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Study on the Shear Capacity of an SRC-RC Transfer Column

Study on the Shear Capacity of an SRC-RC Transfer Column The truncation of steel sections in Steel Reinforced Concrete-Reinforced Concrete (SRC-RC) transfer columns may lead to a distortion in the internal force transmission. A refined finite element model of SRC-RC transfer columns was developed in this study taking into consideration the effects of different confinement around concrete. According to the internal force and deformation characteristics of a transfer column, the shear capacity of the SRC-RC transfer column was investigated, and the results compared well with existing experimental results. Extensive parametric studies were conducted and crosschecked with the current code. It is found that the current specification may not always ensure the shear failure capacity since it is intrinsically affected by both the internal force and deformation characteristics of the transfer column. A modified formula has been proposed, by which more rational design of structural members may be expected, brittle failure can be avoided and ductility will be improved. Keywords: SRC-RC transition column; transmission distortion; finite element model; shear capacity 1. Introduction dominated by shear failure, and the flexural failure A Steel Reinforced Concrete-Reinforced Concrete and bond failure were mainly observed in specimens (SRC-RC) transfer column behaves as the connection with greater extending height of steel. The influence between the upper and lower members by extending of different structural measures on the seismic the steel of the SRC or steel column to the adjacent performance of transfer columns was studied through members. Suzuki et al. (1999) investigated the the cyclic tests of 8 SRC-RC transfer columns by Zhao influence on the mechanical behavior of transfer and Shao (2010). columns by extending the height of steel. Low In the Chinese Code for Design of Concrete frequency cyclic tests of 3 transfer columns and 1 RC Structures GB 50010-2010, only a few structural column were conducted to compare their behaviors. measures are presented. However, calculation methods Konno et al. (1998) tested 13 specimens of transfer of transfer columns, such as formulas for flexural members under cyclic load to obtain the seismic capacity and shear capacity, are not provided. The performance of transfer columns. Cyclic tests of 7 shear capacity formula for transfer columns in the SRC-RC transfer columns were performed by Kimura Japanese Code, which is derived from the ultimate et al. (1998), to evaluate the effects of the enhanced flexural capacity, does not consider all kinds of failure reinforcement and extending the height of steel on the modes of transfer columns (Feng et al., 1998). Thus, seismic performance and mechanical behavior of the it is difficult for engineers to evaluate the performance transfer columns. Xue et al. (2010) and Wu et al. (2012) of transfer columns in structural design. Though tested 21 SRC-RC transfer columns under cyclic load. several experimental studies have been conducted, The results found that the specimens were mostly no systematic results have been achieved because the number of tests and experimental conditions are limited. To generally investigate the behavior of *Contact Author: Wei Huang, Lecturer, SRC-RC transfer columns, the constitutive model Department of Mechanics and Engineering Structure, of concrete, which considers the effect of different Wuhan University of Technology, confinements is used according to the principle of 122 Luoshi Road, Wuhan 430040, China effective additive confined stress. Then, the finite Tel: +86-18807199155 Fax:+86-21-65982668 element model for an SRC-RC transfer column is E-mail: whuang@whut.edu.cn established in ABAQUS. Then, the security and ( Received April 3, 2017 ; accepted July 23, 2018 ) rationality of the shear capacity calculation for SRC- DOI http://doi.org/10.3130/jaabe.17.557 RC transfer columns are explored. Journal of Asian Architecture and Building Engineering/September 2018/564 557 2. Finite Element Modeling The master surface in the contact property is defined Finite element analysis (FEA) was performed by as the concrete surface surrounding the steel. When the ABAQUS to develop reliable models that can simulate two surfaces remain in contact, the slave surface can be the behavior of SRC-RC transfer columns, based on displaced in relation to the master surface based on the experimental results. coefficient of friction between the two surfaces, which 2.1 Modeling Approach is taken as 0.25 (Ellobody et al., 2011). Moreover, The SRC-RC transfer column studied in this paper the reinforcements were embedded into the concrete is composed of two parts, the SRC part and the RC using the *Embedded Constraint option in ABAQUS, part. The SRC part includes four components, the steel assuming a perfect bond. section, longitudinal reinforcement bars, transverse 2.3 Material Modeling of Steel Section and reinforcement bars and concrete. Furthermore, the Reinforcement Bars RC part is divided into three zones, which are highly The stress-strain curves for structural steel and the confined concrete, partially confined concrete and reinforcement bars, provided by the Chinese Code for unconfined concrete zones with different states of Design of Concrete Structures GB 50010-2010 (2010), confinement, as shown in Fig.1. were adopted in this study with values of yield stress (f ) and ultimate stress (f ) measured in the tests. The ys us material behavior provided by ABAQUS (using the *PLASTIC option) allows a nonlinear stress-strain curve to be used. The first part of the nonlinear curve represents the elastic behavior up to the proportional limit stress with a Young's modulus of 200 GPa and Poisson's ratio equal to 0.3. 2.4 Material Modeling of Concrete In this case, the concrete strength is considerably improved because of confinement by the steel and reinforcements. Thus, a confined concrete model needs to be developed, based on the experimental results. The model proposed by Popovics (1973) and Collins et al. (1993) was adopted to simulate the concrete behavior Fig.1. Modeling of SRC-RC Transfer Column in compression. The compressive stress (f ) and strain Fig. 1 Modeling of SRC-RC transfer column c (ε ) relation of the concrete is defined as follows: The highly confined concrete is taken from the web f  (/ ) of steel to the mid-width of each flange outstand. The c c0  = (1) d partially confined concrete is taken from the mid- −1( +  / ) c 0 width of each flange outstand to the centerline of the  = (2) longitudinal reinforcement. Finally, the unconfined Ef − (/)  c c0 concrete is the remaining external zone, as shown in d 1, /  1 Fig.2.  c 0 (3) d= 0.67+ f / 62 1, /  1  c c0 where f is the ultimate compressive strength of concrete with or without confinement, λ is the curve- fitting factor, E is the initial tangent modulus, ε is c 0 the strain when σ reaches f , and d is the factor which c c controls the slope of the stress-strain curve. Fig.3. shows the equivalent uniaxial stress–strain curves for both unconfined and confined concrete. a) Confinement zones b) Simple model a) Confinement zones b) Simple model Fig. 2 Confinement zones in concrete 应力/ 应力/ Stress/σ Confined Fig.2. Confinement Zones in Concrete concrete 约束混凝土 约束混凝土 f f c cc c'' 2.2 Finite Element Type and Modeling of Interfaces f f c c'' Unconfined 无约束混凝土 无约束混凝土 The steel and concrete were modeled by an 8-node concrete solid element with reduced integration (C3D8R), and Strain/ε 应变/ 应变/   tu tu t t the reinforcements were modeled by 3-D linear truss    c c c cc c c cu u elements (T3D2). The interface elements (using the f f t t *Contact Pair option) available within the ABAQUS Fig. 3 Compression stress-strain model of concrete Fig.3. Compression Stress-strain Model of Concrete element library (SIMULA, 2011) were used to model the interaction between the steel-section and concrete. 558 JAABE vol.17 no.3 September 2018 Wei Huang = The initial Young's modulus of concrete is The ultimate compressive strain ε of confined cu reasonably calculated using Eq. (4) given by the ACI concrete is given by Paulay et al. (2009). Specification (2011). The Poisson's ratio of concrete is  0.004+1.4 ff / (15) taken as 0.2. CU s yh sm c (4) Ef = 4700 c c where ε is the strain when the tensile stress of the sm steel bar reaches the maximum, and ε is the transverse 1) Unconfined Concrete reinforcement ratio. The ultimate compressive strain of f =f , ε =ε . the confined concrete varies from 0.012 to 0.05, which c c0 0 c0 where f is the ultimate compressive strength of is 4 to 16 times that of the unconfined concrete. c0 unconfined concrete and ε is the strain when σ Concrete was modeled using the damaged plasticity c0 c reaches f (taken as 0.002 in this case). model implemented in the ABAQUS standard and c0 2) Partially Confined Concrete explicit material library. Under uniaxial tension, The compressive strength f and the corresponding the stress–strain response follows a linear elastic strain ε of confined concrete can be determined by relationship until reaching the value of the failure Eqs. (5) and (6), respectively, proposed by Mander et stress. The tensile failure stress was assumed to be al. (1988) and improved by Denavit et al. (2011). 0.1 times the compressive strength of concrete. The softening stress–strain response, past the maximum (5) f = Kf c c0 tensile stress, was represented by a linear line defined by the fracture energy and crack bandwidth, as shown = (1+− 5(K 1)) (6) c c0 in Fig.4. The fracture energy G in N/mm (energy 0.9 required to open a unit area of crack) was taken as Eq. K= 1++ Af (0.1 ) (7) 1+ Bf (16) as recommended by the CEB Specification (1996): −4.989 r (8) σ A=6.8886−+ (0.6069 17.275re ) εtu, ft Gf/lc 4.5 A B − 5 (9) −3.8939 r E0 5(0.9849− 0.6306eA )− 0.1 ff + l1 l 2 f = (10) εtu ε 2 f c0 Fig.4. Tensile Stress-strain Curve of Concrete Fig. 4 Tensile stress-strain curve of concrete r f /, ff f (11) l1 l 2 l1 l 2 0.7 Gf =(0.1 ) (16) where f is the equivalent lateral confining pressure, fc f and f are the lateral confining pressures imposed l1 l2 by the reinforcement bars with different directions, where f is the compressive strength in MPa; the respectively, as given by Mander et al. (1988). coefficient α is concerned with the maximum diameter 3) Highly Confined Concrete of concrete aggregate, and can be taken as D = 8 max High confinement of concrete is provided by the mm, α = 0.025; D =16 mm, α = 0.03; D = 32 mm, max max steel and reinforcements. The lateral confining pressure α = 0.058. (f' ) imposed by the flange of the steel is given by ly Huang et al. (2016): 3. Validation of the Finite Element Model Based on the simulation method above, numerical f = Kf (12) ly e ly analyses of 9 transfer columns are performed to study the nonlinear mechanical behavior of transfer columns ft ys (Suzuki et al. 1994, Kimura et al. 1998, Xue et al. f= (13) ly 4 22 93 l + lt 2010), as shown in Table 1. The load-displacement curves of the FEM analyses (L− h)(Ht −− 2) (Ht − 2) are compared with those of the tests in Fig.5. 3 (14) K = The corresponding load eigenvalues and ductility (L−− hH )( 2t) coefficients are listed in Table 2. The yield point is where f is the yield strength of the steel, L is the determined by using the energy equivalent method, ys flange length, H is the web length, and t is the flange while the ultimate lateral displacement is considered to thickness of the steel. be the corresponding displacement to the shear capacity The compressive strength f and the corresponding when the load decreases to 85% of the capacity in strain ε of the highly confined concrete can be the load-displacement curve. It can be found that the determined by the lateral confining pressure imposed results of the finite element analysis agree with those by the reinforcements and steel in different directions. of the tests. The FEM reflects the pinching effect and JAABE vol.17 no.3 September 2018 Wei Huang 559 = Table 1. Dimensions and Test Parameters of the Specimens Extending height Dimension(mm) Stirrup Stirrup enhancement at Longitudinal Reference Test No. Steel section coefficient of configuration truncated place of steel reinforcement Section Height steel η S3-30 400×400 1200 H204×200×12×12 0.3 Φ10@120 -- 8Φ19 Suzuki et al. 1994 S3-60 400×400 1200 H204×200×12×12 0.6 Φ10@120 -- 8Φ19 S4-2-JM 220×160 1000 H100×68×7.4×4.5 0.4 Φ6.5@48 -- 4Φ16 SRC4-4- 220×160 1000 H140×80×9.1×5.5 0.4 Φ6.5@48 -- 4Φ16 Kimura JM SRC6-2 220×160 1000 H140×80×9.1×5.5 0.6 Φ6.5@96 Φ6.5@48 4Φ16 et al. 1998 SRC8-2 220×160 1000 H140×80×9.1×5.5 0.8 Φ6.5@96 Φ6.5@48 4Φ16 SRC8-4 220×160 1000 H140×80×9.1×5.5 0.8 Φ6.5@96 Φ6.5@48 4Φ16 Xue SRC-2-JM 220×160 1000 H140×80×9.1×5.5 0.4 Φ6.5@48 -- 4Φ16 et al. 2010 SRC-2-SD 220×160 1000 H140×80×9.1×5.5 0.4 Φ6.5@96 Φ6.5@48 4Φ16 500 150 S3-30 test S3-60 test FEA FEA 200 0 -60 -40 -20 0 20 40 60 100 △/mm -50 -100 0.000 0.010 0.020 0.030 0.040 0.000 0.005 0.010 0.015 0.020 0.025 S4-2-JM test 层间位移角R/rad FEA Interstory drift R/rad 层间位移角R/rad Interstory drift R/rad -150 (1) S3-30 (2) S3-60 (3) S4-2-JM 180 150 120 100 60 50 0 0 -50 -40 -30 -20 -10 0 10 20 30 40 50 -50 -40 -30 -20 -10 0 10 20 30 40 50 -50 -40 -30 -20 -10 0 10 20 30 40 50 △/mm △/mm △/mm -60 -50 -50 -120 -100 -100 SRC4-4-JM test SRC6-2 test SRC8-2 test FEA FEA FEA -180 -150 -150 (4) SRC4-4-JM (5) SRC6-2 (6) SRC8-2 180 180 150 120 120 100 60 60 50 0 0 0 -30 -20 -10 0 10 20 30 -50 -40 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 △/mm △/mm △/mm -60 -60 -50 -120 -100 -120 SRC-2-JM test SRC-2-SD test SRC8-4 test FEA FEA FEA -180 -180 -150 (7) SRC8-4 (8) SRC-2-JM (9) SRC-2-SD Fig. 5 Comparison between tests and finite element results Fig.5. Comparison between Tests and Finite Element Results the damage conditions of the members under cyclic 4. The Shear Capacity of the Transfer Column load, as well as the decline after the maximum load. An The change in stiffness caused by the local existence obvious difference between the numerical result and of steel results in a change of the inflection point test result is observed in specimens under continuous location at approximately 0.4 times the column height beam loading, as shown in Figs.5.(1) and (2), because that is near the RC part, thus easily generating a short- the next load step is conducted before the stress of the column shear failure. The steel and concrete in the member becomes stable. It is caused by the principle SRC part mutually squeeze together along the height of one-time loading. However, the overall trend of the of the column. The concrete transfers part of the results is similar. shear and axial forces to the steel. The co-working of the concrete and steel is based on the force transfer 560 JAABE vol.17 no.3 September 2018 Wei Huang P/kN P/kN P/kN P/kN P/kN P/kN P/kN P/kN P/kN Table 2. Comparison between Tests and Finite Element Results Ductility coefficient Yield load/kN Shear capacity/kN Reference Test No. Q /Q V /V μ μ /μ TEST FEA TEST FEA TEST FEA Test Q FEA Q Test V FEA V Test μ FEA μ TEST FEA TEST FEA TEST FE S3-30 345.00 354.00 0.97 401.00 394.00 1.02 2.14 2.70 0.79 Suzuki et al. (1994) S3-60 325.00 343.50 0.95 400.00 384.80 1.04 3.32 3.91 0.85 S4-2-JM 90.04 91.00 0.99 119.60 123.00 0.97 5.99 5.47 1.10 SRC4-4-JM 114.75 112.00 1.02 147.35 147.00 1.00 3.39 3.51 0.97 Kimura et al. SRC6-2 99.55 99.80 1.00 127.65 132.70 0.96 3.78 4.43 0.85 (1998) SRC8-2 104.30 106.00 0.98 133.20 136.00 0.98 3.63 3.78 0.96 SRC8-4 113.70 120.00 0.95 146.25 144.00 1.02 3.54 3.29 1.08 SRC-2-JM 102.05 104.00 0.98 134.70 142.00 0.95 4.65 5.00 0.93 Xue et al. (2010) SRC-2-SD 98.70 96.90 1.02 130.65 128.00 1.02 3.30 3.04 1.09 between them, which also results in the distortion of the internal force transmission. Fig.6. shows the ideal Shear Sliding Failure failure surface of a transfer column under a compound Principal Tensile stress condition. Fig.7. presents the stress distribution Fracture Failure of the reinforced concrete part of a transfer column. According to Figs.6.-7., the failure angle θ (θ≤45 ) f σ between the column axis and the trace of the principle tension stress can be obtained by Eqs. (17)-(18). The Shear Sliding Failure lower limitation of θ is determined by cot θ=2, which σ is provided by Zhao (1998). The minimum value of θ is 26.6 . Fig. 8 Mohr-Coulomb failure criterion Fig.8. Mohr-Coulomb Failure Criterion (17)  f − f t 0t  （f− sin ）/sin 2 (19) p t0  h 12 −1 s −1  min tan ( ), tan (− ) (18) When shear slip of concrete occurs, the shear  LL − 2   s0 capacity V can be obtained by the following equation: where σ =N/(bh); b and h are the width and height of  bh the section; f is the compressive strength of concrete; f (20) c t V = 1.5 is the tensile strength of concrete; and h is the space of longitudinal reinforcements. where the factor κ is taken as 1.2. The modified Mohr-Coulomb failure criterion is The stirrups not only provide shear capacity, but also adopted as the three black polylines presented in Fig.8. limit the cracking of the concrete. In considering of the Under the combination of shear stress and normal failure mode of the transfer column, the shear capacity stress, shear slip failure occurs when the Moore stress of the stirrups V is reduced and is more conservative circle is tangent to the oblique line, and principle than the code. tensile failure occurs when the Moore stress circle is tangent to the vertical line. V = 0.6A fh / s (21) s sv y s According to the geometric relations of the Moore stress circle, the maximum shear stress of the section is where A is the area of stirrups; f is the yield strength sv y determined by: of reinforcement; s is the space of stirrups. Ideal Failure Surface Considering the shear capacity of both stirrups and M Q concrete, the shear capacity of a transfer column can N be determined by: Ls (22) V =V +V 1 c s Fig.6. Ideal Failure Surface of Fig. 6 Ideal failure surface oT f ransform Column transform column When the shear span ratio is greater, the flexural behavior becomes dominant. Meanwhile, the flexural capacity of the steel can be fully developed, thus Q Q M M f f delaying the flexural yielding at the bottom of the N N t t ττ m mean ean σσ 0 0 N N θθ ττ SRC part and improving its shear capacity. The shear Q Q ττ M M capacity of a transfer column under flexural failure is determined by the flexural capacity of the ends of Fig. 7 Stress condition of the failure surface Fig.7. Stress Condition of the Failure Surface JAABE vol.17 no.3 September 2018 Wei Huang 561 hs τ τ = Table 3. Comparison between Test and Computer Results the column. The ultimate flexural capacity of the RC and SRC parts can be obtained by Eqs. (23) and (24), Reference Test No. Test V /kN V /kN V /kN V/V t 1 2 t respectively, according to the Japanese code (Feng 400.08 S3-30 401.00 724.70 1.00 Suzuki et et al., 1998). Then, the shear capacity of a transfer 399.35 al. S3-60 400.00 724.70 1.00 column under flexural failure can be calculated by Eq. (1994) 399.35 (25). S3-90 446.00 724.70 0.90 124.25 SRC4-2-N 124.00 133.44 1.00 (23) M= 0.8A f h+− 0.5Nh[1 N / (bh f )] RC s y s c 125.69 S4-2-N 115.50 117.27 1.02 (24) 124.25 SRC4-2 129.90 133.44 0.96 M = 0.8A f h+− 0.5Nh[1 N / (bh f )]+W f SRC sy s c sys 153.45 SRC4-4 152.30 170.81 1.01 (25) VM （ + M ）/L 2 RC SRC S4-2 125.20 124.25 120.26 0.96 where A is the cross-section area of tensile longitudinal S4-4 139.00 170.81 136.31 0.98 reinforcement, h is the height of the section, h is the 125.69 SRC6-2 127.70 134.41 0.98 space of longitudinal reinforcement, W is the elastic Kimura et 136.31 S6-4 135.80 170.81 1.00 resistance moment of steel, f is the yield strength of ys al. steel, and f is the yield strength of a reinforcement bar. 124.25 y SRC8-2 133.20 133.44 0.93 (1998) Eqs. (22) and (25) show the shear capacity of a 153.45 SRC8-4 146.30 170.81 1.05 transfer column under different failure modes. The S8-2 115.10 124.25 120.26 1.04 shear capacity can be calculated as: S8-4 131.70 170.81 136.31 1.04 (26) V = min(VV , ) 133.44 SRC4-2-JM 134.70 151.46 0.99 153.45 SRC4-4-JM 147.40 199.46 1.04 Based on Eq. (26) above, the test results by Suzuki et al. (1994) and Kimura et al. (1998) are compared 119.82 S4-2-JM 119.60 151.46 1.00 in Table 3., which indicates that the values obtained S4-4-JM 136.10 199.46 136.31 1.00 by Eq. (26) agree with the test results. Though some values are conservative, it is reasonable to increase Table 4. Comparison between Specification and Test the strength of a transfer column. The shear capacity V V Code Mod Reference Test No. V /kN V /kN obtained by the principle tension method differs greatly code Mod V V Test Test from that of the flexural shear capacity method, which S3-30 365.02 0.91 296.63 0.81 Suzuki is caused by the failure characteristics of a transfer et al. S3-60 365.02 0.91 296.63 0.81 column. The method above can initially present the (1994) S3-90 365.02 0.82 296.63 0.81 failure characteristics of a transfer column. Hence, SRC4-2-N 96.42 0.78 78.28 0.81 measures can be taken to prevent brittle failure and S4-2-N 98.83 0.86 79.72 0.81 improve ductility. SRC4-2 96.42 0.74 78.28 0.81 The Chinese Code for Design of Concrete Structures SRC4-4 121.54 0.80 102.44 0.84 (2010) provides the formula of shear capacity for RC S4-2 96.42 0.77 78.28 0.81 members under eccentric compressive load as follows: S4-4 121.54 0.87 102.44 0.84 SRC6-2 98.83 0.77 79.72 0.81 Kimura 1.75 A sv S6-4 121.54 0.90 102.44 0.84 (27) V= f bh++ f h 0.07 N et al. code t 0 yv 0 + 1 s SRC8-2 96.42 0.72 78.28 0.81 (1998) SRC8-4 121.54 0.83 102.44 0.84 where the factor λ is the shear span ratio and h is the 0 S8-2 96.42 0.84 78.28 0.81 effective height of the section. S8-4 121.54 0.92 102.44 0.84 The stirrups not only provide shear capacity, but SRC4-2-JM 141.78 1.05 105.50 0.74 also limit the cracking of the concrete, preventing SRC4-4-JM 169.30 1.15 131.10 0.77 shear failure. To improve safety, the shear capacity is S4-2-JM 141.78 1.19 105.50 0.74 reduced by the stirrups. The shear capacity is modified S4-4-JM 169.30 1.24 131.10 0.77 as follows: have a large space, but is not safe when the space of 1.75 A sv (28) V = f bh++ 0.6 f h 0.07N the stirrups gets smaller. For a transfer column, the Mod t 0 yv 0 + 1 s local existence of steel causes a change in the inflection point near the RC part, thus easily generating a short- The shear capacities of a transfer column obtained column shear failure. Moreover, when the location of by the code and the proposed modified formula are the inflection point changes, the shear span ratio of the shown in Table 4. It can be found that the shear RC part tends to decrease. As is commonly known, the capacity obtained by the code is safe when the stirrups 562 JAABE vol.17 no.3 September 2018 Wei Huang = Table 6. Comparison of Column Shear Capacity by FEA and Table 5. Specimen Material Properties for FEA Calculate No. Length/mm η Stirrup space/mm Axial load ratio V V Code Mod S1 1200 0.2 100 0.2 No. V /kN V /kN V /kN FEA Code Mod V V FEA FEA S2 1200 0.4 100 0.2 S1 432.89 475.81 1.1 397.88 0.92 S3 1200 0.6 100 0.2 S2 447.9 475.81 1.06 397.88 0.89 S4 1200 0.8 100 0.2 S3 474.37 475.81 1.00 397.88 0.84 S5 1200 0.2 200 0.2 S4 534.19 475.81 0.89 397.88 0.74 S6 1200 0.4 200 0.2 S5 392.18 378.39 0.96 339.43 0.87 S7 1200 0.6 200 0.2 S6 407 378.39 0.93 339.43 0.83 S8 1200 0.8 200 0.2 S7 430.66 378.39 0.88 339.43 0.79 S9 2400 0.2 100 0.2 S8 520.67 378.39 0.73 339.43 0.65 S10 2400 0.4 100 0.2 S9 357.7 388.95 1.09 311.01 0.87 S11 2400 0.6 100 0.2 S10 359.53 388.95 1.08 311.01 0.87 S12 2400 0.8 100 0.2 S11 364.47 388.95 1.07 311.01 0.85 S13 2400 0.2 200 0.2 S12 360.99 388.95 1.08 311.01 0.86 S14 2400 0.4 200 0.2 S13 322.86 291.53 0.90 252.56 0.78 S15 2400 0.6 200 0.2 S14 338.4 291.53 0.86 252.56 0.75 S16 2400 0.8 200 0.2 S15 342.23 291.53 0.85 252.56 0.74 S17 1200 0.2 100 0.4 S16 336.87 291.53 0.87 252.56 0.75 S18 1200 0.4 100 0.4 S17 461.72 504.82 1.09 426.89 0.92 S19 1200 0.6 100 0.4 S18 485.88 504.82 1.04 426.89 0.88 S20 1200 0.8 100 0.4 S19 527.85 504.82 0.96 426.89 0.81 S21 1200 0.2 200 0.4 S20 599.17 504.82 0.84 426.89 0.71 S22 1200 0.4 200 0.4 S21 423.15 407.4 0.96 368.44 0.87 S23 1200 0.6 200 0.4 S22 442.59 407.4 0.92 368.44 0.83 S24 1200 0.8 200 0.4 S23 477.31 407.4 0.85 368.44 0.77 S25 2400 0.2 100 0.4 S24 582.06 407.4 0.7 368.44 0.63 S26 2400 0.4 100 0.4 S25 406.22 417.95 1.03 340.02 0.84 S27 2400 0.6 100 0.4 S26 413.26 417.95 1.01 340.02 0.82 S28 2400 0.8 100 0.4 S27 417.06 417.95 1.00 340.02 0.82 S29 2400 0.2 200 0.4 S28 412.09 417.95 1.01 340.02 0.83 S30 2400 0.4 200 0.4 S29 375.58 320.54 0.85 281.57 0.75 S31 2400 0.6 200 0.4 S30 383.49 320.54 0.84 281.57 0.73 S32 2400 0.8 200 0.4 S31 390.76 320.54 0.82 281.57 0.72 S32 384.37 320.54 0.83 281.57 0.73 bigger the shear span ratio, the lower the shear capacity is. Therefore, the calculation of the shear capacity for a 6. Conclusions transfer column is much safer when the inflection point In an SRC-RC transfer column, the sudden change is simply considered to be at the center of the column in stiffness caused by the local variation in the steel according to the code. section will result in moment distribution changes To validate the rationality and reliability for the at the ends of the column. Thus, in consequence, the proposed modified formula for the shear capacity, the inflection point of the column may move toward the above finite element method is adopted to establish RC part. Based on the mechanical behavior of SRC- the models of specimens as in Suzuki et al. (1994). RC transfer columns, the shear capacity formula The dimensions of section (B × D) are 400 mm × 400 under different failure modes has been studied. The mm, and the other parameters of the specimens are calculated values agree with the test results. It is presented in Table 5. found that the shear capacity formula provided by the The values calculated by the code and the modified current code may not always ensure the shear failure formula are compared with the ultimate shear capacity capacity while the proposed modified formula, which of the tests, as shown in Table 6. It can be found that reduces the shear capacity provided by stirrups, will the shear capacity calculated by the code is close to lead to a more rational design of structural members by the test results. However when the space of stirrups preventing brittle failure and improving ductility. gets smaller, the shear capacity tends to be greater and unsafe. Meanwhile, the values obtained by the modified formula are approximately 0.7-0.9 times that of the test values, providing enough redundancy and safety. JAABE vol.17 no.3 September 2018 Wei Huang 563 16) Wu Kai, Xue Jianyang and Zhao Hongtie (2012). Experimental Acknowledgements study of lateral stiffness of transfer column in SRC-RC hybrid The authors acknowledge with thanks support from structure. Engineering mechanics, 29(12): 307-315. (in Chinese). (a) the National Natural Science Foundation of China 17) Xue Jianyang, Wu Kai, Zhao Hongtie, et al. (2010). Experimental (Grant No. 51608406); (b) the State Key Laboratory study on seismic behavior of SRC-RC transfer columns. Journal of of Disaster Reduction in Civil Engineering (Project: Building Structures, 31(11): 102-110 (in Chinese). 18) Zhao Yong and Shao Yongjian (2010). Experimental study on SLDRCE15-B-06); (c) the Open Foundation of seismic behavior of SRC-RC transfer columns with different Hubei Key Laboratory of Theory and Application of constructional measures. World earthquake engineering, 26(2). Advanced Materials Mechanics (Wuhan University of 119-124. (in Chinese). Technology) (Grant No.: TMA201810). 19) Zhao Guofan (1998). High reinforced concrete structural study. Beijing: Science Press: 50-99 (in Chinese). References 1) ACI Committee (2011). Building code requirements for structural concrete (ACI 318-11) and commentary (ACI 318R-11). American Concrete Institute. 2) CEB. (1996). RC Elements Under Cyclic Loading: State of the Art Report [C], SOTA report. 3) Collins M P, Mitchell D, MacGregor J G (1993). Structural design considerations for high-strength concrete. Concrete International, 15(5): 27-34. 4) Denavit M D, Hajjar J F, and Leon R T. (2011). Seismic Behavior of Steel Reinforced Concrete Beam-Columns and Frames. Proceedings of the ASCE/SEI Structures Congress: 14-16. 5) Ellobody E and Young B (2011). Numerical simulation of concrete encased steel composite columns. Journal of Constructional Steel Research, 67(2): 211-222. 6) Feng Naiqian and Ye Lieping (1998). Japanese architectural society SRC structure calculation standard and explanation. Beijing: atomic energy press. 7) GB20010-2010 (2010), Code for design of concrete structures. Beijing: China Architecture and Building Press. 8) Huang Wei, Qian Jiang and Zhou Zhi (2016). Numerical simulation of the seismic performance of steel reinforced concrete columns by considering the lateral confining pressure. Engineering mechanics, 33(5): 157-165. (in Chinese). 9) Kimura J and Shingu Y (1998). Structural performance of SRC- RC mixed member under cyclic bending moment and shear [C]. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. Kyushu: 1067-1068. (in Japanese) 10) Konno S, Imaizumi T, Yamamoto K, et al. (1998). Experimental study on high-rise building with lower floor composed of SRC structure. Part1: Outline of the tests about deformation capacity of SRC columns. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, Kyushu: 1029-1030. (in Japanese) 11) Mander J B, Priestley M J N and Park R (1988). Theoretical stress-strain model for confined concrete. Journal of structural engineering, 114(8): 1804-1826. 12) Paulay T, Priestly M J N. seismic design of reinforced concrete and masonry buildings. John Wiley & Sons, Inc., 2009:300-500. 13) Popovics S (1973). A numerical approach to the complete stress- strain curve of concrete. Cement and concrete research, 3(5): 583- 14) SIMULA (2011), Dassault Systems, ABAQUS Analysis User's Manual. 15) Suzuki H, Nishihara H and Matsuzaki Y (1999). Shear performance of the column where structural form changes from SRC to RC. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, Chyugoku: 1069-1070. (in Japanese) 564 JAABE vol.17 no.3 September 2018 Wei Huang http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Asian Architecture and Building Engineering Taylor & Francis

Study on the Shear Capacity of an SRC-RC Transfer Column

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Taylor & Francis
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© 2018 Architectural Institute of Japan
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1347-2852
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10.3130/jaabe.17.557
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Abstract

The truncation of steel sections in Steel Reinforced Concrete-Reinforced Concrete (SRC-RC) transfer columns may lead to a distortion in the internal force transmission. A refined finite element model of SRC-RC transfer columns was developed in this study taking into consideration the effects of different confinement around concrete. According to the internal force and deformation characteristics of a transfer column, the shear capacity of the SRC-RC transfer column was investigated, and the results compared well with existing experimental results. Extensive parametric studies were conducted and crosschecked with the current code. It is found that the current specification may not always ensure the shear failure capacity since it is intrinsically affected by both the internal force and deformation characteristics of the transfer column. A modified formula has been proposed, by which more rational design of structural members may be expected, brittle failure can be avoided and ductility will be improved. Keywords: SRC-RC transition column; transmission distortion; finite element model; shear capacity 1. Introduction dominated by shear failure, and the flexural failure A Steel Reinforced Concrete-Reinforced Concrete and bond failure were mainly observed in specimens (SRC-RC) transfer column behaves as the connection with greater extending height of steel. The influence between the upper and lower members by extending of different structural measures on the seismic the steel of the SRC or steel column to the adjacent performance of transfer columns was studied through members. Suzuki et al. (1999) investigated the the cyclic tests of 8 SRC-RC transfer columns by Zhao influence on the mechanical behavior of transfer and Shao (2010). columns by extending the height of steel. Low In the Chinese Code for Design of Concrete frequency cyclic tests of 3 transfer columns and 1 RC Structures GB 50010-2010, only a few structural column were conducted to compare their behaviors. measures are presented. However, calculation methods Konno et al. (1998) tested 13 specimens of transfer of transfer columns, such as formulas for flexural members under cyclic load to obtain the seismic capacity and shear capacity, are not provided. The performance of transfer columns. Cyclic tests of 7 shear capacity formula for transfer columns in the SRC-RC transfer columns were performed by Kimura Japanese Code, which is derived from the ultimate et al. (1998), to evaluate the effects of the enhanced flexural capacity, does not consider all kinds of failure reinforcement and extending the height of steel on the modes of transfer columns (Feng et al., 1998). Thus, seismic performance and mechanical behavior of the it is difficult for engineers to evaluate the performance transfer columns. Xue et al. (2010) and Wu et al. (2012) of transfer columns in structural design. Though tested 21 SRC-RC transfer columns under cyclic load. several experimental studies have been conducted, The results found that the specimens were mostly no systematic results have been achieved because the number of tests and experimental conditions are limited. To generally investigate the behavior of *Contact Author: Wei Huang, Lecturer, SRC-RC transfer columns, the constitutive model Department of Mechanics and Engineering Structure, of concrete, which considers the effect of different Wuhan University of Technology, confinements is used according to the principle of 122 Luoshi Road, Wuhan 430040, China effective additive confined stress. Then, the finite Tel: +86-18807199155 Fax:+86-21-65982668 element model for an SRC-RC transfer column is E-mail: whuang@whut.edu.cn established in ABAQUS. Then, the security and ( Received April 3, 2017 ; accepted July 23, 2018 ) rationality of the shear capacity calculation for SRC- DOI http://doi.org/10.3130/jaabe.17.557 RC transfer columns are explored. Journal of Asian Architecture and Building Engineering/September 2018/564 557 2. Finite Element Modeling The master surface in the contact property is defined Finite element analysis (FEA) was performed by as the concrete surface surrounding the steel. When the ABAQUS to develop reliable models that can simulate two surfaces remain in contact, the slave surface can be the behavior of SRC-RC transfer columns, based on displaced in relation to the master surface based on the experimental results. coefficient of friction between the two surfaces, which 2.1 Modeling Approach is taken as 0.25 (Ellobody et al., 2011). Moreover, The SRC-RC transfer column studied in this paper the reinforcements were embedded into the concrete is composed of two parts, the SRC part and the RC using the *Embedded Constraint option in ABAQUS, part. The SRC part includes four components, the steel assuming a perfect bond. section, longitudinal reinforcement bars, transverse 2.3 Material Modeling of Steel Section and reinforcement bars and concrete. Furthermore, the Reinforcement Bars RC part is divided into three zones, which are highly The stress-strain curves for structural steel and the confined concrete, partially confined concrete and reinforcement bars, provided by the Chinese Code for unconfined concrete zones with different states of Design of Concrete Structures GB 50010-2010 (2010), confinement, as shown in Fig.1. were adopted in this study with values of yield stress (f ) and ultimate stress (f ) measured in the tests. The ys us material behavior provided by ABAQUS (using the *PLASTIC option) allows a nonlinear stress-strain curve to be used. The first part of the nonlinear curve represents the elastic behavior up to the proportional limit stress with a Young's modulus of 200 GPa and Poisson's ratio equal to 0.3. 2.4 Material Modeling of Concrete In this case, the concrete strength is considerably improved because of confinement by the steel and reinforcements. Thus, a confined concrete model needs to be developed, based on the experimental results. The model proposed by Popovics (1973) and Collins et al. (1993) was adopted to simulate the concrete behavior Fig.1. Modeling of SRC-RC Transfer Column in compression. The compressive stress (f ) and strain Fig. 1 Modeling of SRC-RC transfer column c (ε ) relation of the concrete is defined as follows: The highly confined concrete is taken from the web f  (/ ) of steel to the mid-width of each flange outstand. The c c0  = (1) d partially confined concrete is taken from the mid- −1( +  / ) c 0 width of each flange outstand to the centerline of the  = (2) longitudinal reinforcement. Finally, the unconfined Ef − (/)  c c0 concrete is the remaining external zone, as shown in d 1, /  1 Fig.2.  c 0 (3) d= 0.67+ f / 62 1, /  1  c c0 where f is the ultimate compressive strength of concrete with or without confinement, λ is the curve- fitting factor, E is the initial tangent modulus, ε is c 0 the strain when σ reaches f , and d is the factor which c c controls the slope of the stress-strain curve. Fig.3. shows the equivalent uniaxial stress–strain curves for both unconfined and confined concrete. a) Confinement zones b) Simple model a) Confinement zones b) Simple model Fig. 2 Confinement zones in concrete 应力/ 应力/ Stress/σ Confined Fig.2. Confinement Zones in Concrete concrete 约束混凝土 约束混凝土 f f c cc c'' 2.2 Finite Element Type and Modeling of Interfaces f f c c'' Unconfined 无约束混凝土 无约束混凝土 The steel and concrete were modeled by an 8-node concrete solid element with reduced integration (C3D8R), and Strain/ε 应变/ 应变/   tu tu t t the reinforcements were modeled by 3-D linear truss    c c c cc c c cu u elements (T3D2). The interface elements (using the f f t t *Contact Pair option) available within the ABAQUS Fig. 3 Compression stress-strain model of concrete Fig.3. Compression Stress-strain Model of Concrete element library (SIMULA, 2011) were used to model the interaction between the steel-section and concrete. 558 JAABE vol.17 no.3 September 2018 Wei Huang = The initial Young's modulus of concrete is The ultimate compressive strain ε of confined cu reasonably calculated using Eq. (4) given by the ACI concrete is given by Paulay et al. (2009). Specification (2011). The Poisson's ratio of concrete is  0.004+1.4 ff / (15) taken as 0.2. CU s yh sm c (4) Ef = 4700 c c where ε is the strain when the tensile stress of the sm steel bar reaches the maximum, and ε is the transverse 1) Unconfined Concrete reinforcement ratio. The ultimate compressive strain of f =f , ε =ε . the confined concrete varies from 0.012 to 0.05, which c c0 0 c0 where f is the ultimate compressive strength of is 4 to 16 times that of the unconfined concrete. c0 unconfined concrete and ε is the strain when σ Concrete was modeled using the damaged plasticity c0 c reaches f (taken as 0.002 in this case). model implemented in the ABAQUS standard and c0 2) Partially Confined Concrete explicit material library. Under uniaxial tension, The compressive strength f and the corresponding the stress–strain response follows a linear elastic strain ε of confined concrete can be determined by relationship until reaching the value of the failure Eqs. (5) and (6), respectively, proposed by Mander et stress. The tensile failure stress was assumed to be al. (1988) and improved by Denavit et al. (2011). 0.1 times the compressive strength of concrete. The softening stress–strain response, past the maximum (5) f = Kf c c0 tensile stress, was represented by a linear line defined by the fracture energy and crack bandwidth, as shown = (1+− 5(K 1)) (6) c c0 in Fig.4. The fracture energy G in N/mm (energy 0.9 required to open a unit area of crack) was taken as Eq. K= 1++ Af (0.1 ) (7) 1+ Bf (16) as recommended by the CEB Specification (1996): −4.989 r (8) σ A=6.8886−+ (0.6069 17.275re ) εtu, ft Gf/lc 4.5 A B − 5 (9) −3.8939 r E0 5(0.9849− 0.6306eA )− 0.1 ff + l1 l 2 f = (10) εtu ε 2 f c0 Fig.4. Tensile Stress-strain Curve of Concrete Fig. 4 Tensile stress-strain curve of concrete r f /, ff f (11) l1 l 2 l1 l 2 0.7 Gf =(0.1 ) (16) where f is the equivalent lateral confining pressure, fc f and f are the lateral confining pressures imposed l1 l2 by the reinforcement bars with different directions, where f is the compressive strength in MPa; the respectively, as given by Mander et al. (1988). coefficient α is concerned with the maximum diameter 3) Highly Confined Concrete of concrete aggregate, and can be taken as D = 8 max High confinement of concrete is provided by the mm, α = 0.025; D =16 mm, α = 0.03; D = 32 mm, max max steel and reinforcements. The lateral confining pressure α = 0.058. (f' ) imposed by the flange of the steel is given by ly Huang et al. (2016): 3. Validation of the Finite Element Model Based on the simulation method above, numerical f = Kf (12) ly e ly analyses of 9 transfer columns are performed to study the nonlinear mechanical behavior of transfer columns ft ys (Suzuki et al. 1994, Kimura et al. 1998, Xue et al. f= (13) ly 4 22 93 l + lt 2010), as shown in Table 1. The load-displacement curves of the FEM analyses (L− h)(Ht −− 2) (Ht − 2) are compared with those of the tests in Fig.5. 3 (14) K = The corresponding load eigenvalues and ductility (L−− hH )( 2t) coefficients are listed in Table 2. The yield point is where f is the yield strength of the steel, L is the determined by using the energy equivalent method, ys flange length, H is the web length, and t is the flange while the ultimate lateral displacement is considered to thickness of the steel. be the corresponding displacement to the shear capacity The compressive strength f and the corresponding when the load decreases to 85% of the capacity in strain ε of the highly confined concrete can be the load-displacement curve. It can be found that the determined by the lateral confining pressure imposed results of the finite element analysis agree with those by the reinforcements and steel in different directions. of the tests. The FEM reflects the pinching effect and JAABE vol.17 no.3 September 2018 Wei Huang 559 = Table 1. Dimensions and Test Parameters of the Specimens Extending height Dimension(mm) Stirrup Stirrup enhancement at Longitudinal Reference Test No. Steel section coefficient of configuration truncated place of steel reinforcement Section Height steel η S3-30 400×400 1200 H204×200×12×12 0.3 Φ10@120 -- 8Φ19 Suzuki et al. 1994 S3-60 400×400 1200 H204×200×12×12 0.6 Φ10@120 -- 8Φ19 S4-2-JM 220×160 1000 H100×68×7.4×4.5 0.4 Φ6.5@48 -- 4Φ16 SRC4-4- 220×160 1000 H140×80×9.1×5.5 0.4 Φ6.5@48 -- 4Φ16 Kimura JM SRC6-2 220×160 1000 H140×80×9.1×5.5 0.6 Φ6.5@96 Φ6.5@48 4Φ16 et al. 1998 SRC8-2 220×160 1000 H140×80×9.1×5.5 0.8 Φ6.5@96 Φ6.5@48 4Φ16 SRC8-4 220×160 1000 H140×80×9.1×5.5 0.8 Φ6.5@96 Φ6.5@48 4Φ16 Xue SRC-2-JM 220×160 1000 H140×80×9.1×5.5 0.4 Φ6.5@48 -- 4Φ16 et al. 2010 SRC-2-SD 220×160 1000 H140×80×9.1×5.5 0.4 Φ6.5@96 Φ6.5@48 4Φ16 500 150 S3-30 test S3-60 test FEA FEA 200 0 -60 -40 -20 0 20 40 60 100 △/mm -50 -100 0.000 0.010 0.020 0.030 0.040 0.000 0.005 0.010 0.015 0.020 0.025 S4-2-JM test 层间位移角R/rad FEA Interstory drift R/rad 层间位移角R/rad Interstory drift R/rad -150 (1) S3-30 (2) S3-60 (3) S4-2-JM 180 150 120 100 60 50 0 0 -50 -40 -30 -20 -10 0 10 20 30 40 50 -50 -40 -30 -20 -10 0 10 20 30 40 50 -50 -40 -30 -20 -10 0 10 20 30 40 50 △/mm △/mm △/mm -60 -50 -50 -120 -100 -100 SRC4-4-JM test SRC6-2 test SRC8-2 test FEA FEA FEA -180 -150 -150 (4) SRC4-4-JM (5) SRC6-2 (6) SRC8-2 180 180 150 120 120 100 60 60 50 0 0 0 -30 -20 -10 0 10 20 30 -50 -40 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 △/mm △/mm △/mm -60 -60 -50 -120 -100 -120 SRC-2-JM test SRC-2-SD test SRC8-4 test FEA FEA FEA -180 -180 -150 (7) SRC8-4 (8) SRC-2-JM (9) SRC-2-SD Fig. 5 Comparison between tests and finite element results Fig.5. Comparison between Tests and Finite Element Results the damage conditions of the members under cyclic 4. The Shear Capacity of the Transfer Column load, as well as the decline after the maximum load. An The change in stiffness caused by the local existence obvious difference between the numerical result and of steel results in a change of the inflection point test result is observed in specimens under continuous location at approximately 0.4 times the column height beam loading, as shown in Figs.5.(1) and (2), because that is near the RC part, thus easily generating a short- the next load step is conducted before the stress of the column shear failure. The steel and concrete in the member becomes stable. It is caused by the principle SRC part mutually squeeze together along the height of one-time loading. However, the overall trend of the of the column. The concrete transfers part of the results is similar. shear and axial forces to the steel. The co-working of the concrete and steel is based on the force transfer 560 JAABE vol.17 no.3 September 2018 Wei Huang P/kN P/kN P/kN P/kN P/kN P/kN P/kN P/kN P/kN Table 2. Comparison between Tests and Finite Element Results Ductility coefficient Yield load/kN Shear capacity/kN Reference Test No. Q /Q V /V μ μ /μ TEST FEA TEST FEA TEST FEA Test Q FEA Q Test V FEA V Test μ FEA μ TEST FEA TEST FEA TEST FE S3-30 345.00 354.00 0.97 401.00 394.00 1.02 2.14 2.70 0.79 Suzuki et al. (1994) S3-60 325.00 343.50 0.95 400.00 384.80 1.04 3.32 3.91 0.85 S4-2-JM 90.04 91.00 0.99 119.60 123.00 0.97 5.99 5.47 1.10 SRC4-4-JM 114.75 112.00 1.02 147.35 147.00 1.00 3.39 3.51 0.97 Kimura et al. SRC6-2 99.55 99.80 1.00 127.65 132.70 0.96 3.78 4.43 0.85 (1998) SRC8-2 104.30 106.00 0.98 133.20 136.00 0.98 3.63 3.78 0.96 SRC8-4 113.70 120.00 0.95 146.25 144.00 1.02 3.54 3.29 1.08 SRC-2-JM 102.05 104.00 0.98 134.70 142.00 0.95 4.65 5.00 0.93 Xue et al. (2010) SRC-2-SD 98.70 96.90 1.02 130.65 128.00 1.02 3.30 3.04 1.09 between them, which also results in the distortion of the internal force transmission. Fig.6. shows the ideal Shear Sliding Failure failure surface of a transfer column under a compound Principal Tensile stress condition. Fig.7. presents the stress distribution Fracture Failure of the reinforced concrete part of a transfer column. According to Figs.6.-7., the failure angle θ (θ≤45 ) f σ between the column axis and the trace of the principle tension stress can be obtained by Eqs. (17)-(18). The Shear Sliding Failure lower limitation of θ is determined by cot θ=2, which σ is provided by Zhao (1998). The minimum value of θ is 26.6 . Fig. 8 Mohr-Coulomb failure criterion Fig.8. Mohr-Coulomb Failure Criterion (17)  f − f t 0t  （f− sin ）/sin 2 (19) p t0  h 12 −1 s −1  min tan ( ), tan (− ) (18) When shear slip of concrete occurs, the shear  LL − 2   s0 capacity V can be obtained by the following equation: where σ =N/(bh); b and h are the width and height of  bh the section; f is the compressive strength of concrete; f (20) c t V = 1.5 is the tensile strength of concrete; and h is the space of longitudinal reinforcements. where the factor κ is taken as 1.2. The modified Mohr-Coulomb failure criterion is The stirrups not only provide shear capacity, but also adopted as the three black polylines presented in Fig.8. limit the cracking of the concrete. In considering of the Under the combination of shear stress and normal failure mode of the transfer column, the shear capacity stress, shear slip failure occurs when the Moore stress of the stirrups V is reduced and is more conservative circle is tangent to the oblique line, and principle than the code. tensile failure occurs when the Moore stress circle is tangent to the vertical line. V = 0.6A fh / s (21) s sv y s According to the geometric relations of the Moore stress circle, the maximum shear stress of the section is where A is the area of stirrups; f is the yield strength sv y determined by: of reinforcement; s is the space of stirrups. Ideal Failure Surface Considering the shear capacity of both stirrups and M Q concrete, the shear capacity of a transfer column can N be determined by: Ls (22) V =V +V 1 c s Fig.6. Ideal Failure Surface of Fig. 6 Ideal failure surface oT f ransform Column transform column When the shear span ratio is greater, the flexural behavior becomes dominant. Meanwhile, the flexural capacity of the steel can be fully developed, thus Q Q M M f f delaying the flexural yielding at the bottom of the N N t t ττ m mean ean σσ 0 0 N N θθ ττ SRC part and improving its shear capacity. The shear Q Q ττ M M capacity of a transfer column under flexural failure is determined by the flexural capacity of the ends of Fig. 7 Stress condition of the failure surface Fig.7. Stress Condition of the Failure Surface JAABE vol.17 no.3 September 2018 Wei Huang 561 hs τ τ = Table 3. Comparison between Test and Computer Results the column. The ultimate flexural capacity of the RC and SRC parts can be obtained by Eqs. (23) and (24), Reference Test No. Test V /kN V /kN V /kN V/V t 1 2 t respectively, according to the Japanese code (Feng 400.08 S3-30 401.00 724.70 1.00 Suzuki et et al., 1998). Then, the shear capacity of a transfer 399.35 al. S3-60 400.00 724.70 1.00 column under flexural failure can be calculated by Eq. (1994) 399.35 (25). S3-90 446.00 724.70 0.90 124.25 SRC4-2-N 124.00 133.44 1.00 (23) M= 0.8A f h+− 0.5Nh[1 N / (bh f )] RC s y s c 125.69 S4-2-N 115.50 117.27 1.02 (24) 124.25 SRC4-2 129.90 133.44 0.96 M = 0.8A f h+− 0.5Nh[1 N / (bh f )]+W f SRC sy s c sys 153.45 SRC4-4 152.30 170.81 1.01 (25) VM （ + M ）/L 2 RC SRC S4-2 125.20 124.25 120.26 0.96 where A is the cross-section area of tensile longitudinal S4-4 139.00 170.81 136.31 0.98 reinforcement, h is the height of the section, h is the 125.69 SRC6-2 127.70 134.41 0.98 space of longitudinal reinforcement, W is the elastic Kimura et 136.31 S6-4 135.80 170.81 1.00 resistance moment of steel, f is the yield strength of ys al. steel, and f is the yield strength of a reinforcement bar. 124.25 y SRC8-2 133.20 133.44 0.93 (1998) Eqs. (22) and (25) show the shear capacity of a 153.45 SRC8-4 146.30 170.81 1.05 transfer column under different failure modes. The S8-2 115.10 124.25 120.26 1.04 shear capacity can be calculated as: S8-4 131.70 170.81 136.31 1.04 (26) V = min(VV , ) 133.44 SRC4-2-JM 134.70 151.46 0.99 153.45 SRC4-4-JM 147.40 199.46 1.04 Based on Eq. (26) above, the test results by Suzuki et al. (1994) and Kimura et al. (1998) are compared 119.82 S4-2-JM 119.60 151.46 1.00 in Table 3., which indicates that the values obtained S4-4-JM 136.10 199.46 136.31 1.00 by Eq. (26) agree with the test results. Though some values are conservative, it is reasonable to increase Table 4. Comparison between Specification and Test the strength of a transfer column. The shear capacity V V Code Mod Reference Test No. V /kN V /kN obtained by the principle tension method differs greatly code Mod V V Test Test from that of the flexural shear capacity method, which S3-30 365.02 0.91 296.63 0.81 Suzuki is caused by the failure characteristics of a transfer et al. S3-60 365.02 0.91 296.63 0.81 column. The method above can initially present the (1994) S3-90 365.02 0.82 296.63 0.81 failure characteristics of a transfer column. Hence, SRC4-2-N 96.42 0.78 78.28 0.81 measures can be taken to prevent brittle failure and S4-2-N 98.83 0.86 79.72 0.81 improve ductility. SRC4-2 96.42 0.74 78.28 0.81 The Chinese Code for Design of Concrete Structures SRC4-4 121.54 0.80 102.44 0.84 (2010) provides the formula of shear capacity for RC S4-2 96.42 0.77 78.28 0.81 members under eccentric compressive load as follows: S4-4 121.54 0.87 102.44 0.84 SRC6-2 98.83 0.77 79.72 0.81 Kimura 1.75 A sv S6-4 121.54 0.90 102.44 0.84 (27) V= f bh++ f h 0.07 N et al. code t 0 yv 0 + 1 s SRC8-2 96.42 0.72 78.28 0.81 (1998) SRC8-4 121.54 0.83 102.44 0.84 where the factor λ is the shear span ratio and h is the 0 S8-2 96.42 0.84 78.28 0.81 effective height of the section. S8-4 121.54 0.92 102.44 0.84 The stirrups not only provide shear capacity, but SRC4-2-JM 141.78 1.05 105.50 0.74 also limit the cracking of the concrete, preventing SRC4-4-JM 169.30 1.15 131.10 0.77 shear failure. To improve safety, the shear capacity is S4-2-JM 141.78 1.19 105.50 0.74 reduced by the stirrups. The shear capacity is modified S4-4-JM 169.30 1.24 131.10 0.77 as follows: have a large space, but is not safe when the space of 1.75 A sv (28) V = f bh++ 0.6 f h 0.07N the stirrups gets smaller. For a transfer column, the Mod t 0 yv 0 + 1 s local existence of steel causes a change in the inflection point near the RC part, thus easily generating a short- The shear capacities of a transfer column obtained column shear failure. Moreover, when the location of by the code and the proposed modified formula are the inflection point changes, the shear span ratio of the shown in Table 4. It can be found that the shear RC part tends to decrease. As is commonly known, the capacity obtained by the code is safe when the stirrups 562 JAABE vol.17 no.3 September 2018 Wei Huang = Table 6. Comparison of Column Shear Capacity by FEA and Table 5. Specimen Material Properties for FEA Calculate No. Length/mm η Stirrup space/mm Axial load ratio V V Code Mod S1 1200 0.2 100 0.2 No. V /kN V /kN V /kN FEA Code Mod V V FEA FEA S2 1200 0.4 100 0.2 S1 432.89 475.81 1.1 397.88 0.92 S3 1200 0.6 100 0.2 S2 447.9 475.81 1.06 397.88 0.89 S4 1200 0.8 100 0.2 S3 474.37 475.81 1.00 397.88 0.84 S5 1200 0.2 200 0.2 S4 534.19 475.81 0.89 397.88 0.74 S6 1200 0.4 200 0.2 S5 392.18 378.39 0.96 339.43 0.87 S7 1200 0.6 200 0.2 S6 407 378.39 0.93 339.43 0.83 S8 1200 0.8 200 0.2 S7 430.66 378.39 0.88 339.43 0.79 S9 2400 0.2 100 0.2 S8 520.67 378.39 0.73 339.43 0.65 S10 2400 0.4 100 0.2 S9 357.7 388.95 1.09 311.01 0.87 S11 2400 0.6 100 0.2 S10 359.53 388.95 1.08 311.01 0.87 S12 2400 0.8 100 0.2 S11 364.47 388.95 1.07 311.01 0.85 S13 2400 0.2 200 0.2 S12 360.99 388.95 1.08 311.01 0.86 S14 2400 0.4 200 0.2 S13 322.86 291.53 0.90 252.56 0.78 S15 2400 0.6 200 0.2 S14 338.4 291.53 0.86 252.56 0.75 S16 2400 0.8 200 0.2 S15 342.23 291.53 0.85 252.56 0.74 S17 1200 0.2 100 0.4 S16 336.87 291.53 0.87 252.56 0.75 S18 1200 0.4 100 0.4 S17 461.72 504.82 1.09 426.89 0.92 S19 1200 0.6 100 0.4 S18 485.88 504.82 1.04 426.89 0.88 S20 1200 0.8 100 0.4 S19 527.85 504.82 0.96 426.89 0.81 S21 1200 0.2 200 0.4 S20 599.17 504.82 0.84 426.89 0.71 S22 1200 0.4 200 0.4 S21 423.15 407.4 0.96 368.44 0.87 S23 1200 0.6 200 0.4 S22 442.59 407.4 0.92 368.44 0.83 S24 1200 0.8 200 0.4 S23 477.31 407.4 0.85 368.44 0.77 S25 2400 0.2 100 0.4 S24 582.06 407.4 0.7 368.44 0.63 S26 2400 0.4 100 0.4 S25 406.22 417.95 1.03 340.02 0.84 S27 2400 0.6 100 0.4 S26 413.26 417.95 1.01 340.02 0.82 S28 2400 0.8 100 0.4 S27 417.06 417.95 1.00 340.02 0.82 S29 2400 0.2 200 0.4 S28 412.09 417.95 1.01 340.02 0.83 S30 2400 0.4 200 0.4 S29 375.58 320.54 0.85 281.57 0.75 S31 2400 0.6 200 0.4 S30 383.49 320.54 0.84 281.57 0.73 S32 2400 0.8 200 0.4 S31 390.76 320.54 0.82 281.57 0.72 S32 384.37 320.54 0.83 281.57 0.73 bigger the shear span ratio, the lower the shear capacity is. Therefore, the calculation of the shear capacity for a 6. Conclusions transfer column is much safer when the inflection point In an SRC-RC transfer column, the sudden change is simply considered to be at the center of the column in stiffness caused by the local variation in the steel according to the code. section will result in moment distribution changes To validate the rationality and reliability for the at the ends of the column. Thus, in consequence, the proposed modified formula for the shear capacity, the inflection point of the column may move toward the above finite element method is adopted to establish RC part. Based on the mechanical behavior of SRC- the models of specimens as in Suzuki et al. (1994). RC transfer columns, the shear capacity formula The dimensions of section (B × D) are 400 mm × 400 under different failure modes has been studied. The mm, and the other parameters of the specimens are calculated values agree with the test results. It is presented in Table 5. found that the shear capacity formula provided by the The values calculated by the code and the modified current code may not always ensure the shear failure formula are compared with the ultimate shear capacity capacity while the proposed modified formula, which of the tests, as shown in Table 6. It can be found that reduces the shear capacity provided by stirrups, will the shear capacity calculated by the code is close to lead to a more rational design of structural members by the test results. However when the space of stirrups preventing brittle failure and improving ductility. gets smaller, the shear capacity tends to be greater and unsafe. Meanwhile, the values obtained by the modified formula are approximately 0.7-0.9 times that of the test values, providing enough redundancy and safety. JAABE vol.17 no.3 September 2018 Wei Huang 563 16) Wu Kai, Xue Jianyang and Zhao Hongtie (2012). Experimental Acknowledgements study of lateral stiffness of transfer column in SRC-RC hybrid The authors acknowledge with thanks support from structure. Engineering mechanics, 29(12): 307-315. (in Chinese). (a) the National Natural Science Foundation of China 17) Xue Jianyang, Wu Kai, Zhao Hongtie, et al. (2010). Experimental (Grant No. 51608406); (b) the State Key Laboratory study on seismic behavior of SRC-RC transfer columns. Journal of of Disaster Reduction in Civil Engineering (Project: Building Structures, 31(11): 102-110 (in Chinese). 18) Zhao Yong and Shao Yongjian (2010). Experimental study on SLDRCE15-B-06); (c) the Open Foundation of seismic behavior of SRC-RC transfer columns with different Hubei Key Laboratory of Theory and Application of constructional measures. World earthquake engineering, 26(2). Advanced Materials Mechanics (Wuhan University of 119-124. (in Chinese). Technology) (Grant No.: TMA201810). 19) Zhao Guofan (1998). High reinforced concrete structural study. Beijing: Science Press: 50-99 (in Chinese). References 1) ACI Committee (2011). Building code requirements for structural concrete (ACI 318-11) and commentary (ACI 318R-11). American Concrete Institute. 2) CEB. (1996). RC Elements Under Cyclic Loading: State of the Art Report [C], SOTA report. 3) Collins M P, Mitchell D, MacGregor J G (1993). Structural design considerations for high-strength concrete. Concrete International, 15(5): 27-34. 4) Denavit M D, Hajjar J F, and Leon R T. (2011). Seismic Behavior of Steel Reinforced Concrete Beam-Columns and Frames. Proceedings of the ASCE/SEI Structures Congress: 14-16. 5) Ellobody E and Young B (2011). Numerical simulation of concrete encased steel composite columns. Journal of Constructional Steel Research, 67(2): 211-222. 6) Feng Naiqian and Ye Lieping (1998). Japanese architectural society SRC structure calculation standard and explanation. Beijing: atomic energy press. 7) GB20010-2010 (2010), Code for design of concrete structures. Beijing: China Architecture and Building Press. 8) Huang Wei, Qian Jiang and Zhou Zhi (2016). Numerical simulation of the seismic performance of steel reinforced concrete columns by considering the lateral confining pressure. Engineering mechanics, 33(5): 157-165. (in Chinese). 9) Kimura J and Shingu Y (1998). Structural performance of SRC- RC mixed member under cyclic bending moment and shear [C]. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan. Kyushu: 1067-1068. (in Japanese) 10) Konno S, Imaizumi T, Yamamoto K, et al. (1998). Experimental study on high-rise building with lower floor composed of SRC structure. Part1: Outline of the tests about deformation capacity of SRC columns. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, Kyushu: 1029-1030. (in Japanese) 11) Mander J B, Priestley M J N and Park R (1988). Theoretical stress-strain model for confined concrete. Journal of structural engineering, 114(8): 1804-1826. 12) Paulay T, Priestly M J N. seismic design of reinforced concrete and masonry buildings. John Wiley & Sons, Inc., 2009:300-500. 13) Popovics S (1973). A numerical approach to the complete stress- strain curve of concrete. Cement and concrete research, 3(5): 583- 14) SIMULA (2011), Dassault Systems, ABAQUS Analysis User's Manual. 15) Suzuki H, Nishihara H and Matsuzaki Y (1999). Shear performance of the column where structural form changes from SRC to RC. Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, Chyugoku: 1069-1070. (in Japanese) 564 JAABE vol.17 no.3 September 2018 Wei Huang

Journal

Journal of Asian Architecture and Building Engineering – Taylor & Francis

Published: Sep 1, 2018

Keywords: SRC-RC transition column; transmission distortion; finite element model; shear capacity

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