Cyclic shear behavior and shear strength of steel tubed-reinforced-concrete short columns

Abstract

The steel jacketing approach is effective and economic for retrofitting reinforced concrete short column. Steel jacketed concrete columns are referred as steel tubed-reinforced-concrete columns when applying in new building structures. To investigate the cyclic shear behavior and shear strength of tubed-reinforced-concrete short columns with a large diameter-to-thickness/width-to-thickness ratio (D/t), four specimens were designed and tested under a constant axial compression combined with quasi-static cyclic lateral loading. Three main system parameters were considered in the test: (1) type of column cross section (circular and square), (2) D/t (106–150), and (3) axial load ratio (0.4 and 0.6). All the columns showed shear-failure mode during the tests, and the sheared plates of steel tubes yielded when the peak load had reached. The circular columns showed good ductility, while the square ones were just in opposite. Based on the analysis results, a simplified shear strength model for both circular and square columns is proposed, in which the relationship between cyclic shear strength and lateral drift ratio of the columns and the shear-resisting mechanisms for both shear and hoop stresses of the tube are considered.

Keywords

composite column cyclic behavior shear strength steel jacketed concrete column steel tubed-reinforced-concrete column

Introduction

Concrete-filled steel tubes (CFSTs) have been used extensively throughout the world in building and transportation structures as columns, piers, braces, truss elements, and foundation components. Steel tubed-reinforced-concrete (TRC) columns shown in Figure 1(a) and (b) are a kind of special CFST columns, in which the outer thin-walled steel tube does not pass through the beam–column joint and thus can avoid the direct transfer of an axial load and maximize the confinement effect from the steel tube (He et al., 2017; Liu et al., 2009; Tomii et al., 1985). TRC columns are similar to steel jacketed concrete columns. In TRC columns, placement of reinforcement cages is required to resist tensile forces and flexural moments. The steel tube can serve as the formwork for casting the concrete and hence eases the construction work. In recent years, TRC columns have become more popular in constructing new building structures and bridge piers (Chen et al., 2012). Recently, TRC columns have been successfully applied in a high-rise building-Harbin Poly Technology Building, China. They are served as columns of the basement and the lower three stories (Figure 1(c)).

Figure 1.

Tubed RC columns: (a) circular shape, (b) square shape, and (c) TRC columns in Harbin Poly Technology Building, China.

Current researches about circular TRC columns have been focused primarily seismic flexural behavior. Test results showed that the load-carrying capacities, deformational behavior, and energy dissipation capacity of the circular TRC columns subjected to flexural failure were superior (Fam et al., 2004; Han et al., 2005; Prion and Boehme, 1994). As for square TRC columns, the infilled concrete is non-uniformly confined and the effectiveness of confinement is much reduced compared with circular steel tubes. The test results (Aboutaha and Machado, 1999; Zhou and Liu, 2010) showed that the deterioration of response was inevitable for square or rectangular columns unless a thick steel tube was employed, particularly for columns a high axial load ratio. Thus, elliptical steel jackets (Priestley et al., 1994b) and partially stiffened square/rectangular steel jackets in the plastic hinge region (Liu et al., 2011; Sakino and Sun, 2000a, 2001; Xiao and Wu, 2003) were adopted to enhance the confinement efficiency and seismic behavior of square/rectangular TRC columns. However, to date, a very few shear tests have been conducted.

In steel confined concrete under shear, concrete would initiate shear cracks at certain axial strain. After the onset of shear cracks, steel tubes will be rapidly mobilized. In confined concrete under compression or bending, concrete will also initiate tensile splitting crack at certain axial strain. After the onset of splitting cracks, the lateral–axial strains development will be more rapid. The above two phenomena are similar and closely related to the shear strength (Dong et al., 2015; Kwan et al., 2015; Priestley et al., 1994a). By considering the tube acting as a series of independent hoops and adopting the truss-action strength of transverse reinforcement, researchers (Chen et al., 2011, 2012; Priestley et al., 1994a; Sakino and Sun, 2000; Sun and Miyake, 2006) proposed the methods for shear design. However, the shear force resisting mechanism of TRC columns is different from that of RC columns. For a more rigorous estimation, the tube can resist shear force through the tensile stress of a truss model, and the direct shear stress (Liu et al., 2011).

The above literature review indicates that research on shear behavior of TRC columns is still limited, especially for tubes with large diameter-to-thickness/width-to-thickness ratio (D/t ⩾ 100, where D is the cross-sectional diameter/width and t is the thickness of steel tube). Furthermore, to the best of the authors’ knowledge, no experimental work on the cyclic shear failure of circular TRC columns is available. To address these research gaps, this article describes an experimental investigation on the cyclic shear behavior of both circular and square TRC columns with large D/t of 134 and 150. Specifically, the shear-failure mechanisms, the stress state of the steel tube under cyclic loads and the effect of axial load on the composite response are discussed. Moreover, a simplified shear strength model for both circular and square columns is proposed, in which the relationship between cyclic shear strength and lateral drift ratio of the columns and the shear-resisting mechanisms for both shear and hoop stresses of the tube are considered instead of considering the tube acting as a series of independent hoops only.

Experimental program

Experimental setup

As shown in Figure 2, each column was rigidly supported by the rigid beams at the top and bottom, thus simulating the column in a real frame. The steel tube was terminated at 15 mm away from each end of the column to avoid the direct bearing of load. The stirrups in the columns were used to erect the longitudinal reinforcement.

Figure 2.

Details of specimens (mm).

The schematic of the test setup is shown in Figure 3(a). The test rig consists of a lateral reaction system supporting the lateral hydraulic actuator and a vertical system supporting the vertical hydraulic actuator. The lateral reaction system has a rigid reaction wall, a 630 kN hydraulic actuator, and a stiff L beam. The vertical reaction system includes reaction racks, two rollers, a 2500 kN hydraulic jack, a 2000 kN load cell, and distribution beams.

Figure 3.

Test setup and instrumentation layout: (a) schematic of column test setup and (b) instrumentation layout.

Figure 3(b) depicts the instrumentation layout. Two LVDTs were used to measure the horizontal displacement at the top of the column. Three strain gauges were placed at the mid-height of both sheared plates of the tube (Figure 4): one transverse, one longitudinal, and one 45° diagonal strain gauges.

Figure 4.

Strain gages layout: (a) C-55-1.3-150 and (c) S-55-1.5-134.

Details of specimens and test matrix

The circular and square TRC columns were designed with the same cross-sectional area (40,000 mm²), tube thickness (1.49 mm), longitudinal reinforcement ratio (4.02%), and specimen height (600 mm), so the diameter and width of the cross sections were 226 and 200 mm for circular and square columns, respectively. Consequently, D/t ratios of the circular and square steel tubes were 150 and 134, respectively. The aspect ratios of the circular and square columns were 1.3 and 1.5, respectively.

A summary of the specimens is presented in Table 1. In the group designation, the first letter represents circular (C) or square (S) TRC specimens; the second number (55 MPa) represents the nominal cubic strength of concrete (the concrete strength class is stipulated by nominal cubic strength of concrete in Chinese standard), noting that the measured concrete compressive prismatic strength f_co is 36.6 MPa; the third number (1.3 and 1.5) represents the aspect ratio λ = H/2D, where H is the height of the column and D is the cross-sectional diameter/width; and the fourth number (134 and 150) means the diameter-to-thickness/width-to-thickness ratio of the tube D/t. The specimen designation has the fifth number implying the axial load ratio n₀ (40% or 60%) defined as n₀ = N/(f_coA_g), where N is the axial load applied during the test and A_g is the gross area of the cross section. The properties of steel tubes and rebars are listed in Table 2.

Table 1.

Parameters, nomenclature, and failure modes of the specimens.

Group	Specimens	H (mm)	D (mm)	λ	D/t	α	f_co (MPa)	n ₀	Failure mode
C-55-1.3-150	C-55-1.3-150-4	600	226	1.3	150	2.7%	36.6	0.4	Shear
	C-55-1.3-150-6							0.6
S-55-1.5-134	S-55-1.5-134-4	600	200	1.5	134	3.0%	36.6	0.4	Shear
	S-55-1.5-134-6							0.6

α is the steel ratio of the steel tube.

Table 2.

Properties of steel tubes and rebars.

Type	Thickness (or diameter) t (mm)	Yield strength f_y (MPa)	Ultimate strength F_u (MPa)
Tube	1.49	314.1	414.9
Longitudinal rebars	16.36	357.0	554.5
Stirrups	8.02	316.4	458.3

Loading regime

The specimen was pre-loaded to 300 kN which was then decreased to 0 before the test, and then an axial load was applied again until the specified N = n₀f_coA_g. During the test, a constant axial load N = n₀f_coA_g was maintained by re-adjusting the hydraulic jack.

Because the force–deformation relation of RC members and TRC members may not have a well-defined yield point, there has been difficulty in reaching consensus within the research community as to the appropriate definition of yield and ultimate loads/displacements, especially for specimens with shear failure (Park, 1988). In this article, the yield load was defined as 75% of the peak load which was calculated by a preliminary finite element method before the test. Before the specimen yielded, the applied lateral load was controlled by a force and one loading cycle was performed at each force level. A total of four force magnitudes were considered: 50 kN, 100 kN, 150 kN, and the yield load (note: 50 kN = 0.20–0.25 times the yield load). Later, two other loading cycles were repeated using the predicted yield force. The loading was then switched to a displacement control mode where the controlling horizontal displacement was set equal to 2, 3, 4,…, times the measured displacement corresponding to 75% of the anticipated peak load until the specimen failed. Two loading cycles were also repeated at each displacement level. In each loading cycle, a pull (positive loading) was exerted first followed by a push (negative loading), as shown in Figure 5.

Figure 5.

Definition of sheared plate of and loading direction.

Test results and discussions

Damage and failure mode

Shear-failure mode was seen in Group C-55-1.3-150 and Group S-55-1.5-134 (Figure 6(a) to (d)). The specimens did not show a clear failure pattern during the test due to the existence of tube. When the peak load was reached, the concrete cover at the gaps between the tube and the rigid beam crushed and the RC core column dilated, but the tube did not buckle. After the test, the tubes were removed and several cracks were observed at the mid-height of the shear plane. The cracks were inclined at about 36°–38° along the specimen’s longitudinal direction for Specimen C-55-1.3-150-4, 24°–33° for Specimen C-55-1.3-150-6, and 31°–33° for the square columns. The specimens with higher axial load ratio (C-55-1.3-150-6 and S-55-1.5-134-6) displayed more cracks, steeper inclined angle, and more severe damage.

Figure 6.

Failure patterns of the beam–columns: (a) C-55-1.3-150-4, (b) C-55-1.3-150-6, (c) S-55-1.5-134-4, (d) S-55-1.5-134-6.

Force–displacement relationship

Figure 7 shows the relationships between the measured lateral force and the displacement for all specimens. The hysteresis loops for Specimen C-55-1.3-150-4 (Figure 7(a)) were stable and not significantly pinched. They were almost identical before the peak load point at the two same-displacement cycles. This showed that the circular tube efficiently improved the confinement effect of square tubes. As for Specimen C-55-1.3-150-6 (Figure 7(b)) and the square specimens (Figure 7(c) and (d)), degradation of stiffness and residual deformation were observed during the unloading stage in every second cycle after the cracks of concrete initiated. After the peak load, the strength and stiffness degradation became noticeable, especially for square TRC columns.

Figure 7.

Lateral force versus displacement relationships of all specimens: (a) C-55-1.3-150-4, (b) C-55-1.3-150-6, (c) S-55-1.5-134-4, and (d) S-55-1.5-134-6.

Lateral load-carrying capacity and deformation capacity

Figure 8 depicts the envelope curves of lateral force versus drift ratio of all specimens. The drift ratio is calculated as R = Δ/H, where H denotes the height of the specimen.

Figure 8.

Envelope curves of lateral force versus drift ratio.

Table 3 lists the yield displacement Δ_y, yield load P_y, peak displacement Δ_u, peak load P_u, ultimate displacement Δ_0.85, and ultimate drift ratio R_0.85 values for the specimens. The values shown in the table are meant for both push and pull directions. Δ_0.85 and R_0.85 are defined as the post-peak displacement and the post-peak drift ratio at the instant when the lateral load decreases to 85% of the peak lateral load, respectively. The displacement ductility ratio μ_Δ of the specimens is calculated by μ_Δ = Δ_0.85/Δ_y. P_y and Δ_y values can be determined from the geometrical method, as shown in Figure 9.

Table 3.

Lateral load-carrying capacities, deformation capacities, and ductility ratios of the specimens.

Specimens	P_y (kN)	P_u (kN)	P_y/P_u	Δ_y (mm)	Δ_u (mm)	Δ_0.85 (mm)	Δ_u/Δ_y	μ _Δ	R _0.85
C-55-1.3-150-4	258.1	300.8	0.86	7.10	20.73	43.9	2.92	6.18	7.3%
C-55-1.3-150-6	282.0	344.5	0.82	4.99	16.29	28.0	3.26	5.61	4.7%
S-55-1.5-134-4	216.5	283.3	0.76	6.92	20.1	25.3	2.91	3.66	4.3%
S-55-1.5-134-6	242.2	297.2	0.81	5.89	10.2	15.1	1.73	2.56	2.5%

Figure 9.

The geometrical method for determining the yield point.

Among all two groups, the specimens with higher axial load ratio showed a greater lateral stiffness and bearing capacity within the range of test parameters considered. The peak loads for Specimen C-55-1.3-150-6 were 12.6% greater compared to Specimen C-55-1.3-150-4; the peak load for Specimen S-55-1.5-134-6 was 4.9% greater compared to Specimen S-55-2-134-4. However, the specimens under higher axial load were accompanied by the rapid strength and stiffness degradation when a shear failure occurred. The lateral load decreased dramatically to 60% and 50% of the peak value at the end of the test for Specimens S-55-1.5-134-4 and S-55-1.5-134-6, respectively. The ratio of yield load to peak load ranged from 0.76 to 0.86.

Larger the axial load was, lower values of μ_Δ and θ_0.85 were. Under the same axial load, EuroCode 8 (European Committee for Standardization (CEN), 2004) stipulates that the displacement ductility ratio shall be not less than 4.0 for MDC (medium ductile columns) RC columns, while the Chinese code (GB 50011-2010) (CMC, 2010) states that the ultimate drift ratio is not less than 0.02 for ductile RC columns. The test results show that the circular shear-failure specimens satisfy ductility requirements, but the square shear-failure specimens do not meet the displacement ductility requirement of the Eurocode. It can be concluded that the thin-walled circular tubes with D/t = 150 could provide enough confinement for the RC columns. However, the deformation capacities for square TRC specimens without stiffeners subjected to shear failure were poor, especially for specimen under high axial load ratio. The cyclic shear behavior of stiffened square TRC specimens would be further studied

Energy dissipation capacity

The area enclosed by a hysteresis loop is the energy dissipated by the specimen. Figure 10 shows the energy dissipation curves for all specimens, in which E_total is the cumulative area of the hysteresis hoops, that is, the cumulative energy dissipated. In each studied group, the specimens with lower axial load ratio experienced larger ultimate displacements, resulting in greater total energy dissipation.

Figure 10.

Energy dissipation curves.

Stress analysis of steel tube

The steel tube’s strains can be averaged due to the symmetrical arrangement of strain gauges (Figure 4). The relationship between the experimentally measured strains ε_v, ε_h, ε_45°, and shear strain γ_xy can be expressed as

ε_{45^{\circ}} = \frac{ε_{h} + ε_{v}}{2} + \frac{γ_{xy}}{2}

(1)

where ε_h is the horizontal strain, ε_v is the vertical strain, $ε_{45^{\circ}}$ is the diagonal strain, and γ_xy is the shear stain.

The elasto-plastic analysis method (Zhang et al., 2005) was adopted to analyze the stress state on a steel tube. Figure 11 shows the load–strain and load–stress curves for the TRC columns, in which σ_v and σ_h are the vertical and transverse steel stresses at the mid-height of the tube; τ is the shear stress; σ_z is the equivalent stress.

Figure 11.

Load–strain and load–stress relationships of tubes: (a) C-55-1.3-150-4 load–strain at mid-height, (b) C-55-1.3-150-4 load–stress at mid-height, (c) S-55-1.5-134-4 load–strain at mid-height, and (d) S-55-1.5-134-4 load–stress at mid-height.

As for the circular specimens experiencing shear failure (Figure 11(a) and (b)), a small longitudinal stress (–50 MPa for C-55-1.3-150-4) was induced by the adhesion and friction between the steel tube and the concrete during the axial loading stage. The shear strain and stress increased with the increment of lateral load. The hoop strain or stress did not increase until the lateral load reached the bearing capacity of the core RC column. Then, the shear and hoop strains or stresses increased dramatically. The vertical compression stress decreased and even reversed to tension. The load–strain and load–stress curves of Specimen C-55-1.3-150-6 follow a similar trend to that of Specimen C-55-1.3-150-4. The square specimens experiencing shear failure behave a similar trend in stress state except that both the shear and hoop strains (stresses) did not increase until the lateral load reached the bearing capacity of the core RC column for Specimens S-55-1.5-134-4 and S-55-1.5-134-6 (Figure 11(c) and (d)). The difference is because the square tube and core concrete could not bear lateral load jointly until the core concrete column cracked.

At the peak load, the sheared plates of steel tubes reached the yield point for the specimens subjected to shear failure. The stress components for the sheared plate of the shear-failure specimens at the peak load, as shown in Table 4, were utilized to determine the key parameters of the simplified shear strength model described in section “Simplified model for shear strength of TRC columns.”

Table 4.

Experimental results at the peak load.

Specimens	Loading direction	Peak load	Load when tube yields	σ_v (MPa)	σ_h (MPa)	τ (MPa)	σ_z (MPa)
C-55-1.3-150-4	Negative	−301.7	−301.7	26.6	164.3	153. 7	306.9
	Positive	298.2	294.2	66.7	201.2	146.3	309.3
C-55-1.3-150-6	Negative	−344.5	−344.0	26.3	179.3	152.6	313.1
	Positive	339.8	330.8	47.3	131.4	166.8	311.1
S-55-1.5-134-4	Negative	−301.7	−274.1	36.2	126.3	169.0	313.6
	Positive	298.2	286.9	53.1	130.7	167.2	311.2
S-55-1.5-134-6	Negative	−344.5	−290.1	60.9	143.2	166.0	313.3
	Positive	339.8	304.3	26.5	178.7	148.5	306.7

The composite response and failure mechanisms

The experimental results show that the steel tube plays an important role in resisting the external lateral forces. The concrete forms an ideal core to withstand the external loading; it prevents the local buckling of the steel tubes with large D/t ratio. The TRC structures are therefore expected to have a good seismic performance through the greater inelastic deformation and energy dissipation.

According to the lateral load–strain/stress analyses of the shear-failure circular specimens, the tube resisted the lateral load through shear stress together with the core RC column at the beginning. When the applied load reached the shear capacities of core RC columns, the shear-resisting contribution of core RC columns would be degraded with an increasing displacement due to the widening of cracks, resulting in a reduced aggregate interlocking (Priestley et al., 1994a). To resist the increasing external load and the load released from the cracked RC columns, the shear and hoop stresses of the tube may increase largely to provide the shear-resisting force. The shear stress resists the lateral load by working with the core concrete columns, whereas the hoop stress withstands the lateral load by a truss model and provides the confinement to the RC columns to constrain the shear cracks from widening and increases the compressive strength of concrete. The circular TRC columns reached the peak load when the sheared plates of tubes yielded. The steel tube could continually provide an effective confinement to concrete and constrain the shear cracks from widening due to the good ductility of steel. As a result, the circular TRC columns subjected to shear failure show good ductility and deformation capacity.

However, there are a few differences between the unstiffened square TRC columns and the circular TRC columns subjected to shear failure. The unstiffened square tube resisted the lateral load through the shear stress together with the core RC column until the applied load reached the shear strength of the RC column. The square TRC columns reached the peak load when the sheared plates of tubes yielded. After the peak load, the applied lateral load decreased quickly due to the reduced confinement of the square tube.

The benefits from an appropriate stiffening method for square tubes are twofold. First, the shear stress of the square tube is able to carry the lateral load through a coordination work with the core concrete columns once the lateral load is applied. Second, the confinement effect for the concrete in the plastic hinge region is significantly improved. The circular and stiffened square steel jacket acts as the passive confinement reinforcement to restrain the dilation of the concrete. As such, the crushing and spalling-off of concrete are prevented, thus enhancing the compressive strength and effective ultimate compression strain.

Simplified model for shear strength of TRC columns

By considering the tube acting as a series of independent hoops and adopting the truss-action strength of transverse reinforcement, researchers (Chen et al., 2011, 2012; Priestley et al., 1994a; Sakino and Sun, 2000; Sun and Miyake, 2006) proposed that the total shear strengths of TRC columns were provided by transverse steel shear-resisting mechanisms, concrete shear-resisting mechanisms, and axial load. However, based on analysis mentioned above and the authors’ previous studies (Liu et al., 2011), the tube can resist shear force through the tensile stress of a truss model, and the direct shear stress.

Thus, the total nominal shear strength V_A of a TRC column can be predicted by

V_{A} = V_{c} + V_{s} + V_{p} + V_{τ} + V_{σ h}

(2)

where V_c and V_s are the concrete shear-resisting and stirrups shear-resisting mechanisms, respectively; V_p is the shear capacity provided by the axial load through an arching action; V_τ and V_σh are the shear and transverse stress of tube shear-resisting mechanisms, respectively.

Since the stirrups are normally spaced largely to erect the longitudinal reinforcement, equation (2) can be expressed as

V_{A} = V_{c} + V_{τ} + V_{σ h} + V_{p}

(3)

Concrete shear-resisting mechanisms V_c

The concrete mechanisms V_c can be expressed as (Priestley et al., 1994c)

V_{c} = α β γ \sqrt{{f_{c}}^{'}} (0.8 A_{g})

(4)

where $A_{g}$ is the column gross section area, α is a factor accounting for the columns shear span-to-depth ratio = 3 – M/(VD), 1 ⩽ α ⩽ 1.5 (M is the bending moment, V is the shear force, and D is the section depth); β is a modifier factor accounting for the longitudinal steel ratio = 0.5 + 20ρ₁ ⩽ 1 ( $ρ_{l}$ is the longitudinal steel ratio); γ is the parameter reflecting the strength reduction of the concrete shear-resisting mechanism which decreases with an increasing ductility, as shown in Figure 12; ${f_{c}}^{'}$ is the concrete compressive cylindrical or prismatic strength.

Figure 12.

γ versus displacement ductility μ.

Shear stress of tube shear-resisting mechanisms V_τ

Figure 13 depicts the shear stress in the sheared plate of both circular and square tubes. The maximum shear stress of the sheared web (τ_max) can be calculated by

τ_{max} = \frac{V_{τ} S}{I (2 t)}

(5)

Figure 13.

Shear-resisting mechanism of the shear stress of a steel tube: (a) circular tube and (b) square tube.

Thus, $V_{τ}$ can be calculated by

For circular tubes, V_{τ} = \frac{I \cdot 2 t}{S} τ_{x} = π rt \cdot τ_{\max} = \frac{1}{2} A_{s} τ_{\max}

(6a)

\begin{array}{l} For square tubes, V_{τ} = 2 \cdot \frac{D^{2} t + \frac{1}{3} D^{2} t}{D t + \frac{1}{2} D t} \cdot t \cdot \\ τ_{\max} = V_{τ} = 2 \cdot \frac{8}{9} \cdot D \cdot t \cdot τ_{\max} \end{array}

(6b)

where I and S are the moment of inertia and area moment of the tubes around x-axis, respectively.

The maximum hoop stress $σ_{h}$ of the circular tube can be taken as 0.5f_y based on the obtained experimental results (f_y is the yield strength of steel tube). The maximum shear stress $τ_{\max}$ equals to 0.5f_y based on the von Mises yield criteria when the vertical stress is considered as zero. A modifier index of 1.5 is adopted to account for the elasto-plastic distribution of shear stresses, namely

V_{τ} = 1.5 \times \frac{1}{2} A_{s} τ_{\max} = 0.375 π Dt f_{y}

(7a)

For square tubes, the transverse stress at the peak load $σ_{h}$ of a square tube can be taken as 0.4f_y instead based on the experimental results. The maximum shear stress $τ_{\max}$ equals to 0.53f_y based on the von Mises yield criteria when the vertical stress is considered as zero. From the test results of Zhou and Liu (2010) and Liu et al. (2011), square tubes could not be fully used without an appropriate stiffening method when involving the shear-resisting mechanism. To account for this effect, an empirical factor h_e, the effective width, is employed. $V_{τ}$ can be obtained by

V_{τ} = \frac{8}{9} h_{e} (2 t) τ_{x} = 0.94 h_{e} t f_{y}

(7b)

where h_e = min(2D/t, D) (without stiffeners) or h_e = D (with stiffeners).

Transverse stress of tube shear-resisting mechanisms V_σh

By considering the tube acting as a series of independent stirrups and adopting the truss mechanism strength of stirrups, $V_{σ h}$ can be obtained as follows (Figure 14):

For circular tubes (Kowalsky and Priestley, 2000)

V_{σ h} = 0.5 π t f_{σ h} D' \cot θ

(8a)

For square tubes

V_{σ h} = 2 t f_{σ h} D' \cot θ = 0.8 f_{y} tD' \cot θ

(8b)

where the transverse stress $f_{σ h}$ at the peak load is taken as 0.5f_y and 0.4f_y for circular and square tubes, respectively; θ is the assumed inclination angle between a shear crack and the vertical column axis; D′ is the width of the confined core diameter given by

D' = D - cov - c

(9)

in which cov is the concrete cover measured to the outside of the longitudinal reinforcement and c is the neutral axis depth.

Figure 14.

Shear-resisting mechanism of the hoop stress of a circular tube: (a) elevation and (b) plan.

The following equation for θ is adopted in this article, which is based on the principle of minimum energy (Kim and Mander, 2007)

θ = \tan^{- 1} {(\frac{(\frac{ρ_{v}}{ρ_{t}}) (\frac{A_{v}}{A_{g}})}{0.61 Λ})}^{\frac{1}{4}}

(10)

where ρ_v is the volumetric ratio of shear steel to concrete = 2t/D, ρ_t is the volumetric ratio of longitudinal steel to concrete = A_st/A_g (A_st is the sectional area of longitudinal steel), A_v is the shear area of concrete section, A_g is the gross sectional area of columns, and Λ is an end fixity parameter (Λ = 1 for fixed-pinned ends and Λ = 2 for fixed–fixed ends).

Shear strength provided by axial load V_p

The axial load component V_p recognizes the enhanced shear strength provided by axial load N. The shear capacity provided by the axial load can be predicted as

V_{p} = KN

(11)

where K = 0.07 when considering seismic effects or K = 0.056 when N ⩾ 0.6f_cA_g (f_c is compressive strength of the concrete and A_g is the gross area of the cross section) and N should be taken as 0.6f_cA_g.

Based on the analysis results, the total nominal shear strength V_A of the circular and square TRC columns can be predicted from the combination of equations (4), (7), (8), and (11). V_A becomes as

V_{A} = α β γ \sqrt{{f'}_{c}} (0.8 A_{g}) + 0.3 π Dt f_{y} + 0.3 π t f_{y} D' \cot θ + KN

(12a)

V_{A} = α β γ \sqrt{{f'}_{c}} (0.8 A_{g}) + 0.94 h_{e} t_{w} f_{y} + 0.8 f_{y} tD' \cot θ + KN

(12b)

where the shear-resisting mechanisms of concrete, shear stress, hoop stress, and axial load are all included.

Table 5 summarizes the comparisons between the predicted nominal shear strengths and the test results of circular TRC columns. The predicted nominal shear strengths V_cal1 and V_cal2 were obtained from Sun and Miyake (2007) and equation (12a), respectively. The predictions of Sun and Fujinaga (2007) are slightly overestimated for cyclically loaded specimens and are conservative for monotonically loaded specimens without an axial load. For equation (12a), the mean value of 0.91, root-mean-square deviation of 0.045, and correlation coefficient of 0.996 are derived. Table 5 lists the comparisons between the predicted nominal shear strengths and the test results of square TRC columns. The predicted nominal shear strengths V_cal1 and V_cal2 were obtained from Sakino and Sun (2000) and equation (12b), respectively. For equation (12b), the mean value of 0.936, root-mean-square deviation of 0.047, and correlation coefficient of 0.997 are derived. For Sakino and Sun’s (2000) model, the predicted results are generally in good agreement with the test results while slightly more conservative. It should be noted that the designation method of all the specimens in Table 5 was in accord with this article.

Table 5.

Comparisons between the predicted shear strengths and the test results (circular columns and square columns).

Specimens	n ₀	V_e (kN)	V_cal1 (kN)	V_cal1/V_e	V _cal2	V_cal2/V_e	Loading conditions	Sources
Circular columns
C-55-1.3-150-4	0.4	300.0	316.2	1.05	265.4	0.88	Cyclic	This article
C-55-1.3-150-6	0.6	339.0	342.5	1.01	286.9	0.84	Cyclic	This article
C-60-1.3-225-0(16)	0	1094.0	697.6	0.64	973.2	0.89	Monotonic	Chen et al. (2012)
C-60-1.3-225-0(12)	0	978.5	702.1	0.72	942.2	0.96
C-60-1.6-225-0(16)	0	987.4	695.6	0.70	904.3	0.92
C-60-1.6-225-0(14)	0	916.4	699.6	0.76	887.7	0.97
Square columns
S-55-1.5-150-4	0.4	280.5	218.6	0.78	251.6	0.90	Cyclic	This article
S-55-1.5-150-6	0.6	297.2	242.1	0.81	280.3	0.94	Cyclic	This article
S-60-1.5-67-6	0.55	319.9	221.6	0.73	293.9	0.97	Cyclic	Zhou and Liu (2010)
S-60-1.5-106-4	0.35	301.6	248.8	0.66	326.9	0.87	Cyclic	Liu et al. (2011)
S-60-1.43-300-0	0	1481.0	1132.9	0.76	1391.4	0.94	Monotonic	Chen et al. (2011)
S-60-1.43-150-0	0	1472.0	1225.0	0.83	1436.4	0.98
STU-60-1.43-300-0	0	1567.0	1132.9	0.72	1391.4	0.89
S-30-1-115-0.33	0.33	364.0	321.6	0.88	373.8	1.03	Cyclic	Sakino and Sun (2001)
S-30-1-80-0.33	0.33	406.0	322.7	0.79	318.6	0.78
S-30-1-58-0.33	0.33	390.0	332.9	0.85	333.2	0.85
S-30-1-42-0.33	0.33	396.0	346.3	0.87	359.6	0.91
S-30-1-26-0.33	0.33	410.0	346.3	0.84	378.3	0.92

Summary and conclusion

This article describes the experimental and theoretical analysis on the cyclic shear behavior of circular and square TRC columns. The following major findings and conclusions are offered:

All the four columns showed shear-failure mode: ductile shear failure occurred for the circular TRC short columns, while brittle shear failure happened for the square ones. The stiffness and lateral strength of both circular and square TRC columns tended to increase with an increment in axial load, whereas the ductility index tended to decrease. The strength of the square column degraded faster than that of the circular one after the peak load due to the reduced confinement. The sheared plate of a tube yielded at the peak load.

The circular tube of a circular TRC column resisted the lateral load through shear stress together with the core RC column once the lateral load applied, while the square one could not cooperatively work with the core RC column to resist the lateral load until the lateral load reached the shear strength of the core RC column. This also shows that the composite response between circular tube and concrete is more effectively.

Both transverse and shear stresses of the tube could provide shear load-carrying capacities. Design formulas based on a simplified shear strength model were proposed to calculate the shear strength of both circular and square TRC columns. The predictions from the formulas are in good agreement with the experimental results.

Footnotes

Acknowledgements

The authors greatly appreciate the financial supports provided by the National Natural Science Foundation of China (nos 51438001 and 51378068), Chongqing Research Program of Basic Research and Frontier Technology (no. cstc2016jcyjA0284), and China Scholarship Council. The opinions expressed in this article are solely of the authors, however.

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) received no financial support for the research, authorship, and/or publication of this article.

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Cyclic shear behavior and shear strength of steel tubed-reinforced-concrete short columns

Abstract

Keywords

Introduction

Experimental program

Experimental setup

Details of specimens and test matrix

Loading regime

Test results and discussions

Damage and failure mode

Force–displacement relationship

Lateral load-carrying capacity and deformation capacity

Energy dissipation capacity

Stress analysis of steel tube

The composite response and failure mechanisms

Simplified model for shear strength of TRC columns

Concrete shear-resisting mechanisms Vc

Shear stress of tube shear-resisting mechanisms Vτ

Transverse stress of tube shear-resisting mechanisms Vσh

Shear strength provided by axial load Vp

Summary and conclusion

Footnotes

Acknowledgements

Declaration of Conflicting Interests

Funding

References

Concrete shear-resisting mechanisms V_c

Shear stress of tube shear-resisting mechanisms V_τ

Transverse stress of tube shear-resisting mechanisms V_σh

Shear strength provided by axial load V_p