Design of Concrete-filled Steel Tubular Members According to the Australian Standard as 5100 Model and Calibration

9Design of concrete-filled steel tubular members according to the Australian Standard AS 5100 model and calibration * Z Tao University of Western Sydney, Sydney, NSW, Australia Fuzhou University, Fuzhou, Fujian Province, China Brian Uy † University of Western Sydney, Sydney, NSW, Australia L-H Han and S-H He Tsinghua University, Beijing, China SUMMARY: Procedures given in the Australian bridge design standard AS 5100 (Standards Australia, 2004) for the design of concrete-filled steel tubular (CFST) columns, beams and beamcolumns are presented and described briefly in this paper. A wide range of experimental data from two currently available test databases (2194 test results altogether) is used to evaluate the applicability of AS 5100 in calculating the strength of CFST members. Some other existing design codes, such as the Japanese code AIJ (1997), American code AISC (2005), British bridge code BS 5400 (2005), Chinese code DBJ 13-51-2003 (2003) and Eurocode 4 (2004), are also compared with the test results in this paper. From the comparisons, useful information is provided for future possible revision of AS 5100 and for the suggestion that this model be used for building construction. 1 INTRODUCTION In recent times, concrete-filled steel tubular (CFST) members have been widely used in civil engineering in Australia and other countries (Uy, 2000; Han, 2007). Several examples of such engineering practice in Australia include: the Latitude building and Market City in Sydney; the Casselden Place and the Commonwealth Centre in Melbourne; Riverside Office and Myer Centre in Adelaide; and the Forrest Centre, Exchange Plaza and Westralia Square in Perth (Uy & Patil, 2006). Figure 1 shows the Latitude building in Sydney during construction. This building was completed in 2005, and is on George Street on the World Square Site, directly adjacent to Sydney’s Chinatown at Haymarket. It is a landmark building, which was designed by Hyder Consulting and constructed by * Paper S08-977 submitted 29/02/08; accepted for publication after review and revision 6/05/08. † Corresponding author Prof Brian Uy can be contacted at [email protected]. Multiplex. The building has a total height of 222 m over 45 floors and has some very innovative features in its design. The building uses twin composite columns on the perimeter frame, using 508 mm diameter steel tubes filled with 80 MPa concrete. The building has required the design of 7 m deep transfer trusses using large diameter steel tubes filled concrete and large high strength steel boxes filled with concrete (Chaseling, 2004; Australian Steel Institute, 2004). The practical application of CFST construction is now supported by many well-known national standards or recommendations, such as the Japanese code AIJ (1997), American code AISC (American Institute of Steel Construction, 2005), British bridge code BS5400 (British Standards Institution, 2005), Chinese code DBJ 13-51-2003 (2003) and Eurocode 4 (2004). Research and practice of CFST members and structures has also led to the development of these design codes. In 2004, a new version of the Australian bridge design standard AS 5100 (Standards Australia, 2004) for bridge design was issued, where design Australian Journal of Structural Engineering Online © Institution of Engineers Australia, 2008 10 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He Design Code. Seven parts are included in AS 5100 with objectives to provide nationally acceptable requirements for the design of road, rail, pedestrian and bicycle-path bridges; the specific application of concrete, steel and composite construction; and the assessment of the load capacity of existing bridges. Part 6 of the standard AS 5100 is concerned with the design of steel and composite construction, in which procedures are given for the design of concrete-filled circular and rectangular hollow steel members, which take account of the composite action between the various components forming the cross-section. The specifications in AS 5100 related to the design of CFST members are described briefly as follows. In AS 5100, it is specified that the steel tube should be fabricated from steel with a maximum yield stress of 350 MPa. The elastic modulus of steel (E) is given as 200,000 MPa by AS 5100. The selection of wall thickness (t) should ensure that the plate element slenderness (λe) is less than the yield slenderness limit (λey). The value of λe for rectangular hollow sections (RHS) is calculated as ( h / t) f y /235 , where h is the overall height of a RHS, fy is the characteristic yield strength of the steel. For circular hollow sections (CHS), the slenderness (λe) is given as (do/t)(fy/235), where do is the outside diameter of a CHS. The yield slenderness limit (λey) for CHSs is equal to 82, while slightly different values of λey (35, 40 and 45) are specified for RHSs with different fabrication process. The larger the residual stress remaining in the section, the smaller the λey resulting. For lightly welded (longitudinally) tubes or cold formed sections, a moderate value of 40 is used for λey. It should be noted that the yield slenderness limit specified in AS 5100 for CFST members is virtually the same as those for hollow steel sections, that is, the beneficial effects from concrete restraint is neglected. Concrete with normal density and strength is recommended in AS 5100 to fill the steel tubes. The characteristic compressive cylinder strengths (fc’) of the standard strength grades of concrete are 25, 32, 40, 50 and 65 MPa, respectively. The maximum aggregate size is 20 mm. As far as the concrete modulus of elasticity (Ec) is concerned, a similar formula presented in AISC is recommended in AS 5100 as follows: Figure 1: Latitude, Sydney (2005). guidance for composite columns (including CFST columns) was incorporated. The aim of this paper is to provide useful information for a future possible revision of AS 5100 and for the suggestion that this model be used for building construction. To fulfil this task, procedures given in AS 5100 for the design of CFST columns, beams and beam-columns are firstly presented and described briefly. In order to evaluate the applicability of AS 5100 in calculating the strength of CFST members, a wide range of experimental data from two currently available test databases (2194 test results altogether) are used for comparison. Effects of different parameters such as steel strength, concrete strength and section slenderness on the accuracy of the strength predictions are discussed. This is to check the possibility of relaxing the limitations specified in AS 5100. The above-mentioned existing design codes are also compared with the test results in this paper. For simplicity, these codes are to be referred to as “AIJ”, “AISC”, “BS 5400”, “DBJ 13-51-2003” and “EC4” in the following. 2 2.1 AS 5100 PROVISIONS General specifications Ec = ρ 1.5 × 0.043 f c ′ (1) where ρ is the concrete density taken as not less than 2400 kg/m3 for normal weight concrete. A steel contribution factor αs is specified in AS 5100 with an allowed range from 0.2 to 0.9, where αs is defined as the ratio of the contribution of the steel section (φAsfy) to the total axial capacity (Nus). The above notation of φ and As, as well as the calculation method of N us, will be given in the following section. Online The Australian Standard AS 5100 was prepared by the Standards Australia Committee BD-090, Bridge Design, to supersede HB 77.6-1996, Australian Bridge Australian Journal of Structural Engineering “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 11 In AS 5100, it is suggested that reinforcement is not normally required in CFST compression members. Also, almost all currently available tests were carried out without steel reinforcement used. Therefore, the contribution from reinforcement is omitted in the following review of design methods. 2.2 Members subjected to axial compression α c = ξ ⎢1 − 1 − ⎜ ⎟ ⎥ ⎢ ⎝ ξλ ⎠ ⎥ ⎣ ⎦ ⎡ 2 ⎛ 90 ⎞ ⎤ (4) 2.2.1 Ultimate section capacity To calculate the section capacity under axial compression, an assumption was used that the steel yields before the concrete reaches its ultimate stress state. Thus, the ultimate section capacity (Nus) for rectangular CFST members can be calculated by summing up the axial load capacities of the tube and the concrete. This leads to: Nus = φAsfy + φcAc fc’ (2) where ξ and λ are coefficients related to the relative slenderness (λr). λr is defined herein as N s / N cr , in which Ns is determined according to equation (2) or (3), with φ and φc taken as 1.0, and Ncr is the elastic critical load. The expression for Ncr is given as equation (5), where (EI)e is the effective flexural stiffness determined according to equation (6), and Le is the effective length of a composite compression member. N cr = π 2 (EI )e Le 2 (5) (6) (EI)e = φEIs + φcEcIc where As and Ac are the areas of the steel tube and the core concrete, respectively; and φ and φc are the capacity factors for steel and concrete respectively, given as 0.9 and 0.6 in AS 5100 for section capacity. For a circular CFST member, the benefits of the increase in concrete strength due to confinement may be taken into account if the relative slenderness of the member (λr) is not greater than 0.5, and the load eccentricity (e) under the greatest design bending moment is not greater than do/10. Otherwise, Nus should be calculated using equation (2). If the benefits of confinement are taken into account, Nus may be calculated as follows: In equation (6), Is and Ic are the second moment of areas of the steel section and the uncracked concrete section, respectively, and φ and φc herein are also taken as 1.0. After the slenderness reduction factor αc is determined from equation (4), the member capacity of a composite column can be expressed as: Nuc = αcNus ≤ Nus 2.3 Members under combined compression and bending (7) ⎛ η1tf y ⎞ N us = φ Asη2 f y + φc Ac fc ' ⎜ 1 + ⎟ ⎝ do f c ' ⎠ (3) in which, η1 and η2 are coefficients used to reflect the confinement benefit that are dependent on the relative slenderness (λr) and load eccentricity (e). The coefficient of η2 is used to account for the strength reduction of the steel because of the circumferential tensile strains in the steel induced by confining the concrete, while the coefficient of η1 is used for the concrete to reflect the strength increase from the tube confinement. The calculation formulae for η1 and η2 are given in Clause 10.6.2.2 of AS 5100: Part 6. From the above introduction, it can be seen that the formula for calculating the ultimate section capacities is virtually the same as those suggested in EC4, except different values have been used for the capacity factors. 2.2.2 Ultimate member capacity Like many other codes, a slenderness reduction factor αc is introduced in AS 5100 to reflect the basic relationship between strength and stability for an axially loaded column, as follows: Australian Journal of Structural Engineering In AS 5100, strengths of CFST beams and beamcolumns should be calculated on the basis of rectangular stress blocks, assuming that the maximum concrete compressive stress is (φc fc’) and the maximum steel stress is (φfy). An interaction curve based on the plastic resistance analysis can be obtained as shown in figure 2(a). It should be noted that both φ and φc are taken as 0.9 for a composite member subjected to combined axial and flexural actions. To verify the resistance of a beam-column subjected to compression and uniaxial bending, the following criterion should be satisfied: Mx* ≤ 0.9Mrx My* ≤ 0.9Mry (8a) (8b) where Mx* and My* are the design bending moments about the principal major x-axis and minor y-axis, respectively; Mrx and Mry are the section moment capacities reduced by the effect of axial compression, slenderness and imperfection (see figure 2(a)). In figure 2(a), Mdx and Mdy are the total moment capacities of the section when the design axial force N* is acting on the section; αn is a factor for the interaction curve, given by αc(1 + βm)/4; βm is the ratio of the smaller to the larger end bending moments taken as positive when the member is bent in reverse curvature. Online 12 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He N Nus Nuc(= cNus) N* Mrx or Mry Interaction curve for the cross-section N Nus A E Interaction curve for the cross-section C D B o nNus (a) Figure 2: Msx Mdx (or Mdy) (or Msy) M o (b) Msx (or Msy) M Interaction curve for CFST members subjected to combined compression and bending. determine the plastic compressive stress for circular members in accordance with section 2.2.1. It should also be noted that the above methodology generally follows that presented in the last version of Eurocode 4 (1994). To simplify the design process, point E in figure 2(b) has been removed in the new version of Eurocode 4 (2004). Due to page limitations, the design procedures given in other standards is not presented herein. More details and limitation provisions for them can be found in Chung & Matsui (2005) and Zhang et al (2007). 3 COMPARISONS BETWEEN TEST AND PREDICTED CAPACITIES Brief introduction to test databases In order to simplify the design process, the full interaction curve shown in figure 2(a) may be approximated by the polygon joining the five points A, B, C, D and E, as shown in figure 2(b). These points are determined as follows: 1. Point A is defined by the nominal axial capacity (Nus) of the member without bending. 2. Point B is defined by the nominal section moment capacity (Msx or Msy) of the member. 3. Point C is determined by moving the neutral axis determined for point B to a new position equidistant from the centroid, but on the other side of the centroid, and parallel with its previous position. Therefore, the stresses in the section with the neutral axis in this position will create a moment equal to that derived from point B, ie. Msx or Msy, but with a compression load equal to the axial load in that part of the section between the neutral axis positions for points B and C. 4. Point D is determined by placing the neutral axis at the centroid of the section. At this location, the axial load in the section is half that for point C, and the moment is a maximum. 5. Point E is any point approximately mid-way between points A and C, determined with the neutral axis approximately mid-way between its location for point C and the edge of the section, which is in tension when determining point C. In determining the value of Mrx or Mry, the second order moment Mp due to imperfections (imperfection moment) of the column can be determined using the simplified interaction curve shown in figure 2(b). By reading off the horizontal distance representing the imperfection moment as shown in figure 2(a), the moment resistance of the composite column under combined compression and bending may then be evaluated. It should be noted that the benefits of the confining stresses on the concrete may be considered to Australian Journal of Structural Engineering 3.1 Over the last few decades, numerous tests have been carried out on CFST members. A database was established by Goode (2006) recently, in which 1792 test results from 92 references were included. These test results can be accessed via the website http:// web.ukonline.co.uk/asccs2 (ASCCS, 2007). In this paper, 1575 test results from Goode’s database, including 918 for circular specimens and 657 for rectangular specimens (square sections mainly), are used to perform the code comparisons. The other test results in this database have been discarded because they are not relevant to this study. Apart from the test results in Goode’s database, another database developed by Wu (2006) contains 1514 experimental results from 104 references, where some of them have not been included in Goode’s database, especially for 81 tests on beams. No test results on beams are available in Goode’s database. After merging the two databases, 1232 and 962 test results (2194 altogether) from 130 references on circular and rectangular specimens, respectively, are used in this paper. The ranges of the test properties are given in table 1. It should be noted that in some Online “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 13 Table 1: Summary of test properties. Member type Stub column do(h) (mm) 48-1020 25-500 76-200 34-300 60-400 60-360 76-323 100-306 Section type λe 13-237 9-192 17-198 23-196 13-181 19-163 18-94 22-115 fy (MPa) 186-853 178-682 186-433 262-436 192-835 217-550 205-761 194-750 fc’ (MPa) 10-110 10-96 18-114 23-82 12-103 10-94 18-103 19-88 No. of tests 484 420 304 24 445 234 226 57 No. of references 39 28 19 4 34 25 20 7 Circular Column Beam-column Beam Stub column Column Beam-column Beam Rectangular 2 Normalized calculated strength N ue/N uc 15% 2 Normalized calculated strength N ue/N uc 1.5 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 (a) Figure 3: 1000 2000 3000 4000 Test strength N ue (kN) 5000 (b) 0 5000 12000 19000 26000 Test strength N ue (kN) 33000 Comparison between test results and predictions using AS 5100 (circular stub column). effect is expected to be considered. “Beam-column” is defined as a member subjected to the combined action of compression and flexure. It is worth noting that, the classification standards for short and long columns in different codes are quite different. Some of them are very complex to follow and, in some codes, a slenderness reduction factor is applicable even for a very short column. Therefore, the above rather simple criterion used by Goode (2006) is also adopted in this paper. In order to better reflect the deviations of code predictions from the experimental results, the –15% and +15% error bounds are depicted in figures presented in the following sub-sections. It is worth noting that this is not a criterion used to assess the acceptability of prediction accuracy. Generally, a reliability analysis should be performed based on a regional reliability standard to accomplish this task (Han, 2007). 3.2.1 Section capacity under axial compression Currently available test results are 484 and 445 for circular and rectangular stub columns, respectively. Figure 3 shows the comparison between experimental ultimate strength Nue and predicted strength Nuc Online references no concrete cylinder strength (fc’) was available. Instead, a compressive strength (fcu) of 150 mm cubes was reported. In general, fc’ can be taken as 0.8fcu for normal strength concrete, but this relationship is not quite applicable for high-strength concrete (Chen et al, 1996; Mansur & Islam, 2002). Therefore, equivalent cylinder strengths (fc’) were determined according to Chen et al (1996), where a table demonstrating the approximate relationship of two types of concrete strengths can be found in Yu et al (2008). This relationship is quite close to that given by Mansur & Islam (2002). 3.2 Strength comparison When comparing design calculations with the tests, the material partial safety factors specified in all design codes have been taken as unity. At the same time, all code limitations are ignored with a purpose to check the feasibility of those design codes in predicting the load-carrying capacities of the test specimens. In the following sections, “stub column” is defined as a short member (Le/do or Le/b ≤ 4; b is the section width of a rectangular tube) under axial compression to determine section capacity, while “column” is defined as a long one (Le/do or Le/b > 4) under axial compression, where the slenderness Australian Journal of Structural Engineering 14 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He Table 2: Section type Comparison results of code predictions with test results. Member type AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 μ σ EC4 μ σ μ σ μ σ μ σ μ σ Stub 1.037 0.139 1.097 0.154 1.275 0.199 0.966 0.150 1.155 0.149 1.048 0.139 column Circular Column 1.163 0.170 1.115 0.177 1.195 0.172 1.130 0.302 1.080 0.189 1.133 0.162 Beam0.997 0.146 1.138 0.211 1.385 0.467 1.185 0.234 1.078 0.161 1.004 0.160 column Beam 1.194 0.151 1.422 0.323 1.422 0.323 1.236 0.281 1.204 0.213 1.194 0.151 Stub 1.062 0.123 1.061 0.123 1.150 0.138 1.169 0.147 1.037 0.125 1.061 0.123 column Rectangular Column 1.049 0.120 1.036 0.127 1.130 0.133 1.195 0.161 1.092 0.161 1.030 0.124 Beam0.952 0.134 1.041 0.138 1.278 0.305 1.300 0.278 1.076 0.192 0.966 0.138 column Beam 1.141 0.146 1.306 0.196 1.306 0.196 1.188 0.158 1.164 0.160 1.141 0.146 conservative prediction results. As far as AS 5100 is concerned, its predictions are generally accurate, but it underestimates the load-bearing capacity of circular columns (16% lower on average). The same trend is found for the predicted results from EC4. The reason is attributed to the fact that no confinement effect is considered for columns with a relative slenderness λr greater than 0.5. In fact, the apparent concrete confinement can still be expected even for a very slender circular column (Han, 2000). Figure 8 compares the calculated strength of column members based on different code provisions. Test results reported by Matsui et al (1995) are shown as dots in this figure. Parameters for the circular specimens are as follows: do =165.2 mm, t = 4.08 mm, fy = 353 MPa, fc’ = 40.9 MPa; while those for the square ones are: b = 149.8 mm, t = 4.27 mm, fy = 412 MPa, fc’ =31.9 MPa. From the comparisons, it seems that all curves are close and generally agree with the test results, except that BS 5400 gives an obvious conservative prediction for square columns. Also, there are apparent discrepancies amongst predictions for circular columns when the relative slenderness λr is less than 0.5. 3.2.3 Beam-column member capacity The comparisons between predicted load-bearing capacities (Nuc) and test results (Nue) are illustrated in figures 9 and 10 for circular and rectangular beamcolumns, respectively. It has been demonstrated that AISC gives the most conservative results for circular beam-columns (μ = 1.385, σ = 0.467), and BS 5400 does that for rectangular beam-columns (μ = 1.300, σ = 0.278). All codes except BS 5400 give less conservative predictions for rectangular members than for circular ones. The predictions from AS 5100 are quite close to those from EC4, which demonstrates that they are quite accurate in predicting load-bearing capacities for circular Online using AS 5100 for circular stub columns. Table 2 also shows both the mean value ( μ ) and the standard deviation (σ) of the ratio of Nue/Nuc for all the strength predictions. As can be seen, generally good agreement is achieved with an average value (μ) of 1.037 and a standard deviation (σ) of 0.139. In the test databases, some tests were performed on specimens with a rather large diameter. In order to illustrate more clearly, those tests are compared in figure 3(b), which demonstrates that AS 5100 is also applicable in this circumstances without apparent size effect observed. Comparison results from other design codes are given in figure 4 and table 2, which clearly show that AISC is quite conservative in its prediction and BS 5400 gives slightly (3.4%) higher capacities on average than the test results. For clarity, the test results for those specimens with large diameters are not given in figure 4. The agreement of the measured and predicted strengths is generally good. Figure 5 compares the test strength (Nue) with the calculated strength (N uc) using different design codes for rectangular stub columns. All codes give accurate predictions except that AISC and BS 5400 underestimates the strength by as much as 15% on average (table 2). At the same time, all predictions have smaller variations compared to those for circular stub columns. This may be attributed to the fact that a lot of circular specimens did not show strain softening behaviour, thus different definitions of ultimate strength have been applied by different authors. 3.2.2 Column member capacity Figures 6 and 7 show the comparisons between test results (N ue) and code predictions (N uc) for circular and rectangular columns, respectively. It appears that AISC and BS 5400 give the most Australian Journal of Structural Engineering “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 15 2 Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 2 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 (a) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 (b) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 2 Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 2 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 (c) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 (d) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 2 Normalized calculated strength N ue/N uc 1.5 15% 1 0.5 15% 0 0 (e) Figure 4: 1000 2000 3000 4000 Test strength N ue (kN) 5000 Comparison between test results and predictions using other codes (circular stub columns) – (a) AIJ, (b) AISC, (c) BS 5400, (d) DBJ 13-51-2003, and (e) EC4. test results of circular members obtained by Matsui et al (1995). The section properties are the same as those of the columns given before (figure 8 (a)). As can be seen from figure 11, there are considerable discrepancies among predictions from different codes. For shorter members, AS 5100 and EC4 give accurate predictions. As the slenderness increases, they tend to overestimate the strength compared Online beam-columns, but overestimate those of rectangular beam-columns (4-5% on average). It seems that the assumed rectangular stress blocks are less valid for rectangular beam-columns. To illustrate the differences among the code predictions more clearly, the predicted axial load (N) versus moment (M) interaction curves using different methods are compared in figure 11, with the Australian Journal of Structural Engineering 16 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 2 2 1.5 15% Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 (a) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 (b) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 2 2 1.5 15% Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 (c) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 (d) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 2 Normalized calculated strength N ue/N uc 1.5 15% 1 0.5 15% 0 0 (e) Figure 5: 1000 2000 3000 4000 Test strength N ue (kN) 5000 Comparison between test results and code predictions (rectangular stub columns) – (a) AS 5100, (b) AIJ (EC4), (c) AISC, (d) BS 5400, and (e) DBJ 13-51-2003. rectangular beams, respectively. The ratios of Mue/Muc for all codes are presented in table 2. As can be seen, all predicted results are conservative overall. AIJ and AISC give the most conservative predictions due to ignoring the concrete contribution. AS 5100, EC4 and DBJ give the best predictions for both circular and rectangular beams. Online to the test results reported by Matsui et al (1995). Overall, DBJ 13-51-2003 gives the best prediction in this comparison. 3.2.4 Beam moment capacity The moment capacities (Muc) predicted using the six design codes are compared with test results (Mue) shown in figures 12 and 13 for circular and Australian Journal of Structural Engineering “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 17 2 Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 2 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 (a) 2 Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 (b) 2 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 0 (c) (d) 1000 2000 3000 4000 Test strength N ue (kN) 5000 2 Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 2 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 (e) Figure 6: 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 (f) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 Comparison between test results and code predictions (circular columns) – (a) AS 5100, (b) AIJ, (c) AISC, (d) BS 5400, (e) DBJ 13-51-2003, and (f) EC4. 3.3.1 Effect of steel strength Figure 14 shows the effect of steel strength (fy) on the prediction accuracy of AS 5100. Table 3 provides the mean values (μ) and the standard deviations (σ) of measured to calculated strength ratios for test specimens with fy larger than 350 MPa. From the comparisons, it can be seen that there is a decrease of 2-3% in μ except circular beam-columns with a Online 3.3 Discussion For design purposes, all codes have provided some limitations on material strengths and section slenderness. However, many tests have been conducted to date beyond those limitations, which makes it possible to check the possibility of relaxing those limitations. The following sections discuss this topic for AS 5100. Australian Journal of Structural Engineering 18 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 2 Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 2 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 (a) 2 Normalized calculated strength N ue/N uc (b) 2 Normalized calculated strength N ue/N uc 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 0 (c) 2 Normalized calculated strength N ue/N uc (d) 2 Normalized calculated strength N ue/N uc 1000 2000 3000 4000 Test strength N ue (kN) 5000 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 (e) Figure 7: (f) 0 1000 2000 3000 4000 Test strength N ue (kN) 5000 Comparison between test results and code predictions (rectangular columns) – (a) AS 5100, (b) AIJ, (c) AISC, (d) BS 5400, (e) DBJ 13-51-2003, and (f) EC4. 2500 Ultimate strength (kN) 2000 1500 1000 500 0 0 0.5 1 1.5 Ultimate strength (kN) Test results AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 EC4 2000 1600 1200 800 400 0 Test results AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 EC4 2 r 2.5 0 0.5 1 1.5 r 2 2.5 (a) Figure 8: Relative slenderness (b) Relative slenderness Column strength based on different code provisions – (a) circular section, and (b) square section. Online Australian Journal of Structural Engineering “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 19 2 2 1.5 15% Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 600 1200 1800 2400 Test strength N ue (kN) 3000 0 (a) 2 (b) 2 600 1200 1800 2400 Test strength N ue (kN) 3000 1.5 15% Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 600 1200 1800 2400 Test strength N ue (kN) 3000 0 (c) 2 (d) 2 600 1200 1800 2400 Test strength N ue (kN) 3000 1.5 15% Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 600 1200 1800 2400 Test strength N ue (kN) 3000 0 (e) Figure 9: (f) 600 1200 1800 2400 Test strength N ue (kN) 3000 Comparison between test results and code predictions (circular beam-columns) – (a) AS 5100, (b) AIJ, (c) AISC, (d) BS 5400, (e) DBJ 13-51-2003, and (f) EC4. values ( μ ) and the standard deviations ( σ ) of measured to calculated strength ratios are presented in table 3. From figure 15 and table 3, it seems that the effect of concrete strength on circular specimens is different from that on rectangular specimens. For circular specimens, a decrease of 3-6% in the mean value μ is found. In the case of rectangular specimens, only a decrease of 4% is found for stub columns while an increase of 3-4% is found for columns, beamOnline decrease of 5% and circular beams with an increase trend. But all mean values are still above unity except those for beam-columns. 3.3.2 Effect of concrete strength The effect of concrete strength (fc’) on the prediction accuracy of AS 5100 is shown in figure 15. For test specimens with fc’ larger than 65 MPa, the mean Australian Journal of Structural Engineering 20 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 2 2 1.5 15% Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 600 1200 1800 2400 Test strength N ue (kN) 3000 0 (a) 2 (b) 2 600 1200 1800 2400 Test strength N ue (kN) 3000 Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 600 1200 1800 2400 Test strength N ue (kN) 3000 0 (c) 2 (d) 2 600 1200 1800 2400 Test strength N ue (kN) 3000 1.5 15% Normalized calculated strength N ue/N uc Normalized calculated strength N ue/N uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 600 1200 1800 2400 Test strength N ue (kN) 3000 0 (e) Figure 10: (f) 600 1200 1800 2400 Test strength N ue (kN) 3000 Comparisons between test results and code predictions (rectangular beam-columns) – (a) AS 5100, (b) AIJ, (c) AISC, (d) BS 5400, (e) DBJ 13-51-2003, and (f) EC4. deviations (σ) of measured to calculated strength ratios for test specimens with section slenderness beyond the allowed values given in AS 5100. Though different yield slenderness limits have been specified for RHSs, only the middle value of 40 is used herein to analyse the data for simplicity considerations. It can be seen from figure 16 that there is a declining trend of the measured to calculated strength ratios as λe increases. For circular specimens, a decrease of Online columns or beams. Once again, all mean values of measured to calculated strength ratios are above or near unity except those for beam-columns. 3.3.3 Effect of section slenderness Figure 16 illustrates the effect of section slenderness (λe) on the prediction accuracy of AS 5100. Table 3 provides the mean values (μ) and the standard Australian Journal of Structural Engineering “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 21 2500 2000 Axial load N (kN) 1500 1000 500 0 0 15 30 Axial load N (kN) Test results AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 EC4 2500 2000 1500 1000 500 0 Test results AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 EC4 45 60 0 15 30 45 60 (a) 2500 Moment M (kN m) Test results AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 EC4 (b) 2500 Moment M (kN m) Test results AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 EC4 Axial load N (kN) 1500 1000 500 0 0 15 30 Axial load N (kN) 2000 2000 1500 1000 500 0 45 60 0 15 30 45 60 (c) 1500 Moment M (kN m) Test results AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 EC4 (d) 1000 Moment M (kN m) Test results AS 5100 AIJ AISC BS 5400 DBJ 13-51-2003 EC4 Axial load N (kN) 900 600 300 0 0 15 30 Axial load N (kN) 1200 800 600 400 200 0 45 60 0 15 30 45 60 (e) Figure 11: Moment M (kN m) m) (f) Moment M (kN m) Comparison of predicted interaction curves with test results by Matsui et al (1995) – (a) λr = 0.18, (b) λr = 0.35, (c) λr = 0.51, (d) λr = 0.80, (e) λr = 1.22, and (f) λr = 1.82. 4 CONCLUSIONS about 5% in the mean value μ is found when λe is larger than 82. However, only 1-2% in the mean value μ is found for rectangular members when λe is larger than 40. It can also be seen from table 3 that all mean values of measured to calculated strength ratios are above or near unity except those for beam-columns. This demonstrates the fact that there is a tendency to relax the limitation of section slenderness. Australian Journal of Structural Engineering In this paper, the AS 5100 approach to the design of CFST members has been described briefly. 2194 test results from two currently available test databases are used to evaluate the design approach of AS 5100. Some other existing design codes are also compared with the test results. The following conclusions may be made within the present scope of investigation: Online 22 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 2 2 1.5 15% Normalized calculated strength M ue/M uc Normalized calculated strength M ue/M uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 100 200 300 Test strength M ue (kN) 400 0 (a) 2 (b) 2 100 200 300 Test strength M ue (kN) 400 Normalized calculated strength M ue/M uc Normalized calculated strength M ue/M uc 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 0 100 200 300 Test strength M ue (kN) 400 0 (c) Figure 12: (d) 100 200 300 Test strength M ue (kN) 400 Comparison between test results and code predictions (circular beams) – (a) AS 5100 (EC4), (b) AIJ (AISC), (c) BS 5400, and (d) DBJ 13-51-2003. 2 2 1.5 15% Normalized calculated strength M ue/M uc Normalized calculated strength M ue/M uc 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 60 0 120 180 240 Test strength M ue (kN) 300 0 60 (a) 2 (b) 2 120 180 240 Test strength M ue (kN) 300 Normalized calculated strength M ue/M uc Normalized calculated strength M ue/M uc 1.5 15% 1.5 15% 1 1 0.5 15% 0.5 15% 0 0 60 0 120 180 240 Test strength M ue (kN) 300 0 60 (c) Figure 13: (d) 120 180 240 Test strength M ue (kN) 300 Comparison between test results and code predictions (rectangular beams) – (a) AS 5100 (EC4), (b) AIJ (AISC), (c) BS 5400, and (d) DBJ 13-51-2003. Online Australian Journal of Structural Engineering “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 23 2 2 Normalized calculated strength Normalized calculated strength fy=350 MPa fy=350 MPa 1.5 15% 1.5 15% 1 1 0.5 Stub column Beam-column Column Beam 15% 0.5 Stub column Beam-column Column Beam 15% 0 180 (a) Figure 14: 360 540 720 Steel yield strength f y (MPa) 900 0 180 (b) 360 540 720 Steel yield strength f y (MPa) 900 Effect of steel strength on the prediction accuracy of AS 5100 – (a) circular section, and (b) square section. 2 2 fc =65 MPa Normalized calculated strength Normalized calculated strength fc =65 MPa 1.5 15% 1.5 15% 1 1 0.5 Stub column Beam-column Column Beam 15% 0.5 Stub column Beam-column Column Beam 15% 0 0 0 30 60 90 120 Concrete cylinder strength f c (MPa) 0 (a) Figure 15: 2 (b) 30 60 90 120 Concrete cylinder strength f c (MPa) Effect of concrete strength on the prediction accuracy of AS 5100 – (a) circular section, and (b) square section. 2 e Normalized calculated strength =82 15% Normalized calculated strength e =40 15% 1.5 1.5 1 1 0.5 Stub column Beam-column Column Beam 15% 0.5 Stub column Beam-column 15% Column Beam 0 0 44 0 88 132 Section slenderness 176 e 220 0 40 (a) Figure 16: (b) 80 120 160 Section slenderness 200 Effect of section slenderness on the prediction accuracy of AS 5100 – (a) circular section, and (b) square section. 1. The approach in AS 5100 gives generally accurate predictions, thus it is also possible to be used for building construction. However, it should be noted that it overestimates the strength of rectangular beam-columns by 5% on average. 2. After ignoring all code limitations and taking material partial safety factors as unity, there are Australian Journal of Structural Engineering considerable differences among different code predictions. The predicted results using AS 5100 are quite close to those from EC4. 3. All three factors of steel strength, concrete strength and section slenderness slightly affect the prediction accuracy, but the comparisons still indicate a tendency to relax the limitations Online 24 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He Table 3: Comparison results for tests beyond the limitations of AS 5100. fy > 350 MPa No. of tests 213 141 45 2 166 65 82 28 fc’ > 65 MPa Section type Member type Stub column λe > 82 (circular) or λe > 40 (rectangular) σ 0.115 0.081 0.112 0.088 0.088 0.146 0.115 0.092 No. of tests 161 58 31 10 237 141 113 2 μ 1.024 1.137 0.947 1.320 1.038 1.011 0.929 1.121 σ 0.130 0.135 0.100 0.058 0.104 0.118 0.140 0.088 No. of tests 153 13 55 4 64 36 55 4 μ 0.994 1.102 0.944 1.383 1.020 1.093 0.988 1.172 μ 0.996 1.085 0.957 1.322 1.044 1.039 0.951 1.021 σ 0.105 0.151 0.072 0.083 0.124 0.125 0.129 0.045 Circular Column Beamcolumn Beam Stub column Rectangular Column Beamcolumn Beam of AS 5100. This relaxation will allow a designer to use higher strength materials and to design composite members with larger section slenderness. 4. Additional concrete confinement at higher slenderness ratios can be expected for circular columns. This beneficial effect may be considered in a column design. ACKNOWLEDGEMENTS This research work has been partially supported by the International Research Initiatives Scheme provided by the University of Western Sydney. REFERENCES American Institute of Steel Construction, 2005, ANSI/ AISC 360-05 Specification for structural steel buildings, Chicago, Illinois, USA. Architectural Institute of Japan (AIJ), 1997, Recommendations for design and construction of concrete filled steel tubular structures, Japan (in Japanese). ASCCS, 2007, Database of Concrete-Filled Steel Tube Columns, http://web.ukonline.co.uk/asccs2. Australian Steel Institute, 2004, “Latitude reaches skyward in steel: Construction technology at its best”, Steel Australia, Vol. 17, No. 1, pp. 10-12. British Standards Institution, 2005, BS 5400 Steel, concrete and composite bridges, Part 5, Code of practice for the design of composite bridges, London, UK. Chaseling, C. 2004, “Star attraction”, Modern Steel Construction, Vol. 44, No.12, pp. 36-42. Chen, Z. Y., Zhu, J. Q. & Wu, P. G. 1996, High strength concrete and its application, Tsinghua University Press, Beijing, China (in Chinese). Chung, J. & Matsui, C. 2005, “SRC standards in Japan and comparison of various standards for CFT columns”, International Journal of Steel Structures, Vol. 5, No.4, pp. 315-323. DBJ 13-51-2003, 2003, Technical specification for concrete-filled steel tubular structures, The Construction Department of Fujian Province, Fuzhou, China (in Chinese). Eurocode 4, 2004, Design of composite steel and concrete structures, Part1.1, General rules and rules for Building, BS EN 1994-1-1: 2004, British Standards Institution, London, UK. Eurocode 4, 1994, Design of composite steel and concrete structures, Part1.1, General rules and rules for Building, DD ENV 1994-1-1: 1996, British Standards Institution, London, UK. Goode, C. D. 2006, “A review and analysis of over one thousand tests on concrete filled steel tube columns”, Proceedings of 8th International Conference on Steel-Concrete Composite and Hybrid Structures, Harbin, China, pp. 17-23. Han, L. H. 2000, “Tests on concrete filled steel tubular columns with high slenderness ratio”, Advances in Structural Engineering – An International Journal, Vol. 3, No. 4, pp. 337-344. Australian Journal of Structural Engineering Online “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He 25 Han, L. H. 2007, Concrete filled steel tubular structures – theory and practice, China Science Press, Beijing, China (in Chinese) Mansur, M. A. & Islam, M. M. 2002, “Interpretation of concrete strength for non-standard specimens”, Journal of Materials in Civil Engineering, ASCE, Vol. 14, No. 2, pp. 151-155. Matsui, C., Tsuda, K. & Ishibashi, Y. 1995, “Slender concrete filled steel tubular columns under combined compression and bending”, Proceedings of the 4th Pacific Structural Steel Conference, Vol. 3, Steel-Concrete Composite Structures, Singapore, pp. 29-36. Standards Australia, 2004, AS5100.6-2004 Bridge design, Part 6: Steel and composite construction, Sydney, Australia. Uy, B. 2000, “Strength of concrete filled steel box columns incorporating local buckling”, Journal of Structural Engineering, ASCE, Vol. 126, No. 3, pp. 341-352. Uy, B. & Patil, S. B. 2006, “Concrete filled high strength steel box columns for tall buildings: Behaviour and design”, The Structural Design of Tall Buildings, Vol. 5, No. 2, pp. 75-94. Wu, F. Y. 2006, “Compressive behaviour of recycled concrete-filled steel tubes”, Masters thesis, College of Civil Engineering, Fuzhou University, China (in Chinese). Yu, Q., Tao, Z. & Wu, Y. X. 2008, “Experimental behaviour of high performance concrete-filled steel tubular columns”, Thin-Walled Structures, Vol. 46, No. 4, pp. 362-370. Zhang, S. M., Ma, X. B. & Goode, C. D. 2007, “Comparison between Chinese and three worldwide codes for circular-filled steel tube members”, Proceedings of the 3 rd International Conference on Steel and Composite Structures, Manchester, UK, pp. 633-638. Australian Journal of Structural Engineering Online 26 “Design of concrete-filled steel tubular members according to the Australian ... ” – Tao, Uy, Han & He ZHONG TAO Zhong Tao is Professor of Structural Engineering at Fuzhou University, China, and is currently visiting the University of Western Sydney. He received his MS and PhD degrees from the Harbin Institute of Technology, China. His main research interests are steel-concrete composite structures and FRPconfined concrete. Zhong has published more than 80 journal papers, and recently published a Chinese book about innovative composite columns. He has played an important role in drafting five Chinese design codes on steelconcrete composite structures, including DBJ13-61-2004, DBJ13-51-2003 and GJB4142-2000. He was awarded three patents by the Chinese National Bureau of Knowledge Property Rights since 2005. He is currently on the Editorial Board of the international journal of Steel & Composite Structures. BRIAN UY Brian Uy is Professor of Structural Engineering and Head of the School of Engineering at The University of Western Sydney. He has been involved in research in steel and steel-concrete composite structures for over 15 years and published more than 300 articles. Much of his research has been underpinned by competitive grant research funding from the Australian Research Council (ARC) and industry. He is currently a member of the ARC College of Experts, providing advice to the federal government on peer reviewed research in civil and structural engineering. Brian currently serves on the Australian Standards Committee for Composite Structures (BD 32), the AISC Task Committee 5 on Composite Construction, ASCE Technical Committee on Composite Construction, and the IABSE Working Commission 2 for Steel, Timber and Composite Structures. He also holds roles on the Editorial Board for seven major international journals in steel and composite structures, including being the Chief Editorial Asia-Pacific of Steel & Composite Structures. Brian is a chartered civil and structural engineer in Australia, the UK and the USA. LIN-HAI HAN Lin-Hai Han is Professor of Structural Engineering at Tsinghua University, China. He has published 60 refereed international journal papers and 40 refereed international conference papers. He has received several excellence awards from the Chinese government since 1995 in recognition of his contributions to the research and application of steel-concrete composite construction. He is one of the outstanding young researchers awarded by the National Natural Science Foundation of China. He holds roles on the Editorial Board for several international and national journals. Lin-Hai has consulted industry and government authorities on a wide range of structural engineering projects. He has played an important role in drafting several design codes on steel-concrete composite structures in China. His current research interests include steelconcrete composite and hybrid structures under different kinds of loadings, such as static, dynamic and fire. SHAN-HU HE Shan-Hu He is a PhD candidate at Tsinghua University and her supervisor is Professor Lin-Hai Han. She received her bachelor’s degree from Tsinghua University in 2007 and is currently working in the field of concrete-filled steel tubular columns. Australian Journal of Structural Engineering Online