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Punching-shear behavior of slabs with bar truss shear reinforcement on rectangular columns
Engineering Structures 134 (2017) 390–399
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Punching-shear behavior of slabs with bar truss shear reinforcement on rectangular columns Tae-Sung Eom a, Jeong-Won Song b, Jin-Kyu Song b, Gi-Sung Kang c, Jang-Keun Yoon d, Su-Min Kang e,⇑ a
Department of Architectural Engineering, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do 16890, South Korea Department of Architectural Engineering, Chonnam National University, Gwangju 61186, South Korea c Architectural Engineering & Research Team, Daelim Industrial Co., Ltd., 25 Yulgokro 2-Gil, Jongno-Gu, Seoul 110-140, South Korea d D-IC Team, Daelim Industrial Co., Ltd., 36 Jongno 1-Gil, Jongno-Gu, Seoul 110-732, South Korea e Department of Architectural Engineering, Chungbuk National University, 1 Chungdae-ro, Seowon-Gu, Cheongju, Chungbuk 361-763, South Korea b
a r t i c l e
i n f o
Article history: Received 21 June 2016 Revised 27 October 2016 Accepted 23 December 2016
Keywords: Punching shear Slab Truss shear reinforcement Rectangular column Shear test
a b s t r a c t In this study, punching-shear tests were performed to investigate the behavior of slabs supported by rectangular columns with capital. The slabs were subjected to an uneven shear transfer in two orthogonal directions by using the rectangular columns and different span lengths. Column capitals were used at the slab-column joints and preassembled bar trusses were placed at the periphery of the column capital to enhance the punching-shear capacity. Furthermore, the corners of the rectangular column and column capital were rounded to alleviate the shear stress concentration at the corners of the critical perimeter for shear. The test results show that the punching-shear strength of the slabs were significantly enhanced by the bar trusses. The shear resistance of the bar trusses was mostly contributed by the diagonal bars undergoing significant strains. On the basis of the results, the effects of the uneven shear transfer and bar truss arrangement on the slab shear behavior were investigated. In addition, the punching-shear strengths predicted by ACI 318-14, Eurocode 2, and KCI 2012 were compared with the test strengths. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Fig. 1 shows a flat-plate system for underground parking garage in which cast-in-place reinforced concrete (RC) slabs are supported by precast concrete (PC) columns with capital. In the flat-plate system, the PC columns are erected on the lower floor slab by bolting, and the bolt joints are then covered with cast-in-place concrete for protection. At the top of the PC columns, column capitals are placed to increase shear resistance against punching. Finally, cast-in-place RC slab for the upper floor is constructed on top of the PC column capitals. Fig. 1a shows a prototype floor plan for the proposed flat-plate system. The PC columns and capitals have rectangular sections because the flat plate slab has different spans in two orthogonal directions. Such rectangular columns and column capitals are beneficial in reducing the effective span length along the long-span direction, thereby decreasing negative design moments near the columns. Furthermore, the rectangular columns and column capitals are rounded at the corners to relax shear stress concentration. ⇑ Corresponding author. E-mail addresses: [email protected] (T.-S. Eom), [email protected] (J.-W. Song), [email protected] (J.-K. Song), [email protected] (G.-S. Kang), [email protected] (J.-K. Yoon), [email protected] (S.-M. Kang). http://dx.doi.org/10.1016/j.engstruct.2016.12.048 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
Generally, the flat plate system is vulnerable to punching-shear failure. Particularly, previous studies have shown the following limitations with respect to the punching-shear strength of the slabs supported by rectangular columns or column capitals [1–4]. (1) Generally, the distribution of concrete shear stresses around the perimeter of a column or column capital is not uniform. This indicates that higher shear stresses are transferred through the corners of the column or column capital rather than the sides. Such uneven shear stress transfer becomes more significant in a slab supported by rectangular columns or column capitals, because the shear stress along the longer sides of the column or column capital is less than that at the corners. Thus, the punching-shear strength of the slab might be affected by the rectangularity of the supporting columns and column capitals. (2) In Fig. 1a, bending moments and shear forces at the shorter sides of the column and column capital are greater than those at the longer sides because the slab span along the vertical direction is longer. Thus, flexural/shear cracking of the slab occurs earlier near the shorter sides. This indicates that if shear transfer along the both orthogonal directions is unsymmetrical, the punching-shear resistance of shear reinforcements can be affected by their locations and arrangements.
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Fig. 1. Cast-in-place RC slab – PC column construction for flat-plate system.
The effects of the column rectangularity on the slab punchingshear strength have been considered in ACI 318 [5] and Eurocode 2 [6]. For example, in ACI 318-14, the punching-shear strength p carried by concrete (Vc) is defined as the minimum of 0.33 fc0 bod, p 0 p 0 0.33(0.5 + 1/b) fc bod, and 0.33(0.5 + 0.25asd/bo) fc bod, where f0c = compressive strength of the concrete, bo = length of the critical shear perimeter, d = effective depth of the slab, b = ratio of the long side-to-short side dimensions of the column, and as = a coefficient considering the concentration of shear stresses at the corners of the critical shear perimeter in large columns with bo/d > 20 (as = 40 for interior columns). In these equations, if the column rectangularity and the shear-stress concentration at the corners are significant (i.e., b > 2.0 and d/bo > 20) the maximum value of Vc is limited by b and asd/bo. On the other hand, in Eurocode 2 [6], the control perimeter bo is determined at a distance 2d from the column face or column capital face where the shear stress concentration is significantly reduced. This indicates that coefficients such as b and asd/bo are not necessary for Eurocode 2. The column rectangularity is not considered in KCI 2012 [7], either. Thus, the primary objective of the present study is to investigate the effects of the uneven shear transfer around rectangular columns on the slab punching-shear strength. Another objective of the present study is to verify the effects of preassembled bar trusses on the punching-shear strength and failure mode of the slab. Stirrup-type shear reinforcements such as single-leg, multi-leg, and closed stirrups have been successfully used [8]. However, it is difficult to place the stirrups within thin slabs due to bar intervention because anchorage hooks are required to engage the top and bottom flexural reinforcing bars. Hence, preassembled bar trusses can be used as an alternative slab shear reinforcement for easier bar placement [9–11]. The bar trusses consist of the top/bottom chord bars and crossing diagonal bars, as shown in Fig. 2. The shear resistance of the bar trusses is contributed by the diagonal and vertical bars crossing shear cracks. By welding with the top/bottom chord
bars, the anchorage capacity of the shear-resisting diagonal and vertical bars can be enhanced. These preassembled bar trusses are placed on top of the bottom slab flexural bars without engaging the slab bars. Thus, bar placement is very convenient. In the present study, punching-shear tests were performed to investigate the shear behavior of the slabs supported by rectangular columns. By using different span lengths in both orthogonal directions, the slabs were subjected to an uneven shear transfer. To enhance the punching-shear strength, the column capitals were used at the slab-column joints and the preassembled bar trusses were placed around the column capitals. From the test results, the effects of the column rectangularity and bar trusses on the punching-shear behavior were investigated. In addition, the punching-shear strengths predicted by ACI 318-14, Eurocode 2, and KCI 2012 were compared with the test strengths.
Fig. 2. Bar truss for shear reinforcement of slabs.
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2. Test plan 2.1. Specimen geometry and reinforcement details Direct punching-shear tests were performed for four RC slab specimens, DSN, DSS, DST1, and DST2, supported by the rectangular PC column with capital. As shown in Fig. 3, the overall dimensions of the slabs were 2000 mm 2300 mm 240 mm. The dimensions of the PC column and column capital were 180 mm 480 mm 400 mm and 420 mm 720 mm 180 mm, respectively. The four corners of the column and column capital were rounded: for the column, semicircles with a diameter of 180 mm were used at both ends; for the column capital, four quartile circles with a radius of r = 90 mm were used at the corners. For the top tension reinforcement, D13 and D16 bars along the y direction (reinforcement ratio qly = 0.0163) and D10 and D13 bars along the x direction (qlx = 0.009) were alternated at a spacing of 50 mm. For the bottom compression reinforcement, D10 bars were placed at spacings of 50 and 100 mm in the y and x directions, respectively. The clear cover of the outmost top and bottom flexural bars was 20 mm. The depths from the bottom surface of the slab to the center of the top tension bars placed along the x and y directions were 213 and 199 mm, respectively, and the average depth of the two was taken as the effective depth of the slab, d = 206 mm. In the column, eight D19 reinforcing bars with 90° hook anchorage were used. In the column capital, D10 and D13 U-bars were placed to prevent premature concrete cracking and to achieve integrity with the cast-in-place RC slab (refer to the bar details shown in Fig. 1b). Fig. 4 shows the details of the shear reinforcement used in the specimens. In DSN, no shear reinforcement was used. On the other hand, conventional single-leg D10 stirrups with 135° and 90° end hooks were used at a spacing of 100 mm in DSS (see Fig. 4b). The stirrups engaging the top and bottom flexural bars were placed in four rows along the x direction and in three rows along the y direction. The first stirrup in each direction was located at a distance of 30 mm from the face of the PC column capital.
In DST1 and DST2, preassembled bar trusses were used for the shear reinforcement of the slab (see Fig. 4c and d). In DST1, two bar trusses were placed at each face of the column capital, parallel to the x and y directions. On the other hand, in DST2, eight bar trusses were placed radially around the column capital (see Fig. 4d): four bar trusses were arranged along the x or y directions while the other four bar trusses were arranged radially at an angle of 45°. In the bar trusses, D10 bars were used as the top and bottom chord bars, and D8 bars were used at a spacing of 130 mm as the vertical and diagonal bars. The bar inclination angles were hl = 90° and ht = 59.2° (tan ht = 151/90) for the vertical bars, and hl = 49.3° (tan hl = 151/130) and ht = 59.2° (tan ht = 151/90) for the diagonal bars (see Fig. 2). The vertical and diagonal bars were welded to the top and bottom chord bars by flare-bevel welding. Unlike the single-leg stirrups engaging the top and bottom flexural bars in DSS, the bar trusses used in DST1 and DST2 were placed between the top and bottom flexural bars. Thus, the height of the bar trusses (=151 mm) was significantly less than the stirrup height (=210 mm), as shown in Fig. 4. 2.2. Material strengths The concrete compressive strength of the RC slab on the day of testing was f0c = 31.8 MPa for DSN and DSS, and 32.4 MPa for DST1 and DST2. In the PC columns and capitals, the concrete compressive strength was f0c = 33.7 MPa for DSN and DSS and 24.6 MPa for DST1 and DST2. The concrete compressive strengths of the RC slabs and PC columns were obtained from direct compression tests of 100 mm diameter 200 mm height cylinders. The maximum aggregate size used for the concretes of the RC slabs and PC columns was 25 mm. Yield strengths of the top/bottom slab flexural bars, D10 (diameter db = 9.5 mm), D13 (db = 12.7 mm), D16 (db = 15.9 mm), and D19 (db = 19.1 mm) were fy = 595, 552, 614, and 617 MPa, respectively. High-strength steel bars of fy = 552–617 MPa were used for the slab flexural reinforcement so that punching-shear failure preceded flexural yielding. In DSS, the yield strength of D10 stirrup bars was fyt = 595 MPa, which considerably exceeded the design yield stress limit (=420 MPa) specified in ACI 318-14. In DST1 and DST2, the yield strengths of D10 chord bars and D8 (db = 8.0 mm) vertical/diagonal bars used for the bar trusses were 535 and 609 MPa, respectively. 2.3. Loading method and support condition
Fig. 3. Configurations and reinforcement details of the RC slab and PC column and capital.
Fig. 5 shows the setup for punching-shear tests. A 2000 kN – oil jack with a maximum stroke of 300 mm was used. The punchingshear tests were performed by increasing gradually the oil jack stroke (or slab deflection). For the test setup, the specimens were placed on the oil jack. At the top surface of the slab, four steel channel sections with a height 150 mm, flange width 75 mm, web thickness 9 mm, and flange thickness 9 mm were placed along the slab edges. Each channel section was supported by four highstrength steel bars (db = 42 mm, specified elastic modulus 200 GPa, and specified yield strength 1000 MPa) anchored to the strong laboratory floor. Thus, if a compressive load acts upon the column by the oil jack, the reaction force at each slab edge is resisted by the four steel bars. The channel sections help the reaction forces of the steel bars be distributed along the slab edges. The lengths of shear span in the x and y directions, defined as the distances from the face of the column capital to the centerline of the channel section at the support, were ax = 600 mm and ay = 450 mm, respectively. Thus, the shear span-to-effective depth ratios were ax/d = 2.91 and ay/d = 2.18. The span length in the x direction (ax) was intentionally determined to be greater than that in the y direction (ay) so that the bending moments and shear
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Fig. 4. Details of the shear reinforcement.
Fig. 5. Test setup for punching-shear tests.
forces at the longer sides of the column capital were less than those at the shorter sides. It is noted that the shear span-to-effective depth ratios, ax/d = 2.91 and ay/d = 2.18, were lower than those of
the existing punching-shear tests. Such low ax/d and ay/d ratios were chosen to ensure punching-shear failure before flexural yielding.
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3. Test results 3.1. Load-deflection relationships and failure modes Figs. 6 and 7 show the load-deflection relationships and crack patterns of the specimens. In Fig. 6, the vertical and horizontal axes denote the vertical column load P and the slab deflection D, respectively. The slab deflection D was taken as the mean value of the deflections measured from LVDT1 and LVDT2 (refer to Fig. 5). D is not the differential deflection between the center and supports of the slab. Thus, the effects of the elongations of the supporting high-strength steel bars placed along the slab edges were included in D. In Fig. 6, the points where the overall stiffness began to decrease significantly in the P-D relationships are denoted as circles. In fact, it is difficult to check visually whether punchingshear cracks occurred within the slab at the reference points. However, further investigation of the strains of shear reinforcements showed that the width of punching-shear cracks significantly increased at the reference points, which was discussed later in Section 3.4. Thus, the reference points were named the points of punching-shear cracking. It is noted that punching-shear cracks were not initiated at the reference points, but began to occur much earlier before the reference points. Thus, the reference points designated as the points of punching-shear cracking indicate the points where the shear resistance of the slab concrete was significantly degraded due to excessive concrete cracking and damage. For comparison, the points where the maximum loads occurred are denoted as triangles in Fig. 6.
In DSN without shear reinforcement, the maximum load Pu (=1361 kN) occurred at the point of punching-shear cracking (D = 8 mm), and then the load-carrying capacity decreased rapidly. As shown in Fig. 7a, slab flexural and shear cracks occurred significantly outside the column capital and a truncated cone of punching-shear failure formed at the periphery of the column capital. In DSS with stirrup shear reinforcement, the stiffness began to decrease significantly at the same deflection D = 8 mm as that in DSN. However, the ensuing behavior of DSS was completely different from DSN showing brittle failure. In DSS, a ductile behavior with the maximum load Pu (=1543 kN) at D = 9 mm followed until D = 24 mm. As shown in Fig. 7b, pop-out failure of the cover concrete occurred at the tension surface of the slab due to the straightening of the 135° hook tails of stirrups. The saw-cut section of the slab at the periphery of the column capital showed that inclined shear cracks occurred in both the x- and y-directions, developing into delaminating horizontal cracks along the slab flexural bars. In DST1 and DST2 with preassembled bar trusses, the slab deflection and column load at the points of punching-shear cracking increased to approximately D = 10 mm and P = 1850 kN. Thus, the maximum loads Pu (=1939 and 2029 kN) of DST1 and DST2 were significantly greater than those of DSN and DSS. The maximum loads occurred during the ductile behaviors after the points of punching-shear cracking (see Fig. 6). As shown in Fig. 7c and d, punching-shear failure occurred outside the column capital, and flexural and shear cracks in the slab were similar to those of DSN and DSS.
3.2. Strains of supporting steel bars
Fig. 6. Vertical column loads v. slab deflections.
Fig. 8 shows the strains of four high-strength steel bars E, W, N, and S at the slab supports (refer to Fig. 5); E and W of which supported the channels arranged along the x direction while N and S supported the channels arranged along the y direction. In Fig. 8, the horizontal and vertical axes denote the slab defection D and steel bar strains (eE, eW, eN, and eS), respectively. The strains of the steel bars reflect the relative magnitude of support reactions at the slab edges. For example, in DSN (see Fig. 8a), the values of eE and eW were approximately twice those of eN and eS. This indicates that the reactions resisted by the E and W channel supports were approximately twice those resisted by the N and S channel supports.
Fig. 7. Cracking and failure modes at the end of the test.
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Fig. 8. Strains in high-strength steel bars supporting channel supports.
In Fig. 8, the ratios of steel bar strains, c (=[eE + eW]/[eN + eS]), varying with the slab defection D, were plotted. In DSN and DST1, the c values at the points of punching-shear cracking were close to 2 (refer to the vertical dashed lines in Fig. 8). Thus, twothirds and one-third of the column load were transferred to the E-W and N-S channel supports, respectively. On the other hand, in DSS and DST2, the c values were significantly greater than 2 before the points of punching-shear cracking. This indicates that the majority of the column load was transferred to the E-W channel supports through the shorter sides of the column and column capital. However, the c values in DSS and DST2 decreased approximately to 2 as the slab deflection increased further, which indicates the ratio between the loads transferred through the shorter and longer sides of the column was approximately 2–1 at the punching-shear failure. In Fig. 8, the steel bar strains and resulting c values varying with the slab deflection D indicate that: (1) the shear forces transferred from the column to the slab supports along the x and y directions were different due to the different span lengths; and (2) force redistribution occurred after and even before the points of punching-shear cracking where the stiffness began to decrease significantly.
L1–L5 denote the stains measured from the D16 bars placed along the y direction. As shown in Fig. 9, the top tension bars in both the x and y directions did not reach the yield strains. Thus, in DSN, punching-shear failure occurred before flexural yielding. The shear force transferred horizontally through the longer sides of the column and column capital was significantly less (i.e. approximately a third of the column load). However, strains S1–S5 of the top tension bars arranged along the x direction exceeded strains L1–L5 in the y direction. This is because the shear span ax (=600 mm) was relatively longer and the cross-sectional areas of D10 and D13 flexural bars (qlx = 0.009) were less. Flexural bar strains were not measured in the other specimens. In DSS where the maximum load Pu (=1534 kN) was only 13% greater than Pu of DSN, it seems that flexural yielding did not occur when considering the difference between the maximum strain of the tension bars placed along the x direction in DSN and the yield strain (see Fig. 9a). On the other hand, in DST1 and DST2 where the maximum loads Pu (=1939 and 2029 kN) were greater than Pu of DSN by factors of 1.42 and 1.49, respectively, it is thought that yielding of the top tension bars might have occurred at least in the x direction. 3.4. Strains of shear reinforcements
3.3. Strains of flexural reinforcements Fig. 9 shows the strains of the top tension bars in DSN without shear reinforcement. In the figure, S1–S5 denote the stains measured from the D10 or D13 bars placed along the x direction, and
Fig. 10a–c shows the strains et of shear reinforcements measured from DSS, DST1, and DST2, respectively. In Fig. 10a and b, three measurements varying with the slab deflection D are shown: the vertical column load P, strains LS1–LS5 of the shear
Fig. 9. Strains in the top tension bars of the slab (DSN).
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reinforcements arranged along the y direction, and strains SS1–SS5 of the shear reinforcements arranged along the x direction. In Fig. 10c, four measurements are shown: the vertical column load P, strains LS1–LS5 and SS1–SS5 of the shear reinforcements
arranged along the y and x directions, respectively, and strains DS1–DS5 of the shear reinforcements arranged in the diagonal direction. In the P-D curve of each figure, the point of punchingshear cracking and the point of maximum load are denoted as a
Fig. 10. Strains in the shear reinforcements.
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circle and triangle, respectively. In addition, the region between the points of punching-shear cracking and maximum load is shown shaded. The strains of shear reinforcements are expressed as ratios to the yield strain (=et/eyt, where eyt = fyt/Es, fyt = 595 MPa for DSS (D10 stirrups) and 609 MPa for DST1 and DST2 (D8 truss bars), and Es = 200 GPa). In DSS (see Fig. 10a), the strains et in each direction were measured from five vertical stirrups placed at a spacing of 100 mm. In DST1 and DST2 with bar trusses (see Fig. 10b and c), the strains et in each direction were measured from two vertical bars (LS1 and LS3; SS1 and SS3; or DS1 and DS3) and three diagonal bars (LS2, LS4 and LS5; SS2, SS4, and SS5; or DS2, DS4, and DS5). At the point of punching-shear cracking (D = 8 mm) in DSS with single-leg stirrups (see Fig. 10a), the stirrup strains occurred significantly only in the second stirrups from the column, SS2 and LS2. In contrast, the strains of the other stirrups (i.e., LS1, LS4, LS5, and SS3–SS5) began to increase after the point of punching-shear cracking as shear cracks crossing the stirrups propagated toward the slab edge (as shown in the saw-cut section of the slab in Fig. 7b). The stirrup strains reached approximately 0.5eyt at the maximum load (D = 11 mm). On average, the stirrup strains LS1–LS5 in the y direction were greater than SS1–SS5 in the x direction due to the greater shear transfer along the y direction. It is noted that, due to the premature anchorage failure of stirrup hook tails, the stirrup strains were limited to approximately 0.5eyt or less. In DST1 with bar trusses (see Fig. 10b), at the point of punching-shear cracking (D = 10.1 mm), the diagonal bar strains LS2 and LS4 in the y direction were approximately 0.5eyt while the diagonal bar strains SS2 and SS4 in the x direction were 0.25eyt. On average at the maximum load (D = 12.7 mm), the diagonal bar strains LS2 and LS4 in the y direction increased to the yield strain eyt, while the diagonal bar strains SS2 and SS4 in the x direction were less than 0.4eyt. The difference in the diagonal bar strains in the x and y directions was caused by the uneven shear transfer around the rectangular column and column capital (refer to Fig. 8). The shear force transferred vertically along the y direction was approximately twice that transferred along the x direction. It should be noted that the vertical bar strains LS1, LS3, SS1, and SS3 remained at almost zero throughout the test. This indicates that the vertical bars used along with the diagonal bars in a bar truss did not contribute to the punching-shear strength even at large slab deflections. Immediately after the maximum load (D = 12.7 mm), the column load P slightly decreased and the electric signal from the diagonal bar LS2 was suddenly lost. This indicates that a tensile fracture might have occurred at the weld joint between the diagonal and chord bars of the bar truss (see Fig. 10b). In DST2 with bar trusses arranged radially at the periphery of the column capital, the diagonal bar strains LS2 and LS4 in the x direction, SS2 and SS4 in the y direction, and DS2 and DS4 in the diagonal direction were approximately 0.5eyt at the point of punching-shear cracking (D = 9.9 mm). Further, at the maximum load (D = 15.2 mm) and during the ensuing ductile behavior, the diagonal bar strains in all directions increased to more or less eyt. However, the vertical bar strains LS1, LS3, SS3, and DS3 in all directions were not significant compared to the diagonal bar strains or even in negative values (compressive strains). It is noted that, in DST2 with radially arranged bar trusses, the diagonal bar strains were almost the same in all bar trusses regardless of their directions, although the shear forces transferred along the x and y directions differed. This indicates that, in two-way slabs supported by rectangular columns or column capitals, the radial placement of bar trusses (DST2) could be more effective in resisting punching-shear than the orthogonal placement (DST1).
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4. Factors affecting punching-shear strength 4.1. Uneven shear transfer around rectangular column If slabs with different span lengths in both orthogonal directions are supported by rectangular columns, the shear stresses of concrete are different in four sides and corners of the rectangular columns [3,2]. According to the test results of the present study, the shear resistance carried by shear reinforcements can be also significantly affected by such uneven shear transfer. In DSS and DST1 (refer to Fig. 10a and b) where the stirrups and bar trusses were placed along the two orthogonal directions, the shear reinforcement strains SS2 and SS4 in the x direction were less than LS2 and LS4 in the y direction both at the points of punching-shear cracking and maximum load. This indicates that the stirrups and bar trusses placed along the y direction contributed more significantly to the punching-shear resistance than those placed along the x direction did. On the other hand, in DST2 (refer to Fig. 10c) where the bar trusses were placed radially around the rectangular column capital, the variations of the diagonal bar strains according to the directions of bar trusses were significantly reduced (compare SS2 and SS4 in the x direction, LS2 and LS4 in the y direction, and DS2 and DS4 in the diagonal direction). Thus, in slabs supported by rectangular columns and column capitals, the radial arrangement of bar trusses was beneficial to relaxing the uneven punching-shear resistances among the bar trusses depending on their arrangement directions. The punching-shear design provisions in current design codes, such as ACI 318-14, Eurocode 2, and KCI 2012, are based on the assumption that the shear reinforcement contributes to the punching-shear strength uniformly regardless of its arrangement direction. Thus, if span lengths of the slab are different in both orthogonal directions and column rectangularity is significant (i.e. b > 2 where b = ratio of the longer side to shorter side dimensions of the column or column capital), it is recommended to place shear reinforcement radially at the periphery of the rectangular column or column capital.
4.2. Contribution of shear reinforcement at the points of punchingshear cracking and maximum load The magnitude of shear reinforcement strains represents its relative contribution to the slab punching-shear strength. As shown in Fig. 10, the strains of the stirrup and diagonal bars significantly varied with the level of slab deflections. This indicates that the contributions of the stirrups and diagonal bars to the punching-shear strength differed between the points of punching-shear cracking and maximum load. In DST1 and DST2 with preassembled bar trusses (refer to Fig. 10b and c), the strains of the diagonal bars were about 30–60% of the yield strain (i.e. et/eyt = 0.3–0.5) at the points of punching-shear cracking. This indicates that the contribution of the truss diagonal bars to the punching-shear strength was limited to 30–60% of the yield strength at the points of punching shear cracking. This might be because the width of punching-shear cracks did not increase significantly at the points of punchingshear cracking. Then, as the slab deflections and punching-shear cracks increased further, the strains of the truss diagonal bars increased close to or greater than the yield strain at the points of maximum load, except the diagonal bars of the bar trusses placed along the x direction in DST1. Thus, the stress of the truss diagonal bars finally reached the yield strength only at the points of maximum load. In DSS with single-leg stirrups (refer to Fig. 10a), the stirrup strains were 30–50% of the yield strain (i.e. et/eyt = 0.3–0.5) at the
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point of punching-shear cracking. The stirrup strains did not increase further even at the point of maximum load, which might be because premature anchorage failure occurred in the stirrups (refer to Fig. 7b). If such premature anchorage failure did not occur the stirrup strains would reach the yield strain at the point of maximum load. 5. Comparison with nominal strengths The maximum loads Pu of the specimens were compared with the nominal punching-shear strengths Vn specified in current design codes, ACI 318-14, Eurocode 2, and KCI 2012. In each design code, the nominal punching-shear strength of slabs with shear reinforcement is defined as follows: For ACI 318-14,
V n;ACI ¼ 0:5V c;ACI þ V s where
V c;ACI
ð1Þ
n o qffiffiffiffi 0 as d 1 f c bo d, ¼ min 1; 12 þ 1b ; 12 þ 4b 3 o
V s ¼ Av f yt d=s,
f yt 6 420 MPa, and bo ¼ 2ðcx þ cy 4rÞ þ pð2r þ dÞ (refer to Fig. 5a). For Eurocode 2,
V n;EC2 ¼ 0:75V c;EC2 þ V se
ð2Þ
qffiffiffiffi 1=3 0 2=3 0 f c Þ, ¼ 0:18kð100f c qÞ bo dðP 0:035k
k¼ where V c;EC2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 200=dð6 2Þ, V se ¼ 1:5Av f yte d=s, f yte ¼ 250 þ 0:25dð6 f yt Þ, and bo ¼ 2ðcx þ cy 4rÞ þ pð2r þ 4dÞ. For KCI 2012,
V n;KCI ¼ V c;KCI þ 0:5V s
ð3Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi where V c;KCI ¼ ðks kbo f te ½cu =d cos wÞbo d, ks ¼ 4 300=dð6 1:0Þ, qffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 kbo ¼ 4= bo =dð6 1:25Þ, cosw ¼ f te ðf te þ f cc Þ=f te , cu =d ¼ 25 q=f c qffiffiffiffi 0 0 0 300q=f c , f te ¼ 0:21 f c , f cc ¼ 0:67f c , V s ¼ Av f yt d=s, f yt 6 400 MPa, and bo ¼ 2ðcx þ cy 4rÞ þ pð2r þ dÞ (refer to Fig. 5a). In Eqs. (1)–(3), d = effective depth of the slab, r = radius of the rounded corner of the column capital, Av = area of the shear reinforcement along the critical perimeter bo, s = spacing of the shear reinforcement, q = average tension reinforcement ratio of the slab in the x and y directions, and cx and cy = the shorter and longer dimensions of the rectangular column capital, respectively. In ACI 318-14 (see Eq. (1)), the contribution of the concrete is reduced to 50% (i.e. 0.5Vc,ACI) while the contribution of the shear reinforcement is equal to the yield force. This indicates that the punching-shear strength of ACI 318-14 corresponds to the strength at the point of maximum load after the shear reinforcement yields, as seen in the test results of DST1 and DST2 (refer to Fig. 10). On the other hand, in KCI 2012 (see Eq. (3)), the contribution of the concrete is not reduced while the contribution of the shear reinforcement is reduced to 50% (i.e. 0.5Vs). This indicates that the punching-shear strength of KCI 2012 corresponds to the strength at the point of punching-shear cracking before the shear reinforcement yields. In Eurocode 2 (see Eq. (2)), the contribution of the concrete is reduced to 75% (i.e. 0.75Vc,EC2) and the contribution of the shear
reinforcement was also limited to the effective yield stress fyte (=250 + 0.25d in MPa). Thus, the punching-shear strength of Eurocode 2 corresponds to the strength between the points of punching-shear cracking and shear reinforcement yielding. Further, the critical perimeter bo was defined at a distance of 2d from the face of the column or column capital. This indicates that Eurocode 2 allows a greater number of shear bars to contribute to the punching-shear strength. Table 1 shows the punching shear strengths Vn calculated from Eqs. (1)–(3). The material and geometric properties used for the punching-shear strength calculation are as follows: f0c = 31.8 MPa for DSN and DSS and 32.4 MPa for DST1 and DST2, d = 206 mm, r = 90 mm, q = 0.0126, cx = 420 mm, cy = 720 mm, b = 720/420 = 1.71, as = 40, and Av = 71.3 mm2 14 = 998 mm2 for DSS, and 50.2 mm2 16 = 803 mm2 for DST1 and DST2. In DSN without shear reinforcement, the nominal shear strength Vn was defined as the shear strength carried by concrete; Vn = Vc. In DSS with conventional single-leg stirrups, the stirrup yield strength for the calculation of Vs or Vse was reduced to the design yield stress limits specified in the design codes, such as 420 MPa for ACI 31814, 302 MPa (=250 + 0.25 206) for Eurocode 2, and 400 MPa for KCI 2012. In DST1 and DST2 with bar trusses, only the D8 diagonal bars undergoing large strains were included in the calculation of Vs and Vse while the vertical bars were excluded (refer to Fig. 10b and c). Since the diagonal bars were inclined at an angle of hl = 49.3° with respect to the longitudinal direction, d/s in Vs and Vse was modified as d/s (sin hl + cos hl) (refer to Fig. 2). Further, considering the inclination angle of ht = 59.2° with respect to the transverse direction, the Vs and Vse were reduced by multiplying sin ht. Although the truss diagonal bars of DST1 and DST2 reached the yield strain during the tests, the design yield stress limits specified in the design codes (i.e. 420 MPa for ACI 318-14, 302 MPa for Eurocode 2, and 400 MPa for KCI 2012) were used for the calculation of Vs and Vse, instead of using the actual yield strengths. Table 1 also compares the predicted punching-shear strengths Vn with the test strengths (=Pu). In ACI 318-14, the Vn (=0.5Vc,ACI + Vs) values were less than the test strengths even in DSS where the stirrup strains did not reach the yield strain due to the premature anchorage failure at the hook tails of stirrups. Particularly, ACI 318-14 considerably underestimated the punching-shear strengths of DST1 and DST2 with preassembled bar trusses. Similarly in KCI 2012 and Eurocode 2, the Vn (=Vc,KCI + 0.5Vs or 0.75Vc,EC2 + Vse) values were less than the test strengths and thus conservative estimations were made, except for DSS. Although the critical shear perimeters bo and punching-shear strength equations were significantly different, the calculated Vn and Vu/Vn values of Eurocode 2 and KCI 2012 were similar.
6. Summary and conclusions Punching-shear tests were performed to investigate the shear behavior of the slabs supported by rectangular columns with capital. The slabs with the shear span-depth ratios of ax/d = 2.91 and ay/d = 2.18 were subjected to uneven shear transfer in both orthogonal directions. To increase the punching-shear resistance of the
Table 1 Nominal shear strengths as predicted by ACI 318-14, KCI 2012, and Eurocode 2. Specimen
DSN DSS DST1 DST2
ACI 318-14
EC2
KCI 2012
Comparison with test results
Vc,ACI
Vs
Vn (1)
Vc,EC2
Vse
Vn (2)
Vc,KCI
Vs
Vn (3)
Vu (4)
(4)/(1)
(4)/(2)
(4)/(3)
1073 1073 1083 1083
– 864 648 648
1073 1401 1190 1190
1187 1187 1195 1195
– 932 699 699
1187 1822 1595 1595
1214 1214 1223 1223
– 823 617 617
1214 1626 1532 1532
1361 1543 1939 2029
1.27 1.10 1.63 1.71
1.15 0.85 1.22 1.27
1.12 0.95 1.27 1.32
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slabs, column capitals were used at the slab-column joints and preassembled bar trusses were placed at the periphery of the column capital. The major findings of the present study were summarized as follows. (1) In DSS with high-strength D10 single-leg stirrups (fyt = 595 MPa), premature anchorage failure occurred before flexural yielding of the slab due to the pop-out failure of the cover concrete caused by the strengthening-out of stirrup hook tails. As a result, the stirrup strains were limited to half of the yield strain throughout the test. (2) In DST1 and DST2 with preassembled bar trusses (fyt = 609 MPa), the strains of the diagonal bars crossing shear cracks reached about 50% of the yield strain at the point of punching-shear cracking and 100% of the yield strain at the maximum load. However, the strains of the vertical bars remained nearly at zero. Thus, it is recommended that, in the calculation of the slab shear strength, the contribution of the vertical bars be ignored. (3) In DSS, DST1, and DST2, the contributions of the stirrups and bar trusses to the punching-shear strength were significantly affected by the uneven shear transfer around the rectangular columns and column capitals. In DSS and DST1 where the stirrups and bar trusses were placed along the both orthogonal directions, the stirrups and bar trusses placed along the direction where a greater shear force was transferred were subjected to greater stresses and strains. On the other hand, in DST2 where the bar trusses were placed radially around the column, all bar trusses significantly contributed to the slab shear strength regardless of their arrangement directions. Thus, if span lengths of the slab are different in both orthogonal directions and the column or column capital rectangularity is significant (i.e. b > 2), it is recommended to place shear reinforcement radially at the periphery of the rectangular column or column capital. (4) Existing design methods specified in ACI 318-14, Eurocode 2, and KCI 2012 estimated conservatively the punching-shear strengths of the slab specimens, supported by rectangular columns and subjected to the uneven shear transfer, except for DSS where premature anchorage failure occurred at the
399
hook tails of stirrups. Particularly in DST1 and DST2 with bar trusses, the test-to-nominal punching-shear strength ratios (=Vu/Vn) were 1.63–1.71 for ACI 318-14, 1.22–1.27 for Eurocode 2, and 1.27–1.32 for KCI 2012. These results were obtained both by applying the design yield stress limits of shear reinforcements and by excluding the contribution of the truss vertical bars. Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) (No. 2015R1C1A1A01053471). And this research was financially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (NRF2015R1A2A2A01003777). The authors are grateful for their support. References [1] Sagaseta J, Tassinari L, Fernández Ruiz M, Muttoni A. Punching of flat slabs supported on rectangular columns. Eng Struct 2014;77:17–33. [2] Wight JK, MacGregor JG. Reinforced concrete: mechanics and design. 6th ed. New Jersey, US: Pearson Education, Inc.; 2011. [3] Hawkins NM, Fallsen HB, Hinojosa RC. Influence of column rectangularity on the behavior of flat plate structures. Detroit: SP-30, American Concrete Institute; 1971. p. 127–46. [4] Vanderbilt MD. Shear strength of continuous plates. J Struct Div, ASCE 1972;98 (ST5):961–73. [5] ACI Committee 318. Building code requirements for structural concrete (ACI 318-14) and commentary. Farmington Hills, MI: American Concrete Institute; 2014. [6] EN 1992-1-1. Eurocode 2: design of concrete structures. Part 1-1: general rules and rules for building. Brussels, Belgium: CEN; 2004. [7] Korean Concrete Institute. Concrete structure design code (KCI 2012). Seoul: Korean Concrete Institute; 2012. [8] Robertson IN, Kawai T, Lee J, Enomoto B. Cyclic testing of slab-column connections with shear reinforcement. ACI Struct J 2005;99(5):605–13. [9] Park HG, Kim YN, Song JK, Kang SM. Lattice shear reinforcement for enhancement of slab-column connections. J Struct Eng, ASCE 2001;138 (3):425–37. [10] Park HG, Ann KS, Choi KK, Chung L. Lattice shear reinforcement for slabcolumn connections. ACI Struct J 2007;104(3):294–303. [11] Kang S-M, Park H-G, Kim Y-N. Lattice-reinforced slab-column connections under cyclic lateral loading. ACI Struct J 2013;110(6).
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Punching-shear behavior of slabs with bar truss shear reinforcement on rectangular columns Tae-Sung Eom a, Jeong-Won Song b, Jin-Kyu Song b, Gi-Sung Kang c, Jang-Keun Yoon d, Su-Min Kang e,⇑ a
Department of Architectural Engineering, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do 16890, South Korea Department of Architectural Engineering, Chonnam National University, Gwangju 61186, South Korea c Architectural Engineering & Research Team, Daelim Industrial Co., Ltd., 25 Yulgokro 2-Gil, Jongno-Gu, Seoul 110-140, South Korea d D-IC Team, Daelim Industrial Co., Ltd., 36 Jongno 1-Gil, Jongno-Gu, Seoul 110-732, South Korea e Department of Architectural Engineering, Chungbuk National University, 1 Chungdae-ro, Seowon-Gu, Cheongju, Chungbuk 361-763, South Korea b
a r t i c l e
i n f o
Article history: Received 21 June 2016 Revised 27 October 2016 Accepted 23 December 2016
Keywords: Punching shear Slab Truss shear reinforcement Rectangular column Shear test
a b s t r a c t In this study, punching-shear tests were performed to investigate the behavior of slabs supported by rectangular columns with capital. The slabs were subjected to an uneven shear transfer in two orthogonal directions by using the rectangular columns and different span lengths. Column capitals were used at the slab-column joints and preassembled bar trusses were placed at the periphery of the column capital to enhance the punching-shear capacity. Furthermore, the corners of the rectangular column and column capital were rounded to alleviate the shear stress concentration at the corners of the critical perimeter for shear. The test results show that the punching-shear strength of the slabs were significantly enhanced by the bar trusses. The shear resistance of the bar trusses was mostly contributed by the diagonal bars undergoing significant strains. On the basis of the results, the effects of the uneven shear transfer and bar truss arrangement on the slab shear behavior were investigated. In addition, the punching-shear strengths predicted by ACI 318-14, Eurocode 2, and KCI 2012 were compared with the test strengths. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Fig. 1 shows a flat-plate system for underground parking garage in which cast-in-place reinforced concrete (RC) slabs are supported by precast concrete (PC) columns with capital. In the flat-plate system, the PC columns are erected on the lower floor slab by bolting, and the bolt joints are then covered with cast-in-place concrete for protection. At the top of the PC columns, column capitals are placed to increase shear resistance against punching. Finally, cast-in-place RC slab for the upper floor is constructed on top of the PC column capitals. Fig. 1a shows a prototype floor plan for the proposed flat-plate system. The PC columns and capitals have rectangular sections because the flat plate slab has different spans in two orthogonal directions. Such rectangular columns and column capitals are beneficial in reducing the effective span length along the long-span direction, thereby decreasing negative design moments near the columns. Furthermore, the rectangular columns and column capitals are rounded at the corners to relax shear stress concentration. ⇑ Corresponding author. E-mail addresses: [email protected] (T.-S. Eom), [email protected] (J.-W. Song), [email protected] (J.-K. Song), [email protected] (G.-S. Kang), [email protected] (J.-K. Yoon), [email protected] (S.-M. Kang). http://dx.doi.org/10.1016/j.engstruct.2016.12.048 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved.
Generally, the flat plate system is vulnerable to punching-shear failure. Particularly, previous studies have shown the following limitations with respect to the punching-shear strength of the slabs supported by rectangular columns or column capitals [1–4]. (1) Generally, the distribution of concrete shear stresses around the perimeter of a column or column capital is not uniform. This indicates that higher shear stresses are transferred through the corners of the column or column capital rather than the sides. Such uneven shear stress transfer becomes more significant in a slab supported by rectangular columns or column capitals, because the shear stress along the longer sides of the column or column capital is less than that at the corners. Thus, the punching-shear strength of the slab might be affected by the rectangularity of the supporting columns and column capitals. (2) In Fig. 1a, bending moments and shear forces at the shorter sides of the column and column capital are greater than those at the longer sides because the slab span along the vertical direction is longer. Thus, flexural/shear cracking of the slab occurs earlier near the shorter sides. This indicates that if shear transfer along the both orthogonal directions is unsymmetrical, the punching-shear resistance of shear reinforcements can be affected by their locations and arrangements.
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Fig. 1. Cast-in-place RC slab – PC column construction for flat-plate system.
The effects of the column rectangularity on the slab punchingshear strength have been considered in ACI 318 [5] and Eurocode 2 [6]. For example, in ACI 318-14, the punching-shear strength p carried by concrete (Vc) is defined as the minimum of 0.33 fc0 bod, p 0 p 0 0.33(0.5 + 1/b) fc bod, and 0.33(0.5 + 0.25asd/bo) fc bod, where f0c = compressive strength of the concrete, bo = length of the critical shear perimeter, d = effective depth of the slab, b = ratio of the long side-to-short side dimensions of the column, and as = a coefficient considering the concentration of shear stresses at the corners of the critical shear perimeter in large columns with bo/d > 20 (as = 40 for interior columns). In these equations, if the column rectangularity and the shear-stress concentration at the corners are significant (i.e., b > 2.0 and d/bo > 20) the maximum value of Vc is limited by b and asd/bo. On the other hand, in Eurocode 2 [6], the control perimeter bo is determined at a distance 2d from the column face or column capital face where the shear stress concentration is significantly reduced. This indicates that coefficients such as b and asd/bo are not necessary for Eurocode 2. The column rectangularity is not considered in KCI 2012 [7], either. Thus, the primary objective of the present study is to investigate the effects of the uneven shear transfer around rectangular columns on the slab punching-shear strength. Another objective of the present study is to verify the effects of preassembled bar trusses on the punching-shear strength and failure mode of the slab. Stirrup-type shear reinforcements such as single-leg, multi-leg, and closed stirrups have been successfully used [8]. However, it is difficult to place the stirrups within thin slabs due to bar intervention because anchorage hooks are required to engage the top and bottom flexural reinforcing bars. Hence, preassembled bar trusses can be used as an alternative slab shear reinforcement for easier bar placement [9–11]. The bar trusses consist of the top/bottom chord bars and crossing diagonal bars, as shown in Fig. 2. The shear resistance of the bar trusses is contributed by the diagonal and vertical bars crossing shear cracks. By welding with the top/bottom chord
bars, the anchorage capacity of the shear-resisting diagonal and vertical bars can be enhanced. These preassembled bar trusses are placed on top of the bottom slab flexural bars without engaging the slab bars. Thus, bar placement is very convenient. In the present study, punching-shear tests were performed to investigate the shear behavior of the slabs supported by rectangular columns. By using different span lengths in both orthogonal directions, the slabs were subjected to an uneven shear transfer. To enhance the punching-shear strength, the column capitals were used at the slab-column joints and the preassembled bar trusses were placed around the column capitals. From the test results, the effects of the column rectangularity and bar trusses on the punching-shear behavior were investigated. In addition, the punching-shear strengths predicted by ACI 318-14, Eurocode 2, and KCI 2012 were compared with the test strengths.
Fig. 2. Bar truss for shear reinforcement of slabs.
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2. Test plan 2.1. Specimen geometry and reinforcement details Direct punching-shear tests were performed for four RC slab specimens, DSN, DSS, DST1, and DST2, supported by the rectangular PC column with capital. As shown in Fig. 3, the overall dimensions of the slabs were 2000 mm 2300 mm 240 mm. The dimensions of the PC column and column capital were 180 mm 480 mm 400 mm and 420 mm 720 mm 180 mm, respectively. The four corners of the column and column capital were rounded: for the column, semicircles with a diameter of 180 mm were used at both ends; for the column capital, four quartile circles with a radius of r = 90 mm were used at the corners. For the top tension reinforcement, D13 and D16 bars along the y direction (reinforcement ratio qly = 0.0163) and D10 and D13 bars along the x direction (qlx = 0.009) were alternated at a spacing of 50 mm. For the bottom compression reinforcement, D10 bars were placed at spacings of 50 and 100 mm in the y and x directions, respectively. The clear cover of the outmost top and bottom flexural bars was 20 mm. The depths from the bottom surface of the slab to the center of the top tension bars placed along the x and y directions were 213 and 199 mm, respectively, and the average depth of the two was taken as the effective depth of the slab, d = 206 mm. In the column, eight D19 reinforcing bars with 90° hook anchorage were used. In the column capital, D10 and D13 U-bars were placed to prevent premature concrete cracking and to achieve integrity with the cast-in-place RC slab (refer to the bar details shown in Fig. 1b). Fig. 4 shows the details of the shear reinforcement used in the specimens. In DSN, no shear reinforcement was used. On the other hand, conventional single-leg D10 stirrups with 135° and 90° end hooks were used at a spacing of 100 mm in DSS (see Fig. 4b). The stirrups engaging the top and bottom flexural bars were placed in four rows along the x direction and in three rows along the y direction. The first stirrup in each direction was located at a distance of 30 mm from the face of the PC column capital.
In DST1 and DST2, preassembled bar trusses were used for the shear reinforcement of the slab (see Fig. 4c and d). In DST1, two bar trusses were placed at each face of the column capital, parallel to the x and y directions. On the other hand, in DST2, eight bar trusses were placed radially around the column capital (see Fig. 4d): four bar trusses were arranged along the x or y directions while the other four bar trusses were arranged radially at an angle of 45°. In the bar trusses, D10 bars were used as the top and bottom chord bars, and D8 bars were used at a spacing of 130 mm as the vertical and diagonal bars. The bar inclination angles were hl = 90° and ht = 59.2° (tan ht = 151/90) for the vertical bars, and hl = 49.3° (tan hl = 151/130) and ht = 59.2° (tan ht = 151/90) for the diagonal bars (see Fig. 2). The vertical and diagonal bars were welded to the top and bottom chord bars by flare-bevel welding. Unlike the single-leg stirrups engaging the top and bottom flexural bars in DSS, the bar trusses used in DST1 and DST2 were placed between the top and bottom flexural bars. Thus, the height of the bar trusses (=151 mm) was significantly less than the stirrup height (=210 mm), as shown in Fig. 4. 2.2. Material strengths The concrete compressive strength of the RC slab on the day of testing was f0c = 31.8 MPa for DSN and DSS, and 32.4 MPa for DST1 and DST2. In the PC columns and capitals, the concrete compressive strength was f0c = 33.7 MPa for DSN and DSS and 24.6 MPa for DST1 and DST2. The concrete compressive strengths of the RC slabs and PC columns were obtained from direct compression tests of 100 mm diameter 200 mm height cylinders. The maximum aggregate size used for the concretes of the RC slabs and PC columns was 25 mm. Yield strengths of the top/bottom slab flexural bars, D10 (diameter db = 9.5 mm), D13 (db = 12.7 mm), D16 (db = 15.9 mm), and D19 (db = 19.1 mm) were fy = 595, 552, 614, and 617 MPa, respectively. High-strength steel bars of fy = 552–617 MPa were used for the slab flexural reinforcement so that punching-shear failure preceded flexural yielding. In DSS, the yield strength of D10 stirrup bars was fyt = 595 MPa, which considerably exceeded the design yield stress limit (=420 MPa) specified in ACI 318-14. In DST1 and DST2, the yield strengths of D10 chord bars and D8 (db = 8.0 mm) vertical/diagonal bars used for the bar trusses were 535 and 609 MPa, respectively. 2.3. Loading method and support condition
Fig. 3. Configurations and reinforcement details of the RC slab and PC column and capital.
Fig. 5 shows the setup for punching-shear tests. A 2000 kN – oil jack with a maximum stroke of 300 mm was used. The punchingshear tests were performed by increasing gradually the oil jack stroke (or slab deflection). For the test setup, the specimens were placed on the oil jack. At the top surface of the slab, four steel channel sections with a height 150 mm, flange width 75 mm, web thickness 9 mm, and flange thickness 9 mm were placed along the slab edges. Each channel section was supported by four highstrength steel bars (db = 42 mm, specified elastic modulus 200 GPa, and specified yield strength 1000 MPa) anchored to the strong laboratory floor. Thus, if a compressive load acts upon the column by the oil jack, the reaction force at each slab edge is resisted by the four steel bars. The channel sections help the reaction forces of the steel bars be distributed along the slab edges. The lengths of shear span in the x and y directions, defined as the distances from the face of the column capital to the centerline of the channel section at the support, were ax = 600 mm and ay = 450 mm, respectively. Thus, the shear span-to-effective depth ratios were ax/d = 2.91 and ay/d = 2.18. The span length in the x direction (ax) was intentionally determined to be greater than that in the y direction (ay) so that the bending moments and shear
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Fig. 4. Details of the shear reinforcement.
Fig. 5. Test setup for punching-shear tests.
forces at the longer sides of the column capital were less than those at the shorter sides. It is noted that the shear span-to-effective depth ratios, ax/d = 2.91 and ay/d = 2.18, were lower than those of
the existing punching-shear tests. Such low ax/d and ay/d ratios were chosen to ensure punching-shear failure before flexural yielding.
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3. Test results 3.1. Load-deflection relationships and failure modes Figs. 6 and 7 show the load-deflection relationships and crack patterns of the specimens. In Fig. 6, the vertical and horizontal axes denote the vertical column load P and the slab deflection D, respectively. The slab deflection D was taken as the mean value of the deflections measured from LVDT1 and LVDT2 (refer to Fig. 5). D is not the differential deflection between the center and supports of the slab. Thus, the effects of the elongations of the supporting high-strength steel bars placed along the slab edges were included in D. In Fig. 6, the points where the overall stiffness began to decrease significantly in the P-D relationships are denoted as circles. In fact, it is difficult to check visually whether punchingshear cracks occurred within the slab at the reference points. However, further investigation of the strains of shear reinforcements showed that the width of punching-shear cracks significantly increased at the reference points, which was discussed later in Section 3.4. Thus, the reference points were named the points of punching-shear cracking. It is noted that punching-shear cracks were not initiated at the reference points, but began to occur much earlier before the reference points. Thus, the reference points designated as the points of punching-shear cracking indicate the points where the shear resistance of the slab concrete was significantly degraded due to excessive concrete cracking and damage. For comparison, the points where the maximum loads occurred are denoted as triangles in Fig. 6.
In DSN without shear reinforcement, the maximum load Pu (=1361 kN) occurred at the point of punching-shear cracking (D = 8 mm), and then the load-carrying capacity decreased rapidly. As shown in Fig. 7a, slab flexural and shear cracks occurred significantly outside the column capital and a truncated cone of punching-shear failure formed at the periphery of the column capital. In DSS with stirrup shear reinforcement, the stiffness began to decrease significantly at the same deflection D = 8 mm as that in DSN. However, the ensuing behavior of DSS was completely different from DSN showing brittle failure. In DSS, a ductile behavior with the maximum load Pu (=1543 kN) at D = 9 mm followed until D = 24 mm. As shown in Fig. 7b, pop-out failure of the cover concrete occurred at the tension surface of the slab due to the straightening of the 135° hook tails of stirrups. The saw-cut section of the slab at the periphery of the column capital showed that inclined shear cracks occurred in both the x- and y-directions, developing into delaminating horizontal cracks along the slab flexural bars. In DST1 and DST2 with preassembled bar trusses, the slab deflection and column load at the points of punching-shear cracking increased to approximately D = 10 mm and P = 1850 kN. Thus, the maximum loads Pu (=1939 and 2029 kN) of DST1 and DST2 were significantly greater than those of DSN and DSS. The maximum loads occurred during the ductile behaviors after the points of punching-shear cracking (see Fig. 6). As shown in Fig. 7c and d, punching-shear failure occurred outside the column capital, and flexural and shear cracks in the slab were similar to those of DSN and DSS.
3.2. Strains of supporting steel bars
Fig. 6. Vertical column loads v. slab deflections.
Fig. 8 shows the strains of four high-strength steel bars E, W, N, and S at the slab supports (refer to Fig. 5); E and W of which supported the channels arranged along the x direction while N and S supported the channels arranged along the y direction. In Fig. 8, the horizontal and vertical axes denote the slab defection D and steel bar strains (eE, eW, eN, and eS), respectively. The strains of the steel bars reflect the relative magnitude of support reactions at the slab edges. For example, in DSN (see Fig. 8a), the values of eE and eW were approximately twice those of eN and eS. This indicates that the reactions resisted by the E and W channel supports were approximately twice those resisted by the N and S channel supports.
Fig. 7. Cracking and failure modes at the end of the test.
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Fig. 8. Strains in high-strength steel bars supporting channel supports.
In Fig. 8, the ratios of steel bar strains, c (=[eE + eW]/[eN + eS]), varying with the slab defection D, were plotted. In DSN and DST1, the c values at the points of punching-shear cracking were close to 2 (refer to the vertical dashed lines in Fig. 8). Thus, twothirds and one-third of the column load were transferred to the E-W and N-S channel supports, respectively. On the other hand, in DSS and DST2, the c values were significantly greater than 2 before the points of punching-shear cracking. This indicates that the majority of the column load was transferred to the E-W channel supports through the shorter sides of the column and column capital. However, the c values in DSS and DST2 decreased approximately to 2 as the slab deflection increased further, which indicates the ratio between the loads transferred through the shorter and longer sides of the column was approximately 2–1 at the punching-shear failure. In Fig. 8, the steel bar strains and resulting c values varying with the slab deflection D indicate that: (1) the shear forces transferred from the column to the slab supports along the x and y directions were different due to the different span lengths; and (2) force redistribution occurred after and even before the points of punching-shear cracking where the stiffness began to decrease significantly.
L1–L5 denote the stains measured from the D16 bars placed along the y direction. As shown in Fig. 9, the top tension bars in both the x and y directions did not reach the yield strains. Thus, in DSN, punching-shear failure occurred before flexural yielding. The shear force transferred horizontally through the longer sides of the column and column capital was significantly less (i.e. approximately a third of the column load). However, strains S1–S5 of the top tension bars arranged along the x direction exceeded strains L1–L5 in the y direction. This is because the shear span ax (=600 mm) was relatively longer and the cross-sectional areas of D10 and D13 flexural bars (qlx = 0.009) were less. Flexural bar strains were not measured in the other specimens. In DSS where the maximum load Pu (=1534 kN) was only 13% greater than Pu of DSN, it seems that flexural yielding did not occur when considering the difference between the maximum strain of the tension bars placed along the x direction in DSN and the yield strain (see Fig. 9a). On the other hand, in DST1 and DST2 where the maximum loads Pu (=1939 and 2029 kN) were greater than Pu of DSN by factors of 1.42 and 1.49, respectively, it is thought that yielding of the top tension bars might have occurred at least in the x direction. 3.4. Strains of shear reinforcements
3.3. Strains of flexural reinforcements Fig. 9 shows the strains of the top tension bars in DSN without shear reinforcement. In the figure, S1–S5 denote the stains measured from the D10 or D13 bars placed along the x direction, and
Fig. 10a–c shows the strains et of shear reinforcements measured from DSS, DST1, and DST2, respectively. In Fig. 10a and b, three measurements varying with the slab deflection D are shown: the vertical column load P, strains LS1–LS5 of the shear
Fig. 9. Strains in the top tension bars of the slab (DSN).
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reinforcements arranged along the y direction, and strains SS1–SS5 of the shear reinforcements arranged along the x direction. In Fig. 10c, four measurements are shown: the vertical column load P, strains LS1–LS5 and SS1–SS5 of the shear reinforcements
arranged along the y and x directions, respectively, and strains DS1–DS5 of the shear reinforcements arranged in the diagonal direction. In the P-D curve of each figure, the point of punchingshear cracking and the point of maximum load are denoted as a
Fig. 10. Strains in the shear reinforcements.
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circle and triangle, respectively. In addition, the region between the points of punching-shear cracking and maximum load is shown shaded. The strains of shear reinforcements are expressed as ratios to the yield strain (=et/eyt, where eyt = fyt/Es, fyt = 595 MPa for DSS (D10 stirrups) and 609 MPa for DST1 and DST2 (D8 truss bars), and Es = 200 GPa). In DSS (see Fig. 10a), the strains et in each direction were measured from five vertical stirrups placed at a spacing of 100 mm. In DST1 and DST2 with bar trusses (see Fig. 10b and c), the strains et in each direction were measured from two vertical bars (LS1 and LS3; SS1 and SS3; or DS1 and DS3) and three diagonal bars (LS2, LS4 and LS5; SS2, SS4, and SS5; or DS2, DS4, and DS5). At the point of punching-shear cracking (D = 8 mm) in DSS with single-leg stirrups (see Fig. 10a), the stirrup strains occurred significantly only in the second stirrups from the column, SS2 and LS2. In contrast, the strains of the other stirrups (i.e., LS1, LS4, LS5, and SS3–SS5) began to increase after the point of punching-shear cracking as shear cracks crossing the stirrups propagated toward the slab edge (as shown in the saw-cut section of the slab in Fig. 7b). The stirrup strains reached approximately 0.5eyt at the maximum load (D = 11 mm). On average, the stirrup strains LS1–LS5 in the y direction were greater than SS1–SS5 in the x direction due to the greater shear transfer along the y direction. It is noted that, due to the premature anchorage failure of stirrup hook tails, the stirrup strains were limited to approximately 0.5eyt or less. In DST1 with bar trusses (see Fig. 10b), at the point of punching-shear cracking (D = 10.1 mm), the diagonal bar strains LS2 and LS4 in the y direction were approximately 0.5eyt while the diagonal bar strains SS2 and SS4 in the x direction were 0.25eyt. On average at the maximum load (D = 12.7 mm), the diagonal bar strains LS2 and LS4 in the y direction increased to the yield strain eyt, while the diagonal bar strains SS2 and SS4 in the x direction were less than 0.4eyt. The difference in the diagonal bar strains in the x and y directions was caused by the uneven shear transfer around the rectangular column and column capital (refer to Fig. 8). The shear force transferred vertically along the y direction was approximately twice that transferred along the x direction. It should be noted that the vertical bar strains LS1, LS3, SS1, and SS3 remained at almost zero throughout the test. This indicates that the vertical bars used along with the diagonal bars in a bar truss did not contribute to the punching-shear strength even at large slab deflections. Immediately after the maximum load (D = 12.7 mm), the column load P slightly decreased and the electric signal from the diagonal bar LS2 was suddenly lost. This indicates that a tensile fracture might have occurred at the weld joint between the diagonal and chord bars of the bar truss (see Fig. 10b). In DST2 with bar trusses arranged radially at the periphery of the column capital, the diagonal bar strains LS2 and LS4 in the x direction, SS2 and SS4 in the y direction, and DS2 and DS4 in the diagonal direction were approximately 0.5eyt at the point of punching-shear cracking (D = 9.9 mm). Further, at the maximum load (D = 15.2 mm) and during the ensuing ductile behavior, the diagonal bar strains in all directions increased to more or less eyt. However, the vertical bar strains LS1, LS3, SS3, and DS3 in all directions were not significant compared to the diagonal bar strains or even in negative values (compressive strains). It is noted that, in DST2 with radially arranged bar trusses, the diagonal bar strains were almost the same in all bar trusses regardless of their directions, although the shear forces transferred along the x and y directions differed. This indicates that, in two-way slabs supported by rectangular columns or column capitals, the radial placement of bar trusses (DST2) could be more effective in resisting punching-shear than the orthogonal placement (DST1).
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4. Factors affecting punching-shear strength 4.1. Uneven shear transfer around rectangular column If slabs with different span lengths in both orthogonal directions are supported by rectangular columns, the shear stresses of concrete are different in four sides and corners of the rectangular columns [3,2]. According to the test results of the present study, the shear resistance carried by shear reinforcements can be also significantly affected by such uneven shear transfer. In DSS and DST1 (refer to Fig. 10a and b) where the stirrups and bar trusses were placed along the two orthogonal directions, the shear reinforcement strains SS2 and SS4 in the x direction were less than LS2 and LS4 in the y direction both at the points of punching-shear cracking and maximum load. This indicates that the stirrups and bar trusses placed along the y direction contributed more significantly to the punching-shear resistance than those placed along the x direction did. On the other hand, in DST2 (refer to Fig. 10c) where the bar trusses were placed radially around the rectangular column capital, the variations of the diagonal bar strains according to the directions of bar trusses were significantly reduced (compare SS2 and SS4 in the x direction, LS2 and LS4 in the y direction, and DS2 and DS4 in the diagonal direction). Thus, in slabs supported by rectangular columns and column capitals, the radial arrangement of bar trusses was beneficial to relaxing the uneven punching-shear resistances among the bar trusses depending on their arrangement directions. The punching-shear design provisions in current design codes, such as ACI 318-14, Eurocode 2, and KCI 2012, are based on the assumption that the shear reinforcement contributes to the punching-shear strength uniformly regardless of its arrangement direction. Thus, if span lengths of the slab are different in both orthogonal directions and column rectangularity is significant (i.e. b > 2 where b = ratio of the longer side to shorter side dimensions of the column or column capital), it is recommended to place shear reinforcement radially at the periphery of the rectangular column or column capital.
4.2. Contribution of shear reinforcement at the points of punchingshear cracking and maximum load The magnitude of shear reinforcement strains represents its relative contribution to the slab punching-shear strength. As shown in Fig. 10, the strains of the stirrup and diagonal bars significantly varied with the level of slab deflections. This indicates that the contributions of the stirrups and diagonal bars to the punching-shear strength differed between the points of punching-shear cracking and maximum load. In DST1 and DST2 with preassembled bar trusses (refer to Fig. 10b and c), the strains of the diagonal bars were about 30–60% of the yield strain (i.e. et/eyt = 0.3–0.5) at the points of punching-shear cracking. This indicates that the contribution of the truss diagonal bars to the punching-shear strength was limited to 30–60% of the yield strength at the points of punching shear cracking. This might be because the width of punching-shear cracks did not increase significantly at the points of punchingshear cracking. Then, as the slab deflections and punching-shear cracks increased further, the strains of the truss diagonal bars increased close to or greater than the yield strain at the points of maximum load, except the diagonal bars of the bar trusses placed along the x direction in DST1. Thus, the stress of the truss diagonal bars finally reached the yield strength only at the points of maximum load. In DSS with single-leg stirrups (refer to Fig. 10a), the stirrup strains were 30–50% of the yield strain (i.e. et/eyt = 0.3–0.5) at the
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point of punching-shear cracking. The stirrup strains did not increase further even at the point of maximum load, which might be because premature anchorage failure occurred in the stirrups (refer to Fig. 7b). If such premature anchorage failure did not occur the stirrup strains would reach the yield strain at the point of maximum load. 5. Comparison with nominal strengths The maximum loads Pu of the specimens were compared with the nominal punching-shear strengths Vn specified in current design codes, ACI 318-14, Eurocode 2, and KCI 2012. In each design code, the nominal punching-shear strength of slabs with shear reinforcement is defined as follows: For ACI 318-14,
V n;ACI ¼ 0:5V c;ACI þ V s where
V c;ACI
ð1Þ
n o qffiffiffiffi 0 as d 1 f c bo d, ¼ min 1; 12 þ 1b ; 12 þ 4b 3 o
V s ¼ Av f yt d=s,
f yt 6 420 MPa, and bo ¼ 2ðcx þ cy 4rÞ þ pð2r þ dÞ (refer to Fig. 5a). For Eurocode 2,
V n;EC2 ¼ 0:75V c;EC2 þ V se
ð2Þ
qffiffiffiffi 1=3 0 2=3 0 f c Þ, ¼ 0:18kð100f c qÞ bo dðP 0:035k
k¼ where V c;EC2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 200=dð6 2Þ, V se ¼ 1:5Av f yte d=s, f yte ¼ 250 þ 0:25dð6 f yt Þ, and bo ¼ 2ðcx þ cy 4rÞ þ pð2r þ 4dÞ. For KCI 2012,
V n;KCI ¼ V c;KCI þ 0:5V s
ð3Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi where V c;KCI ¼ ðks kbo f te ½cu =d cos wÞbo d, ks ¼ 4 300=dð6 1:0Þ, qffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 kbo ¼ 4= bo =dð6 1:25Þ, cosw ¼ f te ðf te þ f cc Þ=f te , cu =d ¼ 25 q=f c qffiffiffiffi 0 0 0 300q=f c , f te ¼ 0:21 f c , f cc ¼ 0:67f c , V s ¼ Av f yt d=s, f yt 6 400 MPa, and bo ¼ 2ðcx þ cy 4rÞ þ pð2r þ dÞ (refer to Fig. 5a). In Eqs. (1)–(3), d = effective depth of the slab, r = radius of the rounded corner of the column capital, Av = area of the shear reinforcement along the critical perimeter bo, s = spacing of the shear reinforcement, q = average tension reinforcement ratio of the slab in the x and y directions, and cx and cy = the shorter and longer dimensions of the rectangular column capital, respectively. In ACI 318-14 (see Eq. (1)), the contribution of the concrete is reduced to 50% (i.e. 0.5Vc,ACI) while the contribution of the shear reinforcement is equal to the yield force. This indicates that the punching-shear strength of ACI 318-14 corresponds to the strength at the point of maximum load after the shear reinforcement yields, as seen in the test results of DST1 and DST2 (refer to Fig. 10). On the other hand, in KCI 2012 (see Eq. (3)), the contribution of the concrete is not reduced while the contribution of the shear reinforcement is reduced to 50% (i.e. 0.5Vs). This indicates that the punching-shear strength of KCI 2012 corresponds to the strength at the point of punching-shear cracking before the shear reinforcement yields. In Eurocode 2 (see Eq. (2)), the contribution of the concrete is reduced to 75% (i.e. 0.75Vc,EC2) and the contribution of the shear
reinforcement was also limited to the effective yield stress fyte (=250 + 0.25d in MPa). Thus, the punching-shear strength of Eurocode 2 corresponds to the strength between the points of punching-shear cracking and shear reinforcement yielding. Further, the critical perimeter bo was defined at a distance of 2d from the face of the column or column capital. This indicates that Eurocode 2 allows a greater number of shear bars to contribute to the punching-shear strength. Table 1 shows the punching shear strengths Vn calculated from Eqs. (1)–(3). The material and geometric properties used for the punching-shear strength calculation are as follows: f0c = 31.8 MPa for DSN and DSS and 32.4 MPa for DST1 and DST2, d = 206 mm, r = 90 mm, q = 0.0126, cx = 420 mm, cy = 720 mm, b = 720/420 = 1.71, as = 40, and Av = 71.3 mm2 14 = 998 mm2 for DSS, and 50.2 mm2 16 = 803 mm2 for DST1 and DST2. In DSN without shear reinforcement, the nominal shear strength Vn was defined as the shear strength carried by concrete; Vn = Vc. In DSS with conventional single-leg stirrups, the stirrup yield strength for the calculation of Vs or Vse was reduced to the design yield stress limits specified in the design codes, such as 420 MPa for ACI 31814, 302 MPa (=250 + 0.25 206) for Eurocode 2, and 400 MPa for KCI 2012. In DST1 and DST2 with bar trusses, only the D8 diagonal bars undergoing large strains were included in the calculation of Vs and Vse while the vertical bars were excluded (refer to Fig. 10b and c). Since the diagonal bars were inclined at an angle of hl = 49.3° with respect to the longitudinal direction, d/s in Vs and Vse was modified as d/s (sin hl + cos hl) (refer to Fig. 2). Further, considering the inclination angle of ht = 59.2° with respect to the transverse direction, the Vs and Vse were reduced by multiplying sin ht. Although the truss diagonal bars of DST1 and DST2 reached the yield strain during the tests, the design yield stress limits specified in the design codes (i.e. 420 MPa for ACI 318-14, 302 MPa for Eurocode 2, and 400 MPa for KCI 2012) were used for the calculation of Vs and Vse, instead of using the actual yield strengths. Table 1 also compares the predicted punching-shear strengths Vn with the test strengths (=Pu). In ACI 318-14, the Vn (=0.5Vc,ACI + Vs) values were less than the test strengths even in DSS where the stirrup strains did not reach the yield strain due to the premature anchorage failure at the hook tails of stirrups. Particularly, ACI 318-14 considerably underestimated the punching-shear strengths of DST1 and DST2 with preassembled bar trusses. Similarly in KCI 2012 and Eurocode 2, the Vn (=Vc,KCI + 0.5Vs or 0.75Vc,EC2 + Vse) values were less than the test strengths and thus conservative estimations were made, except for DSS. Although the critical shear perimeters bo and punching-shear strength equations were significantly different, the calculated Vn and Vu/Vn values of Eurocode 2 and KCI 2012 were similar.
6. Summary and conclusions Punching-shear tests were performed to investigate the shear behavior of the slabs supported by rectangular columns with capital. The slabs with the shear span-depth ratios of ax/d = 2.91 and ay/d = 2.18 were subjected to uneven shear transfer in both orthogonal directions. To increase the punching-shear resistance of the
Table 1 Nominal shear strengths as predicted by ACI 318-14, KCI 2012, and Eurocode 2. Specimen
DSN DSS DST1 DST2
ACI 318-14
EC2
KCI 2012
Comparison with test results
Vc,ACI
Vs
Vn (1)
Vc,EC2
Vse
Vn (2)
Vc,KCI
Vs
Vn (3)
Vu (4)
(4)/(1)
(4)/(2)
(4)/(3)
1073 1073 1083 1083
– 864 648 648
1073 1401 1190 1190
1187 1187 1195 1195
– 932 699 699
1187 1822 1595 1595
1214 1214 1223 1223
– 823 617 617
1214 1626 1532 1532
1361 1543 1939 2029
1.27 1.10 1.63 1.71
1.15 0.85 1.22 1.27
1.12 0.95 1.27 1.32
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slabs, column capitals were used at the slab-column joints and preassembled bar trusses were placed at the periphery of the column capital. The major findings of the present study were summarized as follows. (1) In DSS with high-strength D10 single-leg stirrups (fyt = 595 MPa), premature anchorage failure occurred before flexural yielding of the slab due to the pop-out failure of the cover concrete caused by the strengthening-out of stirrup hook tails. As a result, the stirrup strains were limited to half of the yield strain throughout the test. (2) In DST1 and DST2 with preassembled bar trusses (fyt = 609 MPa), the strains of the diagonal bars crossing shear cracks reached about 50% of the yield strain at the point of punching-shear cracking and 100% of the yield strain at the maximum load. However, the strains of the vertical bars remained nearly at zero. Thus, it is recommended that, in the calculation of the slab shear strength, the contribution of the vertical bars be ignored. (3) In DSS, DST1, and DST2, the contributions of the stirrups and bar trusses to the punching-shear strength were significantly affected by the uneven shear transfer around the rectangular columns and column capitals. In DSS and DST1 where the stirrups and bar trusses were placed along the both orthogonal directions, the stirrups and bar trusses placed along the direction where a greater shear force was transferred were subjected to greater stresses and strains. On the other hand, in DST2 where the bar trusses were placed radially around the column, all bar trusses significantly contributed to the slab shear strength regardless of their arrangement directions. Thus, if span lengths of the slab are different in both orthogonal directions and the column or column capital rectangularity is significant (i.e. b > 2), it is recommended to place shear reinforcement radially at the periphery of the rectangular column or column capital. (4) Existing design methods specified in ACI 318-14, Eurocode 2, and KCI 2012 estimated conservatively the punching-shear strengths of the slab specimens, supported by rectangular columns and subjected to the uneven shear transfer, except for DSS where premature anchorage failure occurred at the
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hook tails of stirrups. Particularly in DST1 and DST2 with bar trusses, the test-to-nominal punching-shear strength ratios (=Vu/Vn) were 1.63–1.71 for ACI 318-14, 1.22–1.27 for Eurocode 2, and 1.27–1.32 for KCI 2012. These results were obtained both by applying the design yield stress limits of shear reinforcements and by excluding the contribution of the truss vertical bars. Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) (No. 2015R1C1A1A01053471). And this research was financially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (NRF2015R1A2A2A01003777). The authors are grateful for their support. References [1] Sagaseta J, Tassinari L, Fernández Ruiz M, Muttoni A. Punching of flat slabs supported on rectangular columns. Eng Struct 2014;77:17–33. [2] Wight JK, MacGregor JG. Reinforced concrete: mechanics and design. 6th ed. New Jersey, US: Pearson Education, Inc.; 2011. [3] Hawkins NM, Fallsen HB, Hinojosa RC. Influence of column rectangularity on the behavior of flat plate structures. Detroit: SP-30, American Concrete Institute; 1971. p. 127–46. [4] Vanderbilt MD. Shear strength of continuous plates. J Struct Div, ASCE 1972;98 (ST5):961–73. [5] ACI Committee 318. Building code requirements for structural concrete (ACI 318-14) and commentary. Farmington Hills, MI: American Concrete Institute; 2014. [6] EN 1992-1-1. Eurocode 2: design of concrete structures. Part 1-1: general rules and rules for building. Brussels, Belgium: CEN; 2004. [7] Korean Concrete Institute. Concrete structure design code (KCI 2012). Seoul: Korean Concrete Institute; 2012. [8] Robertson IN, Kawai T, Lee J, Enomoto B. Cyclic testing of slab-column connections with shear reinforcement. ACI Struct J 2005;99(5):605–13. [9] Park HG, Kim YN, Song JK, Kang SM. Lattice shear reinforcement for enhancement of slab-column connections. J Struct Eng, ASCE 2001;138 (3):425–37. [10] Park HG, Ann KS, Choi KK, Chung L. Lattice shear reinforcement for slabcolumn connections. ACI Struct J 2007;104(3):294–303. [11] Kang S-M, Park H-G, Kim Y-N. Lattice-reinforced slab-column connections under cyclic lateral loading. ACI Struct J 2013;110(6).