Combined Action Of Bending Research Articles

Generalized Deplanation Hypotheses for Linear and Angular Deformations in Reinforced Concrete Structures under Combined Torsion and Bending

Statement of the problem. The analysis of the deplanation hypothesis for linear and angular deformations in reinforced concrete in bending with torsion has been carried out. Results. A simple new method from the method of grids has been developed for complex functions under the combined action of bending and torsion. Diagrams of linear and angular deformities and a new hypotheses have been analyzed. Complex functions have been found to determine the linear and angular deformations, bending and torque moments in the compressed area of concrete. The author has found the projection coefficients of linear and angular deformations using diagrams of compressed concrete and main reinforcement. Deplanations from a special geometric figure of deformations in a complex function have been found. There are vectors of several triangles and gradients where the proportions of a hypotenuse, cathetuses and vectors have been derived. Conclusions. It is also important that similar relative values can be obtained for any vectors. A field of small squares have been plotted and jumps from lateral, normal and other cracks appear have been determined. Fillings of the deformation (stress) diagrams have been obtained for the analysis of the moments in bending with torsion using simple expressions or in a full form. The research on the complex function of linear and angular deformations and the approximation of a function from Timoshenko-Goodyear have been carried out. The error of the deformations value of using the complex function at the points under study is 2% and is 7% at any points of the cross section.

Design method of HSS welded H-section beams subjected to bending-shear combination

High-strength steel (HSS) welded H-section beams are increasingly used in steel structures considering their advantage of high strength, but the stability is a concern especially near the supports, where the beams are prone to buckling under the combined actions of bending and shear. In this paper, finite element method was used to analyze the mechanical performance of HSS welded H-section beams under shear and bending-shear loads. A parametrical analysis for the H-section beams under pure shear loads was conducted, and a new shear buckling coefficient calculation method considering the interaction between plates was proposed. This coefficient was then applied to calculate the shear strength, and a design method for shear buckling strength based on the direct strength method (DSM) was proposed. Finally, a new bending-shear interaction curve was developed to predict the ultimate resistance of HSS welded H-section beams under bending-shear combination, and the reliability analysis results demonstrate the feasibility and safety of the design method proposed in this paper for HSS welded H-section beams.

Numerical and experimental analysis of the notch effect on fatigue behavior of polymethylmethacrylate metal based on strain energy density method and the extended finite element method

Abstract This work investigates the effect of the notch on fatigue behavior by combining two methods: the extended finite element method (XFEM) and the averaged strain energy density (ASED) method, which considers the combined action of bending and shear loading. The ASED method has already been proven accurate for assessing the failure of components in the presence of sharp and blunt notches, and several results are available in the literature for different materials. These results were compared with those obtained from the experimental tests reported here. The main purpose of this study was twofold: The first part is an experimental study of fatigue in rotary bending of specimens weakened by U and V notches made of polymethyl-methacrylate (PMMA) material. Two values for the radius were used for the U-notches (0.2 and 2 mm) and two angles for the V-notches (20° and 140°). The second part of the study consisted of performing several simulation tests using the Cast3m software for different angles and radii. The local approach based on the mean value of the ASED acted over a finite-sized volume surrounding the highly stressed regions. The maximum principal stress located at the notch edge defined the center of the control volume. If the notch is blunt, the control volume assumes a crescent shape with its width measured along the notch bisector line. When the notch is considered pointed (V-notched) or is a crack, the control volume becomes a circle with its center at the notch tip. The presence of geometric discontinuities in structures affects their lifetime by reducing it, producing a high concentration of local energy around the notch tip. Good convergence was obtained between the numerical simulation and experimental results for the ASED in a finished zone surrounding the notch tip.

Relationship between stress and magnetic signal of steel box girder based on magnetic memory method

Metal magnetic memory testing (MMMT) is a nondestructive testing technique that can detect early signs of damage in components. Many scholars have studied the effect of uniform stress on the self-leakage magnetic field (SLMF) strength of ferromagnetic materials. However, there is still insufficient research on the stress concentration caused by uneven stress, under the combined action of bending and shear. In this study, we studied the law of distribution of the magnetic signal, HP(y) and magnetic gradient, K, on a part of the surface of a steel box girder damaged by buckling, using a four-point bending pattern. The results showed that combining the three peak positions, namely, the magnetic signal, its newly added comparing initial magnetic signal, and magnetic gradient distribution curves, could accurately determine all stress concentration positions on the flange of the steel box girder, and reduce the interference of the initial complex residual magnetic field. Furthermore, we studied the quantitative relationship between normal stress, shear stress, and a magnetic signal. It was found that the stress-magnetic relationship conformed to the Jiles–Atherton model. The peak value of HP(y) – 𝜎, |HP(y)|a – 𝜎, and Kmax – 𝜎 relationship curves could be used as the characteristic point of the critical yield stress at the action of normal and shear stress. The degree of stress concentration of the flange and web could be quantitatively evaluated by fitting the Kmax – 𝜎 relationship. This study can provide an experimental reference for the application of MMMT in the evaluation and early warning of the state of damage to a steel box girder.

Magnetic Signal Characteristics in Critical Yield State of Steel Box Girder Based on Metal Magnetic Memory Inspection

Metal magnetic memory testing (MMMT) is a nondestructive testing technique that can detect early signs of damage in components. Many scholars have studied the effect of uniaxial stress on the self-magnetic-leakage field (SMLF)’s strength. Nevertheless, there is still insufficient research on the combined action of bending and shear. We studied the law of distribution of the magnetic signal, ΔHSF(y), at different stress parts of a steel box girder and the quantitative relationship between the magnetic characteristic parameters and the external load. The results showed that the MMMT could accurately detect the early stress concentration zone (SCZ) and predict the final buckling zone of steel box girders. It could be judged that the corresponding parts of the steel box girder had entered the elastic-plastic working stage by the reverse change of the ΔHSF(y)-F and |HSF(y)|a -F curve trends, this feature could be used as an early warning sign before the steel box girder was deformed or destroyed. The fitted |HSF(y)|ave -F linear expression could be used as the expression between the magnetic signal and the shear capacity. All the evaluation methods were expected to provide a basis for effectively evaluating the stress state of steel box girders with the MMMT method.

МЕХАНИЧЕСКАЯ АНИЗОТРОПИЯ СУГЛИНИСТОЙ ПОЧВЫ ПРИ РАЗНЫХ ТИПАХ НАГРУЖЕНИЯ

The results of the study of the mechanical properties of the soil, relevant from the point of view of the effective use of slatted rollers, are given in the article. It has been established that the most important technological property of the soil is its anisotropy. As a result, the limiting stresses sufficient for the destruction of the soil differ by 6-10 times with different methods of impact on it. The minimum is the tensile strength and the ultimate bending strength of the soil derived from it. It is the most important way of influencing the arable layer, since it provides the minimum energy intensity of soil crumbling. In particular, the slatted roller destroys soil clods by the combined action of bending and compression. In this regard, a study was made of loamy soil of different moisture content for its resistance to bending and crumbling. It has been established that the strength of the soil increases with a decrease in its moisture content. At the same time, the minimum limiting stress is typical for a moisture content of 20-23%. With a further increase in moisture, the strength of the soil again slightly increases. In general, the dependence of soil strength on moisture both in bending and in compression is described by a quadratic equation. To determine the magnitude of the bending stress, a new version of the calculation of the moment of resistance to bending of a rectangular section of the sample is proposed, taking into account the anisotropy of the soil. Instead of the middle layer, the surface (upper) layer was used as a “neutral” layer. This is due to the fact that with the existing difference in the tensile and compression strength of the soil, the upper layer practically does not deform until the destruction of the lower layer. As a result, it is advisable in the calculation to take the cross section as a composite one, shifted from its geometric axis by half the height.

Experimental study on ageing characteristics of electric locomotive ethylene propylene rubber cable under mechanical–thermal combined action

The train-mounted ethylene propylene rubber (EPR) cables of electric locomotive are partly restricted by the body structure and spatial layout and are in a combined environment of strong mechanical bending and thermal ageing. The degradation characteristics of the insulation layer have not yet received sufficient attention. In order to study the ageing characteristics of EPR cables of electric locomotive under the combined action of machine and thermal, this paper designs a bending–thermal combined ageing test platform for cables with a temperature of 135°C, bending diameter of 393.52 mm, 590.28 mm and unbending cables, and tests after ageing. The product has been tested by infrared spectroscopy, scanning electron microscopy, elongation at break and broadband dielectric spectroscopy. The research results show that the bending outer part of the train-mounted EPR cable is a pain point. Under the combined action of bending and thermal, whether it is microstructure or macro performance, the degradation rate and degree of the bending of outer insulation layer are greater than the value under a single thermal ageing condition. Mechanical bending has an accelerating effect on the ageing of the EPR insulation layer. The research results can provide a reference for the ageing characteristics of the train-mounted EPR cable under the bending–thermal synergy and the evaluation of operating state of the train-mounted EPR cable under bending–thermal operating conditions.

Analysis and research on fracture cause of connecting bolt of wind turbine spindle

On a certain day in 2018, the main shaft connecting bolt of a wind turbine in a wind farm broke and failed during operation. In order to find out the cause of fracture, the fractured spindle connecting bolt was comprehensively detected and analyzed by means of appearance state analysis, chemical element composition analysis, mechanical property detection analysis, microstructure detection and fracture micro area analysis. The results show that the main reason for the fracture of the main shaft connecting bolt is that the hydrogen penetrates into the bolt surface due to improper process control during the production process, resulting in hydrogen embrittlement in the local area of the thread root. Thus, during the operation of the fan, under the combined action of bending, shear and tensile stress, the connecting bolt of the main shaft cracks at the bottom of the first thread on the side of the self rigid rod with the most concentrated stress, and expands in the form of “herringbone” brittle fracture until the overall fracture failure. It is recommended to check the bolts in the same batch to prevent hydrogen embrittlement in the whole batch.

Разработка методики модельных испытаний уторных сварных соединений вертикального цилиндрического резервуара

The methodology of laboratory modeling of the loading of utor welded joint of the tank is presented. The methodology is based on testing of the special design sample. It allows under uniaxial tension on the typical servo-hydraulic machines to reproduce in the zone of a utor welded joint the combined action of bending and shear forces, similar to that which occurs during the operation of a vertical cylindrical tank. To assess the distribution of the stress-strain state in the proposed design of the sample under its loading, the finite element modeling was performed in the ANSYS software package. It showed the fundamental correspondence of the stress distribution in the zone of the utor node in the sample and in the real tank. The experimental studies consisted in carrying out tests for the durability of a series of 16 samples loaded with the maximum force in the cycle, causing the calculated stresses in the zone of the welded utor node in the range of 100–200 % from the maximum permissible ones. The obtained results showed that the maximum loaded zone, where the destruction of the samples occurred, is the near-seam zone of the utor welded joint on the inside of the tank. This corresponds to the statistics of the real tank failures. It is established that the developed methodology ensures the possibility of carrying out correct resource tests of the tank utor welded joints. It is also possible to vary the stress-strain state scheme within a wide range in the area of the utor welded joint by changing the design parameters of the test sample. In compliance with the regulated welding technologies and the absence of unacceptable defects in the welded joint, the utor node has a high resource, which significantly exceeding 50 years of the tank operation.

Analysis of the Shear Capacity of Ultrahigh Performance Concrete Beams Based on the Modified Compression Field Theory

An analysis model of the shear capacity of prestressed ultrahigh performance concrete (UHPC) beams under the combined action of bending and shearing was established in this paper based on the modified compression field theory and by considering the unique material constitutive relation of UHPC. Shear tests were performed using three prestressed UHPC‐T beams with different shear‐span ratios to verify the correctness of the model. The results showed that the shear‐span ratio greatly influenced the shear capacity and failure modes of UHPC‐T beams. Upon increasing the shear‐span ratio, the failure modes of the three beams were inclined compression failure, shear compression failure, and diagonal tension failure, successively. When the shear‐span ratio changed from 1.04 to 2.12, the shear bearing capacity decreased greatly; however, when the shear‐span ratio changed from 2.12 to 3.19, the decrease of the shear bearing capacity was very small. In addition, the MCFT analysis model was used to analyze the experimental data, and the predicted results were in good agreement, which proved the applicability of the model. Finally, according to the existing shear test results of UHPC beams and based on the main influencing factors, a simplified formula for predicting the shear capacity of UHPC beams was obtained by fitting. Comparing the MCFT model with the results of other pieces of literature, this formula accurately predicted the shear capacity of UHPC beams. The MCFT model and the simplified formula presented in this paper provide a powerful tool for predicting the shear performance of UHPC‐T beams, which will contribute to the design and analysis of UHPC‐T beams.

Effective torsional stiffness of reinforced concrete structural walls

When a structural wall is subjected to multi-directional ground motion, torsion-induced cracks degrade the stiffness of the wall. The effect of torsion should not be neglected. As a main lateral load resisting member, reinforced concrete (RC) structural wall has been widely studied under the combined action of bending and shear. Unfortunately, its seismic behavior under a combined action of torsion, bending and shear is rarely studied. In this study, torsional performances of the RC structural walls under the combined action is assessed from a comprehensive parametrical study. Finite element (FE) models are built and calibrated by comparing with the available experimental data. The study is then carried out to find out the critical design parameter affecting the torsional stiffness of RC structural walls, including the axial load ratio, aspect ratio, leg-thickness ratio, eccentricity of lateral force, longitudinal reinforcement ratio and transverse reinforcement ratio. Besides, to facilitate the application in practice, an empirical equation is developed to estimate the torsional stiffness of RC rectangular structural walls conveniently, which is found to agree well with the numerical results of the developed FE models.

Combined Bending with Tension of Isotropic Plate with Crack Considering Crack Banks Contact and Plastic Zones at its Tops

Abstract Stress-strain state of isotropic plate with rectilinear through-crack at combined action of bending and tension, realized by applying distributed forces and bending moments at infinity, the vectors of which are parallel and perpendicular to the crack, is investigated. Under the influence of the internal stress the crack faces contacts on area of constant width near the upper base of plate, and plastic zones forms in its tips. Using methods of the theory of complex variables, complex potentials plane problem of elasticity theory and the classical theory of plates bending, solving of the problem is reduced to the set of linear conjugation problems and their analytical solution is built in a class of functions of limited plastic zones in the crack tips. The conditions of existence of the solution of the problem in these terms are determined. Using Treska plasticity conditions in the form of surface layer or the plastic hinge, the length of plastic zone and crack opening displacement are found analytically. Their numerical analysis for various parameters of the problem is conducted.

Strength Analysis of Superyacht Superstructures with Large Openings

The superyacht manufacturing industry is currently facing big challenges, mainly related to the present economic crisis. Manufacturers are then competing on the ground of better and more aesthetic external and interior designs. This trend often leads to structural strength related issues, which can compromise the static or dynamic stability of superyacht hull. In several instances, the aforementioned fact is met, as in large openings and docks to recover tenders and the enlargement of windows to allow for better lighting of internal living spaces. So, for what the hull is concerned, large windows replaced small portholes on the yacht sides at mid length, rising non trivial problems about longitudinal strength. The same trend appeared on superstructures sides where traditional windows have been enlarged till to become glass doors extended from deck to deck allowing passengers to enjoy full sea landscapes. Despite the positive effect on the general design performance, this nice innovation implies serious structural problems. In fact in side areas where these doors are fitted the only structural elements are represented by very slender vertical stiffeners. The combined action of bending and compressive loads, together with the fact that superstructures are usually made by aluminium light alloy, can be the cause of buckling phenomena with severe consequences on structure and glass integrity. The same aspect has a negative influence on the bending efficiency of superstructures, meaning by that the level of cooperation of superstructures with hull strength. In this paper the contribution to steel hull strength of light alloy superstructures with large openings is studied by the finite element approach. The contribution of glazing windows to the primary response to global bending moment has been assessed as well.

Shear strengthening of fire-damaged reinforced concrete beams using bolted-side plating

Abstract Six reinforced concrete (RC) beams were fabricated and exposed to fire in accordance with the international standards ISO834 temperature curve, four of which were retrofitted employing the bolted side-plating (BSP) technique. The shear tests of two control beams and four beams strengthened with BSP after fire were carried out. The influence of the plate depth and bolt spacing on the shear strength, ductility and stiffness was investigated. The testing results indicated that the BSP method can significantly increase the shear capacity of fire damaged RC beams and improve the overall shear and flexural performance. The strengthening effect increases as the increase of plate depth and the decrease of bolt spacing. When the external load is very large, local buckling of steel plate will occur under the combined action of bending and shearing. Both longitudinal and transverse slips coexist on the plate–RC interface of BSP beams. The bolt spacing exerts an important influence on the degree of partial interaction between the plate and the concrete. In the design of BSP reinforcement, the relative relation between the number of anchor bolts and the plate depth should be taken into consideration.

In-plane strength of concrete-filled steel tubular circular arches

More than 400 concrete-filled steel tubular (CFST) arch bridges have been constructed worldwide so far. However, design codes or guidance for the in-plane strength design of CFST arches are yet to be developed. In current design practice, the philosophy for the in-plane strength design of reinforced and prestressed concrete arches is widely adopted for CFST arches. For this, the CFST arches are considered under central or eccentric axial compression and are treated similarly to CFST columns, and the classical buckling load of CFST columns is used as the reference elastic buckling load of CFST arches. However, under transverse loading, the in-plane elastic buckling behaviour of CFST arches, particularly shallow CFST arches, is very different from that of CFST columns under axial compression. In addition, different from CFST columns under central or eccentric axial compression, CFST arches are subjected to significant nonlinear bending actions and transverse deformations prior to buckling and these will influence the strength of CFST arches greatly. Therefore, it is doubtful if the current method for in-plane strength design of CFST arches can provide correct strength predictions. In this paper, a method for the in-plane strength design of CFST circular arches, which is consistent with the current major design codes for steel structures, is developed by considering both geometric and material nonlinearities. A design equation for the in-plane strength capacity of CFST arches under uniform compression, and a lower-bound design equation for the in-plane strength check of CFST arches under combined actions of bending and compression are proposed.

On the stability of elastic curved bars

A general discussion about the stability of arbitrary elastic curved bars in space under combined actions of bending and twisting is given in this paper. A system of Eqs. (28)–(36) for perturbation functions near some equilibrium state is presented. With appropriate boundary conditions, the nontrivial solution corresponds to the critical state. Five examples are analysed in this paper. Some of them are new results and others are old problems treated using the new method.

7) 鉄筋コンクリート格子梁の塑性的性質について

In case we study on a reinforced concrete framework, we have to investigate on the influences of the plasticity of reinforced concrete members on the mechanical properties of that frame. It is necessary both in utilizing them in practical purpose and in clarifying the ultimate strength mechanism of a reinforced concrete frame. On this subject, some theoretical works have been carried out today, but we have very few experimental studies. In this paper, the auther investigated experimentally on the plastic mechanical properties of reinforced concrete grid-frameworks subjected to the concentrated load perpendicularly at the center of their plane. The experiments was carried out by using ⊞-type and ⊞-type models. The ultimate strength, collapse mechanism, stress distribution and deformation of the frames are examined both experimentally and theroretically. The result showed the following fundamental properties on the plastic behaviour of reinforced concrete grid-frameworks. 1. Except the torsional failure of a member of the frame takes place, ultimate strength theory based on the perfect plasticity of reinforced concrete flexural members gives almost exact answer for the ultimate strength of a reinforced concrete grid-framework, in which we must take it into account that bending bearing capacity of a reinforced concrete beam is sometimes much reduced under the combined action of bending and orstional moment together. 2. On the torsional failure of a reinforced concrete combined-stress-member of torsion and bending, it seemed that the place and the pattern of the torsional crack is governed by the existing bending cracks. As to the torsional strength of that kind of members we could not get enough data. 3. General aspect of plastic deformation and plastic stress distribution of the frame is given by applying the perfect plastic theory. 4. Rigidity reduction of a member, which is caused by cracks, sometimes causes much change of stress distribution in the frame. This rigidity reduction of a member, by one bending crack, was also observed for torsion at the same time for bending.

6 水平力をうける立体架構のLimit Analysis

There have been some studies an the limit analysis of plane framework subjected to various loading. As yet, however, little attention has been paid to that of space frame. Particularly, since the final capacity of actual structure subjected to lateral force is decided according to the entire collapse of structure, it will be necessary to treat structure as space frame. From this viewpoint, on the present paper the authors intended to study the conditions of collapse of space frame subjected to lateral force, relations between final capacity and eccentricity of lateral force, the states of stress in yield hinge, and so on. At first, the interaction curve for bending and twisting of plastic bar of circular section was obtained by means of the application of the method which P.G. Hodge used in his paper (Jour, of App. Mech. Sept. 1957), and it was shown that the curve coincides with the approximation from above according to R. Hill and M.P.I. Siebel (Jour, of Mech. and Phys. of Solid, 1953). And the equation (M/M_0)^2+(T/T_0)^2=1 being approximate to the interaction curve was adopted as yield limit of column under combined action of bending and twisting. The analysis on the final capacity of space frame subjected to lateral force was shown under the assumption that sections of all columns are circular and the floor is aufficiently rigid, and some examples were taken. As the result, the relation between the final capacity and the eccentricity of lateral force, the ratio of T/T_0 to M/M_0 in yield hinge and phases of collapse of space frame were discussed. Particularly, the fact that T/T_0 is generally negligible in the comparison with M/M_0 for the formation of yield hinge was certified. And a practical method of calculation of the final capacity was shown by means of the neglection of torsion based on the fact mentioned above.