame and the wall must take place at the real interface of the two substructures, i.e. at the extreme fiber of the bar elements (beams and columns). The transmission of force from the wall to the RC frame is done by transforming the tangent stresses of the wall into moment in the beam.

Joint stress of a hinged platform composed of eight boxes

The box-type hinged platform has important applications in ocean engineering. In this paper, a multi-module assembled box-type platform is described. The mid-section load of the platform is numerically simulated based on the three-dimensional velocity potential theory and the indirect time-domain method through the hydrodynamic module AQWA in ANSYS. The stress of the hinged joints of platforms was performed using finite element analysis software in ANSYS software. The results show that: (1) In irregular waves, the shear force and bending moment in the middle section of the platform increases with the increase of the significant wave height; (2) Under the same towing scheme, the stress of the hinged joints between box platforms shows an increasing trend with the increase of wave level. Under the same wave working condition, the stress at the uniaxial nut of the hinged joints is relatively high, which is prone to fracture.

Cyclic response of laterally loaded pile after storm loading

Offshore wind farms in China are in tropical cyclone zones, where typhoons or tropical revolving storms will pass through every year and can produce huge loads on the offshore wind turbines. Therefore, the stability of OWT foundations after storm loading is critical to ensure the safe operation and design life of turbines. While monopile is the most used foundation type for offshore wind, little studies exist on the cyclic response of monopile after storm loading. To fill the gap, this study presents a unique centrifuge and numerical study on the cyclic deflection response of monopile in medium dense sand after extreme storm loading. The centrifuge test was performed at 100g on a typical monopile with a prototype diameter (D) and embedded depth (L) of 4 m and 60 m, respectively. Finite element (FE) simulations using the advanced hypoplastic model for sand were performed to back-analyze the centrifuge test and provide further insights into the test results. From the centrifuge test, a unique “self-healing” beahviour of monopile was observed for the first time, where the foundation exhibited a deflection recovery response and tilted back to its initial position under the small amplitude cyclic load after the storm loading. This “self-healing” beahviour was also replicated by the FE model. By looking into the computed pile-soil interaction and soil element states around the pile, it was found that the “self-healing” response is attributed to the “lock-in” bending moment after the storm loading. This “lock-in” bending moment generated significant compressive horizontal stress on the soil elements behind the pile and produced more compressive strain under cyclic loading. As a result, the pile exhibited the “self-healing” response and tilted back against the loading direction.

Numerical Simulation Study on the Spacing of Landslide Anti-slip Piles Based on Strength Reduction Method

In landslide control engineering, anti-slip piles are the most commonly used means. This article established a numerical model of the interaction between fully weathered granite landslides and anti-slip piles based on the strength reduction method. Firstly, five pile-soil interaction models with different pile spacing were established using Abaqus software, and individual components were generated and assembled using the stretching function. The friction surface is used between the pile and soil, and the normal and tangential contact characteristics are both Penalties. Secondly, the strength reduction method based on displacement criteria is used to reduce the rock and soil parameters to the unstable stage before failure, while calculating the slope safety factor. Then, the influence of anti-slip pile spacing on slope stability, pile shear force, bending moment, and soil arch effect are studied. The strength reduction method and pile-soil interaction model used in this article can effectively avoid single pile effects and have high accuracy in characterizing soil arching effects. The results afford certain application and promotion values by providing theoretical references and technical guidance for similar anti-slide pile reinforced slope projects.

Ultimate Lateral Resistance of Single Piles in Sand

The p-y curve method is currently the most widely utilized analytical approach for horizontally loaded piles. Precisely determining the ultimate soil resistance is essential to enhance the accuracy of the p-y curve. Despite various scholars proposing methods to establish the law governing ultimate soil resistance with soil depth in the sand, significant discrepancies exist among these approaches. This paper posits that the three-dimensional failure mode of the shallow soil in front of the pile manifests as a cone when it reaches the limit state. The expression for the ultimate soil resistance of a single pile in shallow soil is derived through limit equilibrium theory, and subsequently, the modified p-y curve is obtained. The accuracy was validated through a comparison between the corrected p-y curve and results obtained from centrifugation experiments and field studies. In contrast to the API specification method, the refined hyperbolic function p-y curve demonstrates enhanced precision, facilitating precise predictions of pile head displacement and pile bending moments under horizontal loads.

Numerical simulation of bending characteristics of geosynthetic encased stone column

A numerical model of the cantilever bending structure of a geosynthetic encased stone column (GESC) of length 3 m and diameter 0.3 m was established using Z-Soil. The aim was to analyze the stress distribution and bending characteristics of the GESC under a bending load and to investigate the impact of encasement strength, encasement stiffness, gravel friction angle, and diameter on the bending characteristics of the GESC. The maximum bending moment of the GESC under bending conditions occurs at the anchored end. The dividing line of tensile and compressive stresses on the gravel in the anchored end section after bending failure appears at a radius of 0.5 of the column above the section centerline. The geosynthetic sleeve exhibits good resistance to tensile stress. The dividing line between the tensile and compressive stresses is located at the centerline of the section. The mechanical properties of the encasements and gravel has a significant impact on bending characteristics of the GESC. Increasing the strength of the encasement and friction angle of the gravel may significantly improve the bending capacity of the GESC, whereas an increase in the stiffness of encasement and diameter of the column decreases the bending deformation of the GESC.

Application of PISA method for monopile design in layered soil

The foundation design for offshore wind turbines (OWTs) is critical to ensuring their structural integrity and long-term stability. Large-diameter monopiles are widely used for OWTs owing to their proven effectiveness. The conventional design approach, derived from the oil and gas industry’s p-y model, has limitations when applied to monopiles for OWTs. Consequently, a novel design method based on the PISA joint industry research project was developed, which extends beyond the traditional lateral soil resistance (p-y curves) and incorporates additional soil reaction components from shaft friction, pile base shear, and base moment. Unlike the simplistic rule-based conventional approaches, the proposed method necessitates site-specific 3D finite element (FE) simulations for precise calibration of soil reaction curves. Although successfully applied in European offshore wind farms, the PISA method’s performance in regions with distinct seabed compositions, such as China, remains to be verified. Therefore, this paper presents a comprehensive case study conducted at the Xiangshan wind farm, a representative site characterized by layered soil. The study employed in-situ investigations (cone penetration test, borehole) and laboratory tests (direct simple shear, bender element) to delineate the seabed soil profile and derive essential soil parameters for accurate foundation design. To facilitate the design, an Abaqus-based design tool was developed, which automated the extraction of soil reaction curves from the 3D FE simulations, calibration of PISA springs, and execution of one-dimensional beam-spring analyses employing Timoshenko beam theory. Comparative analyses were performed on the computed responses of piles, encompassing load-deflection curves, pile deflections, and bending moment profiles. The outcomes from the 3D FE simulations, uncalibrated rule-based PISA model, and calibrated PISA model were compared to validate the PISA method for monopile design in layered soil conditions.

Rotational Load Fatigue Performance of a One-Size Implant- Abutment Connection System.

One-size implant-abutment (OSIA) connection systems have been developed for simplicity of clinical use and for a range of implant diameters. The aim of this in vitro study was to investigate the rotational load fatigue performance of different implant diameters and abutment platforms of an OSIA connection system. Narrow, regular and wide diameter implants were tested with Regular Base (RB/WB) abutments of an OSIA system (Straumann. BLX). Wide diameter implants were also tested with Wide Base (WB) abutments. This resulted in 4 test groups (n&#61;5): N-RB/WB (Narrow, 3.5mm, RB/WB abutment), R-RB/WB (Regular, 4.0mm, RB/WB abutment), W-RB/WB (Wide, 5.0mm, RB/WB abutment) and W-WB (Wide, 5.0mm, WB abutment). A rotational load fatigue machine applied a sinusoidally varying stress at an angle of 45o, producing an effective bending moment of 35Ncm at a frequency of 10 Hz in air at 20 oC. The number of cycles to failure was recorded. Results were evaluated using ANOVA. Failed specimens were examined with SEM to evaluate the failure mode. Pristine specimens were sectioned to examine the implant-abutment connection. All specimens in the 3 test groups with RB/WB abutments failed within the range of 558,750 cycles to 4,497,619 cycles, while the W-WB test group reached the upper limit of 5 million cycles without failure. Significant difference was found between abutment platforms (P < .001). There were no significant differences found for implant diameters (P &#61;.857). However, with increasing implant diameter, implant fracture was less common and the location of failure was more coronal and consistently at the level of the implant platform for the abutment, and at the screw neck. For wide diameter implants, WB abutments exhibited a superior fatigue performance than RB/WB abutments, and would be preferred in situations of high mechanical risk. Increasing implant diameter, when used with RB/WB abutments, did not improve fatigue performance due to the one-size prosthetic connection, but failures were less catastrophic, and coronally located, which may be advantageous in managing failures.

Numerical analysis of failure mechanism and stability of reinforced embankment with DCM soft soil composite foundation

The deep cement mixing (DCM) method has been widely used in offshore geotechnical engineering. At present, the reinforcement form of pile has been researched widely, but there is a lack of understanding of the failure mode of DCM pile composite foundation reinforcement for bank slopes. In this paper, a series of unconfined compression tests was conducted to obtain necessary numerical analysis parameters. A series of study on the failure mechanism and stability control of DCM pile composite foundation reinforcement bank slope has been conducted through numerical analysis. The results of numerical analysis indicate that under different reinforcement conditions, there exists an optimal reinforcement depth, and the safety coefficient will gradually stabilize at 1.45; The bending moment of the piles under the bank slope the bending moment of the pile body under the road surface Under different overloads. The maximum bending moment of the pile body is located near one-third of the pile body, and the maximum bending moment of the pile body is located between the shoulder and foot of the slope.

New method for incorporating foundation damping in time-domain analysis of integrated offshore wind turbine structures

Foundation damping has significant potential for reducing the loads of monopile-supported offshore wind turbines. However, the contribution of foundation damping is not well understood, primarily because of the absence of suitable methods for incorporating it into the time-domain analysis of wind turbine structures. This paper presents a novel approach for this purpose. In this approach, a dashpot is attached parallel to each of the p-y springs along a monopile, which models the stiffness and damping of soil-pile interactions. Employing this approach, the influence of foundation damping on the structural dynamic response is investigated using the time-domain analysis of a monopile-supported IEA 15 MW reference wind turbine. The results demonstrate that foundation damping has a limited impact on the overall dynamic response and fatigue loads of wind turbines during power production. However, the foundation fatigue loads after an emergency shutdown can be reduced by 29-46% owing to the inclusion of foundation damping. In addition, foundation damping is found to significantly influence the bending moment, horizontal displacement, and angular rotation of the monopile at the mudline under parked conditions, with load reductions of up to 20%.