The Effects of the Longitudinal Axis of Loading upon Bending, Shear and Torsion of a Thin-Walled Cantilever Channel Beam

Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoretically and numerically in terms of two longitudinal axes of loading not coincident with the shear centre. In particular, the warping displacements, stiffness and stress distributions are calculated for torsion applied to longitudinal axes passing through the section’s centroid and its web centre. The stress conversions derived from each action are superimposed to reveal a net sectional stress distribution. Therein, the influence of the axis position upon the net axial and shear stress distributions is established compared to previous results for each beam when loading is referred to a flexural axis through the shear centre. Within the net stress analysis is, it is shown how the constraint to free warping presented by the end fixing modifies the axial stress. The latter can be identified with the action of a ‘bimoment’ upon each thin-walled section.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT_VENANT BENDING

Using the single crack solution and the regular solution of plane harmonic function, the problem of Saint_Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross_section is not thin_walled, but of small torsion rigidity is proposed. Some numerical examples are given.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

Effects of surface roughness on bending properties of rolled AZ31 alloy

This study investigated the effects of mechanical-polishing-induced surface roughness and the direction of polishing lines on the bending properties of a rolled AZ31 alloy.To this end,three-point bending tests were performed on one sample without polishing lines(SS sample)and two samples with polishing lines—one in which the polishing lines were parallel to the rolling direction(RS-RD sample)and the other in which they were parallel to the transverse direction(RS-TD sample).In all three samples,macrocracks were formed in the width direction on the outer surface,where tensile stress was predominantly generated in the longitudinal direction.However,the macrocracks formed in the SS sample were curved because of the merging of uniformly formed fine microcracks,whereas those formed in the RS-TD sample were linear owing to the formation of relatively coarse microcracks along the polishing lines.The bendability of the samples was in the order of SS>RS-RD>RS-TD,and their limiting bending depths were 4.8,4.6,and 4.4 mm,respectively.In the presence of mechanical-polishing-induced surface roughness,polishing lines perpendicular to the direction of the major stress(i.e.,tensile stress along the longitudinal direction)resulted in a greater degree of stress concentration on the outer surface of the bending specimen.This higher stress concentration promoted the formation of undesirable{10–11}contraction and{10–11}–{10–12}double twins—which typically act as crack initiation sites—and thereby facilitated crack generation and propagation.Consequently,the surface roughness caused premature fracture during bending deformation,which,in turn,caused deterioration of the bendability of the rolled Mg alloy.

Optimisation of Effective Design Parameters for an Automotive Transmission Gearbox to Reduce Tooth Bending Stress

Optimisation of effective design parameters to reduce tooth bending stress for an automotive transmission gearbox is presented. A systematic investigation of effective design parameters for optimum design of a five-speed gearbox is studied. For this aim contact ratio effect on tooth bending stress by the changing of contact ratio with respect to pressure angle is analysed. Additionally, profile modification effects on tooth bending stress are presented. During the optimisation, the tooth bending stress is considered as the objective function, and all the geometric design parameters such as module, teeth number etc. are optimised under two different constraints, including tooth contact stress and constant gear centre distance. It can be concluded that higher the contact ratio results in a reduced tooth bending stress, while higher the pressure angle caused an increase in tooth bending stress and contact stress, since decreases in the contact ratio. In addition, application of positive profile modification on tooth reduces tooth bending stress. All of the obtained optimum solutions satisfy all constraints.

Bending stress of rolling element in elastic composite cylindrical roller bearing

A new structure design method of elastic composite cylindrical roller bearing is proposed, in which PTFE is embedded into a hollow cylindrical rolling element, according to the principle of creative combinations and through innovation research on cylindrical roller bearing structure. In order to systematically investigate the inner wall bending stress of the rolling element in elastic composite cylindrical roller bearing, finite element analysis on different elastic composite cylindrical rolling elements was conducted. The results show that, the bending stress of the elastic composite cylindrical rolling increases along with the increase of hollowness with the same filling material. The bending stress of the elastic composite cylindrical rolling element decreases along with the increase of the elasticity modulus of the material under the same physical dimension. Under the same load, on hollow cylindrical rolling element, the maximum bending tensile stress values of the elastic composite cylindrical rolling element after material filling at 0° and 180° are 8.2% and 9.5%, respectively, lower than those of the deep cavity hollow cylindrical rolling element. In addition, the maximum bending-compressive stress value at 90° is decreased by 6.1%.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT-VENANT BENDING

Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.

STRESS ANALYSIS OF RESTRAINED BENDING FOR BOX BEAM WITH RECTANGULAR CROSS-SECTION FILLED BY HONEYCOMB CORE

On the basis about studying free bending for box beam with rectangular cross_section filled by honeycomb core,supplementary displacements and stresses of restrained bending for such beam were analyzed.The hypothesis for separated variables was adopted to solve displacement.According to this,three aspect equations of geometrical,physical and balance were obtained.With Galerkin's method,it is summed up as two_order ordinary differential equations with the attenuation character.Analysis makes clear that attenuation speed of stress is concerned with a big load or a small one,geometric dimensions of cross_section of beam,and physical parameter of material.

Effect of Grinding and Polishing on the Residual Stress and Bending Strength of a Silicon Nitride Ceramic

The residual stresses on the surface of the d ifferently ground and polished silicon nitride ceramics were measured using X-r ay diffraction and identified by SEM.The effect of the residual stress on the be nding strength was investigated.The investigations show that the grinding proces s can introduce subatantial tensile residual stresses up to 290MPa on the surfac e of silicon nitride ceramics,which has a significant effect on reducing the ben ding strength of the ceramics after grinding.Thus,in comparison with the ceramic s with a rough surface,the ceramics with a mirror image surface may have a lower strength.Polishing can smooth the residual stresses.When we evaluate the qualit y of the ceramic components after grinding,we must take residual stress into con sideration. The grinding methods and grinding conditions must be carefully selec ted in order to get the favorite residual stress as well as the surface smoothne ss.

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally~ the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method （FEM）. Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.

STRAIN-GRADIENT STRESS ANALYSIS IN SAINT-VENANT BENDING

Light beam deflections caused by stress or strain gradients are inves- tigated analytically and experimentally in homogeneous beam specimens which are subjected to a particular case of flexure with shear. This study is a generalization of the prior an alytical-experimental examination of strain-gradient light deflections produced in stressed plates, which had concentrated on the simplest case where in- formation of interest is collected along a line of symmetry of the stress field. Main purpose of the present investigation is to document the efficacy of the strain-gradient method in analysis of the general case of stress state. The most interesting stress state is that in a beam subjected to the Saint-Venant bending, where the transversal and the longitudinal axes of the beam are in pure shear. The obtained results are compared with the predictions of the developed analytical models and with the pre- dictions of Filon's stress function. The procedures of evaluating the photoelastic and material coefficients using strain-gradient techniques were tested positively.

Fatigue tests of composite beam by steel fiber reinforced self-stressing concrete in the hogging bending

Through the experiments of 7 T-section composite beams, steel fiber reinforced self-stressing concrete （SFRSC） as the composite beam in the composite layer was studied under the hogging bending. The tests simulated composite layer tensile strain under the hogging bending of inverted loading composite beams, giving the relationship under the different fatigue stress ratios between fatigue cycles and steel bar’s stress range, crack width, stiffness loss and damage, etc., in composite layer. This article established fatigue life equation, and analyzed SFRSC reinforced mechanism to crack width and stiffness loss. The results show that SFRSC as the composite beam concrete has excellent properties of crack resistance and tensile, can reinforce the fatigue crack width and stiffness loss of composite beams, and improve the durability and in normal use of composite beams in the hogging bending zone.

EXPERIMENTAL STUDY ON CRACK CURVING PROPAGATION IN BENDING BEAMS UNDER IMPULSIVE LOAD

Dynamic fracture behaviour of crack curving in bent beams has been investigated. In order to understand the propagation mechanism of such cracks under impact, an experimental method is used that combines dynamic photoelasticity with dynamic caustics to study the interaction of the flexural waves and the crack. From the state change of the transient stresses in polymer specimen, the curving fracture in the impulsively loaded beams is analyzed. The dynamic responses of crack tips are evaluated by the stress intensity factors for the cracks running in varying curvature paths under bending stress wave.

SHORT FATIGUE CRACK BEHAVIOUR IN ISO-STRESS SPECIMENS

Fatigue tests were made on a vibration machine using specially designed specimens to investi- gate the initiation and propagation features of short fatigue cracks in a weld metal.The spec- imens were triangular in shape so that when loaded as a cantilever beam the surface tensile stress is constant.Test results show that short fatigue cracks mainly originate from slip bands within ferrite grains.The development of short fatigue cracks is marked by a gradual increase in crack density with fatigue cycles.Coalescence of short cracks leads to crack propagation and the crack path is predominantly transgranular.

Theoretical Prediction of the Bending Stiffness of Reinforced Thermoplastic Pipes Using a Homogenization Method

The accurate prediction of bending stiffness is important to analyze the buckling and vibration behavior of reinforced thermoplastic pipes(RTPs)in practical ocean engineering.In this study,a theoretical method in which the constitutive relationships between orthotropic and isotropic materials are unified under the global cylindrical coordinate system is proposed to predict the bending stiffness of RTPs.Then,the homogenization assumption is used to replace the multilayered cross-sections of RTPs with homogenized ones.Different from present studies,the pure bending case of homogenized RTPs is analyzed,considering homogenized RTPs as hollow cylindrical beams instead of using the stress functions proposed by Lekhnitskii.Therefore,the bending stiffness of RTPs can be determined by solving the homogenized axial elastic moduli and moment of inertia of cross sections.Compared with the existing theoretical method,the homogenization method is more practical,universal,and computationally stable.Meanwhile,the pure bending case of RTPs was simulated to verify the homogenization method via conducting ABAQUS Explicit quasi-static analyses.Compared with the numerical and existing theoretical methods,the homogenization method more accurately predicts the bending stiffness and stress field.The stress field of RTPs and the effect of winding angles are also discussed.

Analysis of Stresses and Deflection of Sun Gear by Theoretical and ANSYS Method

Gearing is one of the most critical components in mechanical power transmission systems. This article examines the various stresses and deflection developed in sun gear tooth of planetary gearbox which is used in Grabbing Crane. Article includes checking sun gear wear stresses and bending stresses using IS 4460 equations. Also calculate various forces acting on gear tooth. In this study, perform the calculation for sun gear tooth to calculate bending, shear, wear & deflection using theoretical method. 3D model is created of circular root fillet & trochoidal root fillet of gear tooth for simulation using ProE Wildfire 3. In Pro-E, the geometry is saved as a file and then it is transferred from Pro-E to ANSYS 10 in IGES format. The results of the 3 D analyses from ANSYS are compared with the theoretical values. Comparison of ANSYS results in circular root fillet & trochoidal root fillet also carry out.

An analytical model for predicting sheet springback after V-bending

Springback is caused by the redistribution of stress in sheet material after the tooling is removed. Precise prediction of sheet springback is very important in die design. Based on Hill’s yielding criterion and plane strain condition, an analytical model is proposed in this paper which takes into account the effects of contact pressure, the length of bending arm between the punch and die, transverse stress, neutral surface shifting and sheet thickness thinning on the sheet springback of V-bending. The predicted results by this analytical model indicated that the contact pressure and transverse stress have much effect on the springback when the bending ratio (the ratio of punch radius to sheet thickness) is less than five. The contact pressure declined when the length of bending arm goes up, which means that shorter length of bending arm will result in larger springback. The effect of neutral surface shifting on the springback is less than that of contact pressure and decreases with the bending ratio. However, this research showed that the influence of thickness thinning on the springback can be ignored. Comparison with finite element method (FEM) simu-lating results shows that the predicted results by the analytical model accord well with simulation results by FEM. In addition to that, the bending ability—the limit bending ratio for a given sheet thickness and material properties was also determined.

Effect of non-uniform stress characteristics on stress measurement in specimen

There is a remarkable difference in stress distribution between a specimen and a plate removed from the specimen.The plate presents a uniform stress distribution whereas the specimen presents a non-uniform stress distribution.Firstly,the real stress distributions in plates with thickness of 30,40 and 50 mm and then in the specimens were obtained through simulation and X-ray surface stress measurement.Secondly,in order to study the impact of specimens shapes and processing ways on the results accuracy,two irregular shapes (parallelogram and trapezoid) and two processing ways (saw and electron discharge machining (EDM)) were compared and analyzed by simulation and experiment using layer removal method,then the specimen effects on measurement results were evaluated.The results show that:1) the non-uniform stress distribution characteristics of the specimen near the surface of the cut is significant,the range of non-uniform stress distribution is approximately one-thickness distance away from the cut,and it decreases gradually along the depth;2) In order to ensure the stability in the results,it is suitable to take the specimen plane size 2-3 times of its thickness;3) Conventional processing methods have little effect on experimental results and the average deviation is less than 5%.

Springback Mechanism Analysis and Experiments on Robotic Bending of Rectangular Orthodontic Archwire

Fixed-appliance technology is the most common and effective malocclusion orthodontic treatment method, and its key step is the bending of orthodontic archwire. The springback of archwire did not consider the movement of the stress-strain-neutral layer. To solve this problem, a spring- back calculation model for rectangular orthodontic archwire is proposed. A bending springback experiment is conducted using an orthodontic archwire bending springback mea- surement device. The springback experimental results show that the theoretical calculation results using the proposed model coincide better with the experimental testing results than when movement of the stress-strain-neutral layer was not considered. A bending experiment with rectangular orthodontic archwire is conducted using a robotic orthodontic archwire bending system. The patient expriment result show that the maximum and minimum error ratios of formed orthodontic archwire parameters are 22.46% and 10.23% without considering springback and are decreased to 11.35% and 6.13% using the proposed model. The proposed springback calculation model, which considers the move- ment of the stress-strain-neutral layer, greatly improves the orthodontic archwire bending precision.