External Bending Moment Research Articles

Bending technology of high strength steel sheets and tools for its realization

The article proposes and theoretically justifies a method for bending high-strength steels with compression. The technology allows to get parts from high-strength steels without cracks along the bending line. In the case of bending according to the proposed method, the deformation is carried out by the combined action of longitudinal and lateral forces. Equitations are derived showing the stress distribution over the cross section in the deformation zone. The article proposes and theoretically justifies a method for bending high-strength steels with compression. The technology allows you to get parts from high-strength steels without cracks along the bending line. In the case of bending according to the proposed method, the deformation is carried out by the action of longitudinal and transverse forces. Equitations were derived for finding the longitudinal compressive force at which the neutral layer in the workpiece moves to the outer surface based on the equations of stress distribution. Equitations are derived for finding the moment created by the longitudinal compressive force, as well as the moment formed by the action of compressive stresses, which made it possible to derive the equation for the external bending moment during bending with compression. Equitation is derived for finding the shoulder of the force action creating an external bending moment. Equitation is derived for finding the force of the punch for bending with compression.

Effect of Shaft Misalignment on Hypoid Gear Pair Driven Through a Universal Joint

An enhanced hypoid geared rotor system model incorporating a universal joint that connects driveline propeller shaft and pinion shaft is introduced in this study. The effect of shaft misalignment and pinion mass unbalance on hypoid gear dynamic response is evaluated under different assembly conditions. A nonlinear 14-DOF lumped parameter model based on coupled multi-body dynamics is applied by considering large rotational displacement in torsional direction. Results demonstrate three main influences from shaft misalignment and mass unbalance including speed and torque fluctuation as well as external bending moment on pinion shaft. It is also observed that bending moment generated can exert additional load on pinion shaft bearings which is found to be more sensitive to misalignment angle compared to dynamic response along line-of-action. Besides, shaft misalignment and mass unbalance excitation will interact with gear internal excitation from transmission error (TE) which can affect mesh parameters.

Fracture Mechanism of Fibre Reinforced Concrete Pavement Based on a RILEM Design Approach

Using fibre-reinforced concrete pavement (FRCP) offers excellent performance in terms of enhancing the concrete’s physical properties. The most popular fibres used in creating concrete for pavements are steel, polypropylene, and polyvinyl alcohol (PVA) fibres, though these come in a variety of geometries (lengths, shapes, sizes, and thickness). This paper utilises steel and PVA fibres at different low volume fractions to examine the improvement mechanism of FRC. The volume fractions of fibre (Vf) used were 0.04, 0.12, and 0.2 % and 0.3, 0.4, and 0.6% for PVA and steel hooked end fibres, respectively. There are many theoretical methods available for determining the effect of fibre inclusion on the load-carrying capacity of concrete pavements. One of these methods is analysing the stress-strain diagram (σ-ε method) according to RILEM TC-162-TDF. This paper used the (σ-ε) method to evaluate these types of fibre, showing that the stress-strain diagram, residual flexural tensile strength, and toughness are improved by adding both types of fibre. The improvement in fracture mechanisms enhances the ability of FRCP to bear stresses and moments, helping to avoid premature failure in the pavement. PVA FRC showed better performance than steel FRC in terms of supporting the external bending moment capacity, however, which reduces the thickness of the concrete required.

Experimental Study on Residual Cross-Sectional Flattening of Thin-Walled Pipes Under Pure Plastic Bending

Abstract Cross-sectional ovalization (ovalization) usually occurs when thin-walled pipe is subjected to large plastic bending. This paper is concerned with residual deformation of thin-walled pipe's cross section in a radial direction when external bending moment is removed. In order to clarify the fundamental ovalization characteristics, find out what factors influence the residual flattening (value of ovalization), the ovalization behavior is investigated experimentally. The experiments are carried out on 21 stainless steel specimens with different geometric parameters under different bending radii by means of a four-point pure bending device. The residual cross-sectional flattenings are monitored continuously by scanning the cross section periodically along the circumferential direction. From the experimental results, it is observed that the cross-sectional shape of the thin-walled pipe is not perfect standard ellipse, and the appearance of the maximum residual flattening is usually found in the direction normal to the neutral surface. It is also revealed the relationships between the residual flattening and the bending radius, the wall thickness, and the pipe outer diameter, i.e., the residual flattening increases as the bending radius and the wall thickness reduce, but it increases as the outer diameter increases. These results are expected to find their potential application in thin-walled pipe bending operation.

Measurement of small rotation angle of flange joints by a novel flexure magnifying mechanism

Bolted flange joints are indispensable components in process industries due to the good sealing, assemble and disassemble capacities. Generally, the flange rigidity characterized by the rotation angle is a key index to evaluate the sealing tightness of flange joints. However, the rotation angle of flange is usually too small (less than 1°) to monitor during the assemble and operation stages. Accordingly, a novel flexure magnifying mechanism is designed to measure the small rotation angle of flange joints under internal pressure and external bending moment. The magnification factor and calculation approach of the flexure amplification mechanism are deduced and verified by experimental data and finite element simulation. Results indicate that the proposed measuring apparatus has good performance to monitor the maximum rotation angle. It is of great interest that the measured location of the maximum rotation angle is in good agreement with that in the experiment, and the average error is 7.3%, which is acceptable for practical application. Additionally, the leakage rate at the top of flange joints slowly and almost linearly increases with the increment of external bending moment ascribing to the decrease the gasket stress near the top of flange joints.

Theoretical prediction for maximum residual cross-sectional deformation of thin-walled cylindrical steel tubes under pure plastic bending

Cross-sectional ovalization（ovalisation）usually occurs when thin-walled tube is subjected to large plastic bending. This paper is concerned with residual deformation of tube's cross-section in radial direction when external bending moment is removed. A combination of experiments and theoretical modeling is used to study this issue. Firstly the four-point pure bending experiments involving fifteen stainless steel specimens with a range of diameter-to-thickness ratios are carried out to observe the shape of the ovalized cross-section and to obtain the cross-sectional flattening (value of ovalization) along the circumferential direction. Secondly the theoretical modeling procedure is performed to derive a rational model for predicting the maximal residual cross-sectional flattening of the thin-walled tube subjected to pure bending after unloading process, employing the thin-shell kinematics, the principle of virtual work and the classic unloading rule. Finally the model is validated by comparing the theoretical results with the experimental ones with less than 10% error. And the relationships between the residual flattening and the bending radius as well as the wall thickness are also revealed by the numerical results. The application of this investigation will play a positive role in thin-walled steel tube bending operation.

Design of Grinding Machine Spindle

Abstract When grinding high demands are usually placed on the geometrical tolerances of the workpiece surface. For this reason, the spindles of the grinding machines are normally designed with requirements for a minimum position change of the grinding disks due to external forces and bending moments. The design theory of these spindles is relatively well elaborated, as it represents the most frequently used solution in practice. However, there are also cases where it is necessary to grind some hard-to-reach areas, using a great ejection of the spindle. In these cases, it is necessary to reassess the required geometrical tolerances with regard to its necessity to comply with the minimal changes in the position of the grinding discs due to the great ejection. Where it is necessary to maintain high geometrical tolerances, it is necessary to ensure a greater rigidity of the spindle. This rigidity is usually improved by increasing its diameter. By doing this we also increase the weight of the spindle that is heavily ejected, and thus its deformation can occur due to gravity forces. That is why it is necessary to analyse the deflection of the spindle depending on its ejection in the course of its design. In the case we increase the diameter of the grinder spindle the possible applicable grinding disc diameter decreases, due to the growing size of its housing. Any grinding of hard-to-reach surfaces is therefore done in particular to improve the quality of the surface with low requirements on the geometrical tolerances. This article deals with the design patterns for a spindle used in axial grinding for inner rotating surfaces. The article contains a spindle design solution and an analysis of its deflections, depending on its ejection, and the size of the passive forces.

Analysis of the metal-to-metal contact flange joint subject to external bending moment

Metal-to-metal contact flange joints are widely used in nuclear and petrochemical industry for severe conditions, because of the relative stability of the sealing gasket stress under complex service condition. In the present work, finite element models were used for analyzing the stress distribution of metal-to-metal contact pipe flange connection under different internal pressures, temperatures, and external bending moments to evaluate the sealing and strength performance. A metal-to-metal contact pipe flange connection device was also experimented. It was found that the results of the axial bolt force and flange hub stress obtained from the experiments were in fairly good agreement with the finite element simulations. The leakage test of metal-to-metal contact type gasket was conducted to highlight its leakage characteristics under different temperatures. The methods to determine the maximum allowable bending moment of a metal-to-metal contact flange joint according the strength criterion and the sealing criterion were analyzed. The results showed that the maximum allowance bending moment was determined by the strength criterion rather than by the sealing criterion with different thermal loadings when the initial bolt-up stress was high enough to achieve metal-to-metal contact contact.

Variational principles for shakedown analysis of materials with internal rotation

Based on the extended lower bound shakedown theorem for materials with internal rotation, variational principles for elastic and plastic shakedown are presented considering the indeterminate and modified couple-stress theory, proposed by Yang et al. (Int J Solids Struct 39(10):2731–2743, 2002), combined with the first strain gradient plasticity of Fleck and Hutchinson (J Mech Phys Solids 41(12):1825–1857, 1993). Using the concepts of convex analysis, a dual principle and the optimum conditions are derived. A numerical method based on the Newton’s method is derived from the plastic shakedown variational principle to find the load amplification factor. Two illustrative numerical examples are presented: a cantilever beam subjected to a constant axial load and to a variable external bending moment and a cylindrical bar subjected to an axial load and to a variable external torque. In both cases, the external torque and external bending moment vary arbitrarily between prescribed symmetric bounds. The results are compared with those obtained considering classical plastic shakedown theory in order to see the influence of the length scale on the load amplification factor.

04.15: New design rules for tubes in combined walls in EN1993‐5

ABSTRACTSteel tubes can be applied for many applications, structural as well as in pipelines. They may be loaded by combinations of internal or external pressure, soil load, bending moment and normal force. Important failure modes are local buckling, severe ovalisation (flattening of the cross section) and rupture of the pipe wall at local buckles or welds.Within the framework of a European research project called Combitube sponsored by RFCS (Research Fund for Coals and Steel), the structural behaviour of spiral‐welded tubes for application in combined walls has been investigated. The main loads are bending moment, normal force, soil loads and loads from the infill sheeting.Analytical models were developed to predict the elastic‐plastic behaviour under these loads, i.e. the bending moment curvature diagram, the curvature ovalisation diagram and curvature strain diagrams.The analytical models as presented in this paper are an extension of previous analytical models developed for pipelines, now including more parameters that influence the load deformation behaviour, in particular local buckling. The new rules are intended for the new version of EN1993‐5 on Piling. They are validated with the results of full scale tests and extensive parameter studies.

Evaluation of Mechanical Characteristics of Bolted Pipe Flange Connections with PTFE Blended Gaskets Subjected to External Bending Moments

Evaluation of Mechanical Characteristics of Bolted Pipe Flange Connections with PTFE Blended Gaskets Subjected to External Bending Moments

A theoretical study of the critical external pressure for casing collapse

A new theoretical casing collapse model is proposed on the basis of a refined reduced modulus calculation method. The reduced modulus of considers the co-existence of the elastic and plastic regions on the casing cross section. The collapse pressure for an ideal circular casing is expressed as a weighted harmonic sum of the critical elastic pressure and casing yielding pressure. Three kinds of casing imperfections including the wall thickness variation, ovality and non-uniform external pressure on casing collapse are further considered to amend the ideal casing collapse model. The equivalent wall thickness due to wall thickness variation is introduced, and the critical elastic pressure and yielding pressure under the effects of initial ovality and non-uniform external pressure are obtained. On this basis, the collapse pressure for an oval casing with thickness variation under non-uniform external pressure is obtained with superposition principle. The effects of axial force, bending moment and torque on collapse pressure are included with the reduced yielding point. All the above factors are integrated into a unified casing collapse model. At last, the comparison between the new model and API specification is further discussed. The results indicate that the new model gives a more sophisticated description of casing collapse problem. Introducing the casing imperfections improves the consistency between the theoretical and experimental results at the transition between elastic and plastic ranges. The non-uniform external pressure plays the most important role in the casing collapse problem. The existence of non-uniform external pressure, axial force, bending moment and torque also reduces the critical casing collapse pressure a lot.

Three dimensional finite element analysis of 4 inch smart flange on offshore pipeline

Smart flanges are used for pipeline and riser repair in subsea. In a typical case in the gas export pipeline project, the end cap bolts of a 4inch smart flange were broken during operation, and in turn leakage occurred. This work presents the detail of three dimensional finite element analysis of the smart flange to support the observed end cap bolts failure. From finite element analysis it turns out that in the presence of external bending moment, an uneven contact distribution is present between seal and end cap, which in turn changes the uniform load distribution on bolts and threaten the integrity of bolts. On the other hand, 3D finite element analysis of interaction between pipeline and seabed is presented by means of Abaqus to explore the distribution of bending moment along the pipeline route. It is found that lateral buckling occurs in the pipeline which introduces large bending moment.

Collapse of reinforced thermoplastic pipe (RTP) under combined external pressure and bending moment

With shear deformation and pre-buckling deformation included, a 2D mathematical model for composite pipes is developed to analyze the collapse of RTP pipe under pure external pressure, pure bending moment, or combined external pressure and bending moment. The models for RTP pipes are developed based on the models of steel pipe proposed by Kyriakides and his co-workers. Theoretical analyses of collapse of RTP pipe under short-term hydrostatic external pressure, bending moment, or combined external pressure and bending moment have been presented in this paper. The effects of radius–thickness ratios, initial ovality and initial stresses, pre-buckling deformation and modulus of elasticity have been discussed. Through data fitting, formulas of RTP collapse under pure external pressure, pure bending moment, or combined external pressure and bending moment have been developed. A good agreement between the calculation based on formulas and finite element analysis verifies the efficiency of the formulas.

FEM Stress Analysis and the Sealing Performance Prediction of Pipe Flange Connections under External Bending Moments and Internal Pressure

FEM Stress Analysis and the Sealing Performance Prediction of Pipe Flange Connections under External Bending Moments and Internal Pressure

The influence of external bending moments on the lifetime of bends in hot reheat pipelines

The influence of various factors (the initial pipe cross section ovality and external bending moments) on the lifetime of bends used in high-temperature pipelines is estimated using the techniques of continuum damage mechanics of metal. The investigation was carried out for two typical bends used in hot reheat pipelines. To this end, the bend lifetime was numerically analyzed taking into account the accumulated extent of damage based on the results of finite-element computations in geometrically nonlinear statement.

A Fiber Pull-Out Based Model for Synthetic Fiber Reinforced Concrete Beams under a Flexural Load

This work is intended to be a simple contribution to building a model able to implement theoretical results related to the random oriented fiber reinforced concrete in a procedure that could be used in structures analysis and design involving fiber reinforced elements. Here follows a short outline: In the introduction chapter the problem is presented together the work done. Section 2 develops some ancillary concepts of this material and its mechanical properties, while in Section 3, following the path of other researchers, the assumptions made to solve the problem are presented, together with the most relevant results related to presence of 3D randomly oriented fiber. In the following section a review of the mechanical process of fiber pull-out is done, and the results, mostly due to Victor Li researches, of a 3D randomly oriented synthetic fiber stress vs crack opening in a pull-out process from a cement matrix. In Section 5 the author, after making some assumptions about the configuration of the strain and crack geometry in the cross section where failure is assume to occur under flexural bending moment, the resultant stress is integrated to find the resultant internal moment vs increasing strain and crack width. In this analysis, the crack bridging law for synthetic fiber in FRC presented in the previous section is taken into account. In Section 6, a procedure to find a cross section configuration in equilibrium under external bending moment has been built. Under the assumption of a perfectly plastic collapse mechanism a numerical simulation is conducted on a specimen that undergoes a four-point bending test. A comparison with the trend of a similar test on a synthetic FRC sample has been done. The work is completed by the conclusions that could be inferred from this work.

Calculation Methods of the Local Structure Behavior of Unbonded Flexible Pipes

In this paper, the nonlinear relationship between the bending moment and curvature of non-bonded flexible pipes was studied. It was found that the relation was a function of internal and external pressure, axial force, and bending moment load. The model used in this paper took into consideration of the flexural, tensile and torsional strength of layers as well as the frictions between them. Symmetrical axial load was first applied, and then the bending load. Due to friction, the response of the unbonded flexible pipes is hysteretic to the loads. In conclusion, the response of unbonded flexible pipes are both related to its own structural properties and external loads.Coupling factors of different conditions should also be considered.

The Simulation and Sensitivity Analysis of S-Lay Installation in Deep Water

Pipelines being laying is subjected the high external water pressure, axial tension and bending moment, influencing the large deformation and the stability of pipelines. It is a key problem about the pipeline deformation and stress analysis under installation. The paper is focused on the analysis of the S-Lay method in deep water, modeling the deepwater S-lay installations considering interactions among the pipeline and stinger and the barge, which make the simulations more realistic. The large work of the paper issues the sensitivity analysis in the installation procedure, several examples are presented to calculate the pipeline configuration and mechanical analysis for different laying water depth, pipe diameter, thickness of wall and concrete weighted coating layer and stinger radius. Some results are presented as well.

A one-dimensional model for dynamic analysis of generally layered magneto-electro-elastic beams

A new one-dimensional model for the dynamic problem of magneto-electro-elastic generally laminated beams is presented. The electric and magnetic fields are assumed to be quasi-static and a first-order shear beam theory is used. The electro-magnetic problem is first solved in terms of the mechanical variables, then the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-electro-mechanical couplings into account. Additional terms, which involve the third spatial derivative of the transverse displacement, also occur as a result of the piezoelectric and/or piezomagnetic behavior. It is also shown that the magneto-electric inputs can be treated as equivalent external axial forces and bending moments per unit length. Free vibrations and frequency response solutions are presented to validate the model by comparing the present results with those found in the literature or obtained by finite element analysis. Based on the successful validation of the model, new results for free vibrations of functionally graded magneto-electro-elastic beams are presented.