Modelling of cold-formed purlin-sheeting systems- Part 1: Full model

Purlin-sheeting systems used for roofs and walls commonly take the form of cold formed channel or zed section purlins, screw-connected to corrugated sheeting. These purlin-sheeting systems have been the subject of numerous theoretical and experimental investigations over the past three decades, but the complexity of the systems has led to great difficulty in developing a sound and general model. This paper presents a non-linear elasto-plastic finite element model, capable of predicting the behaviour of purlin-sheeting systems without the need for either experimental input or over simplifying assumptions. The model incorporates both the sheeting and the purlin, and is able to account for cross-sectional distortion of the purlin, the flexural and membrane restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The validity of the model is shown by its good correlation with experimental results. A simplified version of this model, which is more suitable for use in a design environment, is presented in a companion paper.     

Modelling of cold-formed steel sandwich purlin-sheeting systems to estimate the rotational restraint

Sandwich panels are attached to cold-formed steel purlins in roofs of industrial buildings to provide insulation. As the strength of the attached purlins is considerably increased due to the lateral and rotational restraints provided by the sandwich panels, estimating these restraints is important in the design of purlins. The rotational restraint is generally determined by experiments, as no design rules exist for sandwich purlin-sheeting systems. In this paper, a non-linear finite element model is presented to estimate the rotational restraint provided by the sandwich panels to the attached purlin. The model is validated with experimental tests and is in good agreement. In order to develop a design method for estimating the rotational restraint in sandwich purlin-sheeting systems, the model could be useful for parametric studies to investigate the influencing factors.     

Simplified design approach for cold-formed stainless steel compression members subjected to flexural buckling

The design criteria of stainless steel compression member are more complicated than those of carbon steels due to the nonlinear stress strain behavior of the material. In general, the tangent modulus theory is used for the design of cold-formed stainless steel columns. The modified Ramberg–Osgood equation given in the ASCE Standard can be used to determine the tangent modulus at specified level of stresses. However, it is often tedious and time-consuming to determine the column buckling stress because several iterations are usually needed in the calculation. This paper presents new formulations to simplify the determination of flexural buckling stress without iterative process. Taylor series expansion theory is utilized in the study for numerical approximations. The proposed design formulas are presented herein and can be alternatively used to calculate the flexural buckling stress for austenitic type of cold-formed stainless steel columns. It is shown that the column strengths determined by using the proposed design formulas have good agreement with those calculated by using the ASCE Standard Specification. A design example is also included in the paper for cold-formed stainless steel column designed by using the ASCE Standard equations and the proposed design formulas.     

A finite element analysis model for the behaviour of cold-formed steel members

A finite element analysis model for the post-local buckling behaviour of cold-formed steel (CFS) members subjected to axial compression has been developed. The finite element model consists of a Total Lagrangian nonlinear 9-node “assumed strain” shell finite element, and experimental-based material properties models to represent the body of the CFS sections. Experimentally derived residual stress variations, and initial geometric imperfections have also been incorporated. A special loading technique and a displacement solution algorithm were employed to obtain a uniform displacement condition at the loading edges. Details of a test program involving 20 non-perforated, and perforated cold-formed stub-column steel sections have been presented in the second part of the paper. The comparison between the test results, and the finite element results was performed for axial and lateral displacement behaviour, buckling loads, ultimate loads, and axial stress distribution. The comparison forms the basis for the evaluation of the efficiency, and the accuracy of the finite element model, and it indicated that the finite element analysis model constructed herein gives accurate and consistent results for the behaviour of the cold-formed steel members subjected to axial compression.     

Computational modeling of cold-formed steel

The objective of this paper is to provide an overview of computational modeling, both elastic buckling and nonlinear collapse analysis, for cold-formed steel members. Recent research and experiences with computational modeling of cold-formed steel members conducted within the first author's research group at Johns Hopkins University are the focus of the presented work. This admittedly biased view of computational modeling focuses primarily on the use of the semi-analytical finite strip method and collapse modeling using shell finite elements. Issues addressed include how to fully compare finite strip and finite element solutions, and the importance of imperfections, residual stresses, material modeling, boundary conditions, element choice, element discretization, and solution controls in collapse modeling of cold-formed steel. Examples are provided to demonstrate the expected range of sensitivity in cold-formed steel collapse modeling. The paper concludes with a discussion of areas worthy of future study that are within the domain of cold-formed steel modeling.     

土体电阻率测试的简化模型及应用

把土的导电组分分为孔隙水和土骨架,用计算模型对取自连云港地区的粘土电阻率进行了计算,并与实测结果相比较,验证了将该模型运用到土体电阻率计算中可以减少土体电阻率室内试验的工作量。     

冷弯薄壁型钢混凝土剪力墙受剪承载力计算模型

冷弯薄壁型钢混凝土剪力墙（CTSRC剪力墙）在水平地震作用下经历整截面墙体受力和分缝墙体受力两个阶段,破坏模式和受力机理与传统剪力墙不同。剪跨比小于2.0 的CTSRC剪力墙在峰值荷载前表现为整截面墙体的受力性能,峰值荷载时宏观竖向裂缝两侧混凝土发生滑移,墙体逐渐演变为分缝剪力墙,有较好的耗能能力。针对CTSRC剪力墙的受力特征,将钢筋混凝土剪力墙的软化拉压杆模型与混凝土界面直剪受力的软化拉压杆模型相结合,考虑竖向裂缝处短细斜裂缝间混凝土破坏引起的竖向裂缝两侧混凝土的滑移,建立了CTSRC剪力墙受剪承载力的拉压杆－滑移分析模型和计算方法,计算结果和试验结果吻合良好,表明拉压杆 滑移模型可以较好地反映剪跨比小于2的CTSRC剪力墙的受力机理,能够较准确地预测CTSRC剪力墙的受剪承载力。     

Shape optimization of cold-formed steel columns

The objective of this paper is to demonstrate the application of formal optimization tools towards maximizing the compressive strength of an open cold-formed steel cross section. In addition, in the work presented here the cross section shape is not limited by pre-determined elements (flanges, webs, stiffeners, etc.), as is commonly required to meet the necessity of conventional code-based procedures for design that employ simplified closed-form stability analysis. Instead, by utilizing the finite strip method for stability analysis and the Direct Strength Method for the strength calculation, the full solution space of cold-formed steel shapes may be explored. In the analysis herein, a given width of sheet steel is allowed to be bent at 20 locations along its width, thus providing the ability to form nearly any possible shape. Three optimization algorithms are explored: the gradient-based steepest descent method and two stochastic search methods, genetic algorithms and simulated annealing. Compared with a standard cold-formed steel lipped channel the final optimized capacities are found to be more than double the original design. Steepest descent solutions are shown (as expected) to be highly sensitive to the initial guess, but they provide symmetrical and conceptually clean solutions. The stochastic search methods require significantly more computational capacity, explore the solution space more fully, and generate solutions that are largely insensitive to the initial guess. For long and intermediate length cold-formed steel columns the optimization methods identify two non-conventional alternative designs that maximize capacity. The future of this work lies in further integrating the optimization methods with additional manufacturing and construction constraints; for now, the method suggests several interesting alternative cross sections that are worthy of future study.     

Probabilistic Fire Simulation Assessment Using Simplified Model and Zone Modelling of a Kitchen Fire Scenario

Fire Technology - Probabilistic fire simulation has been gaining interest in performance-based design approach. Very few evaluations on modelling performance can lead to...     

高强超薄壁冷弯型钢低层住宅足尺模型振动台试验

进行了两层高强超薄壁冷弯型钢住宅结构足尺模型的振动台试验,模型采用屈服强度550 MPa、厚度2 mm以下超薄壁冷弯型钢龙骨,外墙内外侧覆面板分别采用12 mm厚石膏板和0.42 mm厚屈服强度550 MPa带肋波纹钢板,内墙两侧覆面板均为12 mm厚石膏板。试验选取3条实测地震波记录和1条人工合成地震波,地震加速度考虑7度多遇到9度罕遇的烈度水平。试验结果表明：结构破坏均发生在连接部位和覆面板的局部区域,破坏模式为自攻螺钉的脱落和石膏板的局部破裂,而内部主体型钢龙骨基本无破坏;结构水平刚度虽有较大削弱,但在地震作用下结构无倒塌危险;采用双面覆板构造的复合墙体结构,能够满足抗震设防地区“大震不倒”的要求;墙体开洞部位为结构的薄弱区域,结构设计时应加强门、窗等开洞部位的构造措施以及自攻螺钉连接的可靠性。     

Shape optimization of cold-formed steel columns

The objective of this paper is to demonstrate the application of formal optimization tools towards maximizing the compressive strength of an open cold-formed steel cross section. In addition, in the work presented here the cross section shape is not limited by pre-determined elements (flanges, webs, stiffeners, etc.), as is commonly required to meet the necessity of conventional code-based procedures for design that employ simplified closed-form stability analysis. Instead, by utilizing the finite strip method for stability analysis and the Direct Strength Method for the strength calculation, the full solution space of cold-formed steel shapes may be explored. In the analysis herein, a given width of sheet steel is allowed to be bent at 20 locations along its width, thus providing the ability to form nearly any possible shape. Three optimization algorithms are explored: the gradient-based steepest descent method and two stochastic search methods, genetic algorithms and simulated annealing. Compared with a standard cold-formed steel lipped channel the final optimized capacities are found to be more than double the original design. Steepest descent solutions are shown (as expected) to be highly sensitive to the initial guess, but they provide symmetrical and conceptually clean solutions. The stochastic search methods require significantly more computational capacity, explore the solution space more fully, and generate solutions that are largely insensitive to the initial guess. For long and intermediate length cold-formed steel columns the optimization methods identify two non-conventional alternative designs that maximize capacity. The future of this work lies in further integrating the optimization methods with additional manufacturing and construction constraints; for now, the method suggests several interesting alternative cross sections that are worthy of future study.     

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements—the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.     

Transient buoyancy-driven ventilation: Part 2. Modelling heat transfer

A new mathematical model for buoyancy-driven ventilation [Sandbach SD, Lane-Serff GF. Transient buoyancy-driven ventilation: Part 1. Modelling advection. Building and Environment, 2011] is modified to include heat transfer at the boundaries. Heat transfers at the ceiling and floor are included, using Newton’s law of cooling to model convective heat transfer between the air and the solid boundaries, Fourier’s law to model conductive heat transfer through the floor and ceiling, and a linear version of the Stefan–Boltzmann law to model radiative heat transfer from the ceiling to the floor. The effectiveness of the model was assessed using experimental results obtained in a full-scale test room. In these experiments, the vertical temperature stratification was measured using an array of T-type thermocouples. Speed measurements were obtained to estimate the ventilation flow rate (for displacement ventilation) and the velocity profile across the doorway (for doorway ventilation). Buoyancy was introduced using a twin-hob (∼2.35 kW) heat source, and in most cases a diffuse two-layer temperature stratification developed. The results from these experiments are compared with the model and existing adiabatic models. Our results indicate that the effect of heat transfer at the boundaries on the final stratification is significant and should not be ignored. Furthermore, direct comparisons between the measured and modelled results are in general very good.     

Buckling modes of double-channel cold-formed beams

The present paper starts from the analysis of previous experimental results on double-channel cold-formed beams subjected to local and lateral-torsional buckling. The scope of this reanalysis is to identify the range of definition of the buckling modes, which influence the ultimate behaviour of such beams. The verification approach of EC3 and AISI have been compared to the experimental results, giving a satisfactory agreement. The definition of coupled instability range has been set up by means of EC3 formulations. The proposed equations relate together the main geometrical parameters of the beam, giving useful indications to the designer.     

Modelling of geosynthetic-reinforced column-supported embankments using 2D full-width model and modified unit cell approach

Soil-cement deep mixing (DM) columns combined with geosynthetic basal reinforcement are an accepted technique in geotechnical engineering to construct road and railway embankments over soft foundations. Both full-width and unit cell models have been used to numerically simulate the performance of geosynthetic-reinforced and column-supported (GRCS) embankments. However, the typical unit cell model with horizontally fixed side boundaries cannot simulate the lateral spreading of the embankment fill and foundation soil. As a result, the calculated reinforcement tensile loads using typical unit cell models are much less than those from matching full-width models. The paper first examines GRCS embankments using a full-width model with small- and large-strain modes in FLAC and then compares the calculated results from the full-width model with those using a typical unit cell model, a recently proposed modified unit cell model, and a closed-form solution. The paper also examines the influence of the soft foundation soil modulus, reinforcement tensile stiffness, and DM column modulus on the reinforcement tensile loads. Numerical analyses show that the reinforcement tensile loads from the modified unit cell model are in good agreement with those from the full-width model for zones under the embankment crest for all cases and conditions examined in the paper. Both the full-width model and modified unit cell model perform better than the typical unit cell model for the prediction of the reinforcement tensile load when compared to the closed-form solution. However, while the modified unit cell developed by the writers is shown to be more accurate than the typical unit cell when predictions are compared to results using full-width numerical simulations, the benefit of using this approach to reduce computation times may be limited in practice.     

Simplified model for damage in squat RC shear walls

In this paper, a new simplified model for simulating damage of squat RC shear walls under lateral loads is proposed. This simplified model is based on damage and fracture mechanics. It describes the reduction in stiffness and strength due to diagonal cracking, permanent deformations due to yielding of transverse reinforcement and sliding across shear cracks. First, the analytical expressions are developed for the particular case of monotonic loading. A yield function to describe permanent deformations due to yielding of transverse reinforcement is proposed. Then, a crack resistance function, based on the Griffith criterion, is introduced and experimentally identified. Finally, the necessary analytical expressions are developed for hysteretic behavior. The proposed numerical model is implemented in a commercial finite element program and validated against experimental results. It is shown that the model can predict well the response of RC shear walls.     

高层建筑简化层模型及其动力响应

以剪切型层计算模型对高层建筑的计算模型进行了简化,并将频率、模态等动力性能计算结果与有限元计算结果相比较,结果十分吻合,同时利用该模型进行了高层建筑的风致振动时程分析,得出了计算结果能够满足工程计算需要的结论。     

高层建筑结构计算软件中的剪力墙模型简化

在高层结构分析中 ,对剪力墙的模型化是其关键问题 ,它直接决定了高层结构分析模型的科学性 ,同时也决定了分析软件的精度。本文主要介绍现在高层结构分析计算软件中剪力墙的三种简化模型。最后就高层建筑结构计算分析软件在分析剪力墙的精确性方面作一点展望     

Behaviour of cold-formed singly symmetric columns

An experimental investigation into the behaviour of cold-formed plain and lipped channel columns compressed between fixed and pinned ends is presented in this paper. It is shown experimentally that local buckling does not induce overall bending of fixed-ended singly symmetric columns, as it does of pin-ended singly symmetric columns. Consequently, local buckling has a fundamentally different effect on the behaviour of pin-ended and fixed-ended singly symmetric columns. In order to show this fundamental different effect caused by local buckling, a series of tests was performed on plain and lipped channels brake-pressed from high strength structural steel sheets. Four different cross-section geometries were tested over a range of lengths which involved pure local buckling, distortional buckling as well as overall flexural buckling and flexural-torsional buckling. The different effects of local buckling on the behaviour of fixed-ended and pin-ended channels are investigated by comparing strengths, load–shortening and load–deflection curves, as well as longitudinal profiles of buckling deformations. The purpose of the paper is to demonstrate experimentally the different effects of local buckling on the behaviour and strengths of fixed-ended and pin-ended channels.