The Comparison of Behaviors
for Circular and Square ConcreteFilled Steel Tube (CFST) under
Axial Compression.
Shan Tong Zhong1
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡SAMMARY
¡¡¡¡The behaviors of concentrically loaded short concretefilled 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
(¦Òi) versus strain intensity (¦Åi) for steel under complex stress
state is shown in Fig.1.
¡¡¡¡
¦Òi=1/¡Ì2 [(¦Òx¦Òy)2+(¦Òy¦Òz)2+(¦Òz¦Òx)2+6(¦Óxy2+¦Óyz2+¦Ózx2)]1/2 ¡¡¡¡¡¡¡¡¡¡¡¡¡¡
¡¡(1)
¦Åi=¡Ì2/3 [(¦Åx¦Åy)2+(¦Åy¦Åz)2+(¦Åz¦Åx)2+3/2 (¦Ãxy2+¦Ãyz2+¦Ãzx2)]1/2 ¡¡¡¡¡¡
¡¡¡¡¡¡(2)
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Fig. 1 ¦Òi¦Åi curve of steel
¡¡¡¡The constitutive relationship of steel can be expressed
As follows:
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡{d¦Òij}=[D]{d¦Åij} ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡(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 plasticcrack theory is used to drive the constitutive relationship
of core concrete under complex stress situation. It adopts the following
expression(Cheng 2001):
¡¡¡¡ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡{d¦Ò}=[D]{d¦Å} ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡(4)
¡¡¡¡In which. Matrix of rigidity [D] is 6¦¶6 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
stressstrain 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 tryerror 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 Crosssections
¡¡¡¡Owing to analysis and to compare the behaviors
of CFST with various forms, the equivalent crosssections should
be toke for comparison each other. Equivalent crosssection means
that the area of steel As, area of concrete Ac for various form
are equality each other.. Then the steel ratio ¦Á=As/Ac and the confining
factors (¦Î=¦Á fy /fck; ¦Î0=¦Á 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
crosssection are:
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡D=2b/¡Ì¦Ð=1.1284B ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡(5)
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡T=D/2  (B©¤2ts )/ ¡Ì¦Ð=0.5D©¤0.5642(B©¤2ts ) ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡(6)
1.3 The behaviors of concentrically
loaded short CFST
¡¡¡¡With the constitutive relationships for
steel and concrete, the complete average longitudinal stressstrain
curves of concentrically loaded short CFST columns with different
crosssection geometries are obtained using FE analyses. 3D 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 ¦Ò©¤¦Å relationship curves for A3 group (¦Î=1.06),
A7 group (¦Î=2.69) and A10 group (¦Î=2.9). Each group consists of
four columns, which have circular, octagonal, square and rectangular
equivalent crosssections respectively.
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
¡¡¡¡¡¡
Fig.2 The ¦Ò©¤¦Å relationship curves for A3, A7,A10 Fig. 3 Typical
¦Ò©¤¦Å curves
¡¡¡¡From Fig.2, we can see that the behavior
of circular Crosssection is better than that of square one. The
behavior of octagonal CFST is situated between circular and square
crosssection, but it closes to circular. Behavior of equivalent
rectangular is more close to square's, the ¦Ò©¤¦Å curves of them always
exist descending stages and always expresses brittle damage.
¡¡¡¡Fig.3 shows the Typical ¦Ò©¤¦Å curves of concentrically loaded CFST
short columns with different crosssection 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 crosssections,
descending appears when ¦Î is smaller than 1.0, while for those with
square and rectangular crosssections, descending occurs when ¦Î
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 crosssection, the strain corresponding to point B
is slightly larger or smaller than 3000¦Ì¦Å. 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 3000¦Ì¦Å.
¡¡¡¡(2) For columns which have no plastic stage and show only descending
loaddisplacement 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+B¦Î+C¦Î2)fck ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡(7)
¡¡¡¡The compressive design strength:
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡fsc=(1.212 +B¦Î0+C¦Î02)fc ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ (8)
¡¡¡¡In which, B and C are coefficients. They depend on the crosssection
geometry, as follows.
¡¡¡¡For circular crosssection:
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Bc= 0.1759fy/235 + 0.794
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Cc=©¤0.1038fck/20 +0.0309
¡¡¡¡For square crosssection:
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Bs= 0.131 fy/235 + 0.723
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Cs=©¤0.07fck/20 +0.0262
¡¡¡¡The confining factors ¦Î= ¦Á fy / fck; ¦Î0=¦Á f / fc .
¡¡¡¡For three kinds of steel (Q235, Q345, Q390 ), six kinds of concrete
(C30~C80), steel ratio ¦Á= 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 crosssection Es is lower
~13% than that of circular one. Hence, the equivalent axial rigidity
and bending rigidity for square crosssection 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'=¦Õc Asc fscc ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ (11)
For square ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ Ns'=¦Õs Asc fscs¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡(12)
Then, ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡K= Ns'/ Nc'=(¦Õs/¦Õc) (fscs/ fscc) ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡(13)
¡¡¡¡Value of K shows in Tab. 1 for steel ratio ¦Á=0.1.
Table 1 Value of ratio
K
Steel

Q235

Q345

Q390

Concrete

C30¡¡C40

C40 C50
C60

C60 C70
C80

¦Á£½0.1

0.86 ¡¡0.88

0.86¡¡0.87¡¡0.88

0.88¡¡0.89¡¡0.89

¡¡¡¡Here, ¦Õc and ¦Õs are toke from Chinese standards DL/T 50851999
and GJB 41422000 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 beamcolumns
¡¡¡¡In tall and super tall buildings, the columns
are under eccentric compressive load in two directions. The calculate
formula is as follows:
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡N/¦ÕN0 +Mx/¦ÃxWscx +My/¦ÃyWscy ¡Ü 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;
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¦Ãx and ¦Ãyplastic coefficients of x and y directions for
columns ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡respectively.
¡¡¡¡For circular crosssection, it works under axial compressive load
N with the bending moment M=¡Ì( 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 ¦Õs Nos is
less than that of circular one (¦Õc Noc ).
¡¡¡¡3. The comparison of structures and
manufactures
3.1 The composition of crosssections
¡¡¡¡The spiral welding steel tube is always
used for circular crosssection if the thickness of plate is t¡Ü
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
crosssection, two welds even four welds are necessary to form a
box crosssection. 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 antiseismic 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 antiseismic and fireproofing
4.1 The behaviors of antiseismic
¡¡¡¡The research work of antiseismic 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 antiseismic 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 =¦ÐD, for square is
Ls =4B.
¡¡¡¡According to the equivalent area, D=1.1264B, hence,
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Ls/ Lc = 4B/(1.1284¦ÐB =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
crosssection. As everyone knows, the area of square crosssection
should be enhanced to bear the same loadings of circular crosssection.
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 fireproofing.
¡¡¡¡The advantages are as followings:
¡¡¡¡1) The load carrying capacity under axial compression is about
20% more than that of square crosssection. 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 antiseismic 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.
£¶. 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

Crosssection

¡¡¡¡¡¡¡¡§¶1000§ç22
¡¡¡¡¡¡¡¡¡¡

§¶1000§ç22

¡¡¡¡¡¡¡¡¡¡square940§ç22
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡

square960§ç22

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 ScienceTechnical Publishing House, Harbin,1995.
3) Design Regulation of Composite Structures(S), DL/T 50851999.
4) Design Regulation of Composite Structures Square CFST Members(S),
GJB41422000.
5) Bazant Z.P. and Kim S.S. PlasticFracturing 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); email:
zhongst@vip.0451.com
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
¡¡¡¡¡¡¡¡¡¡¡¡¡¡
¡¡¡¡¡¡
