Combined Bending Research Articles

Nonlinear Isogeometric Analyses of Instabilities in Thin Elastic Shells Exhibiting Combined Bending and Stretching

Abstract Thin structures like shells are highly susceptible to mechanical instabilities. They can undergo large nonlinear elastic deformations while exhibiting combined bending and stretching modes of deformation. Here, we propose a new displacement-based finite element (FE) formulation based on the isogeometric discretization of Koiter’s nonlinear shell theory and use of the method of dynamic relaxation (DR) to solve equilibrium configurations of problems involving fine-scale and hierarchical wrinkling and buckling. No imperfection seeding is required to trigger instabilities. The use of the NURBS basis provides a rotation-free, conforming, higher-order spatial continuity such that curvatures and membrane strains can be computed directly from interpolating the position vectors of the control points using spatial finite differences. The pseudo-dissipative FE dynamical system is updated through explicit time integration and made scalable for parallel computing using a message passing interface (MPI). The proposed FE method is successfully benchmarked against several numerical and experimental results.

Application of ANN Concepts for Prediction of Crack Growth and Remaining Life of Circumferentially Cracked Piping Components under Different Loading Scenarios

This paper presents the details of Artificial Neural Network (ANN) based models to predict crack depth and remaining life of circumferentially part-through cracked piping components used in the nuclear industry. Crack growth data from experimental studies on (i) straight pipes made up of SA 312 Type 304LN stainless steel having part-through circumferential notch under combined bending and torsion and (ii) dissimilar metal pipe weld joints having circumferential through-wall crack in the weld were used. The dissimilar metal pipe weld joint is made up of SA312 Type 304LN austenitic stainless steel and SA508 Gr. 3 Cl. 1 low alloy carbon steel and joined by Nickel-rich Inconel alloy weld. About 75% of the mixed experimental data has been used for development of model and the remaining data for validation. For the development of ANN model, (i) back propagation technique (ii) sigmoidal transfer functions and (iii) Levenberg-Marquardt algorithm are used. The maximum percentage difference observed between the predicted and the experimental results for crack depth and remaining life was 19.59% and 15.78% respectively. The efficiency of the developed model was verified using several statistical parameters. The developed models are useful for the structural integrity assessment of piping components under different loading scenarios.

Calculating shear lag in steel-concrete composite beams under combined compression and bending

Long and complex composite steel-concrete structures are becoming common, requiring a deep understanding of the effects induced by the simultaneous action of axial forces and bending. In fact, the axial force generated, for instance, by cable inclination in cable-supported structures can modify the stress distribution within the elements compared to bending scenarios, thereby necessitating a revision of the effective width to be utilized. Nonetheless, current design codes, including Eurocode specifications and others, lack provisions for addressing the combined effects of axial force and bending, as they are exclusively tailored for bending. This limitation can introduce design complexities, necessitating the implementation of intricate Finite Element (FE) models, which impose substantial computational loads and design efforts. The methodology proposed in this paper overcomes these challenges allowing to assess the stress distribution and resistance of composite deck at Serviceability Limit State (SLS) and Ultimate Limit States (ULS) by leveraging results obtained from standard beam models typically used by structural designers or practitioners. A comprehensive parametric analysis using nonlinear finite element models is performed to validate the developed methodology. A comparison with the Eurocode 4 formulations highlights that the proposed method provides superior accuracy in estimating peak stress in concrete slabs under combined compression and bending. Additionally, it facilitates straightforward verification at the ULS in compliance with Eurocode requirements.

Numerical analysis of flexural behaviour of UHPC-CFTS columns as enclosure supports for electrical substations

Abstract This study establishes a finite element analysis model of ultra-high-performance concrete (UHPC) encased concrete filled steel tube (CFST) composite columns under combined compression and bending. Appropriate constitutive models and element types are selected as the basis. The finite element model simulates the test results of steel-concrete composite columns, and the applicability of the model is verified by comparison with existing test data of UHPC encased CFSTs. On the basis of demonstrating model reliability, the full-range load-deformation curves of UHPC encased CFSTs with different concrete strengths under compression-bending are compared. The failure modes and material stress distributions are analyzed to elucidate the influence mechanism of the UHPC on the flexural performance of UHPC encased CFSTs under combined compression and bending. The results show that compared to normal concrete, UHPC can effectively improve the flexural capacity of UHPC encased CFST columns. Owing to the addition of steel fibers, the failure mode of UHPC encased CFSTs under combined compression and bending is more integral compared to normal concrete. The research results of this study can provide references for the performance evaluation and design of UHPC encased CFSTs in the structural enclosures for electrical equipment in high/low voltage substations.

Osteoking prevents bone loss and enhances osteoblastic bone formation by modulating the AGEs/IGF-1/β-catenin/OPG pathway in type 2 diabetic db/db mice.

Type 2 diabetic osteoporosis (T2DOP) is a skeletal metabolic syndrome characterized by impaired bone remodeling due to type 2 diabetes mellitus, and there are drawbacks in the present treatment. Osteoking (OK) is widely used for treating fractures and femoral head necrosis. However, OK is seldom reported in the field of T2DOP, and its role and mechanism of action need to be elucidated. Consequently, this study investigated whether OK improves bone remodeling and the mechanisms of diabetes-induced injury. We used db/db mice as a T2DOP model and stimulated MC3T3-E1 cells (osteoblast cell line) with high glucose (HG, 50 mM) and advanced glycation end products (AGEs, 100 µg/mL), respectively. The effect of OK on T2DOP was assessed using a combined 3-point mechanical bending test, hematoxylin and eosin staining, and enzyme-linked immunosorbent assay. The effect of OK on enhancing MC3T3-E1 cell differentiation and mineralization under HG and AGEs conditions was assessed by an alkaline phosphatase activity assay and alizarin red S staining. The AGEs/insulin-like growth factor-1(IGF-1)/β-catenin/osteoprotegerin (OPG) pathway-associated protein levels were assayed by western blot analysis and immunohistochemical staining. We found that OK reduced hyperglycemia, attenuated bone damage, repaired bone remodeling, increased tibial and femoral IGF-1, β-catenin, and OPG expression, and decreased receptor activator of nuclear kappa B ligand and receptor activator of nuclear kappa B expression in db/db mice. Moreover, OK promoted the differentiation and mineralization of MC3T3-E1 cells under HG and AGEs conditions, respectively, and regulated the levels of AGEs/IGF-1/β-catenin/OPG pathway-associated proteins. In conclusion, our results suggest that OK may lower blood glucose, alleviate bone damage, and attenuate T2DOP, in part through activation of the AGEs/IGF-1/β-catenin/OPG pathway.

Extension of the GISSMO fracture model for thin-walled structures under combined tensile and bending loads

Ductile fracture prediction for thin-walled structures requires computationally efficient simulation tools able to approximately represent the key effects that occur on the sub-thickness scale. Unfortunately, classical shell elements, typically used to model deformation and failure of thin components, are inherently in a state of plane stress and therefore unable to capture the through-thickness stress distribution. This is consequential considering recent studies that demonstrated the differences between fracture in bending vs. in-plane tension. A laterally constrained thin metal plate under in-plane tension is likely to fracture under significantly lower plastic strain than the same plate under bending (with fracture initiating on the tensile side), even though both these conditions are examples of plane strain tension. Under in-plane tension fracture is preceded by a through-thickness neck, and therefore higher stress triaxiality than in the case of plane strain bending, where necking is absent. To account for these differences, we propose an extension of the GISSMO model, which relies on a simple fracture criterion based on stress-dependent fracture strain defined by the user (i.e. fracture locus). The fracture strain is typically determined experimentally using a combination of in-plane tensile tests under varying degree of lateral constraint and shear tests. The proposed extension involves defining a separate fracture locus for bending, also determined experimentally using bending tests. Fracture occurs when the equivalent plastic strain reaches its critical level represented by interpolation between the two bounding cases, i.e. bending and in-plane tension, with a bending index Ω used as an interpolation parameter.

A study of the effect of coconut fiber on reinforced concrete beams subjected to combined bending and shear

This review paper examines the impact of coconut fiber reinforcement on the behavior of reinforced concrete beams subjected to combined bending and shear. Coconut fibers, also known as coir fibers, are a sustainable and cost-effective alternative to traditional steel reinforcement. The use of coconut fibers in concrete has shown promise in enhancing the ductility, energy absorption capacity, fracture resistance, and durability of concrete structures. The study highlights the mechanical properties and applications of coconut fiber reinforced concrete (CFRC) and investigates the effects of varying fiber content on concrete performance. Factors affecting the properties of fiber-reinforced concrete, such as the relative fiber matrix index, volume of fibers, aspect ratio of fibers, fiber orientation, workability, compaction, size of coarse aggregate, and mixing techniques, are also discussed. Understanding these factors is crucial for designing and constructing durable and sustainable concrete structures.

Effect of Residual Stresses on the Fatigue Stress Range of a Pre-Deformed Stainless Steel AISI 316L Exposed to Combined Loading

AISI 316L austenitic stainless steel is utilized in various processing industries, due to its abrasion resistance, corrosion resistance, and excellent properties over a wide temperature range. The physical and mechanical properties of a material change during the manufacturing process and plastic deformation, e.g., bending. During the combined tensile and bending loading of a structural component, the stress state changes due to the residual stresses and the loading range. To characterize the component’s stress state, the billet was bent to induce residual stress, but a phase transformation to martensite also occurred. The bent billet was subjected to combined tensile–bending and fatigue loading. The experimentally measured the load vs. displacement of the bent billet was compared with the numerical simulations. The results showed that during fatigue loading of the bent billet, both the initial stress state at the critical point and the stress state during the dynamic loading itself must be considered. Analysis was demonstrated only for one single critical point on the surface of the bent billet. The residual stresses due to the phase transformation of austenite to martensite affected the range and ratio of stress. The model for the stress–strain behaviour of the material was established by comparing the experimentally and numerically obtained load vs. displacement curves. Based on the description of the stress–strain behaviour of the pre-deformed material, guidelines have been provided for reducing residual tensile stresses in pre-deformed structural components.

Mechanical behavior of prestressed UHPC wind turbine tower columns under combined axial compression and bending

Mechanical behavior of prestressed <scp>UHPC</scp> wind turbine tower columns under combined axial compression and bending

Stress relaxation assessment of high-temperature bolts under combined biaxial loads: Theory and simulation

Estimating bolt stress within high-temperature bolted connection systems is crucial for determining bolt preload and assessing bolt assembly integrity. This work proposes a theoretical model for estimating high-temperature bolt load under combined tension, bending, torque, and shear loads, considering the characteristics of bolt stress distribution and relaxation. To assess the model's accuracy, finite element analysis was employed to examine the impact of various creep parameters and load combinations on bolt stress relaxation. The results indicate that the introduction of bending moments, torque, and shear loads accelerates axial stress relaxation in bolts. Under a high-temperature load for 300,000 h, the stress relaxation predicted by the theoretical model aligns well with the results from finite element analysis.

Analytical model for flexural-torsional coupling behavior of prestressed corrugated steel-concrete composite girders

Prestressed corrugated steel-concrete (PCSC) composite girders are often subjected to combined bending and torsion in practice, but the existing theoretical models have mainly focused on pure torsional behavior. Thus, this paper proposed a modified combined action softened truss model (MCA-STM) to predict the flexural-torsional coupling behavior and failure modes of PCSC composite girders. The equivalent loading and nonlinear equations were modified, and the convergence criteria of flexural and torsional failure were established, considering the structural characteristics of PCSC composite girders. A new optimized algorithm was employed to solve the MCA-STM, providing a more efficient and numerically stable solution procedure. A 3D finite element analysis (FEA) model of the PCSC composite girder was established, which was verified by comparing the available test results. A parametric study was carried out based on the verified FEA model to get more datasets with various parameters, and the results were compared to the proposed analytical model. The curves obtained by the FEA and MCA-STM are in good agreement, indicating that the proposed analytical model can predict the full flexural-torsional coupling behavior and failure modes of the PCSC composite girders.

FGM concept used in damage analysis of heat-treated elbows under out-of-plane combined bending moment

The elbow is presented in pressurized tubular structures as a connecting element, generally subjected to bending moments either out-of-plane or in-plane, in closure or opening. Another mode of bending moment that can also occur in these tubular structures is the combined bending moment between out-of-plane and in-plane in closure, or out-of-plane and in-plane in opening. In this work, to better present the potential severity caused by this loading mode, an elbow structure attached by straight tubular sections made of X60 steel is analyzed and its damage under this combined bending moment with orientations between the plane and out-of-plane of the structure is discussed. A reinforcement proposal will be made in the second part of this work. Indeed, the structure is pretreated thermally at the elbow, resulting in a graded structure along the thickness with two different material constituents: the base metal and the thermally affected zone (HAZ). Based on the concept of Functionally Graded Materials (FGM), the gradation is by volume fraction between the base metal and the HAZ, following a power law function of a volume fraction index (n). This graded property is introduced along the thickness by finite element layers. The elastic-plastic behavior of the HAZ-base metal mixture is modeled using the Voce model and the Von Mises equivalent stress flow theory. Using the XFEM technique(extended finite element method), the damage of the pressurized and thermally treated structure under a combined out-of-plane bending moment shows that these parameters condition the response and the level of damage.

Ultimate strength of multi-ring-stiffened tube-gusset joints with dual-function stiffeners under combined bending and compressive loads

Tube-gusset (TG) joints play a crucial role in connecting crossarm chords to tower bodies in steel-pipe power transmission towers, bearing the highest loads in the entire tower structure. This study investigated TG joints with five-ring stiffeners under combined bending and compressive loads, using the middle stiffener plate as the connecting plate. Through experimental studies, numerical simulations, and theoretical analyses, insights were obtained into the failure mechanism and mechanical characteristics of TG joints. This study identifies the key factors influencing the ultimate strength of TG joints under combined bending and compressive loads and proposes a method for determining the joint bearing capacity. Notably, the mechanical performance of multi-ring-stiffened tube-gusset joints was minimally affected by the initial geometric defects under combined compression and bending moments. The load exerted on the gusset plate was primarily supported by the stiffeners, with the gusset plate demonstrating minimal bending deformation, owing to its substantial in-plane stiffness. Consequently, the gusset plate underwent an overall rotation or translation under the combined effects of compression and the bending moment. The proposed method accurately predicted the joint bearing capacity, ensuring the safety of TG joints. These findings provide valuable insights into the meticulous design of joints in steel-pipe transmission towers, thereby ensuring the safety and stability of transmission lines in the field of civil engineering.

Damage investigation in steel pipe under pressure and combined bending moment: Application in structure connected by elbow and reduced tee

Steel tubular structures in pipelines, or those connections such as concentric reductions, reduced tees, and elbows, all differ in their response to loading, they are sometimes solicited to complex and combined loads, which accumulate with the internal pressure to their solicitation cause in certain situation their damage, the objective in this analysis is to numerically predict the mechanical behavior until damage of a complete tubular structure, which contains the connecting elements of an elbow and a reduced tee attached to each other by straight tubular parts, this structure, by its standardized dimensions presents a real design of a main pipeline spigot for a possible supply line, this tubular structure is analyzed in this work under these real pressure conditions, and combined loads probably coming from the weight of a valve, or a pipe flanged to this spigot element or other, in X60 steel This structure is solicited under different combined modes of loading. The elastic-plastic behavior is under Voce’s model and Von Mises’ equivalent stress flow theory, the damage of the structure by crack initiation and propagation is ensured by using the XFEM technique, the response up to damage of the structure is evaluated under the effect of the parameters of the combined loading mode, we present by angular bendingrotation moment curves that these parameters clearly condition the response and the level of damage.

Testing and design methods for high-strength aluminium alloy CHS members under combined axial compression and bending

The overall buckling behaviour of 7A04-T6 high-strength aluminium alloy circular hollow section (CHS) members subjected to combined compression and bending were investigated in this paper. Eight CHS beam-columns with two section wall thickness of 7.5 mm and 15 mm were tested, with the mechanical properties, initial geometric imperfections, failure modes and stability capacity of the specimens analyzed. The experimental findings were utilized in simulation analysis to verify the finite element (FE) model. Following this, a detailed parametric study including 486 numerical results was performed, with the variable parameters of section diameter to thickness ratio, member relative slenderness ratio and eccentricity. The experimental results and FE results were employed to assess the applicability of the existing design recommendations in European, Chinese, and American specifications for calculating the stability capacity of extruded 7A04-T6 high-strength aluminium alloy CHS beam-columns. The findings indicated that the three standards were not accurate in predicting the stability capacity of the CHS beam-columns, among which the European and American codified predictions were sometimes unsafe and much more discrete, and the Chinese code was too conservative by 35 %. Lastly, within the framework of the three standards evaluated in this paper, a approach of modifying the interaction buckling factors was proposed to improve the accuracy and consistency of the stability capacity predictions of 7A04-T6 high-strength aluminium alloy CHS beam-columns, which was also safe to some extent.

Failure envelopes of rigid tripod pile foundation under combined vertical-horizontal-moment loadings in clay

The problem considered in this computational study is for the bearing capacity determination of three-dimensional (3D) rigid tripod-pile groups subjected to combined vertical (V), horizontal (H), and bending moment (M) loads. Using the adaptive 3D finite element limit analysis (FELA) coupled with lower bound, upper bound and mixed Gauss element formulations, numerical results are compared with those of the previous study under a single-component loading (V, or H, or M). The failure envelope in the 3D V–H–M loading space is then constructed, and several failure mechanisms presented to complement the discussions on the complex 3D responses. This is followed by a parametric study for the various factors such as the pile length, pile spacing, pile-soil adhesion factors as well as the loading direction angle. Finally, a closed-form design expression of failure envelopes considering the abovementioned influential parameters and the combined load are derived. Noting that the current industry-based design procedures for tripod-pile groups are rarely found, the outcome of the present study can be used with great confidence in design practice.

Post-fire behavior and residual resistances of S890 ultra-high strength steel circular hollow sections under combined compression and bending

This paper presents experimental and numerical investigations into the post-fire local buckling behavior and residual resistances of S890 ultra-high strength steel (UHSS) circular hollow section (CHS) under combined compression and bending. The physical testing was firstly conducted and encompassed heating, soaking and cooling of specimens, as well as post-fire tensile coupon tests, measurements of initial local geometric imperfections and eccentrically loaded stub column tests. Then, finite element models were developed and validated with reference to the experimental observations and then adopted for parametric analyses to derive additional numerical data, considering various cross-section dimensions and loading combinations. As a result of the lack of design provisions for ultra-high strength steel structures after exposure to elevated temperatures, the applicability of the relevant ambient temperature design interactive curves given in the current European, American and Australian standards to post-fire S890 UHSS CHS under combined compression and bending was assessed, with post-fire material properties used. The assessment results showed that all design standards exhibited conservative and scattered predictions of residual resistances for S890 UHSS CHS under combined compression and bending at ambient temperature and after exposure to elevated temperatures. The American specification provided more precise predictions of residual failure loads for non-compact and slender (Class 3 and 4) sections than the Eurocode and Australian standard, due to the accurate compression and bending endpoints. In comparison to the American and Australian specifications, the Eurocode resulted in more precise results in predicting residual failure loads of compact (Class 1 and 2) sections, owing to the accurate compression and bending endpoints as well as the nonlinear design interaction curve.

Structural behaviour and design of cold-formed austenitic stainless steel flat-oval hollow section beam-columns

This paper presents experimental and numerical investigations into the global buckling behaviour and resistances of cold-formed austenitic stainless steel flat-oval hollow section beam-columns under combined compression and bending. A testing programme, including initial geometric imperfection measurements and ten beam-column tests about the cross-section major and minor principal axes, was firstly conducted. The key obtained test results, including failure loads, load–deformation histories and failure modes, were reported. Following the testing programme, a numerical modelling programme was performed, with finite element models developed to simulate the beam-column test results and then used to conduct parametric studies for generating additional numerical data. Then, the applicability of relevant codified design interaction curves to cold-formed austenitic stainless steel flat-oval hollow section beam-columns was evaluated based on the test and numerical data. The evaluation results revealed that the design interaction curve of the American specification resulted in an overall good level of design accuracy and consistency, while the design interaction curve of the European code led to slightly conservative resistance predictions, mainly due to the conservative bending end point. To address this shortcoming, a revised Eurocode design interaction curve with an improved bending end point was proposed and shown to provide more accurate resistance predictions for cold-formed austenitic stainless steel flat-oval hollow section beam-columns than the original Eurocode design interaction curve.

Finite element modeling and injury criteria investigation for the lower leg of the Chinese human body under impact loads

The widely used human body injury criteria were established based on the biomechanical response of the Euro-American human body, without considering the difference in the body anthropometry and injury characteristics among different races, particularly the Chinese human body that has the smaller body size. The absence of such race specific design considerations negatively influences the injury prevention capability for these populations, and weakens the applicability of injury criteria. To resolve these issues, this study aim to develop a lower leg finite element model of a 50th percentile Chinese male. The model is built based on the medical images of an average size Chinese male with detailed ankle ligaments and lower leg muscles modeled. Sixty experiments available in the literature are used to validate its biofidelity. Using the validated model, the lower leg model is subjected to combined axial compression and bending loads to evaluate its injury criteria. Compared with a typical Euro-American human body mode, the Chinese lower leg presents lowered mechanical tolerance, and the revised tibia index may be an option to be the injury criteria for the Chinese lower leg. Additionally, the validated model reproduces the pedestrian lower leg fracture in a domestic accident.

Scale modeling of thermo-structural fire tests of multi-orientation wood laminates

The stacking sequence of laminated wood significantly impacts the composite mechanical behavior of the material, especially when scaling down thermo-mechanical tests on plywood. In previous research, we developed a scaling methodology for thermo-structural tests on samples with similar cross sections, however this paper focused on testing plywood samples with different stacking sequences between the scales. Plywood samples at ½-scale and ¼-scale were subjected to combined bending and thermal loading, with the loading scaled to have the same initial static bending stresses. While the ¼-scale 4-layer [0°/90°]s laminate and the ½-scale 8-layer [0°/90°/90°/0°]s laminate had an equal number of 0° and 90° layers, as the char front progresses, the sections behave differently. Thus, modeling becomes essential to extrapolating the data from the smaller ¼-scale test to predict the behavior of the larger ½-scale test. Reduced cross-sectional area models (RCAM) incorporating classical laminated plate theory were used to predict the mechanical response of the composite samples as the char front increased. Three methods were proposed for calibrating the RCAM models: Fourier number scaling, from detailed kinetics-based pyrolysis GPyro models, and fitting to data from fire exposure thermal response tests. The models calibrated with the experimental char measurements produced the most accurate predictions. The experimental char models validated to predict the behavior of the ¼-scale tests within 2.5%, were then able to predict the ½-scale test behavior within 4.5%.