Bending Moment In Plane Research Articles

Local joint flexibility of tubular K-joints reinforced with external plates under out of plane bending moments

ABSTRACT In this research work, the Local Joint Flexibility (LJF) of steel tubular K-joints reinforced with external plates is investigated. In the first step, a finite element (FE) model was generated and verified. In the next step, a set number of 300 FE analysis was carried out to investigated the effect of the stiffener plate size (η and λ), the angle between brace and chord (θ), the joint geometry (γ, τ, ξ and β) and the loading conditions (balanced and un-balanced OPB moments) on the LJF factor (f LJF) and f LJF ratios (ψ). The results showed that the f LJF of an external plate reinforced K-joint can be down to 26% of the f LJF of the corresponding un-reinforced joint. Also, the gap factor (ξ) has effect on the f LJF. Finally, FE results were used to derive two parametric equations for determining the f LJF in the strengthened K-joints.

Mechanical behaviour of a novel floor system with horizontal K-shaped brace in Long-span High-speed railway steel truss Cable-stayed bridge

In this study, a novel floor system with horizontal K-shaped braces was applied to long-span high-speed railway steel truss cable-stayed bridges to reduce the crossbeams’ out-plane bending moment which is significant in the traditional stringer-crossbeam floor system. Based on the new floor system of Beijiang Bridge, a 1:4 scaled floor system specimen was experimentally tested; subsequently, two detailed finite element (FE) models for comparison of the specimen were established to investigate the stress distributions, force transferring and deformation characteristics. Furthermore, the ratio formula of the longitudinal force transmitted by the K-braces to that by crossbeam was determined. The results of the comparative analysis of FE models indicate that the horizontal K-shaped brace can reduce 81.0% of the crossbeam’s maximum stress caused by the out-plane bending moment and alleviate the longitudinal deformations. The measured stresses of the model increased linearly with the applied load from 0.4 to 2.2 times the maximum tension force cases. The K-shaped brace mainly bears axial force; additionally, the out plane bending moment of the crossbeam is small. The longitudinal force transmission ratio is determined by the geometric parameters of the floor system structure, such as section area Ak of the K-shaped brace, and the distance between the side stringer and the lower chord Lc (rather than load type or value). The longitudinal force transmission ratio calculated by experimental and numerical stresses were in the ranges of 1.35 to 6.46 and 1.39 to 7.30, respectively. This indicates that the horizontal K-shaped brace transmits 57.45 to 86.60 % and 58.16 to 87.95 % of the longitudinal force, for experimental and normal stresses, respectively. The similar ratio ranges in both cases reveal that the K-shaped brace can effectively transfer longitudinal forces, reduce the out-plane moment of the crossbeam, and improve the mechanical characteristic of the floor system.

Effect of welded joint imperfection on the load-carrying capacity of pipe elbows subjected to in – plane bending moment

The defects in pipe elbows can, depending on their size and position, affect the integrity and safe service, as well as deformation ability of the piping systems in exploitation. Incompletely filled groove, which is the type of defect examined here, was observed by ultrasonic measurement on the pipeline in the regulation system of the hydro power plant Djerdap. Three-dimensional finite element analysis is performed using Simulia Abaqus software package. First, the models with dimensions of the defects observed by non-destructive examination are formed. Stress and strain fields for different loading types are shown and commented. The influence of the defect dimensions on the pipe elbow load-carrying capacity is determined through plastic collapse loads, which are obtained from bending moment - rotation angle diagrams. Twice elastic slope (TES) technique is applied. Additionally, some more severe defects are considered, in the form of sharp pre-cracks at the bottom of the defect; plastic collapse loads are also determined for these geometries. Both opening and closing bending moments are taken into consideration and the results are discussed and compared to two closed-form solutions from the literature. The influence of the boundary conditions applied for examination of the pipe elbows is commented.

Validation of the dynamic load characteristics on a Tidal Stream Turbine when subjected to wave and current interaction

A comparison of a tidal turbine's performance and structural loads is conducted using lab-scale numerical models and experimental testing under multiple current-only and wave-current conditions at the IFREMER wave-current flume. Experimental testing, used to validate CFD models, was accomplished using a 0.9 m diameter, 3-bladed tidal turbine and had a blockage ratio of 8% while the turbine was submerged. Initial investigations analysed the performance and loads on the turbine under uniform and profiled current-only conditions. The presence of a profiled velocity gradient was found to have a negligible effect on the average performance characteristics; however, transient thrust, torque and out of plane bending moment loads experienced much greater variations. These load fluctuations were further increased with increasing levels of shear in the velocity profile, while peaks in the turbine loads coincided with its rotational frequency. The addition of regular, Stokes 2nd Order Theory waves added to the complexity of the flow conditions experienced by the turbine. The effect on the average performance characteristics were negligible while the total turbine thrust and torque fluctuations increased by 35 times that of the current-only cases. Peaks in the loads aligned with the wave surface elevation, indicating the importance of transient analyses of dynamic loads.

Analysis of tubular joint of offshore structure

The Jacket of an offshore structure is made up of tubular members. These tubular members are made up of steel and designed to resist yield and buckling loads. The tubular sections form various types of joints like K joint, KT joint, Y joint, etc. These joints are subjected to various types of cyclic loading conditions, due to which fatigue failure starts and increases as the time passes. As a result, the most critical section of the jacket fails first epically joint. The excessive strains due to axial forces, in-plane, and out plane bending moment accelerate the failure mechanism. In this paper, the comparative study is made between K joint and KT joint for the same loading conditions is made by selecting a finite method approach. By referring to API RP 2A and DNV RP C203. The observations are made on the behavior of joints for the same loading conditions, to the made conclusion of this project. Keywords: K Joint, KT joint, Axial force, in plane bending moment, out plane Bending moment, API RP 2A, DNV RP C203

Experimental studies of ringlock scaffolding joint

Experimental studies were performed on ringlock scaffolding joints. The most characteristic element of these joints is a rosette, which provides a temporary connection between the vertical standard and the ledger. Laboratory tests were performed using a typical testing machine and a grip handle developed by the authors, which allows loading the ringlock scaffolding joint with any type of load, regardless of the manufacturer of the scaffolding considered and the material used. A normal force, a shear force in horizontal plane, a shear force in vertical plane, a bending moment in vertical plane, a bending moment in horizontal plane, and torque were applied to the joint. The obtained data could be used to determine the load-bearing capacity of the joint, as well as the nature of the connection. In cases of bending in horizontal plane and torque, the joint should be treated as a hinge, whereas the connection is semi-rigid in case of bending in vertical plane. Four different approaches were employed for determining the joint stiffness. By analysing various modes of joint damage, critical elements could be identified, which could then be used as comparative data when analysing damages to actual structures. Additionally, laboratory tests investigating the material characteristics of individual joint elements were performed. Each joint element had different material characteristics, particularly the ledger end because it was manufactured via moulding.

Bending analysis of laminated beams using isogeometric variational asymptotic method

Variational asymptotic method (VAM) is a robust mathematical method employed to arrive at a reduced order governing equations in solid mechanics. VAM for beam analysis is accomplished in two stages: first stage involves performing a two-dimensional cross-sectional analysis, and the last stage is one-dimensional beam analysis. Cross-sectional analysis stage involves determining the stiffness coefficients for the beam cross section. VAM can be implemented either by developing analytical solutions or by adopting numerical methods. For beams with arbitrary cross-sectional shapes and material heterogeneity, cross-sectional analysis in VAM is generally carried out by adopting a finite element type procedure. In this study, a numerical procedure for the two-dimensional analysis and the one-dimensional beam analysis based on isogeometric framework is presented. NURBS functions are employed to model the geometry of a cross section and the warping displacement field. Warping represents the deformation of cross section of the beam. Stiffness coefficients obtained by cross-sectional analysis are input to the one-dimensional analysis. A NURBS-based one-dimensional method for bending analysis of laminated composite beams is proposed which can handle axial forces, twisting moments, in-plane and out-of plane bending moments. The one-dimensional analysis features four unknown variables, namely axial displacement, twist and two transverse displacements. The one-dimensional beam geometry and the unknown variables are modelled using NURBS functions. The one-dimensional formulation requires $$C^1$$ continuity which can be easily satisfied by NURBS functions. Numerical examples are solved to ascertain accuracy of the proposed methods. Results obtained were compared with exact solution and was found to be accurate. The one-dimensional analysis based on NURBS functions is non-intrinsic. Application of boundary conditions is far simpler to implement in comparison with the intrinsic one-dimensional analysis methods existing in traditional one-dimensional analysis of VAM literature.

Effect of wall thinning on the Shakedown Interaction Diagrams of 90-degree back-to-Back Bends Subjected to Simultaneous Steady Internal Pressures and Cyclic In Plane Bending Moments

This research studies the effect of wall thinning on generated shakedown (SD) interaction diagrams of pressurized low-carbon steel 90-degree (90-Deg) back-to-back (B2B) bends. More precisely, the SD limit moments are determined for various steady internal pressure spectra thus generating the targeted SD boundaries. The SD limit moments are computed utilizing a direct non-cyclic technique termed: SD-DNT short for Shakedown-Direct Noncyclic Technique. The bends analyzed are subjected to simultaneous steady internal pressure spectra and cyclic in-plane closing (IPC) and in-plane opening (IPO) bending moment modes discretely. The finite element (FE) method is utilized for solution and analyses. The wall thinning accounted for is solely due to service conditions. Different thinning locations are selected and analyzed along with different selected thinning percentages. The selected thinning locations within both bends include intrados, extrados, crowns, and both intrados and extrados once at a time. Thinning locations are analyzed for maximum selected thinning percentages of 30%, 50%, and 60%. Additionally, SD interaction diagrams of sound 90-Deg B2B bends are generated for comparisons. Outcomes of the SD-DNT are successfully validated against full elastic-plastic cyclic loading FE simulations. Outcomes of conducted analyses, generally, revealed that thinnings at crowns resulted in least combined cyclic moment-steady internal pressure capacities respectively followed by intrados, intrados and extrados, and finally extrados thinnings. Post-SD responses namely, alternating plasticity and ratcheting responses are accurately determined upon crossing the generated SD boundaries. Finally, an exemplary generated SD boundary is expressed in mathematical equation for selected analyzed thinned case.

Aerodynamic modelling of wind turbine blade loads during extreme deflection events

Long, flexible wind turbine blades experience significant deflections during operation. Historically, the blade element momentum model in Bladed assumed that the blade is split into a set of radial aerodynamic sections which are aligned perpendicular to the pitch axis, and that any rotation of the sections due to deflection, pre-bend or pre-sweep in the blade can be ignored. For modern-day flexible rotor blades, under extreme loading conditions, this assumption no longer holds. Including this rotation when calculating inflow velocities and angle of attack, and when resolving the resultant forces at the element, causes a significant change in axial force (Fz) along the pitch axis, and therefore the blade out of plane bending moment (My). This in turn drives a change in overturning moments on the hub (which is driven by differences in bending moments between blades). An example 160m rotor shows an increase of 68% in hub overturning moment during an extreme gust event when aerofoil rotation due to deflection is included. This is verified through comparison to the alternative free vortex wake rotor model in Bladed. DNV GL Bladed includes the rotation of aerofoils by default at version 4.8.

Non–Linear Analysis of Slender Masonry Beam

Abstract This paper deals with numerical analysis and design of slander prismatic masonry beams loaded predominantly by axial force and bending moment in plane of the principal moment of inertia. Because of the material non-linearity, classical mathematical theory of slender columns cannot be applied for masonry elements, therefore the proposed method uses iterative non–linear calculation considering both material and geometrical non–linearity.

Attainment rate as a surrogate indicator of the intervertebral neutral zone length in lateral bending: an in vitro proof of concept study.

BackgroundLumbar segmental instability is often considered to be a cause of chronic low back pain. However, defining its measurement has been largely limited to laboratory studies. These have characterised segmental stability as the intrinsic resistance of spine specimens to initial bending moments by quantifying the dynamic neutral zone. However these measurements have been impossible to obtain in vivo without invasive procedures, preventing the assessment of intervertebral stability in patients. Quantitative fluoroscopy (QF), measures the initial velocity of the attainment of intervertebral rotational motion in patients, which may to some extent be representative of the dynamic neutral zone. This study sought to explore the possible relationship between the dynamic neutral zone and intervertebral rotational attainment rate as measured with (QF) in an in vitro preparation. The purpose was to find out if further work into this concept is worth pursuing.MethodThis study used passive recumbent QF in a multi-segmental porcine model. This assessed the intrinsic intervertebral responses to a minimal coronal plane bending moment as measured with a digital force guage. Bending moments about each intervertebral joint were calculated and correlated with the rate at which global motion was attained at each intervertebral segment in the first 10° of global motion where the intervertebral joint was rotating.ResultsUnlike previous studies of single segment specimens, a neutral zone was found to exist during lateral bending. The initial attainment rates for left and right lateral flexion were comparable to previously published in vivo values for healthy controls. Substantial and highly significant levels of correlation between initial attainment rate and neutral zone were found for left (Rho = 0.75, P = 0.0002) and combined left-right bending (Rho = 0.72, P = 0.0001) and moderate ones for right alone (Rho = 0.55, P = 0.0012).ConclusionsThis study found good correlation between the initial intervertebral attainment rate and the dynamic neutral zone, thereby opening the possibility to detect segmental instability from clinical studies. However the results must be treated with caution. Further studies with multiple specimens and adding sagittal plane motion are warranted.

Performance Analysis of Thin Shell Bends under High Pressure and Temperature

Around 70% of the cost in piping industry is spent in the pipe manufacturing with optimum design of pipes without defects. Research on design of pipes has gained importance from the last decade. There are numerous methods being developed to improve the efficiency of piping units considering various parameters. The pipe tends to flatten when they are forced to bend, this geometrical changes has a significant role in the acceptability criteria of pipes. It is necessary to bend pipes in order to transmit liquid or gas from one place to other place. In this work special attention is given to pipe bends because of high stress concentration due to various loading conditions. From several kinds of piping systems, process piping systems are chosen for analysis since pipes used here transport important and hazardous materials. Damage to such piping system can cause serious loss to economy and human lives. The geometrical imperfection associated with bending of pipes is ovality. This degree of ovality determines the acceptance of pipes. Thickening and thinning effects cause additional problems like large plastic deformation and loss of flexibility respectively. Hence estimation of the best degree of ovality is required. In this work effect of ovality is estimated by taking the internal fluid pressure and In plane bending moment into account.

Bone stress in runners with tibial stress fracture

BackgroundCombinations of smaller bone geometry and greater applied loads may contribute to tibial stress fracture. We examined tibial bone stress, accounting for geometry and applied loads, in runners with stress fracture. Methods23 runners with a history of tibial stress fracture & 23 matched controls ran over a force platform while 3-D kinematic and kinetic data were collected. An elliptical model of the distal 1/3 tibia cross section was used to estimate stress at 4 locations (anterior, posterior, medial and lateral). Inner and outer radii for the model were obtained from 2 planar x-ray images. Bone stress differences were assessed using two-factor ANOVA (α=0.05). Key contributors to observed stress differences between groups were examined using stepwise regression. FindingsRunners with tibial stress fracture experienced greater anterior tension and posterior compression at the distal tibia. Location, but not group, differences in shear stress were observed. Stepwise regression revealed that anterior–posterior outer diameter of the tibia and the sagittal plane bending moment explained >80% of the variance in anterior and posterior bone stress. InterpretationRunners with tibial stress fracture displayed greater stress anteriorly and posteriorly at the distal tibia. Elevated tibial stress was associated with smaller bone geometry and greater bending moments about the medial–lateral axis of the tibia. Future research needs to identify key running mechanics associated with the sagittal plane bending moment at the distal tibia as well as to identify ways to improve bone geometry in runners in order to better guide preventative and rehabilitative efforts.

The role of atmospheric stability/turbulence on wakes at the Egmond aan Zee offshore wind farm

The aim of the paper is to present results from the NREL SOWFA project that compares simulations from models of different fidelity to meteorological and turbine data from the Egmond aan Zee wind farm. Initial results illustrate that wake behavior and impacts are strongly impacted by turbulence intensity [1]. This includes both power losses from wakes and loading illustrated by the out of plane bending moment. Here we focus on understanding the relationship between turbulence and atmospheric stability and whether power losses due to wakes can effectively be characterized by measures of turbulence alone or whether atmospheric stability as a whole plays a fundamental role in wake behavior. The study defines atmospheric stability using the Monin-Obukhov length estimated based on the temperature difference between 116 and 70 m. The data subset selected using this method for the calculation of the Monin-Obukhov length indicate little diurnal or directional dependence of the stability classes but a dominance of stable classes in the spring/unstable classes in fall and of near-neutral classes at high wind speeds (Figure 2). The analysis is complicated by the need to define turbulence intensity. We can select the ratio of the standard deviation of wind speed to mean wind speed in each observation period using data from the meteorological mast, in which case a substantial amount of data must be excluded due to the presence of the wind farm. An alternative is to use data from the wind turbines which could provide a larger data set for analysis. These approaches are examined and compared to illustrate their robustness. Finally, power losses from wakes are categorized according to stability and/or turbulence in order to understand their relative importance in determining the behavior of wind turbine wakes.

Taming the inevitable: significant parameters of teeter end impacts

Two bladed wind turbines are recently discussed more often as the question arises for the most suitable offshore turbine concept. Regarding this turbine concept, a solution for the more challenging dynamics is required. A teetered hub has been a solution for quite an amount of the former two bladed turbines. During normal operation this is an efficient possibility to eliminate the hub bending moment coming from unequal blade loading. But looking at extreme load cases the teeter end impact is a major problem. The teeter end impact is quite often described as the occasion which destroys the load reducing advantage of the teeter mechanism. However, a more detailed analysis of the intensity of the hub out of plane bending moment of the teeter end impact including influencing parameters is not given in literature. For this study, the teetered turbine CART2 from NREL is simulated with the aeroelastic tool Bladed 4.5. Design load cases leading to teeter end impacts have been identified for the CART2. The influence of different parameters of teeter end impacts will be analysed. A distinction of these parameters can be made between turbine parameters and teeter system parameters. Rotor mass and speed are turbine parameters. Pitch-teeter-coupling, the free teeter angle and the damping or stiffness of the restraint system belong to the teeter system parameters. The importance of these parameters will be investigated on three different IEC 61400-1-ed. 2 load cases leading to teeter end impacts. The simulation results will be compared with a dimensional analysis of the analytical teeter equations. Results of this study show which parameters have the most significant influence on teeter end impacts. In short, this paper will contribute to a better understanding of teeter end impacts, which are widely regarded as a severe problem but whose nature has not been the subject of a detailed analysis so far.

Aerodynamic Design Optimization Studies of a Blended-Wing-Body Aircraft

The blended wing body is an aircraft configuration that has the potential to be more efficient than conventional large transport aircraft configurations with the same capability. However, the design of the blended wing is challenging due to the tight coupling between aerodynamic performance, trim, and stability. Other design challenges include the nature and number of the design variables involved, and the transonic flow conditions. To address these issues, a series of aerodynamic shape optimization studies using Reynolds-averaged Navier–Stokes computational fluid dynamics with a Spalart–Allmaras turbulence model is performed. A gradient-based optimization algorithm is used in conjunction with a discrete adjoint method that computes the derivatives of the aerodynamic forces. A total of 273 design variables—twist, airfoil shape, sweep, chord, and span—are considered. The drag coefficient at the cruise condition is minimized subject to lift, trim, static margin, and center plane bending moment constraints. The studies investigate the impact of the various constraints and design variables on optimized blended-wing-body configurations. The lowest drag among the trimmed and stable configurations is obtained by enforcing a 1% static margin constraint, resulting in a nearly elliptical spanwise lift distribution. Trim and static stability are investigated at both on- and off-design flight conditions. The single-point designs are relatively robust to the flight conditions, but further robustness is achieved through a multipoint optimization.

Lateral‐torsional buckling checks of steel frames using second‐order analysis

AbstractThis article summarizes the rules given in EN 1993‐1‐1 [2] for using second‐order analysis to check the flexural and lateral‐torsional buckling of members and systems loaded in the strong plane of their cross‐section which may not fail due to out‐of‐plane instability.The rules relevant in EN 1993‐1‐1 [2] are those for equivalent geometrical imperfections resulting from the elastic buckling modes with amplitudes derived from column buckling tests according to EN 1990 Annex D [1] plus those for the linear superposition of utilization rates in the strong and weak planes as used for evaluating tests to determine the amplitude of imperfections and the partial factors.Computer assistance is generally required for determining the elastic buckling modes; the computer outputs gives both modal out‐of‐plane displacements and modal out‐of‐plane bending moments for the relevant flanges of the sections. The use of out‐of‐ plane bending moments makes the assessment clear and simple. It leads to a magnification factor for the in‐plane‐utilization rate that allows the design point x = xd to be found along the length of the member or system where the cross‐sectional check is relevant. It also shows that the results of the second‐order analysis for this design point and the use of buckling curves for member checks at this design point are identical.The assessment procedure with second‐order analysis is generic and applicable to all design cases, whereas the member checks with buckling curves as specified in EN 1993‐1‐1 [2] are intended to be valid for specific loadings and boundary conditions only (object‐oriented rules). They should be consistent with the generic rules. In this respect, this article is a contribution towards the further evolution of EN 1993‐1‐1 [2].

Feasibility study for a controllable orthotic knee joint

Purpose. The purpose of this study was to demonstrate the feasibility of producing an orthotic knee joint that could lock and unlock during ambulation for eventual use in a reciprocating gait orthosis (RGO) for severely disabled patients.Method. Three prototype orthotic knee joints incorporating braking mechanisms were designed and manufactured to demonstrate their ability to withstand a maximum calculated sagittal plane bending moment of 73 Nm. Each was then subjected to bench trials to test their performance against the required specification.Results. Although all three joints achieved the requirement to sustain the specified externally applied bending moments, the hydraulic disc brake system proved significantly superior and was selected for more comprehensive testing.Conclusions. The results confirmed the feasibility of utilising a hydraulic braking mechanism within an orthotic knee joint to withstand the knee flexing moments during walking in a lower limb orthosis. This gave the development group confidence to progress to the prototype design phase with the specific aim of eventually incorporating such a joint in an RGO designed for severely disabled patients such as those with complete paraplegia up to level T4 and those with severe neurological dysfunction.

Simulación de esfuerzos en pórticos

<p>Los laboratorios virtuales constituyen una herramienta de gran potencial para la transmisión del conocimiento científico. En el marco de las enseñanzas universitarias actuales, dichas herramientas adquieren una importancia capital dadas las posibilidades de autoaprendizaje que ofrecen a los estudiantes de los títulos técnicos de grado. En este marco, el presente trabajo describe un laboratorio virtual desarrollado con la interfaz gráfica de usuario (Gui) de MatlabQc , que permite obtener los diagramas de esfuerzos axiles, cortantes y flectores en estructuras aporticadas isostáticas planas, con las cargas contenidas en su propio plano.</p>

Sagittal plane bending moments acting on the lower leg during running

Sagittal bending moments acting on the lower leg during running may play a role in tibial stress fracture development. The purpose of this study was to evaluate these moments at nine equidistant points along the length of the lower leg (10% point–90% point) during running. Kinematic and ground reaction force data were collected for 20 male runners, who each performed 10 running trials. Inverse dynamics and musculoskeletal modelling techniques were used to estimate sagittal bending moments due to reaction forces and muscle contraction. The muscle moment was typically positive during stance, except at the most proximal location (10% point) on the lower leg. The reaction moment was predominantly negative throughout stance and greater in magnitude than the muscle moment. Hence, the net sagittal bending moment acting on the lower leg was principally negative (indicating tensile loads on the posterior tibia). Peak moments typically occurred around mid-stance, and were greater in magnitude at the distal, compared with proximal, lower leg. For example, the peak reaction moment at the most distal point was −9.61 ± 2.07%Bw.Ht., and −2.73 ± 1.18%Bw.Ht. at the most proximal point. These data suggest that tensile loads on the posterior tibia are likely to be higher toward the distal end of the bone. This finding may explain the higher incidence of stress fracture in the distal aspect of the tibia, observed by some authors. Stress fracture susceptibility will also be influenced by bone strength and this should also be accounted for in future studies.