Concrete is very strong in compression but brittle. When a concrete member is subjected to compression, it laterally expands which will generate tensile stress horizontally. As concrete is weak in tension, cracks will form and thus the concrete starts to lose strength. However, in a CSFT, the expansion of an axially loaded concrete member will be hindered by the confining effects of the steel tube surrounding it. This results in higher load carrying capacity of the member. In addition, as cracking of the concrete is also minimised by the confinement, the overall ductility can also be improved.
Japanese researchers S. Morino & K Tsuda (2003) stated that the difference between ultimate strength and nominal squash load of a centrally loaded circular short column is provided by the confining effect and estimated by a linear function of the steel tube yield strength (Sakino, K., Ninakawa, T., Nakahara, H. and Morino, S., 1998),. For a square short column, strength increase due to the confining effect is much smaller compared to a circular short column. Local buckling significantly affects the strength of a square short column. The buckling strength of a CFST long column can be evaluated by the sum of the tangent modulus strengths calculated for a steel tube long column, and a concrete long column, separately. There is no confining effect on the buckling strength, regardless of the cross-sectional shape (Tsuda, K., Matsui, C. and Fujinaga, T., 2000),.
The sum of the stiffness of the steel tube and the concrete can be generally be used to evaluate the elastic axial stiffness. However, careful consideration must be given to the effects of stresses generated in the steel tube at the construction site, the mechanism which transfers beam loads to a CFST column through the steel tube/concrete interface, and the creep and drying shrinkage of the concrete. These factors may affect the stiffness. The increase in concrete strength due to confinement, the scale effect on concrete strength, the strain softening in concrete, the increase in tensile strength and decrease in compressive strength of the steel tube due to ring tension stress, the local buckling of the steel tube, the effect of concrete restraining the progress of local buckling deformation, as well as the strain hardening of steel have been taken into account in the constitutive laws for concrete and steel in a CFST column, (Nakahara, H., Sakino, K. and Inai, E., 1998).
The bending strength of a circular CFST beam-column exceeds the superposed strength (the sum of the strengths of concrete and steel tube) due to the confining effect. For a square CFST beam- column, strength increase due to the confining effect is much smaller compared to a circular CFST beam-column because of local buckling of the steel member. Circular CFST beam- columns show larger ductility than square ones. Use of high-strength concrete generally causes the reduction of ductility. However, in the case of a circular CFST beam-column, non-ductile behaviour can be improved by confining concrete with high strength steel tubes. S. Morino & K Tsuda (2003) indicated that the Architectural Institute of Japan (AIJ) has proposed empirical formulas to estimate the rotation angle limit of a CFST beam-column. Fiber analysis based on the constitutive laws mentioned above traces the flexural behavior and ultimate strength of an eccentrically loaded CFST column (Nakahara, H. and Sakino, K., 2000). The effective mathematical model has been established to trace the cyclic behavior of a CFST beam-column subjected to combined compression, bending, and shear but not the behavior after the local buckling of the steel tube. A hysteretic restoring force characteristic model for a CFST beam- column has been proposed, which accurately predicts the behavior when the rotation angle is less than 1.0%.
The design of CSFT members will be discussed in detail in Chapter 3 of this report.
Fire Resistance of CFST
According to the research experience for the Hew Urban Housing Project in Japan (S. Morino & K. Tsuda, 2003), CFST columns elongate at an early stage of heat loading, and then shorten until failure. CFST columns can sustain axial load from filled concrete after the capacity of the steel tube is lost by heating, and thus, fireproof material can be reduced or omitted. Rigidity at the beam-to-column connection reduces because of the heat loading, which leads to the reduction of bending moments transferred from beams to columns. Thus, the column carries only axial load at the final stage of heat loading. Fire tests of CFST beam-columns forced to sway by the thermal elongation of adjacent beams have shown that square and circular CFST beam-columns could sustain the axial load for two hours and one hour, respectively, under an axial load ratio of 0.45 and a sway angle of 1/100, but CFST beam-columns could not resist bending caused by the forced sway after 30 minutes of heating
Other findings on fire resistance of reinforced concrete filled steel (RCFS) columns, which is traditionally determined by expensive furnace tests, have also been given by K.H. Tan & C.Y. Tang (2002).
Their research shows that steel tube of RCFS columns softens quickly at elevated temperatures and the load is transferred to the cooler concrete core, which is reinforced by steel reinforcement. Therefore, the concrete core largely determines the load capacity of RCFS columns, with only small contribution from the steel tube.
The moment capacity of steel tube is also greatly reduced. This phenomenon is particularly detrimental to columns with steel tubes filled with plain concrete, as the concrete section cannot resist bending moment by itself. At ambient temperature, such a column can resist large bending moment by the steel tube. However, when subjected to elevated temperatures, the moment capacity of the column diminishes quickly as the steel tube softens. The confinement effect to the concrete core will also diminish as a result of the softening of steel tube. This will likely lead to a loss of ductility and thus a premature failure, as observed by Lie and Stringer (1994). As a general comment, only design plain concrete filled steel (PCFS) columns to carry axial loads in fire conditions. Where load eccentricity is anticipated, reinforced concrete filled steel (RCFS) columns should always be used.
Design of CFST Members
General Recommendations
This chapter discusses the ultimate design of CSFT members based on the findings from S. Morino & K Tsuda (2003). Interaction between concrete and steel has been considered and the design formulae are derived by the ultimate stress blocks that can be developed by the two materials taking into account of the section geometry. The following assumptions/limitations shall be observed when applying the design formulae.
1. The specified yield stress of steel tubes ranges from 235MPa (215 if plate thickness t > 40mm) to 355MPa (335 if t > 40mm) in accordance with several steel grades which contain high-strength steel SM520 and centrifugal high-strength cast steel tube SCW520CF.
2. The limiting values of the width-to-thickness ratio for a rectangular tube and the diameter- to-thickness ratio for a circular tube are as follows (see Fig. 3.1):
Rectangular (3.1)
circular (3.2)
where
B : flange width of a rectangular tube
D : depth or diameter of a circular tube
st : wall thickness of steel tube
F : standard strength to determine allowable stresses of steel = smaller of yield stress and 0.7 times tensile strength (MPa)
These values are relaxed to 1.5 times those of bare steels based on the research of the restraining effect of filling concrete on local buckling of steel tubes.
Figure 3.1 Cross sections of CSFT
3. The long-term allowable bond stress between the filling concrete and the inside of the steel tube is 0.15MPa for a circular tube and 0.1MPa for a rectangular tube. The bond stress does not depend on the strength of the concrete. The values for the short-term stress condition are 1.5 times those for the long-term condition.
4. The allowable compressive stress of concrete cfc is equal to Fc / 3 for the long-term stress condition, and 2Fc / 3 for the short-term one, where Fc is the design standard compressive strength of concrete.
5. The maximum effective length lk of a CFST member is limited to:
for a compression member lk/D (3.3)
for a beam-column (4) lk/D (3.4)
where, lk: effective buckling length of a member; D : minimum depth of a cross section
Ultimate Compressive Strength of a CFST
Ultimate compressive strength of a CFST column is calculated by Eqs. (3.5) through (3.8)
. Ncu1 = cNcu + (1+)sNcu (3.5)
.4 Ncu2 = Ncu1 - 0.125{Ncu1 - Ncu3 (lk / D = 12)} (3.6)
12. Ncu3 = cNcr + sNcr (3.7)
where
lk : effective length of a CFST column
D : width or diameter of a steel tube section
η = 0 for a square CFST column (3.8)
η = 0.27 for a circular CFST column
Ncu1, Ncu2, Ncu3 : ultimate strengths of a CFST column
cNcu : ultimate strength of a concrete column
sNcu : ultimate strength of a steel tube column
cNcr : buckling strength of a concrete column
sNcr : buckling strength of a steel tube column
Ncu1 in Eq. (3.5) gives the cross-sectional strength of a CFST column, in which the strength of confined concrete is considered for a circular CFST column.
Derivation of Eq. (3.5) is as follows. Referring to Fig. 3.2, when the CFST section is under the ultimate compression force Ncu1 , the concrete in a circular CFST section is subjected to axial stress cσcB and lateral pressure σr, and the steel tube is subjected to axial stress sσz and ring tension stress sσϴ, Ncu1 is first given by
Ncu1 = cA•cσcB + sA•sσZ (3.9)
The axial stress of concrete considering the confining effect cσcB is given by
cσcB = cσB + k•σr (3.10)
where k denotes the confining factor. Equilibrium of σr and sσr gives
(D-2st)•σr = 2st•sσϴ ; σr = (3.11)
Substituting Eqs. (3.10) and (3.11) into Eq. (3.9) leads to
Ncu1 = cA•cσB + sA•sσy + sA•sσZ - sA•sσy + cA•k• (3.12)
Figure 3.2 Confining effects for a circular CFST column
The ratio of the cross-sectional area of concrete to that of steel tube is approximately given by
(3.13)
Substituting Eq. (3.13) into Eq. (3.12) yields
Ncu1 = cA•cσB + sA•sσy + sA•sσy (3.14)
Denoting cNcu = cA•cσB; sNcu = sA•sσy and
η = (3.15)
In Eq. (3.15), the value sσ/sσy = 0.19 was obtained empirically by the regression analysis of the test data. Assuming the confining factor k = 4.1 and the diameter-to-thickness ratio D / t = 50, then the value η became 0.27. The expression of Ncu1 is finally given as Eq. (3.5).
Ncu3 in Eq. (3.7) gives the buckling strength of a long column as the sum of the buckling strengths separately computed for the filled- concrete and steel tube long columns. The accuracy of Eq. (3.7) compared with the tangent modulus load of the CFST column is discussed by Tsuda, K., Matsui, C. and Fujinaga, T (2000).
Ultimate compressive strength cNcu and buckling strength cNcr of a concrete column are calculated by Eqs. (3.16) and (3.17), respectively.
cNcu = cA•cru•Fc (3.16)
cNcr = cA•cσcr (3.17)
where
cA : cross-sectional area of a concrete column
Fc : design standard strength of filled concrete
cσcr : critical stress of a concrete column
cru = 0.85: reduction factor for concrete strength
Critical stress cσcr is given by Eqs. (3.18) through (3.22).
cλ1 1.0 ; cσcr = (3.18)
1.0 cλ1 ; cσcr = 0.83 exp {Cc (1- cλ1)}ru·Fc (3.19)
where
cλ1 = (3.20)
cεu = 0.93(cru·Fc)1/4 x 10-3 (3.21)
Cc = 0.568 + 0.00612Fc (3.22)
cλ: slenderness ratio of a concrete column
Equations (3.18) and (3.19) are obtained by curve fitting numerical results of the tangent modulus load of long concrete columns (see Fig. 3.3). The strength increase of confined concrete is not considered.
The ultimate compressive strength of a steel tube column is calculated by Eq. (3.23).
Figure 3.3 Critical stress of a concrete column
sNcu = sA‧F (3.23)
where
sA : cross-sectional area of a steel tube column
F : design standard strength of steel tube
Buckling strength sNcr of a steel tube column is calculated by Eqs. (3.24) through (3.28).
sλ1 0.3 ; sNcr = sA‧F (3.24)
0.3 sλ1 1.3 ; sNcr = {1-0.545 (sλ1 - 0.3)} sA‧F (3.25)
1.3 sλ1 ; sNcr = (3.26)
where
sλ1 = (3.27)
sNE = (3.28)
sλ : slenderness ratio of a steel tube column
sE : Young's modulus of steel tube
sI : cross-sectional moment of inertia of a steel tube column
Equations (3.24) through (3.26) are the expressions of column curves used in Japan for the plastic design of steel structures (see Fig. 3.4).
Figure 3.4 Allowable and buckling strength of a steel tube column
Ultimate Bending Capacity of a CFST
Ultimate bending strength Mu of a CFST beam- column subjected to axial load Nu is determined by the following procedures. First, Mu of a beam- column not greater than 12 times the width or diameter of the steel tube section is calculated by Eqs. (3.29) and (3.30).
Nu = cNu + sNu (3.29)
Mu = cMu + sMu (3.30)
The strengths appearing on the right side of Eqs. (3.29) and (3.20) are given as follows:
For a square CFST beam-column:
cNu = xn1‧cD2‧cru‧Fc (3.31)
cMu = (1 - xn1) xn1‧cD3‧cru‧Fc (3.32)
sNu = 2(2xn1 - 1)cD2‧st‧sσy (3.33)
sMu = (3.34)
For a circular CFST beam-column:
cNu = (Ï´n - sinÏ´n cosÏ´n) (3.35)
cMu = sin3Ï´n (3.36)
sNu = {β1ϴn +β2 (ϴ2 - π)}D‧st‧sσy (3.37)
sMu = (β1 +β2)sinϴn D2‧st‧sσy (3.38)
where
xn1 = (3.39)
Ï´n = cos-1(1-2xn1) (3.40)
cσcB = cru‧Fc + (3.41)
β1 = 0.89; β2 = 1.08 (3.42)
cD: width or diameter of a concrete section
st : thickness of a steel tube section
xn : position parameter of neutral axis
Sσy : yield stress of steel tube
Equilibrium conditions between internal and external forces are given by Eqs. (3.29) and (3.30), and axial and bending strengths of the concrete and steel tube beam-columns at the ultimate state are calculated by Eqs. (3.31) to (3.42). These strengths are based on the stress distributions shown in Fig. 3.5 with the neutral axis at a distance xn from the extreme compression fiber. P-δ effects are not considered, and thus, they are simply the cross-sectional strengths. The strength increase of confined concrete is considered in cσcB, and the changes in axial compressive and tensile yield stresses of the steel tube due to ring tension are considered by β1 and β2, respectively.
Figure 3.5 Stress blocks for ultimate bending strength
Mu of a CFST beam-column longer than 12 times the width or diameter of the steel tube section is calculated by Eqs. (3.43) and (3.44):
Nu cNcr ; Mu = (3.43)
Nu cNcr ; Mu = (3.44)
where
cMu = (3.45)
cMmax = (3.46)
cMmax0 = for a square CFST (3.47)
cMmax0 = for a circular CFST (3.48)
(3.49)
sMu0: full plastic moment of a steel tube section
Nk = (3.50)
cE' = (3.32 + 6.90) x 103 (3.51)
CM = 1 - 0.5 for sidesway prevented (3.52)
CM = 1 for sidesway permitted (3.53)
M1, M2: end moments where M2 is numerically larger than M1. M1 / M2 is positive when the member is bent in single curvature and negative in reverse curvature.
Cb = 0.923 - 0.0045 Fc (3.54)
Equations (3.43) and (3.44) are derived from the concept proposed by Wakabayashi (1976 & 1977), who states that the M-N interaction curve for a long composite column is given by superposing two M-N interaction curves separately computed for a long concrete portion and a long steel portion. M-N interaction formulas used here for the concrete portion and the steel potion are given by Eqs. (3.45) and (3.48), respectively. Equation (3.45) is newly proposed in by Tsuda, K., Matsui, C. and Fujinaga, T. (2000) (see Figs. 3.6 and 3.7), and Eq. (3.48) is a well-known and international design formula for steel beam-columns. A simple superposition of these two interaction curves produces conflicting results, because the deformations of the concrete portion and the steel portion do not coincide. For example, consider a design of a CFST long column subjected to axial load and bending moment and assume that the axial load is carried solely by the concrete, while the steel carries bending moment only. In this case, the ultimate bending strength of the steel is given by sMu0, the full-plastic moment of the steel, because the steel does not carry any axial load. This assumption, how6ever, is not correct, because the CFST column is bent; hence the secondary moment (P-δ moment) caused by the axial load Nu that acts on the CFST column should be considered. The term (1-Nu / Nk) appearing in Eqs. (3.43) and (3.44) considers the additional P-δ effect, which reduces the bending moment capacity of the steel. In this way, the conflict in deformation compatibility is resolved.
Figure 3.6 cMmax/cMmax0 Figure 3.7 cMmax - cλ1 relations
Equation (3.43) corresponds to the case that the axial load Nu is small enough to be carried by the concrete portion only, and the total bending strength of a CFST beam-column is given by the sum of the remaining bending strength of the concrete portion and the bending strength of the steel portion. On the other hand, Eq. (3.44) corresponds to the case that the concrete portion carries the axial load equal to its full strength, since the axial load Nu is larger than the concrete capacity, and the steel portion carries the remaining axial load and bending. Details of Eqs. (3.43) through (3.54) and their accuracy are discussed by by Tsuda, K., Matsui, C. and Fujinaga, T. (2000).
Ultimate Shear Strength
The ultimate strength of a shear panel Qpu to resist shear force Qpc is given by
Qpu = cA‧cτu + ‧sτu (3.55)
where
cτu, sτu : ultimate shear stresses of concrete and steel tube, respectively
Equation (3.55) gives the ultimate shear strength as a sum of the strengths of concrete and two webs of a steel tube, and it is also applicable to a circular CFST shear panel. The ultimate shear stresses are given as follows:
cτu = β x min (0.12Fc, 1.8 + 0.036Fc)≡β‧JFs (3.56)
sτu = sσy (3.57)
where
Jβ = 2.5 and 4 for a square CFST shear panel (3.58)
Jβ = 2.0 and 4 for a circular CFST shear panel (3.59)
sBd : center-to-center distance of beam flanges adjacent to the shear panel
sD : diameter of steel tube
The shear force acting on a concrete panel may actually be resisted by the horizontal force carried by a diagonal strut forming in the shear panel, and it becomes larger as the inclination angle of the strut becomes smaller (i.e., sD/sBd becomes larger). The parameter β considers this effect.
Ultimate panel moment jMu (≡Qpu‧sBd) is calculated by Eq. (3.60).
jMu = cV‧JFs‧Jβ + 1.2sV‧ (3.60)
where
cV : volume of concrete portion of a beam-to- column connection (= cA‧sBd)
sV : volume of steel web of a beam-to-column connection (= ‧sBd)
Checking the transmission in bending moment between a bare steel beam and a CFST column at the connection is not necessary if Eq. (3.61) is satisfied. If it is not satisfied, smooth transfer of forces must be assumed by an adequate method.
0.4 (3.61)
where
sCMa, sBMa,: sum of allowable flexural moments of all columns and all beams adjacent to the connection, respectively.
