James B.P. Lim

Stiffness prediction for bolted moment-connections between cold-formed steel members

The authors have recently described a cold-formed steel portal framing system in which simple bolted moment-connections, formed through brackets, were used for the eaves and apex joints. Such connections, however, cannot be considered as rigid because of localised in-plane elongation of the bolt-holes caused by bearing against the bolt-shanks. To therefore predict the initial stiffness of such connections, it is necessary to know the initial bolt-hole elongation stiffness kb. In this paper, a finite element solid idealisation of a bolted lap-joint in shear will be described that can be used to determine kb; the results obtained are validated against experimental data. A beam idealisation of a cold-formed steel bolted moment-connection is then described, in which spring elements are used to idealise the rotational flexibility of the bolt-groups resulting from bolt-hole elongation. Using the value of kb in the beam idealisation, the deflections predicted are shown to be similar to those measured experimentally in laboratory tests conducted on the apex joint of a cold-formed steel portal frame.

Ultimate strength of bolted moment-connections between cold-formed steel members

The behaviour and design of bolted moment-connections between cold-formed steel members, formed by using brackets bolted to the webs of the section, is considered. The particular problem of the moment-capacity of such joints being lower than that of the cold-formed steel sections being connected because of web buckling, caused by the concentration of load transfer from the bolts, is addressed. In this paper, a combination of laboratory tests and finite element analyses is used to investigate this mode of failure. It is demonstrated that there is good agreement between the measured ultimate moment-capacity and that predicted by using the finite element method. A parametric study conducted using the finite element model shows that the moment-capacity of a practical size joint can be up to 20% lower than that of the cold-formed steel sections being connected. Web buckling so-caused must therefore be considered in the design of such connections.

Design optimization of cold-formed steel portal frames taking into account the effect of building topology

Cold-formed steel portal frames are a popular form of construction for low-rise commercial, light industrial and agricultural buildings with spans of up to 20 m. In this article, a real-coded genetic algorithm is described that is used to minimize the cost of the main frame of such buildings. The key decision variables considered in this proposed algorithm consist of both the spacing and pitch of the frame as continuous variables, as well as the discrete section sizes. A routine taking the structural analysis and frame design for cold-formed steel sections is embedded into a genetic algorithm. The results show that the real-coded genetic algorithm handles effectively the mixture of design variables, with high robustness and consistency in achieving the optimum solution. All wind load combinations according to Australian code are considered in this research. Results for frames with knee braces are also included, for which the optimization achieved even larger savings in cost.

Optimum joint detail for a general cold-formed steel portal frame

In cold-formed steel portal framing systems that use bolted moment connections, formed through brackets, for the eaves and apex joints, it is well-known that the joints are semi-rigid, have finite connection-lengths and limited moment capacity. For such frames, it is therefore necessary for these joint effects to be taken into account when conducting frame design and analysis. However, as the semi-rigidity and the finite connection-lengths of each joint influence the bending moment distribution as well as the deflected profile of the frame, the joint detail for the eaves and the apex should not be designed independently of the frame. In this paper, a method of determining the optimum joint detail is described. It is demonstrated that careful selection of the joint detail can result in as much as a 25% increase in efficiency of the frame. Including joint effects explicitly into the design process provides better opportunities to devise the most appropriate balance between joints and member properties and thus reduce material use and construction costs.

The Collapse Behaviour of Cold-formed Steel Portal Frames at Elevated Temperatures

This paper describes the results of non-linear elasto-plastic implicit dynamic finite element analyses that are used to predict the collapse behaviour of cold-formed steel portal frames at elevated temperatures. The collapse behaviour of a simple rigid-jointed beam idealisation and a more accurate semi-rigid jointed shell element idealisation are compared for two different fire scenarios. For the case of the shell element idealisation, the semi-rigidity of the cold-formed steel joints is explicitly taken into account through modelling of the bolt-hole elongation stiffness. In addition, the shell element idealisation is able to capture buckling of the cold-formed steel sections in the vicinity of the joints. The shell element idealisation is validated at ambient temperature against the results of full-scale tests reported in the literature. The behaviour at elevated temperatures is then considered for both the semi-rigid jointed shell and rigid-jointed beam idealisations. The inclusion of accurate joint rigidity and geometric non-linearity (second order analysis) are shown to affect the collapse behaviour at elevated temperatures. For each fire scenario considered, the importance of base fixity in preventing an undesirable outwards collapse mechanism is demonstrated. The results demonstrate that joint rigidity and varying fire scenarios should be considered in order to allow for conservative design.

Design of cold-formed stainless steel lipped channel sections with web openings subjected to web crippling under end-one-flange loading condition:

This article presents a numerical investigation on the web crippling strength of cold-formed stainless steel lipped channel sections with circular web openings under end-one-flange loading condition. In order to take into account the influence of the circular web openings, a parametric study involving 1992 finite element analyses was performed, covering duplex EN1.4462, austenitic EN1.4404 and ferritic EN1.4003 stainless steel grades; from the results of the parametric study, strength reduction factor equations are proposed. The web crippling strengths predicted by the reduction factor equations are first compared to the strengths calculated using the equations recently proposed for cold-formed carbon steel lipped channel sections. It is demonstrated that the strength reduction factor equations proposed for cold-formed carbon steel are unconservative for the stainless steel grades by up to 7%. Unified strength reduction factor equations are then proposed that can be applied to all three stainless steel grades.

Web crippling strength of cold-formed stainless steel lipped channels with web perforations under end-two-flange loading

This article presents a finite element investigation into the web crippling strength of cold-formed stainless-steel lipped channels with circular web perforations under end-two-flange loading. The cases of web openings located both centred and offset to the load bearing plates are considered. In order to take into account the influence of the circular web openings, a parametric study involving 2190 finite element analyses was performed, covering duplex EN 1.4462, austenitic EN 1.4404 and ferritic EN 1.4003 stainless-steel grades; from the results of the parametric study, strength reduction factor equations are determined. The strength reduction factor equations are first compared to equations recently proposed for cold-formed carbon-steel lipped channels. It is demonstrated that the strength reduction factor equations proposed for cold-formed carbon steel are conservative for the stainless-steel grades by up to 10%. New coefficients for web crippling strength reduction factor equations are then proposed that can be applied to all three stainless-steel grades.

Effect of screw spacing on behavior of axially loaded back-to-back cold-formed steel built-up channel sections

In cold-formed steel structures, such as trusses, wall frames, and portal frames, the use of back-to-back built-up cold-formed steel channel sections for the column members is becoming increasingly popular. In such an arrangement, intermediate fasteners at discrete points along the length prevent the individual channel sections from buckling independently. Current guidance by the American Iron and Steel Institute and the Australian and New Zealand Standards for built-up sections describes a modified slenderness approach, to take into account the spacing of the screws. Limited experimental tests or finite element analyses, however, have been reported in the literature for such sections to understand the effect of screw spacing. This issue is addressed herein. The results of 30 experimental tests are reported, conducted on back-to-back built-up cold-formed steel channel sections covering stub columns to slender columns. A finite element model is then described which shows good agreement with the experimental test results. The finite element model is then used for the purposes of a parametric study comprising 144 models. It is shown that while the modified slenderness approach is in general conservative, for stub columns it can be unconservative by around 10%.

Behaviour of steel portal frames in fire : Comparison of implicit and explicit finite element methods

The use of finite element methods to determine the collapse behavior of steel portal frames in fire requires temperature, large deformation, complex geometry, boundary conditions and degradation of material stiffness to be taken into account. For such analyses, the cost of computation is important as well as the accuracy, robustness and stability of the analyses. The implicit dynamic method is a rigorous technique that considers the equilibrium of every time step. However, convergence may become an issue, particularly if the frame undergoes structural instability while using a direct time incrementation scheme. In contrast, the explicit dynamic method does not require the equilibrium criteria to be met in every time step, and thus convergence problems are not encountered, although the cost of computation may be tremendous if the natural time scale is used. This paper presents a comparison between the efficiency, stability and accuracy of computations using the implicit and explicit dynamic methods, in determining the collapse behavior of portal frames at elevated temperatures; the models are quasi-static since inertia forces are ignored. It is found that similar results can be obtained using both the implicit and explicit dynamic methods, although the analysis times differ significantly. It is shown that, if the applied artificial inertia forces, in terms of residual forces, are magnified and an automatic time incrementation scheme is activated in the implicit dynamic method, then this method shows significant superiority over the explicit dynamic method both in terms of the cost of computation and the accuracy of results obtained for such structures.

Practical application of CFD for wind loading on tall buildings

This paper is concerned with assessing the scope of appicabiity for computational fluid dynamics(CFD) in the field of structural engineering, with a particular reference to tall buildings. Modern design trends and advances in engineering materials have encouraged the demand for taller and more slender structures. This pattern induces inherent structural flexibility; these cases exceed the limitations of the quasi-static method offered by current codes of practice. Wind tunnel testing is the traditional solution for such dynamically sensitive structures. However, even this scaled modelling approach is clouded by some uncertainties, including scaling the Reynolds number and assuming damping values for the aeroelastic model. While CFD cannot be used as a replacement for wind tunnel testing, there are results within the literature to suggest it has the potential to act as a complimentary tool - provided it is used within its capabilities. The paper outlines the various turbulence models that are available and summarises the extent of their application in a practical structural engineering sense. It also details the user-defined criteria that must be satisfied and discusses the potential for simplified models in tall building CFD analyses, with a view to promoting more efficient and practical solutions.