Combined Bending Research Articles

A research on similarity law for combined ultimate bending and torsional strength

ABSTRACT As basic structural components of the ship hull, stiffened plates suffer both thrust and shear loads while ships sail in rough sea environments. In order to guide the scaled model design effectively, the similarity law is investigated in this paper. The parameters that determine the nonlinear behaviour of the stiffened plate under compression and shear loading are defined and the nonlinear similarity method is improved. This method is applied to design a scaled model under combined bending and torsional moment, and the collapse test is conducted to research the collapse characteristics. The collapse behaviour of actual ship structures under combined loads predicted by the model test is compared with that obtained by the nonlinear finite element analysis. The good agreement represents the capability of the newly improved nonlinear similarity law. The present research provides a proper way to investigate the collapse characteristics of actual ship structures through a model test.

A Critical Plane-Based Multiaxial High-Cycle Fatigue Criterion Considering Mean Stress and Phase Shift Effects for Hard Metals

Abstract Based on the critical plane method, a high-cycle fatigue criterion considering the effects of the phase shift and mean stress on multiaxial fatigue strength is proposed for hard metals. When the materials obey the von Mises criterion and are subjected to proportional loading without the mean stress, the proposed criterion can be reduced to the von Mises criterion. The experimental data conducted under combined bending and torsion loading from some studies were employed to validate the applicability of the proposed criterion. The results demonstrate that the proposed criterion has good agreement with the experimental data under loading conditions with both the mean stress and phase shift effects.

Mid-infrared integrated silicon–germanium ring resonator with high Q-factor

We report the realization of a silicon–germanium on silicon ring resonator with high Q-factor at mid-infrared wavelengths. The fabricated ring exhibits a loaded Q-factor of 236 000 at the operating wavelength of 4.18 µm. Considering the combined waveguide propagation losses and bending losses, which are measured to be below 0.2 dB/cm, even higher Q-factors could be achieved on this platform. Furthermore, our dispersion engineering of the waveguides should make these microrings suitable for nonlinear optical applications. These results pave the way for sensing applications and nonlinear optics in the mid-infrared range.

Hull Girder Ultimate Strength Analysis of 17500 LTDW Oil Tanker under the Combined Global and Local Load using Explicit Finite Element Analysis

This study investigates the hull girder’s ultimate strength of 17500 LTDW Oil Tanker. The explicit finite element analysis is carried out to estimate the hull girder longitudinal strength of the Oil Tanker. The numerical analysis starts with the longitudinal strength analyses that examine the ship’s structural response behavior due to sagging and hogging bending moment load. The structural strength analyses were conducted to determine the maximum structural response behavior for withstanding the operational load. Afterward, the hull girder’s ultimate strength is undertaken to reflect the progressive collapse behavior of the oil tanker structure under the combined global bending moment and local hydrostatic pressure load. The explicit finite element analysis is performed to estimate the ultimate strength behavior, considering the effect of the hydrostatic pressure load and the material nonlinearities. The typical 17500 LTDW oil tanker represents Indonesia’s common oil vessel that supports national fuel oil distribution. Furthermore, this study can recognize the oil tanker’s ultimate hull girder strength characteristics.

Performance of corrugated steel plate flange joint under combined compression and Bending: Experimental and numerical investigations

Prefabricated corrugated-steel-plate (CSP) structures have been increasingly applied in tunnel maintenance. In practice, the varying stiffness of bolted joints can change their mechanical characteristics and failure mechanism. This paper presents experimental and numerical investigations of the joint behavior and bending resistance of CSP flange joints under combined compression and bending forces. Full-scale tests were conducted on CSP flange joints with and without axial forces, and the deformation characteristics and failure modes were analyzed and discussed. Numerical simulations were then conducted to simulate the test joint responses and applied to conduct parametric studies. The influence of the axial force, CSP thickness, flange plate thickness, and bolt preload on bending performance was evaluated based on the test and numerical data. The results revealed that the flange joint specimen under combined axial and bending load exhibited superior integrity, less flange plate deformation, and less vertical midspan displacement, compared with the pure bending condition. An increase in the axial force, CSP thickness, and flange plate thickness greatly improved the bending stiffness of the joint, with the flange plate thickness having the greatest effect and the bolt preload having no obvious effect on the bending performance. Comprehensive structural economy and safety considerations suggested that the CSP thickness should exceed 6 mm and the flange plate thickness should be between 10 and 15 mm. Additionally, for practical purposes, a backpropagation neural network was developed. The proposed neural network model accurately and effectively predicted the joint rotation angle using the joint geometric parameters and load conditions. This paper provides a reference for the flange-joint design of corrugated-steel structures.

Influence of cyclic hardening characteristic on seismic performance of welded austenitic stainless steel H-section beam-column

Previous studies have revealed that the cyclic hardening feature of austenitic stainless steel depended on the applied strain amplitude and exhibited unsaturation prior to failure, which greatly affected the seismic response of austenitic stainless steel structures. In view of the limited research on the seismic performance and design of structural stainless steel members, this study investigates the influence of cyclic hardening characteristic on the performance of welded austenitic stainless steel H-section beam-column under combined uniaxial cyclic bending and constant compression. The finite element (FE) models of unsaturated cyclic hardening austenitic stainless steel grade S30408 beam-columns with H-section were initially created and validated with the available test data. The effects of loading history in conjunction with the axial compressive load level and the cross-section slenderness on the seismic performance of specimens were then studied through extensive parameter analysis. Results show that the capacities of load-carrying and deformation for the austenitic stainless steel member are discrete under different loading histories. Apparently, the unsaturated cyclic hardening property of stainless steel S30408 influences the performance of the member under seismic loading. Moreover, current codified design methods and the Continuous Strength Method (CSM) underestimated the ultimate strengths of stainless steel beam-columns under seismic loading. The over-strength factor and seismic deformation capacity design formulae of welded austenitic stainless steel H-section beam-columns were finally proposed.

Hook crane shape design improvement for reducing the maximum stress

The stress analysis of a hook crane submitted to some vertical static force is a simple FEM problem, approached here using SolidWorks Simulation software. Our purpose was to simulate different possibilities to slightly modify the shape of the hook crane, without adding too much material, in order to reduce the maximum stress induced in the hook. The shape design concerned here both the shape of the (transversal) cross-section and the shape of the hook longitudinal profile. The stress distribution is strongly depending on the shape of the hook crane, but it is almost independent on the hook material, since the bending mechanical stress, which is dominant in this combined bending and elongation case study, is not depending on the elastic modulus of the hook material. Obviously, the material choice is crucial from the point of view of the yield strength, usually hardened steels with increased yield strength are preferred. In what concerns the shape design improvement from the point of view of the cross-section (of equal area), our study confirmed that the trapezoidal section proposed generally in the literature corresponds to a reduced maximum induced stress. As a new result, a T-shape hook crane cross-section seems to prove better results that the trapezoidal section. To avoid stress concentrators, a combination between the trapezoidal and T-shape cross-sections has been also considered. The idea is to avoid as much as possible the discontinuity points on the outer contour of hook cross-section, since these discontinuity points are usually mechanical stress concentrators. A shape design improvement has been performed also in what concerns the longitudinal section/profile of the hook crane.

Improved fire design of steel I-sections under combined compression and bending

The fire resistance of hot-rolled and welded I-sections under combined compression and bending is numerically investigated in this study. Advanced non-linear shell models were developed and validated against existing experimental data on steady-state and transient-state tests. These models have been further used within parametric studies to gather a large cross-sectional resistance dataset. Various cross-section slenderness, section shapes, steel grades, fire temperatures and load combinations have been considered. The numerical results were used to evaluate the design rules suggested by current and upcoming European provisions, the EN 1993–1-2 and prEN 1993–1-2, respectively. It is observed that these two design recommendation sets usually lead to scattered and discontinuous resistance predictions, owing to the inappropriateness of the cross-sectional classification system and to inaccurate interaction equations. The Overall Interaction Concept (O.I.C.), which has been formerly proposed for the fire design of I-sections under axial compression or pure bending, is extended in this paper to combined compression and bending load cases and shown to yield more accurate, consistent and straightforward resistance predictions than EN 1993–1-2 and prEN 1993–1-2.

Evaluation of limit curves double corrugated profiles of arched roofs

Double corrugated profiles made of thin sheet metal are susceptible to loss of local stability and their shapes exclude the possibility of applying design standards. Arch structures made of these profiles can have a different state of combined axial force and bending moment. Previous scientific research allowed the identification of the load carrying capacity and stability only for selected axial force parameters. The article presents the distribution of the interaction between the bending moment and the axial force, allowing the evaluation of the load-carrying capacity within the entire for static forces. Limit curves were developed using parametrised non-linear numerical analyses. Ansys software and the digital copy of the test model were used for the analysis. Limit curves were generated for two grades of steel and six thicknesses of sheet metal. In addition to the envelope, the limits for the elastic range, the pre-buckling elastoplastic range, and the post-buckling plastic range were estimated. The results are summarised in diagrams and tables.

Bearing capacities of single piles under combined HM loading near slopes

Piles are widely used to transfer the horizontal load of high-rise buildings, transmission towers, and bridges, especially for superstructures constructed near slopes. This study investigated bearing capacities of single piles under the combined horizontal force (H) and bending moment (M) for the pile in sloping ground. A 3D finite element model was proposed to simulate the non-linear pile–soil interaction and was verified by a model test. A series of numerical tests were conducted to obtain the failure envelope of bearing capacities of single piles under various combinations of H and M. The existence of slopes significantly reduced the bearing capacity of piles, especially when the horizontal and rotational displacements moved to the dip direction of the slope. An oblique ellipse was able to describe the failure envelope of bearing capacities of single piles near slopes in the HM plane. As the pile was installed away from the crest of the slope, both the width and height of the ellipse increased and the center of the ellipse was approaching the origin. The results of this article can provide useful references for designing horizontally loaded piles near slopes.

Analytical investigation on the buckling of cylindrical shells under combined non-uniform axial compression and external pressure

This paper focuses on the buckling problem of cylindrical shells under combined non-uniform axial compression and external pressure. To obtain buckling loads, a completely new method called two-parameter perturbation method is established. Using this method, governing differential equations are solved and buckling loads expressed by load functions, load parameters, and shell dimensions are derived for the first time. Comparative studies show that buckling loads by the analytical formulas coincide with those for combined uniform loads or single wind load in literatures. Buckling of a cylinder subjected to combined bending and wind loads is analyzed, and confirmed by the Galerkin method for the case of small load variations. Therefore, the presented formulas are adequately validated. The numerical calculations are carried out to analyze the effects of non-uniform load parameters on buckling load coefficient. The obtained results in this paper can be applied to evaluate buckling loads for cylinders subjected to combined non-uniform loads in actual engineering.

Predicting the yield surface in a two-dimensional stress system: A student's laboratory experiment

This paper is concerned with the determination of the yield surface in a two-dimensional stress field within an undergraduate Mechanics of Materials student laboratory experiment. In this experiment, the two-dimensional stress field is obtained by subjecting a steel specimen to a combined bending and torsion load. The motivation for the paper was the lack of correlation between the von Mises and Tresca yield criteria and the principal stresses calculated at the load at which students were predicting material yielding. The latter yield loci were based on the uniaxial 0.2% proof stress. The lack of correlation was creating a lot of frustration amongst students. This is undesirable, especially within an undergraduate student experiment. Two hypotheses for the lack of agreement were considered. The first hypothesis was the uncertainty involved in the method that the students were using to predict the onset of material yielding. The second hypothesis was that the specimens being used for the experiment had anisotropic properties, given that little information on their manufacture was provided. The need for determining accurate yield stress values and on methodologies found in literature that are used to determine the material proof stress or lower yield stress in a uniaxial tensile test are discussed. Four methods taken from literature are used and adapted to detect the first yield of the specimen under a combined bending and torsional load. The resulting experimentally yield loci are compared with the theoretical von Mises and Tresca isotropic yield loci over half of the second quadrant of the two-dimensional principal stress field plot. Correlation between the four methods was quite good but not so when compared with the von Mises and Tresca’ loci. A lack of correlation occurred for an increasing torsional load indicating a possible anisotropy in the material properties. These results hinted towards the second hypothesis. A number of tensile test specimens were hence heat treated so as to induce isotropy in the material properties. The combined loading experiments were repeated using the heat-treated samples. A very good correlation was obtained between the experimental yield points for the two-dimensional stress field and the von Mises and Tresca yield loci. This good correlation for the heat-treated specimens confirmed the authors’ second hypothesis on the anisotropic properties in the as-received state and, therefore, the requirement to heat treat the specimens for a meaningful student undergraduate laboratory activity.

Cross-section resistance and design of stainless steel CHS and EHS at elevated temperatures

The structural behaviour and design of stainless steel circular hollow sections (CHS) and elliptical hollow sections (EHS) at elevated temperatures are investigated in this paper. Shell finite element models of stainless steel CHS and EHS are created and validated against experimental results from the literature, which are subsequently used to generate benchmark structural performance data. Parametric studies are performed on a large number of cold-formed and hot-rolled austenitic, duplex and ferritic stainless steel CHS and EHS subjected to (i) pure axial compression, (ii) pure bending, (iii) combined axial compression and bending and (iv) combined bending and shear at elevated temperatures; the studied cases comprise 24,495 stainless steel CHS and EHS in fire and cover a wide range of cross-section slendernesses and elevated temperature levels. Calibrated against the benchmark structural performance data obtained from the numerical parametric studies, new design proposals for predicting the cross-section resistances of stainless steel CHS and EHS in fire are put forward. The accuracy, safety and reliability of the new design proposals are assessed. It is shown that in comparison to the design provisions of the European structural steel fire design standard EN 1993-1-2, the proposed design methods provide more accurate and safe-sided cross-section resistance predictions for stainless steel CHS and EHS at elevated temperatures.

Experimental Investigation of the Tensile Properties with Bending of CFRP Tendons in Suspension Bridges

Carbon-fiber-reinforced polymer (CFRP) has gradually become a new material to replace traditional steel due to its outstanding advantages. Because of its poor transverse stress performance, there is a reduction effect on the tensile strength in the bending state. To study the mechanical properties of CFRP tendons subjected to combined tension and bending at the saddle of a suspension bridge, a series of bond-type anchorages were made. Specimens with different diameters of CFRP tendons were tensioned on the device with different bending radius saddles. The test results revealed that the tensile properties were significantly affected by the severity of the bending of the CFRP tendons, including the failure mode, fracture force, and stress distribution. The highest reduction in fracture force was found at the bending radius of 3 m, of up to 38.05%. Furthermore, the tensile properties were also found to be influenced by the diameter of CFRP tendons. It was found that increasing the bending radius was more conducive to improving the performance of CFRP tendons with a smaller diameter. When the bending radius increased from 3 to 12 m, the efficiency coefficient (the ratio of the fracture force to the ultimate force) of D8, D10, and D14 increased by 11.21%, 7.74%, and 2.26%, respectively. Decreasing the bending radius leads to unevenness of the stress distribution and increasing the diameter of the CFRP tendon leads to brittleness and difficulties in anchoring, thus resulting in the decrease in the efficiency coefficient. In addition, the ratio of the bending radius to the tendon diameter was less than 2.4, the efficiency coefficient of the specimen was less than 80%, and the specimen mostly suffered shear failure. Furthermore, the finite element (FE) models validated by the test results were used to reveal the stress state and study the effect of contact friction on the properties of CFRP tendons. The FE results show that the CFRP tendons with a smaller bending radius presented higher shear stress concentrations. As the contact friction increased, the load-bearing capacity of CFRP tendons decreased significantly.

Numerical Investigation of Axial Force–Bending Moment Interaction for FRP-Confined Reinforced Concrete Columns with Internal Steel Transverse Reinforcement

Externally bonded fiber-reinforced polymer (FRP) laminates are widely used in the retrofitting and rehabilitation of reinforced concrete (RC) columns because they can increase the axial and bending moment capacities of these columns through a confinement mechanism. The confinement produced by FRP laminates acts in addition to that exerted by the internal transverse steel, although the latter is often neglected in current design standards and guidelines. In this study, a recently developed FRP-and-steel-confined concrete constitutive model was employed to numerically investigate the axial force–bending moment interaction for FRP-confined RC columns modeled using finite-element (FE) analysis. The proposed model was first validated against experimental data available in the literature and then used to quantify, through an extensive parametric study, the effects of transverse steel confinement, FRP strength, FRP stiffness, FRP reinforcement ratio, column diameter, concrete compressive strength, and load eccentricity ratio on the strength of FRP-confined RC columns subject to combined axial compression and bending moment. It was found that the internal steel confinement can substantially enhance the strength of these columns, especially for low concrete compressive strengths, large cross sections, and small eccentricities. When design code provisions limiting concrete and FRP deformations were considered for eccentrically loaded columns, the contribution of the steel confinement increased for increasing FRP reinforcement ratio. Based on the parametric study results, this investigation proposed an extension to eccentric axial compression of two relative confinement coefficients, which were previously developed to describe the contribution of transverse steel confinement to the peak strength of FRP-confined RC columns subject to pure compression.

Behavior and modeling of large-scale concrete-filled FRP tubes with longitudinal steel rebars under lateral impact loading

Fiber-reinforced polymer (FRP) has been utilized extensively as a confining material for concrete in civil engineering. Concrete-filled FRP tubes (CFFTs), consisting of a FRP tube, a concrete core and optional longitudinal rebars, are particularly attractive to be used as bridge piers in harsh environments. Most studies on CFFTs have been focused on their behaviors under static loading conditions. To extend existing studies, three identical large-scale CFFTs with longitudinal steel rebars (SR-CFFTs) were investigated experimentally, two of which were tested under lateral impact loading and one was under lateral static loading. To compare the confining behavior between FRP tube and steel stirrups, three identical large-scale reinforced concrete (RC) columns with approximately the same hoop confinement stiffness as SR-CFFTs (i.e., steel stirrups for RC columns, FRP tube for SR-CFFTs) were tested as companion specimens. The test results indicated that, (1) under lateral static loading, the RC column failed with a shear-failure manner, while the SR-CFFT specimen failed with combined bending and shear failure characteristics; (2) under lateral impact loading, the shear-dominant failure mechanism was evident for RC columns, while the failure mechanism of SR-CFFTs was flexural-dominant owing to the effective hoop confinement provided by FRP; (3) under the same impacting velocity, the SR-CFFT specimen had much less damage and much less lateral displacement than the corresponding RC column. The established FE models could provide reasonably accurate predictions for the dynamic behaviors, the impact force–time history curves and the column deformations for both RC columns and SR-CFFTs. Parameter studies were conducted to analyze the effects of the concrete strength, the longitudinal steel ratio, the impact velocity and the impact mass.

Investigation of the quality category approach for BS7910-based rapid fatigue assessment of welded structures containing cracks

PurposeThis study aims to extend the application of the quality category approach in rapid fatigue assessment of complex welded structures containing defects under arbitrary loadings, following the investigation of their core data and fatigue assessment procedures based on fracture mechanics.Design/methodology/approachThe analysis methods and procedures for calculating equivalent sizes of semi-elliptic cracks and initial sizes of through-width cracks at the weld toe were developed based on the life equivalence principle. Different stress concentration solutions, i.e. 2D-Mk and 3D-Mk solutions, and different bending ratios were considered. Then, approximate equations were proposed to calculate the crack size under combined stress. In addition, a procedure for calculating the fatigue life by interpolation was proposed and applied to engineering examples.FindingsThe fatigue lives of fillet and butt weld joints obtained with the 3D-Mk solution for large L/B are longer than those obtained with the 2D-Mk solution. The results of the fatigue life of the brake unit bracket show that the average error between the proposed approximation equations and the quality category approach is 1.6%.Originality/valueThe quality category and equivalent size curves of different stress concentration solutions under combined membrane and bending stresses are newly added, which further expands the application of the quality category approach. When the proposed fatigue life calculation methods are employed, the remaining life can be quickly derived in addition to the qualitative conclusion on the safety of the structure. These provide the necessary conditions to perform a rapid fatigue assessment adapted to engineering purposes.

Predicting Failure of Additively Manufactured Specimens with Holes

Experimental and computational studies were conducted to predict failure loads of specimens containing different-sized holes made using the additive manufacturing (AM) technique. Two different types of test specimens were prepared. Flat specimens, manufactured from polylactic acid (PLA), were subjected to uniaxial loading. Tubular specimens, made of polycarbonate (PC), were subjected to combined loading that was applied using uniaxial testing equipment. Test specimens were uniquely designed and printed to apply the combined bending and torsional loads to tubular specimens. A newly developed failure theory was applied to predict the loads that would result in the fracture of these test specimens. This theory is composed of two conditions related to stress and the stress gradient to be simultaneously satisfied to predict failure. The failure loads predicted using the new failure criteria were compared closely with the experimental data for all test specimens. In addition, a semi-empirical equation was developed to predict the critical failure surface energy for different printing angles. The critical failure surface energy is a material property and is used for the stress gradient condition. Using the semi-empirically determined values for the failure criterion provided close agreement with experimental results.

Design of a novel 2D ultrasonic transducer for 2D high-frequency vibration–assisted micro-machining

Ultrasonic vibration–assisted machining (VAM) is a process in which a tool or workpiece is vibrated using ultrasonic frequency small-amplitude vibrations to improve cutting performance, and an ultrasonic transducer usually generates these vibrations. This study investigates how two-dimensional vibrations are generated using axially polled piezoceramics. Modifying the wave propagation in geometric ways by creating a notch at the front mass, the longitudinal response excited by the axially polled piezoceramic discs can be converted into combined longitudinal and bending vibrations at the transducer front mass. Finite element analysis (FEA) software COMSOL is used to study wave propagation, and ANSYS is used to optimize the transducer’s mechanical structure, while an equivalent circuit approach is used to analyze the electrical impedance spectra and confirm its resonance frequency. An experimental analysis of impedance response and amplitude of generated vibrations using the novel 2D ultrasonic transducer is conducted to validate the numerical and analytical results, which shows that resonance frequency results are in very good agreement with the theoretical model. Finally, the proposed design is validated by preliminary test results that demonstrate its performance and principles.

More accurate design equations for cold-formed steel members subjected to combined axial compressive load and bending

Cold-formed steel (CFS) load-bearing members in multi-storey frame systems are subjected to combined actions sourced from gravity and lateral loads. However, limited information is available on the complex interaction behaviour of such elements affected by different buckling modes. This study aims to provide a better understanding of the behaviour and design of CFS sections under various combinations of compression and bending about both major- and minor-axes. Experimentally validated finite element (FE) models of CFS elements were developed in ABAQUS software, accounting for material nonlinearity and geometric imperfections. The validated models were then used to conduct a parametric study to assess the structural performance and failure modes of over 500 CFS elements with various lengths, thicknesses and cross-sectional dimensions under 19 different load eccentricities. It was demonstrated that the element and web slenderness ratios and the magnitude and direction of eccentricity are the key factors affecting the behaviour of the CFS beam–column elements. The accuracy of current design specifications, including American Iron and Steel Institute (AISI-S100), Australian/New Zealand Standard (AS/NZS-4600) and European standard (Eurocode-3) was then investigated. Subsequently, the results were used to propose a new design interaction equation as a function of element and web slenderness ratios. It was shown that the proposed equation could considerably improve the accuracy of the code strength predictions, especially in the case of medium to high slenderness elements. Finally, a reliability analysis was conducted within the framework of the AISI-S100 to ensure that the proposed design equation provides the required level of safety.