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The Comparison of Behaviors for Circular and Square Concrete-Filled Steel Tube (CFST) under Axial Compression.

Shan Tong Zhong1

                    SAMMARY

  The behaviors of concentrically loaded short concrete-filled steel circular columns are better than that of square one. Its load carrying capacity is higher and it has more economical benefit. Hence, it is adopted in buildings widely. But in some developed countries, architects are willing to adopt the square CFST columns from the view of convenient arrangement inside the rooms. In our country, the square CFST columns have begun to use in tall buildings also in recent years.
  In this paper, the behaviors, structures and economical benefits of circular and square CFST under axial compression are compared detailed. The results of comparison can be referred for designers.

Keywords: Circular and square CFST, axial compression, behaviors, comparison

INTRUDUCTION

  As every one knows, the behaviors of circular CFST are better than that of square one. Its load carrying capacity is higher and the steel expanse can be cut down. But the some architects are willing to adopt the square CFST columns from the view of convenient arrangement inside the rooms. Hence, in recent years, the square CFST columns have begun to use in some tall buildings.
  In developed countries, save steel is not so importance. But in our country, cost reduction of buildings is most importantly. Hence, the advantages and disadvantages for both of these two kinds of CFST columns should have a clearly understands.

  1) Behaviors of circular and square CFST under axial compression

1.1 The constitutive relationships of materials

  According to the inference of "Unified Theory" suggested by author (Zhong 1995), the change of behaviors for CFST is along with the change of cross sections, and the change is continuously. And the design formula is unified. From which the stress strain relation curves of circular and square CFST under axial compression should be found. Therefore, the constitutive

  relationships of steel and concrete under complex stress states should be determined firstly.The relation curve of stress intensity (σi) versus strain intensity (εi) for steel under complex stress state is shown in Fig.1.

  
σi=1/〔2 [(σx-σy)2+(σy-σz)2+(σz-σx)2+6(τxy2+τyz2+τzx2)]1/2          (1)
εi=〔2/3 [(εx-εy)2+(εy-εz)2+(εz-εx)2+3/2 (γxy2+γyz2+γzx2)]1/2        (2)

                  
                  Fig. 1 σi-εi curve of steel

  The constitutive relationship of steel can be expressed
As follows:
                    {dσij}=[D]{dεij}               (3)
  in which [D] is the stiffness matrix of steel, in the elastic range is the elastic stiffness matrix [D]e, in the plastic range is the plastic stiffness matrix [D]p. while in the elastic plastic range is [D]ep=[D]e-[D]p.
  The plastic-crack theory is used to drive the constitutive relationship of core concrete under complex stress situation. It adopts the following expression(Cheng 2001):
                      {dσ}=[D]{dε}                (4)
  In which. Matrix of rigidity [D] is 6Χ6 matrix. There are 6 unknown parameters in it. And in these parameters there are 22 coefficients, 19 coefficients of which are toke from reference [5] after a little revised. While 3 of these 22 coefficiences are determined by test results. By use of the try and rectification method, Cheng (2001) managed to determine the 3 coefficients from a number of experimental curves of circular compression members. Based on the constitutive relationships of core concrete and steel, and longitudinal and radial displacement compatibility, Chen (2001) obtained the average longitudinal stress-strain curves by calculation. By comparing the calculated curves with the experimental curves and adjusting the 3 coefficients thereafter, a satisfying agreement between the calculated and experimental curves was achieved. This method means "The try-error method". The right constitutive relationship of concrete under complex stress state was got. Owing to the tangent constitutive matrix is the function of concrete's stress and strain only, hence, this constitutive relationship of concrete suites various form of members. The detail derivation and analysis please refer to Reference [1].
  For verification the right of constitutive relationships of steel and concrete mentioned above, especially for verification the right of parameters adopted in the constitutive relationship of core concrete, we calculated a lot of circular CFST axial compressive stub columns to compare with the test curves. It coincides very well. The test curves are toke from the references of Japan, Russia, England and ours. It is a tremendous achievement in the research work of CFST.

1.2 Equivalent Cross-sections

  Owing to analysis and to compare the behaviors of CFST with various forms, the equivalent cross-sections should be toke for comparison each other. Equivalent cross-section means that the area of steel As, area of concrete Ac for various form are equality each other.. Then the steel ratio α=As/Ac and the confining factors (ξ=α fy /fck; ξ0=α f /fc ) are equal to each other for circular and square CFST. Here fy and f is yield stress and design strength of steel respectively, fck and fc is standard compressive strength and design compressive strength of concrete respectively.
  If B denotes the side length of square form, ts denotes the thickness of plates, then the diameter D and thickness t of equivalent circular cross-section are:
                   D=2b/〔π=1.1284B                 (5)
            T=D/2 - (B2ts )/ 〔π=0.5D0.5642(B2ts )         (6)

1.3 The behaviors of concentrically loaded short CFST

  With the constitutive relationships for steel and concrete, the complete average longitudinal stress-strain curves of concentrically loaded short CFST columns with different cross-section geometries are obtained using FE analyses. 3-D FE models are developed using the incremental Lagrange formula, where both material and geometric nonlinearities are toke into consideration. The detail analysis is referred to the reference [1] please.
  Fig.2 shows the σう relationship curves for A3 group (ξ=1.06), A7 group (ξ=2.69) and A10 group (ξ=2.9). Each group consists of four columns, which have circular, octagonal, square and rectangular equivalent cross-sections respectively.
                 
Fig.2 The σう relationship curves for A3, A7,A10 Fig. 3 Typical σう curves

  From Fig.2, we can see that the behavior of circular Cross-section is better than that of square one. The behavior of octagonal CFST is situated between circular and square cross-section, but it closes to circular. Behavior of equivalent rectangular is more close to square's, the σう curves of them always exist descending stages and always expresses brittle damage.
  Fig.3 shows the Typical σう curves of concentrically loaded CFST short columns with different cross-section geometries. When the confining factors change from large, medium to small, the final parts of the curves vary from ascending, horizontal to descending. For composite columns with circular and octagonal cross-sections, descending appears when ξ is smaller than 1.0, while for those with square and rectangular cross-sections, descending occurs when ξ is smaller than 3.

  2) The comparison of bearing capacity for circular and square CFST

2.1 Compressive strength

  According to the definition of limit state, the damage criterion is determined as follows.
  (1) For columns which have plastic failure with strain hardening or plastic stage, the ultimate strength should correspond to point B, which is the turning point from elastic plastic stage to strain hardening or to plastic stage.
  After numerous analyses, it is well justified that for columns with circular cross-section, the strain corresponding to point B is slightly larger or smaller than 3000με. For the convenience of design, the compressive strength fscy of a CFST circular stub column is determined to be the stress
corresponding to the longitudinal strain of 3000με.
  (2) For columns which have no plastic stage and show only descending load-displacement curve, the ultimate strength should be toke as the highest stress on the curve..
  Based on the analyses above, the following formulae are recommended.
  The compressive standard strength:
                  fscy=(1.212+Bξ+Cξ2)fck              (7)
  The compressive design strength:
                  fsc=(1.212 +Bξ0+Cξ02)fc              (8)
  In which, B and C are coefficients. They depend on the cross-section geometry, as follows.
  For circular cross-section:
                  Bc= 0.1759fy/235 + 0.794
                  Cc=0.1038fck/20 +0.0309
  For square cross-section:
                  Bs= 0.131 fy/235 + 0.723
                  Cs=0.07fck/20 +0.0262
  The confining factors ξ= α fy / fck; ξ0=α f / fc .
  For three kinds of steel (Q235, Q345, Q390 ), six kinds of concrete (C30~C80), steel ratio α= 0.04~0.20, the standard strength of square CFST fscsy is lower 5%~16% than that of circular one. Moreover, we derived the elastic module (E) of circular and square CFST, It shows that the elastic module of square cross-section Es is lower ~13% than that of circular one. Hence, the equivalent axial rigidity and bending rigidity for square cross-section CFST are lower about 13% than that of circular one.
2.2 The bearing capacity of concentrically loaded CFST columns

Strength: For circular         Nc= Asc fscc                 (9)
For square                Ns=Asc fscs                 (10)
Stability: For circul         Nc'=φc Asc fscc                (11)
For square                Ns'=φs Asc fscs               (12)
Then,              K= Ns'/ Nc'=(φs/φc) (fscs/ fscc)          (13)
  Value of K shows in Tab. 1 for steel ratio α=0.1.

Table 1 Value of ratio K

Steel
Q235
Q345
Q390
Concrete
C30 C40
C40 C50 C60
C60 C70 C80
α0.1
0.86  0.88
0.86 0.87 0.88
0.88 0.89 0.89


  Here, φc and φs are toke from Chinese standards DL/T 5085-1999 and GJB 4142-2000 respectively.
  From Tab. 1, we can see that the bearing capacity of concentrically loaded square CFST columns are lower than that of circular one.

2.3 The comparison of bearing capacities for beam-columns

  In tall and super tall buildings, the columns are under eccentric compressive load in two directions. The calculate formula is as follows:
               N/φN0 +Mx/γxWscx +My/γyWscy + 1          (14)
  In which, N, Mx, My ---axial compressive load, bending moments of x and y directions               respectively;
           N0 ----bearing capacity of concentrically loaded CFST columns;
     Wscx and Wscy ----section modulus of x and y directions for columns                     respectively;
       γx and γy----plastic coefficients of x and y directions for columns                  respectively.
  For circular cross-section, it works under axial compressive load N with the bending moment M=〔( Mx2 +My2 ). But for square one, it works under axial compression N with two direction bending moments Mx and My. The calculation is not only complex, but also the research work does not ripen yet. The load bearing capacity of square CFST column is lower than that of circular one owing to the φs Nos is less than that of circular one (φc Noc ).

  3. The comparison of structures and manufactures

3.1 The composition of cross-sections

  The spiral welding steel tube is always used for circular cross-section if the thickness of plate is t+ 20mm. The quality of weld can be guaranteed perfectly, and it saves labor. When the thickness of plate is greater than 20mm, the longitudinal butt weld is adopted, there is only one weld necessary. For square cross-section, two welds even four welds are necessary to form a box cross-section. Therefore, the weld of circular form is less than that of square one. Hence, the manufacturing cost of circular member is cheaper.
  In addition, the butt weld for circular steel tube bears tensile force only, while the butt weld of square steel tube is under complex stress states.

3.2 The connections of columns with beams

  The inner diaphragm is always used for square CFST column as shown in Fig.4a. Fig.4b shows the outside strengthening ring is used for circular column. Although the research works of this connection is more ripe, its anti-seismic behavior is well and it is more safety and reliability, but the steel used is more. If the inner diaphragm is used for circular column, the structure of connection is the same as square column as shown in Fig.4c.
  Obviously, the welding of inner diaphragm is more difficulty, and it will impede pouring concrete into the tube..

       
             Fig.4 The connections of column with beams
  4. The behaviors of anti-seismic and fireproofing

4.1 The behaviors of anti-seismic

  The research work of anti-seismic behaviors for circular CFST columns is riper than that of square CFST columns.
  The slenderness of circular column is controlled instead of limited compression ratio. It caused to save steel. Compression ratio means the ratio of compressive force to nominal compression capacity of the column.

  Fig. 5 shows the hysteretic curves of concentrically loaded circular CFST members (axial compressive load N=Asc fsc, and the compression ratio equals to 1.0) under repeat horizontal load. The hysteretic curves are very full and round. The absorbing energy ability is very well.
  The research of anti-seismic behaviors for square CFST columns is lack yet. When it is used as the columns in tall building, the axial compression ratio should be limited as for steel structures.

4.2 The behaviors of fireproofing
    
Fig. 5 Hysteretic curves of circular CFST members with concentrically load N=Sscfsc

  We have had completed the research works about fire proofing of circular CFST members, and obtained the calculation formula for determination the thickness of fireproofing coating. The needed thickness of fireproofing coating for circular and square CFST members can be compared as follows.
  The circumferential length of circle is Lc =πD, for square is Ls =4B.
  According to the equivalent area, D=1.1264B, hence,
                Ls/ Lc = 4B/(1.1284πB =1.1284
  It means that the coat needed for square members is over 13% more than that for circular one. It is calculated according to the equivalent cross-section. As everyone knows, the area of square cross-section should be enhanced to bear the same loadings of circular cross-section. Hence, the needed fireproofing coat of square members will be still more.
  Except fireproofing coat, the fireproofing plates can be used also as shown in Fig.6. If the thickness of plate is 50mm, the 3h required fireproofing time can be reached.

  5.Conclussion

  From the comparison of circular and square CFST columns, we can see that the advantages of
circular CFST columns are far exceed than that of square one. This is got from the comparisons of the behaviors, structures, manufactures and fire-proofing.

  The advantages are as followings:
  1) The load carrying capacity under axial compression is about 20% more than that of square cross-section. And under eccentric compression, is 20% more at least. From this the steel and concrete can be saved.
  2) The axial and bending rigidities are more 13% about.
  3)The behavior of anti-seismic is well. The slenderness of column is controlled instead of to limit the compression ratio.
  4) Manufacture is more convenient.
  5) The fireproofing coat can be saved 13%.

       
           Fig 6 Wrap up the column with fireproofing plates

  In a word, the circular CFST column has more advantages. It should be adopted prior in tall and super tall buildings especially in seismic region.
6. Calculating example
  Design a CFST column for a tall building,
  Known conditions: N= 45200kN; Mx= 265kNM; My= 38kNM; V=385kN; Calculating length L0 =4.5m. Used steel Q345 and concrete C50.
  The design results are listed in Table 2.
Table 2 Design results

Circular CFST
Square CFST

  without considered   

    Seismic acting           

 With considered

  Seismic acting

   Without considered

      Seismic acting             

  With considered

  Seismic acting

Cross-section
    Ф1000х22      
Ф1000х22
     square940х22         
square960х22
Rigidity B=EscmIsc
3148748 kNm2
Steel used
530.6kg/m
634.2kg/m                  
648kg/m
Save of steel
100%
119.53%                    
122.1%


Reference:
1) Cheng Hongtao, Dissertation of the doctoral degree in engineering(D), Harbin Institute of Technology, Harbin 2001.
2) Zhong Shantong, Concrete Filled Steel Tubular Structures(M), Heilongjiang Science-Technical Publishing House, Harbin,1995.
3) Design Regulation of Composite Structures(S), DL/T 5085-1999.
4) Design Regulation of Composite Structures---- Square CFST Members(S), GJB4142-2000.
5) Bazant Z.P. and Kim S.S. Plastic-Fracturing Theory for Concrete.(J), Journal of Engineering Mechanics Division. 1979, 105(EM3).

_________________________
1Proffessor,The School of Civil Engineering, Harbin Institute of Technology; Harbin,, Heilongjiang Province (150090); e-mail:
zhongst@vip.0451.com

 

                        

 

 

 

 
 
 
 

 

       

 

 

 


 

   

 

 

 

 

 



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