Experimental and numerical studies on the seismic behavior of steel reinforced concrete compression-bending members with new-type section steel

Abstract

There has been no significant improvement on the seismic performance of the ordinary steel reinforced concrete columns compared with the reinforced concrete columns mainly because I- and H-shaped section steel cannot provide sufficient confinement for core concrete. This article presents a study on the seismic behavior of two improved steel reinforced concrete columns by constructing with new-type section steel, a cross-shaped steel whose flanges are in contact with concrete cover by extending the geometry of webs, and a rotated cross-shaped steel whose webs coincide with diagonal line of the column’s section. Seismic behavior of the developed steel reinforced concrete columns, mainly including the failure patterns, hysteretic loops, skeleton curves, energy dissipation capacity, and ductility, was experimentally investigated by testing five specimens subjected to low reversed cyclic loading. The test results indicate that both types of steel reinforced concrete columns exhibit bending failure and improved seismic behavior: increased vertical bearing capacity could keep better stability, although yielding of the longitudinal reinforcement and local bucking of flanges happen, and the strength degradation becomes slow and the deformation capacity improves. A finite element model has been established to predict the seismic performance of the developed steel reinforced concrete compression-bending members. The numerical model is validated by the test data, and the numerical results are in close agreement with the experimental ones. A parametric study has been conducted to analyze the effects on the seismic behavior from the axial compression ratio, stirrup spacing, and concrete strength of the developed columns. Eventually, limited values of axial compression ratio for three seismic grades are proposed for the potential design guidance revision and promotion of in situ application.

Keywords

cross-shaped steel limit values of axial compression ratio numerical simulation quasi-static test seismic behavior steel reinforced concrete compression-bending members

Introduction

During the past few decades, steel reinforced concrete (SRC) structural systems have been used in many tall buildings all over the word. This system combines the rigidity and formability of reinforced concrete (RC) with the strength and speed of construction associated with structural steel to produce an economic structure. The concrete used for encasing structure steel section not only increases its strength and stiffness but also improves its fire resistance. The seismic behavior of SRC members and its influence factors have been studied by many researchers abroad (De Sousa and Caldas, 2005; Karimi et al., 2012; Kim et al., 2011; Kitano et al. (2008) Minae and Koichi (2008); Paulay and Priestley, 1992; Tawil and Deierlein, 1999; Viest et al., 1997; William and Arvind, 2011; Yasushi et al., 2004). From the early 1990s, with the wide use of SRC structures in China, many Chinese scholars began to do some research on the seismic behavior of SRC columns (Chen et al., 2005, 2014; Chou and Uang, 2007; Lu et al., 2014; Ma et al., 2011; Yan and Jia, 2010; Zhang et al., 2012; Zheng et al., 2012). The results have shown that SRC columns embedded with I- or H-shaped section steel were mainly adopted in the engineering practice while these ordinary section steel could provide limited confinement for core concrete, and it has become more essential to develop new SRC structures to promote the earthquake resistance, the workability, and economy.

Two improved SRC columns embedded with new-type section steel are developed in the study to overcome the shortcomings of ordinary SRC columns on this background. The first type is a cross-shaped steel whose flanges are in contact with concrete cover (short for “enlarging cross-shaped steel”), and the second type is a rotated cross-shaped steel whose webs coincide with diagonal line of the column’s sections (short for “diagonal cross-shaped steel”). It is clear that the area and strength of confined concrete increase because of cross-shaped steel arrangements, which helps to improve bearing capacity and deformation ability of SRC columns. Failure patterns, hysteretic characteristics, and ductility performance of SRC compression-bending column specimens under low reversed cycle loading were experimentally investigated through a test of four improved and one ordinary specimen. On this basis, seismic behavior of SRC compression-bending members with new-type section steel under earthquake action was broadly detected through a numerical study, and limited values of axial compression ratio for three seismic grades were pronounced for design purpose eventually.

Experimental program

Description of specimens

The test presented in this study consisted of totally five SRC compression-bending members, named SRC1–SRC5. The specimen SRC2 was constructed by adopting enlarging cross-shaped steel, and specimens SRC3–SRC5 were composed of diagonal cross-shaped steel whose flange width was about half of the specimen SRC2. An ordinary SRC compression-bending member (SRC1) as control specimen was tested for comparison. Dimensions and reinforcement arrangement of all specimens are illustrated in Figure 1.

Figure 1.

Geometry and steel arrangement of specimens: (a) overview of specimen, (b) photo of steel skeleton, and (c) cross section of specimen.

As shown in Figure 1, the cross section of columns was 250 × 250 mm². The concrete used in the specimens was C40, the embedded steel was Q235, the longitudinal reinforcement was HRB335, the stirrup was HPB235, and the concrete cover thickness was 20 mm. Different parameters were involved in those specimens to investigate the influences on the seismic behavior of SRC compression-bending members, including axial compression ratio, steel shape, and steel content. Table 1 summarizes values of all the parameters. Spiral hoop was used to provide better confinements for concrete whose side length was determined by considering the concrete cover thickness and steel size. The longitudinal reinforcement were fixed together with stirrup that placed along the full height of column. The steel skeleton was then lifted into the rebar frame and its both ends were fixed by tying with rebar frame.

Table 1.

Specimen sectional dimensions.

Specimen	Axial compression ratio n_t	Steel section h_w × b_f × h_f × t_w (mm⁴)	Steel ratio (%)	Shear span ratio λ	Detailing of reinforcement	Reinforcement ratio ρ_s (%)	Detailing of stirrup	Stirrup ratio ρ_v (%)
SRC1	0.30	130 × 60 × 8 × 6	5.26	4.0	4ϕ14	1.13%	ϕ6@50	0.98%
SRC2	0.42	210 × 100 × 8 × 6	8.85	4.0	4ϕ14	1.13%	ϕ6@50	0.98%
SRC3	0.30	238 × 60 × 8 × 6	7.32	4.0	4ϕ14	1.13%	ϕ6@50	0.98%
SRC4	0.42	238 × 60 × 8 × 6	7.32	4.0	4ϕ14	1.13%	ϕ6@50	0.98%
SRC5	0.60	238 × 60 × 8 × 6	7.32	4.0	4ϕ14	1.13%	ϕ6@50	0.98%

b _f and h_f are the flange width and height, respectively, and h_w and t_w are the web height and thickness, respectively.

Material properties

Material strength used to evaluate ultimate stress uses the result of the material test. The mechanical properties of steel, longitudinal reinforcement, and stirrup from test are listed in Table 2. The mean concrete cube strength by averaging eight standard cube specimens (150 × 150 × 150 mm³) is 51.5 MPa.

Table 2.

Material properties of steel.

Material	Grade	Yield strength f_y (MPa)	Ultimate strength f_u (MPa)	Elastic modulus E (MPa)
Steel	Q235	248.3	348.6	2.1 × 10⁵
Longitudinal reinforcement	HRB335	355.5	514.0	2.0 × 10⁵
Stirrup	HPB235	257.8	332.6	2.1 × 10⁵

Test procedures

A schematic view of the loading apparatus is shown in Figure 2. There were two loading steps in the test, as follows: (1) an axial compression force was first induced by a load-jack (in accordance with the target axial compression ratio) and maintained constant during the whole course of loading, and (2) the cyclic reversed load was then applied laterally by an MTS actuator (servo-controlled hydraulic type). In the phase before specimen yielding, the lateral loading was triggered by increments of force. The first level of the force was 20% of the calculated capacity of the specimens P_u-cal and 10% of P_u-cal was gradually increased on the next levels. On every force level, the lateral load was repeated only once. In the phase after specimen yielding, the lateral loading was triggered by increments of displacement. The yielding displacement Δ_y was gradually increased on the next levels. On every displacement level, the lateral load was repeated three times, where Δ_y is the calculated lateral displacement of the column when the steel flange yields. The test was stopped until the lateral load reduced to 85% of the ultimate load or the axis load could not keep its stability.

Figure 2.

Test setup: (a) sketch map and (b) photo of the actual load.

During the test, the lateral load in addition to the displacement and the strain of the steel, concrete, and reinforcement were measured and recorded automatically. The lateral load is measured by the sensor installed on the actuator and the lateral displacement is measured by the displacement meter installed on top of the specimens.

Experimental results

General behavior and failure pattern

The final failure pattern of specimens is depicted in Figure 3. All specimens displayed bending failure and the failure process complied with the general compression-bending members. No macro-cracks occurred on the specimen surface while the horizontal loading was at R (drift ratio) of 0.002 rad. As the load increased, micro-cracks occurred in the four corners at bottom of the specimens at R of 0.003 rad and these cracks extended to the upper position of plastic hinge region. Continuing to increase the load, the horizontal cracks extended to diagonal and turned to vertical at the end of the column. Penetrating and flexural cracks occurred on the opposite side of columns, and then the vertical and diagonal cracks were on lateral face at R of 0.006 rad. The specimen SRC1 yielded at R of 0.008 rad and specimens SRC2–SRC5 yielded successively at R of 0.011 rad.

Figure 3.

Failure modes of specimens: (a) specimen SRC1, (b) specimen SRC2, (c) specimen SRC3, (d) specimen SRC4, and (e) specimen SRC5.

At the stage of displacement-controlled, it was observed that the vertical cracks at bottom of the specimens widened and the lateral load of specimens started to decrease. Apart from the specimen SRC1, there was a rising trend in the applied lateral load for other specimens, which is caused by the combined effect of the steel flange and spiral stirrup, following the initial decrease. There were no further cracks formed at 2Δ_y, and part of concrete cover at column base dropped at 3Δ_y (R = 0.02 rad). Eventually, as the concrete crushed and the steel buckled, the load capacity of specimens decreased rapidly and failed.

Generally, the axial force for SRC compression-bending members with new-type section steel could keep better stability in the experiment than the ordinary one. This illustrates that the improved SRC columns could fully meet the requirements of earthquake resistance.

For convenience, SRC specimens embedded with new-type section steel are hereinafter referred to as new-type SRC compression-bending members. And when “new-type SRC compression-bending members” are used at the beginning of one paragraph, the following sentences are allowed to adopt “new-type SRC column” for simplicity.

Hysteretic characteristics

Hysteretic curve is a very important chart to reflect the seismic behavior of structural members, from which, the load-carrying capacity, stiffness, energy dissipation ability, and ductility can be obtained. The hysteretic curves of the test specimens are shown in Figure 4, which also includes the analytical hysteretic curve for the comparison in section ‘Comparison between the test and simulation results’. Some inferences can be drawn from Figure 4, as follows:

The specimens behave approximately elastic before the horizontal load increases to the yield load (about 40% of the ultimate load). The rigidity of the specimens decreases slowly from the yield load to the ultimate load and the plastic deformation is small. It is clear that the hysteretic curves start to fall after the ultimate load for all specimens. However, it exhibits a positive ductility as the displacement dramatically develops with smaller loss of load-bearing capacity.

The hysteretic loops of test specimens are plump except specimen SRC1 during the elastoplastic range. The hysteretic loops for specimens SRC2–SRC4 are close to rhombus, reflecting a strong capacity of plastic deformation and energy dissipation. They are compression-bending members with no slip and shear failure during the load process.

The strength of specimens SRC3 and SRC4 only slightly deteriorates when their axial compression ratios are 0.30 and 0.42, respectively, indicating that SRC compression-bending members with diagonal cross-shaped steel have better energy dissipation with axial load level below 0.42. Even if the axial compression ratio reaches to 0.60, pinching phenomenon and decline of the bearing capacity are still not significant (SRC5). Therefore, the ultimate axial compression ratio of specimens SRC3–SRC5 could be higher than that of ordinary SRC columns unveiled in Chinese specification JGJ 138 (JGJ 138-2001, 2010).

Different section steel is applied in specimens SRC1 and SRC3, and the hysteretic characteristics and ultimate deformation of the latter are better than those of the former. It thus can be extracted that the section steel has a critical effect on the seismic performance of SRC compression-bending members. The specimens SRC2 and SRC4 have similar hysteretic curve shapes, reflecting that their seismic performance should be identical excellent.

Figure 4.

Experimental and analytical hysteretic curves of specimens: (a) specimen SRC1, (b) specimen SRC2, (c) specimen SRC3, (d) specimen SRC4, and (e) specimen SRC5.

Skeleton curves

A skeleton curve can be obtained by connecting the peak points of the hysteretic curves under every level of load. A skeleton curve is used to observe the deformation capacity and strength decay of specimens. The typical lateral load–displacement skeleton curves for all specimens are plotted in Figure 5. Based on the figures, it can be seen that both the bearing and deformation capacity of new-type SRC compression-bending members (SRC2–SRC5) are better than that of the ordinary one (SRC1), and this may be due to the better confinement effect of cross-shaped steel. It can also be found from the skeleton curves that (1) under the same axial compression ratio, the load capacity and deformation ability of SRC column with enlarging and diagonal cross-shaped steel are basically the same, while about 20% steel can be saved by the latter; and (2) under other same conditions, with the decrease of the axial compression ratio, the specimens have a better deformation capacity and strength decay comes more slowly.

Figure 5.

Skeleton curves: (a) effect of steel arrangement and (b) effect of axial compression ratio.

Energy dissipation

The equivalent viscous damping coefficient h_e (h_e = E/2π(PΔ)) is adopted to evaluate energy dissipation capacity of specimens under reversed cyclic load, where E is the area of a hysteretic loop, and PΔ is the product of peak load and maximum displacement of the first loading cycles of various incremental steps in the process of cyclic loading (the positive and negative values are averaged). The stronger the energy dissipation ability, the larger the factor h_e is. The relationship between h_e and Δ for all specimens is shown in Figure 6.

Figure 6.

Equivalent viscous damping coefficients: (a) effect of steel arrangement and (b) effect of axial compression ratio.

The value of h_e is about 0.60 for the specimen SRC3 and drops to 0.45 for the specimen SRC1 with the same axial compression ratio, indicating that the energy dissipation capacity of SRC compression-bending members with diagonal cross-shaped steel is greater than the ordinary one. Moreover, h_e from the specimen SRC2 is slightly larger than that from the specimen SRC4, but steel ratio of the latter is 20% less than that of the former. It may reflect that energy dissipation of the two improved SRC columns is essentially equal. Meanwhile, the energy dissipation capacity reduces with increasing axial compression ratio, which could be explained as that h_e decreases by 48% when the axial compression ratio increases from 0.30 to 0.42, and it decreases by 73% corresponding to an increase of the axial compression ratio from 0.30 to 0.60.

Deformation and ductility performance

Ductility is used to determine the deformation capacity and seismic behavior of structure members. The ductility factor µ, defined as the ratio of the ultimate displacement Δ_u to the yield displacement Δ_y, is generally used to quantitatively describe the ductility, where Δ_y is calculated using the Park method (Park, 1989), and Δ_u is the corresponding displacement as the horizontal load decreases to 85% of the ultimate load. Table 3 shows the ductility factors of all the specimens.

Table 3.

Ductility factors of specimens.

Specimen	Axial compression ratio n_t	Steel ratio ρ_a (%)	Ultimate drift ratio θ_u	Displacement ductility factor µ
Specimen	Axial compression ratio n_t	Steel ratio ρ_a (%)	Ultimate drift ratio θ_u	Tension	Compression	Average
SRC1	0.30	5.26	1/45	2.95	2.57	2.76
SRC2	0.42	8.85	1/31	5.21	4.89	5.05
SRC3	0.30	7.32	1/30	4.55	4.95	4.75
SRC4	0.42	7.32	1/33	4.08	4.62	4.35
SRC5	0.60	7.32	1/43	2.39	2.99	2.69

It can be found from Table 3 that θ_u and µ of the ordinary SRC compression-bending member are 1/45 and 2.76, respectively, while the corresponding values for new-type ones are around 1/30 and 4.0. The average value of µ is greater than 2.5 for the new-type SRC column specimens even if the axial compression ratio is as large as 0.60. It can be concluded that there is no effect on the ductility performance of new-type SRC compression-bending member when the axial compression ratio is lower than 0.42; however, µ can be reduced to 2.69 with a larger axial compression ratio of 0.60.

The effects of the axial compression ratio on ductility performance can be analyzed from two following aspects. Firstly, the lower axial compression ratio leads to a smaller compressive stress and strain of concrete at the sectional edge, and eventually upgrades the deformability and ductility of specimens (such as SRC2–SRC4). Four steel flanges and continuous spiral hoop form an integrated constraint which helps to improve the compressive strength of core concrete. Secondly, the deformation is rarely stable after peak load with higher axial compression ratio (such as SRC5) which causes increasing of second-order moment and additional deformation, and it weakens the ultimate displacement and ductility of the compression-bending members.

Numerical analysis

In order to further study the influences of more factors on the seismic behavior of SRC compression-bending members, a nonlinear finite element (FE) method has been conducted in this study. The validity of the FE method must be verified by the experimental results, and therefore, the comparison of the FE analytical results on the experimental model with the experimental results should be carried out first.

Establishment of SRC column model

The FE analysis has been undertaken using the commercial FE software ABAQUS. A typical 3D FE model is shown in Figure 7(a), where 3D stress element (type: C3D20R) and truss elements (type: T3D2) are adopted to model the steel and rebar, respectively. The boundary condition of the model is shown in Figure 7(b), which includes a base beam. The translational and rotational degrees of freedom of concrete at the column base are all constrained according to the actual loading method. For convenient calculation, the concrete cover at top of the column is removed at modeling time, and the load is directly applied on the coupling point between steel and concrete.

Figure 7.

Finite element model and gridding division: (a) element division and (b) restraint of column end.

The adaptive meshing method is used for the FE mesh division, through which the regular hexahedron or quadrilateral elements could be obtained. The dense mesh can get a more precise result but will reduce the computational efficiency. Different mesh increments were selected during the trial course, and 50 mm is a proper mesh dimension through the calculation and comparison. The reason is that the calculation requires relatively moderate computational time with a mesh dimension of 50 mm, and the ultimate strength of the specimen in this situation is close to that with the finer mesh.

To consider the slip effect impact, three spring elements are chosen to model the bond behavior between steel (reinforcement) and concrete, which represent the contacting performance in the x, y, and z directions, respectively, as shown in Figure 8. For reinforcement and concrete, the normal and transverse tangential springs are used to simulate the grip power, and the longitudinal spring for the bond slip. The bond stress between reinforcement and concrete is calculated according to equation (1) (Houde and Mirza, 1974)

\begin{matrix} τ = & (5.3 \times 10^{2} s - 2.52 \times 10^{4} s^{2} + 5.86 \times 10^{5} s^{3} - 5.47 \\ \times 10^{6} s^{4}) \sqrt{\frac{f_{c}'}{40.7}} \end{matrix}

(1)

where $τ$ is the bong stress, s is the slip displacement between reinforcement and concrete, and $f_{c}'$ is the compression strength of concrete cylinder.

Figure 8.

Spring elements.

For steel and concrete, a large value is selected for the normal spring coefficient, and the model of bond stress and slip displacement for the transverse and longitudinal tangential spring is shown as equation (2) (Wang and Zhong, 1990)

τ = 0.759 + 1.315 s - 1.343 s^{2} + 0.140 s^{3} - 1.556 s^{4}

(2)

where s is the slip displacement between steel and concrete.

Material properties

Uniaxial constitutive laws

The concrete of SRC columns is divided into two portions in terms of the appearance of stirrups, a constraint region surrounded by stirrup, and the other nonconstraint region out of stirrup. The uniaxial stress–strain relationship of the unconfined and confined concrete used in the SRC columns is given by Figure 9 and equations (3) to (4)

\begin{matrix} For unconfined concrete : \\ σ (ε) = {\begin{matrix} σ_{0} [2 (\frac{ε}{ε_{0}}) - {(\frac{ε}{ε_{0}})}^{2}], (ε < ε_{0}) \\ σ_{0} [1 - 0.15 (\frac{ε - ε_{0}}{ε_{u} - ε_{0}})], (ε_{0} < ε < ε_{u}) \end{matrix} \end{matrix}

(3)

\begin{matrix} For confined concrete : \\ σ (ε) = {\begin{matrix} E_{0} ε_{0} [\frac{ε}{ε_{0}} - \frac{1}{n} {(\frac{ε}{ε_{0}})}^{n}], (0 \leq ε \leq ε_{0}) \\ (\frac{λ - 1}{μ_{1} - 1} \cdot \frac{σ_{c}}{ε_{c}}) \cdot ε, (ε_{0} \leq ε \leq μ_{1} {ε_{0}}_{u}) \end{matrix} \end{matrix}

(4)

where ε₀ and ε_u are strain corresponding to peak stress and ultimate compressive stress, respectively, and n is the constraint intensity coefficient of concrete.

Figure 9.

Uniaxial constitutive models: (a) unconfined concrete and (b) confined concrete.

For steel in the SRC column, an idealized elastic–plastic stress–strain relationship based on the test result is suggested, which is described by equation (5)

σ_{s} = {\begin{matrix} E_{s} ε_{s}, ε_{s} \leq ε_{y} \\ f_{y}, ε_{y} \leq ε_{s} \leq ε_{sh} \end{matrix}

(5)

where $ε_{y}$ is the yield strain, E_s is the elastic modulus, and $ε_{sh} = 0.01$ .

Hysteretic constitutive laws

The concrete damaged plasticity model (CDP model for short) has been provided in ABAQUS software to simulate the behavior of concrete under reversed cyclic loading. The damage variable d is introduced to reduce the elastic stiffness matrix of concrete in CDP model, which could reflect the performance (such as stiffness degradation caused by damage in tension and compression) of concrete in SRC columns. Cauchy stress $σ$ is linked to the effective stress $\bar{σ}$ through the damage variable d, and their relationship is shown in equation (6)

σ = (1 - d) \bar{σ}

(6)

where d is the stiffness damage variable which varies from 0 (no damage) to 1 (complete damage). (1 − d) is the ratio of effective bearing area to gross sectional area, and the external loads are only carried by the effective stress area when there is any damage.

When the concrete section is in compression after tension crack under the repeated loadings, the cracked area will produce crack effect caused by aggregate interlock, and this makes a large part of compressive stress to be transferred before the cracked area closure completely. Therefore, the total damage index under cyclic loads could be defined by equations (7) to (10)

1 - d = (1 - s_{c} d_{t}) (1 - s_{t} d_{c}) 0 \leq s_{c}, s_{t} \leq 1

(7)

s_{t} = 1 - ω_{t} r^{*} ({\bar{σ}}_{11}) 0 \leq ω_{t} \leq 1

(8)

s_{c} = 1 - ω_{c} (1 - r^{*} ({\bar{σ}}_{11})) 0 \leq ω_{c} \leq 1

(9)

r^{*} ({\bar{σ}}_{11}) = H ({\bar{σ}}_{11}) = {\begin{matrix} 1 if {\bar{σ}}_{11} > 0 \\ 0 if {\bar{σ}}_{11} < 0 \end{matrix}

(10)

where indexes d_t and d_c reflect the damaged condition of concrete in tension and compression process, respectively; w_t and w_c are stiffness recovery coefficients varying from 0 to 1. When the compression concrete is in tension again after reloading (w_t = 0), the ratio of the tensile stiffness to the compressive unloading–stiffness is (1 − d_t). And, the compressive stiffness could fully recover when the cracked concrete is in compression again (w_c = 1). The default values w_t = 0 and w_c = 1 are adopted in this article. The hysteretic constitutive model for concrete is shown in Figure 10(a).

Figure 10.

Hysteretic constitutive models: (a) concrete and (b) steel.

The kinematic hardening model is used for steel under the lateral reciprocating loading, and it is as shown in Figure 10(b). The Bauschinger effect is considered in the model, namely the development of plastic deformation in one direction could cause strength decrease in the opposite direction. This stress–strain constitutive curve has been adopted to simulate the behavior of steel–concrete composite structures by former researchers and has gained a good effect.

In Figure 10(b), E_s and f_y are the elastic modulus and yield strength of steel, respectively. The stress–strain relationship obeys the elastic loading–unloading criteria before yielding, while the phenomenon of steel strengthening appears during the elasto-plasticity stage. The modulus of steel in the hardening stage is αE_s and 0.01 is usually adopted as the coefficient α. The unloading rigidity of the model is the same with either loading or unloading rigidity at the elastic stage, both of which are E_s. After reaching the ultimate tensile strength f_u, the steel strength is no longer increased and the corresponding strain can be expressed by equation (11)

ε_{u} = \frac{f_{y}}{E_{s}} + \frac{(f_{u} + f_{y})}{α E_{s}}

(11)

Comparison between the test and simulation results

The load–displacement hysteretic curves from the FE analysis of specimens SRC1–SRC5 are displayed in Figure 4 along with the test values. Table 4 compares the experimental lateral load capacities and ultimate displacement with the results predicted from the FE analysis. It can be observed that the FE approach of SRC specimens gives an approximately equal load but a lower deformation capacity than those of the measured ones. However, the analysis results also have a reasonable accuracy.

Table 4.

Comparisons of experimental results with predictions based on the Finite Element Modeling(FEM) analyses.

Specimen	P _u (kN)	P _u-s* (kN)	P _u/P_u-s*		Δ_u (mm)	Δ_u-s* (mm)	Δ_u/Δ_u-s*
SRC1	174.86	176.14	0.99	Mean value: 1.00	22.62	21.12	1.07	Mean value: 1.10
SRC2	214.62	209.52	1.02		32.25	30.29	1.06
SRC3	238.50	220.00	1.08		34.33	31.26	1.10
SRC4	210.35	220.89	0.95		31.30	28.82	1.09
SRC5	160.32	170.25	0.94		24.26	20.95	1.16

P _u-s* and Δ_u-s* are the simulated lateral peak load and ultimate displacement, respectively.

The discrepancy for specimens lies in that the pinch phenomenon is not obvious for simulated hysteretic curves and the rigidity degeneration could not be reflected. This may be attributed to the following aspects: (1) the plastic damage model of concrete adopted affects the analytical hysteretic curves. The plastic damage model in ABAQUS is obtained on the basis of a series of ideal assumptions, but as a matter of fact, there is some difference between the assumption and the actual damage process for concrete; (2) an underestimate of the effects of the bond slip on constitutive relationship; (3) the loading condition and boundary conditions of the models are not completely consistent with the experiment; moreover, the factors such as temperature and eccentricity have not been considered.

Effect of axial compression ratio

Load–displacement skeleton curves of both new-type SRC compression-bending members with different axial compression ratios predicted from the proposed FE analysis are shown in Figure 11. It can be found that (1) the peak load P_u increases with an increase of axial compression ratio in range of 0–0.70, and P_u of the new-type SRC columns with 0.70 axial compression ratio is about 15.8% and 13.6% higher than that of specimens with 0.30 and 0.50 axial compression ratios, respectively. However, the load capacity of the specimen with 0.85 axial compression ratio decreases to some extent. (2) After the peak load, the skeleton curve quickly drops with the increase of axial load. It indicates that the ductility of specimens with lower axial compression axial is much better. New-type SRC columns are not very sensitive to the axial compression ratio compared with the ordinary ones, which may imply that the limit value of axial compression ratio suggested by Chinese specification JGJ 138 (JGJ 138-2001, 2001) is underestimated.

Figure 11.

Effect of axial compression ratio: (a) SRC columns with enlarging cross-shaped steel and (b) SRC columns with diagonal cross-shaped steel.

Effect of stirrup spacing

The stirrup provides effective confinement for core concrete, and stirrup spacing directly affects the seismic behavior of new-type SRC compression-bending members. Load–displacement skeleton curves of both new-type SRC columns corresponding to different stirrup spacing are shown in Figure 12 where the concrete strength and axial compression ratio are as constant as C40 and 0.7, respectively. It can be found that the bearing capacity and ductility are reduced along with increasing of stirrup spacing. Furthermore, the decrease extent of bearing capacity and ductility is greater when the stirrup spacing increases from 75 to 100 mm than that corresponding to the increase of spacing from 50 to 75 mm. This shows that stirrup has negligible effect on ductility of new-type SRC columns as long as the stirrup spacing does not exceed a certain value. It indicates that it is necessary to limit the maximum interval of stirrup spacing in the encrypted region, for example, a value of 100 mm is proposed for SRC columns according to Chinese specification JGJ 138 (JGJ 138-2001, 2010).

Figure 12.

Effect of stirrup spacing: (a) SRC columns with enlarging cross-shaped steel and (b) SRC columns with diagonal cross-shaped steel.

The stirrup ratios are respectively 0.98%, 0.66%, and 0.49% corresponding to the stirrup spacing 50, 75, and 100 mm. It can be seen from Figure 12 that when the stirrup ratio decreases from 0.98% to 0.49%, the bearing capacity is decreased by 16.8% and 10.0% for SRC columns with enlarging and diagonal cross-shaped steel, and 11.5% and 7.2% for ductility factor of the two improved SRC columns, respectively. It could be inferred that the seismic performance of new-type SRC columns is reduced along with decrease of stirrup ratio, and the compression-bending behavior of SRC column with diagonal cross-shaped steel is better than that with enlarging cross-shaped steel.

Effect of concrete strength

Load–displacement skeleton curves of new-type SRC compression-bending members with different concrete strengths are shown in Figure 13. It is clear that increasing of concrete strength leads to a greater shear capacity and a smaller deformability. The skeleton curve of SRC columns with diagonal cross-shaped steel has been less affected by the concrete strength compared with that consisting of enlarging cross-shaped steel. Descent part of skeleton curve from lower concrete strength shows better ductility than that from the higher concrete strength because the concrete with greater strength shows more brittle behavior. In other words, once tensile stress reaches the tensile strength of concrete, the cracks appear and expand. The shear bearing capacity of concrete thus falls rapidly.

Figure 13.

Effect of concrete strength: (a) SRC columns with enlarging cross-shaped steel and (b) SRC columns with diagonal cross-shaped steel.

It can be concluded that the ultimate bearing capacity could be promoted using higher strength concrete. On the contrary, the higher strength concrete results in a lower deformability and ductility due to brittle behavior. Compared with SRC columns with enlarging cross-shaped steel, the seismic behavior of SRC columns with diagonal cross-shaped steel is more uniform while the concrete strength changes.

Recommendation for design and in situ application

Based on above analysis, the conclusion can be drawn that limit values of axial compression ratio for new-type SRC columns could be higher than the ordinary ones. The determination of the ultimate axial compression ratio needs to ensure that SRC columns fail in the large eccentric compression failure mode and possess a better lateral resistance to satisfy a certain seismic ductility. The majority of existing literature works think that µ = 3.0 is suitable for ordinary SRC columns. Test and numerical simulation results show that the load capacity and ductility of new-type SRC compression-bending members are improved than that of ordinary ones. On the basis of this fact, it is thought that the ductility of new-type SRC columns can be larger than 3.0 and the recommended value is 3.5, with which the new-type SRC columns still have larger lateral resistance.

Ductility factors of new-type SRC compression-bending members with different axial compression ratio are summarized in Table 5. When the axial compression ratio is 0.85, the ductility factor could be 3.5 to satisfy the seismic resistance requirements. According to the Chinese code GB50011 (GB50011-2010, 2010), the values in Table 5 are suitable for seismic grade II and 0.85 could be referred to as ultimate axial compression ratio for grade II. The lower and higher bound values, 0.95 and 0.75, are respectively identified as the ultimate axial compression ratio for seismic grade I and grade III. Comparison of ultimate axial compression ratio for new-type and ordinary SRC columns is shown in Table 6.

Table 5.

Displacement ductility for new-type SRC compression-bending members.

SRC compression-bending members	n = 0.30	n = 0.50	n = 0.70	n = 0.85
With enlarging cross-shaped steel	5.50	5.28	4.95	3.85
With diagonal cross-shaped steel	5.35	4.75	4.40	3.62

SRC: steel reinforced concrete.

Table 6.

Comparison of ultimate axial compression ratio.

SRC columns	Seismic grade
SRC columns	Grade I	Grade II	Grade III
With new-type section steel	0.75	0.85	0.95
With ordinary section steel	0.65	0.75	0.85

SRC: steel reinforced concrete.

It can be concluded from Table 6 that ductility performance of SRC columns with new-type section steel is better than that with I- or H-shaped section steel. Following rules are given according to Chinese code GB50011 (GB50011-2010, 2010): (1) the values in Table 6 are suitable for SRC columns whose concrete strength grade is lower than C60, and (2) limit values of axial compression ratio in Table 6 decrease by 0.05 and 0.10 as suggested values for new-type SRC columns with concrete strength grades of C65–C70 and C75–C85.

Conclusion

The seismic behavior of improved (also known as “new-type”) SRC compression-bending members has been tested and simulated under the low reversed cyclic loading. The main results are summarized as follows:

The new-type SRC compression-bending members with shear span ratio of 4.0 display bending failure under combined loadings of compression, bending, and shear. Although yielding of the longitudinal reinforcement and local bucking of steel flanges happen, vertical bearing capacity of the new-type SRC columns could still keep better stability, and the specimens have the capacity of bearing load and resisting collapse at the elastic–plastic stage.

The hysteretic curves of the new-type compression-bending members are in plump shapes and have no significant pinch phenomenon, and the degeneration of bearing capacity is slow with the increase of the displacement. The ultimate drift ratio and the ductility factor are greater than 1/45 and 2.5, respectively, and the equivalent viscous damping coefficient is also larger than 0.45 for new-type SRC columns. It proves that the improved SRC columns exhibit better capacity of deformation and energy dissipation.

The steel arrangement is an important factor that affects the seismic behavior of new-type SRC compression-bending members. Under the same conditions, both the load capacity and deformation ability of SRC compression-bending members embedded with enlarging and diagonal cross-shaped steel are larger than that embedded with ordinary I-shaped section steel, and the average increasing rate is 26.6% and 30.3% for the two aspects. Thus the mechanical behavior of the SRC columns has obvious improvement with new-type section steel.

The effect law of axial compression ratio on the seismic behavior of new-type SRC compression-bending members is that n_t ≤ 0.42 (the corresponding design value is 0.7) has no obvious effect on bearing capacity and deformation behavior of specimens, while the ductility of the columns is decreased greatly by higher axial compression ratio.

Stirrup spacing and concrete strength also affect the seismic behavior of new-type SRC compression-bending members. The ductility of the new-type SRC columns decreases with the increase of stirrup spacing; the ductility factor will be reduced by 0.5 and 1.0–2.0 when the stirrup spacing changes from 50 to 75 mm and 100 mm, respectively. As the concrete strength is improved, the shear capacity increases but the deformability declines. By comparison, the seismic behavior of SRC columns embedded with enlarging cross-shaped steel is more influenced by the concrete strength.

The numerical model is validated by the test data, and the numerical results are in close agreement with the experimental ones. The ductility factor of 3.5 is defined to satisfy the seismic requirements, and the limit values of axial compression ratio for anti-seismic grade I, II, and III are 0.75, 0.85, and 0.95, respectively, for SRC columns with new-type section steel according to numerical simulation results. The suggested values can be used as a reference for the design of engineering.

Footnotes

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 described in this article was supported by Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT13089) and by the National Natural Science Foundation of China (No. 51178380 and No. 51108370). This support is sincerely appreciated.

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