The present dissertation contributes to advancing methods of determining the elastic and inelastic buckling resistance of compressive members with single angle and back-to-back double angle cross-sections with end conditions representative of those commonly used in steel construction. The first contribution develops an elastic buckling solution for members with asymmetric sections, such as unequal-leg angle members, connected to gusset plates at both ends and subjected to pure compression. In this case, the gusset plate connections at the member ends provide a fixity restraint to the member within the plane of the gusset and nearly a pin restraint in a plane normal to the gusset. Since both directions do not coincide with the principal directions of the member, the classical flexural-torsional buckling solutions provided in standards become inapplicable. In this context, a variational principle is formulated based on non-principal directions and then used to derive the governing differential equations and associated boundary conditions for the problem. The coupled equations are then solved analytically subject to the boundary conditions, and the characteristic equations are recovered and solved for the flexural-torsional buckling load of the member. The validity of the solutions derived is assessed against 3D shell elastic eigen-value buckling models based on ABAQUS for benchmark cases and the solution is shown to accurately predict the elastic buckling load and mode shapes. The effect of non-principal end restraints on the buckling load of compression members is then investigated for members with angle and zed cross-sections in a parametric study. It is observed that when a member end is fixed about a non-principal direction and pinned about the orthogonal direction, the flexural-torsional buckling load of the member is significantly influenced by the angle of inclination between the fixity axis and the minor principal axis. The second contribution aims to obtain the inelastic buckling resistance for single angle compression members with end gusset plate connections by taking into consideration the effects of material and geometric nonlinearity, initial out-of-straightness, residual stresses, and load eccentricity induced by the offset of the member centroidal axis from the end gusset plate connection. Towards this goal, a series of 3D shell models based on ABAQUS are developed and validated through comparisons against experimental results by others and then used to generate a database of compressive capacities for over 900 eccentrically loaded angle members with various geometrical dimensions and load eccentricities. The database is then used to investigate the effect of slenderness ratio, leg width ratio, connected leg width-to-thickness ratio and gusset plate-to-angle thickness ratio on the compressive resistance of the members, assess the accuracy of solutions available in present design standards, and develop improved design expressions for the compressive resistance for the members. The third contribution develops solutions for predicting the elastic buckling resistance of back-to-back double angle assemblies with end gusset plates and intermediate interconnectors subjected to compressive loads. Towards this goal, two novel models are developed. (1) A thin-walled finite element buckling solution is formulated and implemented into a MATLAB code. The formulation treats each angle member as a line of 1D thin-walled beam elements where then both angle members are connected at intermediate points along the span at the locations of interconnectors. The formulation is equipped with a multi-point constraint feature to enforce the kinematic constraints at the interconnector locations and at both extremities of the member. The model captures the tendency of both angles to open relative to one another in between interconnectors while undergoing flexural-torsional buckling. (2) An analytical buckling solution is developed for the limiting case where enough interconnectors are provided between members to force the two angles to essentially behave as a monolithic entity. The resistance predicted by the former model was then shown to asymptotically approach that predicted by the later model as the number of interconnectors is increased. The validity of the finite element model is assessed against 3D shell models based on ABAQUS and published experimental results, and then used to assess the validity of present design rules based on the effective slenderness concept. The present models are then used to carry out a parametric study of 1250 runs while varying the member slenderness ratio, leg width ratio, connected leg width-to-thickness ratio, and angle spacing-to-thickness ratio. The database of results generated is used to develop a simple expression to characterize the elastic buckling load/stress of the assembly. The possible integration of the new expression with present design provisions in standards to predict the inelastic buckling resistance of the member is illustrated through a design example.

This research investigates if the LRFD strength reduction factor for cold-formed steel compression members can be increased above its current value of Ï c = 0.85, which was established by the LRFD Cold-Formed Steel Design Manual (1991) on the basis of 264 column tests. The resistance factor in the Canadian code for cold-formed steel compression members is also evaluated. A total of 675 concentrically loaded plain and lipped C-section columns, plain and lipped Z-section columns, hat and angle columns, including members with holes, are considered in the study. The predicted strengths are calculated with the AISI-S100-07 Main Specification and the AISI Direct Strength Method. The test-to-predicted strength statistics are employed with the first order second moment reliability approach in AISI-S100-07 Chapter F as well as a higher order method to calculate the resistance factor per cross-section type, ultimate limit state, and considering partially and fully effective columns. The observed trends support a higher resistance factor for columns buckling in a distortional buckling limit state and an expansion of the current DSM prequalified limits. The results also show that DSM predicts the column capacity more accurately than the Main Specification. The test-to-predicted ratios for plain and lipped angle columns exhibit a high coefficient of variation and become more and more conservative as global slenderness increases. It is concluded that fundamental research on the mechanics of angle compression members is needed to improve existing design methods. / Master of Science

Thesis (MScEng (Civil Engineering))--Stellenbosch University, 2008. / The Southern African Institute of Steel Construction expressed concern with regard to the unit definition of the effective length factor, K, stipulated for compressive elements of parallel chord trusses in Clause 15 of SANS 10162-1:2005 - Limit state design of hot-rolled steelwork. The simplified method for truss design specified in the code assumes all compression members are pin-connected, which allows for greater design simplicity and reduces the amount of code interpretation required by the designer. In addition to this, Clause 15 requires the additional reduction in resistance of the first web compression members by a factor of 0.85. However, this approach may be considered overly conservative and in current design practice the effective length factor is often reduced to less than 1.0. This research investigates the effective length factor of web compression members in parallel chord trusses, by means of investigative structural analyses of representative trusses using ANGELINE and Prokon analytical programs, and by designing, constructing and testing six representative trusses, using current design practices. A comparative study of a number of different countries’ codified approaches to truss design is also included. The structural analyses revealed that in-plane buckling of the web compression members was the consistent mode of failure, however at a much greater applied load than the design load determined according to SANS 10162-1:2005. Contrary to the expected mode of failure, all six tests performed on the representative trusses exhibited elastic out-of-plane buckling, or strongaxis buckling, of the web compression members, but still at a much greater applied load than the design load. The unexpected out-of-plane buckling of the web members is due to the inplane stiffness of the end connections used. In order to stay true to current design practice, gusset plates and longitudinal welds were used to join the web members to the chords. The stiffness of the gusset plates therefore significantly reduced the effective length of the web compression members in-plane, but did not reduce the effective length out-of-plane. Despite the unanticipated behaviour of the tests performed, certain conclusions can still be drawn from the results. The unit definition of the effective length factor for in-plane buckling of web compression members is too conservative and a K factor of 0.8 is recommended. In addition to this an effective length factor for out-plane-buckling of web compression members of 1.1 is recommended for trusses with welded connections. The necessity of the reduction in resistance of 0.85 of the first web compression members requires further investigation. The most important conclusion to be drawn is that out-of-plane buckling of web compression members can be the dominant failure mode, which is not taken into consideration in current design practice.

In recent times, light gauge cold-formed steel sections have been used extensively in residential, industrial and commercial buildings as primary load bearing structural components. This is because cold-formed steel sections have a very high strength to weight ratio compared with thicker hot-rolled steel sections, and their manufacturing process is simple and cost-effective. However, these members are susceptible to various buckling modes including local and distortional buckling and their ultimate strength behaviour is governed by these buckling modes. Fire safety design of building structures has received greater attention in recent times due to continuing loss of properties and lives during fires. Hence, there is a need to fully evaluate the performance of light gauge cold-formed steel structures under fire conditions. Past fire research has focused heavily on heavier, hot-rolled steel members. The buckling behaviour of light gauge cold-formed steel members under fire conditions is not well understood. The buckling effects associated with thin steels are significant and have to be taken into account in fire safety design. Therefore, a research project based on extensive experimental and numerical studies was undertaken at the Queensland University of Technology to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. As the first phase of this research program more than 115 tensile coupon tests of light gauge cold-formed steels including two steel grades and five thicknesses were conducted at elevated temperatures. Accurate mechanical properties including the yield strength, elasticity modulus and stress-strain curves were all determined at elevated temperatures since the deterioration of the mechanical properties is one of the major parameters in the structural design under fire conditions. An appropriate stress-strain model was also developed by considering the inelastic characteristics. The results obtained from the tensile coupon tests were then used to predict the ultimate strength of cold-formed steel compression members. In the second phase of this research more than 170 laboratory experiments were undertaken to investigate the distortional buckling behaviour of light gauge coldformed steel compression members at ambient and elevated temperatures. Two types of cross sections were selected with various thicknesses (nominal thicknesses are 0.6, 0.8, and 0.95 mm) and both low and high strength steels (G250 and G550 steels with minimum yield strengths of 250 and 550 MPa). The experiments were conducted at six different temperatures in the range of 20 to 800°C. A finite element model of the tested compression members was then developed and validated with the help of experimental results. The degradation of mechanical properties with increasing temperatures was included in finite element analyses. An extensive series of parametric analyses was undertaken using the validated finite element model to investigate the effect of all the influential parameters such as section geometry, steel thickness and grade, mechanical properties and temperature. The resulting large data base of ultimate loads of compression members subject to distortional buckling was then used to review the adequacy of the current design rules at ambient temperature. The current design rules were reasonably accurate in general, but in order to improve the accuracy further, this research has developed new design equations to determine the ultimate loads of compression members at ambient temperature. The developed equation was then simply modified by including the relevant mechanical properties at elevated temperatures. It was found that this simple modification based on reduced mechanical properties gave reasonable results, but not at higher temperatures. Therefore, they were further modified to obtain a more accurate design equation at elevated temperatures. The accuracy of new design rules was then verified by comparing their predictions with the results obtained from the parametric study. This thesis presents a description of the experimental and numerical studies undertaken in this research and the results including comparison with simply modified current design rules. It describes the laboratory experiments at ambient and elevated temperatures. It also describes the finite element models of cold-formed steel compression members developed in this research that included the appropriate mechanical properties, initial geometric imperfections and residual stresses. Finally, it presents the details of the new design equations proposed for the light gauge coldformed steel compression members subjected to distortional buckling effects at elevated temperatures.

Cold-formed steel members have been widely used in residential, industrial and commercial buildings as primary load bearing structural elements and non-load bearing structural elements (partitions) due to their advantages such as higher strength to weight ratio over the other structural materials such as hot-rolled steel, timber and concrete. Cold-formed steel members are often made from thin steel sheets and hence they are more susceptible to various buckling modes. Generally short columns are susceptible to local or distortional buckling while long columns to flexural or flexural-torsional buckling. Fire safety design of building structures is an essential requirement as fire events can cause loss of property and lives. Therefore it is essential to understand the fire performance of light gauge cold-formed steel structures under fire conditions. The buckling behaviour of cold-formed steel compression members under fire conditions is not well 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 at the Queensland University of Technology to investigate the buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. As the first phase of this research, a detailed review was undertaken on the mechanical properties of light gauge cold-formed steels at elevated temperatures and the most reliable predictive models for mechanical properties and stress-strain models based on detailed experimental investigations were identified. Their accuracy was verified experimentally by carrying out a series of tensile coupon tests at ambient and elevated temperatures. As the second phase of this research, local buckling behaviour was investigated based on the experimental and numerical investigations at ambient and elevated temperatures. First a series of 91 local buckling tests was carried out at ambient and elevated temperatures on lipped and unlipped channels made of G250-0.95, G550-0.95, G250-1.95 and G450-1.90 cold-formed steels. Suitable finite element models were then developed to simulate the experimental conditions. These models were converted to ideal finite element models to undertake detailed parametric study. Finally all the ultimate load capacity results for local buckling were compared with the available design methods based on AS/NZS 4600, BS 5950 Part 5, Eurocode 3 Part 1.2 and the direct strength method (DSM), and suitable recommendations were made for the fire design of cold-formed steel compression members subject to local buckling. As the third phase of this research, flexural-torsional buckling behaviour was investigated experimentally and numerically. Two series of 39 flexural-torsional buckling tests were undertaken at ambient and elevated temperatures. The first series consisted 2800 mm long columns of G550-0.95, G250-1.95 and G450-1.90 cold-formed steel lipped channel columns while the second series contained 1800 mm long lipped channel columns of the same steel thickness and strength grades. All the experimental tests were simulated using a suitable finite element model, and the same model was used in a detailed parametric study following validation. Based on the comparison of results from the experimental and parametric studies with the available design methods, suitable design recommendations were made. This thesis presents a detailed description of the experimental and numerical studies undertaken on the mechanical properties and the local and flexural-torsional bucking behaviour of cold-formed steel compression member at ambient and elevated temperatures. It also describes the currently available ambient temperature design methods and their accuracy when used for fire design with appropriately reduced mechanical properties at elevated temperatures. Available fire design methods are also included and their accuracy in predicting the ultimate load capacity at elevated temperatures was investigated. This research has shown that the current ambient temperature design methods are capable of predicting the local and flexural-torsional buckling capacities of cold-formed steel compression members at elevated temperatures with the use of reduced mechanical properties. However, the elevated temperature design method in Eurocode 3 Part 1.2 is overly conservative and hence unsuitable, particularly in the case of flexural-torsional buckling at elevated temperatures.

Dieses Projekt widmete sich einer neuen Bauweise für stabförmige Drucktragglieder aus ultrahochfestem Beton (UHFB), die - als UHFB-Rohre mit Stahlrohren ummantelt - hier als Hybridrohre bezeichnet werden. Durch eine äußere Wickelverstärkung aus kohlenstofffaserverstärktem Kunststoff (CFK) werden die beiden, für sich alleine betrachtet ausgeprägt spröden Hochleistungsmaterialien UHFB und CFK so kombiniert, dass sie zu besonders leichten Bauteilen hoher Tragfähigkeit mit ausgeprägt duktilem Versagensverhalten zusammengefügt werden. [Aus: Motivation und Zielsetzung] / This project was dedicated to a new construction method for rod-shaped support elements made of ultra-high performance concrete (UHPC), which - as UHPC tubes coated with steel sheets - are called hybrid tubes in this report. Through an exterior wrapping-reinforcement made of carbon fibre reinforced plastic (CFRP), the two high-performance materials UHPC and CFRP, which are distinctly brittle when viewed on their own, are combined in such a way that they form particularly light components of high load-bearing capacity with profound ductile failure behaviour. [Off: Motivation and objective]

The importance of fire safety design has been realised due to the ever increasing loss of properties and lives caused by structural failures during fires. In recognition of the importance of fire safety design, extensive research has been undertaken in the field of fire safety of buildings and structures especially over the last couple of decades. In the same period, the development of fire safety engineering principles has brought significant reduction to the cost of fire protection. However the past fire research on steel structures has been limited to heavier, hot-rolled structural steel members and thus the structural behaviour of light gauge cold-formed steel members under fire conditions is not well understood. Since cold-formed steel structures have been commonly used for numerous applications and their use has increased rapidly in the last decade, the fire safety of cold-formed steel structural members has become an important issue. The current design standards for steel structures have simply included a list of reduction factors for the yield strength and elasticity modulus of hot-rolled steels without any detailed design procedures. It is not known whether these reduction factors are applicable to the commonly used thin, high strength steels in Australia. Further, the local buckling effects dominate the structural behaviour of light gauge cold-formed steel members. Therefore an extensive research program was undertaken at the Queensland University of Technology to investigate the local buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. The first phase of this research program included 189 tensile coupon tests including three steel grades and six thicknesses to obtain the accurate yield strength and elasticity modulus values at elevated temperatures because the deterioration of the mechanical properties is the major parameter in the structural design under fire conditions. The results obtained from the tensile tests were used to predict the ultimate strength of cold-formed steel members. An appropriate stress-strain model was also developed by considering the inelastic mechanical characteristics. The second phase of this research was based on a series of more than 120 laboratory experiments and corresponding numerical analyses on cold-formed steel compression members to investigate the local bucking behaviour of the unstiffened flange elements, stiffened web elements and stiffened web and flange elements at elevated temperatures up to 800°C. The conventional effective design rules were first simply modified considering the reduced mechanical properties obtained from the tensile coupon tests and their adequacy was studied using the experimental and numerical results. It was found that the simply modified effective width design rules were adequate for low strength steel members and yet was not adequate for high strength cold-formed steel members due to the severe reduction of the ultimate strength in the post buckling strength range and the severe reduction ratio of the elasticity modulus to the yield strength at elevated temperatures. Due to the inadequacy of the current design rules, the theoretical, semi-empirical and empirical effective width design rules were developed to accurately predict the ultimate strength of cold-formed steel compression members subject to local buckling effects at elevated temperatures. The accuracy of these new design methods was verified by comparing their predictions with a variety of experimental and numerical results. This thesis presents the details of extensive experimental and numerical studies undertaken in this research program and the results including comparison with simply modified effective width design rules. It also describes the advanced finite element models of cold-formed steel compression members developed in this research including the appropriate mechanical properties, initial imperfections, residual stresses and other significant factors. Finally, it presents the details of the new design methods proposed for the cold-formed steel compression members subject to local buckling effects at elevated temperatures.