Strengthening Concrete Slabs for Punching Shear with Carbon Fiber-Reinforced Polymer Laminates

Transcription

1 ACI STRUCTURAL JOURNAL Title no. 104-S06 TECHNICAL PAPER Strengthening Conrete Slabs for Punhing Shear with Carbon Fiber-Reinfored Polymer Laminates by Kyriakos Sissakis and Shamim A. Sheikh This paper desribes an innovative approah for strengthening reinfored onrete slabs in shear with arbon fiber-reinfored polymer (CFRP) laminates. A proess analogous to stithing is used to retrofit onrete slabs with fiber-reinfored polymer (FRP) strands. The experimental study reported herein was arried out on 28 square, isotropi two-way slab speimens simulating onditions in the viinity of an interior square olumn in a ontinuous flat plate struture. Parameters suh as the onrete strength, flexural apaity, and shear reinforement arrangement were investigated, and the appliability of existing CSA A and ACI standard speifiations for punhing shear resistane were examined. Results from the tests show that marked inreases in the punhing shear apaity and dutility (over 80 and 700%, respetively) an be ahieved with CFRP retrofitting of slabs. Keywords: flat plate; punhing shear; shear reinforement; slab. INTRODUCTION The rehabilitation and strengthening of strutural members with omposite materials, suh as arbon, glass, kevlar, and aramid fiber-reinfored polymers (FRPs), has reently reeived great attention. Redued material osts, oupled with labor savings inherent with its lightweight and omparatively simple installation, its high tensile strength, low relaxation, and immunity to orrosion, have made FRP an attrative alternative to traditional retrofitting tehniques. Field appliations over the last years have shown exellent performane and durability of FRP-retrofitted strutures. 1 Researh into the appliation of externally bonded FRPs to reinfore onrete slabs has onentrated on improving the flexural apaity. There is also the potential for FRP laminates to improve the shear apaity of reinfored onrete slabs. Shear failures our suddenly and without warning and an be atastrophi, espeially in seismi zones. The avoidane of suh a failure is of paramount importane; and the benefits from strengthening existing slabs in shear, either for purposes of improved apaity and strutural modifiation or due to deterioration and aging or mistakes in design, are great. This paper reports on a series of tests onduted to assess the ability of arbon fiber-reinfored polymer (CFRP) laminates to inrease the two-way shear apaity of existing reinfored onrete slabs. 2,3 In a pilot test series, three slab speimens retrofitted with CFRP were tested in 2000 and ompared with a ontrol speimen. 2 Based on these results, a program was initiated in whih 28 square isotropi two-way slab speimens, simply supported on all four sides, were subjeted to a onentri monotonially inreasing load until failure. 3 Twenty-four of these slab speimens ontained CFRP laminate shear reinforement. The slabs were designed to fail in shear prior to flexure so that the shear strength ontribution of the CFRP laminates ould be measured. Pilot tests on three slab speimens reinfored in shear found substantial inreases in onentri punhing shear apaity and dutility. 2 This paper onfirms the potential of CFRP laminates to reinfore existing onrete slabs in shear; expands on the influene of variables suh as the onrete strength, flexural apaity, and shear reinforement arrangement on punhing shear behavior; and investigates the appliability of existing CSA and ACI standard speifiations for punhing shear resistane. RESEARCH SIGNIFICANCE This researh investigates an innovative idea for inreasing the two-way shear strength of onrete slabs with FRP. FRP reinforement is provided in holes that are perpendiular to the plane of the slab in a manner that is equivalent to stithing the slab. The onfiguration of the holes determines the effiieny of the reinforement in enhaning the performane of the retrofitted slab. Although the proedure was tested for retrofitting of existing slabs, the results are equally appliable to new strutures. With the exeption of fire resistane, the proedure proposed herein is onsidered to be tehnially superior, easier to implement, and produes more durable strutures than traditional strengthening tehniques. THEORETICAL RESPONSE Conentri punhing shear apaity without shear reinforement Punhing shear failure is haraterized by the slab fraturing along planes that extend from the olumn-slab interfae on the ompressed fae of the slab through the depth of the slab in an inlined diretion away from the olumn. For square olumns, the punhing shear failure takes the form of a frustum of a pyramid (Fig. 1). Most researh on the shear strength of slabs has been onerned with developing empirial formulas based on a nominal shear stress resistane. 6 Nominal shear stress is obtained by dividing the shearing fore by the area of an assumed ritial setion a ertain distane from the olumn perimeter. The CSA and ACI standards 4,5 assume the shear failure plane to have an angle of inlination of 45 degrees from the slab surfae and propose the use of a ritial setion perimeter half the effetive slab thikness from the olumn periphery (Fig. 2). The depth of the ritial setion is taken as the effetive slab thikness. In the absene of an unbalaned moment, the shear stress due to fatored loads v f is alulated as v f = V f /(b o d) (1) ACI Strutural Journal, V. 104, No. 1, January-February MS No. S R1 reeived February 6, 2006, and reviewed under Institute publiation poliies. Copyright 2007, Amerian Conrete Institute. All rights reserved, inluding the making of opies unless permission is obtained from the opyright proprietors. Pertinent disussion inluding author s losure, if any, will be published in the November- Deember 2007 ACI Strutural Journal if the disussion is reeived by July 1, ACI Strutural Journal/January-February

2 Kyriakos Sissakis is a Strutural Engineer with Halsall Assoiates Limited, Toronto, Ontario, Canada. His researh interests inlude omplex strutures, advaned digital appliations, and design innovations. Shamim A. Sheikh, FACI, is a Professor of ivil engineering at the University of Toronto, Toronto. He is a member of ACI Committee 374, Performane-Based Seismi Design of Conrete Buildings, and a member and former Chair of Joint ACI-ASCE Committee 441, Reinfored Conrete Columns. In 1999, he reeived the ACI Strutural Researh Award. His researh interests inlude earthquake resistane of onrete strutures, onfinement of onrete, use of fiber-reinfored polymer in onrete strutures, and expansive ement and its appliations. Fig. 3 Closed stirrup and stud shear reinforement. Fig. 1 Punhing shear failure. where β is the ratio of the long to short side of the olumn, α s is a modifiation fator for the support type (α s = 40 for interior olumns), and f is the unonfined onrete ompressive strength. The CSA standards 4 formulation is idential to the aforementioned with the exeption of inflated oeffiients to ompensate for stringent material redution fators originating from olumn design. 7 The same applies to Eq. (7) through (11) that follow. Equation (4) governs for the speimens tested in this study. Thus, the onentri load required to fail the slab speimens without shear reinforement in punhing shear 4,5 is P v = 0.33b o d f ( MPa) = 4b o d f ( psi) (5) Fig. 2 Critial shear setion perimeters for slabs with and without shear reinforement. where V f is the shear fore due to fatored loads, d is the effetive slab thikness for shear, and b o is the perimeter of the shear ritial setion d/2 from the olumn periphery. Aording to the ACI standard, 5 the nominal shear strength for a ritial shear setion d/2 from the olumn periphery is omputed from the smallest of Eq. (2) to (4) v r = v = f β (MPa) 4 = f ( psi) β v r v α s = = d + 2 f b o ( MPa) α s d = f ( psi) b o (2) (3) Conentri punhing shear apaity with shear reinforement The CSA and ACI standards 4,5 permit the use of losed stirrups or vertial shear studs as shear reinforement that are positioned prior to asting and are typially loated along perimeters that parallel the olumn periphery (Fig. 3). Reinforements of these types also ontribute to shear strength by onfining the onrete and failitating the distribution of shearing stresses outwards toward the unraked onrete. It is proposed that CFRP laminates an be applied to existing slabs within vertial holes drilled through the depth of the slab around the olumn. The holes an be arranged into a series of perimeters offset from the olumn in a manner similar to shear stud reinforement. In new slabs, the FRP reinforement an be provided in a similar onfiguration before or after asting. Conrete slabs reinfored with shear studs an fail in shear outside or within the shear-reinfored zone. Failures an our within the reinfored zone when the umulative strength of the shear reinforement and the onrete is less than the fore required to fail the slab in shear outside the reinfored zone or when the shear reinforement does not suffiiently distribute shearing fores. To ensure adequate distribution of shearing fores, Joint ACI-ASCE Committee and CSA Standard 4 speify Eq. (6) through (8) to determine the spaing of shear stud reinforement. s o 0.40d (6) v r = v = 0.33 f ( MPa) = 4 f ( psi) (4) s 0.75d for v f 0.5 f ( MPa) or 6 f ( psi) (7) 50 ACI Strutural Journal/January-February 2007

3 s 0.50d for v f > 0.5 f ( MPa) or 6 f ( psi) (8) In Eq. (6) through (8), s o is the distane between the olumn periphery and the first onentri line of shear studs parallel to the olumn periphery and s is the spaing between onseutive perimeters of shear studs (Fig. 2). In addition, the ACI doument 8 reommends that shear studs be positioned at the olumn orners, in-line with the olumn fae (Fig. 3), and that the spaing of shear studs in the diretion parallel to the olumn fae be less than 2d (Fig. 2). For this researh program, several shear-reinforing arrangements were investigated. Exessive amounts of shear reinforement were applied to the slab speimens in an attempt to avoid failures within the shear-reinfored zone. The CSA standard and ACI doument, 4,8 however, both impose a limit on the umulative nominal shear stress resistane of onrete v and the shear reinforement v s for a ritial setion d/2 from the olumn periphery to guard against diagonal rushing of the onrete. For headed shear stud reinforement Fig. 4 Shear reinforement arrangements and assumed ritial shear setion perimeters of tested slab speimens with three peripheral lines of shear reinforement. v r = v + v s 0.67 f ( MPa) or 8 f ( psi) (9) The shear strength of onrete at a ritial setion varies with distane from the olumn. The onfinement indued by the triaxial stress ondition in the viinity of the olumn dereases with inreasing distane from the olumn, ausing a loss in shear strength. In general, immediately adjaent to the olumn, a triaxial ompressive state exists and at some greater distane the triaxial ompressive state dissipates to a uniaxial ompressive state. The CSA and ACI standards 4,5 speify a nominal shear strength at a distane d/2 from the outermost perimeter of shear reinforement v r = v = f ( MPa) = 2 f ( psi) (10) Assuming adequate onfinement by the shear-reinforement, the ultimate onentri load required to fail the slab speimens in punhing shear is thus P v = 0.167bd f 0.67b o d f = 2bd f 8b o d f ( psi) ( MPa) (11) where b is the perimeter of the ritial setion d/2 from the outermost perimeter of shear reinforement (Fig. 2 and 4). Flexural apaity The flexural apaity of square isotropi two-way slab, simply supported on all four sides and subjeted to a onentri square load, an be estimated using Johansen s yield line theory, 9 8 P Y = m r π L 1 (12) where L is the length of the supported slab, is the loading plate side length, and m r is the flexural apaity of the slab per unit width given by Fig. 5 Slab speimen B5 speifiations, load, and supports. m r ρd 2 f y ρ f y = ---- f (13) where ρ, d, and f y are the flexural reinforement ratio, depth, and yield strength, respetively. Equation (12) orresponds to a ollapse mehanism where the slab yields and divides into quartered irular fans radiating from the orners of a square olumn. For the speimens in this study, L and are 1.35 m (53 in.) and 200 mm (8 in.), respetively (Fig. 5). EXPERIMENTAL PROGRAM Test speimens All of the slab speimens had the same external dimensions and ontained either 15 M (0.31 in. 2 area) or 20 M (0.465 in. 2 area) flexural reinforement bars. The effetive depth was 120 mm (4.75 in.) in both types of flexural reinforement (Fig. 5). The slabs were ast with normal density onrete in four separate bathes, resulting in four different onrete strengths. Eah bath onsisted of several slab speimens ast with one of the four patterns of 25 mm (1 in.) diameter holes shown in Fig. 4. The holes were later used to reinfore the slabs with CFRP laminates. One slab in eah bath was the ontrol speimen and not reinfored in shear. ACI Strutural Journal/January-February

4 Table 1 Slab speimen variables and material properties Conrete Flexural reinforement Shear reinforement Calulated properties Speimen f, MPa (ksi) f Y, MPa (ksi) f U, MPa (ksi) ρ, % b, mm (in.) s/d A CFRP, mm (in.)/perimeter P Y, kn P V, kn Control (6.18) 428 (62.1) 730 (105.9) (50.4) 643 (144.7) 331 (74.5) A (6.18) 428 (62.1) 730 (105.9) (88.0) (32.0) 643 (144.7) 304 (65.7) Control (5.23) 428 (62.1) 730 (105.9) (50.4) 631 (142.0) 305 (68.6) A (5.23) 428 (62.1) 730 (105.9) (88.0) /1012/ (142.0) 269 (60.5) (19.9/39.8/19.9) B (92.8) (29.4) 284 (53.8) B (92.8) (29.4) 284 (53.8) C (116.5) (36.4) 356 (80.2) 36.1 (5.23) 428 (62.1) 730 (105.9) (142.0) C (116.5) (36.4) 356 (80.2) D (116.5) (36.4) 356 (80.2) D (116.5) (36.4) 356 (80.2) Control (5.00) 480 (69.6) 623 (90.3) (50.4) 966 (217.4) 298 (67.1) A (5.00) 480 (69.6) 623 (90.3) (74.6) /924/ (217.4) 223 (50.2) (18.2/36.4/18.2) A (5.00) 480 (69.6) 623 (90.3) (101.3) /858/660/1320/ (217.4) 303 (68.1) (33.8/33.8/26/52/26) B (79.4) (24.3) 237 (53.4) B (106.1) (31.2) 317 (71.4) C (97.6) (31.2) 292 (65.7) 34.5 (5.00) 480 (69.6) 623 (90.3) (217.4) C (135.4) (46.8) 405 (91.1) D (97.6) (31.2) 292 (65.7) D (135.4) (31.2) 405 (91.1) Control (3.86) 480 (69.6) 623 (90.3) (50.4) 902 (203.0) 261 (58.7) A (88.0) (25.1) 231 (52.0) A (114.6) (36.4) 301 (67.7) B (92.8) (26.0) 244 (54.8) B (119.5) (36.4) 314 (70.6) 26.6 (3.86) 480 (69.6) 623 (90.3) (203.0) C (116.5) (36.4) 306 (68.8) C (154.3) (50.2) 405 (91.2) D (116.5) (33.8) 306 (68.8) D (154.3) (49.4) 405 (91.2) The flexural reinforement was spaed equally in all the speimens and did not interfere with the holes intended for the CFRP laminates. The development of the flexural reinforement was attained mehanially by welding the ends of the reinforing bars to flat steel plates, whih oupied the perimeter of the slab speimens (Fig. 5). The number of peripheral lines of shear reinforement varied between three and six among the slab speimens and the spaing between the onseutive lines was 0.5d or 0.75d. The first perimeter was offset 0.25d from the loading plate periphery for all the slab speimens. Table 1 summarizes the slab speimen details and material properties. The slab speimens with primed pattern labels ontained 15 M flexural reinforement bars, while other slab speimens ontained 20 M bars. Those speimens with shear reinforement are labelled in aordane with their shear reinforement pattern, A, B, C, or D, with numerial subsripts denoting the number of peripheral lines of shear reinforement. The amounts of CFRP laminate A CFRP used in eah onentri shear-reinforing perimeter are presented in width of CFRP laminate. For slab speimens A 3, A 3, and A 5, the amount of CFRP laminate applied in eah reinfored perimeter varied and is listed in Table 1 starting from the 52 perimeter nearest the loading plate. P Y and P V represent the predited applied loads required to fail the slab speimens in flexural yield and shear, respetively. P Y is derived from Eq. (12) and P V is derived from Eq. (5) or (11). The ritial shear setions perimeters outside the shear-reinfored zone b, speified by the CSA and ACI standards, 4,5 are depited in the upper portion of Fig. 4. A ommerially available CFRP system was used. The ultimate tensile strength and tensile modulus per unit width of CFRP laminate was determined experimentally to be 97 kn/m (66.6 kips/ft) and 79.5 MN/m (5452 kips/ft), respetively. The rupture strain was 1.30% and the speified thikness of the CFRP laminate was 0.89 mm (0.035 in.). The CFRP was applied to the slab speimens by utting long thin strands that ould pass through the holes positioned in the slab. The CFRP strands were soaked in epoxy and looped ontinuously between pairs of holes several times, in a stithlike manner, until the desired amount of CFRP laminate spanned the depth of the slab (Fig. 5 and 6). The ontinuous loop of CFRP laminate formed a solid ring of reinforement that also onfined the onrete. Shear reinforement Pattern A with odd numbers of peripheral lines of shear reinforement ACI Strutural Journal/January-February 2007

5 had the two adjaent outer rings of CFRP share a ast hole and as suh, the shared hole had twie the CFRP reinforement (Table 1). The voids that remained after the appliation of the CFRP laminates were subsequently filled with epoxy. Speimens in the pilot test series 1 had shorter strands of CFRP laminate that were passed through the ast holes one and had their ends adhered to the top and bottom surfaes of the slab. Large sheets of CFRP laminate were later installed on the top and bottom surfaes to ensure anhorage to the onrete (Fig. 7). The experiment found partial separation of the CFRP laminates from the onrete surfae during testing and onsiderable inreases in flexural stiffness and strength due to the added CFRP laminates on the top and bottom surfaes of the speimens. The newly proposed solid rings of CFRP reinforement minimized the dependene on bond between the onrete and the FRP and avoided inreases in flexural strength and stiffness. Test setup The slabs were tested under a vertial monotonially inreasing onentri load distributed by means of a 200 mm (8 in.) square by 100 mm (4 in.) thik loading plate. A losed-loop servo-ontrolled stiff frame test mahine (Fig. 8) was used to apply the load in displaement ontrol mode at a rate of 0.01 mm/seond ( in./seond). A universal ball joint was attahed to the loading plate to prevent moments from being imposed onto the slab speimens. The slabs were positioned horizontally and simply supported on all four sides by rollers omprised of solid 44 mm (1.75 in.) diameter steel rods. The rollers rested on a steel podium plaed diretly onto the solid metal base of the test mahine. Two of the rollers were welded to the podium, while the opposite two rollers were left free to rotate. The rollers were positioned 75 mm (3 in.) within the edges of the slab speimens. Metal plates 150 x 25 mm (6 x 1 in.) in setion, were loosely positioned in between the slab speimens and rollers to distribute bearing fores. To monitor the displaement of the slab speimens, six linearly variable differential transduers (LVDTs) were used four to measure the displaements of the supporting struture and two for the displaement of the loading plate. The four LVDTs used to measure the displaement of the supporting struture were positioned at the four orners of the slab, diretly above the supporting rollers (Fig. 8). Loal strains in the CFRP laminates and the flexural reinforement were measured with eletrial resistane strain gauges. Four strain gauges were applied with yanoarylate adhesive to the lower two entral reinforing bars that passed underneath the loading plate. Two of the gauges were positioned at the middle of the reinforing bars and the other two were offset 200 mm (8 in.) from the middle in opposing diretions. Long-gauge strain gauges were applied to every vertial stem of the CFRP laminate rings. The gauges were adhered to epoxied segments on separate CFRP strands (Fig. 9) that were later attahed with epoxy to the solid rings of CFRP reinforement (Fig. 6). Two gauges were adhered to eah strand. The gauges were positioned suh that when the strands were applied to the CFRP rings; the gauges were aligned with the enter of the slab depth in two adjaent holes. The epoxied segments were formed by sandwihing a small amount of epoxy resin on the CFRP strands between sheets of polyethylene. This made a smooth surfae on to whih the gauges ould be adhered. Several layers of polyurethane and foam mounting tape were applied Fig. 6 Slab speimen D4 before and after CFRP appliation. Fig. 7 CFRP appliation of slab speimen in pilot studies. Fig. 8 Test setup. to all the gauges to prevent moisture penetration and any tangential pressures from being exerted on to the gauges. EXPERIMENTAL RESULTS The slabs were designed suh that they would fail in shear. With retrofitting, the shear apaity inreased signifiantly ausing yield of flexural steel in some slabs. Stress in steel, however, was signifiantly lower than rupture. Therefore, eah slab failed in shear as learly demonstrated by the failure modes observed during the tests. The results from the tests on the slab speimens are presented in the following. After the desription of the failure patterns, responses of the slab speimens are disussed to evaluate different CFRP reinforement patterns. Theoretial predition of apaity and the design aspets onlude this setion of the paper. Failure plane desription Figure 10 shows skethes of the shear fratures, portrayed as dotted lines, on the ompressed surfae of failed slab speimens. Figure 11 shows photographs of the ross setions of seleted slab speimens ut in half. The slab speimens were ut suh that those with CFRP laminate Patterns A and C had the ut pass through the CFRP laminates and in speimens with reinforement Patterns B and D the ut passed between the CFRP laminates. The fratures have been ACI Strutural Journal/January-February

6 Fig. 9 CFRP strands with adhered strain gauges. Fig. 11 Photographs of seleted slab speimen ross setions. Fig. 10 Skethed slab speimen ompressed surfae fratures relative shear reinforement. highlighted with a blak marker. No speimen experiened tensile or ompressive flexural failure before failing in shear. The punhing shear failures ourred outside, within or prior to the shear-reinfored zones. In plan, the shear fratures outside the shear-reinfored zone were typially irular in shape. CFRP laminate Pattern A exhibited greater tendeny towards shear failures within the shear-reinfored zone than CFRP laminate Patterns B and C. All and only the slab speimens with CFRP laminate Pattern D failed in shear at the perimeter of the loading plate. The speimens with larger spaing of onseutive shear-reinforing perimeters s were more prone to shear failures within the shear-reinfored zone than the speimens with smaller spaing and equivalent potential ritial setion perimeters (that is, A 3 versus A 4, B 3 versus B 4, C 3 versus C 4, and D 3 versus D 4 ). In setion, the shear fratures extended through the depth of the slabs at an angle of inlination generally smaller than 45 degrees. Upon reahing the flexural reinforement, the failure planes ontinued horizontally toward the perimeter of the slab between the layers of flexural reinforement. Varying degrees of shear and flexural raking were evident among the slab speimens. The speimens with greater number of shear-reinforing perimeters, larger onseutive spaing of shear-reinforing perimeters and lower flexural reinforement ratios exhibited greater degrees Fig. 12 Slab speimen load-deformation urves. of onrete raking within the shear-reinfored zone. For the speimens ut through the CFRP laminates, it was observed that none of the laminates spanned shear fratures, thus implying the speimens did not undergo progressive shear failures within the shear-reinfored zone and that the shear reinforement and the onrete behaved ohesively. Load-deformation response Load-deformation urves for all the tested slab speimens are given in Fig. 12. The slab deformation is taken as the differene between the defletion at the loading plate and the average defletion at the supports. The load has been normalized with respet to b o d f to ompare speimens with different onrete strengths and orresponds to the umulative shear stress at a distane of d/2 from the loading plate periphery. Table 2 shows the results from all the tests. 54 ACI Strutural Journal/January-February 2007

7 The strain energy absorbed U 80 is taken as the area under the load-deformation urve up to 80% of the ultimate load P TEST beyond the peak. Figure 13 ompares the load deformation urves for slab Speimens A 6, B 6, C 6, and D 6, and their respetive ontrol speimen. The load-displaement urve for Speimen B 5 is shown in Fig. 14 along with the loadaverage strain urves for eah peripheral line of shear reinforement and the flexural reinforement. The CFRP strains and flexural reinforement strains remained less than 3000με and 6500με, respetively, for all the speimens. The slab speimens with shear reinforement demonstrated inreases in load arrying apaity and dutility of up to 82 and 768%, respetively, over that of their respetive ontrol speimens and, in some ases, hanged the mode of failure from punhing shear to flexural (refer to P test /P ontrol, U 80 / (U 80 ) ontrol and P test /P Y in Table 2). The inrease in shear strength and dutility was aompanied by an inrease in audible signs of distress. The formation of a omplete shear failure plane was often not instantaneous and formed partially at various setions of the slab, expanding until failure. This growth of the shear failure plane is identified by the slab speimens without abrupt losses of load and/or losses of load followed by plateaus (Fig. 12). As expeted, stiffness of the slab speimens with a larger amount of flexural steel was higher than that of speimens with a lower amount of flexural steel. The slab speimens reinfored in shear showed no signifiant hange in stiffness over that of their respetive ontrol speimen (Fig. 13). It an be observed from Fig. 12 and Table 2 that the loadarrying apaity of the slab speimens inreased with the inrease in the number of CFRP perimeters. The slab speimens with shear-reinforing Patterns A and D exhibited shear apaity improvements that were approximately half as muh as those with shear-reinforing Patterns B and C. The speimens with larger shear-reinforing perimeter spaing s exhibited no appreiable loss in strength or dutility when ompared with the speimens with smaller shear-reinforing perimeter spaing and equivalent potential ritial setion perimeters (A 3, and versus A 4, B 3 versus B 4, C 3 versus C 4, and D 3 versus D 4 ). Another important observation that an be made from Fig. 12 is related to the lak of signifiant enhanement in deformability and dutility despite the additional CFRP reinforement in slab speimens of Patterns A and D. Contrary to this behavior, for speimens of shear-reinforing Patterns B and C in whih CFRP is distributed more uniformly, an inrease in the number of reinforement perimeters results in a substantial inrease in dutility and hene the energy dissipation apaity of the slabs. Greater inreases in dutility, apaity, and audible distress were exhibited with greater numbers of shear-reinforing perimeters and a greater number of vertial elements of reinforement in eah perimeter. Failure harateristis The onrete ontribution to shear resistane v within the CFRP laminate reinfored zone an be approximated by subtrating the nominal shear resistane of the CFRP laminate shear reinforement v CFRP from the total shear resistane v r. v = v r v CFRP (14) v r = P/bd (15) Fig. 13 Load-deformation urves for slab speimens A 6, B 6, C 6, D 6, and Control 4. Fig. 14 Load-deformation and stress urves for slab Speimen B 5. v CFRP = (F CFRP otθ)/bs (16) where P is the instantaneous applied load, F CFRP is the total tensile fore in the CFRP laminates in-line with the assumed shear ritial setion, b is the perimeter of the assumed ritial shear setion, θ is the angle of inlination of the priniple ompressive stresses from the slab surfae, and s is the spaing of the shear-reinforing perimeters perpendiular from the loading plate periphery. Figure 15 presents the responses of all shear-reinfored perimeters of slab Speimens A 6, B 6, C 6, and D 6 with respet to the applied load. The onrete shear strength was derived from Eq. (14) through (16). Based on the observed angles of inlination of the shear failure planes, a mean angle of 31 degrees was used for θ. The CFRP laminate tensile fore was derived from diret strain measurements during testing, suh as shown in Fig. 14, the A CFRP given in Table 1, and the experimentally determined CFRP laminate modulus. Two general observations an be made. First, the onrete shear strength varies with the distane from the loading plate periphery. Perimeters near the plate exhibit higher onrete shear strengths than perimeters further away from the plate. Seond, the shearing stresses are distributed differently among the slab speimens. Slab Speimen A 6 shows a gradual inrease in shear resistane for all the shear-reinfored perimeters and a sudden loss in shear strength at failure. Slab Speimens B 6 and C 6 also show a gradual inrease in shear resistane for all the reinfored perimeters. These speimens, however, portray a gradual loss in shear strength prior to failure. Slab Speimen D 6 shows a gradual loss in shear ACI Strutural Journal/January-February

8 Table 2 Slab speimen test results and ultimate analysis Test results Ultimate analysis P TEST P Failure , TEST P , TEST P , TEST, within shear U 80, P TEST, b o d f bd f b o d f ϕ o bd f ϕ P TEST P o TEST P TEST U P TEST reinforement Speimen kj (ft-kip) kn (kip) MPa (ksi) MPa (ksi) MPa (ksi) MPa (ksi) P Y P V P V ( U 80 ) ont P ont (Y/N) Control (2.9) 575 (129) 0.57 (6.9) 0.57 (6.9) 0.41 (4.9) 0.41 (4.9) Control (1.5) 439 (99) 0.48 (5.7) 0.48 (5.7) 0.33 (4.0) 0.33 (4.0) Control (1.3) 476 (107) 0.53 (6.3) 0.53 (6.3) 0.31 (3.5) 0.31 (3.5) Control (1.4) 479 (108) 0.60 (7.3) 0.60 (7.3) 0.34 (3.9) 0.34 (3.9) Average 0.55 (6.5) 0.35 (4.1) Standard deviation 0.06 (0.7) 0.04 (0.6) A (3.9) 591 (133) 0.64 (7.7) 0.37 (4.4) 0.44 (5.3) 0.25 (3.1) N A (4.4) 632 (142) 0.63 (7.6) 0.36 (4.3) 0.45 (5.4) 0.26 (3.1) N A (2.9) 646 (145) 0.72 (8.6) 0.48 (5.8) 0.42 (4.8) 0.27 (3.2) Y A (3.4) 595 (134) 0.75 (9.0) 0.43 (5.2) 0.42 (4.9) 0.23 (2.8) Y A (4.7) 671 (151) 0.74 (8.9) 0.37 (4.4) 0.43 (5.0) 0.21 (2.5) N A (3.9) 631 (142) 0.80 (9.6) 0.35 (4.2) 0.44 (5.1) 0.19 (2.3) Y Average 0.39 (4.7) 0.23 (2.8) Standard deviation 0.05 (0.6) 0.03 (0.4) B (4.7) 659 (148) 0.71 (8.6) 0.39 (4.7) 0.49 (6.0) 0.27 (3.2) Y B (3.7) 638 (144) 0.69 (8.3) 0.38 (4.5) 0.48 (5.8) 0.26 (3.1) N B (4.1) 744 (167) 0.82 (9.9) 0.52 (6.3) 0.48 (5.5) 0.29 (3.5) N B (3.8) 701 (158) 0.88 (10.6) 0.48 (5.8) 0.49 (5.7) 0.26 (3.1) N B (7.7) 791 (178) 0.88 (10.5) 0.42 (5.0) 0.51 (5.8) 0.23 (2.8) N B (11) 791 (178) 1.00 (11.9) 0.42 (5.1) 0.56 (6.5) 0.23 (2.7) N Average 0.43 (5.2) 0.26 (3.1) Standard deviation 0.06 (0.7) 0.02 (0.3) C (4.3) 612 (138) 0.66 (8.0) 0.29 (3.4) 0.46 (5.5) 0.20 (2.4) Y C (5.4) 673 (151) 0.73 (8.8) 0.32 (3.8) 0.51 (6.1) 0.22 (2.6) N C (4.3) 775 (174) 0.86 (10.3) 0.44 (5.3) 0.50 (5.7) 0.25 (3.0) N C (5.6) 781 (176) 0.99 (11.8) 0.43 (5.1) 0.55 (6.4) 0.23 (2.8) N C (7.3) 858 (193) 0.95 (11.4) 0.35 (4.2) 0.55 (6.3) 0.20 (2.4) Y C (12) 872 (196) 1.10 (13.2) 0.36 (4.3) 0.61 (7.1) 0.19 (2.3) N Average 0.36 (4.4) 0.21 (2.6) Standard deviation 0.06 (0.7) 0.02 (0.3) D (2.3) 550 (124) 0.60 (7.2) 0.26 (3.1) 0.41 (5.0) 0.18 (2.1) Y D (4.1) 605 (136) 0.66 (7.9) 0.28 (3.4) 0.45 (5.5) 0.20 (2.4) Y D (3.0) 616 (139) 0.68 (8.2) 0.35 (4.2) 0.40 (4.5) 0.20 (2.3) Y D (3.0) 634 (143) 0.80 (9.6) 0.35 (4.2) 0.45 (5.2) 0.19 (2.2) Y D (3.2) 617 (139) 0.68 (8.2) 0.25 (3.1) 0.40 (4.6) 0.14 (1.7) Y D (4.4) 639 (144) 0.81 (9.7) 0.26 (3.2) 0.45 (5.2) 0.14 (1.7) Y Average 0.29 (3.5) 0.17 (2.1) Standard deviation 0.04 (0.5) 0.03 (0.3) strength prior to failure only in the first three reinfored perimeters and a omplete loss in shear strength in the innermost perimeter. The slab speimens with CFRP laminate Patterns A and D were prone to premature shear failures inside the shearreinfored zone. Pattern A mostly failed between the seond and third shear-reinforing perimeters. Pattern D always failed between the loading plate fae and the first perimeter of shear reinforement. It is probable that the shear stresses at the orners of the loading plate are onsiderably higher than those at the fae of the loading plate. This an be attributed to the flexural urvature of the slab speimen onforming to 56 the retangular loading plate. The orners of the loading plate were observed to piere the slab surfae during testing and it is likely that the onrete at these loations fratured in shear initially. The lak of shear reinforement in the viinity of the loading plate orners of Pattern A may have allowed these fratures to propagate. Upon reahing the shear reinforement, the shear raks have developed onsiderably and ould no longer be ontained by the shear reinforement, permitting them to pass between the shear reinforing elements. This is refleted by the sudden loss in v values within the shear reinfored zone prior to failure. The gradual dissolution of v values in the first shear ACI Strutural Journal/January-February 2007

9 reinforing perimeter and the lak of apexes in the v values in the outer shear reinforing perimeters for slab Speimen D 6 imply that the shearing fores were not being adequately transmitted to the outer perimeters of shear reinforement, resulting in the first perimeter being over-stressed and failure of the speimen. The slab speimens with CFRP Patterns B and C were less likely to fail prematurely within the shear reinfored zone. The lak of sudden strength loss and the presene of apexes in the v values for most of the reinfored perimeters imply that the patterns offered suffiient resistane and onfinement to prevent the development of large shear raks and effetively distributed shearing fores to the unraked onrete outside the shear reinfored zone. Evaluation of theoretial preditions Table 2 ontains the test results and ultimate load analysis inluding those using the provisions of the CSA and ACI standards. 4,5 The experimental ultimate loads P TEST have been normalized with respet to b o d f and bd f to make diret evaluation of Eq. (5) and (11). This orresponds to the shear strength of onrete at a distane d/2 from the loading plate periphery and from the outermost perimeter of shear reinforement, respetively. As stated previously, exessive amounts of shear reinforement were provided to avoid failure of the reinforement. Table 2 shows that the CSA and ACI standards 4,5 highly underestimated the punhing shear apaity of the speimens, in partiular those speimens reinfored in shear (refer to P TEST /P V ). This is attributed to the onservative predition of onrete shear strength. The standards did foresee the ourrene of most shear failures inside the shear-reinfored zone. The standards speify that the nominal shear stress resistane of onrete be taken as 0.33 f (MPa) (4 f (psi) ) and f (MPa) (2 f (psi) ) at a distane d/2 from the olumn periphery and from the outermost perimeter of shear reinforement, respetively. The standards also impose a limit of 0.67 f (MPa) (8 f (psi) ) on the umulative shear stress resistane of onrete and the shear reinforement at a ritial setion d/2 from the olumn periphery. The v values of all of the ontrol speimens and the shear reinfored speimens outside the shear reinfored zone were muh greater than 0.33 f (MPa) (4 f (psi) ) and f (MPa) (2 f (psi) ), respetively, (see P TEST /bd f ). Most of the shear reinfored slab speimens attained shear strengths greater than 0.67 f (MPa) (8 f (psi) ) at a distane d/2 from the loading plate periphery (refer to P TEST /(b o d f )). All the slab speimens with CFRP laminate Pattern D and slab Speimens A 3, A 4, A 6, B 3, C 3, and C 5 did not fail in shear outside the shear reinfored zone. As disussed in Failure harateristis, high shear stresses initiate failure at the orners of the loading plate. This is onfirmed by the findings of Sherif and Dilger. 10 Shear reinforing Pattern A did not have shear reinforing at the loading plate orners as reommended by the ACI standards 5 and was inapable of onfining the shear fratures initiating from them. Pattern D had shear reinforement at the orners but was inapable of transferring shear stresses suffiiently away from the loading plate. Slab Speimens B 3 and C 3 had onseutive shear reinforing perimeters spaed at 0.75d. Equation (7) speifies that for this spaing the shear stress shall not exeed 0.5 f (MPa) (6 f (psi) ) at a ritial setion perimeter d/2 from the olumn periphery. Both these speimens exeeded this limitation (refer to P TEST /(b o d f )). Fig. 15 Conrete shear strength for ritial setions in-line with shear reinforement. Fig. 16 Shear strength of onrete outside shear-reinfored zone. Design onsideration The onservative shear strength of onrete speified in the CSA A and ACI standards an be attributed to the assumption that the shear to flexural apaity ratio is almost unity. Shear strength is known to derease as the extent of flexural yielding in the slab inreases. The derease in shear strength is attributed to the loss in membrane ation as a onsequene of greater flexural yielding. 11 Hognestad 12 identified the influene of flexural yielding and introdued the variable φ o equal to the ratio of shear to flexural apaity. A properly designed slab has a flexural strength less than the shear strength. To simplify design proedures, the ACI and CSA standards 4,5 assume φ o equal to unity, whih is onservative beause a value less than unity has higher nominal shear stress resistane, as is evident in the test results presented herein. Using the ultimate apaity and the speified 4,5 ritial setion area, Fig. 16 plots the nominal shear resistane of onrete for the slab speimens with shear failures outside the shear-reinfored zone (Table 2), with and without ACI Strutural Journal/January-February

10 Fig. 17 Shear strength of onrete within shear reinfored zone. onsideration of the flexural to shear apaity ratio. The apaities have been normalized with respet to onrete strength. The shear-to-flexural apaity ratio φ o is taken as that for the respetive ontrol speimen of eah slab (Table 1). The shear strength is referened with respet to α, the ratio of distane between the loading plate periphery and the ritial shear setion to the effetive slab thikness. Evident in Fig. 16 is that the shear strength of onrete is lower in speimens that have larger φ o values (those slab speimens with 15 M flexural reinforement bars) and that the CSA and ACI standards 4,5 speified onrete shear strengths of 0.33 f (MPa) (4 f (psi)) and f (MPa) (2 f (psi)) for the ontrol and shear-reinfored speimens, respetively, are onservative. Also evident is that this disparity in shear strength when ompared with the CSA and ACI provisions appears to be mitigated when onrete strength is normalized with respet to φ o. The shear strength of onrete is approximately 0.33 f (MPa)/φ o (4 f (psi)/φ o ) at a distane α = 0.5 and diminishes asymptotially toward f (MPa)/φ o (2 f (psi)/φ o ) at a distane α > 3 (refer also to P TEST /bd f in Table 2). The umulative φ o nominal shear stress resistane at a distane d/2 from the loading plate periphery does not exeed 0.67 f (MPa)/φ o (8 f (psi)/φ o ) for any of the speimens (refer to P TEST / b o d f in Table 2). φ o From the observed shear fratures (Fig. 10), it an be onluded that the influene of the retangular loading plate to impart a retangular shear stress distribution dissipates with distane from the loading plate and that the failure planes furthest away from the loading plate are of irular shape. The lower portion of Fig. 4 depits the proposed ritial shear perimeters that are irular at the orners. In this way, the proposed perimeters are near retangular immediately adjaent to the loading plate and beome near irular furthest away from the loading plate. Using both the speified and the proposed ritial perimeters, onrete strength is determined by Eq. (14) through (16) for eah peripheral line of shear reinforement for all speimens exept those of Pattern D (Fig. 17). Pattern D was not inluded due to its failure to effetively distribute shear stresses among the shear reinforement. The fat that the interior perimeters of shear reinforement Pattern C are no longer in line with the proposed peripheral lines (Fig. 4), only the outermost perimeter is plotted. It is lear that the satter in the results using the speified ritial shear perimeters is onsiderably redued with the use of the proposed ritial shear perimeters and that the results of Fig. 16 that inlude φ o are further substantiated. In Table 2, olumn P TEST /P V has revised ode preditions based on the proposed ritial shear setions defined in Fig. 4 and onrete strengths normalized with respet to φ o. It is apparent that these preditions are muh loser to atual but still onservative. Beause the CSA and ACI standards speify onrete shear strength of f (MPa) (2 f (psi) ) irrespetive of how far the shear reinforement is extended, the apaity will be underestimated in ases where the shear reinforement is appropriately distributed and extends to a distane α < 5. Sherif and Dilger 10 experiened shear strength less than 0.2 f (MPa) (2.4 f (psi) ) at α > 5 and reommend that shear reinforement not be extended beyond α = 4.5. The shear reinforement was not extended suffiiently in this investigation to evaluate this parameter. CONCLUDING REMARKS An innovative tehnique to retrofit onrete slabs for enhaning their punhing shear apaity was first suggested by the authors in Further tests were ompleted and reported in This extensive experimental work is summarized in this paper. The approah involves reinforing the slab in the viinity of a olumn with FRP laminates through an elaborate pattern of vertial holes. Coneptually, the slab is stithed with FRP fabri and the holes are filled with epoxy. The experimental program onsisted of m (4.9 ft) square and 150 mm (5.9 in.) deep slabs under onentri load to validate the proposed tehnique. Results from four speimens of the pilot series are not inluded herein beause anhorage of FRP laminates resulted in inreased flexural strength of the slabs in addition to the enhaned shear apaity. Results from 28 speimens are presented herein based on whih the following onlusions an be drawn: 1. The slab speimens retrofitted with CFRP laminate shear reinforement demonstrated a substantial inrease in shear strength, dutility, and energy dissipation apaity. Shear strength inrease of over 80% and enhanement of dutility of over 700% were observed; 2. Greater inreases in dutility, apaity, and audible distress are exhibited with greater numbers of shear reinforing perimeters, partiularly in shear-reinforing patterns with loser spaing of shear reinforement along peripheral lines; 3. Within a group of slab speimens with equal potential shear ritial setions outside the shear-reinfored zone, larger onseutive spaing of shear reinforement did not have any adverse effet on strength or dutility but aused greater degrees of onrete raking and inreased the probability of shear failures within the shear-reinfored zone; 58 ACI Strutural Journal/January-February 2007

11 4. Closer spaing of shear reinforement resulted in greater improvements in the behavior of slabs. Thus, shearreinforing Patterns A and D (Fig. 4) exhibited omparatively lower improvements in dutility and shear apaity. The patterns were suseptible to premature shear failures within the shear-reinfored zone. Patterns B and C exhibited omparatively higher dutility and shear apaity improvements. These patterns offered effetive onfinement to prevent the development of shear failure within the shearreinfored zone; 5. The proposed ritial shear setion perimeters with rounded orners in the manner depited in Fig. 4 best represent the behaviors of the shear reinforement patterns tested in this researh program; and 6. The nominal shear stress resistane of onrete varies with distane from the loading area and an be taken as 0.33 f (MPa)/φ o (4 f (psi)/φ o ) at α = 0.5, dereasing asymptotially toward f (MPa)/φ o (2 f (psi)/φ o ) at α > 4, where φ o is the shear to flexural apaity ratio and α is the ratio of the distane between the loading area periphery and the ritial shear perimeter to the effetive slab thikness. All the slab speimens had umulative shear strength less than 0.67 f (MPa)/φ o (8 f (psi)/φ o ) at α = 0.5. ACKNOWLEDGMENTS The researh reported herein was funded by grants from the Natural Sienes and Engineering Counil of Canada (NSERC) and ISIS Canada, an NSERC Network of Centres of Exellene. Tehnial and finanial support from R. J. Watson In. of East Amherst, N. Y., Fyfe Co. LLC of San Diego, Calif., and Premier Corrosion Protetion Servies In. of Oakville, Ontario, Canada, is gratefully aknowledged. The experimental work was arried out at the Strutures Laboratories of the University of Toronto, Toronto, Ontario, Canada. Thanks are extended to O. Bayrak for his help in the experimental program during his post-dotoral tenure at the University of Toronto. NOTATION A CFRP = width of CFRP shear laminate on onentri line parallel to loading area periphery b = shear ritial setion perimeter d/2 from outermost peripheral line of shear reinforement b o = perimeter of shear ritial setion d/2 from loading area periphery = retangular loading plate width d = effetive slab thikness for shear F CFRP = total tensile fore in peripheral line of CFRP laminates f = onrete ylinder ompressive strength f U = ultimate strength of flexural reinforement f Y = yield strength of flexural reinforement L = width of simply supported slab m r = flexural apaity of slab per unit width P = instantaneous applied load P ont = applied ultimate load during testing of respetive ontrol speimen P Test = applied ultimate load during testing P V = CSA A and ACI standards punhing shear apaity P V = P V values based on f normalized with respet to φ o and ritial shear perimeters defined in Fig. 4(b) P Y = yield line theory flexural apaity s = spaing between onseutive peripheral lines of shear reinforement parallel to loading area periphery s o = distane between loading area periphery and first peripheral line of shear reinforement U 80 = strain energy absorbed up to 80% of ultimate load, beyond the peak (U 80 ) ont = strain energy absorbed up to 80% of ultimate load, beyond peak of respetive ontrol speimen V f = shear fore due to fatored loads v CFRP = nominal shear stress resistane of CFRP laminate shear reinforement v = nominal shear stress resistane of onrete v f = nominal shear stress due to fatored loads v r = nominal shear stress resistane α = ratio of distane between loading area periphery and ritial shear setion to effetive shear slab thikness α s = support type modifiation fator β = ratio of long to short side of loading area periphery φ = resistane fator for onrete φ o = alulated ratio of shear to flexural apaity, P V /P Y θ = angle of inlination of priniple ompressive stresses from slab surfae ρ = perent flexural reinforement REFERENCES 1. Sheikh, S. A., and Homam, S. M., A Deade of Performane of FRP- Repaired Conrete Strutures, Proeedings of the Seond International Workshop on Strutural Health Monitoring of Innovative Civil Engineering Strutures, Winnipeg, Manitoba, Canada, Sept. 2004, pp Sissakis, K., and Sheikh, S. A., The Use of CFRP Strands to Improve the Punhing Shear Resistane of Conrete Slabs, Researh Report, Department of Civil Engineering, University of Toronto, Toronto, Ontario, Canada, 2000, 86 pp. 3. Sissakis, K., Strengthening of Conrete Slabs for Punhing Shear with CFRP Laminates, MAS thesis, Department of Civil Engineering, University of Toronto, Toronto, Ontario, Canada, 2002, 215 pp. 4. CSA-A , Design of Conrete Strutures, Canadian Standards Assoiation, Rexdale, Ontario, Canada, 2004, 214 pp. 5. ACI Committee 318, Building Code Requirements for Strutural Conrete (ACI ) and Commentary (318R-05), Amerian Conrete Institute, Farmington Hills, Mih., 2005, 430 pp. 6. Criswell, M. E., and Hawkins, N. W., Shear Strength of Slabs: Basi Priniple and their Relation to Current Methods of Analysis, Shear in Reinfored Conrete, SP-42, V. 2, 1974, pp CPCA, Conrete Design Handbook, Canadian Portland Cement Assoiation, Ottawa, Ontario, Canada, Joint ACI-ASCE Committee 421, Shear Reinforement for Slabs (ACI 421.1R-99), Amerian Conrete Institute, Farmington Hills, Mih., 1999, 15 pp. 9. Johansen, K. W., Yield Line Theory, Cement and Conrete Assoiation, London, 1962, 181 pp. 10. Sherif, A. G., and Dilger, W. H., Critial Review of the CSA A Punhing Shear Provisions for Interior Columns, Canadian Journal of Civil Engineering, V. 23, 1996, pp Hawkins, N. M., and Mithell, D., Progressive Collapse of Flat Plate Strutures, ACI JOURNAL, Proeedings V. 76, No. 7, July 1979, pp Hognestad, E., Shear Strength of Reinfored Conrete Column Footings, ACI JOURNAL, Proeedings V. 50, No. 11, Nov. 1953, pp ACI Strutural Journal/January-February