Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

Effect of frictions on cross section quality of thin-walled tube NC bending

The effect of frictions between dies and tube on the cross section quality of thin-walled tube numerical controlled(NC) bending was studied by numerical simulation method, combined with theoretical analysis and experiment. The results show that the frictions between mandrel, wiper, pressure die, bending die and tube have a significant and complicate effect on the section quality of thin-walled tube NC bending. To improve the section quality, frictions between mandrel, wiper and tube should be decreased, but the frictions between the pressure die, bending die and tube increase. The effect on the section distortion is more significant from mandrel, wiper, pressure die to bending die and the effect on the wall thinning more significant from mandrel, pressure die, wiper, to bending die. The effects of frictions between all dies and tube on wall thinning are smaller than their effects on section distortion. Mandrel and wiper should be lubricated well and drawing oil is used to lubricate them in actual production. The frictions between pressure die, bending die and tube should be increased and the dry friction is used between pressure die, bending die and tube in actual production.

Deformation Calculation of Cross-section Based on Virtual Force in Thin-walled Tube Bending Process

Cross-section deformation is one of important factors affecting the quality of tube formation, and the tube＇s capability of transporting liquid and gas will be reduced because of the cross-section ellipse deformation due to the effect of shear load in plastic bending process. When the tube is bent, the extrados-wall bears the tension stress and the intrados-wall bears the compression stress, synchronously the cross-section is affected by the circumferential stress. According to the above, the distribution function and curve of tangential stress can be obtained according to force balance differential equations on circumferential direction and Trasca rule. Subsequently the real state and virtual state moment equations were established, a new method was presented adopting the virtual principle of deformation system to calculate the x-axis and y-axis displacement of arbitrary point on cross-section. So the major and minor axes of deformed cross-section can be calculated according to the displacements of each point, and the variety value of major and minor axes will be obtained further. Finally the theoretical calculating result is compared with NC tube rotary-bending experiment results to verify the rationality of theoretical analysis, and the cross-section deformation rule of thin-walled tube can be received.

Effect of mandrel on cross section quality of thin-walled tube numerical controlled bending

The effect of mandrel with the structure of ball and socket on the cross section quality of thin-walled tube numerical controlled(NC) bending was studied by numerical simulation method, combined with theoretical (analysis) and experiment. Influencing factors of the mandrel include the count of mandrel heads, the diameter of mandrel and its position. According to the principle of NC tube bending, quality defects possibly produced in thin-walled tube NC bending process were analyzed and two parameters were proposed in order to describe the cross section quality of thin-walled tube NC bending. According to the geometrical dimension of tube and dies, the range of mandrel protrusion was derived. The finite element model of thin-walled tube NC bending was established based on the DYNAFORM platform, and key technological problems were solved. The model was verified by experiment. The effect of the number of mandrel heads, the diameter of mandrel and the protrusion length of mandrel on the cross section quality of thin-walled tube NC bending was revealed and how to choose mandrel parameters was presented.

Inner and outer pressure forming of nickel based super-alloy thin-walled part with variable diameter sections

A novel forming method of nickel based super-alloy thin-walled part with variable diameter sections was proposed by using inner and outer pressure with the visco-elasto-plastic pressure-carrying medium at room temperature,and the principle of the method was provided.Experiments and FE simulations were carried out to analyze the deformation characteristics for the part with larger variable diameter ratio(35%).The results show that visco-elasto-plastic pressure-carrying medium can meet the requirements of the room-temperature deformation condition for nickel based super-alloy sheet.The inner and outer pressure forming with the visco-elasto-plastic pressure-carrying medium can meet the requirements of dimensional accuracy for the thin-walled part with variable diameter sections.The thinning of wall-thickness is less than 4%.This method provides a new approach for near-net shape forming of nickel based super-alloy thin-walled parts with variable diameter sections.

Free torsion of thin-walled structural members of open-and closed-sections

Free torsion of thin-walled structures of open- and closed-sections is a classical elastic mechanics problem, which, in literature, is often solved by the method of membrane analogy. The method of membrane analogy, however, can be only applied to structures of a single material. If the structure consists of both open- and closed-sections, the method of membrane analogy is difficult to be applied. In this paper, a new method is presented for solving the free torsion of thin-walled structures of open- and/or closed- sections with multiple materials. By utilizing a simple statically indeterminate concept, torsional equations are derived based on the equilibrium and compatibility conditions. The method presented here not only is very simple and easy to understand but also can be applied to thin-walled structures of combined open- and closed-sections with multiple materials.

General Stiffness Matrix for a Thin-Walled, Open-Section Beam Structure

This paper is to review the theory of thin-walled beam structures of the open cross-section. There is scant information on the performance of structures made from thin-walled beam elements, particularly those of open sections, where the behavior is considerably complicated by the coupling of tensile, bending and torsional loading modes. In the combined loading theory of thin-walled structures, it is useful to mention that for a thin-walled beam, the value of direct stress at a point on the cross-section depends on its position, the geometrical properties of the cross-section and the applied loading. This applies whether the thin-walled section is closed or open but this study will be directed primarily at the latter. Theoretical analyses of structures are fairly well established, considered in multi-various applications by many scientists. However, due to the present interest in lightweight structures, it is necessary to specify where the present theory lies. It does not, for example, deal with compression and the consequent failure modes under global and local buckling. Indeed, with the inclusion of strut buckling failure and any other unforeseen collapse modes, the need was perceived for further research into the subject. Presently, a survey of the published works has shown in the following: 1) The assumptions used in deriving the underlying theory of thin-walled beams are not clearly stated or easily understood;2) The transformations of a load system from arbitrary axis to those at the relevant centre of rotation are incomplete. Thus, an incorrect stress distribution may result in;3) Several methods are found in the recent literature for analyzing the behaviour of thin-walled open section beams under combined loading. These reveal the need appears for further study upon their torsion/flexural behaviour when referred to any arbitrary axis, a common case found in practice. This review covers the following areas: 1) Refinement to existing theory to clarify those observations made in 1 - 3 above;2) Derivation of a general elastic stiffness matrix for combined loading;3) Calculation of the stress distribution on the cross-section of a thin-walled beam. A general transformation matrix that accounts for a load system applied at an arbitrary point on the cross-section will be published in a future paper.

THE APPROXIMATE ANALYTICAL SOLUTION FOR THE BUCKLING LOADS OF A THIN-WALLED BOX COLUMN WITH VARIABLE CROSS-SECTION

For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so it is very difficult to solve them by means of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations. Based on the energy principle and the Galerkin's method, the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section. This paper is of practical value.

Abdominal Wall Endometriomas at Cesarean Section Scars: A Case Series

Endometriosis, a common gynecological condition, is defined as the presence of functioning endometrial tissue outside the uterine cavity. It often presents as a cyclic, hormonally stimulated pain in women during their reproductive years. While endometriosis is usually located within the pelvis, it may also occur at intraperitoneal, intestinal, perineal, and distant ectopic sites. Although often diffuse, a localized, focal mass of endometrial tissue is termed as an endometrioma. In rare occurrences, an endometrioma will present superficially to the peritoneum within the abdominal wall following gynecologic or obstetric surgery. The presence of an abdominal wall endometrioma within a cesarean section scar may pose a diagnostic dilemma, which is often misdiagnosed, and results in surgery referrals for treatment. The clinical symptoms and sonographic appearance of abdominal wall endometriomas occurring at cesarean section scars are highlighted in this case series.

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors’ earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section’s area properties that are necessary to axial and shear stress calculations within the structure’s thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.

强震区隧道洞口段新型墙-板抗减震措施的效果分析

为了进一步提高强震区铁路隧道的安全以及抗震性能,依托包银铁路甘德尔山隧道,运用数值模拟软件FLAC 3D,针对强震区隧道洞口段墙-板和墙-板-减震层的抗减震作用效果进行研究。研究结果表明,与不采用抗减震措施相比较,采取墙-板抗震措施后,横向位移减小了5.95%,竖向位移减小了45.87%,最小安全系数增大了40.91%~49.25%,最大主应力的抗震作用效果达到了63.56%,最小主应力的抗震作用效果为4.04%,最大剪应力抗震作用效果为8.35%;采取墙-板-减震层减震措施后,横向位移减小了13.11%,竖向位移减小了43.88%,最小安全系数增大了65.82%~74.50%,最大主应力的减震作用效果达到了75.11%,最小主应力的减震作用效果为10.21%,最大剪应力减震作用效果为12.80%。采用墙-板-减震层的抗减震措施优于墙-板结构。推荐采用墙-板-减震层措施对甘德尔山隧道进行抗减震加固设计。

Wing walls for enhancing the seismic performance of reinforced concrete frame structures

A building retrofitted with wing walls in the bottom story, which was damaged during the 2008 M8.0 Wenchuan earthquake in China, is introduced and a corresponding 1/4 scale wing wall-frame model was subjected to shake table motions to study the seismic behavior of this retrofitted structural system. The results show that wing walls can effectively protect columns from damage by moving areas that bear reciprocating tension and compression to the sections of the wing walls, thus achieving an extra measure of seismic fortification. A ‘strong column-weak beam＇ mechanism was realized, the flexural rigidity of the vertical member was strengthened, and a more uniform distribution of deformation among all the stories was measured. In addition, the joint between the wing walls and the beams suffered severe damage during the tests, due to an area of local stress concentration. A longer area of intensive stirrup is suggested in the end of the beams.

Simulation and Experiment on Workability for Cold Pressure Forming of Sheet Metal Part with Step Cross-section

In modem manufacturing, a new type of sheet metal part with step cross-section in both inner hole and outer edge is proposed. The traditional stamping separating processes can only produce sheet metal part with vertical cross-section. According to the latest developing theory and potential of cold pressure forming： combination of pressure and cold forging, a new flow control forming of sheet metal（FCF） is excogitated based on blanking process of general stamping and combined with cold forging processes such as extrusion and coining, etc, which is aiming at the above-mentioned new type of sheet metal part. With utilization of this new process, the new type of sheet metal parts can be manufactured. In order to shorten the testing period, the numerical simulation was carried out by using DEFORM-3D software, and both deformation and mechanics rules were analyzed. Based on the simulation, both punching part and blanked parts of this new type were successfully developed. Then a new conception of optimal distance between the step walls of inner hole and outside edge was proposed and the design principle for its numerical value was inferred. Furthermore, a mold set for combination of stamping ＆ cold forging was designed and manufactured, by which the technologic experiments were taken for validation with Aluminum plate of thickness 2.35 mm for power battery cover board, which verified the principle of the distance between the step walls. The research of cold pressure forming of thin sheet metal with step cross-section is significant, not only to the development of modem mechanical manufacture, but also to metal plastic forming science.

Progressive collapse resisting capacity of reinforced concrete load bearing wall structures

Reinforced concrete(RC) load bearing wall is widely used in high-rise and mid-rise buildings. Due to the number of walls in plan and reduction in lateral force portion, this system is not only stronger against earthquakes, but also more economical. The effect of progressive collapse caused by removal of load bearing elements, in various positions in plan and stories of the RC load bearing wall system was evaluated by nonlinear dynamic and static analyses. For this purpose, three-dimensional model of 10-story structure was selected. The analysis results indicated stability, strength and stiffness of the RC load-bearing wall system against progressive collapse. It was observed that the most critical condition for removal of load bearing walls was the instantaneous removal of the surrounding walls located at the corners of the building where the sections of the load bearing elements were changed. In this case, the maximum vertical displacement was limited to 6.3 mm and the structure failed after applying the load of 10 times the axial load bored by removed elements. Comparison between the results of the nonlinear dynamic and static analyses demonstrated that the "load factor" parameter was a reasonable criterion to evaluate the progressive collapse potential of the structure.

Effects of Solvents on Extraction of Effective Components from Cell Wall Tissues of Chinese Traditional Medicines

The effects of different Chinese traditional medicines were solvents on the extraction of effective studied by the histochemical methods, components from the cell wall tissues of such as the bare-handed section, swelling ratio, paraffin section, IR spectrum and cell wall component analysis. The results show that the ethanol-alkali solvent could increase the swelling ratio as well as the swelling speed. The effective components of cell wall tissues extracted by ethanol-alkali solvent become loose shown by the paraffin section. According to the IR spectrum analysis and the results of cell wall tissue component analysis, it was found that the ethanol-alkali solvent could decrease the contents of pectin and hemicellulose in the cell wall to make the wall broken, and therefore the effective components can be extracted easily by the solvent and the extraction rate is increased.

Investigation of Entrance and Wall Dynamics of the High-Flux Gas-Solid Riser Using Statistical Analysis of Solids Concentration Signals

Statistical analysis of the entrance and wall dynamics of a high-flux gas-solid riser was done using solid concentration time series data collected from a 76 mm internal diameter and 10 m high riser of a CFB system with a twin-riser operated at 4.0 to 10.0 m/s gas velocity and 50 to 550 kg/m2s solids flux. Spent fluid catalytic cracking catalyst particles with 67 μm mean diameter and density of 1500 kg/m3 together with 70% to 80% humid air was used. Solid concentration data were analysed using code prepared using FORTRAN 2008 to get statistical parameters and plot their profiles. Results obtained show that the gas-solid suspension flow in the riser is dominated by low solid concentration in the centre region and high solid concentration in the wall region which forms a core-annulus flow structure. The mean solid concentration in the wall region decreases with riser height from the dense bottom section to less dense in the fully developed flow section at the top of the riser. The gas-solid suspension flow in the centre region is dominated with uniform flow structure while the wall region is dominated with high fluctuations in solid concentration. Further, it was found that the entrance and developing flow sections of the riser exhibit high flow non-uniformities than the fully developed flow section of the riser. The flow non-uniformities in the entrance and developing flow section increase with increase in superficial gas velocity at constant solid flux. The wall region, from the entrance to the top sections of the riser along the axial direction exhibits both dilute and dense suspension flow.

Clinical analysis of abdominal wall endometriosis in 101 cases

Objective: To review the clinical characteristics, treatment and prognoses of abdominal wall endometriosis(AWE).Methods: A retrospective study of 101 cases of AWE from 1992 to 2005 at Obstetric and Gynecologic Department of Peking Union Medical College Hospital was performed. Ninety-eight patients had a history of caesarean section. The mean age of the patients was (33.3±4.8) years and the average size of the mass was 1.5 cm. Abdominal wall mass associated pain during the menstrual cycle was noticed in 89.8% of the patients. The occurrence of AWE after caesarean section was 0.05% at our hospital. In patients without pelvic endometriosis or adenomyosis, 20.5% were presented with high CA125 >35 U/ml and the highest one was 93.4 U/ml. 92.1% of patients were diagnosed before surgery. 4 patients were administrated first in General Surgical Department with painless abdominal mass. Medication was adopted in 16 cases pre-operatively and 14 cases post-operatively.Results: The mean size of the resected mass was 4.2 cm, significantly larger than the estimation with palpation or ultrasonography, which was 0.8-1.2 cm (P=0.006, P<0.001). Pelvic endometriosis or adenomyosis was detected during the operation in 13 patients. One patient was diagnosed as atypical endometriosis by pathological examination in the beginning but transformed to be sarcoma finally. Ten patients recurred after surgery. 2 of them received medication and 5 of them received second operation.Conclusions: Ultrasonography can be used to evaluate the size of the mass and the infiltrative scope pre-operation. The serum CA125 is not specific for diagnosis of AWE. Complete eradication of the lesion with at least 1 cm beyond the edge of the mass is recommended as the primary treatment. Eradication should be considered also in recurrent cases. It may transform to malignant lesions after multiple recurrence.

Analysis and experiment of cross-section flattening incoreless tube bending

In order to predict the flattening rate of the cross-section accurately during the tube ben- ding, the generation principle, the solution and the influence factor of the cross-section flattening were studied. On the basis of the plane-stress and the assumption that the plastic volume is con- stant, three-dimensionai strain formulas were established in consider of the cross-section flattening. Considering the wail-thickness change, the approximate calculation formulas of short axis flattening rate were deduced, with the outer diameter and the inner diameter as parameters. Because different materials have different cross-section flattening rates, a material correction factor was introduced to modify the formula based on experiments. Finally, the validity of the theoretical formulas was proved according to the calculation and the experiment results, which can provide a reference for the forming quality prediction in tube bending.

嵌套加强的LQ550高强冷弯薄壁C型钢连续檩条受力性能研究

为提高LQ550级高强冷弯薄壁C型钢连续檩条的承载能力,采用在支座处嵌套的方法来加强连续檩条。对未加强和采用两种嵌套方式加强的檩条共7组试件进行三点受弯试验,得到了试件的承载性能和破坏形态,试验结果表明加强后的试件出现跨中局部屈曲和嵌套端部局部屈曲两种破坏形态。采用ABAQUS软件建立了非线性有限元模型对嵌套加强的檩条进行数值模拟,有限元分析得到的承载力和破坏形态与试验结果吻合良好,验证了有限元模型的准确性。基于验证的有限元模型,分析了两种嵌套方式和不同嵌套长度对檩条承载力的提升,且表明嵌套檩条的长度宜取为连续檩条跨度的1/5~1/4。