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Investigation of concrete-filled steel composite (CFSC) stub columns with bar stiffeners.

Reference to this paper should be made as follows: Bahrami, A.; Wan Badaruzzaman, W. H.; Osman, S. A. 2013. Investigation of concrete-filled steel composite (CFSC) stub columns with bar stiffeners, Journal of Civil Engineering and Management 19(3): 433-446.

Introduction

Steel columns have the benefits of high ductility and tensile strength; on the other hand, reinforced concrete columns possess the benefits of large stiffness and compressive strength. Composite columns which comprise steel and concrete also have the structural advantages of the two materials. Concrete-filled steel composite (CFSC) columns are an alternative to steel and reinforced concrete columns in modern civil projects worldwide. The steel consumption in the CFSC columns is less than the steel columns which leads to cost saving. Also, the CFSC columns not only have structural benefits such as high strength, large stiffness and high ductility but also possess ecological benefits over reinforced concrete columns: reinforcement and formwork are not utilised in the CFSC columns which result in a clean construction site; when the building is demolished, high-strength concrete which is without reinforcement in the CFSC columns can be easily crushed and reused as aggregates. Also, the steel wall which peels from the concrete core can be used again. A number of theoretical and experimental research works have been done during the past years on the CFSC columns. Shakir-Khalil and Mouli (1990) tested nine 3 m long composite columns of concrete-filled rectangular hollow sections and studied experimentally 12 short specimens under axial compression to establish the squash load of the stub columns. Effects of different materials and geometric properties on the strength and ductility of concrete-filled steel box columns were investigated by Uy (1998). Lakshmi and Shanmugam (2002) presented a semi-analytical method to predict the behaviour of in-filled steel-concrete composite columns. Twelve high-strength rectangular concrete-filled steel hollow section columns were tested under pure bending by Gho and Liu (2004). Liu (2005) evaluated experimentally 22 high-strength rectangular concrete-filled steel hollow section columns in order to investigate three parameters including material strength, cross sectional aspect ratio and volumetric steel-to-concrete ratio. Tests on concrete-filled steel tubular stub columns with inner and outer welded longitudinal stiffeners were reported by Tao et al. (2005) under axial compression. Guo et al. (2007) conducted tests on 24 bare steel and concrete-filled tubes to study the occurrence of local buckling. Reasons of the complex stress state appearance and behaviour of hollow concrete-filled steel tubular element components in various load stages of compressed stub structural member were analysed by Kuranovas and Kvedaras (2007). Han et al. (2008) performed 46 tests on thin-walled steel tube confined concrete stub columns subjected to axial compression to assess effects of sectional type, local compression area ratio and steel tube width-to-wall thickness ratio on the behaviour of the columns. Experimental investigation of stiffened thin-walled hollow steel structural stub columns filled with concrete was carried out by Tao et al. (2008) to uncover strength and ductility of such columns. Load carrying capacity of thin-walled box-section stub columns fabricated by high-strength steel was experimentally evaluated by Gao et al. (2009) under uniaxial compression. Several types of concrete-filled steel columns were tested by Kuranovas et al. (2009) to determine their load-carrying capacities. Petrus et al. (2010) presented effects of tab stiffeners on the bond and compressive strengths of concrete-filled thin-walled steel tubes. Goode et al. (2010) analysed the experimental data of concrete-filled steel tubes. Circular and rectangular hollow section stub and long columns fully with concrete were investigated with and without applied moments at the ends of the specimen. de Oliveira et al. (2010) assessed experimentally passive confinement effect of the steel tube in concrete-filled steel tubular columns. A series of tests were performed on short and slender concrete-filled stainless steel tubular columns by Uy et al. (2011) to illustrate their performance under axial compression and combined action of axial force and bending moment. Twenty-eight concrete-filled steel tubular stub columns subjected to eccentric partial compression were tested by Yang and Han (2011) to study effects of parameters such as section type, load eccentricity ratio and shape of the loading bearing plate. Bahrami et al. (2011a) studied structural behaviour of CFSC slender columns to investigate and develop different shapes (V, T, L, Line & Triangular) and number (1 on side & 2 on side) of longitudinal cold-formed steel sheeting stiffeners and also evaluate their effects on the behaviour of the columns. However, it seems that limited researches have been conducted on the behaviour of the CFSC stub columns with bar stiffeners.

This paper presents the investigation of the CFSC stub columns with bar stiffeners. To establish the accuracy of the modelling in this study, the experimental test result reported by Tao et al. (2005) is used to compare with the proposed three-dimensional (3D) finite element modelling. A special arrangement of bar stiffeners in the columns with various number, spacing and diameters of the bar stiffeners are developed using the non-linear finite element method. The investigation of the CFSC stub columns is further carried out by considering different variables in the non-linear finite element analyses. The main variables are such as number of bar stiffeners (2, 3 and 4), spacing of bar stiffeners (from 50 to 150 mm), diameter of bar stiffeners (from 8 to 12 mm), steel wall thicknesses (from 2 to 3 mm), concrete compressive strengths (from 30 to 50.1 MPa) and steel yield stresses (from 234.3 to 450 MPa). Effects of various number and spacing of the bar stiffeners and also steel wall thicknesses on the ultimate axial load capacity and ductility of the columns are evaluated. Also, effects of different diameters of the bar stiffeners, concrete compressive strengths and steel yield stresses on the ultimate axial load capacity of the columns are assessed. The obtained ultimate axial load capacities from the non-linear finite element analyses are compared with the predicted capacities by the design code Eurocode 4 (2004) and recommended equations by Baig et al. (2006) and Bahrami et al. (2011b).

1. Description of non-linear finite element modelling

The experimental test of a CFSC stub column performed by Tao et al. (2005) has been chosen for the non-linear modelling using the finite element software LUSAS herein. Figure 1 shows the cross section and elevation of the column. The steel wall thickness of the column was 2.5 mm. In the experimental test, concrete was vertically poured in the steel box in layers. Each layer was vibrated using a poker vibrator. The column was then located upright to air until testing. The environmental average temperature and relative humidity were about 15[degrees]C and 80%, respectively. The column was tested to failure under axial compression using a 5000 kN capacity testing machine after 28 days of curing in the laboratory. The test of the column was conducted with a loading rate of 0.2 mm/min before the ultimate load capacity was reached. The loading rate was thereafter changed to 0.5 mm/min.

1.1. Material properties and constitutive models

The steel wall, steel bar stiffener and concrete are the materials used in the numerical analysis of this study. The material properties and their constitutive models are presented as follows.

1.1.1. Steel wall

The steel wall has been modelled as an elasticperfectly plastic material in both tension and compression. Figure 2 illustrates the stress-strain curve used for the steel wall. The yield stress, modulus of elasticity and Poisson's ratio of the steel wall have been adopted identical to those of the corresponding experimental test done by Tao et al. (2005), respectively as 234.3 MPa, 208,000 MPa and 0.247. Von Mises yield criterion, an associated flow rule, and isotropic hardening have been employed in the nonlinear material model.

1.1.2. Steel bar stiffener

The uniaxial behaviour of the steel bar stiffener is similar to that of the steel wall. Accordingly, it can be simulated by the elastic-perfectly plastic material model (Fig. 2). The yield stress and modulus of elasticity of the steel bar stiffener have been taken as 400 MPa and 200,000 MPa, respectively.

1.1.3. Concrete

The compressive strength and modulus of elasticity of concrete have been taken identical to those of the corresponding experimental test done by Tao et al. (2005), respectively as 50.1 MPa and 35,100 MPa. Figure 3 indicates the equivalent uniaxial stress-strain curves utilised for concrete (Ellobody, Young 2006a, b). The unconfined concrete cylinder compressive strength [f.sub.c] is equal to 0.8[f.sub.cu] in which [f.sub.cu] is the unconfined concrete cube compressive strength. The corresponding unconfined strain [[epsilon].sub.c] is usually around the range of 0.002-0.003, as recommended by Hu et al. (2005). The [[epsilon].sub.c] was considered as 0.002 in their study. The same value for [[epsilon].sub.c] has been also adopted in the analyses of this study. When concrete is under laterally confining pressure, the confined compressive strength [f.sub.cc] and the corresponding confined strain [[epsilon].sub.cc] are much higher than those of unconfined concrete.

Eqns (1) and (2) have been respectively used to determine the confined concrete compressive strength [f.sub.cc] and the corresponding confined stain [[epsilon].sub.c] (Mander et al. 1988):

[f.sub.cc] = [f.sub.c] + [k.sub.1][f.sub.1]; (1)

[[epsilon].sub.cc] = [[epsilon].sub.c](1 + [k.sub.2][[f.sub.1]/[f.sub.c]]), (2)

where: [f.sub.1] is the lateral confining pressure provided by the steel wall for the concrete core. The approximate value of [f.sub.1] can be obtained from the interpolation of the values presented by Hu et al. (2003). The factors of [k.sub.1] and [k.sub.2] have been considered as 4.1 and 20.5, respectively (Richart et al. 1928). Because [f.sub.1], [k.sub.1] and [k.sub.2] are known [f.sub.cc] and [[epsilon].sub.cc] can be determined using Eqns (1) and (2).

The equivalent uniaxial stress-strain curve for confined concrete (Fig. 3) is consisted of three parts which should be defined. The first part comprises the initially assumed elastic range to the proportional limit stress. The value of the proportional limit stress has been considered as 0.5[f.sub.cc] (Hu et al. 2003). The empirical Eqn (3) has been used to obtain the initial Young's modulus of confined concrete [E.sub.cc] (ACI 31899 1999). The Poisson's ratio [[upsilon].sub.cc] of confined concrete has been chosen as 0.2:

[E.sub.cc] = 4700[square root of [E.sub.cc]] MPa. (3)

The second part is the non-linear portion which starts from the proportional limit stress 0.5[f.sub.cc] to the confined concrete strength [f.sub.cc]. The common Eqn (4) can be used to obtain this part (Saenz 1964). The values of uniaxial stress f and strain [epsilon] are the unknowns of the equation that define this part of the curve. The strain value o has been adopted between the proportional strain (0.5[f.sub.cc]/[E.sub.cc]), and the confined strain [[epsilon].sub.cc] which corresponds to the confined concrete strength. By assuming the strain values [epsilon], Eqn (4) can be used to calculate the stress values f:

f = [E.sub.cc][epsilon]/[1 + (R + [R.sub.E] - 2)([epsilon][[epsilon].sub.cc]) - (2R - 1)[([epsilon]/[[epsilon].sub.cc]).sup.2] + R[([epsilon]/[[epsilon].sub.cc]).sup.3]], (4)

where:

[R.sub.E] = [E.sub.cc][[epsilon].sub.cc]/[f.sub.cc]; (5)

R = [[R.sub.E]([R.sub.[sigma]] - 1)/[([R.sub.[epsilon]] - 1).sup.2]] - [1/[R.sub.[epsilon]]]. (6)

The constants [R.sub.[epsilon]] and [R.sub.[sigma]] have been considered as 4 in this study (Hu, Schnobrich 1989). The third part of the curve consists of the descending part that is between [f.sub.cc] and r[k.sub.3][f.sub.cc] with the corresponding strain of 11[[epsilon].sub.cc]. The reduction factor [k.sub.3] depends on the H/t ratio and the steel wall yield stress [f.sub.y]. Empirical equations given by Hu et al. (2003) can be used to determine the approximate value of [k.sub.3]. To take into account the effect of different concrete strengths, the reduction factor r was introduced by Ellobody et al. (2006) on the basis of the experimental study performed by Giakoumelis and Lam (2004). The value of r has been considered as 1.0 for concrete with cube strength [f.sub.cu] of 30 MPa and as 0.5 for concrete with [f.sub.cu] greater than or equal to 100 MPa (Mursi, Uy 2003). The value of r for concrete cube strength between 30 and 100 MPa has been interpolated in this study. A linear Drucker-Prager yield criterion G (Fig. 4) has been used to model the yielding part of the curve which is the part after the proportional limit stress (Ellobody, Young 2006a, b; Hu et al. 2005). This criterion has been utilised to define yield surface and flow potential parameters for concrete under triaxial compressive stresses. Also, this criterion has been used with associated flow and isotropic rule. The criterion is expressed as Eqn (7):

G = t - p tan [beta] - d = 0, (7)

in which t, p and d are obtained from the following equations:

t = [[square root of 3[J.sub.2]]/2][1 + [1/k] - (1 - [1/k])[(r/[square root of 3[J.sub.2]]).sup.3]]; (8)

r = [[[9/2]([S.sup.3.sub.1] + [S.sup.2.sub.3] + [S.sup.3.sub.3])].sup.1/3]; (9)

P = -([[sigma].sub.1] + [[sigma].sub.2] + [[sigma].sub.3])/3; (10)

d = (1 - [tan [beta]/3])[f'.sub.cc]. (11)

[S.sub.1], [S.sub.2] and [S.sub.3] are principal stress deviators, [[sigma].sub.1], [[sigma].sub.2] and [[sigma].sub.3] are the principle stresses and [J.sub.2] is the second stress invariant of the stress deviator tensor. The ratio of flow stress in triaxial tension to that in compression K and the material angle of friction [beta] have been chosen as 0.8 and 20[degrees], respectively (Hu et al. 2003).

1.2. Finite element type and mesh

Element types for the steel wall and concrete core of the columns were chosen from the element library of the finite element software LUSAS (2006) in this study. The 6-noded triangular shell element, TSL6, was utilised to model the steel wall. This is a thin, doubly-curved, isoparametric element that can be used to model 3D structures. It has six degrees of freedom per node and provides accurate solution to most applications. This element can accommodate generally curved geometry with varying thickness and anisotropic and composite material properties. The element formulation considers both membrane and flexural deformations. The steel bar stiffeners were modelled by the 3-noded bar element type BRS3. This is an isoparametric bar element in 3D which can accommodate varying cross sectional area. This element is suitable to model stiffening reinforcement with continuum elements. The 10-noded tetrahedral element, TH10, was used for modelling of the concrete core. This element is a 3D isoparametric solid continuum element capable of modelling curved boundaries. This is a standard volume element of the LUSAS software (2006). The elements can be employed for linear and complex non-linear analyses involving contact, plasticity and large deformations.

Different finite element mesh sizes were examined to find a reasonable mesh size which can achieve accurate results. As a result, the mesh size corresponding to 7713 elements was revealed to obtain exact results. A typical finite element mesh used in this study is illustrated in Figure 5.

1.3. Boundary conditions and load application

The pin-pin boundary conditions have been considered in the 3D finite element modelling in this study. Therefore, the rotations of the top and bottom surfaces of the columns in the X, Y and Z directions were considered to be free. Also, the displacements of the bottom and top surfaces in the X and Z directions were restrained. On the other hand, the displacement of the bottom surface in the Y direction was restrained while that of the top surface, in the direction of the applied load and where the load is applied, was set to be free.

The load application on the column in the modelling was on the basis of the loading arrangement in the corresponding experimental test of the column. The axial load of the experimental test was exactly modelled by incremental displacement load with an initial increment of 1 mm in the negative Y direction acting axially to the top surface of the column. Increment is a step in a non-linear analysis where a portion of the total load is applied. The increment change was 0.1 mm in the analysis. Iteration is a step within a load increment where the analysis solver attempts to converge to an acceptable solution. The iterations per increment were 10 in the analysis. Incremental loading adds displacements to a previous increment (LUSAS 2006). Each step in the non-linear analysis was a small amount of the displacement of the column and it was continued up to the failure of the column.

1.4. Modelling of concrete-steel interface

The contact between the concrete core and the steel wall was simulated by slide-lines. The slide-lines attributes can be used to model contact surfaces in the finite element software LUSAS (2006). The slideline contact facility is non-linear. Slave and master surfaces should be selected correctly to provide the contact between two surfaces, steel and concrete. If a smaller surface is in contact with a larger surface, the smaller surface can be best selected as the slave surface. If it is not possible to distinguish this point, the body which has higher stiffness should be selected as the master surface. It needs to be mentioned that the stiffness of the structure should be taken into account and not just the material. Although, the steel material is stiffer than the concrete material, the steel wall may have less stiffness than the volume of the concrete core in this study. Consequently, the concrete core and steel wall surfaces were respectively selected as the master and slave surfaces. Dabaon et al. (2009) has also presented this process of choosing master and slave surfaces. The slide-lines have the capability of defining properties such as friction coefficient. The friction between two surfaces, the steel wall and concrete core, is considered so that they can remain in contact. The Coulomb friction coefficient in slidelines was selected as 0.25. The slide-lines allow the concrete core and steel wall to separate or slide but not to penetrate each other.

1.5. Accuracy of modelling

The finite element modelling result was compared with the experimental test result reported by Tao et al. (2005) to reveal the accuracy of the 3D modelling in this study. According to Figure 6, the curves obtained from the modelling and corresponding experimental test agree well with each other. The difference between the ultimate axial load capacity obtained from the modelling 3325 kN, and that from the experimental test 3230 kN is only 2.9%. This small difference demonstrates the accuracy of the finite element modelling. As a result, the accurate prediction of the behaviour of the columns is absolutely possible by the proposed 3D finite element modelling in this study.

2. Numerical analysis

Since the proposed 3D finite element modelling of this study was demonstrated to be accurate, the method was utilised for the non-linear analysis of stub columns of same size and cross section as that of Tao et al. (2005) but with bar stiffeners. The previously explained modelling specifications were exactly employed for simulating each of the CFSC stub columns. Details of the stiffened CFSC stub columns which were analysed by the use of the non-linear finite element method are illustrated in Figure 7. Figure 7a indicates the arrangement of the bar stiffeners in the columns. Different number (2, 3 and 4) and spacing of the bar stiffeners (50, 100 and 150 mm) are considered in the analyses in which two typical elevations are shown in Figure 7b and c. Moreover, typical finite element meshes of the columns are illustrated in Figure 8.

3. Results and discussion

Features and obtained ultimate axial load capacities of the CFSC stub columns are listed in Table 1. The C in the column labels represents the columns and the first four numbers following C respectively designate the steel wall thickness t (mm), diameter of bar stiffener D (mm), steel wall yield stress [f.sub.y](MPa) and concrete compressive strength [f.sub.c](MPa). Also, the number before the parentheses is the number of bar stiffeners and the number in the parentheses presents the centre-to-centre spacing (mm) between the bar stiffeners. Effects of different variables on the behaviour of the columns are also discussed in the following sections.

3.1. Effect of number of bar stiffeners on ultimate axial load capacity

To study the effect of number of bar stiffeners on the behaviour of the CFSC stub columns, the varied number of bar stiffeners (2, 3 and 4) (Fig. 7a) were considered in the analyses. Figure 9 shows these effects on the ultimate axial load capacity of the columns. Also, Table 1 lists the corresponding ultimate axial load capacity values of the curves. According to the figure and table, the ultimate axial load capacity of the unstiffened CFSC stub column is improved by the use of the bar stiffeners. For instance, the use of four bar stiffeners (C-2.5-10-234-50-4(50)) increases the ultimate axial load capacity of the unstiffened column from 3325 to 3700 kN, an enhancement of 11.3%. Also, increasing the number of bar stiffeners enhances the ultimate axial load capacity of the columns. For example, as the number of bar stiffeners is enhanced from 2 (C-2.5-10-234-50-2(150)) to 4 (C-2.5-10-234-50-4(150)) for the same bar spacing of 150 mm, the ultimate axial load capacity is increased from 3353 to 3557 kN, an improvement of 6.1%.

3.2. Effect of spacing of bar stiffeners on ultimate axial load capacity

Three various bar spacing of 50, 100 and 150 mm were adopted in the analyses to examine the effect of spacing of bar stiffeners on the behaviour of the CFSC stub columns. This effect on the ultimate axial load capacity of the columns is illustrated in Figure 10. As can be seen from the figure and Table 1, the decrease of spacing of the bar stiffeners enhances the ultimate axial load capacity. As an example, the ultimate axial load capacity increases from 3456 (C-2.5-10-234-50-3(150)) to 3606 kN (C-2.5-10-234-50-3(50)) if spacing of the bar stiffeners decreases from 150 to 50 mm with the same number of bar stiffeners, an enhancement of 4.3%.

3.3. Effect of steel wall thickness on ultimate axial load capacity

The effect of steel wall thickness on the behaviour of the CFSC stub columns was evaluated by considering three different steel wall thicknesses of 2, 2.5 and 3 mm in the analyses. Figure 11 shows the results. In accordance with the figure and Table 1, as the steel wall thickness enhances the ultimate axial load capacity increases. For instance, the increase of the steel wall thickness from 2 (C-2-10-234-50-4(50)) to 3 mm (C-3-10-234-50-4(50)) with the same number and spacing of the bar stiffeners improves the ultimate axial load capacity of the columns from 3544 to 3856 kN, an increase of 8.8%.

3.4. Effect of diameter of bar stiffeners on ultimate axial load capacity

To investigate the effect of diameter of bar stiffeners on the ultimate axial load capacity of the CFSC stub columns, three various diameters of the bar stiffeners (8, 10 and 12 mm) were utilised in the analyses. The results are indicated in Figure 12. According to the figure and Table 1, higher ultimate axial load capacity can be obtained by larger diameter of the bar stiffeners. For example, as the diameter of the bar stiffeners increases from 8 (C-2.5-8-234-50-3(50)) to 12 mm (C-2.5-12-234-50-3(50)) for the same number and spacing of the bar stiffeners, the ultimate axial load capacity enhances from 3560 to 3648 kN, an enhancement of 2.5% and not much appreciable.

3.5. Effects of number and spacing of bar stiffeners on ductility

The ductility of the columns is assessed by the use of a ductility index (DI) as following (Lin, Tsai 2001):

DI = [[epsilon].sub.85%]/[[epsilon].sub.y], (12)

in which [[epsilon].sub.85%] is the nominal axial shortening (D/L) corresponding to the load which falls to its 85% of the ultimate axial load capacity and [[epsilon].sub.y] is [[epsilon].sub.75%]/0.75 where [[epsilon].sub.75%] is the nominal axial shortening corresponding to the load that obtains 75% of the ultimate axial load capacity. The values of [[epsilon].sub.85%] and [[epsilon].sub.y] can be taken from Figure 9. Figure 13 illustrates effects of number and spacing of bar stiffeners on the ductility of the columns.

The increase of the number of bar stiffeners enhances the ductility of the columns (Fig. 13). For instance, the ductility of the columns is increased from 3.112 (C-2.5-10-234-50-2(50)) to 3.363 (C-2.5-10-234-50-4(50)) by the enhancement of the number of bar stiffeners from 2 to 4 for the same bar stiffeners spacing of 50 mm, an increase of 8.1%.

In addition, the reduction of spacing of the bar stiffeners leads to increase of the ductility. As an example, if the bar stiffeners spacing is reduced from 150 (C-2.5-10-234-50-4(150)) to 50 mm (C-2.5-10-234-50-4(50)), the ductility of the columns is enhanced from 3.150 to 3.363, an improvement of 6.8%.

3.6. Effect of thickness of steel wall on ductility

The ductility index, Eqn (12), is also used to study the effect of steel wall thickness on the ductility of the columns. This effect on the ductility of the columns is shown in Figure 14. The thicker steel wall results in the greater ductility (Fig. 14). For example, increasing the steel wall thickness from 2 (C-2-10-234-50-2(50)) to 3 mm (C-3-10-234-50-2(50)) improves the ductility from 2.984 to 3.245, an improvement of 8.7%.

3.7. Effect of concrete compressive strength on ultimate axial load capacity

Different concrete compressive strengths (30, 40 and 50.1 MPa) have been considered in the analyses to assess their effect on the ultimate axial load capacity of the columns (Fig. 15). It can be seen from the figure and Table 1 that the increase of the concrete compressive strength enhances the ultimate axial load capacity of the columns. As an example, the ultimate axial load capacity is increased from 2490 to 3700 kN as the concrete compressive strength is enhanced from 30 (C-2.5-10-234-30-4(50)) to 50.1 MPa (C-2.5-10-234-50-4(50)), an improvement of 48.6%.

3.8. Effect of steel yield stress on ultimate axial load capacity

The effect of different steel yield stresses (234.3, 350 and 450 MPa) on the ultimate axial load capacity of the columns is shown in Figure 16. As can be seen from the figure and Table 1, the higher steel yield stress leads to larger ultimate axial load capacity of the columns. For instance, the ultimate axial load capacity is increased from 3700 to 4322 kN respectively for the steel yield stresses of 234.3 (C-2.5-10-234-50-4(50)) and 450 MPa (C-2.5-10-450-50-4(50)), an enhancement of 16.8%.

3.9. Failure modes of stiffened CFSC stub columns

Figures 17 and 18 show the typical failure modes of the columns in the cross section and elevation respectively. According to Figure 18, the failure modes of the columns were characterised as concrete crushing about their mid-height where the steel wall buckled locally. Also, the inward buckling of the steel wall was prevented by the in-filled concrete.

It can be also mentioned that the enhancement of the ultimate axial load capacity and ductility of the columns owing to the use of the bar stiffeners, increase of the number of bar stiffeners, decrease of spacing of the bar stiffeners, increase of the steel wall thickness, or enhancement of diameter of the bar stiffeners can be becauseoftheincreaseofthe confinementeffectprovided by the steel wall on the concrete core. As the confinement effect is enhanced the local buckling of the steel wall is delayed, which results in the improvement of the ultimate axial load capacity and ductility of the columns.

3.10. Comparison of obtained ultimate axial load capacity with predictions

The ultimate axial load capacity of a square or rectangular CFSC stub column can be predicted from Eqns (13), (14) and (15), respectively, based on Eurocode 4 (2004), Baig et al. (2006) and Bahrami et al. (2011b):

[N.sub.EC4] = [A.sub.c][f.sub.c] + [A.sub.s][f.sub.y]; (13)

[N.sub.N] = 1.10[A.sub.c][f.sub.c] + [A.sub.s][f.sub.y]; (14)

[N.sub.B] = 1.05[A.sub.c][f.sub.c] + [A.sub.s][f.sub.y], (15)

in which [A.sub.c] and [A.sub.s] are areas of concrete and steel cross section respectively, and also [f.sub.c] and [f.sub.y] are compressive strength of the concrete core and yield stress of the steel wall, respectively. Table 2 summarises the predicted ultimate axial load capacities based on the mentioned equations and their comparisons with the values obtained from the non-linear analyses of the columns, [N.sub.u]. Standard deviation and coefficient of variation are denoted as SD and COV in Table 2, respectively. A mean ratio ([N.sub.EC4]/[N.sub.u]) of 0.956 is achieved with a COV of 0.031 which reveals that Eurocode 4 (2004) underestimates the ultimate axial load capacity of the columns by 4.4%. Also, a mean of 1.038 is obtained for [N.sub.N]/[N.sub.u] with a COV of 0.034 which shows that Eqn (14) gives the ultimate axial load capacity of the columns by 3.8% higher than those from the non-linear analyses. Moreover, a mean ratio ([N.sub.B]/[N.sub.u]) of 0.999 is achieved with a COV of 0.032 which uncovers that Eqn (15) underestimates the ultimate axial load capacity by only 0.1%. Consequently, the proposed equation by Bahrami et al. (2011b), Eqn (15), can predict the ultimate axial load capacity of the columns with a very good accuracy.

Conclusions

CFSC stub columns with bar stiffeners have been investigated in this paper. The finite element software LUSAS was used to perform the non-linear analyses. Comparison of the modelling result with the existing experimental test result uncovered the accuracy of the proposed 3D finite element modelling. It was revealed that the proposed modelling can predict the behaviour of the columns with a reasonable accuracy. A special arrangement of bar stiffeners in the columns with various number, spacing and diameters of bar stiffeners were developed using the non-linear finite element method. Effects of different variables such as various number, spacing and diameters of the bar stiffeners, steel wall thicknesses, concrete compressive strengths, and steel yield stresses on the structural behaviour of the columns were investigated in this study. It was demonstrated that these variables are effective on the behaviour of the columns. The ultimate axial load capacity and ductility of the columns are improved by the use of the bar stiffeners. The enhancement of the number of bar stiffeners and/or steel wall thickness increases the ultimate axial load capacity and ductility of the columns. As the diameter of the bar stiffeners enhances the ultimate axial load capacity increases. The reduction of spacing of the bar stiffeners increases the ultimate axial load capacity and ductility. Also, the higher concrete compressive strength results in larger ultimate axial load capacity. Moreover, the increase of the steel yield stress enhances the ultimate axial load capacity. Meanwhile, the failure modes of the columns were dominated by concrete crushing about their mid-height, where the local buckling of the steel wall was induced. The in-filled concrete prevented the steel wall from the buckling inward. In addition, the ultimate axial load capacities of the columns were predicted based on Eurocode 4 (2004) and the equations recommended by Baig et al. (2006) and Bahrami et al. (2011b), and also compared with those obtained values from the non-linear analyses. These comparisons showed that Eurocode 4 (2004) and equations of Baig et al. (2006) and Bahrami et al. (2011b), respectively, predicted the ultimate axial load capacities with 4.4% underestimation (a COV of 0.031), 3.8% overestimation (a COV of 0.034), and 0.1% underestimation (a COV of 0.032). Therefore, the proposed equation by Bahrami et al. (2011b) could predict the ultimate axial load capacities of the columns with a very good accuracy.

doi: 10.3846/13923730.2013.768545

References

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Alireza BAHRAMI, Wan Hamidon WAN BADARUZZAMAN, Siti Aminah OSMAN

Department of Civil and Structural Engineering, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia

Received 1 Aug. 2011; accepted 19 Oct. 2011

Corresponding author. Alireza Bahrami

E-mail: bahrami_a_r@yahoo.com

Alireza BAHRAMI. PhD student in the Department of Civil and Structural Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi, Selangor, Malaysia since 2009 to date. BE in Civil Engineering from Bushehr Islamic Azad University in 1998. MSc in Civil and Structural Engineering with an excellent grade from Universiti Kebangsaan Malaysia (UKM) in 2009. Fourteen years of industrial experience in Civil Engineering. A lecturer at some universities in Iran. Research interests: steel-concrete composite structural elements and their behaviour and also engineering software for structural elements analysis.

Wan Hamidon WAN BADARUZZAMAN. Professor in the Department of Civil and Structural Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi, Selangor, Malaysia. PhD in Structural Engineering from the University of Wales, Cardiff, UK in 1994. Twenty-six years of vast teaching, training, research, publication, administration, accreditation and consultancy experiences. On secondment, was the Chief Executive Officer of the UKM Perunding Kejuruteraan & Arkitek Sdn. Bhd., a university professional consultancy company. Research interests: steel-concrete composite structural elements, light weight, cold-formed composite structures and their behaviour.

Siti Aminah OSMAN. Dr, Senior lecturer in the Department of Civil and Structural Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi, Selangor, Malaysia. A member of Board of Engineers Malaysia (BEM). Graduated from Universiti Teknologi Malaysia in 1992 with BE (Hons), MSc in Structural Engineering from University of Bradford, UK in 1995 and PhD in Civil and Structural Engineering from Universiti Kebangsaan Malaysia (UKM) in 2006. After undergraduate studies, started teaching as a lecturer at Universiti Kebangsaan Malaysia (UKM). Research interests: structural engineering, wind engineering and industrial building system (IBS) construction.

Table 1. Features and obtained ultimate axial load capacities
([N.sub.u]) of the columns

No.   Column label             Steel       Bar      Steel wall,
                               wall,    stiffener    [f.sub.y]
                               t (mm)    D (mm)        (MPa)

1     C-2.5-10-234-50-4(50)     2.5        10          234.3
2     C-2.5-10-234-50-3(50)     2.5        10          234.3
3     C-2.5-10-234-50-2(50)     2.5        10          234.3
4     C-2.5-10-234-50-4(100)    2.5        10          234.3
5     C-2.5-10-234-50-3(100)    2.5        10          234.3
6     C-2.5-10-234-50-2(100)    2.5        10          234.3
7     C-2.5-10-234-50-4(150)    2.5        10          234.3
8     C-2.5-10-234-50-3(150)    2.5        10          234.3
9     C-2.5-10-234-50-2(150)    2.5        10          234.3
10    C-3-10-234-50-4(50)       3          10          234.3
11    C-2-10-234-50-4(50)       2          10          234.3
12    C-3-10-234-50-3(50)       3          10          234.3
13    C-2-10-234-50-3(50)       2          10          234.3
14    C-3-10-234-50-2(50)       3          10          234.3
15    C-2-10-234-50-2(50)       2          10          234.3
16    C-2.5-12-234-50-4(50)     2.5        12          234.3
17    C-2.5-8-234-50-4(50)      2.5         8          234.3
18    C-2.5-12-234-50-3(50)     2.5        12          234.3
19    C-2.5-8-234-50-3(50)      2.5         8          234.3
20    C-2.5-12-234-50-2(50)     2.5        12          234.3
21    C-2.5-8-234-50-2(50)      2.5         8          234.3
22    C-2.5-10-234-40-4(50)     2.5        10          234.3
23    C-2.5-10-234-30-4(50)     2.5        10          234.3
24    C-2.5-10-234-40-3(50)     2.5        10          234.3
25    C-2.5-10-234-30-3(50)     2.5        10          234.3
26    C-2.5-10-234-40-2(50)     2.5        10          234.3
27    C-2.5-10-234-30-2(50)     2.5        10          234.3
28    C-2.5-10-450-50-4(50)     2.5        10          450
29    C-2.5-10-350-50-4(50)     2.5        10          350
30    C-2.5-10-450-50-3(50)     2.5        10          450
31    C-2.5-10-350-50-3(50)     2.5        10          350
32    C-2.5-10-450-50-2(50)     2.5        10          450
33    C-2.5-10-350-50-2(50)     2.5        10          350

No.   Column label             Concrete,   [N.sub.u]
                               [f.sub.c]     (kN)
                                 (MPa)

1     C-2.5-10-234-50-4(50)      50.1        3700
2     C-2.5-10-234-50-3(50)      50.1        3606
3     C-2.5-10-234-50-2(50)      50.1        3486
4     C-2.5-10-234-50-4(100)     50.1        3611
5     C-2.5-10-234-50-3(100)     50.1        3516
6     C-2.5-10-234-50-2(100)     50.1        3410
7     C-2.5-10-234-50-4(150)     50.1        3557
8     C-2.5-10-234-50-3(150)     50.1        3456
9     C-2.5-10-234-50-2(150)     50.1        3353
10    C-3-10-234-50-4(50)        50.1        3856
11    C-2-10-234-50-4(50)        50.1        3544
12    C-3-10-234-50-3(50)        50.1        3741
13    C-2-10-234-50-3(50)        50.1        3469
14    C-3-10-234-50-2(50)        50.1        3635
15    C-2-10-234-50-2(50)        50.1        3334
16    C-2.5-12-234-50-4(50)      50.1        3735
17    C-2.5-8-234-50-4(50)       50.1        3658
18    C-2.5-12-234-50-3(50)      50.1        3648
19    C-2.5-8-234-50-3(50)       50.1        3560
20    C-2.5-12-234-50-2(50)      50.1        3504
21    C-2.5-8-234-50-2(50)       50.1        3461
22    C-2.5-10-234-40-4(50)      40          3093
23    C-2.5-10-234-30-4(50)      30          2490
24    C-2.5-10-234-40-3(50)      40          3010
25    C-2.5-10-234-30-3(50)      30          2404
26    C-2.5-10-234-40-2(50)      40          2915
27    C-2.5-10-234-30-2(50)      30          2325
28    C-2.5-10-450-50-4(50)      50.1        4322
29    C-2.5-10-350-50-4(50)      50.1        4052
30    C-2.5-10-450-50-3(50)      50.1        4165
31    C-2.5-10-350-50-3(50)      50.1        3925
32    C-2.5-10-450-50-2(50)      50.1        4034
33    C-2.5-10-350-50-2(50)      50.1        3819

Table 2. Comparison of obtained ultimate axial load capacity
([N.sub.u]) with [N.sub.EC4], [N.sub.N] and [N.sub.B]

No.   Column label             [N.sub.u]   [N.sub.EC4]   [N.sub.EC4]/
                                 (kN)         (kN)        [N.sub.u]

1     C-2.5-10-234-50-4(50)      3700         3409          0.921
2     C-2.5-10-234-50-3(50)      3606         3409          0.945
3     C-2.5-10-234-50-2(50)      3486         3409          0.978
4     C-2.5-10-234-50-4(100)     3611         3409          0.944
5     C-2.5-10-234-50-3(100)     3516         3409          0.970
6     C-2.5-10-234-50-2000)      3410         3409          1.000
7     C-2.5-10-234-50-4(150)     3557         3409          0.958
8     C-2.5-10-234-50-3(150)     3456         3409          0.986
9     C-2.5-10-234-50-2(150)     3353         3409          1.017
10    C-3-10-234-50-4(50)        3856         3499          0.907
11    C-2-10-234-50-4(50)        3544         3380          0.954
12    C-3-10-234-50-3(50)        3741         3499          0.935
13    C-2-10-234-50-3(50)        3469         3380          0.974
14    C-3-10-234-50-2(50)        3635         3499          0.963
15    C-2-10-234-50-2(50)        3334         3380          1.014
16    C-2.5-12-234-50-4(50)      3735         3409          0.913
17    C-2.5-8-234-50-4(50)       3658         3409          0.932
18    C-2.5-12-234-50-3(50)      3648         3409          0.934
19    C-2.5-8-234-50-3(50)       3560         3409          0.958
20    C-2.5-12-234-50-2(50)      3504         3409          0.973
21    C-2.5-8-234-50-2(50)       3461         3409          0.985
22    C-2.5-10-234-40-4(50)      3093         2860          0.925
23    C-2.5-10-234-30-4(50)      2490         2285          0.918
24    C-2.5-10-234-40-3(50)      3010         2860          0.950
25    C-2.5-10-234-30-3(50)      2404         2285          0.950
26    C-2.5-10-234-40-2(50)      2915         2860          0.981
27    C-2.5-10-234-30-2(50)      2325         2285          0.983
28    C-2.5-10-450-50-4(50)      4322         3957          0.916
29    C-2.5-10-350-50-4(50)      4052         3717          0.917
30    C-2.5-10-450-50-3(50)      4165         3957          0.950
31    C-2.5-10-350-50-3(50)      3925         3717          0.947
32    C-2.5-10-450-50-2(50)      4034         3957          0.981
33    C-2.5-10-350-50-2(50)      3819         3717          0.973
Mean                                                        0.956
SD                                                          0.029
COV                                                         0.031

No.   Column label             [N.sub.N]   [N.sub.N]/
                                 (kN)      [N.sub.u]

1     C-2.5-10-234-50-4(50)      3728        1.008
2     C-2.5-10-234-50-3(50)      3728        1.034
3     C-2.5-10-234-50-2(50)      3728        1.069
4     C-2.5-10-234-50-4(100)     3728        1.032
5     C-2.5-10-234-50-3(100)     3728        1.060
6     C-2.5-10-234-50-2000)      3728        1.093
7     C-2.5-10-234-50-4(150)     3728        1.048
8     C-2.5-10-234-50-3(150)     3728        1.079
9     C-2.5-10-234-50-2(150)     3728        1.112
10    C-3-10-234-50-4(50)        3782        0.981
11    C-2-10-234-50-4(50)        3672        1.036
12    C-3-10-234-50-3(50)        3782        1.011
13    C-2-10-234-50-3(50)        3672        1.059
14    C-3-10-234-50-2(50)        3782        1.040
15    C-2-10-234-50-2(50)        3672        1.102
16    C-2.5-12-234-50-4(50)      3728        0.998
17    C-2.5-8-234-50-4(50)       3728        1.019
18    C-2.5-12-234-50-3(50)      3728        1.022
19    C-2.5-8-234-50-3(50)       3728        1.047
20    C-2.5-12-234-50-2(50)      3728        1.064
21    C-2.5-8-234-50-2(50)       3728        1.077
22    C-2.5-10-234-40-4(50)      3090        0.999
23    C-2.5-10-234-30-4(50)      2458        0.987
24    C-2.5-10-234-40-3(50)      3090        1.026
25    C-2.5-10-234-30-3(50)      2458        1.022
26    C-2.5-10-234-40-2(50)      3090        1.060
27    C-2.5-10-234-30-2(50)      2458        1.057
28    C-2.5-10-450-50-4(50)      4245        0.982
29    C-2.5-10-350-50-4(50)      4005        0.988
30    C-2.5-10-450-50-3(50)      4245        1.019
31    C-2.5-10-350-50-3(50)      4005        1.020
32    C-2.5-10-450-50-2(50)      4245        1.052
33    C-2.5-10-350-50-2(50)      4005        1.049
Mean                                         1.038
SD                                           0.035
COV                                          0.034

No.   Column label             [N.sub.B]   [N.sub.B]/
                                 (kN)      [N.sub.u]

1     C-2.5-10-234-50-4(50)      3584        0.969
2     C-2.5-10-234-50-3(50)      3584        0.994
3     C-2.5-10-234-50-2(50)      3584        1.028
4     C-2.5-10-234-50-4(100)     3584        0.993
5     C-2.5-10-234-50-3(100)     3584        1.019
6     C-2.5-10-234-50-2000)      3584        1.051
7     C-2.5-10-234-50-4(150)     3584        1.008
8     C-2.5-10-234-50-3(150)     3584        1.037
9     C-2.5-10-234-50-2(150)     3584        1.069
10    C-3-10-234-50-4(50)        3641        0.944
11    C-2-10-234-50-4(50)        3526        0.995
12    C-3-10-234-50-3(50)        3641        0.973
13    C-2-10-234-50-3(50)        3526        1.016
14    C-3-10-234-50-2(50)        3641        1.002
15    C-2-10-234-50-2(50)        3526        1.058
16    C-2.5-12-234-50-4(50)      3584        0.960
17    C-2.5-8-234-50-4(50)       3584        0.980
18    C-2.5-12-234-50-3(50)      3584        0.982
19    C-2.5-8-234-50-3(50)       3584        1.007
20    C-2.5-12-234-50-2(50)      3584        1.023
21    C-2.5-8-234-50-2(50)       3584        1.036
22    C-2.5-10-234-40-4(50)      2975        0.962
23    C-2.5-10-234-30-4(50)      2371        0.952
24    C-2.5-10-234-40-3(50)      2975        0.988
25    C-2.5-10-234-30-3(50)      2371        0.986
26    C-2.5-10-234-40-2(50)      2975        1.020
27    C-2.5-10-234-30-2(50)      2371        1.020
28    C-2.5-10-450-50-4(50)      4101        0.949
29    C-2.5-10-350-50-4(50)      3861        0.953
30    C-2.5-10-450-50-3(50)      4101        0.985
31    C-2.5-10-350-50-3(50)      3861        0.984
32    C-2.5-10-450-50-2(50)      4101        1.017
33    C-2.5-10-350-50-2(50)      3861        1.011
Mean                                         0.999
SD                                           0.032
COV                                          0.032
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Author:Bahrami, Alireza; Badaruzzaman, Wan Hamidon Wan; Osman, Siti Aminah
Publication:Journal of Civil Engineering and Management
Geographic Code:9MALA
Date:Jun 1, 2013
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