Size effect on axial behavior of concrete-filled box columns

Abstract

The use of concrete-filled box columns could provide an economical alternative to building and bridge construction. Past experimental results showed that current building codes provided an adequate accuracy in determining axial capacity of such composite members. However, the sizes of the previously studied test specimens were mostly smaller than those for practical applications. As the column size increases, the size effect may become significant. Therefore, the applicability of extrapolating those test results to larger concrete-filled box columns needs to be justified. This study was devoted to investigating the potential size effect on axial behavior of concrete-filled box columns. Six short square concrete-filled box columns, with cross-sectional dimensions ranging from 300 to 750 mm, were tested under axial loading. Comparisons between experimental and analytical results were presented. It was observed that the size effect was prominent for the concrete-filled box columns studied herein. The results of this study showed that current design codes overestimated the axial capacity of the test columns with a dimension of 750 mm. In addition, finite element simulations of the axially loaded specimens were conducted to investigate the stress–strain behaviors of the concrete enclosed in different sizes of steel box columns. Results from the finite element analysis suggested that the larger steel box columns were less effective in enhancing the compressive strength of the enclosed concrete than smaller steel box columns.

Keywords

box column composite concrete-filled box column size effect

Introduction

Concrete-filled box columns (CFBCs) and concrete-filled tubes (CFTs) have been used in building and bridge constructions for decades. CFBCs and CFTs possess several advantages, such as excellent axial load capacity and ductility performance, over bare steel box/tube columns, and reinforced concrete (RC) columns. While a CFT member uses a steel tube or two steel channels to form the steel section, the steel section of a CFBC member is manufactured by welding four steel plates at corners of the section. Practical cross-sectional dimensions of CFBCs are typically greater than 500 mm as those of CFTs are generally less than 500 mm. Typical cross sections of square CFBC and CFT members are shown in Figure 1. In addition to providing structural strength, the steel box/tube column serves as forms for concrete casting, which makes the construction of CFBCs and CFTs more economical and efficient than that of conventional RC columns.

Figure 1.

Typical cross sections of square CFBC and CFT members: (a) square CFBC section and (b) square CFT section.

In the past, many studies (Chen et al., 2012; Liang, 2009a, 2009b; Liu, 2005; Liu et al., 2003; Liu and Gho, 2005; Sakino et al., 2004; Uy, 1998, 2001, 2008) investigated axial behavior of CFBCs. Uy (1998) studied the local and post-local buckling behavior of thin-walled CFBCs. He conducted axial compressive testing on 10 square CFBCs. The cross sections of the CFBCs in his study ranged from 126 mm × 126 mm to 306 mm × 306 mm. In his study, the yield stress of steel was 300 MPa, and the compressive strengths of concrete ranged from 45 to 57 MPa. Later, Uy (2001) studied effects of high-strength steel box columns on axial behavior of CFBCs. The yield stress of high-strength steel used in that study was 750 MPa and the compressive strengths of concrete ranged from 28 to 32 MPa. The sizes of the studied CFBC specimens ranged from 110 mm × 110 mm to 210 mm × 210 mm. In his recent study of CFBCs with high-strength steel, Uy (2008) recommended that more research is needed to consider variations of material and geometric parameters that are in a range of practical structural applications. In addition, some other researchers (Liu, 2005; Liu et al., 2003; Liu and Gho, 2005) experimentally investigated effects of material properties and cross-sectional aspect ratios on axial behavior of high-strength rectangular CFBCs. The maximum cross-sectional dimension of the studied CFBCs was only 220 mm. Liang (2009a) developed a performance-based analysis model for concrete-filled steel tubular beam–columns using a fiber element method including strain hardening behavior of steel and confined concrete. In his study, a compressive residual stress of 0.25 f_y and a geometric imperfection incorporating the first local buckling mode were used in his analysis. The developed performance-based analysis method was validated against experimental data (Liang, 2009b). More recently, Chen et al. (2012) studied local buckling and concrete confinement of axially loaded square CFBCs with larger cross-sectional dimensions: 410 and 500 mm. Results of their study showed that differences in the stress–strain behavior of concrete between the two square CFBC sizes studied existed. A reduction in the compressive strength and ductility of concrete was observed in the larger CFBCs, suggesting that an increase in the cross section of CFBCs could adversely affect axial capacity of CFBCs. Furthermore, a previous study by Sakino et al. (2004) also suggested that size effect on compressive strength of concrete should be considered for CFT columns.

As mentioned above, the CFBC sections of the previous studies were relatively small, compared to practical cross-sectional dimensions of CFBCs used in medium- and high-rise buildings, which could be greater than 1000 mm. The largest cross-sectional dimension of the CFBCs tested in the aforementioned studies was only 500 mm. The applicability of extrapolating these test results to CFBCs with larger cross sections needs to be verified by more test data.

The working hypothesis of this study is that CFBCs of larger sizes may behave differently than those of smaller dimensions owing to the size effect. For this reason, it is the objective of this research to study axial behavior of CFBCs of various dimensions, including cross sections of CFBCs that are larger than those used in the past studies. Consequently, the size effect of CFBCs on axial compressive strength can be identified. In this study, six square CFBC specimens with three different cross sections were tested under axial loading. Axial compressive strengths of CFBC specimens determined from the tests were compared with design axial load capacity calculated based on design codes. In addition, a numerical study was carried out to distinguish differences in stress–strain curves of the concrete enclosed by various steel box column sizes.

AISC and ACI codes for analyzing axial load capacity of CFBCs

Design methods for composite members can be found in AISC and ACI design codes (ACI, 2014; AISC, 2010b). A brief review of the design methods is provided as follows.

AISC (2010b) prescribes that the compressive strength of CFBCs is controlled by the limit state of flexural buckling, which is influenced by column slenderness. The design compressive strength of CFBCs is determined by multiplying the nominal compressive strength (P_n) of CFBCs by a reduction factor (ϕ_c). The reduction factor is set to 0.75. The nominal compressive strength is determined as follows.

When $P_{e} \geq 0.44 P_{0}$

P_{n} = P_{0} [{0.658}^{(\frac{P_{0}}{P_{e}})}]

(1)

when $P_{e} < 0.44 P_{0}$

P_{n} = 0.877 P_{e}

(2)

In which

P_{0} = A_{s} F_{y} + 0.85 A_{c} f'_{c}

(3)

where A_s and A_c are the areas of the steel section and concrete, respectively. F_y and $f'_{c}$ are the yield strength of the steel section and compressive strength of the concrete, respectively

P_{e} = \frac{π^{2} (E I_{eff})}{{(KL)}^{2}}

(4)

where

E I_{eff} = E_{s} I_{s} + C_{3} E_{c} I_{c}

(5)

C_{3} = 0.6 + 2 {\frac{A_{s}}{A_{c} + A_{s}}} \leq 0.9

(6)

ACI (2014) determines the compressive strength of CFBCs by superimposing RC column strength with steel box column strength, as shown in equation (7)

P_{0} = 0.85 A_{c} f'_{c} + A_{s} F_{y}

(7)

Local buckling may occur when the lateral support provided by concrete to the steel section becomes insufficient. When elastic local buckling occurs, CFBCs may not achieve desired strength and ductility. Owing to this reason, to ensure that design strength and ductility of CFBCs are not compromised, design codes (ACI, 2014; AISC, 2010a) limit the b/t ratio of the steel section to prevent steel column walls from early local buckling.

The b/t ratio limited by ACI (2014) is determined as follows

\frac{b}{t} \leq \sqrt{\frac{3 E_{s}}{F_{y}}}

(8)

The b/t ratio limited by AISC (2010a) for highly ductile members is determined as follows

\frac{b}{t} \leq 1.4 \sqrt{\frac{E_{s}}{F_{y}}}

(9)

Experimental program

Design and fabrication of test specimens

It was the objective of this study to investigate size effects on axial load capacity of short square CFBCs. The slenderness effect in column was eliminated by limiting the length of the CFBC specimens to three times of the width of the column cross section. While previous CFBC test specimens (Chen et al., 2012; Liu, 2005; Liu et al., 2003; Liu and Gho, 2005; Sakino et al., 2004; Uy, 1998, 2001, 2008) were all relatively small (less than or equal to 500 mm²), this study constructed and tested a total of six square CFBCs with three various sizes, including 300 × 300 mm², 500 × 500 mm², and 750 × 750 mm² under monotonic axial loading. Steel box columns were fabricated by welding four A36 steel plates using full penetration welds at corners of the box columns. Figure 2 provides a schematic of the cross section and full penetration welds of the CFBC specimens studied herein. As part of the specimen fabrication, two steel plates were welded to the top and bottom of the steel box column. A circular hole was created in the middle of the top steel plate for concrete pouring, and the removed circular steel plate was placed back at the end of the concrete pouring. Details of the steel box columns are shown in Figure 3.

Figure 2.

Cross section of the CFBC specimens.

Figure 3.

Details of the steel box columns.

Two identical specimens were fabricated for each of the three column sizes. The specimen ID designation is based on the size of the column; for example, A300-a and A300-b represent the two specimens with a cross-sectional area of 300 × 300 mm². Table 1 shows the dimensions of the test specimens. D is the depth and width of the steel box column, t is the thickness of the steel box column, b is the clear width of steel plates (taken as H − 2t), and L is the length of the specimen. The width-to-thickness (b/t) ratio of the specimens was fixed at 48, satisfying the limiting b/t ratio (√(3E/F_y = 49) prescribed by ACI (2014), to avoid early local buckling. Material properties of the steel and concrete were obtained by conducting tension and compression tests on steel coupons and concrete cylinders, respectively. The yield and tensile strengths of steel listed in Table 2 were the average strengths of three steel coupon specimens. The standard deviations of the determined yield strengths for the 6-, 10-, and 15-mm-thick steel plates were 3.21, 3.00, and 6.81 MPa, respectively. The compressive strength of concrete for all specimens was determined by averaging compressive strengths of six concrete cylinders. The determined compressive strength was 27.9 MPa with a standard deviation of 1.34 MPa.

Table 1.

Dimensions of test specimens.

Specimen ID	D (mm)	t (mm)	b (mm)	b/t	L (mm)
A300-a	300	6	288	48	900
A300-b	300	6	288	48	900
A500-a	500	10	480	48	1500
A500-b	500	10	480	48	1500
A750-a	750	15	720	48	2250
A750-b	750	15	720	48	2250

Table 2.

Mechanical properties of the A36 steel plates.

Steel plate thickness (mm)	Yield strength, $F_{ya}$ (MPa)	Tensile strength, $F_{ua}$ (MPa)
6	334	470
10	302	435
15	315	479

Test setup and procedure

All the specimens were tested under monotonic axial loading to failure using a 30 MN universal testing machine housed in the Material Testing Center of Architecture and Building Research Institute (ABRI) in Taiwan. Four linear variable displacement transducers (LVDTs) were installed to measure the axial shortening over the full height of the specimen, as shown in Figure 4. A thin layer of gypsum wash was applied to the outer surface of steel box columns to observe flaking and deformation. The test setup is shown in Figure 5.

Figure 4.

Test instrumentation.

Figure 5.

Test setup.

At the beginning of the monotonic loading tests, specimens were centrally positioned with a pre-load level of 500 kN. Then, the monotonic loading was applied under displacement control. The initial axial loading was applied at a rate of 1.5 mm/min before the axial displacement reached 15 mm. For the axial displacements between 15 and 30 mm, a loading rate of 3.0 mm/min was used. As the axial displacement exceeded 30 mm, a loading rate of 6.0 mm/min was applied. The axial load testing was terminated as the applied load dropped below 50% of the maximum load achieved during the testing.

Test results and discussions

Figure 6 shows the axial load versus displacement curves for all specimens. All tested CFBC specimens exhibited an abrupt decrease in axial compressive strength when the concrete crushing and the local buckling of steel walls occurred. The failure of the CFBCs was initiated by the concrete crushing at a certain elevation. Owing to the loss of bearing capacity from the concrete core, the steel walls subsequently buckled around the crushed concrete. As the steel walls continued to deform outward, the corners of the steel box column ruptured. The degradation of concrete strength and ruptures of the steel box column resulted in the continuing decrease in the axial compressive strength. Figure 7 shows the final deformed shapes of representative test specimens. All specimens showed substantial local buckling deformations and ruptures at corners of the steel box column. Although the failure of the tested specimens was initiated by local buckling in steel columns, the local buckling occurred after the steel columns yielded, evidenced by the flaking of the gypsum paint on the steel walls. Thus, the design axial capacity of the tested columns should not be affected by the local buckling.

Figure 6.

Axial load versus axial strain curves: (a) A300 specimens, (b) A500 specimens, and (c) A750 specimens.

Figure 7.

Final deformed shapes of representative test specimens: (a) A300-a, (b) A500-a, and (c) A750-a.

Table 3 compares experimental results with analytical axial capacity. Since the tested CFBCs were short columns, the consideration of the column slenderness required by the AISC (2010b) was not necessary. Consequently, the axial compressive strength determined by the AISC equation was essentially the same as that obtained by the ACI equation. The axial compressive strength of specimens, P_max, is the maximum axial load recorded from the monotonic load tests. The analytical axial capacity, P_a0, was computed by equation (7) using the material properties determined from mechanical tests. Results showed that the nominal axial compressive strength calculated by equation (7) provided conservative results for A300- and A500-series specimens (the test axial compressive capacities of A300-series and A500-series specimens were about 10%–12% and 3%–4% higher than the analytical capacities, respectively). However, the test axial compressive strengths of A750-a and A750-b were lower than the predicted value by about 13% and 7%, respectively, suggesting that the reliability of the analytical prediction was influenced by the dimensions of the tested square CFBCs.

Table 3.

Comparisons of axial compressive strength between test and analytical results.

Specimen ID	P_max (kN)	P _a0 (kN)	$\frac{P_{max}}{P_{a 0}}$ (%)
A300-a	4842	4323	112.0
A300-b	4771	4323	110.4
A500-a	11,779	11,388	103.4
A500-b	11,838	11,388	104.0
A750-a	22,876	26,181	87.4
A750-b	24,294	26,181	92.8

Figure 8 plots P_max/P_a₀ versus the dimensions of the CFBCs, showing a strong correlation between the two parameters. The results of this study suggested that the axial compressive strength predicted by the design equation might be unconservative as the size of the cross section of CFBCs increased.

Figure 8.

P_max/P_a ₀ versus dimension of the cross section. P_max is the maximum axial strength obtained from the tests and P_a₀ is the design strength calculated by equation (9).

Finite element simulations

Element types and boundary conditions

In this study, finite element analysis was carried out using the commercial finite element program ABAQUS/CAE 6.5 (ABAQUS, 2002). Finite element models of the tested CFBC specimens, A300, A500, and A750 were created following the methodology presented in Chen et al. (2012). The finite element models were created to evaluate the size effect on stress–strain behavior of the enclosed concrete. Owing to the symmetry of the CFBC specimens, only one-eighth of the CFBC was modeled, as shown in Figure 9. Degrees of freedom normal to the symmetric planes were set to zero. The end plate was modeled as a rigid plate. In addition, the welds and backing bars were also included in the finite element models. The steel box column wall was modeled by two layers of the three-dimensional quadratic solid element C3D20R, consisting 20 nodes per element. The part of concrete contacting the steel column was modeled using the three-dimensional quadratic solid element C3D27R, consisting 27 nodes per element. The other parts of the concrete were modeled using C3D20R to reduce run time. A total of 6006 elements were created for the concrete and steel column. The rigid plate connected to the top of the steel box column was modeled using three-dimensional rigid elements R3D4.

Figure 9.

Finite element model of one-eighth of the CFBC.

Residual stress and initial out-of-flatness

Effects of residual stresses and initial out-of-flatness of the steel box column on axial behavior of CFBCs were included in the finite element models following the same procedures established by Chen et al. (2012). The residual stress distribution of the steel box column was simulated by cooling the welds by 600°C. The initial out-of-flatness can be automatically modeled by ABAQUS using a buckling mode shape. In addition, the initial out-of-flatness was modeled using the second buckling mode shape, with a maximum out-of-flatness equal to D/1000. It was found that this assumed initial out-of-flatness was able to produce reasonable results, compared with experimental data (Chen et al., 2012).

Interface between steel and concrete

The interface/interaction between the steel box column wall and concrete and between the end plate and concrete was modeled using a master–slave algorithm (ABAQUS, 2002) to avoid the intrusion of the nodes of the concrete surface through the contact surface of the steel column wall. The surfaces of the steel box column and end plate were modeled as the master surfaces and the surface of concrete was modeled as the slave surface. The coefficient of friction was expected to be low after the steel plate yielded owing to that the mill scale of the steel plate was not removed. Therefore, the coefficient of friction between the master and slave surfaces was set at 0.15, as recommended by the previous study (Chen et al., 2012).

Loading procedure

An axial compressive load was applied to a reference point, which was set on the rigid plate at the position coincident with the center of the end plate, by incrementing the axial displacement of the reference point. Simulations were terminated when convergence of the solution was judged unlikely by ABAQUS.

Material models

The stress–strain behavior of the steel box column was modeled by creating 20 piece-wise linear segments using the stress–strain data obtained from tension tests, as shown in Figure 10. The stress–strain behavior of the concrete was modeled by a continuum and plasticity-based damage model shown in Figure 10. The unconfined stress–strain model proposed by Mander et al. (1988) was used to determine the stress–strain behavior from the origin to P₁ on the stress–strain curve. Multiple straight lines were used to connect P₁, P₂, P₃, and P₄. Previous studies (Chen et al., 2012; Sakino et al., 2004) indicated that the compressive strength of concrete should be modified to account for different column sizes owing to the size effect. Accordingly, different stress–strain curves should be used for CFBCs with different column sizes in order to achieve satisfactory simulation results. This phenomenon was shown in the previous study (Chen et al., 2012) and confirmed by the experimental results presented in this article, which suggested that size effect on axial load capacity of CFBCs existed.

Figure 10.

Stress–strain curves of the steel used for the studied CFBCs.

The main goal of the finite element study was to identify key points (P₁ to P₄) on the stress–strain model shown in Figure 11. The key points of the concrete material model were determined through finite element model calibrations using the experimental data. The determined values of the key points for each column size are tabulated in Table 4, and the resulting stress–strain curves for the three column sizes are shown in Figure 12. All three CFBC finite element models exhibited a similar deformed shape, controlled by the same buckling mode. A representative final deformed shape of the finite element models is presented in Figure 13.

Figure 11.

Stress–strain model for concrete.

Table 4.

Key parameters of the concrete material model for each CFBC model.

Specimen	P ₁	P ₂	P ₃	P ₄
Specimen	(Strain, stress in MPa)
A300	(0.003, 27.9)	(0.0096, 11.7)	(0.033, 7.6)	(0.099, 1.4)
A500	(0.0026, 23.5)	(0.0086, 9.4)	(0.0286, 7.1)	(0.099, 1.2)
A750	(0.0024, 21.1)	(0.0084, 9.3)	(0.0264, 6.5)	(0.099, 1.1)

Figure 12.

Stress–strain curves for the three finite element models.

Figure 13.

Final deformed shape of the A300 finite element model.

Results and discussion

Figure 14 shows comparisons of axial force versus axial strain curves between the simulation and experimental results for the three CFBC test specimens. The finite element simulations were terminated at axial strains between 0.015 and 0.02 due to the excessive deformations in the columns, causing the solution to diverge. As shown in Figure 14, the finite element simulations, using the stress–strain curves presented in Figure 11, agreed well with the test results for the peak load and post-peak behavior. It was indicated in Chen et al. (2012) that the stress–strain behavior for concrete was crucial for simulating the post-peak behavior. Hence, the determined stress–strain curves for the three CFBCs studied herein were considered adequate. The determined stress–strain curves suggested that the peak compressive strength (Point P₁ of the identified stress–strain curves) of the confined concrete and the corresponding strain decreased with an increase in the column size. A similar trend was also observed for other key points (P₂–P₄) of the stress–strain curves. The observed lower concrete compressive strengths and corresponding strains were most likely owing to the higher probability for a larger CFBC to contain defects in concrete. The size difference caused the concrete in larger CFBCs to fail earlier and at lower strengths than that in smaller CFBCs. As mentioned previously, the dimensions of the CFBC cross sections studied in the past (Chen et al., 2012; Liu, 2005; Liu et al., 2003; Liu and Gho, 2005; Sakino et al., 2004; Uy, 1998, 2001, 2008) were less than or equal to 500 mm, which were much smaller than the practical CFBC cross sections used for mid- and high-rise buildings. The findings of this study suggested that the current design method, developed on the basis of small-scale CFBC test data, could potentially yield an unconservative design for CFBCs with cross-sectional dimensions larger than those tested.

Figure 14.

Comparisons between experimental and numerical results: (a) A300 specimens, (b) A500 specimens, and (c) A750 specimens.

Conclusion

Experimental and numerical studies on axial behavior of CFBCs are presented in this article. As most test results reported in the past literature were from CFBC specimens with cross-sectional dimensions less than 500 mm, whether those findings could be applied to larger CFBCs was indeterminate. In this study, square CFBC specimens with the cross-sectional dimensions ranging from 300 to 750 mm were tested under axial loading to identify effects of cross-sectional dimensions on axial behavior of CFBCs. The experimental results presented herein showed size effects on the axial capacity of CFBCs. In addition, finite element simulations were carried out for the tested CFBCs to investigate stress–strain behavior of concrete confined by the various sizes of steel box columns. The results of the finite element simulations revealed the size effects on the stress–strain relationship of the confined concrete. Based on the experimental and numerical results reported herein, the following conclusions are drawn:

For the three column sizes studied herein, the ratios of the test axial load capacity and the design compressive strength of CFBCs decrease as the sizes of the columns increase. Although the data presented in this study exhibit an inverse linear relationship between P_max/P_a₀ and the column size, this result is only applicable to square CFBCs within the dimensions studied herein.

The AISC and ACI design equations overestimate the axial load capacity of the CFBC specimens with the size of 750 mm × 750 mm, resulting in an unconservative design. More test data of axially loaded CFBCs with dimensions larger than 750 mm are needed in the future for developing an adequate analytical method for large CFBCs (greater than 750 mm × 750 mm).

The results of the numerical study suggest that the compressive strength of concrete in the CFBCs decreases with an increase in the size of the columns, given that the same concrete is used in the columns. It is considered that the decrease in the concrete strength is resulted from the higher likelihood of possessing weak points/defects in the concrete of larger CFBCs. As most past studies focused only on axial behavior of CFTs or small CFBCs (smaller than 500 mm × 500 mm), future studies are needed to identify effects of the aspect ratio, dimension, b/t ratio, and material properties on axial behavior of large CFBCs.

Footnotes

Appendix 1 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: The research reported in this paper was sponsored by the Architecture and Building Research Institute of the Ministry of Interior, ROC. The support of the Architecture and Building Research Institute is greatly appreciated. Statements made in this paper reflect the views and findings of the authors and are not necessarily those of the Architecture and Building Research Institute.

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