Fig. 10. Typical moment (M) versus curvature (ϕ) envelope relation (CN-3)

initial section flexural stiffness (Ki) is defined as the secant stiffness corresponding to the moment of 0.2Mu, whereas the serviceability- level section flexural stiffness (Ks) is defined as the secant stiffness corresponding to the serviceability-level moment of 0.6Mu on the moment versus curvature curve (Varma et al. 2002). The measured initial section flexural stiffness (Kie) and serviceability-level sec- tion flexural stiffness (Kse) from the current experiments are pre- sented in Table 1. It can be seen that the axial load level tended to have a significant effect on the flexural stiffness of the tested CFSST columns. The greater the axial load applied, the higher the measured flexural stiffness (Kie and Kse) was obtained, which is mainly owing to the fact that a higher applied compressive load tended to suppress the development of cracks inside the core con- crete due to tension. Under a same axial load level, the square spec- imens show higher experimental flexural stiffness (Kie and Kse) than the circular counterpart, due to the fact that the square speci- men have a larger cross-sectional  area.

Rigidity Degradation

According to Elremaily and Azizinamini (2002), the flexural stiff- ness (K) can be obtained from the following implicit   equation:

PpL3 .3ðtan u − uÞ.

The stiffness index (K=Kfirst), which is the ratio between the flexural stiffness (K) at different lateral displacements (Δ) and the initial flexural stiffness (Kfirst) at the first cycle, is used to assess the rigidity degradation of the tested CFSST columns. Fig. 11 shows the K=Kfirst versus Δ=Δy relations for the circular and square sections. From the comparison, it can be concluded that the rate of rigidity degradation for specimens with a lower axial load level was more significant than those with a higher axial load level. This phenomenon can be explained by the increasing compression area of the cross section for the columns with higher axial load levels. Generally, the rigidity degradation of the square section is more significant than for the circular counterpart, especially at large deflection values, and there is no obvious difference between the stiffness degradations of the specimens infilled with RAC and normal concrete.

Ductility and Energy Dissipation

The displacement ductility coefficient (μ) is adopted in this paper to assess the ductility of CFSST columns, where μ can be defined as follows (Han et al.  2006):

In Eq. (4), Δy = yielding displacement; and Δu = displacement when the lateral load falls to 85% of the ultimate strength (Pue), as shown in Fig. 12. The ductility coefficients thus determined are presented in Table 1 for all tested CFSST columns. The μ value for each specimen is taken as the average in the push and pull di- rections of cyclic loading. The lateral load (P) of the specimens with n ¼ 0.02 (CN-0 and SN-0) kept increasing during the loading process (Fig. 8). Therefore, in the calculation of ductility coefficient (μ) for these two specimens, the lateral displacement at the end of loading was adopted to replace the defined failure displacement (Δu) in Eq. (4). It is not surprising to see that the ductility coef- ficient (μ) decreases with the increase in axial load level (n). The μ values for specimens CN-3 with normal concrete and CR-3 with RAC are 5.28 and 7.04, respectively. In fact, Specimens CN-3 and CR-3 have close μ values for positive values of Δ, whereas CR-3 has a relatively smaller yield displacement and more gradual post-

peak descending stage for negative values of Δ. Apart from these two specimens, other specimens with RAC generally have close μ

where u ¼ ð1=2ÞpffiNffiffiffiffiffiLffiffiffi2ffiffi=ffiffiffiKffiffiffi and K can be obtained iteratively for a