Maximum Bending Stress Research Articles

Mathematical model and contact characteristics of curvilinear cylindrical gears with line contact

There are two types of curvilinear cylindrical gear drives: those with point contact and those with line contact. In this paper, a mathematical model, tooth contact analysis and stress analysis are investigated for curvilinear cylindrical gears with line contact. Here, fixed-setting face-milling cutters are used for the generation of the tooth surfaces of the gears and their matching gears. Based on the theory of gearing, a mathematical model of curvilinear gears is derived, and the instantaneous contact lines on the gear tooth surfaces are examined under ideal assembly conditions. Meanwhile, the instantaneous contact points on the gear tooth surfaces and transmission errors under assembly error conditions are investigated by a tooth contact analysis algorithm. Finally, contact and bending stresses for curvilinear cylindrical gears with tip relief and without tip relief are explored by the finite element method. This research result shows that (1) under ideal assembly conditions, the length of the instantaneous contact lines is greater than the tooth face width, but the effect is very weak. (2) In terms of the transmission errors, crossing shaft angle errors are more sensitive than intersecting shaft angle errors; axial displacement errors are more sensitive than centre distance errors. (3) Severe contact stresses caused by edge contact are eliminated by the tip relief. (4) The maximum bending stress at every contact position is always distributed in both ends of the gear tooth surfaces.

Stress analysis of subsea risers under the combined action of wave force and seismic wave

The operational safety of subsea risers is challenged due to the complex environmental loads such as a current and seismic wave. This paper presents a comprehensive stress analysis of subsea risers under the combined action of wave and seismic waves. Considering the effect of wave and seismic wave load on maximum axial stress and bending stress of subsea risers, the force and the restraint on subsea risers are simplified. The time-dependent wave force on subsea risers is calculated, and the motion equation of subsea risers passing through a strong seismic zone is obtained. Then, the influencing factors of maximum axial stress and bending stress on subsea risers are studied using the finite-element model. The influence of subsea riser stress on shear wave velocity, diameter, wall thickness, bending angle, and properties of subsea soil is investigated. The results exhibit that the maximum stress appears at the elbow of the riser in the combined effect and the axial stress becomes greater than Mises stress. It is observed that the outcome can provide technical support for site construction in a specific area, and it is of great significance for pipe selection and optimization of subsea riser geometry.

Aerodynamic optimization of the last stage turbine blade for an industrial gas turbine

A multi-objective, aerodynamic optimization of the last stage turbine blade of an 100Hz industrial gas turbine is presented. We aim at maximizing the stage’s efficiency, while at the same time meeting mechanical integrity. The optimization procedure was build, during the optimization process the mass flow rate and stage meridian were kept constant to obtain the required stage loading without changing the operating point. The optimized geometry are chosen taking into account aerodynamic constraints as well as mechanical constrains, such as centrifugal stress and bending stress. The SST turbulence model was used to calculate the flow field of the original and optimized stage, respectively. The geometry of the original and optimized blade was compared. The stage efficiency of the design point and under different operate conditions were compared. Stage and blade efficiency along span was analyzed in details. The blade loading at root mid top span of the original and optimized blade were discussed. Detailed flow field analysis shows that, after optimization, the peak Mach number of the root span profile was decreased from 1.22 to 1.09, which improves the flow field. Profile loss and end wall loss were also reduced. After optimization, maximum centrifugal stress and the maximum air bending stress were decreased which leads to improved blade life and safety. The number of blades and b/h were suggested for the last stage blade.

Study on the strength of glued laminated timber beams with round holes: difference in structural performance between homogeneous-grade and heterogeneous-grade timber

Various design codes and design proposals have been proposed for glued laminated timber beams with round holes, assuming that the entire beam is composed of homogeneous-grade timber. However, in Japan, glued laminated timber composed of homogeneous-grade timber is rarely used for beams. In this study, the difference in the load-bearing capacity of glued laminated beams composed of homogeneous-grade timber and heterogeneous-grade timber with round holes when fractured by cracking was investigated experimentally and analytically. The materials used in the tests were glued laminated beams composed of homogeneous-grade Scots pine timber with a strength grade of E105-F345 and heterogeneous-grade Scots pine timber with a strength grade of E105-F300. Experiments confirmed that although the glued laminated beams composed of heterogeneous-grade timber have a lower material strength in the lamina with holes, its resistance to fracturing due to cracks associated with the holes is almost the same as that of the glued laminated beams composed of homogeneous-grade timber. The stresses acting on the holes in the laminated timber with holes of less than half the beam height were lower in the glued laminated beams composed of heterogeneous-grade timber than in the glued laminated beams composed of homogeneous-grade timber. The ratio of the stresses was found to be approximately equal to the ratio of the maximum bending stress or the maximum shear stress acting on the inner layer lamina, as determined by Bernoulli–Euler theory.

Analysis of a more ductile connection between steel beams and concrete-filled tube columns

To resolve the problem of ductile fracturing of beam flanges in traditional connections with concrete-filled steel tube columns using site-welded side plates, an alternative connection design requiring minimal site welding was designed and studied. An explicit analysis method, considering the fracture strain criterion developed by the stress triaxiality path, was adopted to study the seismic performance and fracture resistance of the proposed connection. The results of a verified finite-element model indicated that the steel beam flange in the connection never fractured. The connection exhibited a notably higher maximum bending moment and ductility than the traditional connection. The side plates in the proposed connection were tension-bending or compression-bending elements, unlike in the traditional connection. The failure modes, maximum bending moment, ductility and stress distribution of the side plates were compared and analysed parametrically. Based on the stress distribution of the side plates according to the finite-element results, a fitting formula related to the width and thickness of the side plates was obtained. A formula to calculate the flexural capacity was also developed according to the force model of the proposed connection. The calculations and finite-element results were in good agreement.

Vortex induced vibration and its controlling of long span Cross-Rope Suspension transmission line with tension insulator

Long span cross-rope suspension structure is an innovative structural system evolved from typical Cross-Rope Suspension (CRS) guyed tower, a type of supporting system with short span suspension cable supporting overhead power transmission lines. In mountainous areas, the span length of suspension cable was designed to be extended to hundreds or over one thousand meters, which is applicable for crossing deep valleys. Vortex Induced Vibration (VIV) of overhead power transmission lines was considered to be one of the major factors of its fatigue and service life. In this paper, VIV and its controlling by Stockbridge damper for long span CRS was discussed. Firstly, energy balance method and finite element method for assessing VIV of CRS were presented. An approach of establishing FE model of long span CRS structure with dampers was introduced. The effect of Stockbridge damper for overall vibration of CRS was compared in both theoretical and numerical approaches. Results indicated that vibration characteristics of conductor in long span CRS compared with traditional tower-line system. Secondly, analysis on long span CRS including Stockbridge damper showed additional dampers installed were essential for controlling maximum dynamic bending stresses of conductors at both ends. Moreover, factors, including configuration and mass of Stockbridge damper, span length of suspension cable and conductor and number of spans of conductor, were assessed for further discussion on VIV controlling of long span CRS.

Design and Simulation of Meshing Performance of Modified Straight Bevel Gears

As key components to transmit power and motion between intersecting shafts, it is necessary to design feasible tooth axial modification to improve the meshing performance and bearing capacity of straight bevel gears. The main purpose of this paper is to propose an effective axial modification method of straight bevel gears considering alignment errors. In this paper, the meshing performance of two kinds of tooth axial modification method (tooth end relief and symmetric crowned modification) for straight bevel gears is investigated by the finite element analysis (FEA). The results show that the tooth end relief is an optimal method to enhance the meshing performance of gears in different installations for decreasing transmission errors, reducing maximum contact stress and bending stress and improving the distribution of contact stress and bending stress. This research provides a suitable tooth end relief method of straight bevel gear with alignment errors.

하이브리드 프로토타입 듀얼 로드 셀 구조 개발

We have developed the hybrid prototype load cell structures. These developed load cell structures may increase the reliability of the load sensing by deriving the load values through the double sensing method through the vertical maximum deflection and bending stress of the simple beams. For this purpose, the structure design was performed so that the load value, the deflection and stress value could be output to the same value through the optimal structure design. The structurally designed dimensions reaffirmed the accuracy of the design through the structural analysis program and the matching of the load value and the deflection value. Based on the designed structural dimension, the prototype form was constructed through laser cutting and production using hot rolled steel materials. The developed prototype load cell structure can be used as good educational material in various subjects such as material mechanics, steel structure design, measurement engineering, and mechatronics engineering. It is also believed that the measurement system ideas can inform the occurrence of errors in the event of a problem, and if a major accident caused by a sensing error is predicted, it will show good utilization to prevent accidents.

Material tailoring in three-dimensional flexural deformations of functionally graded material beams

Soft materials such as rubberlike and biological tissues are usually modeled as incompressible. Mechanical properties of polymeric materials can be controlled either by exposing them to ultraviolet light for different time durations or by changing their molecular structure. A challenge is to find the spatial variation of the moduli to fully utilize the material. One way to achieve this is to have a uniform distribution of the stress component likely to cause their failure. To achieve this, we analytically analyze 3-dimensional infinitesimal flexural deformations of a functionally graded (FG) and linearly elastic beam of rectangular cross-section with Young’s modulus a continuous function of the thickness coordinate. The problem is first studied for an incompressible material and then for a compressible material for which Poisson’s ratio is assumed to be a constant. It is found that when Young’s modulus at a point is inversely proportional to its distance from the neutral axis, then the magnitude of the bending stress is uniform over beam’s cross-section, the beam is the lightest possible and its deflections are 2/3rd of that of the corresponding beam of a homogeneous material that has the same maximum bending stress as the FG beam. Noting that Young’s modulus cannot be infinity at the neutral axis, we avoid this by assuming that it is a constant over a small region around the neutral axis. For a transversely isotropic incompressible material beam, it is shown that (2μ1 + μ2) determines beam’s flexural stiffness where μ1 and μ2 are, respectively, the shear moduli along and perpendicular to the axis of transverse isotropy. Beams of homogeneous materials having the same geometry as the FG beam have different shear moduli depending upon whether the FG and the homogeneous material beams have the same maximum deflection, the same maximum bending stress or the same total strain energy of deformation.

Mathematical modeling in the problems of the geodesic control of the stressed-formated state of the gas pipelines at above-ground parts

Geodetic methods of monitoring the stress-strain state of gas pipelines in the areas of overhead pipeline crossing involve obtaining discrete data on the deformation of its axis in the form of a set of three coordinates (x, y, z). For their elaboration a mathematical model of the experimental-theoretical method of geodetic control of gas pipelines’ SSS is proposed. The simulation process was performed on the basis of geodetic discrete data, based on which, using the Lagrange interpolation polynomial, the equation of the line of bending of the axis of the gas pipeline was obtained, which allowed to pass further to the bending moments along the entire span. The accuracy of the proposed method has been estimated, which showed that the obtained bending moment diagrams reflect the SSS of gas pipelines with an accuracy of 1.5% in the central part of its span, and with the approach to the peripheral sections the error increases to 6%. It is shown that the obtained expression of the maximum bending moment allows us to form the required number of additional equations for the disclosure of a statically indeterminate system of "gas pipeline-support", taking into account the possibility of fastening on stretch marks. The mathematical model is presented aimed at decomposition of overburden gas pipeline structures, which allows to model the SSS at each of the spans separately within the integral structure.. It is established that additional stretch marks reduce the maximum bending stress by 22%, and in case of loss of one of the stretches of the bearing capacity of the gas pipeline SSS increases by 11.1-14.8% depending on the previous stretch tension. The proposed mathematical model for the processing of discrete data forms the basis of the experimental-theoretical method of geodetic control of the gas pipelines’ SSS, taking into account their structural and technological factors.

Refined Zigzag Theory: an appropriate tool for the analysis of CLT-plates and other shear-elastic timber structures

Cross laminated timber (CLT), as a structural plate-like timber product, has been established as a load bearing product for walls, floor and roof elements. In a bending situation due to the transverse shear flexibility of the crossing layers, the warping of the cross section follows a zigzag pattern which should be considered in the calculation model. The Refined Zigzag Theory (RZT) can fulfill this requirement in a very simple and efficient way. The RZT, founded in 2007 by A. Tessler (NASA Langley Research Center), M. Di Sciuva and M. Gherlone (Politecnico Torino) is a very robust and accurate analysis tool, which can handle the typical zigag warping of the cross section by introducing only one additional kinematic degree of freedom in case of plane beams and two more in case of biaxial bending of plates. Thus, the RZT-kinematics is able to reflect the specific and local stress behaviour near concentrated loads in combination with a warping constraint, while most other theories do not. A comparison is made with different methods of calculation, as the modified Gamma-method, the Shear Analogy method (SA) and the First Order Shear Deformation Theory (FSDT). For a test example of a two-span continuous beam, an error estimation concerning the maximum bending stress is presented depending on the slenderness L/h and the width of contact area at the intermediate support. A stability investigation shows that FSDT provides sufficiently accurate results if the ratio of bending and shear stiffness is in a range as stated in the test example. It is shown that by a simple modification in the determination of the zigzag function, the scope can be extended to beams with arbitrary non-rectangular cross section. This generalization step considerably improves the possibilities for the application of RZT. Furthermore, beam structures with interlayer slip can easily be treated. So the RZT is very well suited to analyze all kinds, of shear-elastic structural element like CLT-plate, timber-concrete composite structure or doweled beam in an accurate and unified way.

Mechanical behavior of a drilling riser with buoyant blocks when it enters into deep water

A novel three-dimensional dynamic model is developed to investigate the vortex-induced vibrations (VIVs) in flexible risers with buoyant blocks conveying the internal fluid flow. The unsteady hydrodynamic forces associated with wake dynamics are modeled using two distributed van der Pol wake oscillators that consider the coupling between the structure and the fluid. Furthermore, our model considers the loads of buoyancy weight, tension, pressure, temperature, and seawater current owing to wind, tide, and waves, as well as the nonlinear effect of the large deflection of the riser on the loads. The riser is discretized into slender-beam elements, the distributed van der Pol wake oscillators are also discretized on the element nodes, and each node has six degrees of freedom, allowing it to describe the vibrations of the risers in lateral, axis, and torsion simultaneously. The boundary conditions include the displacements and rotations at the up end and free bottom end in the presence of additional weight. The computational program is prepared using Matlab (R2014a). The simulation results exhibit good agreement with the existing experimental data, verifying the validity of the model and the parameters. Finally, the VIV simulations are conducted for more realistic risers when they are entering 500–3000 m deep water, denoting the effects of buoyant blocks, entry speed, and water depth upon the drop-point offset of the bottom end of the risers, the tension stresses as well as the values and positions of the maximum bending stresses with respect to the risers. These data can be used to select a good operational condition for ensuring the entry of a riser. This study provides a computational framework for conducting subsequent research, and the obtained results can be applied to construct ocean-floating platforms more scientifically, safely, and economically.

Ensayos de tensión y flexión en raíces de dos especies tropicales

Las raíces de las plantas permiten evitar la pérdida del suelo al formar mallas que lo retienen, especialmente en suelos arenosos debido a la poca cohesión de estos sustratos; sin embargo, la literatura técnica sobre la ejecución de las pruebas para caracterizar raíces es escasa, por lo que se requiere documentar su caracterización. Los objetivos de este trabajo fueron documentar y caracterizar las propiedades mecánicas de dos raíces de especies tropicales mediante pruebas de tensión y flexión. Para ello se diseñaron dispositivos especiales para sujetar raíces de Jatropha curcas L. y Ricinus communis L. extraídas de suelos arenosos. Las raíces se sometieron a pruebas de tensión y flexión y se estimaron sus módulos de Young en tensión, así como los esfuerzos máximos de flexión. Los módulos de Young en tensión obtenidos variaron en intervalos de 6.27 MPa a 334 MPa para R. comunis y de 4.56 MPa a 271 MPa para J. curcas, con diámetros entre 0.5 mm y 6.8 mm para ambas especies; en las pruebas de flexión las raíces nunca alcanzaron el punto de ruptura, pero los esfuerzos máximos registrados fueron de 21 MPa y 28 MPa, para Ricinus y Jatropha, respectivamente. Se concluye que las raíces de Jatropha y Ricinus poseen módulos de elasticidad muy bajos, similares a otras raíces de especies herbáceas y arbóreas, con una muy alta flexibilidad y comparables con las propiedades del polietileno de baja densidad.

Evaluation of Deformation and Failure Behaviors of Nuclear Piping Components Under Beyond Design Basis Seismic Loads Using a Simulated Specimen

Abstract This study designed a specimen that simulates the deformation and failure behaviors of the piping components in nuclear power plants (NPPs) under excessive seismic loads beyond the design basis, and conducted ultimate-strength tests using this specimen at room temperature (RT) and 316 °C. SA312 TP316 stainless steel (SS) and SA508 Gr.3 Cl.1 low-alloy steel (LAS) were used in the experiments. Displacement-controlled cyclic loads with constant and random amplitudes of load-line displacement (LLD) were applied as input loads. A set of input cyclic loads consisted of 20 cycles, and the LLD amplitudes of the cyclic load were determined to induce the maximum membrane plus bending stress intensity of 6–42Sm on the specimen, where Sm is the allowable design stress intensity. Multiple sets of input cyclic loads, with increasing amplitude of LLD, were applied to the specimen until cracking initiated. The results demonstrate that the simulated specimen adequately showed the ratcheting deformation and fatigue-induced cracking of piping components under displacement-controlled excessive seismic loads. In addition, samples of both materials failed under displacement-controlled cyclic load levels that were several times higher than those of the design basis earthquake (DBE). The SA316 TP316 SS had greater resistance to failure under large-amplitude cyclic loads than did SA508 Gr.3 Cl.1 LAS. For both materials, resistance to failure was lower at 316 °C than at RT. This study confirmed that the evaluation procedure of the ASME design code predicted the fatigue failure of specimens very conservatively under large-amplitude cyclic loads simulating displacement-controlled excessive seismic loads.

A Novel Full Stressed Energy Harvester with Varied Thickness

This study developed a novel full stressed energy harvester composed of a cantilever with varied thickness in the length direction to harvest energy from ambient vibrations. This harvester owns a higher efficiency of energy harvesting when compared with the harvester of a uniform cross section, since the maximum bending stress is constant in each cross section. The current available models for cantilever harvesters are inapplicable to the new improved fully stressed harvester due to its unique shape. By employing Rayleigh-Ritz method, a corresponding governing equation is hence developed to model the full stressed harvester for estimating the efficiency. The influence of the geometry on the generated electric power is also discussed for the full stressed harvester. The results show that the full stressed harvester can double the electric power generated by the uniform harvester, and the full stressed harvester has a lower natural frequency.

Biomechanical properties enhancement of gamma radiation-sterilized cortical bone using antioxidants.

Gamma radiation sterilization is the method used by the majority of tissue banks to reduce disease transmission from infected donors to recipients through bone allografts. However, many studies have reported that gamma radiation impairs the structural and mechanical properties of bone via formation of free radicals, the effect of which could be reduced using free radical scavengers. The aim of this study is to examine the radioprotective role of hydroxytyrosol (HT) and alpha lipoic acid (ALA) on the mechanical properties of gamma-sterilized cortical bone of bovine femur, using three-point bending and microhardness tests. Specimens of bovine femurs were soaked in ALA and HT for 3 and 7days, respectively, before being exposed to 35-kGy gamma radiation. In unirradiated samples, both HT and ALA pre-treatment improved the cortical bone bending plastic properties (maximum bending stress, maximum bending strain, and toughness) without affecting microhardness. Irradiation resulted in a drastic reduction of the plastic properties and an increased microhardness. ALA treatment before irradiation alleviated the aforementioned reductions in maximum bending stress, maximum bending strain, and toughness. In addition, under ALA treatment, the microhardness was not increased after irradiation. For HT treatment, similar effects were found. In conclusion, the results indicate that HT and ALA can be used before irradiation to enhance the mechanical properties of gamma-sterilized bone allografts.

Определение минимального шага измерений пространственного положения трубопровода при оценке напряженно-деформированного состояния с поверхности грунта

In determining the bending radius of an underground pipeline axis from the soil surface, existing methods have some disadvantages associated with a lack of studies on how pipeline depth and equipment errors affect the results of measurement pitch calculations. The purpose of the study is to determine the minimum measuring pitch relative to the spatial position of the pipeline using line locating equipment to assess the stress-strain state from the soil surface. An assumption was made that the pipeline section has a bend in one plane only. Therefore, it is considered as a combination of three axis points that, when interconnected, form a part of a circle. To find the actual values of the bending radii in two borderline cases, some expressions were proposed. Regarding the absolute difference between the maximum bending stresses and the measuring pitch, dependences were obtained for various values of the absolute error attributed to the equipment used with a 1.400 mm diameter pipe. It was established that to limit an error in the absolute difference of the maximum bending stresses to 50 MPa, the minimum measurement pitch should be 20 to 60 meters (this varies depending on the error of the line locating equipment used). Using the MATLAB programming language, a program code was written to construct a three-dimensional graph representing the dependence between the absolute difference of the maximum bending stresses and the measurement pitch for various values of an absolute error attributed to the equipment. It was found that the pipeline bending radius does not affect the value of the minimum pitch for measuring the spatial position of the pipeline.

Evaluation of the maximum bending stress of pre-hydrided Zircaloy-4 cladding tube after simulated loss-of-coolant-accident test

After the accident at Fukushima dai-ichi nuclear power station, the fracture resistance of fuel rods against aftershock became a concern in the safety evaluation of reactor core during the long-term cooling after a loss-of-coolant-accident (LOCA). In this study, the maximum bending stresses of pre-hydrided cladding tubes which experienced simulated LOCA tests were investigated. The obtained results suggested that the decrease in the maximum bending stress of the cladding tube experienced LOCA conditions was mainly determined by the hydrogen content in the cladding tube after simulated LOCA test, irrespective of initially hydrogen content. It was also suggested that the decreasing trend of the maximum bending stress with the increasing hydrogen content would be expressed by a form of exponential function, in which the maximum bending stress at a hydrogen content of 1500 ppm was estimated to be about a half of that at 0 ppm.

Flexions of the Popliteal Artery and the Culture Could Challenge the Outcomes of the Endovascular Procedures.

Recently a hinge point or the maximum bending stress point of the popliteal artery was identified when the knee bends using a lateral view dynamic angiography and a correlation between the lateral view angiography with the extended limb angiography to predict the potential location of the hinge point was defined. A hinge point has been correlated to stent fracture. These findings allowed us to develop a dynamic classification of the popliteal artery. The dynamic classification is useful for endovascular procedures in the popliteal artery. Cultural aspects of our patient population must be considered previous to the endovascular treatment of the popliteal artery, especially to the Japanese culture, which is commonly observed sitting posture such as “seiza (正座).”

Glass Fiber Reinforced Composite Orthodontic Retainer: In Vitro Effect of Tooth Brushing on the Surface Wear and Mechanical Properties.

Fiber reinforced composites (FRCs) are metal free materials that have many applications in dentistry. In clinical orthodontics, they are used as retainers after active treatment in order to avoid relapse. However, although the modulus of the elasticity of FRCs is low, the rigidity of the material in the form of a relatively thick retainer with a surface cover of a flowable resin composite is known to have higher structural rigidity than stainless steel splints. The aim of the present study is to measure load and bending stress of stainless steel wires, as well as flowable resin composite covered and spot-bonded FRC retainer materials after tooth brushing. These materials were tested with a three point bending test for three different conditions: no brushing, 26 min of brushing, and 60 min of brushing. SEM images were taken before and after different times of tooth brushing. Results showed that stainless steel was not significantly affected by tooth brushing. On the other hand, a significant reduction of values at maximum load at fracture was reported for both FRC groups, and uncovered FRCs were most affected. Concerning maximum bending stress, no significant reduction by pretreatment conditions was reported for the materials tested. SEM images showed no evident wear for stainless steel. Flowable resin composite covered FRCs showed some signs of composite wear, whereas spot-bonded FRCs, i.e., without the surface cover of a flowable resin composite, showed signs of wear on the FRC and exposed glass fibers from the FRC’s polymer matrix. Because of the significant changes of the reduction of maximum load values and the wear for spot-bonded FRCs, this technique needs further in vitro and in vivo tests before it can be performed routinely in clinical practice.