Geometric Imperfection Distribution Research Articles

Design of press-braked stainless steel C-beams subjected to global-distortional interaction buckling

A detailed finite element (FE) model studying the global-distortional (G-D) interaction of press-braked stainless steel C-beams was reported herein. According to previous bearing capacity tests, the model incorporating measured material characteristics and precise geometric imperfections was validated by comparing to the failure mode, load-vertical displacement curve and bearing capacity. Following the calibration of the model, comprehensive parametric investigations were conducted to investigate the influence of the distribution and amplitude of geometric imperfections, material strain hardening coefficient and effect of cold working. It is found that the distribution of geometric imperfections has significant and complex impacts on the failure mode and ultimate capacity, while the amplitude of imperfection could have positive or negative effects on the ultimate capacity. The accuracy of the design methods provided by EN 1993–1-4, AS/NZS 4673 and ASCE 8–22 was assessed using the test data. All codes are found to account for distortional buckling by employing the Effective Width Method (EWM) to reduce the compression plate area. The calculation results were discrete. Therefore, based on the Direct Strength Method (DSM), a novel and accurate design method was developed for the G-D interaction of stainless steel C-beams. The strong correlation between the ratio of ultimate capacity to global buckling bearing capacity and the G-D interaction slenderness was verified by 260 numerical analyses prior to proposing the new design method. The proposed design method underwent a reliability analysis using first order reliability method to meet the requirement of ASCE 8–22.

Calculation method for local–global interaction buckling capacity of stainless steel C-columns

In this paper, based on the completed experimental research, the C-section stainless steel column was simulated in ABAQUS, and the FEM results were compared with the test results to verify the accuracy of the FE model. On this basis, the FE model was used to carry out a parametric analysis of the local–global interaction (L-G) buckling capacity of the C-section stainless steel column, and the effects of the initial imperfection distribution mode, the mechanical properties of the material, and the improvement of the material strength in the corner region were investigated. When the initial geometric imperfection distribution mode is local buckling or L-G buckling, the change of imperfection shape has less effect on the occurrence of L-G buckling and the ultimate capacity of the member. Within a certain range, the stainless steel hardening coefficient and the increase strength of corner region on the L-G buckling capacity of stainless steel columns is small. The nominal yield strength of stainless steel has a more significant effect on the L-G buckling capacity. Finally, based on the parametric analysis results and the direct strength method, the calculation formula for the local–global interaction buckling capacity of stainless steel C-columns under axial compression is proposed, and the accuracy of the calculation results were verified by comparing with the test results.

Experimental and numerical study on flexural behaviour of cold-formed steel hat-shaped beams with geometrical imperfections

Experimental and numerical studies are conducted to investigate cold-formed hat-shaped members' flexural behaviour and determine the effects of different parameters on the behaviour. A total of ten specimens of cold-formed hat-shaped beams with different lengths are chosen for physical tests. The actual geometry and geometric imperfection distributions are acquired by processing 3D point clouds obtained by laser scanners. Four-point bending tests are performed to obtain benchmark results for numerical models. It is observed that numerical results are in accordance with the experimental results with high accuracy. Once the generated finite element models are calibrated based on the experiment results, a parametric study investigating the influence of the length, thickness, lip width, return length, radius, and lip angle on the beam behaviour is undertaken. In addition, the effect of geometric imperfection magnitude selection and imperfection modelling method on the member capacity is considered. The study's outcomes show that the initial geometric imperfections and input parameters selected for the generated numerical models significantly affect the flexural behaviour of CFS hat-shaped beams.

Full-field geometric imperfection and effect on cross-section capacity of circular steel tubes

Measurements on the geometric imperfection of circular steel tubes used in building structures were limited to specific longitudinal lines of the outer surface in existing studies. This study is aimed at detecting full-field geometric imperfection of circular steel tubes and evaluating its influence on cross-section capacity. First, geometric imperfections of 71 specimens consisting of four common types (i.e., hot-rolled and cold-rolled carbon steel circular tubes, cold-drawn and cold-rolled stainless steel circular tubes) were measured using laser scanning techniques. Observations from 3D scanning models demonstrate that the dominant imperfections for seamless tubes (hot-rolled carbon and cold-drawn stainless steel circular tubes) are cross-section ellipticity and uneven thickness, while welded tubes (cold-rolled carbon and stainless steel circular tubes) are mostly influenced by cross-section ellipticity. Based on the measured geometric profile data, imperfection distribution modes of outer-surface and thickness were proposed separately, and then imported to finite element (FE) simulation. Parametric analysis was conducted to evaluate the influence of geometric imperfections on cross-section compression and bending capacity values. Totally, seven types of outer-surface and three types of thickness imperfection distribution modes were used. Simulation results indicate that considering geometric imperfections generates negligible influence on cross-section capacity for the circular steel tubes studied. Finally, the influence of mesh density on capacity prediction of circular steel tubes was discussed. This study illustrates the actual full-field geometric imperfection distribution of circular steel tubes and discusses its effect on cross-section capacity, which provides useful information for improving the efficiency and accuracy of FE analysis on circular steel tubes.

Geometric Imperfection Distributions of Existing Reticulated Shells: Theoretical and Experimental Analysis

Geometric imperfection is one of the most disadvantageous factors that impair mechanical behaviors of existing reticulated shell structures. However, the available consistent mode methods and statistical methods which usually applied in designing structures can hardly estimate the actual geometric imperfection distribution for existing structures, because these methods use the assumed imperfections. In this paper, a Markov Random Field (MRF) theoretical model of existing reticulated shells is established by introducing the theory of probabilistic graphical model. The unit of graphic model named node clique are proposed to deduct the geometric state function of reticulated shells, based on the local Markov property. Then the inversion function along with its iterative equation is established to predict geometric imperfection distribution of existing reticulated shells. The MRF method makes the predicted distribution of the numerical model as consistent as possible with its corresponding actual structure, and only a few measurement nodes are needed as known conditions. An experimental structure of K6 single-layer reticulated shell is built to verify the proposed theory by comparing the calculated geometric imperfection distribution results with the actual measured data. Meanwhile, the significance level of the calculated results between MRF and traditional stochastic method is analyzed, which shows MRF method can effectively predict the geometric imperfections of single layer reticulated shells.

Concentrated load distribution in corrugated steel decks: A parametric finite element study

This paper presents results of an extensive parametric finite element study on a concentrated load distribution in corrugated steel decks. The parametric study was conducted using fine element models developed in ANSYS. Optimal parameters of the finite element models, such as mesh density, deck corner radius, and initial geometric imperfection distributions and magnitudes, were selected based on a study to meet the criteria of accuracy and computational efficiency. The finite element models with the optimal parameters showed good agreement with available test results. In the numerical parametric study, effects of the following parameters on strength and behavior of deck, as well as on the effective transverse distribution width, were studied: deck type, steel thickness, deck span condition, deck span length, concentrated load locations along deck span, and concentrated load application to different elements of the deck cross-section. Design equations for predicting the effective transverse distribution widths were developed. The effective transverse distribution widths predicted by the developed equations agreed well with the transverse distribution widths obtained from the finite element simulations. The paper also presents a worked example showing implementation of the design equations for design of steel deck under concentrated loads.

In situ X-ray micro-computed tomography study of the damage evolution of prefabricated through-holes in SLM-Printed AlSi10Mg alloy under tension

Drilling holes used to mechanically connect complex structures would affect the residual stress of metal alloys, resulting in delamination of selective laser melting (SLM)printed bulk samples. These limitations could be overcome by the pre-fabrication of through-holes during SLM processing using computer-aided design (CAD) models with holes. However, thus far, there has been rarely study discussing the impact of pre-fabricated through-holes on damage evolution and failure mechanisms of SLM-manufactured structures under quasi-static tension. In this study, damage evolution in SLM-printed AlSi10Mg alloys with two prefabricated through-holes was investigated. In situ X-ray tomography tensile tests were performed to evaluate the morphology, location, and distribution of geometric imperfections and to clarify their role in the mechanical response of samples under quasi-static tension. To numerically reproduce the experiments at the meso-scale, an image-based finite element model (FEM) was constructed from 3D images and the results were compared to those obtained by ideal CAD model simulation. In addition, damage evolution of geometric defects was extracted from the FEM and experimental results. The geometric defects increased the in-plane shear stress remarkably and resulted in the crack propagation in AlSi10Mg alloys. It was shown that the mechanical response of AlSi10Mg bulk samples was linked to the initial morphological features of through-holes. This comprehensive combined geometric morphology of defects and the mechanical response will serve to complete the dimensional compensation design and replacement of secondary drilling holes in additive manufacturing technology in future studies.

Numerical Studies on the Buckling Behaviour of Cable-stiffened Steel Columns With Pin-connected Crossarm Systems

In this study, the buckling behaviour of a cable-stiffened steel column with a four-branch pin-connected crossarm system is investigated. A new geometric imperfection distribution is constructed with a nonlinear buckling analysis to trigger interactive buckling, and a method to obtain the actual load carrying capacity of the cable-stiffened steel column is proposed. The effects of different parameters, including the stay diameter, crossarm length, pretension in cables, and imperfection size, have also been analysed and discussed in this article. The findings of this study show that the interactive buckling of steel column stiffened by the four-branch pin-connected crossarms must be taken into account for accurate analysis. It is also demonstrated that the cable-stiffened steel columns are imperfection sensitive, particularly when the critical buckling mode is located at the transition between symmetric and antisymmetric buckling, though the corresponding configuration is proved to be optimal with respect to the material utilisation rate.

Investigation on Simulation Methods of Initial Geometric Imperfection Distribution in Elasto-plastic Stability Analysis of Single-layer Reticulated Shells

Based on the theory of probability and mathematical statistics and on the results of nearly 2000 cases of elasto-plastic stability analysis for single-layer reticulated shells, a new simulation method of initial geometric imperfection distribution, N-order eigenmode imperfection method, is developed. The elasto-plastic stability analyses of four types of commonly used single-layer reticulated domes were conducted with the random imperfection mode method, the eigenmode imperfection method and the N-order eigenmode imperfection method, respectively, by means of ANSYS. The results show that, though the random imperfection mode method can simulate the initial geometric imperfection distribution realistically, the calculation cost of this method is too large to popularize in design practice. Adopting the first order eigenmode to simulate the distribution of initial geometric imperfection may fail to derive the most unfavorable buckling load. The reliability of buckling load obtained from the eigenmode imperfection method cannot be guaranteed effectively. The N-order eigenmode imperfection method can evaluate the influence of initial geometric imperfection on structural stability reasonably, and capture the buckling load satisfying the requirement of the ‘3σ’ principle with less calculation. This method is a convenient and efficient way for designers to estimate stability performance of single-layer reticulated shells accurately and safely.

Experimental and Numerical Analyses of Dented Stiffened Panels

Numerical–experimental correlation study for small scale damaged stiffened panels was performed. Six small scale models were fabricated. Two of them were employed for the correlation of intact panels and the remaining four for the correlation of dented panels. Ultimate strength analyses were carried out in order to adjust the numerical model for further use in parametric studies. The damage was imposed by a local indentation of the panels. Measurements of geometric imperfection distributions and damage shapes have been performed before and after the damage using a laser tracker equipment. The numerical models were represented by shell elements assuming finite membrane strains and large rotations, considering both geometric and material nonlinearities. Results obtained showed very good agreement between experimental and numerical analyses for both intact and dented panels. Additionally, numerical simulations of damaged stiffened panels were performed. The aim of the parametric study was to evaluate the behavior up to and beyond buckling, to observe the strength loss due to the presence of the damage on the panel. The explicit nonlinear finite element code from abaqus program was employed to simulate the dent damage. Therefore, distortions and the residual stresses due to the damage were both considered in subsequent numerical compression analyses.

ANALYSIS OF ULTIMATE STRENGTH OF REINFORCED CONCRETE DOMES SUPPORTED AT FOUR CORNERS

The present paper discusses on ultimate strength of a shallow reinforced concrete domes supported at four corners. The loads for investigation are not only dead load but also approximate earthquake loads considering anti-symmetrical vertical loads caused by horizontal earthquake motions. The method is based on an elastic-plastic geometrically nonlinear analysis considering both effects of initial geometric imperfections and tensile strength of concrete. Based on the results, several important structural features are revealed. The geometric imperfection distribution similar to those caused by dead load reduces the ultimate strength, and the strength is much reduced if no tensile strength is assumed for concrete. If 40% of the shell thickness and no tensile strength are assumed respectively for the imperfections and for concrete, the ultimate strength is reduced by almost half from the perfect case. The ultimate strength interaction between dead load and earthquake loads shows the importance in design to include the anti-symmetrical load components of earthquake loads. The importance of not only stiffeners at free edges but also shell geometries of bending moment free are suggested.