Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Experimental studies of cold-formed steel hollow section columns at elevated temperatures

This paper reports the details of an experimental study of cold-formed steel hollow section columns at ambient and elevated temperatures. In this study the global buckling behaviour of cold-formed Square Hollow Section (SHS) slender columns under axial compression was investigated at various uniform elevated temperatures up to 700℃. The results of these column tests are reported in this paper, which include the buckling/failure modes at elevated temperatures, and ultimate load versus temperature curves. Finite element models of tested columns were also developed and their behaviour and ultimate capacities at ambient and elevated temperatures were studied. Fire design rules given in European and American standards including the Direct Strength Method (DSM) based design rules were used to predict the ultimate capacities of tested columns at elevated temperatures. Elevated temperature mechanical properties and stress-strain models given in European steel design standards and past researches were used with design rules and finite element models to investigate their effects on SHS column capacities. Comparisons of column capacities from tests and finite element analyses with those predicted by current design rules were used to determine the accuracy of currently available column design rules in predicting the capacities of SHS columns at elevated temperatures and the need to use appropriate elevated temperature material stress-strain models. This paper presents the important findings derived from the comparisons of these column capacities.

Local buckling studies of cold-formed steel compression members at elevated temperatures

Cold-formed steel members have been widely used in residential and commercial buildings as primary load bearing structural elements. They are often made of thin steel sheets and hence they are more susceptible to local buckling. The buckling behaviour of cold-formed steel compression members under fire conditions is not fully investigated yet and hence there is a lack of knowledge on the fire performance of cold-formed steel compression members. Current cold-formed steel design standards do not provide adequate design guidelines for the fire design of cold-formed steel compression members. Therefore a research project based on extensive experimental and numerical studies was undertaken to investigate the local buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. First a series of 91 local buckling tests was conducted at ambient and uniform elevated temperatures up to 700oC on cold-formed lipped and unlipped channels. Suitable finite element models were then developed to simulate the behaviour of tested columns and were validated using test results. All the ultimate load capacity results for local buckling were compared with the predictions from the available design rules based on AS/NZS 4600, BS 5950 Part 5, Eurocode 3 Parts 1.2 and 1.3 and the direct strength method (DSM), based on which suitable recommendations have been made for the fire design of cold-formed steel compression members subject to local buckling at uniform elevated temperatures.

Mechanical behavior of circular and square concrete filled steel tube stub columns under local compression

This paper presents a combined experimental and numerical study on the behaviour of both circular and square concrete-filled steel tube (CFT) stub columns under local compression. Twelve circular and eight square CFT stub columns were tested to study their bearing capacity and the key influential parameters. A 3D finite element model was established for simulation and parametric study to investigate the structural behaviour of the stub columns. The numerical results agreed well with the experimental results. In addition, analytical formulas were proposed to calculate the load bearing capacity of CFT stub columns under local compression.

Effects of layer orientation of CFRP strengthened steel hollow members

This paper reveals the effects of layer orientation on structural behaviour of three layers configured (LHL, HHL, LLH) CFRP strengthened circular hollow section (CHS) members subjected to bending. The beams were loaded to failure under four-point bending. The structural behaviour of the CFRP strengthened tubular steel beams with various layer orientations were presented in terms of failure load, stiffness, composite beam action and modes of failure. The LHL and LLH layers oriented strengthened beams perform slightly better than HHL layers oriented strengthened beams. The LHL and LLH layers oriented treated beams showed very similar structural behaviour.

Comparative durability study of CFRP strengthened tubular steel members under cold weather

In strengthening systems, the CFRP (Carbon Fibre Reinforced Polymer) materials typically have excellent resistance against environmental conditions; however, the performance of adhesives between CFRP and steel is generally affected by various environmental conditions such as marine environment, cold and hot weather. This paper presents the comparative durability study of CFRP strengthened tubular steel structures by using two different adhesives such as MBrace saturant and Araldite K630 under four-point bending. The program consisted of testing twelve CFRP strengthened specimens having treated with epoxy based adhesion promoter, untreated surface and one unstrengthened specimen and conditioned under cold weather for 3 and 6 months to determine the environmental durability. The beams were then loaded to failure in quasi-static manner under four-point bending. The structural responses of CFRP strengthened tubular steel beams were compared in terms of failure load, stiffness and modes of failure. The research findings show that the cold weather immersion had adversely affected the durability of CFRP strengthened steel members. Design factor is also proposed to address the short-terms durability performance under cold weather.

Pull-through strength of high tensile steel cladding systems

The profiled steel roof and wall cladding systems in Australia are commonly made of very thin high tensile steels, and are crest-fixed with screw fasteners. A review of current literature and design standards indicated the need to improve the understanding of the behaviour of crest-fixed steel cladding systems under wind uplift/suction loading, in particular, the local failures. Therefore a detailed experimental study using a series of small scale tests and some two-span cladding tests was conducted to investigate the local pull-through and dimpling failures in the commonly used steel cladding systems. The applicability of the current design formulae for the pull-through strength of crest-fixed steel classing systems was investigated first. An improved design formula was then developed in terms of the thickness and ultimate tensile strenth of steel cladding material and diameter of screw head or washer. This paper presents the details of this investigation and its results. A review of current design and test methods is also included.

Effect of bond length on the behaviour of CFRP strengthened concrete-filled steel tubes under transverse impact

Concrete-filled steel tubular (CFST) columns have shown great potential as axial load carrying member and used widely in many mission critical infrastructures. However, attention is needed to strengthen these members where transverse impact force is expected to occur due to vehicle collisions. In this work, finite element (FE) model of carbon fibre reinforced polymer (CFRP) strengthened CFST columns are developed and the effect of CFRP bond length is investigated under transverse impact loading. Initially the numerical models have been validated by comparing impact test results from literature. The validated models are then used for detail parametric studies by varying the length of externally bonded CFRP composites. The parameters considered for this research are impact velocity, impact mass, CFRP modulus, adhesive type, and axial static loading. It has been observed that the effect of CFRP strengthening is consistent after an optimum effective bond length of CFRP wrapping. The effect of effective bond length has been studied for above parameters. The results show that, under combined axial static and transverse impact loads CFST columns can successfully prevent global buckling failure by strengthening only 34% of column length. Therefore, estimation of effective bond length is essential to utilise the CFRP composites cost effectively.

Computer analysis of impact behavior of concrete filled steel tube columns

This paper presents a numerical study of the response of axially loaded concrete filled steel tube (CFST) columns under lateral impact loading using explicit non-linear finite element techniques. The aims of this paper are to evaluate the vulnerability of existing columns to credible impact events as well as to contribute new information towards the safe design of such vulnerable columns. The model incorporates concrete confinement, strain rate effects of steel and concrete, contact between the steel tube and concrete and dynamic relaxation for pre-loading, which is a relatively recent method for applying a pre-loading in the explicit solver. The finite element model was first verified by comparing results with existing experimental results and then employed to conduct a parametric sensitivity analysis. The effects of various structural and load parameters on the impact response of the CFST column were evaluated to identify the key controlling factors. Overall, the major parameters which influence the impact response of the column are the steel tube thickness to diameter ratio, the slenderness ratio and the impact velocity. The findings of this study will enhance the current state of knowledge in this area and can serve as a benchmark reference for future analysis and design of CFST columns under lateral impact.

Fire design rules for load bearing cold-formed steel frame walls exposed to realistic design fire curves

Light gauge Steel Frame (LSF) walls are extensively used in the building industry due to the many advantages they provide over other wall systems. Although LSF walls have been used widely, fire design of LSF walls is based on approximate prescriptive methods based on limited fire tests. Also these fire tests were conducted using the standard fire curve [1] and the applicability of available design rules to realistic design fire curves has not been verified. This paper investigates the accuracy of existing fire design rules in the current cold-formed steel standards and the modifications proposed by previous researchers. Of these the recently developed design rules by Gunalan and Mahendran [2] based on Eurocode 3 Part 1.3 [3] and AS/NZS 4600 [4] for standard fire exposure [1] were investigated in detail to determine their applicability to predict the axial compression strengths and fire resistance ratings of LSF walls exposed to realistic design fire curves. This paper also presents the fire performance results of LSF walls exposed to a range of realistic fire curves obtained using a finite element analysis based parametric study. The results from the parametric study were used to develop a simplified design method based on the critical hot flange temperature to predict the fire resistance ratings of LSF walls exposed to realistic fire curves. Finally, the stud failure times (fire resistance rating) obtained from the fire design rules and the simplified design method were compared with parametric study results for LSF walls lined with single and double plasterboards, and externally insulated with rock fibres under realistic fire curves.

Energy based time equivalent approach to determine the fire resistance ratings of light gauge steel frame walls exposed to realistic design fire curves

Structural fire safety has become one of the key considerations in the design and maintenance of the built infrastructure. Conventionally the fire resistance rating of load bearing Light gauge Steel Frame (LSF) walls is determined based on the standard time-temperature curve given in ISO 834. Recent research has shown that the true fire resistance of building elements exposed to building fires can be less than their fire resistance ratings determined based on standard fire tests. It is questionable whether the standard time-temperature curve truly represents the fuel loads in modern buildings. Therefore an equivalent fire severity approach has been used in the past to obtain fire resistance rating. This is based on the performance of a structural member exposed to a realistic design fire curve in comparison to that of standard fire time-temperature curve. This paper presents the details of research undertaken to develop an energy based time equivalent approach to obtain the fire resistance ratings of LSF walls exposed to realistic design fire curves with respect to standard fire exposure. This approach relates to the amount of energy transferred to the member. The proposed method was used to predict the fire resistance ratings of single and double layer plasterboard lined and externally insulated LSF walls. The predicted fire ratings were compared with the results from finite element analyses and fire design rules for three different wall configurations exposed to both rapid and prolonged fires. The comparison shows that the proposed energy method can be used to obtain the fire resistance ratings of LSF walls in the case of prolonged fires.

Numerical modelling and design of unlined cold-formed steel wall frames

Cold-formed steel wall frame systems using lipped or unlipped C-sections and gypsum plasterboard lining are commonly utilised in the construction of both the load bearing and non-load bearing walls in the residential, commercial and industrial buildings. However, the structural behaviour of unlined and lined stud wall frames is not well understood and adequate design rules are not available. A detailed research program was therefore undertaken to investigate the behaviour of stud wall frame systems. As the first step in this research, the problem relating to the degree of end fixity of stud was investigated. The studs are usually connected to the top and bottom tracks and the degree of end fixity provided by these tracks is not adequately addressed by the design codes. A finite element model of unlined frames was therefore developed, and validated using full scale experimental results. It was then used in a detailed parametric study to develop appropriate design rules for unlined wall frames. This study has shown that by using appropriate effective length factors, the ultimate load and failure modes of the unlined studs can be accurately predicted using the provisions of Australian or American cold-formed steel structures design codes. This paper presents the details of the finite element analyses, the results and recommended design rules for unlined wall frames.

Improved shear design rules of cold-formed steel beams

Light gauge cold-formed steel sections have been developed as more economical building solutions to the alternative heavier hot-rolled sections in the commercial and residential markets. Cold-formed lipped channel beams (LCB), LiteSteel beams (LSB) and triangular hollow flange beams (THFB) are commonly used as flexural members such as floor joists and bearers while rectangular hollow flange beams (RHFB) are used in small scale housing developments through to large building structures. However, their shear capacities are determined based on conservative design rules. For the shear design of cold-formed steel beams, their elastic shear buckling strength and the potential post-buckling strength must be determined accurately. Hence experimental and numerical studies were conducted to investigate the shear behaviour and strength of LCBs, LSBs, THFBs and RHFBs. Improved shear design rules including the direct strength method (DSM) based design equations were developed to determine the ultimate shear capacities of these open and hollow flange steel beams. An improved equation for the higher elastic shear buckling coefficient of cold-formed steel beams was proposed based on finite element analysis results and included in the design equations. A new post-buckling coefficient was also introduced in the design equations to include the available post-buckling strength of cold-formed steel beams. This paper presents the details of this study on cold-formed steel beams subject to shear, and the results. It proposes generalised and improved shear design rules that can be used for any type of cold-formed steel beam.

Buckling behaviour and design of tapered steel lighting masts

Tapered tubular steel masts are commonly used to support floodlights in a range of applications. The design of these slender tapered masts requires a rational elastic flexural buckling analysis as the thickness also varies with height. Therefore a series of finite element analyses of tapered masts with varying geometry parameters was conducted to develop an elastic flexural buckling load formula. This paper briefly discusses the design methods, and then presents the details of the finite element analyses and the results. 1–Associate Professor of Civil Engineering, and Director, Physical Infrastructure Centre 2–Former BE (Civil) Student, QUT

Refined Plastic Hinge Analysis of Steel Frame Structures Comprising Non-Compact Sections: I: Formulation

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity formulation suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. This formulation, referred to as the refined plastic hinge method, implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling.