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Fig. 7. Lateral load (P) versus lateral displacement (Δ) hysteretic curves: (a) CN-0; (b) CN-3; (c) CR-3; (d) CN-6; (e) CR-6; (f) SN-0; (g) SN-3; (h) SR-3; (i) SN-6; (j) SR-6
Fig. 8. P − Δ envelope curves: (a) circular section; (b) square section
© ASCE 04016219-6 J. Struct. Eng.
Fig. 9. Moment (M) versus curvature (ϕ) curves: (a) CN-0; (b) CN-3; (c) CR-3; (d) CN-6; (e) CR-6; (f) SN-0; (g) SN-3; (h) SR-3; (i) SN-6; (j) SR-6
axial load level (n). Such a trend has been well documented for conventional CFST columns under cyclic lateral loading (Han and Yang 2005). From Table 1, it can be seen that the axial load level tended to impose a more-significant influence on Pue for the square sections than the circular sections. When n was increased from 0.02 to 0.3 and then to 0.6, Pue of the square CFSST columns decreased by around 7 and 37%, respectively, whereas Pue of the circular CFSST columns decreased by around 1 and 12% for values of n of 0.3 and 0.6, respectively. Regarding the different types of concrete, infilling RAC or normal concrete has a negligible impact on Pue.
Moment–Curvature Hysteretic Curves
Fig. 9 shows the recorded moment (M) versus curvature (ϕ) hysteretic curves of all specimens, in which the M induced by the lateral load (P) including the second-order moment was calculated as follows (Han et al. 2006):
P · L
M ¼ 4 þ N0 · Δ ð2Þ
The curvature [ϕ ¼ ðεt − εcÞ=D for the circular section and ϕ ¼ ðεt − εcÞ=B for the square section, respectively] was determined
by the measured extreme fiber compressive strain (εc) and tensile strain (εt) at the midspan. In general, the effects of different factors, such as the axial load ratio, cross-sectional type, and concrete type, on the M − ϕ hysteretic curve are similar to those on the P − Δ curves.
Fig. 10 presents the M − ϕ envelope curve of a typical specimen CN-3 (circular section, infilled with normal concrete, and n ¼ 0.3). As can be seen, the M − ϕ envelope curve has an initial elastic stage, followed by inelastic behavior with gradually decreasing se- cant stiffness. Comparing the M − ϕ envelope curve of specimen CN-3 in Fig. 10 with its P − Δ envelop curve in Fig. 8(a), it is found that the lateral load (P) tends to decrease gradually after the peak point, whereas the moment (M) keeps increasing through- out the whole loading process. This might be because that the lost first order moment at large curvatures [ðP · LÞ=4, Eq. (2)] would be compensated by the growing second-order moment [N0 · Δ, Eq. (2)]. It indicates that the CFSST column can still remain a high
moment capacity even at a large curvature.
A careful examination of the test results reveals that the spec- imens developed inelastic curvatures at about 20% of the moment capacity (Mu) because of the cracking of concrete in tension. This phenomenon was also reported by Varma et al. (2002) in their pre- vious cyclic tests on conventional CFST specimens. Therefore, the