ACI STRUCTURAL JOURNAL TECHNICAL PAPER Title no 110-S47 Behavior of Concrete Deep Beams Reinforced with Internal Fiber-Reinforced Polymer—Experimental Study by Matthias F Andermatt and Adam S Lubell Concrete deep beams with small shear span-depth ratios (a/d) are common elements in structures To mitigate corrosion-induced damage in concrete structures, members internally reinforced with fiber-reinforced polymer (FRP) are increasingly specified However, very little experimental data exist for FRP-reinforced concrete deep beams, as prior research has mainly focused on slender beams having a/d greater than 2.5 This paper reports on an experimental study designed to investigate the shear behavior of concrete deep beams internally reinforced with FRP and containing no distributed web reinforcement Test results of 12 large-scale specimens that were loaded in a four-point bending configuration are presented, where the primary variables included the a/d, reinforcement ratio, member height, and concrete strength The results show that an arch mechanism was able to form in FRPreinforced concrete beams having a/d less than 2.1 Keywords: cracks; deep beams; failure mechanisms; fiber-reinforced polymer reinforcement; reinforced concrete; shear span-depth ratio (a/d); shear strength; size effect INTRODUCTION Steel-reinforced concrete structures have been built for over a century and numerous research programs have been conducted to understand the behavior of such structures Many steel-reinforced concrete structures, such as bridges, parking garages, and marine structures, are exposed to aggressive environments which, over time, can cause extensive damage and the need for costly rehabilitation due to corrosion of the steel reinforcement Fiber-reinforced polymers (FRPs), which are a composite material consisting of fibers embedded in a resin, are an alternative type of reinforcement that can be used instead of steel.1,2 Not only is FRP noncorrosive but it is also nonmagnetic, making it useful in many applications where corrosion and electromagnetic interference are problematic.1 The shear behavior of steel-reinforced concrete members has been well-documented and many design procedures have been developed.3 In general, concrete members can be classified in two categories based on shear behavior: slender and deep Of particular interest in this paper is the shear behavior of deep members containing no distributed web reinforcement It is generally accepted that deep members have a shear span-depth ratio (a/d) less than 2.5.3-6 Five shear force-transfer mechanisms have been identified in cracked concrete members without transverse reinforcement.3 These consist of shear stresses in the uncracked flexural compression region, aggregate interlock and residual tensile stresses at diagonal cracks, dowel action of longitudinal reinforcement, and arch action through formation of direct compression struts The shear capacity of reinforced concrete slender members is governed by the breakdown of beam action with failure once equilibrium of forces can no longer be satisfied at the inclined crack locations In deep beams, a major ACI Structural Journal/July-August 2013 reorientation of the internal forces can occur after cracking such that forces tend to flow directly from the loading points to the supports This arch action involves the formation of compression struts to directly transmit the load to the supports, while the longitudinal reinforcement acts as a tie holding the base of the arch together Unlike slender members with no web reinforcement, deep members can have substantial reserve capacity after diagonal cracking Considerable research has been conducted on the shear behavior of slender (a/d > 2.5) FRP-reinforced concrete members The overall shear behavior of slender FRPreinforced members is similar to that of steel-reinforced slender members, but the shear capacity of members reinforced with glass FRP (GFRP) is lower than steelreinforced members having the same reinforcement ratio due to the lower reinforcement stiffness of GFRP.7-9 While numerous shear models have been proposed and incorporated into codes and design guidelines for concrete members internally reinforced with FRP,1,2,10-12 no distinction is made between analysis provisions for slender and deep members In contrast, design guidelines for steel-reinforced concrete construction10,13-15 recognize that different analytical models are required to evaluate the shear capacity of slender and deep members While the steel-reinforced concrete design codes10,13-15 allow the use of strut-and-tie models to analyze deep members, the FRP-reinforced design codes not allow the use of strut-and-tie modeling For example, CSA S806-0212 explicitly states that “analysis by strut and tie models is not permitted.” The use of sectional models in the analysis of FRP-reinforced concrete deep members may result in uneconomical designs in instances where large members are used,16 as is the case when steel-reinforced deep beams are designed using sectional models Limited prior research on FRP-reinforced deep beams containing no distributed web reinforcement has indicated that arch action forms after inclined cracking in specimens having an a/d less than 2.3.17,18 However, the 25 FRPreinforced specimens tested in these prior test programs had small cross-sectional dimensions when compared to the common sizes of beams encountered in industry practice The effective depths d were less than 350 mm (13.8 in.) with 11 specimens having d = 150 mm (5.9 in.) In addition, only limited values for the a/d and longitudinal reinforcement ratios ρ were used in the prior research This paper presents a large-scale experimental program that was undertaken to ACI Structural Journal, V 110, No 4, July-August 2013 MS No S-2011-226.R2 received May 2, 2012, and reviewed under Institute publication policies Copyright © 2013, American Concrete Institute All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors Pertinent discussion including author’s closure, if any, will be published in the May-June 2014 ACI Structural Journal if the discussion is received by January 1, 2014 585 ACI member Matthias F Andermatt is a Bridge Engineer at AECOM, Edmonton, AB, Canada He received his BSc in civil engineering and his MSc in structural engineering from the University of Alberta, Edmonton, AB, Canada His research interests include large-scale testing of structural components and shear transfer in concrete ACI member Adam S Lubell is a Project Engineer at Read Jones Christoffersen Ltd., Vancouver, BC, Canada, and an Associate Adjunct Professor of civil engineering at the University of Alberta He received his PhD from the University of Toronto, Toronto, ON, Canada He is Secretary of ACI Subcommittee 445A, Shear and Torsion-Strut and Tie; and a member of ACI Committees 440, Fiber-Reinforced Polymer Reinforcement; 544, Fiber-Reinforced Concrete; and Joint ACI-ASCE Committee 445, Shear and Torsion His research interests include the design and rehabilitation of reinforced and prestressed concrete structures, and the development of structural detailing guidelines to allow the use of high-performance materials further study the behavior of concrete deep beams internally reinforced with GFRP The new test results presented in this paper are used with the results from the prior research17,18 to develop and validate a modeling technique for FRPreinforced deep beams in a companion paper.16 RESEARCH SIGNIFICANCE The efficient use of FRP reinforcement in deep members has been hindered due to a lack of knowledge on the behavior of such members Due in part to a lack of experimental data, there are currently no separate design guidelines for slender and deep FRP-reinforced concrete beams Prior research has mainly focused on the shear behavior of slender members longitudinally reinforced with FRP and only testing at small scales has been conducted on FRP-reinforced deep members This paper presents the results of an experimental investigation of 12 large-scale concrete deep beams internally reinforced with GFRP The influences on shear capacity from the crosssection geometry, concrete strength, a/d, and reinforcement ratio are discussed The results are used in a companion paper16 to validate modeling techniques for deep members EXPERIMENTAL INVESTIGATION Twelve concrete deep beams internally reinforced with GFRP were constructed and tested to failure in the I F Morrison Structural Engineering Laboratory at the University of Alberta.19 The primary test variables included the a/d, the reinforcement ratio ρ, the effective depth d, and the concrete strength fc′ The objective of the test program was to assess the design parameters that influence the strength and behavior of FRP-reinforced concrete deep beams containing no web reinforcement Specimen configurations The as-built configuration of the specimens is given in Table and Fig The specimens were designed using a preliminary version of the CSA-1 strut-and-tie model described in the companion paper16 and elsewhere.19 The a/d of the specimens were selected to cover a wide range of the deep beam category at the ultimate and equivalent serviceability limit states and to fill gaps in the limited experimental data available on FRP-reinforced concrete deep beams Specimens were grouped into three series having nominal heights h of 300, 600, and 1000 mm (11.8, 23.6, and 39.4 in.) To determine the influence of h on the shear capacity, a/d, ρ, and fc′ were held approximately constant, while h and the bearing plate length Lb were varied The parameter Lb was scaled proportional to h In all cases, the bearing plate width was the same as the member width bw, which was approximately 300 mm (11.8 in.) for all specimens Member width is not considered to have an influence on the shear stress at failure.20,21 To study the effect of concrete strength on the shear capacity, both normal- and high-strength concretes were used The reinforcement in all specimens consisted of GFRP, as this is the most commonly used FRP in the industry Furthermore, GFRP has a lower modulus of elasticity Efrp than carbon FRP, leading to higher strain values for a given reinforcement ratio and overall member configuration High reinforcement strains at the time of failure were desired to better validate the analytical capacity models presented in the companion paper16 for strain values significantly greater than those generally used in the design of steel-reinforced concrete deep beams The behavior of deep beams is not well-understood for the case of where high reinforcement strains would occur The reinforcement ratios were selected such that the stress level in the FRP would not exceed approximately 25% of the specified tensile strength fFRPu of the GFRP bar under the equivalent serviceability limit state loads.10 Note that ACI 440.1R-061 limits the service stress level in the GFRP to 0.20fFRPu The specimens with h = Table 1—As-built specimen properties Specimen a/d ρ, % Height h, mm Effective depth d, mm Shear span a, mm Width bw, mm Overhang length, Plate length Lb, mm* mm Age, days fc′, MPa A1N 1.07 1.49 306 257 276 310 874 100 171 40.2 A2N 1.44 1.47 310 261 376 310 874 100 36 45.4 A3N 2.02 1.47 310 261 527 310 874 100 173 41.3 A4H 2.02 1.47 310 261 527 310 623 100 160 64.6 B1N 1.08 1.70 608 503 545 300 605 200 129 40.5 B2N 1.48 1.71 606 501 743 300 605 200 108 39.9 B3N 2.07 1.71 607 502 1040 300 605 200 105 41.2 B4N 1.48 2.13 606 496 736 300 814 200 111 40.7 B5H 1.48 2.12 607 497 736 300 614 200 96 66.4 B6H 2.06 1.70 610 505 1040 300 460 200 106 68.5 C1N 1.10 1.58 1003 889 974 301 826 330 104 51.6 C2N 1.49 1.56 1005 891 1329 304 821 330 97 50.7 * Overhang length is measured from center of bearing plate to end of specimen/GFRP Notes: mm = 0.0394 in.; MPa = 145 psi 586 ACI Structural Journal/July-August 2013 300 mm (11.8 in.) had one layer of reinforcement, while specimens with h = 600 and 1000 mm (23.6 and 39.4 in.) had three layers of reinforcement Overhangs were provided beyond the supports in all specimens to allow for anchorage of the FRP reinforcement.10 Side and bottom clear cover was 38 mm (1.5 in.) Vertical bar clear spacing between layers was 38 mm (1.5 in.) Refer to Fig for the reinforcement configuration Material properties Commercially available GFRP bars in U.S Customary sizes of No 6, No 7, and No (19, 22, and 25 mm) were used as the longitudinal reinforcement The sand-coated GFRP bars contained surface deformations produced from wrapping groups of fibers diagonally in opposite directions to form a diamond-shaped pattern on top of the main longitudinal core, as shown in Fig Tension coupon tests conforming to CSA S806-0212 were performed on five samples of each bar size to determine the failure stress fFRPu and modulus of elasticity EFRP The GFRP exhibited linear elastic stress-strain responses to brittle failures The crosssectional area of the different nominal bar sizes was determined by using volumetric measurements.19,22 The measured properties of the GFRP bars are provided in Table Two types of concretes were obtained from a local ready mix supplier: a normal-strength mixture and a highstrength mixture having nominal specified 28-day strengths of 35 and 70 MPa (5075 and 10,150 psi), respectively Both mixtures had a maximum aggregate size of 14 mm (0.55 in.) Four batches of concrete were required with three specimens cast from each batch All specimens were moist-cured for days, after which they were removed from the formwork and stored in the laboratory until testing Cylinders with dimensions of 100 x 200 mm (3.9 x 7.9 in.) were cast and cured under the same conditions as the specimens The age of each specimen and the average concrete strength from three cylinders on the day of testing are given in Table Test setup and testing procedure Specimens were tested in a 6600 kN (1484 kip) capacity MTS testing frame with the test setup as shown in Fig A stiff distributing beam was used to apply two equal point loads on the top surface of the specimen Each specimen was supported on roller assemblies and knife edges that allowed longitudinal motion and in-plane rotation Both loading points also contained rollers and knife edges The specimens were tested with all four roller assemblies free to rotate to ensure no global restraint forces were introduced into the test setup One roller assembly was locked prior to failure to provide stability and prevent dangerous movement at failure Bearing plates were 100 x 310 x 38 mm (3.9 x 12.2 x 1.5 in.) and 200 x 300 x 50 mm (7.9 x 11.8 x 2.0 in.) for the h = 300 and 600 mm (11.8 and 23.6 in.) specimens, respectively For specimens with h = 1000 mm (39.4 in.), top and bottom plates were 330 x 330 x 38 mm (13 x 13 x 1.5 in.) and 330 x 330 x 75 mm (13 x 13 x in.), respectively A thin layer of plaster was used between the specimen and the bearing plates to ensure uniform contact Five linear variable differential transformers (LVDTs) were mounted along the bottom of the specimens to measure vertical deflection at the supports, quarter-spans, and midspan All deflection data presented in this paper have been corrected for the measured support settlements Electrical resistance strain gauges were applied to the FRP bars to measure the strain during the test Between 12 and 30 strain ACI Structural Journal/July-August 2013 Fig 1—Test setup and specimen geometry Fig 2—GFRP bars, No at top and two No Table 2—Properties of GFRP bars Reinforcing bar size No (19 mm) No (22 mm) No (25 mm) 19 (0.75) 22 (0.87) 25 (0.98) Cross-sectional area, mm (in ) 322 (0.50) 396 (0.61) 528 (0.82) Failure stress fFRPu, MPa (ksi) 765 (111) 709 (103) 938 (136) 37.9 (5496) 41.1 (5960) 42.3 (6134) 72.0 64.8 64.1 Reinforcement property Nominal diameter, mm (in.)* Modulus of elasticity EFRP, GPa (ksi) Glass content, % vol.* * Provided by manufacturer gauges were applied to the bars at the center of the supports and loading points, midspan, and at a uniform spacing in the shear spans The majority of the strain gauges were applied on the bottom bars except at the location of the supports, loading points, and midspan, where strain gauges were applied on all layers Additional information on instrumentation of the specimens is documented elsewhere.19 587 Table 3—Experimental results Maximum midheight diagonal crack width (last load stage) Ultimate load Specimen Inclined cracking load Pc, kN A1N Equivalent service load Pc/Pmax Failure type* Pmax, kN Dmax, mm† Average midspan strain, mε Width, mm % of Pmax Ps, kN Ds, mm fFRPs/fFRPu, % Crack width, mm 312 0.38 FC 814 12.4 17,400 1.5 94 407 4.0 37 0.9 A2N 187 0.40 SC 471 11.3 8900 1.5 82 235 3.7 22 0.5 A3N 143 0.59 SC 243 10.9 6000 1.5 92 121 2.6 14 0.33 A4H 163 0.85 DT 192 9.5 4800 2.5 96 96 0.9 0.3 B1N 387 0.30 FC 1273 9.1 8400 1.25 76 637 3.5 25 0.9 B2N 287 0.36 SC 799 13.1 6900 3.0 92 400 4.6 16 0.8 B3N 237 0.55 SC 431 15.3 5200 2.75 84 215 2.7 14 0.33 B4N 412 0.50 SC 830 11.5 6200 4.0 98 415 3.4 21 0.5 B5H 387 0.36 S 1062 14.2 6900 4.0 91 531 5.1 21 1.25 B6H 212 0.56 DT 376 12.9 4500 7.0 96 188 1.3 0.3 C1N 613 0.27 SC 2269 15.9 9600 2.5 80 1135 6.1 22 1.5 C2N 413 0.31 S 1324 18.3 6800 4.5 88 662 6.7 15 1.5 * DT is diagonal concrete tension failure; FC is flexural compression failure; SC is shear compression failure; S is compression strut failure † Midspan deflection occurring at Pmax Notes: mm = 0.0394 in.; MPa = 145 psi The specimens were tested under displacement control with a displacement rate of 0.1 to 0.25 mm/min (0.004 to 0.01 in./min) of machine stroke depending on the stiffness of the specimen Each specimen was loaded in five to 10 increments After each increment, the deflection was held while the crack patterns were photographed and the crack widths were measured using a crack comparator gauge Data from the instrumentation were recorded continuously until specimen failure The duration of the tests ranged between and hours depending on the specimen configuration and the number of load increments EXPERIMENTAL RESULTS AND DISCUSSION All 12 specimens were loaded to failure in displacement control, which allowed for the observation of both the preand post-peak behavior The majority of the specimens failed suddenly with a significant drop in load-carrying capacity A summary of the key experimental results for the specimens is given in Table The applied load P is the applied load measured by the internal load cell in the testing frame plus the self-weight of the loading apparatus The self-weight of the specimen is not included in P The peak shear capacity is taken as Pmax/2 For each specimen, the midspan deflection Dmax corresponding to Pmax is given in Table The equivalent service load Ps was taken as 50% of the peak load.19 The equivalent service load was calculated in this study by assuming that the nominal resistance of the specimen was equal to the peak load, a dead to live load ratio of 3:1, and load and resistance factors as per current Canadian design codes.15,19 Note that the actual service to peak load ratio may vary in practice depending on the design code and dead to live load ratio To prevent creep rupture of the GFRP reinforcement, design codes impose a limit on the allowable sustained stress in the FRP.1,2,10,12 ACI 440.1R-061 requires that the stress in the GFRP at the sustained service load be kept below 0.20fFRPu, while CSA S6-0610 has a higher limit of 0.25fFRPu at the serviceability limit state The stress level 588 in the GFRP at the equivalent service load was between 0.04fFRPu and 0.37fFRPu, with only Specimen A1N exceeding 0.25fFRPu Failure mechanisms Among the specimens, four types of failure mechanisms were observed, as given in Table Shear compression was the most common failure mode, occurring in six specimens Shear compression failure was characterized by the crushing of the concrete in the flexural compression zone at the tip of the main diagonal crack The main diagonal crack extended from the inside edge of the support plate toward the inside edge of the loading plate into the flexural compression zone At failure, the crack penetrated through the top of the specimen and an abrupt drop in load-carrying capacity occurred A typical shear compression failure is shown in Fig 3(a) Flexural compression failures occurred in Specimens A1N and B1N—both having an a/d of 1.1 This type of failure was characterized by the crushing of the concrete in the flexural compression zone between the two loading plates, as shown in Fig 3(b) The main diagonal cracks in each shear span propagated from the inside edge of the reaction plates toward the inside edge of the loading plates Near the loading plates, the cracks became horizontal and eventually joined The region above the horizontal crack between the loading plates then slowly deteriorated through crushing of the concrete At failure, there was also movement along the main diagonal cracks; however, this sliding action along the main diagonal cracks occurred after deterioration of the compression zone Failure of the diagonal compression strut region between the loading plates and the supports occurred in Specimens B5H and C2N, as shown in Fig 3(c) Failure of the compression struts occurred in a brittle and noisy manner A drop of more than 60% in the load-carrying capacity of the specimens occurred during this action ACI Structural Journal/July-August 2013 Fig 3—Failure mechanisms: (a) shear compression failure in Specimen A2N; (b) flexural compression failure in Specimen A1N; (c) failure of compression strut in Specimen B5H; and (d) diagonal concrete tension failure of Specimen B6H where vertical crack formed from top surface A concrete diagonal tension failure or splitting failure occurred in Specimens A4H and B6H—both of which had fc′ ≈ 66 MPa (9570 psi) A major S-shaped diagonal crack formed in each shear span from the inside edge of the reaction plate toward the inside edge of the loading plate The diagonal crack extended above the diagonal line between the centerlines of the loading and support plates As the crack width increased, a vertical crack formed from the top surface of the concrete in the shear span and intersected the diagonal crack, leading to an immediate drop in load-carrying capacity The concrete above the diagonal crack was forced upward after the vertical crack formed, as shown in Fig 3(d) Load-deflection behavior The relationship between the applied load P and the midspan deflection ∆ is shown in Fig 4, where the specimens are grouped according to h The failure of Specimen A1N was gradual, with crushing occurring in the main flexural compression zone A2N and A3N exhibited a sudden drop in load-carrying capacity after Pmax was attained, although the load-carrying capacity of Specimen A2N remained largely intact as deflection increased by approximately mm (0.039 in.) The load-carrying capacity of A4H showed little ACI Structural Journal/July-August 2013 change at the peak load as the midspan deflection and inclined crack widths grew larger A gradual decrease in load-carrying capacity occurred after the peak load was reached Specimen B1N reached a load of 1273 kN (286 kip), at which point there was a 3% loss of load The specimen continued to gain load, but the behavior was characterized by a reduced stiffness as crushing of the flexural compression region initiated At 1286 kN (289 kip), a sudden 8% drop in load was recorded As the flexural region continued to crush, the load-carrying ability was slowly regained and reached a new maximum of 1324 kN (298 kip) Extreme deterioration of the flexural compression zone was observed For subsequent discussions, the failure load of B1N was taken as 1273 kN (286 kip), as the drop in load-carrying capacity from this local peak and regain in strength is considered to be an unreliable mechanism Nevertheless, B1N demonstrated that a large amount of member ductility can be provided by the concrete response, even though the reinforcement has a linear-elastic response B2N and B3N experienced brittle failures, while B4N experienced a more ductile failure with a gradual decrease in load-carrying capacity after reaching the peak load The failure of B5H was extremely brittle, with significant damage along the main inclined crack The 589 Fig 4—Experimental load-deflection behavior of specimens: (a) h = 300 mm; (b) h = 600 mm; and (c) h = 1000 mm (Note: mm = 0.0394 in.; MPa = 145 psi.) Fig 5—Crack diagrams after failure of specimens with h = 300 mm (11.8 in.) (Note: MPa = 145 psi.) Fig 4(b), it is also apparent that the post-cracking stiffness of the specimens is dependent on the reinforcement ratio Specimen B4N, which had a reinforcement ratio 24% larger than B2N while all other variables remained constant, had a stiffer loading response and a capacity that was 4% greater than B2N The post-cracking stiffness was not influenced by h, while a/d and ρ were kept approximately constant The post-cracking stiffness of A1N, B1N, and C1N was similar, as was the post-cracking stiffness of A2N, B2N, and C2N, where the only difference between the specimens was h B4N and B5H, which were identical except for the concrete strength, had a similar load-deflection response up to approximately 90% of the B4N failure load Similarly, B3N and B6H, which were also identical except for the concrete strength, exhibited the same load-deflection response A similar result was observed between A3N and A4H Therefore, the concrete strength had no discernible effect on the post-cracking stiffness of the specimens load-carrying capacity immediately dropped by approximately 80% B6H also failed suddenly and the load-carrying capacity dropped by approximately 60% Both specimens having h = 1000 mm (39.4 in.) failed abruptly with a loss in load-carrying capacity of 30% and 60% in Specimens C1N and C2N, respectively The postcracking stiffness of both specimens was approximately linear to failure, indicating a shear type of failure rather than a more gradual flexural compression failure All specimens exhibited a bilinear load-deflection response As seen in Fig 4, the initial flexural stiffness was the same for the specimens having the same h After cracks fully developed, the load-deflection response was linear to failure for most specimens As the a/d increased, the post-cracking stiffness of the specimens decreased From Crack patterns and widths The crack diagrams showing the condition of the specimens after failure are given in Fig through for specimens having h = 300, 600, and 1000 mm (11.8, 23.6, and 39.4 in.), respectively Crushing and spalling of concrete is indicated by shading The crack patterns in all of the specimens indicated the formation of an arch mechanism Inclined cracks developed, joining the supports and loading points, which disrupted the internal force flow from beam action to arch action, similar to documented behavior in steel-reinforced deep beams.6 For all specimens, the first cracks appeared at the bottom near midspan as flexural cracks The flexural cracking load for each specimen was determined from where the bilinear load-deflection curve began to deviate from the initial linear 590 ACI Structural Journal/July-August 2013 Fig 7—Crack diagrams after failure of specimens with h = 1000 mm (39.4 in.) (Note: MPa = 145 psi.) Fig 6—Crack diagrams after failure of specimens with h = 600 mm (23.6 in.) (Note: MPa = 145 psi.) segment Flexural cracking occurred between 14 and 35% of Pmax The flexural cracks in the constant-moment region rapidly propagated to approximately 80% of h in all specimens Subsequently, additional flexural cracks formed progressively closer to the supports in the shear spans These cracks almost immediately became inclined (diagonal) cracks and grew toward the loading plates The inclined cracking load Pc reported in Table corresponds to the load at which the first inclined crack was visually observed during pauses in loading Most of the specimens had diagonal cracks at the equivalent service-load condition The Pc/Pmax ratios reported in Table serve as a measure of the reserve load capacity after the formation of the first inclined crack Specimens with larger a/d had a smaller reserve capacity after diagonal cracking when compared to specimens with smaller a/d Increasing h caused a decrease in the Pc/Pmax ratio The inclined cracking shear stress, normalized by bw d fc′, decreased as either the a/d or h increased, while fc′ and ρ were approximately constant, as shown in Fig In all instances, the low Pc/Pmax ratio or high reserve capacity was indicative of the formation of arch action after inclined cracking occurred The maximum crack widths for the specimens at the equivalent service load varied between 0.3 and 1.5 mm (0.012 and 0.059 in.) The crack widths given in Table are the maximum crack widths measured at the load interval that was closest to the equivalent service load Only half of the specimens met the ACI 440.1R-061 crack width criterion for structures not subjected to aggressive environments, where the maximum allowable crack width is 0.7 mm (0.028 in.) ACI Structural Journal/July-August 2013 Fig 8—Influence of a/d and h on normalized inclined cracking shear stress (Note: MPa = 145 psi.) Specimens that satisfied the ACI 440.1R-061 crack width requirement typically had larger a/d, larger ρ, or smaller h Prior to reaching Pmax, all specimens had at least one main inclined crack in both shear spans The main inclined crack would extend from the inside edge of the reaction plate toward the loading plate In most of the specimens, the crack trajectory was toward the inside edge of the loading plate and the crack would become increasingly horizontal near the flexural compression zone Smaller secondary inclined cracks were observed parallel to the main inclined crack close to the support region in the majority of the specimens These cracks would often initiate near the centroid of the reinforcement above the support plate and expand diagonally away in both the up and down directions In most instances, the secondary cracks would disappear near the midheight of the specimen and the main diagonal crack would be wider at midheight than near the centroid of the reinforcement In Specimens A1N, A2N, B1N, and C1N, a second diagonal crack formed parallel to the main diagonal crack and extended from the support to the loading point The formation of the multiple inclined cracks indicated that reorientation of internal forces was occurring Crack widths measured at the last loading stage prior to Pmax (Table 3) ranged from 1.25 to 7.0 mm (0.049 to 0.28 in.) and were even wider at failure The cracks were large enough in some cases to easily see through the full specimen width, indicating the complete breakdown of the aggregate interlock shear-transfer mechanism The predominant force-transfer mechanism consisted of arch action The main inclined crack in the right shear span (Fig 9) of A4H initiated as a flexural crack approximately 200 mm (8 in.) to the inside of the right support The flexural crack 591 Fig 9—Right shear span of Specimen A4H at conclusion of test extended above the diagonal line between the centerlines of the loading and support plate The crack then grew more horizontal and extended toward the loading plate Near the bottom of this crack, at approximately one-third of the specimen height, a new crack formed that extended toward the inside edge of the reaction plate, which completed the formation of the critical crack Once the crack had formed, very little additional load could be carried before failure Large deflections resulted and the inclined crack width became increasingly larger The specimen continued to hold load past the peak load with the maximum crack width growing to approximately 10 mm (0.39 in.) Splitting cracks formed along the reinforcement after the load reached Pmax (Fig 9) The splitting cracks resulted from the visible downward movement of the center section of the specimen (dowel action) and the clockwise rotation of the right end, which produced a prying action as the diagonal crack width increased (refer to Fig 9) The large crack opening indicated that arch action formed as aggregate interlock was no longer possible However, the arch action was insufficient to support additional load due to the curvilinear nature of the crack, which prevented the efficient transfer of load to the support Specimen B6H had a cracking behavior that was similar to Specimen A4H The main inclined crack in the left shear span initiated as a flexural crack at the bottom of the specimen near the middle of the shear span that rapidly extended above the diagonal line from the centerline of the support and loading plates Subsequently, an inclined crack extended from the existing inclined crack at a dimension of approximately h/3 from the soffit toward the inside edge of the reaction plate forming the critical crack The aggregate interlock ceased to exist once the crack grew in width and the load had to be transmitted mainly by arch action Because the crack was curved and extended above the diagonal line between the support and the loading point, the load had to be transferred in compression around the curve, which produced an outward thrust The lack of top reinforcement and distributed web reinforcement limited the load-carrying ability of the curved strut and a tensile splitting crack formed at the top of the shear span, as shown in Fig 3(d) and 6, which resulted in an immediate drop in load-carrying capacity Influence of fc′ The load-carrying capacity of Specimen B5H was higher than that of comparable Specimen B4N, which differed only by fc′ B5H had a concrete strength 63% greater than B4N and achieved a 28% larger peak load While a higher concrete strength is expected to enable a specimen to carry additional load when compared to an identical specimen 592 Fig 10—Typical reinforcement strain distribution along bottom layer of reinforcement as load increased (Note: mm = 0.0394 in.; kN = 0.2248 kip; MPa = 145 psi.) with lower-strength concrete, this was not the case for the other companion specimens differing only by fc′ A4H had a concrete strength 56% greater than A3N, but the peak load was only 79% of the A3N peak load Similarly, B6H had a concrete strength 66% greater than B3N, but the peak load was only 87% of Specimen B3N These discrepancies can be explained by the nature of the crack patterns, which prevented the specimens from achieving an efficient arch mechanism, as discussed previously Additional research is required to determine if the reduced capacity of A4H and B6H is related to the low stiffness of the reinforcement combined with the brittle nature of the high-strength concrete and at what a/d the transition from deep beam behavior to sectional shear behavior occurs Reinforcement strains The strain distribution in the bottom reinforcement layer of Specimen B1N as the load increased is shown in Fig 10 and is typical of all specimens.19 For all specimens, there was minimal change in the GFRP reinforcement strains until the formation of the first flexural crack The strain readings of the bottom bar increased rapidly in the vicinity of the first crack, usually in the constant-moment region As additional cracks formed closer to the supports, the measured strains in the GFRP reinforcement also increased closer to the supports In the uncracked regions, strain readings showed minimal strain changes in the GFRP As loading progressed, the reinforcement strains became similar over the entire region between the supports Localized strain increases were noted where the strain gauge locations coincided with cracks In the majority of the specimens, the strain in the GFRP over the center of the support was significantly lower than the strain reading at midspan With the exception of A4H, no strain increase was registered in the GFRP past the supports with the first strain gauge typically located 100 to 200 mm (3.9 to 7.9 in.) past the edge of the support In A4H, the reinforcement strain at the right support location was approximately the same as at the midspan once Pmax was reached The increase in ACI Structural Journal/July-August 2013 reinforcement strain in the right end region corresponds to the visual observation of splitting cracks at the level of the reinforcement In specimens containing multiple reinforcement layers, a strain gradient between the lower, middle, and upper reinforcement layers was present The midspan strains in the middle bars and upper bars were, on average, 23 and 28% less than the strain in the bottom bars at midspan The reinforcement strain distribution is an indicator of whether and to what extent a tied-arch mechanism formed in the specimens In a fully developed tied-arch mechanism, the strain level in the reinforcement is expected to be approximately uniform from support to support In all specimens, the strain distribution between the supports at peak load was approximately constant, indicating that a tied-arch mechanism had developed Based on the strain gradient noted previously, the bottom layer of GFRP anchored a greater amount of force than the upper layers Generally, in simplified analysis of a tied arch such as the ACI 318-0813 strutand-tie modeling provisions, it is assumed that all the layers of reinforcement carry the same tensile stress However, this is only true when all reinforcement has yielded (that is, steel reinforcement), which is not the case with the fully elastic FRP reinforcement INFLUENCES ON SHEAR CAPACITY Shear capacity trends are discussed in terms of the a/d, h, ρ, and fc′, which were the main variables in the test program To facilitate these comparisons, the peak shear stress was normalized by fc′, as shown in Eq (1) ν= Pmax (1) 2bw dfc′ a /d and reinforcement ratio Figure 11(a) shows that as the a/d decreased, there was a significant increase in the normalized shear capacity regardless of h, ρ, or fc′ This is similar to the documented trend for steel-reinforced concrete deep beams.5,6 Increasing the reinforcement ratio by 24% resulted in a 3% increase in the normalized shear capacity of B4N compared to B2N Concrete strength Increasing the concrete strength by 63% while maintaining ρ = 2.13% resulted in a 22% decrease in the normalized shear capacity (top curve in Fig 11(b)) As the concrete strength of the specimens increased, the normalized shear capacity decreased regardless of the a/d, ρ, or h, as shown in Fig 11(b) For specimens with a/d = 2.0 and 2.1, increasing fc′ by approximately 64% resulted in a 50% decrease in the normalized shear capacity The decrease was due to the cracking mechanism that occurred in the specimen with the higher fc′ Overall height Specimens having different heights were tested to determine if there was a size effect on the shear-carrying capacity of GFRP-reinforced deep beams The dimensions of the loading and support plates in the direction of the span Lb were scaled in proportion to h to eliminate the bearing plate as an independent variable.23 Figure 11(c) shows the influence of h on the normalized shear stress at failure ν, where the specimens have been grouped by similar a/d and ρ For the three a/d—1.1, 1.5, and 2.1—ν decreased as the specimen height increased, except for Specimen A2N The effect was ACI Structural Journal/July-August 2013 Fig 11—Influence on normalized shear capacity from: (a) a/d; (b) concrete strength; and (c) member height (Note: mm = 0.0394 in.; MPa = 145 psi.) most pronounced for the specimens having an a/d of 1.1 In addition, the specimen height had minimal influence on the normalized shear capacity for a/d = 1.5 and 2.1 when h was less than 600 mm (23.6 in.) However, this observed trend could be due in part to the small differences in ρ between the 300 and 600 mm (11.8 and 23.6 in.) deep beams The reinforcement ratio of the h = 300, 600, and 1000 mm (11.8, 23.6, and 39.4 in.) specimens was 1.5%, 1.7%, and 1.6%, respectively An increase in ρ is known to produce a higher shear capacity in deep beams when other design parameters are kept constant.5,17 Figure 12 shows the relationship between the a/d, the midspan strain in the bottom layer of reinforcement at Pmax, 593 ACKNOWLEDGMENTS Funding for this project was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), Alberta Ingenuity, and the University of Alberta The authors also acknowledge the donation of materials from BP Composites and Lehigh Inland Concrete REFERENCES Fig 12—Midspan strain in bottom layer of reinforcement at peak load (Note: MPa = 145 psi.) and the normalized shear capacity for specimens having fc′ ≈ 40 MPa (5800 psi) and ρ ≈ 1.7% Lower a/d values resulted in higher midspan strain in the reinforcement and higher normalized shear capacities when compared to larger a/d values CONCLUSIONS The following conclusions are drawn from the laboratory testing of 12 GFRP-reinforced concrete deep beam specimens containing no distributed web reinforcement: With the exception of two specimens, failure of the specimens was brittle The majority of the specimens failed by shear compression after the formation of a major diagonal shear crack extending from the inside edge of the support plate toward the loading plate The failure mode was observed to be ductile in Specimen B1N After initial crushing of the flexural region, the specimen continued to resist increasingly more load while undergoing substantial deformation, demonstrating the overall member ductility that can be attained from a member reinforced with a linear elastic material An arch mechanism formed in all specimens This was confirmed by the crack orientations, crack widths, and measured strains in the longitudinal reinforcement Significant reserve capacity was available after the formation of the main diagonal cracks, indicating internal redistribution of forces and the formation of an arch mechanism Prior to failure, the measured crack widths were typically between 1.25 and 7.0 mm (0.05 and 0.28 in.) The reserve capacity after inclined cracking decreased as the a/d increased, indicating that the arch mechanism became less efficient at higher a/d The post-cracking stiffness of the FRP-reinforced deep beam specimens increased as the a/d decreased or ρ increased The specimen height and fc′ had a negligible effect on the post-cracking stiffness of the FRP-reinforced concrete specimens The normalized shear strength of the specimens increased as the a/d decreased and ρ increased, while all other variables were held constant A size effect in shear capacity was observed for specimens having a/d = 1.1, where increased h resulted in reduced normalized shear stress at the peak load Specimens having a/d = 1.5 and 2.1 had no significant size effect in shear for h less than 600 mm (23.6 in.) However, a detailed relationship for size effect could not be established due to some variations in other specimen parameters 594 ACI Committee 440, “Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars (ACI 440.1R-06),” American Concrete Institute, Farmington Hills, MI, 2006, 44 pp ISIS Canada Research Network, “Reinforcing Concrete Structures with Fibre Reinforced Polymers—Design Manual 3, Version 2,” ISIS Canada Corporation, Winnipeg, MB, Canada, 2007, 129 pp Joint ACI-ASCE Committee 445, “Recent Approaches to Shear Design of Structural Concrete (ACI 445R-99) (Reapproved 2009),” American Concrete Institute, Farmington Hills, MI, 1999, 55 pp Zsutty, T., “Beam Shear Strength Prediction by Analysis of Existing Data,” ACI Journal, V 65, No 11, Nov 1968, pp 943-951 Kani, M W.; Huggins, M W.; and Wittkopp, R R., Kani on Shear in Reinforced Concrete, University of Toronto, Toronto, ON, Canada, 1979, 225 pp Wight, J K., and MacGregor, J G., Reinforced Concrete: Mechanics and Design, fifth edition, Pearson Prentice Hall, Upper Saddle River, NJ, 2009, 1126 pp Yost, J R.; Gross, S P.; and Dinehart, D W., “Shear Strength of Normal Strength Concrete Beams Reinforced with Deformed GFRP Bars,” Journal of Composites for Construction, ASCE, V 5, No 4, 2001, pp 268-275 Razaqpur, A G.; Isgor, O B.; Greenaway, S.; and Selley, A., “Concrete Contribution to the Shear Resistance of Fiber Reinforced Polymer Reinforced Concrete Members,” Journal of Composites for Construction, ASCE, V 8, No 5, 2004, pp 452-460 Tureyen, A K., and Frosch, R J., “Shear Tests of FRP-Reinforced Concrete Beams without Stirrups,” ACI Structural Journal, V 99, No 4, July-Aug 2002, pp 427-434 10 CAN/CSA S6-06, “Canadian Highway Bridge Design Code,” Canadian Standards Association, Mississauga, ON, Canada, 2006, 788 pp 11 Hoult, N A.; Sherwood, E G.; Bentz, E C.; and Collins, M P., “Does the Use of FRP Reinforcement Change the One-Way Shear Behavior of Reinforced Concrete Slabs?” Journal of Composites for Construction, ASCE, V 12, No 2, 2008, pp 125-133 12 CAN/CSA S806-02, “Design and Construction of Building Components with Fibre-Reinforced Polymers,” Canadian Standards Association, Mississauga, ON, Canada, 2002, 177 pp 13 ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2008, 473 pp 14 AASHTO, “LRFD Bridge Design Specifications: SI Units,” fourth edition, American Association of State Highway and Transportation Officials, Washington, DC, 2007, 1518 pp 15 CSA A23.3-04, “Design of Concrete Structures,” Canadian Standards Association, Mississauga, ON, Canada, 2004, 232 pp 16 Andermatt, M F., and Lubell, A S., “Strength Modeling of Concrete Deep Beams Reinforced with Internal Fiber-Reinforced Polymer,” ACI Structural Journal, V 110, No 4, July-Aug 2013, pp 595-606 17 El-Sayed, A K., “Concrete Contribution to the Shear Resistance of FRP-Reinforced Concrete Beams,” PhD dissertation, Universite de Sherbrooke, Sherbrooke, QC, Canada, 2006, 252 pp 18 Nehdi, M.; Omeman, Z.; and El-Chabib, H., “Optimal Efficiency Factor in Strut-and-Tie Model for FRP-Reinforced Concrete Short Beams with (1.5 < a/d < 2.5),” Materials and Structures, V 41, No 10, 2008, pp 1713-1727 19 Andermatt, M F., “Concrete Deep Beams Reinforced with Internal FRP,” MSc thesis, University of Alberta, Edmonton, AB, Canada, 2010, 266 pp 20 Kani, G N J., “How Safe Are Our Large Reinforced Concrete Beams?” ACI Journal, V 64, No 3, Mar 1967, pp 128-141 21 Sherwood, E G.; Lubell, A S.; Bentz, E C.; and Collins, M P., “One-Way Shear Strength of Thick Slabs and Wide Beams,” ACI Structural Journal, V 103, No 6, Nov.-Dec 2006, pp 794-802 22 ACI Committee 440, “Guide Test Methods for Fiber-Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures (ACI 440.3R-04),” American Concrete Institute, Farmington Hills, MI, 2004, 40 pp 23 Tan, K.-H.; Cheng, G.-H.; and Zhang, N., “Experiment to Mitigate Size Effect on Deep Beams,” Magazine of Concrete Research, V 60, No 10, 2008, pp 709-723 ACI Structural Journal/July-August 2013 Reproduced with permission of the copyright owner Further reproduction prohibited without permission  ... greater than those generally used in the design of steel -reinforced concrete deep beams The behavior of deep beams is not well-understood for the case of where high reinforcement strains would occur... “Strength Modeling of Concrete Deep Beams Reinforced with Internal Fiber -Reinforced Polymer,” ACI Structural Journal, V 110, No 4, July-Aug 2013, pp 595-606 17 El-Sayed, A K., ? ?Concrete Contribution... Model for FRP -Reinforced Concrete Short Beams with (1.5 < a/d < 2.5),” Materials and Structures, V 41, No 10, 2008, pp 1713-1727 19 Andermatt, M F., ? ?Concrete Deep Beams Reinforced with Internal FRP,”