Experimental study on the cyclic behavior of steel fiber reinforced high strength concrete columns and evaluation of shear strength

Engineering Structures 157 (2018) 250–267

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Experimental study on the cyclic behavior of steel fiber reinforced high strength concrete columns and evaluation of shear strength

T

⁎

Baek-Il Baea, Joo-Hong Chunga, , Hyun-Ki Choib, Hyung-Suk Jungc, Chang-Sik Choid a

Research Institute of Industrial Science, Hanyang University, Seoul, Republic of Korea Department Fire and Disaster Prevention Engineering, Kyungnam University, Gyeongsangnam-do, Republic of Korea c Department of Architectural Engineering, Catholic Kwandong University, Gangneung-si, Gangwon-do, Republic of Korea d Department of Architectural Engineering, Hanyang University, Seoul, Republic of Korea b

A B S T R A C T In this paper, the effectiveness of steel fiber inclusion on the structural performance of steel fiber reinforced high strength concrete columns was investigated with test of 7-high strength concrete specimens with and without steel fiber. All test specimens were subjected to axial load and reversed cyclic lateral loads. It was shown that test steel fiber inclusion significantly increase the structural performance. Steel fiber inclusion was remarkably effective than the transverse reinforcement about structural performance such as strength and energy dissipation capacity. Steel fiber reinforcement was more effective with high volumetric ratio of transverse reinforcement. Compressive strength of matrix affect to the strength and ductility. High strength matrix column specimens showed better performance than normal strength matrix column specimens. In order to verify the safety of existing strength estimation equations, test results were compared with estimated values. Most of the estimation equations were over estimated the shear strength of concrete. Therefore, in this study, for the safe design of steel fiber reinforced high strength concrete columns, newly developed estimation equation was suggested.

1. Introduction Reinforced concrete columns are subjected to compression, shear and bending simultaneously. Under repeated cyclic loading, such as seismic loads, it is necessary to give adequate confinement stress to column core and adequate shear strength should be guaranteed, for the safe structural behavior with flexural mode of failure. Recently, the use of high strength concrete has been increased, but relatively low confinement effect was observed, and researches for resolving this problem have been continuously carried out for the safe design of high strength reinforced concrete columns. And many researchers tried to solve this problem with inclusion of steel fiber to the high strength concrete [1–4]. However, these researches about steel fiber reinforced concrete columns were focused on the compressive behavior under concentric compression. It is hard to find the research results about the steel fiber reinforced high strength concrete (SFRHSC) columns subjected to the axial and lateral loads simultaneously. There were many researches about reinforced concrete columns and many models to describe the behavior of columns under repeated cyclic loading. Priestley et al. [5] suggested shear strength reduction according to the ductility of member using test results of Ang et al. [6]

⁎

and Wong et al. [7]. This model shows high accuracy at low displacement ductility ratios but low accuracy at high displacement ductility ratios because the proposed method assumes that the residual shear strength is independent to the compressive force subjected to column and aspect ratio of column. Shear strength model suggested by Watanabe and Ichinose [8] considered the rotation of crack but cannot predict accurately the shear strength of reinforced concrete columns under high level of axial load. Sezen and Moehle [9] tested the columns simulating the existing structures which have not designed about seismic action. And they collected test results from other researchers. They suggested the shear strength prediction method based on the internal stress distribution and it was evaluated by collected test data. There are many kinds of test and analysis about the reinforced concrete column behavior, except researches mentioned above. However, very limited number of researches about high strength steel fiber reinforced concrete columns have been carried out. Lee [10] tested 6 SFRC columns and 2 RC column under repeated cyclic loading. The main variables were transverse reinforcement ratio and fiber volume fraction. Steel fiber increase the shear strength and ductility of RC columns. The maximum increase rate of shear strength according to the inclusion of steel fiber was observed from the test

Corresponding author. E-mail address: [email protected] (J.-H. Chung).

https://doi.org/10.1016/j.engstruct.2017.11.072 Received 15 September 2017; Received in revised form 23 November 2017; Accepted 30 November 2017 Available online 22 December 2017 0141-0296/ © 2017 Elsevier Ltd. All rights reserved.

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preventing the bond failure and spalling of column. Using collected test results, regression equation was suggested which considers the effect of steel fiber inclusion directly to shear stress. The maximum compressive strength of test specimens which were used for regression analysis were 42 MPa. Because high strength concrete have shown different behavior under compression compared with normal strength concrete and limited number of tests were carried out about SFRC columns, for the safe design of high strength SFRC columns, the behavior of SFRHSC column should be investigated. As mentioned earlier, high strength concrete member had shown different behavior compared with normal strength concrete. Especially, test results of high strength-steel fiber reinforced concrete columns were very limited. It was hard to generalize the behavior of high strength-steel fiber reinforced concrete columns. Therefore, in this study, SFRHSC columns were tested. The structural behavior and performance of SFRHSC columns were investigated compared with steel fiber reinforced normal strength concrete columns. And for the safe design of SFRHSC columns, existing shear strength prediction equations were evaluated and new prediction equation was suggested.

(a) 0 and V series

2. Literature review As mentioned earlier, lateral load resistance of SFRC column are not sufficient to design SFRC column, compared with normal reinforced concrete columns. Therefore, in this study, applicability of shear strength prediction methods based on normal RC columns to the HSSFRC members were evaluated. And applicability of limited number of SFRC column shear strength equations and SFRC beam shear strength equations to SFRHSC column were evaluated. 2.1. Shear strength model for normal RC columns ACI318-14 [12] model considered that the shear strength of RC columns were consists of contribution of concrete, Vc , and contribution of shear reinforcement Vs . This model based on the 45-degree truss model. Nominal shear strength of RC columns and contribution of each component can be calculated as,

(b) T series

Vn = Vc + Vs

(1)

Nu ⎞ Vc = 0.17 ⎜⎛1 + ⎟ λ f c′ b w d 14 Ag ⎠ ⎝

(2)

Vs =

Av f yt d (3)

s

Vc cannot be greater than the Vc calculated by Eq. (4). Vc = 0.29λ fc′ bw d 1 +

0.29Nu Ag

(4)

where Vn is nominal shear strength of member, Vc is nominal shear strength provided by concrete, Vs is nominal shear strength provided by shear reinforcement, Av is area of shear reinforcement within spacing s , f yt is specified yield strength of transverse reinforcement, d is distance from extreme compression fiber to centroid of longitudinal tension reinforcement, s is center-to-center spacing of transverse reinforcement, Nu is factored axial force normal to cross section occurring simultaneously with Vu , Ag is gross area of concrete section, λ is modification factor to reflect the reduced mechanical properties of lightweight concrete to normal weight concrete of the same compressive strength, is specified compressive strength of concrete, bw is web width of section. Shear strength model for RC columns suggested by Priestley et al. [5] is consisted of three components, contribution of concrete, Vc, contribution of shear reinforcement Vs and arch action Vp. Especially, Vc considered the effect of displacement ductility. Contribution of shear concrete on shear strength reduced with increasing displacement

(c) Section of test specimens Fig. 1. Details of test specimen.

results about specimens with 1.5% of steel fiber. Lee also evaluated the RC column shear strength prediction equations. Equation suggested by Priestley et al. [5] had shown good agreement with test results. Using this equation, Lee suggested new prediction equation for SFRC column shear strength. The maximum compressive strength of test specimens which were used for regression analysis were 69 MPa. Nagasaka [11] tested SFRC columns and collected other test results. Steel fiber can increase the shear strength, ductility and energy dissipation capacity 251

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Table 1 Details of test specimens. Specimens

b

d

Concrete

a/d

h

[mm] HSC-0 HSC-V1 HSC-V2 HSC-T HSC-TV1 NSC-V1 NSC-TV1

400

332

1600

2.4

Longitudinal steel

Transverse steel

P/ P0∗

Fiber

f c′

ρl

f y,l

ρw

s

f y,t

Vf

Lf

[MPa]

[%]

[MPa]

[%]

[mm]

[MPa]

[%]

[mm]

62.9 64.8 67.6 62.9 64.8 35.6 35.6

3.97

593.7

0.12

300

570.6

0 1 2 0 1 1 1

0.49

130

478.7

0.12 0.49

300 130

570.6 478.7

Df

0.1 30

0.5

30

0.5

b : width of column section, d : effective width of column section, h: height of column, a/d: effective depth-shear span ratio, f c ′: compressive strength of concrete, ρl : reinforcement ratio of longitudinal steel, f y,l : yield strength of longitudinal steel, ρw : reinforcement ratio of transverse steel, s: spacing of transverse reinforcement, f y,t : yield strength of transverse reinforcement, Vf : volume fraction of steel fiber, Lf : length of steel fiber, Df : diameter of steel fiber, P/ P0∗ : axial force ratio, P: applied axial force, P0∗ = 0.85f c ′ (Ag −Ast ) + f y Ast , Ag : gross sectional area, Ast : total sectional area of longitudinal steel, f y : yield strength of corresponding steel. Table 2 Mix proportion. ID

HSC NSC

Vp =

W/C

S/A

C

W

[%]

[%]

Unit weight [kg/m3]

28.2 63.2

43.5 61.5

563 348

159 220

S

714 1065

G

SP

SF

Vs = 926 666

5.65 2.85

W/C: water cement ratio, S/A: fine aggregated ratio, C: cement, W: water, S: fine aggregated, G: coarse aggregate, SP: super plasticizer, SF: steel fiber.

ductility ratio. Considering reduction of crack angle, which is caused by the existence of axial force, they assumed the crack angle as 30 degree. And they suggested that arch action should be considered to calculate the shear strength of RC column based on the test results they collected. Kowalsky and Priestley [13] revise the original equations considering the effect of aspect ratio and longitudinal reinforcement on shear strength. (5)

Vc = k fc′ Ae = αβγ fc′ (0.8Ag )

(6)

(9)

Av f yt (D−c−c0)cot(θ) (10)

s

where c is the depth from the extreme compression fiber to the neutral axis, c0 is the cover to the center of the transverse reinforcement, θ is the angle of the flexure-shear crack to the member axis M and V are moment and shear at the critical section, respectively. M/VD is equivalent to the value of L/D where L is distance from critical section to the point of contraflexure. ρl is longitudinal reinforcement ratio, γ is the reduction in strength of the concrete shear resisting mechanism with increasing ductility. ASCE/SEI 41-13 model [14] was suggested based on the model proposed by Sezen and Moehle [9]. This model also considered the displacement ductility ratio. However, the effect of displacement ductility ratio was affected to both concrete and shear reinforcement components. Concrete contribution to shear strength calculated based on the principal stress and shear reinforcement contribution to shear strength based on the 45-degree truss theory. Shear strength can be calculated using below equations,

1%: 78.5 2%: 157

Vn = Vc + Vs + Vp

Nu (d−c ) 2a

(11)

Vn = k (Vc + Vs ) 1 ⩽ α = 3−

M ⩽ 1.5 VD

β = 0.5 + 20ρl ⩽ 1.0

(7)

⎛ 0.5 fc′ Nu 1+ Vc = λ ⎜ M /(Vd ) 0.5 fc′ Ag ⎝

(8)

⎞ ⎟ 0.8Ag ⎠

Fig. 2. Properties of steel fiber.

252

(12)

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Table 3 Mechanical properties of concrete. ID

f c′

f

sp

Vs = ft

fr

Remarks

7.45 8.36

No fiber Vf = 1.0%

Vf = 2.0% Vf = 1.0%

62.9 64.8

3.58 6.19

6.45 8.26

HSC-2

67.6

8.06

13.47

14.59

NSC-1

35.6

5.02

6.72

7.62

f c ′: compressive strength tested according to KS F 2405, f

sp :

(13)

s

where k = 1.0 in regions where displacement ductility demand is less than or equal to 2, 0.7 in regions where displacement ductility is greater than or equal to 6, and varies linearly for displacement ductility between 2 and 6, M / Vd is the largest ratio of moment to shear times effective depth under design loadings for the column but shall not be taken greater than 4 or less than 2, d is the effective depth. It shall be permitted to assume that d = 0.8h , where h is the dimension of the column in the direction of shear.

[MPa] HSC-0 HSC-1

Av f yt d

splitting strength tested

according to KS F 2423, f t : flexural tensile strength tested according to JCI-S-001-2003, f r : modulus of rupture tested according to KS F 2408.

2.2. Shear strength model for SFRC columns Most of the researches on the shear strength of SFRC member were based on the test of beams. As a result of reviewing previous researches, two-available shear strength model were found, Lee’s model [10] and Nagasaka’s model [11]. These two models were suggested by regression analysis. Lee’s model [10] based on the 50 specimens. The maximum compressive strength of concrete was 68 MPa but matrix strength which were not reinforced with steel fiber only have compressive strength of 45 MPa. Nagasaka [11] used 128 specimens but the maximum compressive strength was only 45 MPa. Therefore, the applicability of these two models on high strength SFRC column should be investigated. Lee [10] suggested the shear strength model based on the model of Priestley et al. [5]. Shear strength of SFRC column can be calculated as,

Vn = Vc + Vs + Vp + Vsf

(14)

Vsf = 0.146Vf Vc

(15)

where Vsf is shear strength contribution of steel fiber (in percentile vealue), other components, Vc , Vp and Vs can be calculated by using Eqs. (6), (9) and (10), respectively. Nagasaka model [11] consider the all components on shear as stress and calculated as;

ku kp (Fc + 17.657) Qsu = τsu = 0.115 + 0.837 pw σwy + 0.677 Vf + 0.1σ0 a bj + 0.12 d (16) where Qsu is shear strength of SFRC column, b is column width, j is 7/8 of effective depth of section, ku is modification factor considering the effectiveness area of section, kp is modification factor for considering the longitudinal tensile reinforcement ratio, Fc is compressive strength of concrete, a is shear span to depth ratio, pw : shear reinforcement ratio, d σwy is yield strength of shear reinforcement, Vf is volume fraction of steel fiber (%) and σ0 is compressive stress applied to the columns.

Fig. 3. Failure of high strength concrete with and without steel fiber under axial compression.

Fig. 4. Test setup.

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σcu = 0.41τ

lf df

Vf

(l f ⩽ l c )

σfu lf ⎞ σcu = 0.41 ⎜⎛1− ⎟ σfu Vf (l f > l c ) ⎝ 4τ df ⎠

(22)

(23)

where Vw is shear force carried by steel fiber, Vc is shear force carried by concrete, τR is shear strength of concrete, σfu is tensile strength of steel fiber, lc is critical length of steel fiber. 3. Specimen design and test procedure 3.1. Test plan and specimen design In order to evaluate the seismic performance of the high strength steel fiber reinforced concrete columns, a limited number of SFRHSC columns were tested under reversed cyclic loading. The main variables are steel fiber volume fraction, compressive strength of matrix and shear reinforcement ratio. For the evaluation of shear strength, control specimen was designed to be failed in brittle shear failure mode. For this purpose, high flexural strength was provided by comparatively high longitudinal reinforcement ratio, 3.97% with high design yield strength, 500 MPa. Shear reinforcement ratio of control specimen was designed according to the minimum transverse reinforcement of ACI318 [12] with 400 MPa of design yield strength. Sectional dimension of test specimens was 400 × 400 mm, height is 1600 mm. Simulating the double curvature deformation of columns in buildings, shear span to depth ratio was 2.4. Compressive strength of 60 MPa was used for control specimen which was lower than the limitation of compressive strength of concrete on shear strength equation based on the ACI318 [12]. Steel fiber content is main variable and 0, 1 and 2% volume fraction were used for high strength concrete columns for the verification of effect of the steel fiber on the shear strength of high strength concrete column. Comparing the effect of shear strength increase effect according to the shear reinforcement, 4-times shear reinforcement ratio was planned. 30 and 60 MPa compressive strength of concrete were used for the investigation the change of failure mode of SFRC columns according to the compressive strength of concrete matrix. 7 test specimens were planned to test. Details of test specimens were shown in Fig. 1. Fig. 1(a) have shown the test specimens with minimum shear reinforcement and these specimens were categorized in 0 and V series. Fig. 1(b) have shown the test specimens with 4-times the shear reinforcement ratio compared with control specimen. These specimens categorized in T-series. All of the reinforcements have used the standard hook according to ACI318 [12]. Detailed information of test specimens was shown in Table 1.

Fig. 5. Loading history.

2.3. Shear strength model for SRC beams As mentioned earlier, two models for SFRC column shear strength calculation based on the normal strength SFRC column test results. However, as for the shear strength of steel fiber reinforced concrete, much research has been conducted on the beam rather than the column. And comparatively large number of high strength SFRC beam was tested. Therefore, in this study, SFRC beam shear strength models were evaluated. ACI544.4R [15] model was based on the suggestion of Sharma [16]. Shear strength contribution of concrete determined by the splitting strength of SFRC and shear span to depth ratio.

vu =

2 ⎛ d ⎞0.25 f 3 sp ⎝ a ⎠

(17)

where fsp is splitting strength of fiber reinforced concrete. Ashour et al. [17] studied about the shear behavior of high strength SFRC beams which have compressive strength of concrete larger than 90 MPa. They suggested two shear strength equations. One was based on the ACI318 [12] shear strength equation and the other based on the Zsutty’s equation [18] for shear strength of beam. They used fiber factor F for considering the shear strength increase effect of steel fiber. ACImodified prediction method was shown in Eq. (20) and Zsutty’s equations [18] were shown in Eqs. (18) and (20).

vu = (0.7 fc′ + 7F )

d d + 17.2ρl a a

d 0.333 a vu = (2.11 3 fc′ + 7F ) ⎛ρl ⎞ for > 2.5 d ⎝ a⎠ d vu = ⎡ (2.11 3 fc′ + 7F ) ⎛ρl ⎞ ⎢ a⎠ ⎝ ⎣

0.333

3.2. Material properties This study focused on the investigation of column shear strength variation according to the varied material performance. Because SFRC have higher performance than normal concrete especially for tensile strength, splitting and flexural strength were tested with compressive strength. The mix proportion of concrete used for the casting of the test specimens was classified into high strength matrix and normal strength matrix, and steel fibers were mixed in each proportion. Mix proportions used in this study were provided in Table 2. Type I Portland cement was used and maximum size of 19 mm crushed gravel was used as coarse aggregate. Superplasticizer was used for providing adequate workability to fresh SFRC. The steel fiber was hooked and 30 mm long and 0.5 mm in diameter. Steel fiber used in this study was shown in Fig. 2. The nominal tensile strength of fiber was 1100 MPa. As a result of slump test for each mix proportion, HSC without steel fiber, HSC with 1% steel fiber inclusion and 2% inclusion have shown the slump as

(18)

(19)

⎤ ⎛ 2.5 ⎞ + ⎛2.5− d ⎞ for a/ d ⩾ 2.5 ⎥ ⎝ a/d ⎠ ⎝ a⎠ ⎦ (20)

Swamy et al. [19,20] tested beams which have various types of sections. They concluded that shear strength should be related to flexural strength. Considering this observation, using regression analysis they suggested shear strength equation for SFRC beams using flexural strength of SFRC.

Vw + Vc = 0.9σcu bw d + 3.75τR bw d

(21) 254

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reinforcement of column. The longitudinal reinforcement of column had a yield strength and tensile strength of 593.7 MPa and 715.4 MPa respectively. D32 have nominal diameter of 31.8 mm. D13 rebars were used for transverse reinforcement of T series specimens. It had yield strength of 478.7 MPa and ultimate strength of 615.9 MPa. Nominal diameter of D13 is 12.7 mm. D10 rebars were used as transverse reinforcement of test specimens of 0 and V series. According to the test, 570.6 MPa and 691.6 MPa yield and ultimate strength was observed.

190 mm, 200 mm and 205 mm respectively. For NSC, slump of NSC without fiber, 1% and 2% inclusion were 200, 215 and 223 mm respectively. Three cylinder specimens (100 × 200 mm) were tested for each batch of concrete according to KS F 2405 [21]. Steel fiber is more effective under tensile stress than compressive stress. It means that SFRC have higher shear strength compared with normal concrete. Therefore, in order to quantify the tensile strength increase of SFRC, in this study, flexural tensile strength test and splitting tensile strength test were carried out according to the JCI-S-011-2003 [22] and KS F 2423 [23], respectively. And modulus of rupture test was carried out according to KS F 2408 [24]. All material test results were shown in Table 3. As a result of the compressive strength test, the increase of the strength due to the inclusion of the steel fiber was not as great as 8% at maximum. However, as shown in Fig. 3, steel fiber effectively prevented the brittle failure and spalling. The significant increase of strength was found in the tensile strength test. The splitting tensile strength of steel fiber reinforced high strength concrete increased linearly with the amount of steel fiber volume fraction. However, increase rate of flexural tensile strength increased with fiber volume fraction. However, increase of compressive strength of matrix cannot increase tensile strength of SFRC significantly. All reinforcements used for test specimens were tested with test standard of KS B 0802 [25]. D32 rebars were used for main longitudinal

3.3. Test procedure In this study, a double curvature test setup was used. The ends of test specimen were fixed and did not rotate during the test as shown in Fig. 4. The guide frame was attached to L-shaped loading frame in order to make the horizontal movement of loading frame and prevent the outof-plane deformation. Axial load was subjected to the column head by using two hydraulic jacks. Each jacks have 1000 kN capacity. Lateral reversed cyclic loading was subjected by hydraulic actuator of 2000 kN capacity which was installed to the reaction wall. The reversed cyclic loading history was shown in Fig. 5. All tests were carried out with displace control loading scheme. Two times of load reversals were subjected with amplitude of 0.25, 0.5, 1, 2, 3 and 4 times the yield drift ratio. Yield drift(displacement) was determined by using sectional analysis of control specimen, HSC-0. According to the

(b) HSC-V1

(a) HSC-0

(d) HSC-T

(c) HSC-V2

Fig. 6. Failure pattern.

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(f) NSC-V1

(e) HSC-TV1

(g) NSC-TV1 Fig. 6. (continued)

crack was firstly observed at the drift ratio of 0.7%. Other diagonal cracks were occurred during the next cycle and they were connected each other during experiencing the drift ratio of 1%. At drift ratio of 1.5%, diagonal cracks were widen and spalling of cover concrete was occurred along diagonal crack. HSC-V2 showed the similar behavior of HSC-V1. However, during the second cycle of drift ratio of 1.0%, short diagonal cracks were concentrated at the center of the web area. These cracks merged into one vertical crack and failed with significant loss of load resisting capacity. HSC-T have shown the similar behavior of HSC-0 until the occurrence of initial flexural cracking. However, diagonal cracks developed into the center of the web of columns at drift ratio of 0.7%. Experiencing drift ratio of 1% diagonal cracks were widen and concrete cover between diagonal cracks were spalled. Test specimen was failed during drift ratio of 1.5%. Effect of steel fibers was investigated with test of HSC-TV1. Flexural cracks distributed to the mid-height of columns at drift ratio of 0.3%. During the drift ratio of 0.7%, flexural cracks were developed into diagonal cracks. Diagonal cracks were distributed experiencing second cycle of drift ratio of 1.0%. After experiencing maximum loading, diagonal cracks changed into vertical cracks along the main longitudinal reinforcement of column. Test specimen was failed with crushing of column ends. Flexural crack of NSC-V1 was observed at the end of column.

ACI374.2R-13 [26], yielding of member generally occurred at drift ratio of 0.5–0.75%. According to the sectional analysis of HSC-0, yield drift was occurred at drift ratio of about 0.8%. Therefore, yield drift ratio was assumed to 0.75%. For the investigation of stress distribution, strain gauges and LVDTs were mounted to test specimens. 4. Test results One of the main purpose of this study was the investigation of the change of failure pattern of HSC columns after the steel fiber inclusion. Therefore, mode of failure was firstly observed and was defined before investigating the structural performance. 4.1. Failure mode The crack patterns of each specimen at maximum load and failure were shown in Fig. 6. HSC-0 showed the initial flexural cracks at the end of the column during first cycle. Diagonal cracks were shown at the web of column reaching drift ratio of 0.5%. Experiencing second cycle of drift ratio of 0.5%, diagonal cracks were start to widen. After reaching maximum load, drift ratio of 0.75%, significant loss of load resisting capacity was shown. HSC-V1 also experienced the initial flexural cracking during first cycle at the end of the column. Diagonal 256

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subjected to cyclic loading, where displacements were measured at the upper stub of column. Test results were also shown in Table 4. Because performance of reinforced concrete columns depends on the mode of failure, failure mode was shown in Table 4. Mode of failure was categorized into 4 types, ductile flexural failure(D-F), moderately ductile with shear failure(MD-S), limited ductile with shear failure(LD-S) and brittle shear failure(BS), which was suggested by Ang [27]. Failure of test specimen was defined by suggestion of ASCE 41-13 [14], which was the 80% of maximum load carry capacity. Maximum shear resisting capacity of HSC-0 is 378.3 kN. Maximum load was shown just after the widening of diagonal crack as shown in Fig. 6(a). At drift ratio of 1%, load carrying capacity was significantly

Diagonal cracks were crossed at the center of the web area and connected each other during the drift ratio of 0.9%. Vertical cracks were developed after maximum loading and failed with widening of vertical cracks. NSC-TV1 showed similar cracking pattern. However, after occurrence of diagonal cracking, short diagonal cracks were appeared along the main longitudinal reinforcement of column until reaching the maximum load. Crushing of column ends were occurred during the drift ratio of 1.47%. 4.2. Load-displacement relation Fig. 7 illustrates the load–displacement curves of test specimens

(a) HSC-0

(b) HSC-V1

(c) HSC-V2

(d) HSC-T Fig. 7. Load-displacement relation.

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(f) NSC-V1

(e) HSC-TV1

(g) NSC-TV1 Fig. 7. (continued)

specimens, HSC-TV1 failed in flexural-shear failure. Strength and ductility were significantly increased compared with HSC-0. Maximum load carrying capacity was 733.94 kN that is the 194% of maximum load carrying capacity of HSC-0. Especially, ductility was significantly increase. Drift ratio at maximum load carrying capacity was 1.47% which was the drift ratio that other test specimens cannot be experienced until the failure. HSC-TV1 experienced the yielding of longitudinal reinforcement before the drift ratio of maximum load carrying capacity. NSC-V1 showed 389.1 kN of maximum load carrying capacity which is 68% of maximum load carrying capacity of HSC-V1. However, decrease rate of load carrying capacity of NSC-V1 was lower than HSC-V1.

reduced. HSC-V1 had shown the maximum load as 608 kN which is 161% of HSC-0. Transverse reinforcement was yielded at drift ratio of 1%. Maximum load carrying capacity was appeared at drift ratio of 1.24% with widening of diagonal crack. HSC-V2 specimen have 632.1 kN of maximum load carrying capacity which is 167% of HSC-0. Transverse reinforcement was yielded at drift ratio of 1.11%, just before experiencing the maximum load. The difference of maximum load carrying capacity of HSC-V1 and HSV-V2 were not significant, however, failure aspect was different as shown in Fig. 6(b) and (c). HSC-T specimen had shown the 517.8 kN of maximum load carrying capacity. As shown in Fig. 9(d), transverse reinforcement yielded just before reaching the maximum load carrying capacity. Unlike other test 258

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Table 4 Test results. ID

Cracking

Yielding: transverse rebar

Pcr

Py,t

Yielding: longitudinal rebar

Loading direction

Py,l

θcr [%]

[kN]

θ y,t [%]

[kN]

θ y,l [%]

[kN]

HSC-0

0.18

241.04

0.43

347.61

1.02

327.52

HSC-V1

0.18

251.12

1.00

594.26

1.49

563.20

HSC-V2

0.19

252.44

1.11

616.88

1.51

596.90

HSC-T

0.16

227.99

0.71

439.52

1.66

257.84

HSC-TV1

0.18

237.07

1.26

701.16

1.04

640.67

NSC-V1

0.17

227.41

0.61

391.09

0.89

333.83

NSC-TV1

0.16

219.81

1.42

501.71

1.48

512.75

Pos. Neg. Pos. Neg. Pos. Neg. Pos. Neg. Pos. Neg. Pos. Neg. Pos. Neg.

Maximum load

Pu

θu [%]

[kN]

0.42 0.37 1.24 0.61 1.25 0.75 0.98 0.75 1.47 1.49 0.68 0.74 1.48 1.40

378.30 362.40 608.00 593.80 632.13 514.43 517.79 476.77 733.94 782.99 398.09 387.14 587.58 583.20

θcr : drift ratio at first crack, Pcr : load at first crack, θ y,t : drift ratio at the yielding of transverse reinforcements, Py,t : load at the yielding of transverse reinforcements, θ y,l : drift ratio at the yielding of longitudinal reinforcements, Py,l : load at the yielding of longitudinal reinforcements, θu : drift ratio at the maximum load, Pu : load at the maximum load, Pos.: positive direction of loading(push), Neg.: negative direction at loading(pull).

Fig. 9. Strain distribution of transverse reinforcements along the column height.

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Fig. 9. (continued)

HSC-T, steel fiber inclusion is more effective to increase the energy dissipation capacity of reinforced concrete column than increase the transverse reinforcement ratio. Comparing T-series specimens with TV1-series specimens, steel fiber significantly increase the dissipated energy.

This aspect was caused by the dispersion of diagonal cracks as shown in Fig. 6(b) and (f). NSC specimens have shown more dispersed crack than HSC specimens. NSC-TV1 have 587.6 kN of maximum load carrying capacity and it was 80% of HSC-TV1 which have same transverse reinforcement ratio. The effect of matrix strength was decreased with the increase of transverse reinforcement ratio.

5.2. Strain distribution of transverse reinforcements 5. Discussion of test results In this study, strain measurement plan was developed to measure the strain of all the transverse reinforcements placed in the test specimen in order to examine the effectiveness of the transverse reinforcements under seismic action. Fig. 9 showed the strain distribution of the transverse steel obtained from the experiment according to the change of the target displacement of the loading history. For all the figures in Fig. 9, the thick solid line in red indicated the strain distribution at the displacement when the specimen undergoes the maximum load. In the case of HSC-0, it could be seen that all of the transverse reinforcing bars were not experienced large deformation before the maximum strength development. However, transverse reinforcement, which was located at the point where the effective depth of the column from the bottom reached the yield, strain, just after experiencing maximum load. This abrupt increase of strain means that

5.1. Energy dissipation Ductile behavior of a structure under seismic action is directly related to energy dissipation capacity of structural members. In other words, greater energy dissipation improves seismic performance. Fig. 8 shows cumulative dissipated energy obtained by calculating the area which was made by loop of each cycle. As shown in Fig. 8, except for HSC-0 which was failed in brittle shear, all test specimens were experienced significant increase of dissipated energy after development of diagonal shear crack. Comparing HSC-0, HSC-V1 and HSC-V2, inclusion of steel fiber caused significant increase of energy dissipation capacity. However, it did not affected by the volume fraction of steel fiber. Comparing the curve of HSC-V1 and 260

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experience yield strain even after experiencing maximum load. In the case of HSC-V2, it was shown that the rebar experienced yielding at 0.2d above the base when experiencing maximum strength. However, it can be seen that the yield strain cannot be reached due to the development of vertical cracks along the longitudinal reinforcement. This vertical crack developed from the diagonal shear cracks which was occurred after experiencing maximum load. According to these three specimens, it was conformed that proper volume fraction of steel fiber inclusion can prevent the shear failure. In HSC-T, it was also found that the longitudinal reinforcement had not experienced yielding before the maximum strength was developed. However, in the case of HSC-TV1 reinforced with additional transverse reinforcements and 1% steel fiber, it was confirmed that the longitudinal reinforcement yields at a position within 1d from the bottom of the column, reaching maximum load carrying capacity. In addition to the continuous flexural deformation, the strain was continuously increased at the subsequent drift ratio, but it was confirmed that the strain was decreased while experiencing shear failure at the final failure. 1% volume fraction of steel fiber was more effective to the HSCT specimen than HSC-0 specimen. This is because the high transverse reinforcement ratio prevents the increase of the inclined crack width and induces the diffusion of the inclined cracks. And steel fiber is more effective in this situation because steel fiber cannot transfer the stress crossing the cracks which was widen. The strain distribution on the tensile side of NSC-V1 was not significantly different from other specimens. However, it can be seen that the magnitude of the compressive strain rapidly increases at the top of the column directly applying the compressive force. In NSC-TV1, when the maximum load was experienced, the rebar yielded at both the tensile and compressive sides, and the compressive strain was intensively increased at the end of the specimen as in the NSC-V1 specimen. Unlike HSC-series specimens, longitudinal reinforcement of NSC series specimens was yielded under compressive stress. This phenomenon is considered to be caused by the low stiffness of the matrix.

Fig. 8. Cumulative dissipated energy.

cracks crossing the transverse reinforcement were appeared suddenly and test specimen failed in brittle manner. As shown in Fig. 9(b), HSCV1 also experienced brittle shear failure because strain of transverse reinforcement suddenly increased with experiencing maximum load. Unlike HSC-V1, transverse reinforcement strain of HSC-V2 was evenly distributed through the column height. As shown in Fig. 9(b), transverse reinforcement strain of HSC-V1 was concentrated at 600 mm from the bottom of column. It means that steel fiber volume fraction could change the crack angle. HSC-T did not experience yielding of the transverse reinforcement before the maximum load experience. However, when the maximum load was experienced, it was found that the rebar experienced yielding at about 1d and 1.5d away from the top and bottom, respectively. However, unlike HSC-0, HSC-V1, and HSC-V2, the transverse reinforcement located at the center of column height did not experience yielding even after the failure and the damage was concentrated at the transverse reinforcement which was firstly yielded. HSC-TV1 also showed the damage concentration in the upper and lower parts of column. More clear difference could be observed compared with HSC-T specimen. It might be caused by the occurrence of plastic hinge. The failure type of NSC-V1 was similar to that of HSC-V1. However, it was found that the yielding of the transverse reinforcement was occurred earlier as the shear resistance contribution of the concrete was low. In the case of maximum strength, only the reinforcing bars between 1d and 2d were yielded, but all the reinforcing bars were yielded at the final failure. NSC-TV1 showed failure mode as LD-S, but it did not yield to the maximum load experience. As the cracks became concentrated after the maximum strength development, the strain of the transverse reinforcements exceeded the yield strain and it was considered that the plastic hinge was formed.

5.4. Neutral axis depth The neutral axis depth is a key parameter for determining the flexural behavior of the member and is an important parameter for evaluating the contribution of the arch mechanism within the member. The neutral axis depth was calculated using the measured LVDT at the location of extreme flexural reinforcement of the member. LVDT measure the displacement of length from column end to the distance of 400 mm, which was column depth. The change of the neutral axis depth of all specimens is shown in Fig. 11. The neutral axis depth of the HSC-0 was 180 mm in the initial deformation state and increased to 196 mm in the final failure. It is believed that this is due to the flexural deformation before the final failure and the flexural stress was lost due to the sudden shear failure, although the flexural crack progressed to some extent. This aspect had also shown in specimens HSC-V1 and HSC-V2 as shown in Fig. 11. Three specimens were failed in shear as shown in Figs. 6 and 7. As shown in Fig. 10(a), this phenomenon is still present in the strain distributions of longitudinal reinforcement. The reversal of the neutral axis depth in the HSC-0 was also observed in the HSC-V1. However, it was shown that flexural deformation was larger than that of HSC-0, and effect of steel fiber was considered to delay the shear failure and increase the contribution of arch action. In HSC-V2, the inversion of the neutral axis was insignificant, but the movement of the neutral axis was observed to be similar to HSC-V1. HSC-T, which is reinforced with more transverse reinforcements than HSC-0, showed more stable flexural behavior than HSC-0. No inversion of neutral axis depth change was observed. The final neutral axis depth was 152 mm. As shown in Fig. 11, neutral axis changes of specimens with flexureshear failure have shown gradual decrease. HSC-TV1 maintained the flexural deformation continuously after the maximum strength development and the neutral axis depth was changed to decrease. Finally, the

5.3. Strain distribution of longitudinal reinforcements The strains of the longitudinal reinforcement in column were investigated to define the more accurate failure patterns. Fig. 10 shows the strain distributions of the extreme tension steel reinforcement of each specimen by drift ratio. In case of HSC-0 specimen showing BS failure type, the longitudinal reinforcement did not yield even after experiencing the maximum load. Especially, in the region of 1d or less where the damage is concentrated, the reinforcement strain was decreased. It could be seen that when the steel fiber is mixed with 1% volume ratio, the strain experienced greater than HSC0 under the maximum load. However, they did not 261

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concrete columns and the steel fiber reinforced concrete beams which were mentioned earlier were evaluated. The test results of test specimens were compared with estimation results. Predicted values using equations about columns and beams were shown in Table 5. And descriptive statistics results were shown in Table 6. Since the strength of the specimen is closely related to the specimen mode of failure, tow tables summarizes the mode of failure of the specimens. Shear contribution calculated by prediction equations were shown in Fig. 12. Contribution of shear reinforcement on test results were determined by using the strain distribution of transverse reinforcement which were crossing the diagonal shear cracks, as shown in Figs. 9 and 6, respectively. As shown in Table 5, ACI318 [12] and ASCE41 [14] models underestimate the strength of test specimens. As shown in Fig. 12(a) and (c), because these two equations cannot consider the effect of steel fiber, strength of test specimens were underestimated. This phenomenon appeared both in HSC and NSC members. Therefore, contribution of concrete to shear strength should consider the effect of steel fiber. UCSD model, which was suggested by Priesteley et al. [5], overestimated the shear strength of test specimens excepting HSC-V1 and V2 specimens. As shown in Fig. 12(b), estimated value for shear

depth of the neutral axis decreased to about 100 mm, and the flexural deformation continued. In the case of NSC-V1 with a small compressive strength of the concrete matrix, the reversal of the neutral axis depth change started to take place due to compression deformation after the maximum strength development, but not so much. NSC-TV1 can confirm stable flexural behavior like HSC-TV1 by changing the neutral axis depth. It was confirmed that stable bending behavior was achieved even after the maximum load action, and the neutral axis was found to be destroyed by 107 mm.

6. Strength evaluation 6.1. Applicability of previously suggested equations to SFRHSC columns For the safe design of reinforced concrete members, it is necessary to predict the shear strength of the members. As mentioned earlier, the shear strength prediction equation of SFRC column was only in a study of Lee [10] and Nagasaka [11]. Since the strength of the test specimen used in the regression analysis of the estimation equation was mainly limited to the normal strength concrete, the possibility of application of the shear strength of high strength SFRC column should be preceded. In addition, the shear strength prediction equations for normal reinforced

Fig. 10. Strain distribution of longitudinal reinforcement along the column height.

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(e) HSC-TV1

(f) NSC-V1

(g) NSC-TV1 Fig. 10. (continued)

the member. Therefore, although two of them, Ashour Z model and Swamy model [17,19], underestimated the strength of SFRC column and they were suggested based on the high strength SFRC beams, it could be hard to apply these equations to the design of SFRHSC columns.

contribution of shear reinforcement was similar with test results. It was observed that Vp was highly overestimated and contribution of concrete to shear force also be overestimated. Lee’s model [10] considered the effect of steel fiber but it showed the overestimation aspect according to Table 5. Especially, HSC-0 and HSC-T specimen which have no steel fiber were overestimated. But test results of specimens with steel fiber showed good agreement with estimation results. Because, strength contribution of shear reinforcement had shown good agreement with test results, concrete contribution of HSC and highly confined member should be re-evaluated, in order to apply this model to SFRC columns. Nagasaka’s model [11] also overestimated the strength of test specimens as shown in Table 5. Nagasaka’s model [11] highly underestimated the shear contribution of shear reinforcements. Therefore, this model highly overestimated the concrete contribution to the shear strength of the members. As mentioned earlier, according to the dataset of Nagasaka’s works [11], the maximum compressive strength considered was 45.5 MPa. The overestimation of Nagasaka’s model [11] might be caused by this problem. Most of the shear strength equations for SFRC beams were overestimated the concrete contribution of shear strength. This problem mainly caused by the difference of stress distribution in the web area of

6.2. Suggestion of shear strength estimation equation for SFRHSC columns Most of the estimation equations for shear strength of SFRC member also depended on the regression analysis. However, as mentioned earlier, these were only few number of test specimens available. Therefore, in this study, shear strength development method suggested by ASCE41-13 [14] was modified to predict the contribution of concrete. And UCSD model [5] was used to calculate the shear reinforcement contribution on shear strength, because UCSD model [5] had shown the good agreement with test results, especially for shear reinforcement contribution. Because SFRHSC column are also subjected to axial load and lateral load, assumptions for stress distribution of ASCE41-13 were maintained. Because splitting strength of matrix should be changed for SFRC, modification of related variables were suggested, as shown in the below equations; 263

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SFRHSC columns was shown below;

Vc,suggestion = (0.068fsp + 0.56)

⎛ fsp Nu 1+ ⎜ M / Vd fsp Ag ⎝

⎞ 0.8Ag ⎟ ⎠

(26)

Vn,suggestion = Vc,suggestion + Vs,Priestely

(27)

As shown in Fig. 13, most of test specimens have shown approximately 85% of precision. Statistical values for suggested equations for SFRHSC columns were as shown below; Mean value: 1.07, Standard deviation: 0.178, Variance: 0.0314, Coefficient of variation: 0.166. Suggested equation can predict the shear strength of SFRHSC columns relatively higher precision than previously suggested equations, as shown in Table 6. 7. Conclusions From the limited number of experiment on high strength concrete columns reinforced with hooked steel fiber and hoops, the following conclusions were obtained. (1) Under the same transverse reinforcement ratio, inclusion of steel fiber remarkably increase the shear strength, energy dissipation capacity and ductility of the columns. However, increase rate of these performances were decreased with increase of volume fraction of steel fiber. (2) The increase of shear strength and energy dissipation capacity according to the inclusion of steel fiber was more effective than the 4times volume fraction of shear reinforcement(original reinforcement ratio by volume fraction was 0.12%). (3) Steel fiber is significantly effective for preventing the spalling and crack concentration under shear stress. Preventing spalling of cracks, steel fiber reinforced column specimens showed the significant increase of ductility, especially with high transverse reinforcement ratio. (4) Steel fiber inclusion increase the shear contribution of shear reinforcement with decrease of crack angle. However, crack angle did not decrease in the case of specimens with high volume fraction of transverse reinforcement. (5) Strength estimation equations for reinforced concrete columns,

Fig. 11. Neutral axis depth from compression fiber according to the drift ratio.

Vc =

⎛ fsp Nu 1+ ⎜ M / Vd fsp Ag ⎝

fsp =

fcuf 20− F

+ 0.7 +

⎞ 0.8Ag ⎟ ⎠

(24)

F

(25)

where F is fiber factor (= αVf lf / df ), α is bond factor determined by the shape of steel fiber (straight: 0.5, crimped: 0.75, hooked: 1.0), Vf is volume fraction of steel fiber, lf is length of steel fiber, df is diameter of steel fiber, fcuf is cube compressive strength of fiber reinforced concrete. Shear reinforcement contribution was decided by using Priestley’s model [5], in order to considering the varied crack angles. For more precision, concrete contribution was fitted with test results collected by previous researches [10,28–30] and this study. Total of 43 specimens were used. Final form of concrete contribution of shear strength of

Table 5 Evaluation of shear strength of test specimens by using previously suggested shear strength prediction equations. ID

HSC-0 HSC-V1 HSC-V2 HSC-T HSC-TV1 NSC-V1 NSC-TV1

Failure mode

BS BS BS BS LD-S BS LD-S

ACI318

UCSD

ASCE41

Lee

Nagasaka

Sharma

Ashour(A)

Ashour(Z)

Swamy

Vn

Vtest Vn

Vn

Vtest Vn

Vn

Vtest Vn

Vn

Vtest Vn

Vn

Vtest Vn

Vn

Vtest Vn

Vn

Vtest Vn

Vn

Vtest Vn

Vn

Vtest Vn

346 351 356 566 570 283 503

1.09 1.73 1.77 0.91 1.29 1.41 1.17

565 587 586 783 877 439 759

0.67 1.04 1.08 0.66 0.84 0.91 0.77

448 454 462 668 674 353 573

0.84 1.34 1.37 0.78 1.09 1.13 1.03

522 585 626 717 846 490 786

0.73 1.04 1.01 0.72 0.87 0.81 0.75

539 628 676 607 697 465 534

0.70 0.97 0.93 0.85 1.05 0.86 1.10

344 529 733 564 750 446 666

1.10 1.15 0.86 0.92 0.98 0.89 0.88

414 650 888 635 871 570 790

0.91 0.93 0.71 0.82 0.84 0.70 0.74

324 455 588 544 675 412 633

1.17 1.34 1.08 0.95 1.09 0.97 0.93

295 419 545 515 639 372 593

1.28 1.45 1.16 1.01 1.15 1.07 0.99

BS: Brittle shear failure ( μ ⩽ 2.0 ), LD-S: Limited ductile with shear failure (2.0 < μ ⩽ 4.0 ), Vn : shear strength calculated by previously suggested equations, Vtest : test results according to the positive value of Table 4, Ashour(A): ACI equation were modified by Ashour, Ashour(Z): Zsutty equations were modified by Ashour.

Table 6 Statistical analysis of test specimens (Vtest/Vn value). Statistic index

ACI318

UCSD

ASCE41

Lee

Nagasaka

Sharma

Ashour(A)

Ashour(Z)

Swamy

Mean Standard deviation Variance Coefficient of variation

1.339 0.322 0.104 0.240

0.852 0.165 0.027 0.194

1.081 0.225 0.051 0.208

0.846 0.132 0.017 0.156

0.924 0.135 0.018 0.146

0.969 0.113 0.013 0.117

0.809 0.095 0.009 0.117

1.073 0.145 0.021 0.135

1.158 0.163 0.027 0.141

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(a) ACI318

(b) UCSD model

(c) ASCE41-13 model

(d) Lee Model

(e) Nagasaka model Fig. 12. Evaluation of strength of test specimens according to the previously suggested equations.

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(f) Sharma model

(g) Ashour-ACI modification model

(h) Ashour-Zustty modification model

(i) Swamy model Fig. 12. (continued)

steel fiber reinforced concrete columns and steel fiber reinforced concrete beams were evaluated with test specimens of this study. Equations of design code or guideline were under-estimated because they did not consider the effect of steel fiber. Most of other prediction methods for columns over-estimated the shear strength of column because they overestimated the shear contribution of concrete. Over-estimation of concrete contribution was caused by regression analysis which use limited range of compressive strength of concrete. (6) In order to predict the concrete contribution of shear strength of steel fiber reinforced high strength concrete columns, ASCE41-13 model [14] was used because it was developed based on the rational stress distribution assumptions. Shear reinforcement contribution was determined by Priestley’s model [5]. Newly developed equation showed relatively good agreement with test data for steel fiber reinforced concrete columns. (7) In this study we only collect the 36 test specimens from previous researches on SFRC columns under cyclic loading. For the construction of design recommendation on the HSFRC members there should be more test results.

Fig. 13. Evaluation of suggested equation.

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Acknowledgement [14]

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MOE) (NRF2014R1A2A1A11051049 and NRF-2015R1D1A1A01059989).

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