Initial Imperfections Research Articles

Web Shear Buckling of Steel-Concrete Composite Girders – Advanced Numerical Analysis

Load-bearing capacity of plate girders, often used in design of bridges and high-rise buildings, is limited by the shear capacity of connected slender plate elements subjected to shear buckling. To quantify this, experimental investigations on five large-scale steel and steel-concrete composite plate girders loaded solely in shear, with a minimal influence of bending moments, have been conducted and evaluated. In this paper, the phenomenon of web shear buckling is investigated within the numerical analysis using the ABAQUS Software. An advanced numerical model has been developed and results validated against existing experimental findings. One of the focal points of this study represents the methodology of developing such a comprehensive numerical model, implementation of suitable analysis procedures, material models, boundary conditions, finite elements and interactions, in order to correctly replicate the observed response in the tests. In addition, case studies tackling the influence of web slenderness, aspect ratio, initial imperfections, shear connection and concrete classes on the structural-mechanical behavior of steel-concrete composite girders in shear as well as the applicability and suitability of the existing analytical model are also presented and analyzed.

Mechanical Performance Analysis Method for Ribbed H-Section Aluminum Alloy Members with Initial Curvature and Torsion Angle

In this study, an experimental investigation was conducted on the axial compression performance of ribbed H-section aluminum alloy members with initial curvature and torsion angle under varying boundary conditions, including one end hinged with the other rigidly connected, and both ends rigidly connected. Ultimate bearing capacity and failure modes were identified under real loads and subsequently compared with previous findings from our research group on members with hinged ends. To account for initial imperfections introduced during processing and transportation, 3D scanning technology was utilized to capture the precise geometrical dimensions, constructing an accurate numerical simulation model. The experimental results were corroborated with numerical simulations, leading to the proposal of an analytical method for members with initial curvature and torsion angle. Furthermore, extensive parametric analysis elucidated the impact of initial curvature, torsion angle, and slenderness ratio on the ultimate bearing capacity, culminating in the formulation of the stability factor and calculated length factor based on numerical outcomes. The study discovered significant variances in bearing capacity under different boundary conditions, with one-end hinged and one-section rigidly connected, and two-end rigidly connected conditions exhibiting 1.4 and 2.1 times the capacity of the hinged-at-both-ends scenario. Under different boundary conditions, the axial compression members were subjected to flexural-torsional buckling failure. Moreover, when the ultimate bearing capacity was reached, the lower flange of the member and the web near the lower flange appeared obvious buckling phenomenon. The numerical analysis aligned well with experimental data, validating the simulation method's reliability and revealing the stress distribution and evolution during member failure. These findings offer vital theoretical insights and technical support for engineering design and practical applications.

Vibration analysis of rotating functionally graded refined shear deformable microbeams with initial geometric imperfections

Vibration analysis of rotating functionally graded refined shear deformable microbeams with initial geometric imperfections

Post-Fire Stability Bearing Capacity of I-Shaped Aluminum Alloy Members Under Axial Compression

Compared to steel structures, aluminum alloy structures are more susceptible to fire damage. Accurately evaluating the residual bearing capacity of fire-damaged aluminum alloy members is crucial for effective post-disaster management. Therefore, this paper investigates the post-fire bearing capacity of I-shaped aluminum alloy members under axial compression. First, a post-fire test on 16 I-shaped aluminum alloy members under axial compression was carried out. The test results indicate that all specimens fail by the minor axis flexural buckling, and the bearing capacity of the specimens decreases with the increase of the slenderness ratio. Moreover, a trilinear relationship is found between bearing capacity and post-fire temperatures. Second, finite element (FE) models are established using ABAQUS and validated against the test results. Subsequently, numerical analysis is carried out, considering various aluminum alloy brands, post-fire temperatures, slenderness ratios, initial geometrical imperfections, and cross-section dimensions. Through the statistical regression technology and the introduction of strength and stability-bearing capacity reduction coefficients, the formulae for estimating the post-fire stability-bearing capacity of I-shaped aluminum alloy members under axial compression are derived. Finally, the proposed formulae are verified to be accurate through error analysis.

Application of the Southwell Method to Determine the Critical Load of Compression Rods Made of Nonlinear Materials

Experimental determination of the critical force of a compression bar made of linear material does not pose major problems. The widely used Southwell method is also applicable to bars with cross-sections varying in length. The purpose of the research undertaken was to demonstrate that this method can also be successfully applied to bars made of elastic materials exhibiting nonlinear σ(ε) characteristics. Using analytical relationships for a rod satisfying the assumptions of Euler-Bernoulli theory, F(δ) relationships were derived for a rod with an initial arc imperfection, and Southwell diagrams were constructed on this basis. Nonlinear equilibrium paths F(δ) were also determined numerically using the COSMOS/M program for this purpose. For the pre-assumed different nonlinear characteristics, full confirmation of the validity of the application of the Southwell method for determining the critical force was obtained.

Global buckling bearing capacity of corroded H-section steel beams

To understand the effect of seawater corrosion on the stability of steel beams, a global buckling bearing capacity test is conducted on steel beams corroded via an electrochemical method while considering the initial geometric imperfections. The equivalent remaining thickness of the corroded steel beam is calculated based on the yield load obtained from material property tests. Subsequently, this novel approach for calculating the corrosion thickness is utilized to establish a numerical model to simulate the global buckling bearing capacity of the steel beam. Employing this method enables a parameter analysis to be conducted. Furthermore, a new formula for the global buckling of the ultimate bearing capacity of steel beams is proposed based on the differential equilibrium equation of the microdeformation of steel members subjected to bending and torsion. The virtual work principle is employed to develop this formula, which not only simplifies the calculation process, but also assigns clear physical significance to each term.

Study on dynamic post-buckling stability of fast reactor vessels subjected to vertical vibration

Abstract As a lesson learned from the Fukushima nuclear accident, the importance of accident mitigation for Beyond Design Basis Events (BDBEs) is recognized. Excessive earthquake is a typical BDBE. During such events, the Fast Reactor Vessel (FRV) is vulnerable to buckling. The safety goal of FRV under excessive earthquake is to achieve a stable post-buckling state. Our previous study on bending buckling confirmed a global response stability under horizontal vibration. As a parallel study, this paper focuses on axial compression buckling under vertical vibration. Shaking table experiments using thin-walled cylindrical models (R/t=260) are carried out. Similar methodology is applied to investigate the buckling and post-buckling behavior. It is found that axial compression buckling shares an extensive similarity with bending buckling in both buckling mode and post-buckling behavior. Similar global response stability is confirmed due to phase-inverse phenomenon. After buckling, buckling failure becomes stable and does not progress further even when an intense input amplitude is continuously applied. The vibrational load acts as a displacement-controlled load in the out-of-phase domain such that immediate collapse is prevented. Most input energy is dissipated in hysteresis loops rather than being carried by the mass. These mechanisms are independent of input waveform and can be applied to an arbitrary seismic input. In addition, a conservative limit displacement for global response stability is identified. Moreover, the effect of the input frequency ratio, the initial geometrical imperfection and the gravitational force on the post-buckling behavior are clarified.

Analysis using finite element method of the buckling characteristics of stiffened cylindrical shells

ABSTRACT The impact of imperfection/flaws in axially compressed/externally pressurised stiffened cylindrical shells with various shapes was studied using finite element analysis (FE). The study examined imperfection methods such as the Single Perturbation Load Approach (SPLA) and Smooth Inward Dimple (SID) to validate them against existing experimental data. It also explored the influence of initial imperfections in terms of depth, magnitude, size, and location on the buckling strength of the shell. Both methods showed reasonable agreement with published experimental data, with differences ranging from 2% to 13%. The shells’ load-carrying capacity was affected by initial geometric imperfections, particularly in terms of depth, magnitude, size, and location. The study’s findings add to our understanding of how structural imperfections impact the initial phases of designing, fabricating, and analysing axially compressed or externally pressurised stiffened cylindrical shell structures in terms of their magnitude, size, and location.

Dynamic characteristics of shape-memory alloy plates immersed in liquid subjected to blast loading

As a critical structure in ship and marine engineering, axially moving shape-memory alloy (SMA) plates may exhibit complex dynamic behaviors. However, there are few studies investigating the dynamic response of SMA plates under underwater blast, let alone consider the effect of initial geometric imperfection and axial motion. Therefore, further studies on such topic are warranted. Based on this, the current paper dedicates to conducting the dynamic research of the geometrically imperfect SMA plate subjected to underwater blast. Firstly, adopting Falk's polynomial constitutive model, the stress strain constitutive relationship of SMA plate can be determined. Secondly, the Hamilton's principle is employed to derive the vibration equation. Thirdly, the assumed mode method and Runge-Kutta technique are applied for solving the dynamic system. After that, several comparative analyses are performed. Finally, the influences of immersed depth, axially moving velocity, initial geometric imperfection, elastic foundation, pulse load type, aspect ratio, length-to-thickness ratio, as well as blast loading parameter on the transient response path are discussed. These findings can contribute to understanding the dynamic behavior of the geometrically imperfect SMA plates immersed in water when subjected to blast loading, and thus providing valuable thinking for the manufacturing and design of submarine equipment.

A Method for the Coefficient Superposition Buckling Bearing Capacity of Thin-Walled Members

Axial compression tests were conducted on short rhombic tubes of different cross-sectional shapes. The deformation modes of the rhombic short tubes were obtained. To induce a finite element model with deformation modes consistent with the actual working conditions, buckling modes are introduced into the model as the initial imperfections of the structure. However, the buckling modes resulting from finite element buckling analyses often do not meet the needs of actual crushing modes. A coefficient superposition method of solution is proposed to derive modal characteristics consistent with the actual deformation modes by linear superposition of the buckling modes. Through the study of three aspects of theory, test, and simulation, and the comparison and verification of this method with the simulation results of related literature, the results show that the indexes derived from this method are closer to the actual circumstances and are more expandable, which provides a reference for the project.

Static and stability analyses of multi-strut type aluminium alloy suspen-dome structure with large opening

By combining the advantages of the multi-strut concept in cable dome structures with aluminum alloy material, a new type of prestressed spatial structure—the multi-strut aluminum alloy suspen-dome with a large opening—has been developed by integrating a lower prestressed support system into an aluminum alloy reticulated shell. The optimal structural configuration was determined by comparing the static, stability, and economic performance of three types of upper chord mesh topologies for this structure. Subsequently, an analysis of the static performance and large-scale parameters affecting the structural stability of the optimal grid topology was conducted. The study explored the influence of structural prestressing, overall shape, and support stiffness—encompassing three categories and seven parameters—on structural stability and material consumption. Additionally, the effects of initial imperfections and load distribution forms on structural stiffness and stability were further examined. Finally, the static properties, stability, and economic indicators of the structure were compared with two other structural systems: the steel suspen-dome and the cable dome. The results indicate that the pentagonal grid topology provides the best structural performance and that the structure is sensitive to cooling effects. Optimal values for key design parameters, such as the rise-span ratio and thickness-span ratio, were identified. Moreover, the economic advantages of the aluminum alloy suspen-dome compensate for its mechanical performance shortcomings compared to the steel suspen-dome. These findings offer innovative solutions and a scientific basis for the selection and stability design of aluminum alloy suspen-dome structures.

Interpretable machine learning models for predicting probabilistic axial buckling strength of steel circular hollow section members considering discreteness of geometries and material

Steel circular hollow section (CHS) members are widely utilized as axial force-resisting structural members in civil engineering structures. The buckling strength under axial loads is one of the critical parameters to determine the performance of the steel CHS members, which is significantly affected by the discreteness introduced by geometries, material, and initial imperfections. However, the reduction factor employed in the modern design codes (i.e. Chinese codes and EC3) only accounts for the reduction caused by all kinds of discreteness and does not reflect the impacts of every single discreteness and imperfection. To fill the gap, this paper proposed an interpretable machine-learning method to provide the probabilistic axial buckling strength of steel CHS members prediction result in a distribution form with the consideration of detailed discreteness. The model to predict the nominal axial buckling strength of steel CHS members was first developed utilizing ten machine learning algorithms after sufficient numerical simulations, where the numerical model was verified using test results. The artificial neural network (ANN) was selected for developing the prediction model due to its highly reliable performance in testing. The developed ANN models were further interpreted utilizing Shapley Additive exPlanations (SHAP) to determine the interrelationship of different parameters. Then, the probabilistic axial bucking strength prediction model was established based on the developed ANN models, where the Latin hypercube sampling method was applied to address the discreteness of geometries, material, and initial imperfections. The generated probabilistic axial bucking strength prediction model’s effectiveness was verified by the evidence that the machine learning prediction results can highly match the numerical results' probability density function and the result from codes while significantly reducing the computation time. Finally, the design parameters’ impact on the axial buckling strength’s discreteness was evaluated using the global sensitivity analysis (GSA) method. The result shows that the discreteness of design parameters substantially influences the distribution of the axial buckling strength of the steel CHS members and the proposed prediction model can provide an accurate probabilistic distribution prediction.

High-Strength Cold-Formed Steel Stiffened Channel Section: Axial Compressive Strength and Initial Geometric Imperfections

This paper presents a summary of experimental findings from axial compression tests on columns featuring a cold-formed lipped channel section with intermediate stiffeners and return lips, roll-formed from high-strength low-allow steel with a nominal yield strength of 690 MPa (100 ksi). Additionally, the paper provides an analysis of the elastic stability of the studied section, a complete description of the initial geometric imperfections of the tested columns, results of tensile coupon tests, and comparison of the observed strengths of the columns with design predictions. The results provide important additional benchmarks for the wider adoption of high-strength cold-formed steel sections and indicate conditions where existing design methods may be reliably extended.

BUCKLING BEHAVIOUR OF HIGH-STRENGTH RETROFITTED STEEL SECTIONS MANUFACTURED BY POST HEAT-TREATMENT PROCESSES

High-strength steel is increasingly popular in construction for its strength-to-weight ratio, which lowers the self-weight of structures and reduces transportation, erection, and foundation costs. Induction hardening (IH) process which involves rapid heating and cooling of the material leads to microstructural changes which enhance the hardness and strength of conventional steel, elevating it to the level of High Strength (HS) steel. This study reports an extensive investigation on the buckling response and design of IH post-treated structural steel Circular Hollow Sections (CHS). It includes tensile coupon tests, microstructural analyses, initial geometric imperfection measurements, and residual stress evaluations to determine the effects of IH treatment on CHS. Column buckling tests were conducted, and a numerical model was developed and validated against the experimental results which was utilised to study systematically the effect of imperfections. The findings suggest that the magnitude of the imperfections in IH steel sections doubled compared to the non-treated condition, whilst there was a minimal impact on the residual stresses. A comprehensive parametric study was performed using finite element models to study the structural response of IH steel CHS columns over a large range of global slendernesses and allow the assessment of the buckling curves specified in EN 1993-1-1. It was concluded that the buckling curve ‘a’ (imperfection factor, α=0.21) specified in EN 1993-1-1 provides the best buckling load predictions for the IH steel CHS columns, the response of which is superior to that of their virgin counterparts, despite the increased imperfections caused by the heat-treating process.

The application of novel shear deformation theory and nonlocal elasticity theory to study the mechanical response of composite nanoplates

The use of composite structures, which have many layers of materials, has become more prevalent in the field of engineering. One of the advantages of this approach is its ability to use the inherent strengths of the constituent materials, resulting in a substantial increase in their load-bearing capability. Hence, this research represents the pioneering investigation into the static bending and free vibration characteristics of composite nanoplates including several layers of materials, whereby the material layers are interconnected via intricate profiles characterized by square wave and sine waveforms. The purpose of this endeavor is to fully capitalize on the benefits of attending courses in order to enhance practical working efficiency. This study also incorporates the use of two innovative third-order shear deformation theories. Simultaneously, considering the negligible size impact facilitated by the nonlocal theory, the mathematical formulations and equilibrium equations are derived using the Hamilton principle. The issue has been addressed using a four-node element with six degrees of freedom per node. One novel aspect of this study is its consideration of the impact of initial shape imperfections in various manifestations. Additionally, the elastic foundation incorporates characteristics that exhibit spatial variation. This statement provides a somewhat more accurate depiction of the behavior shown by actual structures. The numerical findings have been meticulously computed and thoroughly examined. Notably, it is possible to determine the optimal number of wavelengths in the profile to enhance the load-bearing capability of the structure. The findings derived from this study have significant value in informing the design of operational frameworks in practical settings.

Lateral-Torsional Failure and DSM Design of CFS Lipped Channel Beams at Room and Elevated Temperatures

About a decade ago, in-depth investigations on the behaviour of cold-formed steel (CFS) single-span simply supported lipped channel beams failing in lateral-torsional modes at both room and elevated temperatures were reported at QUT (Queensland Technical University). They revealed a significant underestimation of the lateral-torsional (LT) failure moments by the Direct Strength Method (DSM) global design curve at room temperature, then codified in the Australian/New Zealand and North American specifications. In order to remedy this situation, these authors proposed two novel DSM-based beam strength curve sets, which were found to substantially improve the LT failure moment prediction quality, both at room and elevated temperatures. This work aims at extending the scope of the above investigations, by analysing a visibly larger set of CFS lipped channel beams at elevated temperatures (up to 800 °C), exhibiting (i) various cross-section dimensions and yield stresses, selected to cover wider LT slenderness ranges, (ii) two end support conditions, differing only in the end cross-section wall displacement/rotation and warping restraints (either fully free or fully prevented), and (iii) temperature-dependent steel material properties according with the model prescribed in Part 1-2 of Eurocode 3. The results presented and discussed consist of beam LT post-buckling equilibrium paths and failure moments, obtained through Abaqus shell finite element GMNIA that include critical-mode (LT) initial geometrical imperfections. Lastly, the numerical failure moment data obtained in this work and reported in the literature are used to develop and propose a new unified set of DSM-based strength curves capable of adequately handling beam LT failures at room or elevated temperatures. Since it is shown that the proposed strength curve set provides a quite good LT failure moment prediction quality, it is fair to argue that it constitutes a good starting point to search for an efficient general DSM-based design approach for CFS beams failing in LT modes at room and elevated temperatures.

Experimental Study and Design Method of Cold-Formed Thin-Walled Steel Unequal-Leg Angles under Axial Compression

An experimental study of cold-formed thin-walled steel unequal-leg angles (CFTWS-ULAs) under axially oriented pressure is presented in this paper. Firstly, the initial imperfections and material properties of the angle specimens were measured in detail. The angle specimens were tested under fixed-ended conditions. The results of the experiments showed that the angle specimens with small slenderness ratios were susceptible to local buckling, the angle specimens whose legs had high slenderness ratios and low width–thickness ratios were found to easily suffer from the occurrence of flexural buckling, and the angle specimens whose legs had high width–thickness ratios were found to easily suffer from the occurrence of interactive buckling between local buckling and flexural buckling. The finite element analysis of the ULAs was conducted using ABAQUS6.14 finite element software by creating a model. The buckling modes and ultimate bearing capacities of the test specimens were compared, and the finite element analysis verified that the established model built using the finite element is credible and subsequent parametric analysis was performed. The slenderness ratio had the most significant impact on the ultimate bearing capacities of the unequal-leg angles, as indicated by the analysis results. When the width–thickness ratio and the width ratio of the legs fell within a specific range, the ultimate bearing capacities of the unequal-leg angles increased as the width–thickness ratio and the width ratio of the legs increased. Finally, the comparison results showed that the design strengths predicted by the specifications were very conservative, because the local buckling and torsional buckling were calculated at the same time. Therefore, a recommendation was proposed that the calculation of the load-carrying capacity of an unequal-leg angle should ignore torsional buckling.

СТІЙКІСТЬ ЗАЛІЗОБЕТОННИХ СТІЙОК ПРИ КОРОТКОЧАСНІЙ ТА ТРИВАЛІЙ ДІЇ НАВАНТАЖЕННЯ

The behavior of hinged support at the ends of the rack with initial bending under the action of load is considered. Spring rods are arranged symmetrically. The rack has an initial bend, compressed by forces constant in time. All real elements have one or another imperfections in the form of technological bends, therefore, they begin to bend from the very beginning of the load. The load, when it is exceeded even by an infinitesimally small amount, there is a loss of stability of this type of deformation, is called critical. In the calculation of stability under the long-term action of external forces, it is necessary to determine the load, at which the rate of movement in time monotonically decays. Solving the problem in such a setting is acceptable for systems, the development of movements of which in time leads to a change in the stress state. This condition for a compressed rack is fulfilled only in the presence of initial imperfections (initial bending, off-center application of compressive force, etc.). When solving the problems of the theory of stability, taking into account the creep of the material plays an important role. Creep can be limited in time or unlimited. When solving the problem of the stability of racks with initial imperfections, made of a material that has creep and reinforced with elastic rods, the following assumptions are made: 1) the hypothesis of flat sections is considered valid; 2) the deformations of the creeping material and the elastic rods at the points of contact are the same; 3) the modulus of deformations during stretching and compression are equal; 4) the creep material works in the stretched zone without the appearance of cracks. The relationship between deformations and elasticities in the material of the rack is established by a formula based on the linear relationship between deformations and elasticities. The creep rate of concrete is based on the hereditary theory of aging. In the work, an integro-differential equation was obtained - the equation of slow motion of the rod, expressions were obtained for the study of bends in any at what point in time, the formula for determining the critical force with long-term load action is derived.

Effect of accidental joint eccentricity on the behavior of concentric braces

Concentric braces are designed with the assumption that their joints are concentrically loaded, meaning that the axes of the connected members intersect at a working point within the joint region. To avoid eccentricity at a joint, the load path from each member framing into the joint should intersect at this working point, ensuring alignment within the joint region. However, in real structures, compression members are not perfectly straight, aligned, or concentrically loaded as assumed in design calculations. In AISC 360–22 and EN 1993–1-1, certain safety factors are applied to account for uncertainties related to initial imperfections in concentric braces. However, these safety factors are uniform across all slenderness ratios, and it is unclear up to what level of eccentricity they ensure safety. To address these shortcomings, an experimental and numerical program was conducted to examine the effect of various accidental eccentricity conditions on the behavior of concentric braces. The results showed that the impact of accidental eccentricity on the buckling strength of concentric braces varies according to the slenderness ratio. According to both experimental and numerical studies, the influence of accidental eccentricity becomes insignificant when the normalized slenderness ratio exceeds 1.5. However, when the normalized slenderness ratio is below 1.5, the effect of eccentricity becomes significant, and it increases in importance as the slenderness ratio decreases.

Experimental and numerical studies on the collapse of Titanium alloy ring-stiffened cylinder

This paper investigates the collapse of ring-stiffened Titanium alloy cylinders used for subsea resource exploration under hydrostatic pressure through experimental and numerical methods. Extensive material tests were first conducted on Titanium alloy specimens to obtain the fundamental mechanical properties and variation characteristics. Then, a 4236 mm-long test cylinder was fabricated with an inner radius of 650 mm and a thickness (ts) of 18.85 mm. The initial geometric imperfection was measured at evenly-spaced positions in the axial direction and 48 locations around the circumference by dial gauges. Afterward, the test cylinder was transferred into a custom hyperbaric pressure vessel and pressurized to collapse. As to the numerical analysis, a user-defined material subroutine implementing the incremental J2 deformation theory was developed to predict plastic bifurcation pressure. Moreover, a nonlinear finite element (FE) model, which incorporated the measured geometric imperfection and material nonlinearity, was used to reproduce the experiment. The numerical results were found to exhibit reasonably good agreement with the test data. In addition, parametric studies were conducted regarding material properties, geometric parameters, and imperfection sizes on the load-carrying capacity of Titanium alloy ring-stiffened cylinders.