Modelling of cold-formed purlin-sheeting systems-Part 2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its good correlation with experimental results.     

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.     

Transient buoyancy-driven ventilation: Part 1. Modelling advection

The unsteady development of the vertical temperature profile in a ventilated space containing a heat source is modelled. The buoyant fluid released from the heat source is modelled as a turbulent buoyant plume, using a standard integral plume model with a fixed entrainment coefficient. Two types of natural ventilation flow are considered, with the flow driven entirely by the density contrast between the fluid inside and outside the space (stack effect). The ventilation types are (a) classic displacement ventilation, with outflow of warm air through upper openings and inflow of cool air through lower openings; and (b) doorway ventilation, with an exchange flow through the doorway. An improved version of the doorway exchange flow model is given as compared to previous studies. The boundaries of the space are considered to be perfectly insulating, so that heat is transported entirely by the fluid motion. The temporal stratification that develops within the space (outside the plume) is calculated using a modified filling-box model, with successive layers added to the top of the space over time. Laboratory experiments giving reduced-scale simulations of the flows were also conducted, where saline solution and fresh water are used to model fluid of different density. The developing density profiles in the laboratory experiments compare very well with the model predictions. The use of this type of model, capturing the main physical flow features, allows rapid and accurate calculations of transient stratification in ventilated spaces.     

Semi-rigid composite frames with perfobond and T-rib connectors Part 1: Full scale tests

This paper proposes an alternative construction system for composite portal frames. The proposed process uses a perfobond rib shear connector and a connection element, denominated “T-rib” for composite action. The “T-rib” connection element was developed with the aim of transferring the forces from the reinforcing bars, used in hogging moment regions, to edge and corner column flanges. Full-scale test results of a composite semi-rigid portal frame are presented in terms of load-deflection, load-deformation and load-rotation curves.     

Performance of wall-stud cold-formed shear panels under monotonic and cyclic loading: Part I: Experimental research

The ever-increasing need for housing generated the search for new and innovative building methods to increase speed, efficiency and enhance quality, one direction being the use of light thin steel profiles as load bearing elements and different materials for cladding. The same methodology can be employed to build small steel structures for offices, schools or other purposes. Earthquake behaviour of these structures is influenced, together with other parameters, by the hysteretic characteristics of the shear wall panels. Results of a full-scale shear test programme on wall panels are presented, together with some numerical results concerning expectable earthquake performance of this structural typology.     

Distortional buckling formulae for cold-formed steel C and Z-section members: Part I—derivation

This paper presents the derivation of generalised beam theory (GBT)-based fully analytical formulae to provide distortional critical lengths and bifurcation stress resultant estimates in cold-formed steel C and Z-section members (i) subjected to uniform compression (columns), pure bending (beams) or a combination of both (beam–columns), (ii) with arbitrary sloping single-lip stiffeners and (iii) displaying four end support conditions. These formulae incorporate genuine folded-plate theory, a feature which is responsible for their generality and high accuracy. After a brief outline of the GBT fundamentals and linear stability analysis procedure, the main concepts and steps involved in the derivation of the distortional buckling formulae are described and discussed. Moreover, the paper also includes a few remarks concerning novel aspects related to the distortional buckling behaviour of Z-section beams and C-section beam–columns, which were unveiled by the GBT-based approach. Finally, note that, in a companion paper [Thin-Walled Struct., 2004 doi: 10.1016/j.tws.2004.05.002], the formulae derived here are validated and their application, accuracy and capabilities are illustrated. In particular, the GBT-based estimates are compared with exact results and, when possible, also with values yielded by the formulae developed by Lau and Hancock, Hancock, Schafer and Teng et al.     

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.     

Modelling the dispersion of radionuclides following short duration releases to rivers: Part 1. Water and sediment

This paper evaluates and generalises state-of-the-art approaches for modelling short duration liquid discharges of radionuclides ((3)H, (14)C, (60)Co, (134)Cs, (137)Cs, (65)Zn, (89)Sr, (90)Sr, (125)I, (131)I, (241)Am, isotopes of Pu and U) to rivers. An advection-dispersion model was parameterised and used to predict the concentrations of radionuclides in the river environment, i.e. in river water, river bed sediment and fish (Part II of this paper covers uptake to fish). The coupled transport and bio-uptake model was used to predict the concentrations of radionuclides in the River Thames, UK, and one of its tributaries as a result of hypothetical short duration discharges. A simplified version of this model was developed and presented as "look-up" graphs. The influence of various environmental parameters on model output was evaluated by sensitivity analysis. Time-integrated water and sediment concentrations and maximum sediment concentrations may be predicted for all rivers on the basis of the river volumetric flow rate only. Maximum concentration in water is, however, also dependent on other river characteristics. For this latter case, generalised modelling approaches are tested for use in situations where detailed hydrological and dispersion data are not available.     

A mathematical deterministic river-quality model. Part 1: Formulation and description

A comprehensive river water-quality model, deterministic in type, is described in Part 1 and its application to a river catchment is given in Part 2, for which there is a separate abstract. The eleven processes represented in the model include nitrification, denitrification, photosynthesis, BOD decay, re-aeration and others, the rate equations for each being detailed, as well as the numerical integration employed to solve these. A choice of FORTRAN computer programs is available, each embodying the model—one being for “interactive” use from a computer terminal, one for conventional “batch” use at any computer centre, while a third form is envisaged for incorporation in a minicomputer or microprocessor controlling remote automatic water-quality monitoring stations. This third form would allow predictions of downstream quality immediately data are received from each station, so enabling early warning of impending substandard conditions.     

Performance of wall-stud cold-formed shear panels under monotonic and cyclic loading: Part II: Numerical modelling and performance analysis

The main components to provide earthquake performance of a light-gauge steel house are the shear walls. Understanding shear wall behaviour and finding suitable hysteretic models is important in order to be able to build realistic finite element models and assess structural performance in case of earthquake. As for any building structure expected to exceed its elastic behaviour-range in case of earthquake, the interaction of design capacity, load bearing capacity and structural ductility will influence the performance.In this paper alternative design methods and hysteretic modeling techniques are presented. Based on tests described in Part I, a numerical equivalent model for hysteretic behavior of wall panels working in shear was built and used in 3D dynamic nonlinear analysis of cold-formed steel framed buildings. Preliminary conclusions refer to the effect of over-strength and ductility upon possible earthquake load reduction in case of light-gauge shear wall structures.     

Recent research advances on ECBL approach.: Part I: Plastic–elastic interactive buckling of cold-formed steel sections

The objective of this two parts paper is to present some recent developments and applications of erosion of critical bifurcation load (ECBL) approach for the interactive buckling. Two different types of problems are analysed: (1) plastic–elastic interactive buckling which implements into the Ayrton–Perry interaction formula the plastic strength of the stub columns evaluated by means of local plastic mechanism analysis, and (2) elastic–elastic interactive buckling for members with perforations.The first part of the paper analyses the occurrence of local plastic mechanisms in cold-formed steel sections in compression, and how they can be implemented in the ultimate limit state analysis of the members. Actually, the failure of thin-walled cold-formed members in compression always occurs with a local plastic mechanism. Starting from this observation, the authors suggest to use in the interactive local-overall buckling analysis the sectional plastic mechanism strength instead of traditional ‘effective section’. The ECBL approach is used to implement the proposed interactive buckling model. Results are compared with those of other two recent methods, namely the direct strength method and plastic effective width approach. Relevant tests are used to evaluate the three methods. Comparisons with European and American design codes are also presented in the paper.     

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.     

Distortional buckling formulae for cold-formed steel C- and Z-section members: Part II—Validation and application

General GBT-based fully analytical formulae have been derived in a companion paper, which provides distortional bifurcation stress estimates in cold-formed steel C- and Z-section members acted by arbitrary applied stress distributions and displaying four end support conditions. This paper (i) addresses the implementation of the above general formulae, (ii) illustrates their application in detail, (iii) validates them, by means of comparisons with exact results, and (iv) compares their estimates with values yielded by other formulae available in the literature. After considering a wide range of (i) cross-section geometries and lengths and (ii) applied stress distributions, it is concluded that the GBT-based formulae are both accurate and universal.     

完全和部分剪力连接组合梁的有限元建模

主要采用ANSYS软件对完全和部分剪力连接的组合梁进行建模分析。三维有限元模型可以模拟集中或均布荷载作用下简支组合梁的整体挠曲行为。这包括：负荷挠度、钢-混凝土界面的纵向滑移、剪力分布和失效模式。模型的可靠性通过试验与交互式数值分析得到验证。并采用校准的有限元模型进行了参数研究。此外,针对数值建模、收敛、加载和计算有效性等进行了详细讨论。     

全部和部分剪切连接的组合梁有限元模型

运用商业有限元软件ANSYS,对采用部分以及全部剪切连接的组合梁进行了评估。当简支梁受到集中荷载和不均匀分布荷载时,上述三维有限元模型能够模拟弯曲的简支梁行为,包括:荷载作用下的变形性能、在钢-混界面的纵向滑移、螺栓的剪力分布及破坏的模式。通过与试验或者与数值分析的比较,验证了模型的可靠性。随后采用修正的有限元模型,进行了广泛的参变量研究。同时也详细讨论了几个数值模型中有关收敛、荷载策略、计算效率的问题。所提模型的精确性和简洁性适合于预测或补充试验研究。     

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.     

Performance-based design of blast resistant offshore topsides, Part II: Modelling and design

A simplified analytical model for deck plates of offshore topsides structures is proposed. Based on the theory of virtual work and an assumed deformed shape function in Cartesian coordinates, a set of equilibrium equations in terms of energy are developed. The equations are formed as a static case and a dynamic case with unsolved variables defined as generalized coordinates. When these equations are re-arranged, they are equivalent to a modal analysis, which can be solved using Lagrange’s equation method. The generalized coordinates in the static case can be solved manually while in the dynamic case, the ordinary differential equations are solved numerically by developing a computer program using a symbolic software package, MAPLE. The proposed method is comparable with finite element analysis results up to a certain threshold at which development of membrane strain and plasticity modes become dominant. When comparing the results to the reported experimental data, the proposed shape functions for deformations in the lateral directions are modified in order to accommodate the observed behaviour. The results compare favourably with test data and finite element analysis as a control case.Despite inconsistent ductility ratios between the proposed method and the finite element analysis at very high overpressures, the method shows good correlation of results at practical design values. Hence, the proposed method would be a useful tool for preliminary appraisal methods especially for design engineers involved in evaluating the performance of deck plating subjected to a range of hydrocarbon explosion scenarios.