fc hb- 2td
hc,w- 2tc,w
prepared to let concrete fill inside the columns and connection panels. Since the infilled concrete restrains local distortions of the column walls and diaphragms, these restraining effects can be taken into account when determining the dimensions and details of connections.
Table 9.1 - Ultimate resistance equations for connections with external diaphragms to concrete-filled circular columns (AIJ 2001a)
Tables 9.1 and 9.2 show ultimate limit state design formulae for CHS column connections with external diaphragms and those for RHS column connections with external and
Shape of external diaphragm Ultimate resistance equation Type I connection:
The design resistance is the larger of the values calculated by Eqs. 1 and 2.
(1)
(2) If fc,y≥ fd,y, then calculate with fc,y = fd,y. Type II connection:
The design resistance is given by Eq. 2 . Symbols:
fc,y = Yield strength of column material fd.y = Yield strength of diaphragm
material
fd,u = Ultimate tensile strength of diaphragm material Pb.f = Axial load in tension flange Type III connection:
The design resistance is the smaller of the values given by Eqs. 3 and 4.
(3)
The ultimate resistances in these formulae are represented in terms of the axial tensile load Pb,f* at the beam end. Again these formulae were derived from the yield strength equa-tions, which were multiplied by a factor of 1/0.7 to convert them to the ultimate resistance equations (see section 8.6).
Connections with external diaphragms to CHS columns are divisible into two groups: the first group includes types I and II while the second group includes types III and IV, as shown in table 9.1. For connections of types I and II a critical steel section on the line A-A through the centre of the column and the intersection between the beam flange and diaphragm was assumed. For connections of types III and IV a critical steel section on A-A through the narrowest section of the diaphragm was assumed. Each steel section is assumed to have a T section consisting of a cross section of the diaphragm with the height hdand a portion of the column wall with the effective width be(see figure 9.6).
Figure 9.6 – Critical steel section through diaphragm and column wall
The yield strength of connections was equated to the resultant of the axial and shear strengths of these steel sections calculated by using the lower bound theorem of plastic analysis (Kurobane et al. 1987). The effective width bewas determined based on experi-mental results. These yield strength equations agree well with recent test results (Fukumoto et al. 2000, Kato 2001), except for a specimen in high-strength steel with yield strength of 748 N/mm2.
Two design equations were provided for connections with external diaphragms to RHS columns (see table 9.2). Equation 1 in table 9.2 was derived from the ultimate strength for-mula for connections to plain steel columns (see equation 2 in table 8.3) but with the resis-tance factor greater than that required for connections to steel columns. This increased resistance factor is to take into account restraining effects given by the concrete core.
Equation 2 in table 9.2 was derived from the yield strength equation, namely a lower bound solution of plastic theory following the procedure identical to that used for connections to CHS columns (see table 9.1). Attention should be paid to the fact that for connections to RHS columns (the connections of types I and II in Table 9.2) the critical steel section assumed lies on the line A-A through the narrowest section of the diaphragm irrespective of the connection type, and also to the fact that the height of diaphragms hdis defined differently between tables 9.1 and 9.2.
Equation 1 in table 9.2 tends to underestimate the restraining effect of the concrete core when hd/bcbecomes greater than about 0.15. This equation is applicable only to the
con-hd
be
Equation 3 in table 9.2 was derived from the full plastic strength of a fictitious beam with the critical steel section B-B. Equation 4 in table 9.2 was derived from the full plastic strength of a fictitious tension bar with the critical steel section C-C.
The design provisions shown in table 9.2 were first proposed by Matsui (1981) but were found to compare well with the results of more recent experimental and numerical studies (Kawaguchi et al. 1997, Kawano et al. 1998).
The AIJ standard provides the design guides for connections with through diaphragms to CHS columns and for connections with internal diaphragms to RHS columns, besides those shown in tables 9.1 and 9.2. The design equations were derived from the results of a series of yield line analyses and tests (Fu and Morita 1998, Morita et al. 1991). The details are not shown here because these equations are rather complex.
Local buckling of plate elements always governed the ultimate load of the compression flange-to-concrete-filled column connections according to past tests. No damage in the welded joints or in the concrete was observed. Thus connections between the compres-sion flanges and concrete-filled columns are not considered critical. No design formula has been prepared for these connections.
The flexural resistance of the connections shown in tables 9.1 and 9.2 can be calculated by equations 8.1 and 8.3 with
Mb,f,u= Pb,f*(hb– tb,f) ...9.5
Note that no formula exists to calculate the flexural capacity of welded web joints to concrete-filled columns. Equations 8.3 to 8.5 for steel columns can be substituted for the strength equations for concrete-filled column connections, although this introduces errors on the safe side (see also section 8.6). If one wants to ignore the flexural capacity of welded web joints, the formula for connections to plain columns (equation 8.22) can be used to determine the design strength of the connections to concrete-filled columns.
The required flexural capacity at the column face is given by equation 8.23, where Lhaunch
= hdfor the connection of type III in table 9.2. An overstrength factor of = 1.3, rather than = 1.2, is recommended. The other requirements regarding joint details, fabrication and quality control are identical to those recommended for the connections with external diaphragms and through diaphragms to plain steel columns (see sections 8.1, 8.3 and 8.6).
Significant examples of full-strength connections to concrete-filled columns studied out-side of Japan include split-tee bolted connections (Ricles et al. 1997). High-strength bolts that pass through the column, post-tensioned after the concrete was cured, carry the axial load in the beam flange. These connections achieved good ductility, demonstrating suffi-cient plastic rotation of the beams outside the connections and ductile shear deformation of the column web panels. The study is still in progress.