(kN) δmax

(mm)

μ

E1 2。12 3,062 3。63 6,491 8。17 3。85

E2 5。68 682 8。53 3,873 11。18 1。97

E3 3。44 1,324 4。42 4,553 6。92 2。01

E4 2。67 2,671 4。64 7,131 13。27 4。97

E5 5。85 739 8。96 4,322 15。88 2。71

the lateral confinement of the steel tube。 In E4 and E5, the local buckling strains were estimated as 0。0041 (P ¼ 7,000 kN) and 0。0034 (P ¼ 4,000 kN), respectively, which are comparable to the yield strain of 0。0036 (¼ fy;t=Es)。 This result indicates that the stiffeners successfully restrained the elastic local buckling, thus developing the yield strain。

In the present study, initial imperfections such as residual stress

and out-of-flatness of tube plates were not measured。 Instead, initial buckling strains εcr of tube compressive flanges were evaluated by

(Tort and Hajjar 2007), where εy;t ¼ fy;t=Es。 The equation was calibrated from the test results of concentrically loaded columns implicitly taking into account the  influence  of  residual  stress and geometric imperfection。 For Specimens E1, E2, and E3 without

stiffeners, the predictions agreed with the test results (Fig。 9)。 In the evaluation of E4 and E5, B was defined as the width of the subpanel

an existing empirical equation εcr=εy;t  ¼ 3。14ðB=ttpffifffiffiyffiffi;ffitffi=ffiffiEffiffiffiffisffiÞ−1。48

B=2Þ, considering the effect of vertical stiffeners。

Fig。 7。 Failure modes of the specimens at the end of the test: (a) E1; (b) E2; (c) E3; (d) E4; (e) E5

Fig。 8。 Distribution of axial strain in midheight section of E4 and E5

Evaluation of Test Results

Section  Analysis Using  Fiber Models

In order to evaluate the overall behavior of the specimens, sectional analysis  using  fiber  elements  was  performed,  and  the analysis

results were compared with the test results。 For this study, a constitutive model of laterally confined concrete developed by Nakahara et al。 (1999) was used。 As is well known, the confinement effect of rectangular steel tubes is not significant when compared to that of circular steel tubes。 Thus, in the constitutive model, the confinement effect does not increase the peak strength, though it increases the deformation capacity。 The concrete stress-strain rela- tionship is defined as follows:

VX þ ðW − 1ÞX2

where εc and σc = axial strain and stress of the concrete, respec- tively; εco = axial strain corresponding to the concrete compressive strength fc0 ; Ec = elastic modulus of concrete; W = parameter re- lated to descending branch of the stress-strain relationship; fre = effective confining pressure; and ρh = volumetric ratio of the steel tube to concrete = 4ðB − ttÞtt=b2。