Reliability-based evaluation of design code provisions for circular concrete-filled steel columns

This paper presents an investigation of design code provisions for steel-concrete composite columns. The study covers the national building codes of United States, Canada and Brazil, and the transnational EUROCODE. The study is based on experimental results of 93 axially loaded concrete-filled tubular steel columns. This includes 36 unpublished, full scale experimental results by the authors and 57 results from the literature. The error of resistance models is determined by comparing experimental results for ultimate loads with code-predicted column resistances. Regression analysis is used to describe the variation of model error with column slenderness and to describe model uncertainty. The paper shows that Canadian and European codes are able to predict mean column resistance, since resistance models of these codes present detailed formulations for concrete confinement by a steel tube. ANSI/AISC and Brazilian codes have limited allowance for concrete confinement, and become very conservative for short columns. Reliability analysis is used to evaluate the safety level of code provisions. Reliability analysis includes model error and other random problem parameters like steel and concrete strengths, and dead and live loads. Design code provisions are evaluated in terms of sufficient and uniform reliability criteria. Results show that the four design codes studied provide uniform reliability, with the Canadian code being best in achieving this goal. This is a result of a well balanced code, both in terms of load combinations and resistance model. The European code is less successful in providing uniform reliability, a consequence of the partial factors used in load combinations. The paper also shows that reliability indexes of columns designed according to European code can be as low as 2.2, which is quite below target reliability levels of EUROCODE. (C) 2009 Elsevier Ltd. All rights reserved.

Evaluation of passive confinement in CFT columns

This paper presents the experimental results of 32 axially loaded concrete-filled steel tubular columns (CFT). The load was introduced only on the concrete core by means of two high strength steel cylinders placed at the column ends to evaluate the passive confinement provided by the steel tube. The columns were filled with structural concretes with compressive strengths of 30, 60, 80 and 100 MPa. The outer diameter (D) of the column was 114.3 mm, and the length/diameter (L/D) ratios considered were 3, 5, 7 and 10. The wall thicknesses of the tubes (t) were 3.35 mm and 6.0 mm, resulting in diameter/thickness (D/t) ratios of 34 and 19, respectively. The force vs. axial strain curves obtained from the tests showed, in general, a good post-peak behavior of the CFT columns, even for those columns filled with high strength concrete. Three analytical models of confinement for short concrete-filled columns found in the literature were used to predict the axial capacity of the columns tested. To apply these models to slender columns, a correction factor was introduced to penalize the calculated results, giving good agreement with the experimental values. Additional results of 63 CFT columns tested by other researchers were also compared to the predictions of the modified analytical models and presented satisfactory results. (C) 2009 Elsevier Ltd. All rights reserved.

Influence of concrete strength and length/diameter on the axial capacity of CFT columns

This paper presents an experimental analysis of the confinement effects in steel-concrete composite columns regarding two parameters: concrete compressive strength and column slenderness. Sixteen concrete-filled steel tubular columns with circular cross section were tested under axial loading. The tested columns were filled by concrete with compressive strengths of 30, 60. 80, and 100 MPa, and had length/diameter ratios of 3, 5, 7, and 10. The experimental values of the columns` ultimate load were compared to the predictions of 4 code provisions: the Brazilian Code NBR 8800:2008, Eurocode 4 (EN 1994-1-1:2004), AINSI/AISC 360:2005, and CAN/CSA S16-01:2001. According to the results, the load capacity of the composite columns increased with increasing concrete strength and decreased with increasing length/diameter ratio. In general, the code provisions were highly accurate in the prediction of column capacity. Among them, the Brazilian Code was the most conservative, while Eurocode 4 presented the values closest to the experimental results. (C) 2009 Elsevier Ltd. All rights reserved.

Design of concrete-filled steel tubular columns under axial loading according to NBR 8800:2008 and Eurocode 4:2004: tests results and comparisons

In this paper results of tests on 32 concrete-filled steel tubular columns under axial load are reported. The test parameters were the concrete compressive strength, the column slenderness (L/D) and the wall thickness (t). The test results were compared with predictions from the codes NBR 8800:2008 and EN 1994-1-1:2004 (EC4). The columns were 3, 5, 7 and 10 length to diameter ratios (L/D) and were tested with 30MPa, 60MPa, 80MPa and 100MPa concrete compressive strengths. The results of ultimate strength predicted by codes showed good agreement with experimental results. The results of NBR 8800 code were the most conservative and the EC4 showed the best results, in mean, but it was not conservative for usual concrete-filled short columns.

Preloaded RC columns strengthened with high-strength concrete jackets under uniaxial compression

Although use of high-strength reinforced concrete (RC) jackets has become common practice worldwide, there are still two unresolved issues regarding the contribution of the original concrete and the effects of existing loads. Twelve RC-jacketed columns were tested with and without preloading under uniaxial compression. Tests showed the entire core to contribute to the capacity of the jacketed column, as long as adequate confinement is provided. Also, preloading does not adversely affect the capacity of the jacketed column, while it may increase its deformability, especially in square sections. Transverse reinforcement in the jacket directly improves ductility of the strengthened column, especially in circular sections.

Methodological analysis of gamma tomography system for large random packed columns

Gamma ray tomography experiments have been carried out to detect spatial patterns in the porosity in a 0.27 m diameter column packed with steel Rashig rings of different sizes: 12.6, 37.9, and 76 mm. using a first generation CT system (Chen et al., 1998). A fast Fourier transform tomographic reconstruction algorithm has been used to calculate the spatial variation over the column cross section. Cross-sectional gas porosity and solid holdup distribution were determinate. The values of cross-sectional average gas porosity were epsilon=0.849, 0.938 and 0.966 for the 12.6, 37.9, and 76 mm rings, respectively. Radial holdup variation within the packed bed has been determined. The variation of the circumferentially averaged gas holdup in the radial direction indicates that the porosity in the column wall region is a somewhat higher than that in the bulk region, due to the effect of the column wall. (C) 2009 Elsevier Ltd. All rights reserved.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

Project, modelling and simulation of air stripping columns for the treatment of groundwater contaminated with volatile organic compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for the column design for any particular type of packing and contaminant avoiding the necessity of a pre-defined diameter used in the classical approach. It also renders unnecessary the employment of the graphical Eckert generalized correlation for pressure drop estimates. The hydraulic features are previously chosen as a project criterion and only afterwards the mass transfer phenomena are incorporated, in opposition to conventional approach. The design procedure was translated into a convenient algorithm using C++ as programming language. A column was built in order to test the models used either in the design or in the simulation of the column performance. The experiments were fulfilled using a solution of chloroform in distilled water. Another model was built to simulate the operational performance of the column, both in steady state and in transient conditions. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting system of ODE can be solved, allowing for the calculation of the concentration profile in both phases inside the column. In transient state the system of PDE was numerically solved by finite differences, after a previous linearization.

Experimental assessment of pressure drop in air stripping columns

One important step in the design of air stripping operations for the removal of VOC is the choice of operating conditions, which are based in the phase ratio. This parameter sets on directly the stripping factor and the efficiency of the operation. Its value has an upper limit determined by the flooding regime, which is previewed using empirical correlations, namely the one developed by Eckert. This type of approach is not suitable for the development of algorithms. Using a pilot scale column and a convenient solution, the pressure drop was determined in different operating conditions and the experimental values were compared with the estimations. This particular research will be incorporated in a global model for simulating the dynamics of air stripping using a multi variable distributed parameter system.

A New Approach in the Design of Air Stripping Columns for the Treatment of Groundwater Contaminated With Volatile Organic Compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for column design for any type of packing and contaminant which avoids the necessity of an arbitrary chosen diameter. It also avoids the employment of the usual graphical Eckert correlations for pressure drop. The hydraulic features are previously chosen as a project criterion. The design procedure was translated into a convenient algorithm in C++ language. A column was built in order to test the design, the theoretical steady-state and dynamic behaviour. The experiments were conducted using a solution of chloroform in distilled water. The results allowed for a correction in the theoretical global mass transfer coefficient previously estimated by the Onda correlations, which depend on several parameters that are not easy to control in experiments. For best describe the column behaviour in stationary and dynamic conditions, an original mathematical model was developed. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting ODE can be solved by analytical methods, and in dynamic state the discretization of the PDE by finite differences allows for the overcoming of this difficulty. To estimate the contaminant concentrations in both phases in the column, a numerical algorithm was used. The high number of resulting algebraic equations and the impossibility of generating a recursive procedure did not allow the construction of a generalized programme. But an iterative procedure developed in an electronic worksheet allowed for the simulation. The solution is stable only for similar discretizations values. If different values for time/space discretization parameters are used, the solution easily becomes unstable. The system dynamic behaviour was simulated for the common liquid phase perturbations: step, impulse, rectangular pulse and sinusoidal. The final results do not configure strange or non-predictable behaviours.

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.

Strengthening to seismic action of reinforced columns with rectangular cross-section

The first part of this research work regards the assessment of the mathematical modelling of reinforced concrete columns confined with carbon fibre (CFRP) sheets under axial loading. The purpose was to evaluate existing analytical models, contribute to possible improvements and choose the best model(s) to be part of a new model for the prediction of the behaviour of confined columns under bending and compression. For circular columns, a wide group of authors have proposed several models specific for FRP-confined concrete. The analysis of some of the existing models was carried out by comparing these with several tested columns. Although several models predict fairly the peak load only few can properly estimate the load-strain and dilation behaviour of the columns. Square columns confined with CFRP show a more complex interpretation of their behaviour. Accordingly, the analysis of two experimental programs was carried out to propose new modelling equations for the whole behaviour of columns. The modelling results show that the analytical curves are in general agreement with the presented experimental curves for a wide range of dimensions. An analysis similar to the one done for circular columns was this turn carried out for square columns. Few models can fairly estimate the whole behaviour of the columns and with less accuracy at all levels when compared with circular columns. The second part of this study includes seven experimental tests carried out on reinforced concrete rectangular columns with rounded corners, different damage condition and with confinement and longitudinal strengthening systems. It was concluded that the use of CFRP confinement is viable and of effective performance enhancement alone and combined with other techniques, maintaining a good ductile behaviour for established threshold displacements. As regards the use of external longitudinal strengthening combined with CFRP confinement, this system is effective for the performance enhancement and viable in terms of execution. The load capacity was increased significantly, preserving also in this case a good ductile behaviour for threshold displacements. As to the numerical nonlinear modelling of the tested columns, the results show a variation of the peak load of 1% to 10% compared with tests results. The good results are partly due to the inclusion of the concrete constitutive model by Mander et al. modified by Faustino, Chastre & Paula taking into account the confinement effect. Despite the reasonable approximation to tests results, the modelling results showed higher unloading, which leads to an overestimate dissipated energy and residualdisplacement.

Assessing the production of jet mix columns using alkali activated waste based on mechanical and financial performance and CO2 (eq) emissions

Recent research has proved the potential of alkaline activated fly-ash for soil stabilisation. However, such studies have not focused on the link between financial, mechanical and environmental aspects of this solution, but only on their absolute mechanical properties. The present paper characterises the mechanical behaviour of a large spectrum of activator-ash-soil combinations used to build jet mixing columns, analysing also the cost and CO2 (eq) emissions. The concern with these two vectors forced a decrease in the quantity of stabilising agent added to the soil, relatively to previous research, and the effects of such low quantities have not yet been published. However, the results clearly showed a significant improve in strength, still well above the average values expected when improving the stressstrain behaviour of a weak soil. Uniaxial compressive strength tests were used to assess the effects of the fly-ash percentage, the alkalieash ratio and the water content. The carbon calculator recently developed by the European Federation of Foundation Contractors and the Deep Foundations Institute was used to quantify the CO2 (eq) emissions associated with this technique. The financial cost was estimated based on the experience of a major Portuguese contractor. For comparison purposes, soil cement mixtures were also analysed, using similar conditions and tools used for the soil-ash analysis. Results showed that the cement and ash solutions are very similar in terms of overall performance, with some advantage of the former regarding financial cost, and a significant advantage of the latter regarding the CO2 (eq) emissions. This new grout, although it is in an embryonic stage, it has the potential for broader developments in the field.

Nonsymmetrical separations in thermal diffusion columns

The influence of the feed composition upon the actual degrees of separation attained at the top and bottom sections of a thermogravitational column is discussed using the classical phenomenological theory of Furry, Jones, and Onsager. It is shown that, except for a feed composition of C 0 = 0.5 (mass fraction), the separation profile is nonsymmetric, i.e., the separations in the top and bottom sections of the column are nonsymmetric with respect to the feed composition, the asymmetry increasing as the feed composition moves away from C 0 = 0.5. An equation for the determination of the optimum feed location as a function of the feed composition is derived.

Some observations on asymmetrical separation in thermal diffusion columns

Data have been obtained in steady-state batch operated thermogravitational separation columns using different binary mixtures to test the theory recently published by Morgado et al. The experimental results confirm that separations by thermal diffusion are asymmetrical except when the initial concentration is 0.5 and that the asymmetry is larger as the initial concentration deviates from 0.5 and as the separation potential increases.