Punching-shear design equation for two-way concrete slabs reinforced with FRP bars and stirrups

Punching-shear design equation for two-way concrete slabs reinforced with FRP bars and stirrups

Construction and Building Materials 66 (2014) 522–532 Contents lists available at ScienceDirect Construction and Building Materials journal homepage...

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Construction and Building Materials 66 (2014) 522–532

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Punching-shear design equation for two-way concrete slabs reinforced with FRP bars and stirrups Mohamed Hassan a,1, Ehab A. Ahmed a,2, Brahim Benmokrane b,⇑ a b

Department of Civil Engineering at the University of Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada Innovative FRP Materials for Concrete and Civil Structures, Department of Civil Engineering, University of Sherbrooke, Quebec J1K 2R1, Canada

h i g h l i g h t s  Punching-shear strengths of two-way slabs reinforced with FRP flexural reinforcement and FRP stirrups are introduced.  The strains in the FRP stirrups are presented and analyzed to introduce a design value for the stress in FRP stirrups.  Design equation for the punching-shear strength of two-way slabs reinforced with FRP bars and stirrups is proposed.  The proposed design equation is calibrated against experimentally measured strengths and showed good accuracy.

a r t i c l e

i n f o

Article history: Received 28 November 2013 Received in revised form 10 March 2014 Accepted 2 April 2014 Available online 24 June 2014 Keywords: Punching Shear Two-way Slab Fiber-reinforced polymer GFRP Design Stirrups Concrete

a b s t r a c t Recently, the Canadian Standard Association (CSA) provided its first punching-shear equation in the CSA S806-12, which represented a step forward in designing two-way concrete slabs reinforced with fiberreinforced-polymer (FRP) bars. Yet neither the new CSA S806-12 equation nor any other design guide addresses the contribution of FRP stirrups as shear reinforcement for such elements due to the very limited research work. This study proposes a preliminary design equation to predict the punching-shear resistance of two-way concrete slabs reinforced with FRP bars and stirrups. The proposed equation is based on adopting the concrete contribution equation from the CSA S806-12 and modifying the stirrup contribution equation of the CSA A23.3-04 to reflect using FRP materials instead of steel. The proposed modification was verified against the test results of an extensive experimental work conducted at the University of Sherbrooke on full-scale two-way specimens measuring 2500 mm  2500 mm  200 mm or 350 mm. The accuracy of the predictions was compared to the test results. The results of this study supported the strain limit of 4000 microstrains in the FRP stirrups for calculating the contribution of the FRP stirrups to the punching-shear capacity, as provided by ACI 440 Committee and CSA S6S1-10. In addition, the proposed punching-shear design equation shows good yet conservative predictions with a tested-to-predicted punching-shear ratio (Vtest/Vpred) of 1.17 ± 0.21. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Corrosion of steel reinforcement is one of the major problems that shorten the service life of reinforced-concrete (RC) structures. Parking garages stand out as an example of structures in which the use of deicing salts causes corrosion of steel reinforcement, leading to significant deterioration and rehabilitation requirements. The

⇑ Corresponding author. Tel.: +1 819 821 7758; fax: +1 819 821 7974. E-mail addresses: [email protected] (M. Hassan), [email protected] USherbrooke.ca (E.A. Ahmed), [email protected] (B. Benmokrane). 1 Tel.: +1 819 821 8000x63181; fax: +1 819 821 7974. 2 Tel.: +1 819 821 8000x62135; fax: +1 819 821 7974. http://dx.doi.org/10.1016/j.conbuildmat.2014.04.036 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.

use of fiber-reinforced-polymer (FRP) bars as an alternative to conventional steel bars has emerged as a realistic and cost-effective solution to overcome such corrosion problems. Shear reinforcement is often used as an effective solution to increase the punching-shear strength of flat slabs, especially when slab thickness is subjected to constraints. In the past few years, several reinforcing systems—such as studs, stirrups, and bent-up bars—have been developed to increase punching-shear strength. The efficiency of such systems is influenced by their development conditions (anchorage and bond) and detailing rules [26]. Closed stirrups have also been used to enhance the punching-shear capacity of two-way slabs, as in concrete beams in which closed stirrups enclose the top and bottom flexural reinforcement and increase the shear strength. The use of well-anchored stirrups, such as closed

M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532

523

Nomenclature d db Ef Efv Ec fc0 ffu ffuv ffvb bo;0.5d Vtest

effective slab depth (mm); (slab thickness – 50/or 45mm – db) bar diameter modulus of elasticity of the FRP bars (MPa) modulus of elasticity of the straight portion of the FRP stirrups (MPa) modulus of elasticity of the concrete (MPa) concrete compressive strength of cylinders (MPa) ultimate tensile strength of the FRP bars ultimate tensile strength of the straight portion of the FRP stirrups (MPa) ultimate tensile strength of the FRP stirrups at the bend portion (MPa) critical perimeter at a distance of 0.5d from the column face (mm) ultimate punching-shear load (measured in test) (kN)

stirrups, can increase punching strength by 60% [25], while insufficient anchorage can cause a local crushing of the concrete at the bends [19]. Due to the relatively low modulus of elasticity of FRP bars compared with steel bars, concrete members reinforced with FRP develop wider and deeper cracks than members reinforced with steel. The overall shear capacity of concrete members reinforced with FRP bars as flexural reinforcement is lower than that of concrete members reinforced with steel bars [14]. Considerable research has been undertaken at the University of Sherbrooke through NSERC research activities to investigate the shear behavior of concrete members reinforced with FRP bars. The investigation was initiated by assessing the concrete contribution of FRP-RC beams without FRP shear reinforcement [14,15]. Thereafter, the investigation assessed the structure performance of the FRP stirrups and their contribution to the shear capacity of FRP-RC beams [3,4]. These investigations concluded that the presence of carbon- and glass-FRP (CFRP and GFRP) stirrups in the RC beam specimens, similar to steel stirrups, maintains the concrete contribution after the formation of the first shear crack. In addition, they recommended using 4000 microstrains as the FRP stirrup strain at the ultimate limit state, as specified by ACI [1] and CSA [10] in predicting the shear strength of concrete members reinforced with FRP stirrups. Recently, this research project was extended through a collaborative project with Quebec’s Ministry of Economic Development, Innovation, and Export Trade (MDEIE) to develop and implement GFRP reinforcement for two-way concrete slabs for parking garages. This project included two phases for assessing the punching-shear behavior of GFRP-RC two-way slabs without shear reinforcement (Phase I) and with FRP shear reinforcement in the form of closed stirrups (Phase II). Phase I has been completed and its results already published [12], and [16,17], while Phase II characterized newly developed carbon and glass FRP stirrups and its preliminary test results showed improved punching-shear behavior when FRP stirrups are provided [18]. On the other hand, the design codes present the punching-shear strength as a summation of the concrete contribution (Vc) and the shear-reinforcement contribution (Vs). To date, none of the FRP design codes provides any equation for the shear-reinforcement contribution to the punching-shear capacity. This paper aims at evaluating the concrete contribution to the punching-shear capacity provided by the available FRP design codes and guides in North America and introducing a preliminary equation to calculate the

vtest vc vfv qf qfv ns Afv rb sfv

ultimate punching-shear stress (measured in test) (MPa) ultimate punching-shear stress provided by the concrete (MPa) ultimate punching-stress provided by the FRP shear reinforcement (MPa) FRP reinforcement ratio shear reinforcement ratio at a perimeter of 0.5d = (nsAfv/Sfvbo;0.5d) number of stirrups on a concentric line parallel to the column perimeter cross-sectional area of the FRP shear reinforcement on a concentric line parallel to the column perimeter bend radius (mm) stirrup spacing from the column face according to [9]

FRP shear-reinforcement contribution to the punching-shear capacity of two-way concrete slabs. To achieve that, the test data from literature concerning the two-way concrete slabs without shear reinforcement was used to evaluate Vc, while the experimental program reported herein was used to introduce the Vs equation. A preliminary general equation for calculating the punching-shear capacity is also introduced. 2. Punching-shear design provisions Most of the design equations for FRP-RC sections are based on those for steel-RC sections with modifications to account for FRP instead of steel. Thus, this section highlights the punching-shear design of steel-RC slabs provided by CSA [11], as it forms the basis for introducing the new punching-shear equation to the CSA [9]. It also highlights the punching-shear equations of the CSA [9] and ACI [1], respectively. Thereafter, a proposed design equation for FRP-RC sections will be proposed and calibrated to the results of the experimental program conducted herein. 2.1. CSA A23.3-04 [11] The design method in the CSA [11] code is based on limiting the shear force that can be resisted along a defined failure surface, with the concrete contribution taken as proportional to the square root of the concrete compressive strength. The CSA [11] code calculates the critical section at a distance of d/2 from the concentrated load. The factored shear-stress resistance, vr, provided by the concrete (vc) for slabs without shear reinforcement is calculated as the smallest value of Eqs. (1)–(3):

vr ¼ vc ¼

  qffiffiffiffi 2 0:19k/c fc0 1þ bc

ð1Þ

where k = concrete density factor (1 for normal weight and 0.85 for semi-lightweight); /c = concrete resistance factor (0.65); bc = ratio of the long side to short side of column; and fc0 = cylinder compressive strength of concrete.

vr ¼ vc ¼



as d

bo;0:5d

 qffiffiffiffi þ 0:19 k/c fc0

ð2Þ

where as = 4 for interior columns, 3 for edge columns, and 2 for corner columns; bo;0.5d is the perimeter of the critical section for slabs and footings at a distance of d/2 away from the column face (mm),

M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532

vc

qffiffiffiffi ¼ 0:19k/c fc0 ðMPaÞ ðfor stirrupsÞ

vs ¼

/s Av s fyv b0;0:5d s

ð4Þ

ð5Þ

where Avs is the cross-sectional area of the shear reinforcement on a line parallel to the column perimeter, s is the spacing of the shear reinforcement, and fyv is the yield strength of the shear reinforcement. /s is the resistance factor for non-prestressed reinforcing bars (/s = 0.85). The factored maximum shear stress vf, when stirrups are provided, is determined as:

vf

¼ 0:55k/c

qffiffiffiffi fc0 ðMPaÞ ðfor stirrupsÞ

ð6Þ

2.3. ACI-440.1R-06 [1] The ultimate punching shear capacity provided by the concrete (vc) for the two-way concrete slabs reinforced with FRP bars or grids, which accounts for the effect of reinforcement stiffness and the shear transfer in two-way concrete slabs, is as shown in Eq. (11):

Vc ¼

4 5

qffiffiffiffi fc0 bo;0:5d c

fc0 is the specified compressive strength of the concrete (MPa), bo;0.5d is the perimeter of the critical section for slabs and footings at a distance of d/2 away from the column face (mm), and c is the neutralaxis depth (mm) of the cracked transformed section, c = kd.



qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2qf nf þ ðqf nf Þ2  qf nf

qffiffiffiffi fc0 ðMPaÞ

ð7Þ

The spacing of the shear reinforcement, s, shall not exceed d/2 for stirrup shear reinforcement, with the first stirrup placed at d/4 from the column face. The shear reinforcement shall pbe ffiffiffiffi extended to the section where vf is not greater than 0:19k/c fc0 but at least to a distance 2d from the column face.

ð11bÞ

335 mm

Outside the shear-reinforced zone, the shear stress due to factored shear force at the critical section located d/2 outside the outermost peripheral line of the shear reinforcement shall not exceed:

v c ¼ 0:19k/c

ð11aÞ

335 mm

CFRP/GFRP (No. 13) rb /db=4, rb=50.8 mm

CFRP/GFRP (No. 10) rb /db=4, rb=38.1 mm

(a) C-shaped FRP stirrups Steel stirrups to prevent splitting

300 mm

400 mm

300 mm 300 mm

pffiffiffiffi The value of fc0 used to calculate vr in Eqs. (1)–(3) shall not exceed 8 MPa. Besides, if d exceeds 300 mm, the value of vc obtained from Eqs. (1)–(3) shall be multiplied by 1300/(1000 + d). If vf > vc, vf being the factored shear stress, shear reinforcement has to be used. The factored shear resistance of the concrete, vc, inside the shear-reinforced zone is calculated from Eq. (4), which represents 50% of the contribution calculated from Eq. (3) and the factored shear stress provided by shear reinforcement vs is calculated from Eq. (5).

When calculating vc with Eqs. (8)–(10), the value of fc0 shall not exceed 60 MPa. Besides, if the effective depth d of the structuralslab system exceeds 300 mm, the value of vr obtained from the equations shall be multiplied by (300/d)0.25.

900 mm

ð3Þ

ð10Þ

250 mm

vr ¼ vc

qffiffiffiffi ¼ 0:38k/c fc0

v r ¼ v c ¼ 0:056k/c ðEf qf fc0 Þ1=3

900 mm

d = the distance from the extreme compression fiber to the centroid of tension reinforcement (the effective depth),

250 mm

524

2.2. CSA S806-12 [9] The CSA [9] equations are based on the same forms as the CSA [11] equations for steel-reinforced sections with modifications to account for the FRP instead of steel and employing the cubic root of the concrete compressive strength. This design model is based on the same concept as in the CSA [11], which implies a 45° failure surface and a critical perimeter nearest a column equal to 0.5 times the effective depth (0.5d) from the column face. The strength of the concrete resisting punching shear (vc) is calculated by the smallest of Eqs. (8)–(10):

v r ¼ v c ¼ 0:028k/c

  2 1=3 ðEf qf fc0 Þ 1þ bc

Debonding tube

(b) Preparation of the test specimens for test method B.5

ð8Þ

where bc = the ratio of long side to short side of column, concentrated load, or reaction area; Ef = modulus of elasticity of the FRP bars; and qf = FRP reinforcement ratio.

v r ¼ v c ¼ 0:147k/c



 1=3 ðEf qf fc0 Þ bo;0:5d þ 0:19

as d

ð9Þ

where as = 4 for interior columns, 3 for edge columns, and 2 for corner columns.

(c) Mode of failure Fig. 1. Testing of FRP stirrups in concrete blocks [2], test method B.5).

525

1.88 999 1065

a G(aa)bb-cdd(Sfv): G denotes GFRP tensile reinforcement; (aa) denotes the reinforcement ratio; bb denotes the slab thickness in mm; c denotes the FRP punching-shear reinforcement material (GFRP and/or CFRP); dd denotes stirrup configuration (SS for single spiral stirrups and BSS for bundled spiral stirrups); CS denotes closed stirrups; and Sfv denotes stirrups spacing relative to the effective depth, if any. b Based on 150  300 mm cylinder testing. c Characteristic tensile strength = average value  3  standard deviation. d ffvb actual ultimate tensile bend strength obtained from test method B.5 according to ACI [2].

– 0.53 – 0.53 0.53 0.50 0.50 – 551 – 551 551 774 774 – 2.25 – 2.25 2.25 1.26 1.26 – 1004 – 1004 1004 1562 1562 – 44.6 – 44.6 44.6 124.4 124.4 – 0.63 – 0.64 1.27 0.64 0.45 – 50.8 – 50.8 50.8 50.8 50.8 – 129 – 129 129 129 129 – 12.7 – 12.7 12.7 12.7 12.7 – 70 – 70 70 70 100 – GFRP – GFRP GFRP CFRP CFRP 1.60 700 769

0.34 48.2 0.34 1.61 56.7 1.61 1.61 1.61 1.61 15 15 25 25 25 25 25 No. No. No. No. No. No. No. 12 12 22 22 22 22 22 34.3 29.5 38.2 40.2 37.5 38.2 40.2

– 485 780 – 2.11 1.23 – 948 1598 – 44.8 130.4 – 0.94 0.47 – 38.1 38.1 – 71 71 – 9.53 9.53 – 70 70 – GFRP CFRP 2.07 1079 1334 1.21 64.9 1.21 1.21 14 No. 20 14 No. 20 14 No. 20 37.5 37.5 37.5

284 284 280 280 280 280 280

All specimens experienced punching-shear failure mode. The specimens with FRP shear reinforcement showed a considerably larger punching-shear cone than the reference specimens without

350 G(0.3)350 G(0.3)350-GSS(d/4) G(1.6)350 G(1.6)350-GSS(d/4) G(1.6)350-GBSS(d/4) G(1.6)350-CSS(d/4) G(1.6350-CSS(d/3)

4.1. Punching-shear capacity and failure mode

II

The specimens were tested under monotonic concentric loading until failure as shown in Fig. 4. Since the main objective of this paper is to introduce a preliminary design equation for two-way concrete slabs reinforced with FRP bars and stirrups, the results presented herein are limited to the punching-shear capacity and the strains in the reinforcing bars and stirrups. The other results concerning the general behavior and deflection of the test specimens can be found elsewhere [18].

Table 1 Details of test specimens.

4. Test results

131 131 131

The experimental investigation included 10 full-scale two-way slabs constructed, instrumented, and tested up to punching-shear failure. The specimens measured 2500  2500 mm by 200 mm (Series I) or 350 mm (Series II) (Fig. 2). The test specimens were cast with normal-strength concrete; the concrete strength determined on the day of testing (determined on 150  300 mm cylinders) ranged from 29.5 to 40.2 MPa. The test specimens were simply supported or were held against the laboratory’s rigid floor using a rigid steel frame supported by 8 steel tie rods. The load was applied from the slab bottom through a 300  300 mm column stub using two 1500 kN hydraulic jacks at a loading rate of 5 kN/min until failure. All the slabs had sand-coated GFRP bars as flexural reinforcement, while 7 specimens had CFRP and GFRP stirrups as shear reinforcement; the remaining 3 served as reference specimens to assess stirrup contribution to punching-shear resistance. Figs. 2 and 3 show the geometry and typical reinforcement configuration of the test specimens and the shape of FRP stirrups investigated, respectively. Table 1 presents the test matrix and characteristics for each specimen and provides the mechanical properties of the GFRP bars as determined from testing. The stirrups were distributed along the orthogonal directions of the slabs with spacing of d/4, d/3, and d/2 where d is the average effective depth of the slab. The stirrups were extended to the slab ends to ensure the failure within the shear-reinforced zone. The spacing between the stirrups is reported in Table 1. The deflection of the test specimens at the different locations was captured with 11 linear variable differential transducers (LVDTs), while the strains in the flexural reinforcement bars, concrete, and shear reinforcement located in each orthogonal direction were measured using electrical resistance strain gauges. The strain gauges and LVDTs were connected to a data-acquisition system to record the readings during the test. Crack propagation was marked during the test and the corresponding loads were recorded. More details about the test specimens, materials, specimen instrumentation, and test procedure can be found elsewhere [18].

200

3.2. Test specimens and test procedure

G(1.2)200 G(1.2)200-GCS(d/2) G(1.2)200-CCS(d/2)

No. 10 (9.5 mm diameter) and No. 13 (12.7 mm diameter) sand-coated FRP stirrups with either discrete-closed or continuous-spiral configurations were used. The bend radii (rb) were 38.1 mm and 50.8 mm, which represent 4 times the bar diameter (db) for No. 10 and No. 13 FRP stirrups, respectively. Fig. 1 shows the geometry and dimensions of the CFRP and GFRP stirrups. The tensile strength and modulus of elasticity of the straight portions were determined by testing five samples (directly cut from the FRP stirrups) for each FRP type and diameter in accordance with ASTM D7205M [7]. The bend strength of the FRP stirrups was determined according to ACI [2] test method B.5 (concrete blocks). For each specimen, two C-shaped pieces were assembled to form one stirrup. A total of five specimens of each FRP type and diameter were tested. Fig. 1 also shows specimen preparation and testing as well as the mode of failure, whereas Table 1 presents the bend strength of the FRP stirrups.

I

3.1. Mechanical characterization of FRP stirrups

Series Specimen

3. Experimental investigation

a

Slab thick, d, Effective fc0 b, MPa Tens reinf. qf, % Ef, GPa ffu, MPa f⁄fuc, MPa efu, % Shear reinforcement mm depth, mm RFT type sfv, mm db, mm Afv, mm2 rb, mm qfv, % Efv, GPa ffuv, MPa efvu, % ffvbd, MPa ffvb/ffuv

pffiffiffiffi where nf = Ef/Ec; (modular ratio); Ec ¼ 4700 fc0 (modulus of elasticity of the concrete). To date, none of the FRP design codes provides any equation for the shear-reinforcement contribution to punching-shear capacity. Thus, there is a need for more research work to introduce a design equation for two-way slabs reinforced with FRP flexural and shear reinforcement.

– 0.48 0.49

M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532

526

M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532

Fig. 2. Typical test specimen geometry, reinforcement configuration, stirrup layout, and instrumentation.

shear reinforcement. Fig. 5 shows the typical punching-shear failure (in bold) of some tested specimens. The use of FRP shearreinforcement ratio contributed significantly to the punchingshear resistance, in particular when the flexural reinforcement ratios were high enough to ensure punching-shear failure. Test specimens G(1.2)200-GCS(d/2), G(1.2)200-CCS(d/2), G(0.3)350GSS(d/4), G(1.6)350-GSS(d/4), G(1.6)350-GBSS(d/4), G(1.6)350-CSS(d/4), and G(1.6)350-CSS(d/3) showed 40%, 17%, 7%, 18%, 25%, 36%, and 26% increases in the punching-shear strength compared to their counterparts without shear reinforcement, respectively. Table 3 presents the punching-shear strength of the test specimens.

4.2. Shear-reinforcement effects and strains Using the FRP stirrups around the column zone area of the test specimens mobilized the flexural reinforcement to achieve higher strains. The maximum measured flexural-reinforcement strains of the test specimens with high flexural-reinforcement ratios and with shear reinforcement in series I and II were 8786 and 6801 microstrains of the specimens G(1.2)200-GCS(d/2) and G(1.6)350GSS(d/4) (at the ultimate punching-shear load), which represents 44% and 36% of the characteristic tensile strength in comparison with their counterparts without shear reinforcement (4350 and 3199 microstrains, respectively).

M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532

527

G(1.2)-CCS(d/2)

G(1.2)-GCS(d/2)

(a) 200 mm thickness

G(1.6)-GSS(d/4)

G(1.6)-CSS(d/4)

(b) 350 mm thickness Fig. 3. FRP stirrup configurations.

The strain profiles in the straight portions of the FRP stirrups were plotted at 0.95Vu for all the test specimens as shown in Fig. 7. It was not possible, however, to capture the strains at Vu because of most of strain gauges were damaged at that level. As this figure shows, the strains in the FRP stirrups started to decrease at 1.0d from the column face and completely diminished at 2.5d from the column face in series II (350 mm). In series I the strains at 2.5d from the column face were about 450 and 1500 microstrains for G(1.2)200-CCS(d/2) and G(1.2)200-GCS(d/2), respectively. Since the CSA [11] recommends extending the shear reinforcement (steel) up to 2d from the column face, further research is needed to determine the corresponding distance for the FRP stirrups. In addition, specimen G(0.3)350-GSS(d/4) with the lowest flexural reinforcement ratio showed the highest recorded stirrup strain located at the perimeter d/2 (9032 microstrains). 5. Proposed design method

Fig. 4. Setup configuration and testing of a slab specimen.

Fig. 6 depicts the measured average strains at mid-height of the straight portions of the FRP stirrups located between d/2 to 1.5d from the face of the column, where d is the slab effective depth. As this figure shows, stirrup efficiency was insignificant before cracking. Stirrup efficiency increased, however, after the initiation of inclined shear cracks. In addition, the average strains at midheight of the straight portions of the FRP stirrups located between d/2 to 1.5d was 4470 microstrains, which is close to the strain limit of 4000 le specified in ACI [1] and CSA [10]. It should be noted that no rupture in the FRP stirrups at bend locations was observed, except in specimen G(1.6)350-CSS(d/3). The maximum recorded strain before stirrup rupture was 6522 microstrains at a distance of d/3 from the column face.

Since the main objective of this research work is to introduce a preliminary design equation for two-way slabs reinforced with FRP flexural and shear reinforcement, the concrete contribution to the punching-shear capacity (Vc) of the current design equations was evaluated. Thereafter, an equation for evaluating the FRP shear-reinforcement contribution (Vs) was developed based on the experimental results and a general design procedure was introduced. 5.1. Concrete contribution to the punching-shear capacity, Vc The accuracy of the punching-shear equations in CSA [9], and ACI [1] were assessed herein by comparing their predictions with the experimentally determined punching-shear capacity of 19 GFRP-reinforced specimens tested by the authors [16,17]) and 38 other specimens from the literature [6,8,13,20–23,27,28]. The safety factors included in all the punching-shear equations were

528

M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532

(a) G(1.2)200-GCS(d/2)

(b) G(1.6)350-GSS(d/4)

Fig. 5. Final punching-shear failure surface for some specimens with shear reinforcement (in bold).

Fig. 6. Average stirrup strains in the straight portion located at strain gauges from d/2 to 1.5d perimeters.

set to 1.0. The tested-to-predicted punching shear ratios (Vtest/ Vpred) are presented in Table 2, while Fig. 8 shows comparisons of the CSA [9] and ACI [1] predictions. As shown in Fig. 8, it can be concluded that the CSA [9] equations yielded good yet conservative predictions with average Vtest/Vpred of 1.20 ± 0.17 and a COV of 14%, while ACI [1] showed very conservative predictions with average Vtest/Vpred of 2.21 ± 0.35 and a COV of 16%. The direct implementation of the FRP axial stiffness (qf Ef/Es) into the punching-shear equations of CSA [9] in the punching-shear equations yielded good predictions. On the other hand, Eq. (11) of ACI [1] employs the FRP reinforcement ratio to calculate the depth of the neutral axis and consequently, the punching-shear strength is calculated from compression area of the cross section. Thus, the absence of the axial stiffness of the reinforcement in the punching-shear equation itself may be the reason for the high conservativeness level of this equation. In this regard, the CSA [9] equation was used to determine the concrete contribution to the proposed design method. 5.2. Proposed design method for punching-shear capacity Within the shear-reinforced zone, the shear resistance of steelreinforced two-way slabs computed as a summation of the concrete shear resistance (vc) and shear-reinforcement contribution (vs). Once the punching-shear crack was formed, however, adding

Fig. 7. Strain profile in the straight portion of the stirrups at 0.95Vu: (a) Series I; (b) Series II.

the full concrete shear resistance to the reinforcement contribution was not valid [13]. In order to determine the actual amount of concrete contribution of the specimens tested herein to the punchingshear resistance, the experimental failure loads and average strains in the shear reinforcement within a distance between 0.5d and 1.5d in both directions were used. Then the concrete shear-strength contribution was calculated from the relation, vc = vtest  vfv, where

Table 2 Vtest/Vpred for the FRP-RC slabs without shear reinforcement. Reference

Specimen

L

C

d

fc0

qf

Ef

(mm)

(mm)

(mm)

(MPa)

(%)

(GPa)

Vtest, kN

Vtest/Vpred CSA [9]a

ACI [1]

G(0.7)30/20 G(1.6)30/20 G(1.6)30/20-H G(1.2)30/20 G(0.3)30/35 G(0.7)30/35 G(1.6)30/35 G(1.6)30/35-H G(0.7)30/20-B G(0.7)45/20 G(1.6)45/20-B G(0.3)30/35-B G(0.7)30/35-B-2 G(0.3)45/35 G(1.6)30/20-B G(1.6)45/20 G(0.7)30/35-B-1 G(0.3)45/35-B G(0.7)45/35

2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000

S300 S300 S300 S300 S300 S300 S300 S300 S300 S450 S450 S300 S300 S450 S300 S450 S300 S450 S450

134 131 131 131 284 281 275 275 134 134 131 284 281 284 131 131 281 284 281

34.3 38.6 75.8 37.5 34.3 39.4 38.2 75.8 38.6 44.9 39.4 39.4 46.7 48.6 32.4 32.4 29.6 32.4 29.6

0.71 1.56 1.56 1.21 0.34 0.73 1.61 1.61 0.71 0.71 1.56 0.34 0.73 0.34 1.56 1.56 0.73 0.34 0.73

48.2 48.1 57.4 64.9 48.2 48.1 56.7 56.7 48.2 48.2 48.1 48.2 48.1 48.2 48.1 48.1 48.1 48.2 48.1

329 431 547 438 825 1071 1492 1600 386 400 511 781 1195 911 451 504 1027 1020 1248

1.11 1.11 1.15b 1.12 1.25 1.22 1.26 1.16b 1.25 0.92 0.97 1.13 1.29 0.98 1.23 1.02 1.29 1.26 1.24

2.07 1.90 1.84 1.91 2.58 2.29 2.11 1.87 2.35 1.74 1.66 2.36 2.44 2.07 2.08 1.73 2.37 2.58 2.29

Nguyen-Minh and Rovnˇák [23]

GSL-PUNC-0.4 GSL-PUNC-0.6 GSL-PUNC-0.8

2000 2000 2000

S200 S200 S200

129 129 129

39.0 39.0 39.0

0.48 0.68 0.92

48.0 48.0 48.0

180 212 248

0.91 0.96 1.01

1.80 1.81 1.84

Lee et al. [21]

GFU1

2000

S225

110

36.3

1.18

48.2

222

0.98

1.72

Zhang et al. [28]

GS2

1830

S250

100

35

1.05

42.0

218

1.12

2.02

GSHS

1830

S250

100

71

1.18

42.0

275

1.13b

1.99

Zaghloul and Razaqpur [27]

ZJF5

1500

S250

75

44.8

1.33

100.0

234

1.10

1.78

Hussein et al. [20]

GS1 GS2 GS3 GS4

1830 1830 1830 1830

S250 S250 S250 S250

100 100 100 100

40.0 35.0 29.0 26.0

1.18 1.05 1.67 0.95

42.0 42.0 42.0 42.0

249 218 240 210

1.17 1.12 1.12 1.23

2.11 2.02 1.90 2.21

Ospina et al. [24]

GFR-1 GFR-2 NEF-1

1670 1670 1670

S250 S250 S250

120 120 120

29.5 28.9 37.5

0.73 1.46 0.87

34.0 34.0 28.4

199 249 203

1.03 1.03 0.97

1.98 1.82 1.90

El-Ghandour et al. [13]

SG1 SC1 SG2 SG3 SC2

1700 1700 1700 1700 1700

S200 S200 S200 S 200 S200

142 142 142 142 142

32.0 32.8 46.4 30.4 29.6

0.18 0.15 0.38 0.38 0.35

45.0 110.0 45.0 45.0 110.0

170 229 271 237 317

1.14 1.20 1.25 1.26 1.29

2.58 2.46 2.61 2.55 2.36

Matthys and Taerwe [22]

C1 C10 C2 C20 C3 C30 CS CS0 H2 H20 H3

900 900 900 900 900 900 900 900 900 900 900

C150 C230 C150 C230 C150 C230 C150 C230 C150 C80 C150

96 96 95 95 126 126 95 95 89 89 122

36.7 37.3 35.7 36.3 33.8 34.3 32.6 33.2 35.8 35.9 32.1

0.27 0.27 1.05 1.05 0.52 0.52 0.19 0.19 3.76 3.76 1.22

91.8 91.8 95.0 95.0 92.0 92.0 147.6 147.6 40.7 40.7 44.8

181 189 255 273 347 343 142 150 231 171 237

1.64 1.28 1.49 1.19 1.76 1.34 1.30 1.03 1.28 1.34 1.23

3.20 2.51 2.46 1.97 3.15 2.40 2.48 1.97 2.03 2.12 2.15 529

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M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532

Hassan et al. (2012)

M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532

0.95 0.95 0.95 0.95

113.0 113.0 113.0 113.0

93 78 96 99 Mean S.D. COV (%)

1.40 1.16 1.26 1.32 1.20 0.17 14

2.32 1.92 2.07 2.17 2.20 0.35 16

the FRP stirrup contribution. The actual fraction of the full concrete shear resistances that contributed to the overall capacity of the tested specimens was 0.63 on average. Since the slabs failed in punching-shear failure, the initiation of punching-shear cracks reduced the concrete shear resistance. Accordingly, it is accepted that the concrete contribution to the punching-shear resistance of GFRP-reinforced specimens is reduced after the initiation of the major shear crack up to 50% of the concrete shear resistance. This is in agreement with CSA [11] and ACI (2008) code provisions for steel-reinforced members. Therefore, within the punching shear zone reinforced by stirrup shear reinforcement, the concrete, (vc) was proposed to have a value equal to 50% of the least of Eqs. (8)–(10). For calculating the stirrup contribution from Eq. (5), that the strain in FRP stirrups is assumed to be limited to a specific value to maintain aggregate interlock and concrete contribution vc. The experimental results of the tested specimens indicate that the maximum average strain in the stirrups measured at the midheight of the vertical portions of the FRP stirrups was 4470 le, which is close to the strain limit of 4000 le specified in ACI [1] and CSA [10]. In addition, Ahmed et al. [4,5] provided experimental data on the shear strength of concrete beams reinforced with GFRP and CFRP stirrups. They reported that limiting the ultimate strain in FRP stirrups to 4000 microstrains, as recommended by ACI [1] and CSA [10], yielded good predictions of the FRP stirrups. Therefore, the strain limit of 4000 le is proposed to determine the stress of the stirrups at a critical section of 0.5d from the column face. When the predictions were made using the stress corresponding to 4000 le in Eq. (5), the predictions were rather non-conservative, on average as shown in Table 3 (vtest/vpred = 0.93 ± 0.19). Thus an additional factor of 0.7, determined based on best fitting of the results, was introduced to the FRP stirrup contribution equation. Accordingly, Eq. (12) was proposed to estimate the FRP stirrup contribution to the punching-shear capacity in two-way slabs. It should be mentioned that this proposed equation is a modified form of the shear design equations for steel and FRP stirrups in CSA [11] and CSA [9]. For comparison purposes, the predictions of this equation including and excluding the 0.7 factor are presented in Table 3 and Fig. 9.

55 55

61 61 61 61

C100 C100

S75 S75 S100 S100

42.4 44.6 39.0 36.6

2.79 2.44 1.46 1.26 65 61 100.0 100.0 0.31 0.31

122 95 C80 C150

41.0 52.9

2.65 2.82

(mm) (mm)

32.1 118.0

1.22 0.62

44.8 37.3

217 207

1.51 1.65b

CSA [9]a (GPa) (%)

qf d

fc0

vtest is the ultimate shear stress determined from testing and vfv is

C

(MPa)

Ef

Vtest, kN

Vtest/Vpred

ACI [1]

530

¼

590 590 590 590

500 500

900 900

(mm)

L

v sf

0:7/f Af v ff v bo;0:5d sf v

CFRC-SN1 CFRC-SN2 CFRC-SN3 CFRC-SN4 Ahmad et al. [6]

Note: L; Loaded span (mm); C circular and S square columns. a From Eq. (3). b Using concrete strength of 60 MPa [9].

I II

H3 H1

0

Banthia et al. [8]

Reference

Table 2 (continued)

Specimen

ff v ¼ 0:004  Ef v

ff v ¼

ð0:05r b =db þ 0:3Þffuv 6 ffbend 1:5

ð12aÞ

ð12bÞ

ð12cÞ

where Afv = is the cross-sectional area of the stirrups on a concentric line parallel to the column perimeter (as specified by CSA [11]); db = is the bar diameter; rb = is bend radius; ffv = is the smallest stress in the stirrups from Eqs. (12b) and (12c); bo;0.5d = is the perimeter of the critical section of shear in slabs; and sfv is the spacing of stirrup shear reinforcement measured perpendicular to bo;0.5d. The punching-shear stresses of the tested specimens were predicted using the proposed Eq. (12) and listed in Table 3 and Fig. 9. The predictions using Eq. (12) were in agreement with the experimental results. In addition, the proposed design method showed accurate yet conservative predictions with an average vtest/vpred of 1.17 ± 0.21 and a corresponding COV of 18%. Further research is, however, required to assess the accuracy of equation for different shapes and types of FRP shear reinforcement.

531

M. Hassan et al. / Construction and Building Materials 66 (2014) 522–532 Table 3 Comparisons between the experimental and predicted results using the proposed equation. Series

Specimen

Vtest, kN

vtest, MPa

vc, MPa

Using Eq. (12) without the 0.7 factor

vfv, MPa

vpred. = vfv + 0.5vc; MPa

vtest/vpred

vfv, MPa

vpred. = vfv + 0.5vc; MPa

vtest/vpred.

This study

G(1.2)200 G(1.2)200 GCS(d/2) G(1.2)200-CCS(d/2) G(0.3)350 G(0.3)350-GSS(d/4) G(1.6)350 G(1.6)350-GSS(d/4) G(1.6)350-GBSS(d/4) G(1.6)350-CSS(d/4) G(1.6)350-CSS(d/3)

438 614 514 825 885 1492 1761 1869 2024 1886

1.94 2.72 2.28 1.24 1.33 2.30 2.72 2.88 3.12 2.91

1.73 1.73 1.73 0.99 0.94 1.83 1.86 1.82 1.83 1.86

– 1.69 2.45 – 1.13 – 1.13 2.27 3.16 2.21

– 2.55 3.32 – 1.60 – 2.06 3.18 4.08 3.14 Average SD COV %

– 1.07 0.69 – 0.83 – 1.32 0.91 0.77 0.93 0.93 0.19 21

– 1.18 1.72 – 0.79 – 0.79 1.59 2.21 1.55

– 2.05 2.58 – 1.26 – 1.72 2.50 3.13 2.48 Average SD COV %

– 1.33 0.88 – 1.06 – 1.58 1.15 1.00 1.17 1.17 0.21 18

Using Eq. (12) (with the 0.7 factor)

Notes: vc is the concrete contribution determined from CSA [9] (Eq. (3)).

vfv is the ultimate punching-stress provided by the FRP shear reinforcement (Eq. (12)).

Fig. 9. Tested-to-predicted punching-shear–stress relationship.

analytical results, the following conclusions and recommendation are drawn:

Fig. 8. Comparisons of CSA [9] and ACI [1] predictions.

1. CSA [9] is capable of predicting the concrete contribution to the punching-shear capacity of FRP-RC two-way slabs with reasonable yet conservative vtest/vpred ratios. For FRP-RC slabs without shear reinforcement, the average vtest/vpred of CSA [9] and ACI [1] equations was 1.20 ± 0.17 and 2.21 ± 0.35, respectively. 2. The FRP-stirrup strain limit of 4000 microstrains specified by ACI [1] and CSA [10] was supported by the experimental findings. 3. The preliminary proposed design equation gives good and conservative predictions for the punching-shear strength of FRP-RC two-way slabs. The proposed equations showed an average tested-to-predicted punching-shear ratio (vtest/vpred) of 1.17 ± 0.21 with a COV of 18%. This equation signals a step forward for using FRP stirrups in two-way slabs. More research is, however, needed to refine this equation.

6. Conclusion and recommendation Acknowledgments This paper presents a preliminary equation to quantify the contribution of FRP stirrups in FRP-reinforced concrete (FRP-RC) two-way slabs and proposes a design equation for the punchingshear capacity of such members. The proposed equation is a modified form of the current shear design equations for steel and FRP stirrups in CSA [11] and CSA [9]. Based on the experimental and

The authors wish to acknowledge the financial support of Quebec’s Ministry of Economic Development, Innovation, and Export Trade (MDEIE). The authors are also grateful to the consulting firm EMS Ingénierie inc. (Quebec City) for their technical support. The authors also acknowledge the support of the Natural Sciences

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