Improved design rules for cold-formed steel columns

Current design rules for determining the member strength of cold-formed steel columns are based on the effective length of the member and a single column capacity curve for both pin-ended and fixed-ended columns. This research has reviewed the use of AS/NZS 4600 design rules for their accuracy in determining the member compression capacities of slender cold-formed steel columns using detailed numerical studies. It has shown that AS/NZS 4600 design rules accurately predicted the capacities of pinned and fixed ended columns undergoing flexural buckling. However, for fixed ended columns undergoing flexural-torsional buckling, it was found that current AS/NZS 4600 design rules did not include the beneficial effect of warping fixity. Therefore AS/NZS 4600 design rules were found to be excessively conservative and hence uneconomical in predicting the failure loads obtained from tests and finite element analyses of fixed-ended lipped channel columns. Based on this finding, suitable recommendations have been made to modify the current AS/NZS 4600 design rules to more accurately reflect the results obtained from the numerical and experimental studies conducted in this research. This paper presents the details of this research on cold-formed steel columns and the results.

Improved design rules for fixed ended cold-formed steel columns subject to flexural-torsional buckling

This paper has presented the details of an investigation into the flexural and flexuraltorsional buckling behaviour of cold-formed structural steel columns with pinned and fixed ends. Current design rules for the member capacities of cold-formed steel columns are based on the same non-dimensional strength curve for both fixed and pinned-ended columns. This research has reviewed the accuracy of the current design rules in AS/NZS 4600 and the North American Specification in determining the member capacities of cold-formed steel columns using the results from detailed finite element analyses and an experimental study of lipped channel columns. It was found that the current Australian and American design rules accurately predicted the member capacities of pin ended lipped channel columns undergoing flexural and flexural torsional buckling. However, for fixed ended columns with warping fixity undergoing flexural-torsional buckling, it was found that the current design rules significantly underestimated the column capacities as they disregard the beneficial effect of warping fixity. This paper has therefore proposed improved design rules and verified their accuracy using finite element analysis and test results of cold-formed lipped channel columns made of three cross-sections and five different steel grades and thicknesses.

Refined plastic hinge analysis of steel frame structures comprising non-compact sections : II : verification

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 refined plastic hinge method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in a companion paper. The method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established in this paper by comparison with a comprehensive range of analytical benchmark frame solutions. The refined plastic hinge method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Pseudo plastic zone analysis of steel frame structures comprising non-compact sections

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 method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. The pseudo plastic zone method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established by comparison with a comprehensive range of analytical benchmark frame solutions. The pseudo plastic zone method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Investigation into the bond between CFRP and steel tubes

CFRP material has been widely used to strengthen concrete structures. There is an increasing trend of using CFRP in strengthening steel structures. The bond between steel and CFRP is a key issue. Relatively less work has been done on the bond between CFRP and a curved surface which is often found in tubular structures. This paper reports a study on the bond between CFRP and steel tubes. A series of tensile tests were conducted with different bond lengths and number of layers. The types of adhesive and specimen preparation methods varied in the testing program. High modulus CFRP was used. Tests were carried out to measure the modulus and tensile strength of CFRP. Strain gages were mounted on different layers of CFRP. The stress distributions across the layers of the CFRP were established. Models were developed to estimate the maximum load for a given CFRP arrangement.

Second-order inelastic analysis of composite framed structures based on the refined plastic hinge method

Composite steel-concrete structures experience non-linear effects which arise from both instability-related geometric non-linearity and from material non-linearity in all of their component members. Because of this, conventional design procedures cannot capture the true behaviour of a composite frame throughout its full loading range, and so a procedure to account for those non-linearities is much needed. This paper therefore presents a numerical procedure capable of addressing geometric and material non-linearities at the strength limit state based on the refined plastic hinge method. Different material non-linearity for different composite structural components such as T-beams, concrete-filled tubular (CFT) and steel-encased reinforced concrete (SRC) sections can be treated using a routine numerical procedure for their section properties in this plastic hinge approach. Simple and conservative initial and full yield surfaces for general composite sections are proposed in this paper. The refined plastic hinge approach models springs at the ends of the element which are activated when the surface defining the interaction of bending and axial force at first yield is reached; a transition from the first yield interaction surface to the fully plastic interaction surface is postulated based on a proposed refined spring stiffness, which formulates the load-displacement relation for material non-linearity under the interaction of bending and axial actions. This produces a benign method for a beam-column composite element under general loading cases. Another main feature of this paper is that, for members containing a point of contraflexure, its location is determined with a simple application of the method herein and a node is then located at this position to reproduce the real flexural behaviour and associated material non-linearity of the member. Recourse is made to an updated Lagrangian formulation to consider geometric non-linear behaviour and to develop a non-linear solution strategy. The formulation with the refined plastic hinge approach is efficacious and robust, and so a full frame analysis incorporating geometric and material non-linearity is tractable. By way of contrast, the plastic zone approach possesses the drawback of strain-based procedures which rely on determining plastic zones within a cross-section and which require lengthwise integration. Following development of the theory, its application is illustrated with a number of varied examples.

Direct second-order elastic analysis for steel frame design

The traditional structural design procedure, especially for the large-scale and complex structures, is time consuming and inefficient. This is due primarily to the fact that the traditional design takes the second-order effects indirectly by virtue of design specifications for every member instead of system analysis for a whole structure. Consequently, the complicated and tedious design procedures are inevitably necessary to consider the second-order effects for the member level in design specification. They are twofold in general: 1) Flexural buckling due to P-d effect, i.e. effective length. 2) Sway effect due to P-D effect, i.e. magnification factor. In this study, a new system design concept based on the second-order elastic analysis is presented, in which the second-order effects are taken into account directly in the system analysis, and also to avoid the tedious member-by-member stability check. The plastic design on the basis of this integrated method of direct approach is ignored in this paper for simplicity and clarity, as the only emphasis is placed on the difference between the second-order elastic limit-state design and present system design approach. A practical design example, a 57m-span dome steel skylight structure, is used to demonstrate the efficiency and effectiveness of the proposed approach. This skylight structure is also designed by the traditional design approach BS5950-2000 for comparison on which the emphasis of aforementioned P-d and P-D effects is placed.

Performance-based structural fire design of steel frames using conventional computer software

Fire incident in buildings is common, so the fire safety design of the framed structure is imperative, especially for the unprotected or partly protected bare steel frames. However, software for structural fire analysis is not widely available. As a result, the performance-based structural fire design is urged on the basis of using user-friendly and conventional nonlinear computer analysis programs so that engineers do not need to acquire new structural analysis software for structural fire analysis and design. The tool is desired to have the capacity of simulating the different fire scenarios and associated detrimental effects efficiently, which includes second-order P-D and P-d effects and material yielding. Also the nonlinear behaviour of large-scale structure becomes complicated when under fire, and thus its simulation relies on an efficient and effective numerical analysis to cope with intricate nonlinear effects due to fire. To this end, the present fire study utilizes a second order elastic/plastic analysis software NIDA to predict structural behaviour of bare steel framed structures at elevated temperatures. This fire study considers thermal expansion and material degradation due to heating. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. This finite element stiffness formulation of beam-column elements is derived from the fifth-order PEP element which facilitates the computer modeling by one member per element. The Newton-Raphson method is used in the nonlinear solution procedure in order to trace the nonlinear equilibrium path at specified elevated temperatures. Several numerical and experimental verifications of framed structures are presented and compared against solutions in literature. The proposed method permits engineers to adopt the performance-based structural fire analysis and design using typical second-order nonlinear structural analysis software.

Analysis of steel structures for first- and second-order element (displacement and force) solutions

Finite element method (FEM) relies on an approximate function to fit into a governing equation and minimizes the residual error in the integral sense in order to generate solutions for the boundary value problems (nodal solutions). Because of this FEM does not show simultaneous capacities for accurate displacement and force solutions at node and along an element, especially when under the element loads, which is of much ubiquity. If the displacement and force solutions are strictly confined to an element’s or member’s ends (nodal response), the structural safety along an element (member) is inevitably ignored, which can definitely hinder the design of a structure for both serviceability and ultimate limit states. Although the continuous element deflection and force solutions can be transformed into the discrete nodal solutions by mesh refinement of an element (member), this setback can also hinder the effective and efficient structural assessment as well as the whole-domain accuracy for structural safety of a structure. To this end, this paper presents an effective, robust, applicable and innovative approach to generate accurate nodal and element solutions in both fields of displacement and force, in which the salient and unique features embodies its versatility in applications for the structures to account for the accurate linear and second-order elastic displacement and force solutions along an element continuously as well as at its nodes. The significance of this paper is on shifting the nodal responses (robust global system analysis) into both nodal and element responses (sophisticated element formulation).

Fire resistance rating of light gauge steel frame walls exposed to realistic design fires : a review and development of time equivalent approach

This paper presents the details of research undertaken on the development of an energy based time equivalent approach for light gauge steel frame (LSF) walls. This research utilized an energy based time equivalent approach to obtain the fire resistance ratings (FRR) of LSF walls exposed to realistic design fires with respect to standard fire exposure [1]. It is based on the equal area concept of fire severity and relates to the amount of energy transferred to the member. The proposed method was used to predict the fire resistance of single and double plasterboard lined and externally insulated LSF walls. The predicted fire resistance ratings were compared with the results from finite element analyses and fire design rules for three different wall configurations. This paper presents the review of the available time equivalent approaches and the development of energy based time equivalent approach for the prediction of fire resistance ratings of LSF walls exposed to realistic design fires.

Flexural–torsional buckling behaviour and design of cold-formed steel compression members at elevated temperatures

Current design rules for the member capacities of cold-formed steel columns are based on the same non-dimensional strength curve for both fixed and pinned-ended columns at ambient temperature. This research has investigated the accuracy of using current ambient temperature design rules in Australia/New Zealand (AS/NZS 4600), American (AISI S100) and European (Eurocode 3 Part 1.3) standards in determining the flexural–torsional buckling capacities of cold-formed steel columns at uniform elevated temperatures using appropriately reduced mechanical properties. It was found that these design rules accurately predicted the member capacities of pin ended lipped channel columns undergoing flexural torsional buckling at elevated temperatures. However, for fixed ended columns with warping fixity undergoing flexural–torsional buckling, the current design rules significantly underestimated the column capacities as they disregard the beneficial effect of warping fixity. This paper has therefore recommended the use of improved design rules developed for ambient temperature conditions to predict the axial compression capacities of fixed ended columns subject to flexural–torsional buckling at elevated temperatures within AS/NZS 4600 and AISI S100 design provisions. The accuracy of the proposed fire design rules was verified using finite element analysis and test results of cold-formed lipped channel columns at elevated temperatures except for low strength steel columns with intermediate slenderness whose behaviour was influenced by the increased nonlinearity in the stress–strain curves at elevated temperatures. Further research is required to include these effects within AS/NZS 4600 and AISI S100 design rules. However, Eurocode 3 Part 1.3 design rules can be used for this purpose by using suitable buckling curves as recommended in this paper.

Design of cold-formed steel columns at elevated temperatures subject to flexural-torsional buckling

Cold-formed steel members are often subject to axial compression loads in a range of applications. These thin-walled members can be subject to various types of buckling modes, including flexural-torsional buckling. Design standards provide guidelines for columns subject to flexural-torsional buckling modes at ambient temperature. However, there are no specific design guidelines for elevated temperature conditions. Hence extensive research efforts have gone into the many investigations addressing the flexural-torsional buckling behaviour of cold-formed steel columns at elevated temperatures.This research has reviewed the accuracy of the current design rules in AS/NZS 4600 and the North American Specification in determining the member capacities of cold-formed steel columns using the results from detailed finite element analyses and an experimental study of lipped channel columns. It was found that the current ambient temperature Australian and American design rules accurately predicted the member capacities of pin ended lipped channel columns undergoing flexural torsional buckling at elevated temperatures by simply using the appropriate elevated temperature mechanical properties. However, for fixed ended columns with warping fixity undergoing flexural-torsional buckling, it was found that the current design rules significantly underestimated the column capacities as they disregard the beneficial effect of warping fixity. This research has therefore proposed improved design rules and verified their accuracy using finite element analysis and test results of cold-formed lipped channel columns made of three cross-sections and five different steel grades and thicknesses. This paper presents the details of this research study and the results.

Numerical studies on CFRP strengthened steel columns under transverse impact

Strengthening of metallic structures using carbon fibre reinforced polymer (CFRP) has become a smart strengthening option over the conventional strengthening method. Transverse impact loading due to accidental vehicular collision can lead to the failure of existing steel hollow tubular columns. However, knowledge is very limited on the behaviour of CFRP strengthened steel members under dynamic impact loading condition. This paper deals with the numerical simulation of CFRP strengthened square hollow section (SHS) steel columns under transverse impact loading to predict the behaviour and failure modes. The transverse impact loading is simulated using finite element (FE) analysis based on numerical approach. The accuracy of the FE modelling is ensured by comparing the predicted results with available experimental tests. The effects of impact velocity, impact mass, support condition, axial loading and CFRP thickness are examined through detail parametric study. The impact simulation results indicate that the strengthening technique shows an improved impact resistance capacity by reducing lateral displacement of the strengthened column about 58% compared to the bare steel column. Axial loading plays an important role on the failure behaviour of tubular column.

Finite element modeling of carbon fibre reinforced polymer (CFRP) strengthened steel tubes under axial impact

Steel hollow sections used in structures such as bridges, buildings and space structures involve different strengthening techniques according to their structural purpose and shape of the structural member. One such technique is external bonding of CFRP sheets to steel tubes. The performance of CFRP strengthening for steel structures has been proven under static loading while limited studies have been conducted on their behaviour under impact loading. In this study, a comprehensive numerical investigation is carried out to evaluate the response of CFRP strengthened steel tubes under dynamic axial impact loading. Impact force, axial deformation impact velocities are studied. The results of the numerical investigations are validated by experimental results. Based on the developed finite element (FE) model several output parameters are discussed. The results show that CFRP wrapping is an effective strengthening technique to increase the axial dynamic load bearing capacity by increasing the stiffness of the steel tube.

Web crippling tests of cold-formed steel channels under two flange load cases

Cold-formed steel members have many advantages over hot-rolled steel members. However, they are susceptible to various buckling modes at stresses below the yield stress of the member because of their relatively high width-to-thickness ratio. Web crippling is a form of localized failure mode that can occur when the members are subjected to transverse high concentrated loadings and/or reactions. The four common loading conditions are the end-one-flange (EOF), interior-one-flange (IOF), end-two-flange (ETF) and interior-two-flange (ITF) loadings. Recently a test method has been proposed by AISI to obtain the web crippling capacities under these four loading conditions. Using this test method 42 tests were conducted in this research to investigate the web crippling behaviour and strengths of unlipped channels with stocky webs under ETF and ITF cases. DuraGal sections having a nominal yield stress of 450 MPa were tested with different web slenderness and bearing lengths. The flanges of these channel sections were not fastened to the supports. In this research the suitability of the currently available design rules for unlipped channels subject to web crippling was investigated, and suitable modifications were proposed where necessary. In addition to this, a new design rule was proposed based on the direct strength method to predict the web crippling capacities of tested beams. This paper presents the details of this experimental study and the results.