Seismic performance of concrete-filled steel tube columns using ultra-high-strength steel under long-period ground motion demands

Abstract

The long-period ground motions observed in recent subduction-zone earthquake events (e.g., 2011 Tohoku earthquake in Japan) have subjected high-rise buildings to large numbers of lateral cyclic deformations. Concrete-filled steel tube (CFT) columns, which are often utilized in high-rise buildings in Japan, have been studied under lateral demands with a few loading cycles. However, their seismic performance under a larger number of repeated loading cycles is a considerable concern for future seismic events. Moreover, the use of ultra-high-strength steel materials in CFT columns has recently gained popularity. However, studies on CFT columns made using ultra-high-strength steel materials are still limited. In this study, the seismic performance of CFT columns made using conventional steel or ultra-high-strength steel were investigated experimentally under repeated lateral loading cycles. Four cantilever CFT column specimens were tested with a combined constant compressive axial loading and cyclic symmetric lateral loading. Each specimen was tested with two different lateral loading protocols: the conventional protocol with two cycles at each drift amplitude level, and a second protocol with twenty cycles at each amplitude level to represent the lateral drift demand under a long-period ground motion. The effects of the number of loading cycles on the seismic performance of the CFT columns are discussed. Based on the experimental observations, design recommendations are also presented. Moreover, an approach is proposed to estimate the onset of local buckling of the CFT columns under seismic loading.

Keywords

long-period ground motion cyclic loading concrete-filled steel tube column full-plastic moment local buckling

Introduction

During the 2011 earthquake off the Pacific coast of Tohoku (moment magnitude 9.0), vibrations with durations of five minutes or longer were observed in many high-rise buildings in Japan (JEC-RGEJED, 2015). Such vibrations were due to the long-period ground motions, which contained large spectral components in the long-period range. Some super-high-rise buildings experienced large lateral drift demands with more than 10 cycles (e.g., Kubo et al., 2014), which will be discussed in the next section in more detail. In Japan, similar types of seismic events, such as the Nankai Trough mega-earthquake, are expected to occur in the near future (e.g., Hori, 2017). As the magnitude of the lateral drift demand of repeated cyclic deformation demands may be considerable in the anticipated future earthquakes, it is necessary to examine the seismic performance of structural members of high-rise buildings under lateral drift demands imposed by long-period ground motions (i.e., a large number of loading cycles). However, the conventional symmetric cyclic loading protocols used to assess the seismic performance of structural members typically include only a few loading cycles (i.e., 2–3 cycles) (AIJ, 2017).

Concrete-filled steel tube (CFT) columns are often used as part of super-high-rise or high-rise buildings in Japan. CFT columns are composite structural members containing steel and concrete materials. They are constructed by filling a structural steel tube column with highly flowable concrete material. One of the main advantages of CFT columns is that the concrete provides high compressive axial resistance, while the steel tube provides high flexural resistance. For example, CFT columns were utilized in the 300-m-tall “Abeno Harukas” super-high-rise building in Japan (Aoki et al., 2012). In Japan, where the concept of CFT columns was first developed and proposed, the first structural design standard for CFT members was established in 1967 (AIJ, 1967). Internationally, research on CFT members became popular after the concept of CFT columns attracted the attention of researchers at an international conference held in Harbin, China in 1985 (HACEI, 1985). Although conventional mild steel (with a yield stress of approximately 300 MPa) and standard concrete materials (with a compressive strength of approximately 30 MPa) were initially employed for CFT members, at present, high-strength materials are also utilized for both the steel and concrete [e.g., Aoki et al. (2012); Matsumoto et al. (2012); Fujimoto et al. (2017)].

The seismic performance of CFT columns has been investigated in a number of experimental studies. For example, Knowles and Park (1969) tested CFT columns with several different slenderness ratios under eccentric axial load demands. They investigated the buckling failure mechanism of the CFT columns and proposed equations to estimate the buckling load. Sakino et al. (2004) performed experiments for 114 CFT members in which the cross-sectional dimensions and materials were varied to investigate the force–displacement relationships of the CFT columns under the synergistic interaction between the steel tube and filled concrete. As represented by the studies above, many experimental results have been reported. However, few of these studies adopted a loading protocol with a number of loading cycles comparable to the lateral drift demands associated with a long-period ground motion. This situation is similar in numerical studies. Hajjar et al. (1998) proposed a finite-element modeling approach for CFT columns and composite frames comprising CFT columns and steel beams. While they presented some comparisons of the force–displacement relationships between the experimental and simulation results, the number of loading cycles at each loading amplitude was less than or equal to three. Ahmed and Güneyisi (2019) examined the nonlinear behavior of composite frames with CFT columns and steel beams through finite element simulations utilizing solid elements. They investigated the failure modes as well as the force–displacement relationships of CFT columns composed of high-strength materials. However, large numbers of loading cycles were not considered in their study.

The first study that considered a large number of loading cycles in experiments on CFT columns was performed by Kawano and Matsui (1988). Their uniaxial cyclic experimental results suggested that the ultimate behavior of CFT columns was governed by local buckling of the steel tube. Subsequently, Kawano et al. (2000) focused on the number of loading cycles at which CFT columns subjected to cyclic flexural demands failed through the fracture of the steel tube. They developed equations to predict the number of loading cycles required to induce failure. Elchalakani et al. (2004) tested CFT beam members until fracture under cyclic pure bending with a constant amplitude and compared the peak flexural strength between monotonic and cyclic loading cases. Cao et al. (2019) tested 42 CFT columns under axial loading and compared the responses under monotonic loading and cyclic loading with a large number of loading cycles. Their results suggested that the force–displacement relationship was practically identical until the maximum strength. However, the number of experimental studies in which large numbers of loading cycles were applied is limited. In particular, CFT columns using high-strength steel materials, which are becoming increasingly popular, have not been tested sufficiently.

The peak strength of CFT columns is determined by the local buckling of the steel tube. The prediction of this local buckling is thus essential for the design and/or assessment of CFT columns. Kawano et al. (2000) proposed equations to estimate the number of axial loading cycles required to induce local buckling for a given axial strain amplitude based on numerous finite element simulation results for CFT columns composed of conventional steel. However, the CFT columns in buildings are subjected to combined axial and lateral cyclic loading with varying amplitudes. Moreover, the validity of the proposed equations for CFT columns using ultra-high-strength steel has not been verified. Thus, the method for predicting local buckling needs to be further generalized.

In this study, the seismic performance and ultimate state of CFT columns subjected to lateral demands associated with long-period ground motions were investigated through static CFT column member testing. CFT column specimens made with conventional steel tubes or ultra-high-strength steel tubes were subjected to combined constant compressive axial loading and symmetric cyclic lateral loading. H-SA700 ultra-high-strength steel (Yoshida et al., 2009), which was developed in Japan and is used in high-rise buildings in Japan, was investigated in this study. This steel has a nominal yield stress range of 700–900 MPa and a nominal tensile stress range of 780–1000 MPa. It can achieve remarkably high strength without significant alteration of its chemical composition (a slight increase in alloying elements) or intensive heat treatment. Therefore, the steel is environmentally friendly and suitable for mass production. The results of the testing program in this study were previously presented by the authors (Skalomenos et al., 2016). In this paper, the effects of the number of loading cycles on the seismic performance of the CFT columns are discussed in detail. Based on the experimental observations, recommendations for the design of CFT columns subjected to lateral drift demands associated with long-period ground motions are also presented. Furthermore, the linear cumulative damage rule (i.e., Miner’s rule) is combined with one of the equations proposed by Kawano et al. (2006) to enable the use of the equation for the strain history with varying amplitudes. The proposed local buckling prediction approach is evaluated based on the experimental results for CFT columns obtained using ultra-high-strength steel as well as for those made of conventional steel.

Number of loading cycles measured under a long-period ground motion

The lateral drift response history of a building will differ greatly depending on various aspects, such as the characteristics of the ground motions and building size. Therefore, it is not possible to define a general lateral loading protocol that reproduces the lateral drift response history of a building under a long-period ground motion. The number of loading cycles used in the experimental program in this study was determined based on the seismic response of an existing high-rise building in Japan measured during a past long-period ground motion caused by a subduction-zone earthquake.

Figure 1 shows the response history of a high-rise building (Osaka Prefectural Government Sakishima Building: 55 stories, 256 m tall) observed during the 2011 Tohoku earthquake. The structure continued to vibrate for more than 15 min. A maximum response displacement of 1.46 m was measured at the 52nd floor (i.e., an average lateral drift ratio of 0.006 rad). In the acceleration history shown in Figure 1(a), 20 loading cycles exhibit amplitudes exceeding 60% of the maximum acceleration (1.36 m/s²). Similarly, in the displacement history shown in Figure 1(b), 26 loading cycles exhibit amplitudes exceeding 60% of the maximum displacement. Notably, the summation of the areas enclosed by the displacement history waves with amplitudes exceeding 60% of the maximum amplitude and the horizontal time axis is 24.2 times the single enclosed area containing the maximum amplitude, indicating that the number of cycles with significant displacement amplitudes is quite large. Note that this ratio is 13.8 if the waves with amplitudes exceeding 80% of the maximum amplitude are considered.

Figure 1.

Response histories of a high-rise building measured during the 2011 Tohoku earthquake (52nd floor) (Top: acceleration response history; bottom: displacement response history).

Based on this measurement, the number of loading cycles that represent the lateral demand of a long-period ground motion is simply determined to be 20 in this study. This number of cycles is approximately 10 times greater than that of the loading protocol used in typical static structural member testing (AIJ, 2017).

Static loading tests of CFT columns

Experimental program

A total of four CFT column specimens were subjected to combined cyclic lateral loading and constant compressive axial loading to investigate (a) the seismic performance of CFT columns composed of ultra-high-strength steel or conventional steel and (b) the effect of the number of loading cycles on their seismic performance. Figure 2 shows the configuration of the test specimens. The cross-sectional dimensions as well as the member length are nominally identical among all four specimens. All specimens employ a 150 mm × 150 mm square tube with a thickness of 6 mm. The square steel tubes were fabricated by welding two pieces of cold-formed channel sections using complete joint penetration welding. The bottom side of each CFT column was welded to the steel foundation, which consisted of wide-flange beams reinforced with several stiffeners. On the top of the steel foundation, the bottom end of the CFT column was surrounded by reinforcing plates to shift the plastic hinge away from the heat-affected zone due to the welding (see dashed line in Figure 2). Two parameters were varied among the specimens: (1) the steel material used for the square tube (i.e., ultra-high strength steel, H-SA700 (HS), with a nominal yield stress of 700–900 MPa or conventional steel, SM490 (CS), with a nominal yield stress of greater than 295 MPa) and (2) the cyclic lateral loading protocol (i.e., two cycles or twenty cycles). The testing matrix summarizing the major properties of each specimen is presented in Table 1. The designation of each specimen consists of the type of steel material employed for the steel tube (i.e., HS or CS) and the number of loading cycles applied for each amplitude step (i.e., 2 or 20). The details of each variable are also given.

Figure 2.

Illustration of the test specimen configuration (units: mm).

Table 1.

Testing matrix.

Specimen	Number of loading cycles at each step	Steel			Concrete	Axial load		$α$
		Yield stress	Tensile stress	Elongation	Compressive strength	Axial yield strength	Axial load ratio
		$σ_{y}$ (MPa)	$σ_{u}$ (MPa)	(%)	$σ_{B}$ (MPa)	$N_{O}$ (kN)	$n = N / N_{O}$
CS-2	2	387	488	28.4	79.3	2776	0.25	32.1
CS-20	20	436	545	30.5	44.3	2276	0.25	34.1
HS-2	2	788	837	14.5	79.3	4100	0.25	45.8
HS-20	20	788	837	14.5	47.6	3544	0.25	45.8

Representative engineering stress–strain curves for the H-SA700 and SM490 steels used in the test specimens are depicted in Figure 3 based on the results of tensile coupon tests. The measured properties are also provided in Table 1. Comparing the two curves, the yield stress of H-SA700 is approximately twice that of conventional steel. Therefore, the elastic range is greater in H-SA700. However, H-SA700 has a low rupture elongation, which is measured with a gauge length of 200 mm and low yield ratio (i.e., ratio of the yield stress to ultimate tensile stress). The rupture elongation value of H-SA700 is about half that of conventional steel. The compressive strength of the filled concrete for each specimen is also listed in Table 1. Note that the strengths of the employed materials are not identical between the two-cycle specimens and the twenty-cycle specimens except for the steel strength of the HS specimens. Nonetheless, as discussed in later sections, the impact of this discrepancy on the flexural strength of the CFT column specimens is not substantial (i.e., errors of 1.1%–3.7% in the ultimate flexural strength).

Figure 3.

Stress–strain curves of ultra-high-strength steel (H-SA700) and conventional steel (SM490).

For the lateral loading protocol, two different protocols are adopted, as shown in Figure 4. Both protocols involve cyclic loading with increasing lateral drift amplitudes up to 0.1 rad. However, the number of loading cycles at each loading amplitude step differs. The protocol with two cycles at each loading amplitude step (Figure 4(a)) represents the conventional symmetric cyclic loading protocol that has been widely used. The other protocol (Figure 4(b)) considers a greater number of loading cycles, as discussed in Section 2. The lateral drift ratio is the ratio of the lateral drift to the column height. The measurement of this ratio will be explained later.

Figure 4.

Loading protocols adopted in the tests: (a) two-cycle protocol and (b) 20-cycle protocol.

The loading system shown in Figure 5 was utilized to provide a combined action of bending and compression to the column. The steel foundation was fixed to the strong floor through post-tensioning rods. The top end of each specimen was connected to a 2000 kN vertical oil jack and a 200 kN horizontal oil jack with a mechanical pin. The bracket used to connect these two oil jacks to the column top was braced against out-of-plane movement.

Figure 5.

Loading system (units: mm).

Cyclic lateral loading combined with a constant compressive axial load was applied to the specimen. The horizontal jack was controlled using the displacement-control mode following the loading protocols shown in Figure 4, while the vertical jack was controlled using the force-control mode. In all specimens, the applied constant axial load ratio was 0.25 (see Table 1). The axial load ratio is defined as the ratio of the applied axial compressive load, $N$ , to the axial compressive yield strength, $N_{O}$ (calculated as the yield stress of the steel, $σ_{y}$ , multiplied by the cross-sectional area of the tube plus the compressive strength of the concrete, $σ_{B}$ , multiplied by the cross-sectional area of the filled concrete), of each CFT column calculated with the measured properties. Note that the vertical jack inclines as the lateral displacement at the column top increases. Thus, while the axial load of the vertical jack was kept constant during each test, the actual vertical force applied to the column was not exactly the same as the axial load considered above. However, the inclination of the vertical jack was considered in the calculation of the column base moment, which is discussed in later sections.

Two displacement transducers, DT1 and DT2, were used to obtain the lateral drift of the column, as shown in Figure 5. To evaluate the local buckling behavior of the CFT column members, the longitudinal displacement of the column at a distance 1D (=150 mm) from the top surface of the reinforcing plates was measured by displacement transducers DT3 and DT4. Strain gauges were attached to the outer surface of the steel tube at a distance of 50 mm from the top surface of the reinforcing plates to measure the longitudinal strains (see Figure 2). The height of the column was taken as the distance from the upper surface of the reinforcing plates to the centerline of the horizontal jack (i.e., 1100 mm) (see Figure 5).

Another important parameter is the compactness of the steel tube of the CFT column specimens. In Japan, according to TAAF (2019), which provides general design guidelines for building structures, the local slenderness of a steel tube without concrete is categorized into four different ranks based on $α$ , which is a function of the width-to-thickness ratio

α = \frac{D / t}{\sqrt{235 / σ_{y}}}

(1)

where

D

is the depth of the steel tube,

t

is the steel thickness, and

σ_{y}

is the yield stress of the steel material. The values of

α

for the tubes of each specimen are included in Table 1. For

α \leq 33

33 \leq α \leq 37

37 \leq α \leq 48

, and

48 \leq α

, the corresponding compactness ranks are named FA, FB, FC, and FD, respectively. The FA rank is considered the category for the most ductile profiles, while the FD rank includes the least ductile profiles. For the CFT column members, the Architectural Institute of Japan (AIJ) (AIJ, 2008), which provides design and construction recommendations for CFT structures, recommends that the threshold

α

values for each rank should be 1.5 times greater than those described above. This is because the filled concrete contributes to restraining local buckling of the steel tube. The ranks of the specimen steel tubes calculated based on their measured properties all fall within the FA rank. However, if the presence of the filled concrete is ignored, the ranks of the steel tubes in specimens CS-2, CS-20, and the two HS specimens (HS-2 and HS-20) are classified as FA, FB, and FC, respectively. Thus, although the dimensions of the specimens are the same among all four specimens, the specimens using conventional steel may be considered to have more ductile steel tube profiles owing to the difference in the yield stress. Further details of the testing program are provided in Skalomenos et al. (2016).

Experimental results

Figure 6 shows the base moment–lateral drift ratio relationship for each specimen. The base moment is the moment acting at the height of the top surface of the reinforcing plates at the column centerline, which is calculated as the product of the lateral load and the height of the column, plus the product of the horizontal component of the axial force and the height of the column, plus the product of the vertical component of the axial force and the measured horizontal displacement (i.e., P-Δ moment). For 20-cycle specimens (i.e., CS-20 and HS-20), the results are plotted until 0.06 rad loading cycles, in which fracture of the steel tube occurred.

Figure 6.

Base moment–lateral drift ratio relationships.

The horizontal single chain-dotted lines indicate the elastic limit moment strength, $M_{y}$ , estimated based on the AIJ recommendation (AIJ, 2008; Morino and Tsuda, 2003), while the horizontal double chain-dotted lines indicate the full-plastic moment, $M_{p}$ , estimated based on the superposed strength theory (AIJ, 1987; Morino and Tsuda, 2003). For both calculations, measured properties are used. Figures 7 and 8 present the deformation of each specimen observed after each test. The dotted line in Figure 7(b) indicates the locations where fracture occurred. Table 2 summarizes the estimated elastic limit moment strength, $M_{y}$ , and full-plastic moment, $M_{p}$ , as well as the lateral drift ratios, $R_{y}$ and $R_{p}$ , when $M_{y}$ and $M_{p}$ are reached during each test, respectively. The attained maximum base moment, $M_{u}$ , and the corresponding lateral drift ratio, $R_{u}$ , measured in the experiment as well as the ratio of $M_{p}$ to $M_{u}$ are also presented in Table 2.

Figure 7.

Deformations observed after testing.

Figure 8.

Cross-section of specimen CS-20 observed after testing at the section indicated in Figure 7(b).

Table 2.

Summary of the primary experimental results and estimation values.

Specimen	Elastic limit moment		Full-plastic moment		Maximum attained moment
Specimen	$M_{y}$ (kNm)	$R_{y}$ (rad)	$M_{p}$ (kNm)	$R_{p}$ (rad)	$M_{u}$ (kNm)	$\frac{M_{u}}{M_{p}}$	$R_{u}$ (rad)
CS-2	62.4	0.0098	91.0	0.0218	98.6	1.08	0.0290
CS-20	55.6	0.0093	90.0	0.0239	92.7	1.03	0.0300
HS-2	100.7	0.0180	156.0	0.0335	173.5	1.11	0.0572
HS-20	90.0	0.0191	150.2	-	130.7	0.87	0.0336

The observed cyclic behavior of the specimens is briefly introduced here. More details on the behavior of each specimen can be found in Skalomenons et al. (2016). In all four specimens, the deformation progressed similarly. All of the specimens except for specimen HS-20 exceeded the estimated full-plastic moment, $M_{p}$ . The maximum flexural strength was determined by the onset of local buckling of the steel tube in all cases. The local buckling was induced in the inelastic range, although the lateral drift amplitude at which it occurred differed between the specimens. Once local buckling was triggered, the local buckling continued to evolve in the subsequent loading cycles, accompanied by axial shortening of the column. The two-cycle specimens completed the entire loading protocol without experiencing any cracks or fracturing. Moreover, they retained 76%–86% of the maximum flexural strength at the end of testing. On the other hand, in the twenty-cycle specimens, a crack occurred at the peak of the local buckling deformation during the loading cycles with a lateral drift amplitude of 0.06 rad. Eventually, the crack propagated, and the entire cross-section ruptured during the loading cycles with the same amplitude (see Figure 7(b) and (d)). As shown in Figure 8, the filled concrete was crushed to powder by the repeated cyclic loading.

Effect of the number of loading cycles on the seismic performance of columns

In this section, the effect of the number of loading cycles on the seismic performance of the column specimens is investigated for three separate lateral drift ranges: (1) the elastic range, (2) the pre-peak inelastic range, and (3) the post-peak range. Figure 9 shows the envelope curves for the measured base moment–lateral drift ratio relationships of all specimens. The vertical axis is the normalized moment, $m$ , which is the measured flexural strength divided by the calculated full-plastic flexural strength, $M_{p}$ . At each drift amplitude, the normalized moments obtained at the peaks of the first cycle and the last cycle (i.e., the second cycle for specimens CS-2 and HS-2 and the 20th cycle for specimens CS-20 and HS-20) are plotted. The horizontal axis shows the corresponding lateral drift ratio. The normalized yield flexural strength, $m_{y}$ , and full-plastic strength, $m_{p}$ , are also plotted with one-dot and two-dot chain lines, respectively.

Figure 9.

Effect of the number of loading cycles on the envelope curves of the base moment–lateral drift ratio relationship. (a) Specimens CS (b) Specimens HS.

Elastic range

In the elastic range, the difference between the two-cycle (i.e., CS-2 and HS-2) and twenty-cycle (i.e., CS-20 and HS-20) specimens was negligible for both types of steel materials, although the concrete compressive strength, $σ_{B}$ , differed somewhat between them. Comparing the yielding lateral drifts, $R_{y}$ , between the two-cycle and 20-cycle specimens in each CS and HS case, the errors of $R_{y}$ were only 2.6%–3.0%. This may be because the difference in the concrete compressive strength, $σ_{B}$ , does not significantly affect the modulus of elasticity of concrete (AIJ, 2008). The test results suggest that the elastic behavior of a CFT column is not dependent on the number of loading cycles.

Pre-peak inelastic range

In the pre-peak inelastic range, the effect of the number of loading cycles on the envelope curve is minor in the CS specimens, while it is significant in the HS specimens. For the CS specimens, both the two-cycle and twenty-cycle specimens achieved the calculated full-plastic flexural strength, $M_{p}$ . The difference of $R_{p}$ (i.e., the lateral drift ratio when $M_{p}$ was reached) between the two- and twenty-cycle specimens was also only 4.6%. On the other hand, in the HS specimens, the twenty-cycle specimen did not reach $M_{p}$ , whereas the two-cycle specimen reached it at a lateral drift ratio of 0.034 rad. The envelope curves were similar until the twenty-cycle specimen reached its peak strength.

The test results suggest that the flexural strength deterioration is caused by local buckling of the steel tube in all specimens. In the CS specimens, in which the effective width-to-thickness ratios, $α$ , defined in the equation (1) were 32.1 and 34.1 for specimens CS-2 and CS-20, respectively (i.e., both specimens are FA rank per AIJ (2008) and FA rank and FB rank, respectively, if the presence of filled concrete is ignored (TAAF, 2019)), no evident local buckling occurred until the flexural strength exceeded $M_{p}$ regardless of the number of loading cycles. Consequently, the behavior as well as the envelope curve of the twenty-cycle specimen, CS-20, in the pre-peak inelastic range was similar to those of the two-cycle specimen, CS-2. In contrast, $α$ for the HS specimens was 45.8 (i.e., FA rank per AIJ (2008) and FC rank per TAAF (2019)). In this case, although the steel tube was categorized into the most ductile compactness rank, FA, according to AIJ (2008), local buckling was dominant even prior to reaching $M_{p}$ when the CFT column was subjected to the twenty-cycle loading protocol owing to relatively large effective width-to-thickness ratio, $α$ .

Post-peak range

The twenty-cycle specimens exhibited a sharp drop in flexural strength in the envelope curves due to significant evolution of the local buckling of the steel tube during each loading amplitude step after reaching the ultimate flexural strength, $M_{u}$ . Therefore, their deformation capacity beyond the peak strength was quite limited. In the end, rupture of the entire section occurred when the flexural strength reached about one-third of the maximum strength. For the two-cycle specimens, similarly, local buckling was evident beyond the peak strength (see Figures 7 and 9). Nonetheless, the strength degradation slope in the envelope curve was less sharp than for the twenty-cycle cases. As a result, the two-cycle specimens retained more than 50% of their maximum flexural strength even after the last loading step with an amplitude of 0.1 rad and did not experience any fracture.

Recommendation for the design of CFT columns under long-period ground motion demands

The discussion in Sections 4.1–4.3 can be summarized as follows: (1) the envelope curves obtained from the twenty-cycle specimens are almost identical to those obtained from the two-cycle specimens until the peak flexural strength is reached; (2) the envelope curves obtained from the twenty-cycle specimens exhibit a sharp drop in strength beyond the peak strength; and (3) the magnitude of the peak flexural strength of the CFT columns is dependent on the effective width-to-thickness ratio of the steel tube (i.e., the rank category). Regarding item (3), in the case in which a steel tube with FA rank per TAAF (2019) (i.e., $α \leq 33$ ) is employed, the peak strength exceeds the full-plastic flexural strength of the CFT column even under the twenty-cycle demand. In contrast, with an FC rank steel tube per TAAF (2019) (i.e., $37 \leq α \leq 48$ ), the peak flexural strength exceeds the yield moment of the CFT column, $M_{y}$ , but does not reach $M_{p}$ . Only the rank categories defined by TAAF (2019) are referred to here, as the categories defined by AIJ (2008) (i.e., 1.5 times greater limiting values than TAAF (2019)) does not distinguish the capability of the CFT columns to reach $M_{p}$ under the twenty-cycle demand.

Considering the major findings above, the envelope curve for a CFT column when designing for long-period ground motion demands may be conservatively modeled as follows. Referring to the rank of the steel tube according to TAAF (2019), if the effective width-to-thickness ratio of the steel tube falls in the FA rank, the strength will be lost once $M_{p}$ is reached. For the FC rank, only the strength up to $M_{y}$ should be relied upon, and the strength beyond $M_{y}$ should be conservatively neglected. For CFT columns using steel tubes with the FB rank, the strength may be conservatively applied up to $M_{y}$ .

Estimation of the onset of local buckling

In this section, focusing on the cumulative plastic deformation of the tested CFT columns, the axial shortening of the specimens is assessed first, and then the onset of local buckling is estimated using an equation proposed in a previous study. Figure 10 shows the axial shortening (vertical axis)–cumulative ductility (horizontal axis) relationships of the specimens. The axial shortening behavior of the two-cycle specimens (i.e., CS-2 and HS-2) and twenty-cycle specimens (i.e., CS-20 and HS-20) are shown with red and blue solid lines, respectively. The cumulative ductility is defined as the cumulative plastic lateral drift ratio divided by the yield lateral drift ratio, $R_{y}$ . The cumulative ductility values are computed for every point at which the lateral drift ratio becomes zero during the cyclic loading.

Figure 10.

Axial shortening–cumulative ductility relationships. (a) Specimens CS (b) Specimens HS.

In all specimens, the axial shortening begins to increase sharply at a certain cumulative ductility value. As discussed in Section 4, when designing a CFT member for the lateral loading demand of a number of repeated loading cycles (i.e., long-period ground motion demand), it is recommended that the flexural strength is assumed to be zero after the CFT column experiences local buckling. Therefore, it is important to be able to estimate the points at which axial shortening becomes prominent in each specimen in Figure 10.

As introduced in Section 1, Kawano (2006) focused on CFT members subjected to multiple cyclic axial loading with a constant loading amplitude and used finite element simulations to evaluate the number of loading cycles required to induce local buckling for a given axial displacement amplitude. That study considered only a conventional steel material for the steel tube. The following equation for the criteria to trigger local buckling of a CFT column was proposed

\frac{Δ ε_{p}}{ε_{y}} = 18 {[\frac{σ_{y}}{E_{s}} {(\frac{D}{t})}^{2}]}^{- 1.4} \cdot N_{c y c}^{- 0.4}

(2)

where

Δ ε_{p}

is the plastic axial strain amplitude of the steel tube,

ε_{y}

and

E_{s}

are the yield strain and Young’s modulus of the steel material of the tube, respectively, and

N_{c y c}

is the number of loading cycles required to induce local buckling when the CFT member is subjected to cyclic axial loading with a plastic strain amplitude of

Δ ε_{p}

. Equation (2) was derived from the following ranges,

20 < D / t < 50

and

F_{y} = 360 MPa

, which are equivalent to

20.8 < α < 61.9

. From equation (2), once the amplitude,

Δ ε_{p}

, is known, the estimated number of loading cycles to induce local buckling of the steel tube of the CFT column can be obtained. In this study, the applicability of equation (2) is investigated for CFT columns containing steel tubes made of ultra-high strength steel material and subjected to combined lateral cyclic loading and constant axial loading. In each test, the longitudinal strain was obtained from the strain gauges attached to the outer surface of the steel tube (see Figure 2). The position of the strain gauges was found to be near the peak of the local buckling deformation; thus, the use of these strain gauge measurements may be appropriate. The maximum strain up to the onset of local buckling was approximately 1.2%. In the experiments in this study, unlike the loading conditions in Kawano (2006), the axial strain of the steel tube was not uniform along the length in the tested specimens owing to the presence of a lateral loading demand. The strain amplitude increased as the cyclic loading amplitude increased (i.e., the strain amplitude was variable in each test). Thus, equation (2) cannot be directly applied to the specimens in this study. In this paper, the following linear cumulative damage rule (i.e., Miner’s rule), which was originally used for fatigue failure evaluation, is used to apply equation (2) to the obtained experimental

D I = \sum_{i = 1}^{k} Δ D I_{i} = \sum_{i = 1}^{k} \frac{n_{i}}{N_{i, c y c}}

(3)

where

N_{i, c y c}

is the number of loading cycles required to induce local buckling when the CFT member is subjected to cyclic axial loading with the

i

-th plastic strain amplitude,

Δ ε_{p, i}

, obtained from equation (2);

n_{i}

is the number of loading cycles with the

i

-th plastic strain amplitude measured in each specimen; and

D I_{i}

is the damage index for the

i

-th plastic strain amplitude. When the sum of

D I_{i}

exceeds one, local buckling of the steel tube is expected to occur. Each strain amplitude and corresponding number of loading cycles were determined using rain flow counting. In Figure 10, the cumulative ductility values for each specimen at which the value of

D I

computed based on Equations (2) and (3) exceeds one are plotted with dashed lines. In all specimens, regardless of the steel tube material or cyclic loading protocol, the estimations effectively capture the points at which local buckling begins to occur (i.e., the onset of local buckling). This suggests that the equation proposed by Kawano (2006) has the potential to be utilized to estimate the onset of local buckling of CFT columns subjected to combined constant compressive axial loading and cyclic lateral loading with increasing drift amplitude if the linear cumulative damage rule is applied to the strain history of the outer surface of the steel tube of the CFT column at the section where local buckling occurs. Moreover, it can be applied not only to CFT columns containing steel tubes made using conventional steel materials but also to those with steel tubes made using ultra-high-strength steel materials.

Summary and conclusions

A total of four concrete-filled steel tube column specimens containing steel tubes made using conventional steel or ultra-high-strength steel were statically tested under cyclic symmetric lateral loading with increasing deformation amplitudes combined with constant compressive axial loading. Two different numbers of loading cycles were considered: (a) two cycles at each lateral loading amplitude step, which has been widely adopted globally to represent the lateral drift demand of structures during seismic events and (b) twenty cycles at each lateral loading amplitude step, which may represent the lateral drift demand under the long-period ground motions observed during past subduction-zone earthquakes. The main findings are summarized below.

1. The specimens tested with the twenty-cycle protocol exhibited practically identical behavior in terms of the envelope curves of the column base moment–lateral drift ratio relationship as the specimens tested with the two-cycle protocol until the peak flexural strength. However, beyond the peak strength, the former exhibited a sharp drop in strength due to the greater number of repeated cycles at the same loading amplitude step. Thus, the strength beyond the peak strength should not be relied on in the design of these columns. Moreover, the lateral drift at which strength deterioration occurred under the twenty-cycle protocol can differ than that under the two-cycle protocol. Therefore, when the seismic demands are associated with subduction-zone earthquake demands, which may induce long-period ground motions, the lateral drift corresponding to the peak strength should not be determined from experimental results obtained using a protocol with only a few loading cycles (e.g., two cycles).

2. Based on the test results in this study, in the design of a CFT column for long-period ground motion demands, the flexural strength up to the full-plastic strength can be considered when the width-to-thickness ratio of the steel tube is categorized as the FA rank (per TAAF (2019)). In the case of FB and FC ranks, the flexural strength beyond the yield strength cannot be considered. In either case, the strength beyond the peak should conservatively be assumed to be zero. Note that the rank is determined here according to TAAF (2019) (i.e., the width-to-thickness limiting values recommended by AIJ (2008) should not be used for this determination).

3. The cumulative ductility of the CFT column specimens at which local buckling of the steel tube was induced could be estimated with good accuracy using the equation proposed by Kawano (2006) combined with the linear cumulative damage rule (i.e., Miner’s rule). Although the original equation was developed for CFT columns containing steel tubes made using conventional steel materials subjected to only axial cyclic loading with a constant amplitude, the estimation was found to be accurate for (a) CFT columns containing steel tubes made using ultra-high-strength steel material H-SA700 and (b) those subjected to lateral cyclic loading with increasing deformation amplitudes combined with a constant compressive axial load.

Notably, the findings of this study were obtained from only four test specimens; thus the applicability may be limited. To generalize the findings and design approaches for CFT column members subjected to long-period ground motion demands (i.e., a number of repeated loading cycles), further experimental and/or numerical studies that involve a variety of design parameters, such as the width-to-thickness ratio and axial load demand, are required.

Footnotes

Acknowledgments

The authors are also grateful to Dr Masayoshi Nakashima (president of Kobori Research Complex and professor emeritus of Kyoto University), Dr Taiki Saito (professor of Toyohashi University of Technology), Mr Ryusuke Enomoto and Mr Ryosuke Nishi (former graduate students of Kyoto University) for their valuable assistance throughout this project.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partially supported by the Japan Society for Promotion of Science (JSPS).

ORCID iDs

Kazuhiro Hayashi

Hiroyuki Inamasu

References

Ahmed

Güneyisi

(2019) Structural performance of frames with concrete-filled steel tubular columns and steel beams: finite element approach. Advanced Composites Letters 28: 1–15.

AIJ (Architectural Institute of Japan) (1967) Standard for Structural Calculation of Steel Tubular Concrete Structures. 1st edition. [In Japanese].

AIJ (Architectural Institute of Japan) (1987) Standards for Structural Calculation of Steel Reinforced Concrete Structures.

AIJ (Architectural Institute of Japan) (2008) Recommendations for Design and Construction of Concrete Filled Steel Tubular Structures. 2nd edition. [In Japanese].

AIJ (Architectural Institute of Japan) (2017) Recommendations for Plastic Design of Steel Structures. 3rd edition. [In Japanese].

Aoki

Iwashimizu

Yamada

, et al. (2012) Construction of the ultra-high-strength concrete CFT pillar of design strength 150 N/mm² —‘ABENO HARUKAS’ 300 meters super-high-rise compound Building—. Concrete Journal 50(8): 683–688. [In Japanese].

Cao

Nguyen

(2019) Experimental behaviour of concrete-filled steel tubes under cyclic axial compression. Advances in Structural Engineering 23(l): 74–88.

Elchalakani

Zhao

Grzebieta

(2004) Concrete-filled steel circular tubes subjected to constant amplitude cyclic pure bending. Engineering Structures 26(14): 2125–2135.

Fujimoto

Mikami

Mizuno

, et al. (2017) Statistical survey on structural characteristics of existing high-rise CFT buildings. AIJ Journal of Technology and Design 23(55): 897–902. [In Japanese].

10.

Hajjar

Molodan

Schiller

(1998) A distributed plasticity model for cyclic analysis of concrete-filled steel tube beam-columns and composite frames. Engineering Structures 20(4–6): 398–412.

11.

HACEI (Harbin Architectural and Civil Engineering Institute) (1985) Proc. Of the International Specialty Conference on Concrete Filled Steel Tubular Structures.

12.

Hori

(2017) Earthquake and tsunami scenarios as basic information to prepare next Nankai megathrust earthquakes. Journal of Disaster Research 12(4): 775–781.

13.

JEC-RGEJED (2015) (Joint editorial committee for the report on the great east Japan earthquake disaster). Report on the Great East Japan Earthquake Disaster. Building Series 1-3[In Japanese].

14.

Kawano

Matsui

(1988) An experimental study on hysteretic behavior of concrete filled tubular members under repeated axial loading. Proc. of Ninth World Conference on Earthquake Engineering 4: 133–138.

15.

Kawano

Matsui

Kimura

, et al. (2000) An experimental study on the cyclic local buckling fracture of full-scale concrete-filled tubes. Journal of Structural and Construction Engineering (Transactions of AIJ) 65(536): 163–167. [In Japanese].

16.

Kawano

(2006) A criteria for local buckling of concrete filled tubular members under cyclically repeated loading. Journal of Structural and Construction Engineering (Transactions of AIJ) 71(608): 151–156. [In Japanese].

17.

Knowles

Park

(1969) Strength of concrete filled steel tubular columns. Journal of the Structural Division 95(12): 2565–2588.

18.

Kubo

Hisada

Aizawa

, et al. (2014) Investigation of indoor damage and questionnaire intensity for high-rise building in tokyo during the great east Japan earthquake. Journal of Japan Association for Earthquake Engineering 14(6): 6_118–6_141.

19.

Matsumoto

Goto

Kuroiwa

, et al. (2012) Structural design and construction of a high-rise building using concrete filled tubular column with fc 150 N/mm2 high-strength concrete and 780 N/mm2 class high-strength steel. Concrete Journal 50(12): 1102–1108. [In Japanese].

20.

Morino

Tsuda

(2003) Design and construction of concrete-filled steel tube column system in Japan. Earthquake Engineering and Engineering Seismology 4(1): 51–73.

21.

Sakino

Nakahara

Morino

, et al. (2004) Behavior of centrally loaded concrete-filled steel-tube short columns. Journal of Structural Engineering 130(2): 180–188.

22.

Skalomenos

Hayashi

Nishi

, et al. (2016) Experimental behavior of concrete-filled steel tube columns using ultrahigh-strength steel. Journal of Structural Engineering 142(9): 04016057.

23.

TAAF (Tokyo Association of Architectural Firms) (2019) Building Structure Design Guidelines. [In Japanese].

24.

Yoshida

Obinata

Nishio

, et al. (2009) Development of high-strength (780 n/mm²) steel for building systems. International Journal of Steel Structures 9(4): 285–289.