Initial Geometric Imperfections Research Articles

Effect of variable-thickness webs on shear buckling performance of welded steel plate girders: Numerical analysis and proposed design rules

The use of welded steel members with varying thickness webs is becoming more popular and is often used as plate girders to accommodate varying loading distributions. Such variable-thickness steel plates are more susceptible to experiencing out-of-plane shear buckling, particularly in the thinner sections. However, no research work has been described investigating the shear buckling strength of welded steel plate girders with variable-thickness webs. This study presents an extensive numerical analysis to examine the shear buckling strength of such steel members with variable-thickness webs. Finite element (FE) models incorporating the material non-linearity and initial geometric imperfections were developed. To validate the modelling approach employed in this investigation, a total of 41 experimental results reported by the authors and other researchers were used. A detailed parametric study was subsequently undertaken, exploring various variables including local geometrical imperfections, aspect ratio, thickness change ratio, residual stress, and yield strength. To assess the accuracy of the current design regulations, the test and parametric study results were compared against design strengths. Upon comparison, the current design regulations as specified in Chinese Code (GB 50017), American Specification (ANSI/AISC 360-10) and Eurocodes (EN 1993-1-5) are over-conservative when computing the strength of such members with variable-thickness webs. Finally, new design rules covering both cases of variable-thickness and constant-thickness webs are proposed. A reliability analysis was conducted, and the values of β were 2.87, 3.00, and 3.04, respectively, indicating that new design methods developed in this study could closely determine the shear buckling strength of such welded steel plate girders with variable-thickness webs.

A new set of explicit solutions for postbuckling behaviour of anisotropic shear deformable laminated cylindrical shells with general imperfection distribution and thermal loading

Thermal postbuckling analysis is presented for shear-deformable anisotropic laminated cylindrical shell with general imperfection distribution under several typical temperature fields are analyzed, including uniform temperature, tent-like linear distribution, axial and circumferential quadratic parabolic temperature fields over the shell surface and through the shell thickness. On this basis, the general temperature distribution can be obtained based on the three-dimensional steady-state heat transfer equation. At the same time, based on the high order shear deformation theory including anisotropic coupling effect, geometrically nonlinear large deflection displacement-strain relationship, the general initial geometric imperfections obtained by measurement and analytical means are introduced, and the thermal buckling equilibrium differential equation of anisotropic shear deformable laminated cylindrical shell with initial imperfections is established. A two-step perturbation-Galerkin integral method is used to obtain explicit solutions for the path development direction of post-thermal buckling equilibrium. The results of parameter analysis show that the material properties and temperature dependence, temperature distribution, lay-up and geometric parameters such as radius-to-thickness ratio have important effects on the thermal buckling load and postbuckling equilibrium path. The present method provides an effective theoretical prediction and analysis method for the design of the carrying capacity of submarine pipelines.

Multi-objective optimization of assembly free-form cable-stiffened reticulated shell considering the influence of initial states

In this study, we propose a geometric model of free-form grid structures based on the sliding translation method. Furthermore, an end-flattened inserted-plate joint could be applied to a quadrilateral free-form grid structure. The height of the control point was considered as the optimization variable, while the strain energy, geometric integrated index, and ultimate bearing capacity were considered as the optimization objectives. The results demonstrated the influence of the initial prestress and joint stiffness using multi-objective optimization. Based on the effects of the initial prestress, joint stiffness, and initial geometric imperfections, we propose a multi-objective optimization method for the assembly of a free-form cable-stiffened reticulated shell. The feasibility of the optimization method was verified using examples. Compared with the results of the shape optimization, structures having superior mechanical properties and mesh quality were obtained via the combined method for optimizing the shape and initial prestress, which verified the necessity and effectiveness of the combined optimization method. The mechanical properties of the optimized structures were improved by increasing the joint stiffness; in particular, the ultimate bearing capacity was improved. On using the multi-objective optimization method while considering the initial geometric imperfections, the properties of the structure were improved effectively, and the mechanical properties can be guaranteed even after geometric imperfections are applied.

Experimental and numerical investigations of austenitic stainless steel semi-oval hollow sections under combined compression and bending

Semi-oval hollow section is an innovative cross-section profile, including one semi-circular flange, one flat flange and two flat webs. While the semi-circular flange (exposed to fluid or wind) offers a low level of hydrodynamic or aerodynamic drag, the flat elements facilitate connections with other members. This paper presents experimental and numerical investigations into the local buckling behaviour and resistances of austenitic stainless steel semi-oval hollow sections under combined compression and bending. A testing programme was firstly conducted and included initial local geometric imperfection measurements and ten eccentric compression tests. In conjunction with the testing programme, a numerical modelling programme was performed, where finite element models were developed to validate against the test results and conduct parametric studies for expanding the test data pool over a wider range of cross-section dimensions and loading combinations. The obtained test and numerical data were used to evaluate the applicability of the relevant design interaction curves for austenitic stainless steel rectangular hollow sections, as prescribed in the European code and American specification, to austenitic stainless steel semi-oval hollow sections. On the basis of the evaluation results, the codified design interaction curves were found to provide conservative resistance predictions. Finally, an improved design interaction curve, with more accurate end points and suitable shape, was developed and led to more accurate and consistent resistance predictions for austenitic stainless steel semi-oval hollow sections under combined compression and bending.

Investigation on internal resonance of fluid conveying pipes with initial geometric imperfection

This paper shows numerical research on the 1:2 internal resonance and chaotic bifurcation phenomena of the graphene platelets reinforced metal foams (GPLRMF) pipes, with emphasis on the effect of initial geometric imperfection. To this end, combining the high order shear deformation beam theory and Kelvin-Voigt viscoelasticity, a mathematical model that considers geometric imperfection is established. The fluid in pipeline is supposed to be incompressible and inviscid. Subsequently, the Galerkin discretization and multiscale method are utilized for solving the nonlinear governing equations in the case of 1:2 internal resonance. And the nonlinear dynamic behavior of the fluid conveying pipes can be analyzed through the frequency amplitude diagrams, bifurcation curves, time course curves, phase trajectories, and Poincaré maps. The double jump phenomena are excited to demonstrate the dynamic characteristics of the pipes with 1:2 internal resonance. In the case of small disturbance coefficients, various internal resonance and chaos phenomena can be captured in the pipeline system. Research shows that the coupled effects between initial geometric imperfection and nonlinear geometric relationships is non-monotonic. That is to say, for bimodal internal resonance, when the initial geometric imperfection increase, the unstable region will be compressed, and the response amplitude will increase.

Nonlinear aero-thermo-elastic flutter analysis of stiffened graphene platelets reinforced metal foams plates with initial geometric imperfection

Due to its lightweight design and high load-bearing capacity, the stiffened plate structure is extensively applied in the passive control of aircraft flutter. However, the evolution mechanism of the nonlinear response of stiffened plates within the unstable region remains unclear. In particular, there is a lack of research on the nonlinear aero-thermo-elastic properties of stiffened plates with initial geometric imperfection. Inspired by this, this article investigates the stability and post-instability behavior of stiffened geometrical imperfect graphene platelets reinforced metal foams (GPLRMF) plates under combined thermal load and aerodynamic pressure. Graphene platelets (GPLs) and foam are distributed evenly or unevenly in the plates, while the material properties are calculated by modified Halpin-Tsai model and rule of mixture. Considering initial geometric imperfection, the models of plates and stiffeners are established by first-order shear deformation (FOSD) plate and Timoshenko beam theories, respectively. Using the linear piston theory to simulate supersonic aerodynamic pressure. The stability boundary of stiffened plates is determined by eigenvalue analysis. The Newton-Raphson approach is used to simulate the aero-thermo-elastic static response of stiffened plates, and the dynamic post-flutter behavior of the stiffened plate is determined through the Runge-Kutta method. Finally, the effects of initial geometric imperfection, material parameters (foam distribution type, porosity coefficient, GPLs weight fraction and GPLs distribution type), and stiffeners (size, position, and stiffening scheme) on the thermal aeroelastic behavior of stiffened GPLRMF plates are revealed. It can be found that the presence of initial geometric imperfection will significantly change the nonlinear flutter behavior of the stiffened plates.

Nonlinear Dynamic Analysis of FG Fluid Conveying Micropipes with Initial Imperfections

This paper investigates the nonlinear dynamics of FG-FCMPs with initial imperfections. Based on the MCST, the nonlinear equations of motion and the corresponding boundary conditions are established by applying Hamilton’s principle, the Euler–Bernoulli beam theory, and von-Kármán geometric nonlinearity. To describe the initial geometric imperfection of the FG-FCMP, the first-order vibrational mode is employed. Subsequently, in cases of primary parametric resonance, 1:2 subharmonic resonance for the first-order mode, as well as primary resonance for the second-order mode, Galerkin’s method, and the multiple scale method are utilized to analyze the amplitude–frequency responses of the imperfect FG-FCMP. The numerical simulations test the influence of flow velocity, micro-scale parameter, geometrical imperfections, and external loads on the nonlinear characteristics of a coupled system with two DOFs. It is found that, as the increase of flow velocity, micro-scale effect, and external load, the amplitude of the first two modes can be increased. The hardening characteristics are converted into the softening characteristics due to the imperfect effect. Furthermore, numerical results provide a more comprehensive understanding of the nonlinear dynamics of FCMPs for both periodic and chaotic motions.

Experimental investigation on axial compression behaviour of cold-formed thick-walled steel tubes

This paper presents an experimental and numerical investigation on the stability behaviour of cold-formed thick-walled steel tubes. Axial compression tests were conducted on 15 steel tubes with square and rectangle cross-sections to investigate their structural behaviours. The primary test parameters were slenderness and width-to-thickness ratios. Material properties, failure modes, load-deflection curves, and load-strain curves of the specimens are discussed. Furthermore, a numerical simulation was conducted to further investigate the effects of the slenderness ratio, width-to-thickness ratio, and initial geometric imperfection on the axial compression behaviour of cold-formed thick-walled tubes. Based on the experimental and numerical results, the applicability of the design codes, GB50018–2002, AISI S100–16, and EN 1993-1-1 was assessed. Results revealed that all three codes predicted the yield strength well after considering the cold-formed effect. With an increase in the slenderness ratio, GB50018–2002 and AISI S100–16 yielded increasingly unsafe predictions for overall stability, whereas EN 1993-1-1 yielded safe predictions. Finally, a modified design method for the overall buckling resistance of cold-formed thick-walled rectangular tubes under axial compression was proposed based on EN 1993-1-1 and verified using test and FEM results.

Numerical study and design of S35657 stainless steel welded stub columns

As a new type of austenitic stainless steel with high nitrogen and low nickel, S35657 stainless steel has the characteristics of high strength and low price, and it has a good application prospect in the field of construction. To supplement the relevant research on S35657 stainless steel structures and to evaluate the applicability of existing specifications and design methods, a finite element model was established using ABAQUS software and calibrated using existing test results. Furthermore, a series of parametric analyses were carried out, focusing on the effects of width-to-thickness ratio, initial geometric imperfection, and welding residual stress on the local buckling of S35657 stainless steel welded section columns. On this basis, the critical width-to-thickness ratio limit of the compression plate was proposed. Finally, the test results and the simulation results were compared with the calculation results of load-carrying capacities for local buckling in the European code (EN1993-1-4), the American code (SEI/ASCE8–02), the Chinese specification (CECS410:2015), the direct strength method (DSM) and the continuous strength method (CSM). Based on the effective width method and DSM, two new approaches to calculate the load-carrying capacity for local buckling were proposed and demonstrated to obtain reasonable accuracy.

Numerical investigation of the influence of transverse welds on the strength of aluminum alloy I - shaped members – beams

The weldability of high strength aluminum alloys is an important consideration when designing aluminum structures. While these alloys do suffer significant strength loss in the weld heat affected zone (HAZ), available design codes are often overly conservative in their guidelines regarding the design of welded aluminum members. This paper presents a numerical investigation of the effect of reduced strength in the HAZ adjacent to a transverse weld in simply-supported aluminum alloy beams subject to concentrated end moments. Nonlinear finite element (FE) models were developed, validated, and applied in a parametric study of non-welded and transversely welded 6061-T6 flexural members with an I-shaped cross section. The FE model included initial geometric imperfections and material nonlinearities in both the HAZ and the base material. The parametric study examined 400 unique beam cases defined by the combination of four factors, including slenderness ratio or unbraced length, weld location along the beam span, post-yield material stiffness model, and loading case or resulting moment gradient. The FE results were subsequently compared with capacities predicted by the Aluminum Association’s Specification for Aluminum Structures, with proposed modifications to SAS also provided. A similar study on columns is presented in a companion paper within this issue.

Two Stochastic Methods to Model Initial Geometrical Imperfections of Steel Frame Structures

The stochastic modeling of geometrically imperfect steel frame structures requires statistical inputs for imperfection parameters, often with specific mutual correlations. The stochastic input values of geometrical imperfections are derived from European Standard EN 1090-2:2018 tolerance criteria. Two advanced stochastic methods, #RSS (random storey sway) and #RSP (random storey position), are developed based on these criteria. This paper presents a verification study, using random sampling simulations, for these two stochastic methods (#RSS and #RSP) to directly model the initial global geometrical imperfections of steel frame structures. The proposed methods have been verified for structures with equidistant storey heights and for those comprising up to 24 storeys, making them applicable to a wide range standard steel frame structures. It has been found that the performance of the #RSS method is satisfactory. An advantage of #RSS is that the random parameters are statistically independent. On the other hand, the #RSP method requires the definition of these mutual correlations in order to satisfy the criterion that 95 percent of random realizations of initial imperfections fall within the tolerance limits of the corresponding European Standard. The #RSP method, however, might have certain advantages for structures with a larger number of storeys (above 24), as closely discussed in this study. Additionally, this study provides useful provisions for the advanced numerical analyses of multi-storey steel frames of various geometries.

S890 hot-rolled ultra-high strength steel (UHSS) seamless circular hollow section beam–columns: Testing, modelling and design

With the recent rapid development of manufacturing techniques and material science, advanced hot-rolling of ultra-high strength steel (UHSS) with material grades up to S890 becomes possible. The structural behaviour of S890 hot-rolled ultra-high strength steel (UHSS) seamless circular hollow section (CHS) beam–columns fabricated through the advanced manufacturing method, was investigated through testing and numerical modelling and reported in this paper. In the physical testing, a total of 12 beam–columns were firstly tested featuring the flexural buckling failure mode, with the material coupon tests and initial global geometric imperfection measurements performed. FE modelling was then conducted, where the FE models were developed and validated against the test observations. The validated FE models were then adopted in the parametric studies in a wider spectrum of member lengths, cross-section dimensions and loading combinations, resulting in the additional 300 FE data to be generated. Finally, the current design provisions, as set out in Eurocode, American specification and Australian standard, are assessed for their applicability to S890 hot-rolled UHSS seamless CHS beam–columns. It was revealed from the assessment results that the design provisions in three design codes can be accurately applied to S890 hot-rolled UHSS seamless CHS beam–columns.

Experimental investigations on the collapse of spiral-stiffened cylindrical shells under external hydrostatic pressure

This paper presents a comprehensive experimental investigation into the collapse behavior of spiral stiffened cylindrical shells under external hydrostatic pressure. Spiral stiffened cylindrical shells with two different pitches and cylindrical shells were designed and fabricated. The fabricated specimens were divided into three groups. Each group has two identical specimens. Test specimens were welded from stainless steel. The shell was formed by cold bending, and the spiral ribs were welded to the surface of the shell to form a spiral stiffened cylindrical shell. Measurements of initial geometric imperfections and shell thickness were performed on the fabricated specimens to verify the accuracy of fabricating. Subsequently, the specimens were placed in a pressure chamber and pressurized until collapsed to obtain the ultimate collapse pressure and collapse modes. In addition, a uniaxial tensile test was conducted on the shell material to obtain its material properties. Experimental results indicated that the fabricated specimens had excellent repeatability and reasonable precision. The presence of a spiral rib effectively boosted the ultimate collapse pressure of the cylindrical shell with a more pronounced strengthening effect observed as the rib density increased.

Experimental and numerical study on the load-bearing capacity of cold-formed stiffened high-strength steel box columns

This paper reports a comprehensive experimental and numerical study on the load-bearing capacity of cold-formed stiffened high-strength steel box columns. A novel cold-formed stiffened section for box columns with width-to-thickness ratios exceeding design limits was presented. Column buckling tests were conducted, including precise measurements of initial geometric imperfections, material property tests, and axial compression tests. The results revealed that the stability factors of the stiffened specimens consistently surpassed those of the corresponding box section specimens within the same experimental group, with an average increase ratio of 19.9%. Finite element models were developed, validated, and used for parametric studies, considering variations in width-to-thickness ratios, slenderness ratios, and steel strengths. A total of 144 finite element models were analyzed to comprehensively investigate the effects of the selected parameters. The obtained parameter analysis results were compared with calculation methods and design codes, such as GB 50017–2017, EN 1993-1-1, ANSI/AISC 360–16, and AISI S100-16, to investigate their applicability. The Direct Strength Method (DSM) was found to overestimate the bearing capacity of these columns. Therefore, a modified DSM was proposed specifically for predicting the ultimate strength of cold-formed stiffened high-strength steel box columns. Extensive verification confirmed that the design strengths obtained using the modified DSM provide accurate and reliable predictions for the behavior of these columns.

Shell buckling of suction buckets for offshore wind turbines considering imperfection and soil parameter sensitivity

Suction buckets or suction caissons in combination with jackets as substructures have become a prominent foundation solution for offshore wind turbines. These large shell structures with relatively thin walls are installed by pumping out the water inside the structure, which creates a pressure difference and thus a downward force. The circumferential compression on the cylindrical shell causes a risk of shell buckling. The prediction of the buckling capacity of such large cylindrical shells is challenging, since it depends significantly on the initial geometric imperfections resulting from the manufacturing process and on the boundary conditions imposed by the surrounding soil. Previous work on suction buckets revealed that the choice of a representative imperfection form and amplitude is very challenging and the buckling pressure is sensitive to soil modeling choices. In this work, various imperfection forms and amplitudes as well as different soil parameters are applied to geometrically and materially nonlinear finite element models and the buckling capacities are determined. The novelties in this contribution are in evaluating and comparing the effects of global and local imperfections in form of sinusoidal eigenmodes and weld depressions for an unstiffened cylindrical shell under hydrostatic compression. The results suggest that global imperfections are more detrimental than local imperfections and further, a new approach based on sorting eigenmode imperfections depending on the wave number to identify the most unfavorable eigenmode-affine imperfection pattern is developed. Additionally, this study is the first to show that the inclusion of soil plasticity and contact effects has a significant impact on the buckling pressure.

Testing, numerical modelling and design of G550 high strength cold-formed steel built-up section columns

This paper investigates the buckling behaviour and load-carrying capacity of G550 high strength cold-formed steel built-up section columns under axial compression through experiments and numerical simulations. Two types of built-up sectional profiles were formed, which were defined as built-up OI-section and built-up CB-section. Each built-up OI-section member is formed by connecting two cold-formed steel C-section members in a back-to-back manner using self-drilling screws, while each built-up CB-section member consists of a cold-formed steel C-section member and a cold-formed steel U-section member, which are connected in a face-to-face manner by self-drilling screws. The experimental programme included tensile coupon tests, initial geometric imperfection measurements and 20 pin-ended column compression tests. In the numerical modelling programme, finite element models were developed and validated against the experimental results, and then used for parametric analyses to generate a total of 250 numerical data with different cross-section dimensions and member lengths. Based on the experimental and numerical data, the accuracy of both the effective width method and the direct strength method for predicting the strengths of G550 high strength cold-formed steel built-up section columns, as set out in the American Specification, was evaluated. The evaluation results indicated that both the effective width method and direct strength method provided accurate and consistent failure load predictions for G550 high strength cold-formed steel built-up OI-section columns on average, but with some unsafe failure load predictions, while the predicted failure loads were inaccurate, scattered and conservative for G550 high strength cold-formed steel built-up CB-section columns. Moreover, the effective width method and direct strength method yielded a similar level of design consistency for G550 cold-formed steel built-up section columns, but the direct strength method resulted in more accurate and less conservative failure load predictions than the effective width method. The modifications to the codified DSM equations were proposed for G550 high strength cold-formed steel built-up section columns and shown to provide improved predictions of failure load over the design codes.

Derivation of Knockdown Factors for Common Bulkhead Structures Considering Geometric Initial Imperfection and Heat Transfer Effects

Derivation of Knockdown Factors for Common Bulkhead Structures Considering Geometric Initial Imperfection and Heat Transfer Effects

Shear resistance of perforated QN1803 high-strength stainless steel plate girders through experimental testing and numerical analysis

QN1803, a high-strength stainless steel, has been developed by steel industry recently. Its tensile yield strength can be approximately 40 % (or more) higher than that of the commonly-used EN1.4301, while its cost is 20 % lower due to its reduced nickel content. One obvious application for QN1803 is in plate girders, where web perforations are often required to accommodate building services. However, no research work has been reported in the literature that investigates the reduced shear buckling capacity of QN1803 plate girders as a result of web perforations. This issue is addressed herein. An experimental program comprising six plate girder tests is conducted in this study. Three different hole ratios were considered: 0.2, 0.4 and 0.6. The depths of web were selected as 700 mm and 500 mm, while the thickness of web was fixed as 4.0 mm. The initial geometric imperfections were determined from three-dimensional (3D) scanning prior to the plate girder tests. Finite element (FE) models incorporating the material non-linearity and initial geometric imperfections were then developed and validated against the experimental results. A parametric analysis including 62 FE models was performed to examine the influences of the critical parameters on the shear buckling capacity of such perforated members. The results suggest that for those members with a hole diameter - web height ratio of 0.6, the shear buckling capacity was reduced by 56 % on average due to the web perforation. The design rules for determining the shear buckling capacity of stainless steel plate girders as specified in Eurocodes (EN 1993–1–4 + A1) (2015) and American Specification (ANSI/AISC 370–21) (2021) were evaluated. Upon comparison, it was demonstrated that both EN 1993–1–4 + A1 (2015) and ANSI/AISC 370–21 (2021) cannot provide accurate and safe predictions for determining the shear buckling capacity of such members.

Geometric imperfection sensitivity of nonlinear vibration responses of laminated beams under thermal shock

Initial geometric imperfections are bound to arise during a structure's service life or could emerge during the fabrication process. The exact influence of these geometric imperfections on the thermally-induced vibrations of the structure remains uncertain. This study represents the first endeavor to conduct a sensitivity analysis of geometric imperfections in the nonlinear vibration responses of laminated beams subjected to thermal shock. Considering uncoupled thermoelasticity theory, the temperature distribution is obtained using a one-dimensional Fourier-type transient heat conduction equation, and a nonlinear dynamic beam model accounting for initial geometric imperfections is developed based on the first-order shear deformation theory, Lagrange method, and Ritz method. An exact solution is implemented to capture the temporal temperature profile along the thickness of a beam subjected to a thermal boundary condition of the first kind (constant wall temperature). The sensitivity of various geometric imperfections to the nonlinear vibrations of laminated beams under thermal shocks is obtained using the Newmark scheme and Newton–Raphson iterative technique. A series of parametric studies is conducted to reveal the effects of different parameters on the nonlinear thermally induced vibration responses of the beams. Thermally induced vibration is shown to be sensitive to the initial geometric imperfections.

Structural behaviour and resistances of high strength concrete-filled stainless steel tube (HCFSST) beam-columns

This paper reports experimental and numerical investigations into the structural behaviour and resistances of high strength concrete-filled stainless steel tube (HCFSST) beam-columns under combined compression and bending. An experimental investigation was conducted on sixteen HCFSST beam-columns specimens fabricated from stainless steel tubes with two cross-section sizes and high strength concretes with four material grades, and included concrete cylinder tests, tensile coupon tests, initial global geometric imperfection measurements and eccentric compression tests. The test setups and procedures were fully reported and the experimental observations were discussed and analysed in detail. It was found that the plane cross-section assumption was valid for eccentrically loaded HCFSST sections and the lateral deflection distribution patterns for HCFSST beam-columns were approximately half-sine wave shapes. The test results were used in a subsequent numerical investigation for the validation of finite element models, which were then employed to conduct parametric studies to generate additional numerical data over a wide range of cross-section dimensions, member lengths and loading combinations. Based on the experimental and numerical results, the relevant design rules, as set out in the European code, American specification and Australian/New Zealand standard, were evaluated for their applicability to HCFSST beam-columns. The evaluation results revealed that the European code provided accurate but scattered failure load predictions when used for HCFSST beam-columns, while the American specification and Australian/New Zealand standard resulted in conservative and scattered failure load predictions.