ACI Structural Journal/March-April 2012 193

Title no. 109-S18

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 109, No. 2, March-April 2012.MS No. S-2010-057.R6 received October 25, 2010, and reviewed under Institute

publication policies. Copyright © 2012, 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 January-February 2013 ACI Structural Journal if the discussion is received by September 1, 2012.

Behavior of Steel Fiber-Reinforced Concrete Deep Beams with Large Openingby Dipti R. Sahoo, Carlos A. Flores, and Shih-Ho Chao

Large openings in reinforced concrete (RC) deep beams generally interrupt the load transfer by concrete struts and cause a sharp decrease in strength and serviceability. The reinforcement detailing of these deep beams based on strut-and-tie models (STMs) can be complex and, very often, these models may not predict the failure mechanism of deep beams due to localized damages. This study investigates the performance of two RC and two steel fiber-reinforced concrete (SFRC) deep beams with large openings under monotonically increased concentrated loads. The boundary regions near the supports of two specimens were strengthened with steel cages formed by steel reinforcement bars. The RC specimen with strengthened boundaries exhibited a ductile mode of failure and had significantly higher ultimate strength than predicted by STMs. Although the complex reinforcement detailing as per STMs was not used, the SFRC specimens with 1.5% volume fraction of fibers reached much higher strength than the design load and exhibited significant postpeak residual strength and a ductile mode of failure.

Keywords: deep beam; fiber-reinforced concrete; opening; structural concrete; strut-and-tie model.

INTRODUCTIONReinforced concrete (RC) deep beams are generally used

as load-transferring elements, such as transfer girders, pile caps, tanks, folded plates, and foundation walls. In buildings, a deep beam or transfer girder is used when a lower column on the exterior façade is removed for architectural purposes. Sometimes the full depth of the floor-to-floor height is used to transfer the high axial forces of columns above to the supporting columns below. Large openings through struc-tural members are frequently required for mechanical and electrical conduits or even for means of passageways, such as openings for doors and hallways in buildings. ACI 318-08 (ACI Committee 318 2008) defines a deep beam as a struc-tural element in which either the clear span is equal to or less than four times the overall depth, or the concentrated loads are applied within a distance equal to or less than two times the depth from the face of the support. Code-specified empir-ical formulas used to design these members do not explicitly address the design of D-regions with openings. Strut-and-tie models (STMs) are extensively used for these structures with D-regions since their implementation in various U.S. design codes. These models idealize a deep member as a series of concrete compressive struts and steel tensile ties connected at joints (called nodes) idealized as frictionless “pins” forming a truss. The applied force is transferred from the loading point to supports only through the STM, and the remaining concrete between the trusses is neglected for design and strength calculation purposes. STMs satisfy any load system based on a statically admissible stress field that does not exceed the yield criteria and provide safe and lower-bound designs of discontinuous structures (Schlaich et al. 1987; Muttoni et al. 1997). Hence, no unique STM

exists for a particular structure that results in different calcu-lated capacities.

Large openings, if located between the loading point and the support, will disrupt the flow of force transfer and usually significantly reduce the load-carrying capacity (Ray 1990). ACI 318-08 does not give any explicit guidance for designing these elements with openings. Based on limited experimental studies (Maxwell and Breen 2000; Chen et al. 2002; Park and Kuchma 2007; Tan and Zhang 2007; Ley et al. 2007; Breña and Morrison 2007; Kuchma et al. 2008), it is inferred that STMs provide reliable, consistent, and conservative results for deep beams with openings but fail to predict the ultimate load and failure mode. Also, some tests have shown that large differences can occur between the calculated forces from STMs and the actual instrumented experimental specimens (Breña and Morrison 2007). A poorly detailed STM can lead to unacceptable levels of cracking and damage, and limited postpeak ductility under service loads (Kuchma et al. 2008). Nevertheless, STMs provide flexibility to the designer to focus on safe and performance design; however, the constructibility becomes a main issue due to problems with anchorage and congestion of reinforcement bars.

Steel fiber-reinforced concrete (SFRC) has gained increased popularity in construction industries in recent years. Reinforcing concrete with steel fibers has been used to reduce conventional steel reinforcement in structural members such as slabs (ACI Committee 544 1996). SFRC members exhibit enhanced shear strength, more ductile behavior, and reduced crack widths (Dupont and Vandewalle 2003). Eliminating shear reinforcement in RC structures can potentially reduce the congestion of reinforcing bars and construction costs. In addition, steel fibers offer multi-direc-tional reinforcement in concrete, simple detailing without congestion, and enhanced postcracking residual strength and ductility. Past studies (Narayanan and Darwish 1988; Mansur and Ong 1991) have shown that including discrete fibers enhances the strength and deformation capacities of deep beams and provides better crack control.

This paper presents the performance of two RC deep beams with large openings under monotonically increased concentric loading. The observed ultimate strengths and failure modes of these specimens were compared with those predicted by a design STM. Further, two geometrically similar SFRC specimens with a 1.5% fiber-volume fraction

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Dipti R. Sahoo is an Assistant Professor in the Department of Civil Engineering at the Indian Institute of Technology Delhi, Delhi, India. He received his PhD in civil engineering with structural engineering as a specialization from the Indian Institute of Technology Kanpur, Kanpur, India. His research interests include fiber-reinforced concrete, seismic behavior of structural members, and seismic strengthening of structures.

Carlos A. Flores is an Engineer at Nelson Jones, Flower Mound, TX. He received his master’s and bachelor’s degrees from the University of Texas at Arlington, Arlington, TX. His research interests include design and behavior of reinforced concrete structures.

ACI member Shih-Ho Chao is an Assistant Professor in the Department of Civil Engineering at the University of Texas at Arlington. He is a member of ACI Committee 544, Fiber-Reinforced Concrete. He received the ACI Chester Paul Siess Award for Excellence in Structural Research in 2011. His research interests include fiber-reinforced concrete, prestressed concrete, and seismic behavior of structural members.

were tested under identical loading conditions. The conventional reinforcing bars in the SFRC specimens were used as flexural tensile reinforcement only at the bottom of the specimens. Based on the test results, the detailing of reinforcement bars at the critical locations and the importance of steel fibers in concrete is recognized to enhance the performance of concrete deep beams with openings.

RESEARCH SIGNIFICANCEPast experimental studies have shown the conservative

estimates of ultimate strengths and unpredictable failure mechanisms of RC deep beams with openings designed

using STMs. Moreover, the design method is at times ambig-uous and cumbersome using these models. Experimental investigations are required to evaluate the efficacy of these models for the reliable and consistent prediction of ultimate strengths and to identify the critical region for controlled and predictable failure mechanisms. This study evaluates the behavior of two RC deep beams, with a single large opening, designed as per STMs. Further, the complex reinforcement detailing was nearly completely replaced by steel fibers in two more geometrically similar test specimens. The critical regions in both types of test specimens are identified and subsequently strengthened by reinforcing bars. The effect of strengthening the critical regions of deep beams on their ulti-mate strengths and failure mechanisms is investigated.

DESCRIPTIONS OF TEST SPECIMENSSpecimen geometry

RC deep beams with large discontinuous regions were considered as test specimens in this study. The test specimens were 1/4-scale models of an example deep beam originally considered by Schlaich et al. (1987) to evaluate the design of STMs. Geometrically similar test specimens have also been used previously in other laboratory tests (Maxwell and Breen 2000; Breña and Morrison 2007). All specimens were 74 in. (1880 mm) long, 46 in. (1170 mm) deep, and 4.5 in. (112 mm) thick. A 15 in. (380 mm) square opening was located at the bottom corner near the support of the specimens and at a distance of 5 in. (125 mm) from the boundaries (Fig. 1). It was expected that the direct load paths between the loading point and supports would be interfered with by the position and size of the selected opening (Breña and Morrison 2007). A total of four (that is, two RC and two SFRC) deep beam specimens were tested in this study. The reinforcing bars in the RC specimens were detailed as per a selected STM discussed in the following section. Most of the reinforcing bars required by the STM, however, were eliminated and replaced by steel fibers in the SFRC specimens, in which steel bars were used only for longitudinal tensile reinforcement.

Design STMThe principal factor in the design of concrete elements

with discontinuity regions is the selection of a suitable STM. The position of struts and ties in a model can be based on the elastic principal stress fields (Schlaich et al. 1987; MacGregor 1997; Joint ACI-ASCE Committee 445 2002) or the stress fields at the development plastic hinge mechanisms (Muttoni et al. 1997). An STM approximately following the elastic (principal) stress distribution was considered in this study. It should be noted that the direction of principal stresses may change after the cracking in concrete; however, the flow of forces will help decide the position of struts and ties in the model. The stress distribution shows that the applied load in the test specimen is transferred directly from the loading point to the right support through a bottle-shaped strut; however, the opening near the lower left corner impairs the direct load transfer from the load point to the left support. As shown in Fig. 2, the STM considered in this study is basi-cally a modified model proposed by Schlaich et al. (1987). This model was also previously used by Breña and Morrison (2007) for comparison with laboratory test data. The right part of the STM beyond the loading point consisted of a truss system to resist the transverse tension and the compression in the bottle-shaped concrete strut formed due to the direct flow of forces from the loading point to the support, whereas

Fig. 1—Details of test specimen and location of linear varying differential transformers (LVDTs).

Fig. 2—Design STM adopted in this study (solid lines represent ties and dashed lines represent struts).

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the left part consisted of two truss systems that transfer the applied load to the left support around the opening.

Specimen reinforcementThe test RC specimens were designed for an ultimate

strength of 31.3 kips (139 kN), the same as that used by a previous study (Breña and Morrison 2007). The nominal values of compressive and tensile strengths of the concrete and reinforcement bars were assumed as 5000 and 60,000 psi (35 and 414 MPa), respectively. A strength-reduction factor f equal to 0.75 was used for all struts, nodes, and ties in the STM (Breña and Morrison 2007). Detailed informa-tion about the strut geometry and forces, and the efficiency factor bs can be found elsewhere (Breña and Morrison 2008). No. 3 (10 mm) bars with a nominal area of 0.11 in.2 (71 mm2) were used as steel reinforcing bars, provided in two layers in the RC specimens with a clear concrete cover of 1 in. (25 mm) to the edges of the reinforcing bars. All reinforcing bars ending near the edges of the specimens were provided with standard hooks with required develop-ment lengths to provide sufficient anchorage and avoid their pullout. Secondary reinforcing bars for the temperature and shrinkage cracking for walls were not provided in this study because these bars can significantly enhance the load-carrying capacities of test specimens (Breña and Morrison 2007). Thus, the minimum vertical and horizontal reinforce-ment requirements as per the ACI 318-08, Section 14.3.1, provisions for walls were not satisfied for these specimens. Although the secondary reinforcement was expected to increase the ductility of the concrete, thus allowing a truss-like plastic mechanism to form, it was hardly realized, as evidenced by prior experimental results (Maxwell and Breen 2000; Breña and Morrison 2007; Kuchma et al. 2008). It should also be noted that steel fibers not only enhance the

shear strength of concrete but also control the cracking due to temperature and shrinkage (Mindess et al. 2003).

As shown in Fig. 3(a), the longitudinal reinforcing bars at the bottom of Specimen RC1 were provided with stan-dard 180-degree hooks at both ends, whereas the other reinforcing bars were provided with a 180-degree hook only at the end located near the edge of the specimen. Steel reinforcing bars were positioned to provide the required tie action as per the selected STM. Prior experimental studies (Maxwell and Breen 2000; Breña and Morrison 2007; Flores 2009) showed that deep beam specimens suffered severe cracking and crushing of concrete near the supports. This is primarily due to the insufficient confinement of concrete in the strut near the support under high compres-sion. To avoid these local failures, a steel cage formed by four No. 3 (10 mm) longitudinal reinforcement bars at the corners and No. 3 (10 mm) transverse stirrups at a spacing of 4 in. (100 mm) was used as a boundary element near the supports of Specimen RC2. As shown in Fig. 3(b), the bottom longitudinal reinforcing bars of Specimen RC2 were provided with standard 90-degree hooks and inserted into the steel cage for the required anchorage. Except for the steel cage at the supports, the reinforcement detailing was exactly the same in both RC specimens.

Figure 3(c) shows the reinforcement detailing of Specimen SFRC1, in which only two No. 3 (10 mm) reinforcing bars were used as longitudinal tensile reinforcement at the bottom. Similar to Specimen RC2, Specimen SFRC2 consisted of steel cages at both the left and right ends near the supports in addition to two No. 3 (10 mm) reinforcement bars as longitudinal tensile bars at the bottom. The spacing of stirrups in the steel cage was kept as 4 in. (100 mm), which was exactly the same as that used in Specimen RC2. To restrain the opening and propagation

Fig. 3—Layout of reinforcement (two layers for each bar location) and locations of strain gauges: (a) Specimen RC1; (b) Specimen RC2; (c) Specimen SFRC1; and (d) Specimen SFRC2.

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of cracks emanating from the corner of the opening, two No. 6 (20 mm) bars were placed diagonally in two layers near the opening of Specimen SFRC2, as shown in Fig. 3(d). These bars were purposely overdesigned to prevent the failure initiating from the corner so as to achieve better stress distribution in the specimen. These diagonal bars were oriented as normal to the line connecting the loading point to the corner of the opening. Unlike the RC specimens, the SFRC specimens did not require any reinforcement detailing, which resulted in a very fast and simple construction process.

Mixture compositions and material propertiesA concrete mixture of nominal 28-day compressive

strength equal to 5000 psi (35 MPa) was used in all test specimens. A mixture design was carried out to achieve the target compressive strength of concrete and use the optimum quantity and similar proportions of materials in both the RC and SFRC specimens. The design mixture proportion (by weight) used for all specimens was 1.0 (cement):0.5 (fly ash):1.7 (sand):1.0 (coarse aggregate). Type I portland cement, Class C fly ash, and coarse aggregates of maximum size limited to 0.5 in. (13 mm) were used in the concrete mixture. A constant water-cementitious materials ratio (w/cm) of 0.4 was used in all specimens. No chemical admixtures or high-range water-reducing admixtures were added to the concrete mixture. Both SFRC specimens consisted of end-hooked steel fibers (diameter = 0.03 in. [0.75 mm]; length = 2.4 in. [60 mm]; aspect ratio = 80; tensile strength = 152.3 ksi [1050 MPa]) of volume equal to 1.5% of the total volume of the specimen. Based on an earlier study by Liao et al. (2010) for a highly flowable mixture, the weight of cement and steel fibers used in the SFRC specimen was 312 and 77 lb (142 and 35 kg), respectively.

Standard tests (ASTM C31/C3M-09, ASTM C39/C39M-09, and ACI 318-08) were carried out to evaluate the compres-

sive strength of concrete. The tensile stress-strain response of the steel reinforcing bar was also obtained through coupon tests. Table 1 summarizes the nominal and actual proper-ties of the concrete and steel reinforcement bars used in the test specimens. Six 4 x 8 in. (100 x 200 mm) cylinders and four reinforcing bars 25 in. (63 mm) long were used to evaluate their material properties. The average values of the compressive strengths of concrete used in the RC and SFRC specimens at the day of testing were 6700 and 6300 psi (46 and 44 MPa), respectively. The actual yield strength of the No. 3 (10 mm) steel bars was 81.2 ksi (560 MPa) against their nominal value of 60 ksi (414 MPa). The ulti-mate tensile strength of these bars was 126.7 ksi (874 MPa). Tensile testing of the No. 6 (20 mm) bars was not carried out because they were not expected to yield under the applied loading, which was also monitored by strain gauges, as discussed in the following.

The flexural performance of the SFRC material was evalu-ated by a three-point test on SFRC beams 6 x 6 in. (150 x 150 mm) square in cross section and 20 in. (500 mm) in length in accordance with ASTM C1609/C1609M-10. Figure 4(a) shows a typical load-deflection response of SFRC ASTM beams under three-point loading. The ASTM beams reached an average peak lateral load of 10.8 kips (48 kN) and exhibited appreciable deflection-hardening behavior and postpeak residual strength due to the fiber-bridging effects. As shown in Fig. 4(b), the first flexural crack was initiated at the midspan of the ASTM beam and propagated toward the compression zones until failure. Smaller microcracks also developed from the initial crack after the first crack was formed. The pullout of steel fibers from the concrete was noticed at the failure stage. The tensile behavior of the SFRC materials was investigated by conducting a direct tensile test using a dogbone-shaped specimen having a 4 x 4 in. (102 x 102 mm) square cross section central portion (Chao

Table 1—Nominal and measured material properties

Specimen

Concrete compressive strength Tensile strength of No. 3 (10 mm) bars

Nominal (28-day),psi (MPa)

Measured (day of testing), psi (MPa)

Nominal yield stress, psi (MPa)

Measured yield stress, psi (MPa)

Measured ultimate stress, psi (MPa)

RC1

5000 (35)

6185 (43)

60,000 (414) 81,240 (560) 126,700 (874)RC2 6645 (46)

SFRC1 5867 (41)

SFRC2 6225 (43)

Fig. 4—Flexural behavior of SFRC: (a) load-displacement behavior of ASTM beams; and (b) multiple cracks in ASTM beams. (Note: 1 kip = 4.45 kN; 1 in. = 25.4 mm.)

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et al. 2011). A typical stress-strain/crack opening response of the tensile SFRC specimen is shown in Fig. 5(a). After the formation of the first percolation crack in the specimen, as shown in Fig. 5(b), the tensile stress kept increasing with the development of further multiple cracks. The descending branch of the curve was fairly gradual and ductile with the opening of cracks.

Test setup and instrumentationBoth the RC and SFRC specimens were subjected to mono-

tonic loading using a 400 kip (1780 kN) universal testing machine at the University of Texas at Arlington Civil Engi-neering Laboratory. The loading was gradually increased at an interval of 5 kips (22.5 kN) until the failure of speci-mens was observed. A steel roller of 2 in. (50 mm) diameter placed between two 1 in. (25 mm) thick plates was provided at the supports to allow rotation and translation of the plates (Fig. 1). Horizontal restraints in the plates were provided to the roller only at the left support to resemble a “hinge”

condition, whereas the roller at the right support repre-sented a “pin” support. However, the presence of horizontal restraints at the supports had a negligible effect on the strut-and-tie forces (Breña and Morrison 2007). Several sensors were used to measure the applied load and the response of the specimens at different load levels. A load cell with a capacity of 600 kips (2670 kN) was used at the loading point to measure the magnitude of monotonic load applied to the specimens. Uniaxial 120 Ohm electrical strain gauges with a gauge length of 0.2 in. (5 mm) were attached to the surface of the steel reinforcing bars at specified locations to measure the magnitude of strain and, hence, to compute the tie forces at various load levels (Fig. 3). These locations were finalized where maximum strain would be expected so that the calcu-lated tie forces could be compared with the predicted forces from the STM. Four LVDTs were also used on the surface of the specimens to measure the deformation of concrete struts formed in the specimens during testing (Fig. 1). A linear potentiometer was used below the load point to measure the deflection of the specimens and two additional linear poten-tiometers were used to measure the displacement or slippage of both supports, if any.

TEST RESULTSThe performance of the test specimens was evaluated in

terms of the following parameters: overall cracking, load-deflection response, failure mechanism, ultimate strength, and variation of tie forces. A detailed discussion on these parameters is presented in the following sections.

Overall crackingThe propagation of cracks in the test specimens was

mapped after each load increment of 5 kip (22.5 kN) inter-vals. The first crack in Specimen RC1 was noticed near the supports at a load level of 25 kips (112.5 kN). As shown in Fig. 6(a), diagonal cracks initiated from the opening at a 30 kip (135 kN) load level and propagated with

Fig. 5—Tensile behavior of SFRC: (a) stress-strain/crack opening response of tensile SFRC specimen; and (b) multiple cracking in tensile SFRC specimen. (Note: 1 ksi = 6.89 MPa; 1 in. = 25.4 mm.)

Fig. 6—Crack propagation in test specimens: (a) Specimen RC1; (b) Specimen RC2; (c) Spec-imen SFRC1; and (d) Specimen SFRC2. (Note: Dimensions in kips; 1 kip = 4.45 kN.)

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the further increase of load up to 60 kips (270 kN). At a 50 kip (225 kN) load level, several instances of cracking and crushing of concrete were observed near the right support of Specimen RC1 because of the lack of confinement action to the concrete. The width of the crack originating from the opening to the loading point was 0.016 in. (0.40 mm) at a 65 kip (293 kN) load level. A major flexural crack running almost the full depth of Specimen RC1 was observed just below the load point at a load level of 70 kips (315 kN). The loading in Specimen RC1 was stopped at this point due to severe local damage and instability at the support regions. In contrast to the single diagonal and flexural cracks noticed in Specimen RC1 during the testing, as shown in Fig. 6(a), Specimen RC2 showed several distributed cracks up to failure. The first crack in Specimen RC2 was noticed at a load level of 20 kips (90 kN). As shown in Fig. 6(b), several diagonal cracks initiated at a load level of 40 kips (180 kN) around the opening, and the maximum width of the crack was measured as 0.012 in. (0.3 mm). These diagonal cracks propagated toward the loading point as the applied load levels increased. Flexural cracks started from the bottom of the specimen below the load point at a load level of 65 kips (293 kN) and the maximum width of the crack measured was 0.03 in. (0.75 mm). This was consistent with Specimen RC1, in which a major flexural crack was observed at 70 kips (315 kN). Beyond the load level of 85 kips (382.5 kN), the diagonal cracks started to propagate horizontally toward the load point. The width of the major flexural crack was 0.1 in. (2.54 mm) at the load level of 95 kips (428 kN), and this crack propagated toward the load point up to 130 kips (585 kN) before complete failure. Unlike Specimen RC1, Specimen RC2 did not exhibit any local damages near the supports because of the sufficient concrete confinement provided through steel caging near the supports. However, both RC specimens showed that initial cracks propagating from the opening did not cause the failure of the specimens; instead, flexural cracks developing at the higher load levels controlled the failure mechanism and the ultimate strength. Hence, the RC specimens designed based on an STM effec-tively transferred the applied forces to the supports without any local damage around the opening regions.

The first (minor) crack was observed in Specimen SFRC1 near the support at a load level of 15 kips (67.5 kN). A small crack 0.004 in. (0.10 mm) wide formed near the bottom middle span of the specimen at a 20 kip (90 kN) load level,

as shown in Fig. 6(c). Several microcracks less than 0.004 in. (0.10 mm) wide were observed close to the top of the spec-imen in the vicinity of the point load at a 25 kip (112.5 kN) load level. Similar to Specimen RC1, a diagonal crack initi-ated from the opening of Specimen SFRC1 and propagated toward the loading point at a load level of 30 kips (135 kN). At a 50 kip (225 kN) load level, the width of the crack near the opening of the specimen was measured as 0.01 in. (0.25 mm). The width of the crack increased to 0.016 in. (0.40 mm) and extended to nearly halfway between the corner of the opening and the loading point at a load level of 55 kips (248 kN). Steel fibers hindered the propagation and widening of cracks and increased the number of cracks due to stress redistribution in the SFRC specimen as compared to the RC specimen. Similar to Specimen RC1, Specimen SFRC1 also suffered damage near the support but to a much lesser degree, as shown in Fig. 6 and 7.

As expected, Specimen SFRC2 developed more distrib-uted cracks (Fig. 6(d)) as compared to Specimen SFRC1 due to local strengthening at the critical locations. The first crack in Specimen SFRC2 was observed at a load level of 15 kips (67.5 kN). Several cracks initiated from the bottom and opening of the specimen at a load level of 30 kips (135 kN). Diagonal cracks emanated from the opening at a load level of 45 kips (202.5 kN) and propagated toward the loading point. The maximum crack width of the diagonal crack was 0.008 in. (0.20 mm) at a load level of 70 kips (315 kN) and increased to 0.015 in. (0.38 mm) at a load level of 90 kips (405 kN). Unlike Specimen SFRC1, Specimen SFRC2 did not suffer local damage near the supports because of suffi-cient confinement provided by the steel cage. At the failure stage, however, Specimen SFRC2 exhibited severe cracking just above the opening, as discussed in the following.

Crack propagationThe propagation of cracks in the test specimens under the

applied load was monitored by the nondestructive acoustic emission (AE) technique. This evaluation served as a very valuable tool, as it allowed for the analysis of energy dissipation in the form of crack formation, crack propaga-tion, and reinforcing slippage and yielding (Colombo et al. 2003). In this study, a total of seven AE sensors were mounted on the concrete surface of the test specimens using special glue. Each sensor had a radius of influence of 30 in. (750 mm). The location of an event (microcracking) inside the specimen is captured by three sensors using the prin-ciple of triangulation. Based on the measured time elapsed and the distance between two consecutive sensors for an event, the shear wave velocity for both the RC and SFRC specimens was estimated as 1.1 × 105 in./s (2795 m/s). Figure 8 compares the concrete struts formed in the RC and SFRC specimens at a load level of 65 kips (293 kN). The SFRC specimens showed more events near the cracked area around the diagonal crack from the opening as compared to the RC specimens because of multiple cracking. Thus, the effective redistribution of internal stress was achieved in the SFRC specimens, resulting in better use of the concrete strut to resist the applied lateral load in the specimen.

As noticed in Fig. 8, the width of the compressive strut formed in the RC specimen was smaller as compared to that in the SFRC specimen, indicating that the SFRC specimen dissipated the energy over a wider area. Both specimens dissipated an equal amount of energy. The RC specimen dissipated energy through a large single crack propagation

Fig. 7—Crushing of concrete strut near supports: (a) Spec-imen RC1; and (b) Specimen SFRC1.

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due to the yielding of reinforcing bars. In contrast, the SFRC specimen dissipated energy through multiple fine cracks that branched out in random directions because the steel fibers served as a “bridge” that enabled forces to be redistributed from one area to the next. This characteristic of steel fibers overcomes the weak tensile strength and the brittle nature of plain concrete. Further, the cracking due to splitting of the concrete compressive strut could be delayed due to the better tensile behavior of SFRC. Hence, the SFRC specimen showed better crack distribution and smaller crack width as compared to the RC specimen.

Load-displacement responseFigure 9 shows the load-displacement behaviors of all test

specimens. As expected, the initial stiffness of both RC spec-imens was nearly equal. Specimen RC1 showed an almost linear response up to 55 kips (248 kN), and the maximum load carried by Specimen RC1 was 68.2 kips (307 kN) before the testing was stopped due to severe damage near the supports. In contrast, Specimen RC2 showed excel-lent post-yield behavior because the local failure near the supports was effectively controlled. Specimen RC2 showed linear elastic behavior up to approximately 95 kips (428 kN), beyond which a deflection-hardening behavior was noticed up to a peak load of 132.1 kips (594 kN). The load-carrying capacity of Specimen RC2 was nearly two times that of Specimen RC1. Both RC specimens reached their design load-carrying capacity of 31.3 kips (139 kN), showing overstrength factors of 2.0 and 4.2 for Specimens RC1 and RC2, respectively. The excellent post-yield strain-hardening behavior of Specimen RC2 was achieved due to the yielding of the bottom longitudinal reinforcing bars in tension, which was confirmed from the state of strains measured using uniaxial strain gauges. The delaying of premature local fail-ures near the supports due to the presence of steel cages at the boundaries helped Specimen RC2 to exhibit a displace-ment ductility of nearly 4.0. The descending branch of the load-deflection response of Specimen RC2 exhibited a sudden drop from its peak strength due to the shear failure that occurred below the opening.

As shown in Fig. 9, the load-displacement response of Specimen SFRC1 was nearly linear up to a peak load of 65 kips (293 kN). The initial stiffness of both SFRC specimens was nearly equal to that of the RC specimens. Specimen SFRC2 showed a nearly linear response up to a peak load of 96.8 kips (435 kN), which was much higher than the design load of 31.3 kips (139 kN) for the RC specimens. It should be noted that even though there were almost no steel reinforcing bars (except the steel cage at the supports and longitudinal bars at the bottom) used as per STMs, Specimen SFRC2 reached 3.0 times the design load of the RC specimen. Further, the SFRC specimens showed a very gradual postpeak descending branch in the load-displacement response even without steel reinforcing bars, indicating significant contribution of the steel fibers to the residual strength of the specimen. The displacement ductility of Specimen SFRC2 was approximately estimated as 3.0. The boundary elements and diagonal steel reinforce-ment bars helped Specimen SFRC2 to achieve the design strength without premature local crushing and cracking of concrete near the boundaries in addition to the sufficient residual strength.

Mode of failureBecause different detailing of reinforcing bars was

used in the test specimens, it was expected that the failure modes would be different due to the availability of various load-transfer mechanisms. The ultimate failure of Specimen RC1 was primarily due to the crushing of concrete struts followed by the loss of the concrete wedge near the supports (Fig. 7(a)). A similar mode of failure was also noticed

Fig. 8—Comparison of formation of struts in specimens at 65 kip (293 kN) load level: (a) Specimen RC1; and (b) Spec-imen SFRC1. Note: Dots represent AE events (locations of microcracks).

Fig. 9—Load-displacement response of test specimens. (Note: 1 kip = 4.45 kN; 1 in. = 25.4 mm.)

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for Specimen SFRC1, as shown in Fig. 7(b). However, the crushing of concrete was less severe as compared to that of Specimen RC1 due to the confinement effect provided by the steel fibers. The lack of confinement to the concrete under high axial compressive forces in the vertical segment of the openings and boundaries near the supports caused the ulti-mate failure of the specimens. As shown in Fig. 10(a), local failure at the supports of Specimen RC2 was not observed during the entire loading because of the sufficient confine-ment provided by the steel cage to the concrete under high compressive stresses. A major flexural crack running from the bottom face to the loading point was observed at the failure stage of Specimen RC2. As shown in Fig. 10(b), Specimen RC2 eventually collapsed due to the shear failure of concrete in the horizontal segment of the opening because of inadequate shear reinforcement. This ultimately led to the fracture of the bottom longitudinal tensile reinforcing bars after reaching their failure strains. The major cracks devel-oped away from the opening region, indicating that the flow of force was least affected by the presence of the opening due to the local strengthening of Specimen RC2 near the supports. On the other hand, as shown in Fig. 11(a), the failure mode of Specimen SFRC2 was completely different

from that of Specimen SFRC1. A major crack (compressive strut) developed just above the opening of Specimen SFRC2. Due to the presence of diagonal steel reinforcing bars, the major (failure) crack deviated from the corner of the opening and formed at the end of those bars. The failure of Specimen SFRC2 was fairly ductile, as evidenced by the large deformation and formation of several plastic hinges, as shown in Fig. 11(a) and (b).

Ultimate strengthAs stated previously, the design strength of the RC spec-

imen was 31.3 kips (139 kN). The specimen was analyzed by a strut-and-tie computer program, CAST (Tjhin and Kuchma 2002), in which the analysis of nodes is carried out, ensuring that the geometry and stress limits are not exceeded. Using the specified material strengths and a strength-reduction factor of 0.75, the nominal ultimate strength of the RC specimen was estimated as 41.2 kips (183 kN). The expected capacity of the RC specimen was estimated as 70.3 kips (313 kN) using a strength-reduction factor as unity and the actual material properties obtained from the testing of concrete cylinders and steel bars. The effective width and the width of the tension zone extension in the model were considered as 4.38 and 2 in.

Fig. 10—Mode of failure of Specimen RC2: (a) overall view of specimen at failure stage; and (b) shear failure of horizontal segment near opening.

Fig. 11—Failure mechanism of Specimen SFRC2: (a) specimen at failure stage; and (b) plastic hinge in horizontal segment near opening.

Table 2—Design and measured strengths of test specimens

Specimen Design strength, kips (kN) Nominal strength, kips (kN) Expected strength, kips (kN) Measured strength, kips (kN)

RC1

31.3 (139)

41.2 (183) 70.3 (313)68.2 (303)

RC2 132.1 (588)

SFRC1— —

65.0 (289)

SFRC2 96.8 (431)

Plain concrete* — 14.3 (64) — —

*Modeled by CAST; only bottom reinforcing bars were used as that of SFRC specimens. Nominal strengths are computed by using nominal material properties of material with strength-reduction factor of 0.75. Expected strengths are calculated by using actual material properties.

ACI Structural Journal/March-April 2012 201

(111.3 and 50.8 mm), respectively. A low-efficiency factor bs of 0.63 was used for bottle-shaped struts to reflect the fact that no cracking-controlled reinforcement was used. An efficiency factor of 0.85 was conservatively used for the prismatic struts at the supports. The computer model predicted that failure would occur due to the yielding of the diagonal tie, which is a desirable ductile failure mode as opposed to the brittle failure of concrete struts. Table 2 compares the measured strengths with the designed or predicted values for all test specimens. Although the observed failure strength of Specimen RC1 was close to the predicted one, the failure mode was different due to local damages near one of the supports. The observed ulti-mate strength of Specimen RC2 was 132.1 kips (588 kN), which was 1.9 times the expected strength predicted by the computer model. This was due to the redistribution of stress in the specimen after the yielding of the steel reinforcing bars.

Similarly, Specimen SFRC2 had an ultimate strength of 96.8 kips (431 kN), which was approximately 1.4 times the predicted strength of the RC specimen, even though nearly no steel reinforcement bars were used as tie members. The fiber-bridging effects limited the widening of cracks, enhanced stress redistribution, and allowed a plastic mechanism formation upon failure. The stress redistribution in both the RC and SFRC specimens was enhanced by the strengthening of the vertical segment near the opening and the boundaries. A plain concrete model without using steel reinforcement bars as ties was also evaluated by the computer program to compare its strength with the SFRC specimens. The objec-tive was to quantify the strength that the specimen would gain due to the inclusion of steel fibers, if any. The model consisted of only the bottom steel reinforcement bar as a tie in addition to the concrete tensile strength, conservatively calculated using Eq. (9-10) (fr = 7.5√fc′) of ACI 318-08. The failure strength of the plain concrete model was 14.3 kips (64 kN), which was exceptionally small as compared to the observed strengths of the SFRC specimens.

Tie strains and forcesThe magnitude tie forces were computed from the state of

strain measured in different steel reinforcing bars by uniaxial strain gauges (Fig. 3). The actual material properties of steel and concrete were used to compute tie forces using a strength-reduction factor as unity. Several strain gauges were located along the reinforcing bars corresponding to the same tie in the STM. Table 3 summarizes the measured tie forces in all test specimens at the ultimate load levels and their comparison with the computed tie forces using the design STMs. The large strain differences along the reinforcing bars corresponding to a single tie in the model were due to the variation of bond stresses because of cracking in the concrete. Specimen RC1 showed larger strains in the bottom longitudinal bars and in the tie located in the bottle-shaped concrete strut. Several reinforcing bars reached their yield strain limit of approximately 2000 me at the ultimate load level of Specimen RC1. The ratio of the measured forces to the computed forces in most ties was nearly 1.0 because the ultimate load for Specimen RC1 was nearly equal to the expected ultimate strength predicted from the computed model based on the STM. Nearly all ties except E86 and E90 reached their yield strain limit in Specimen RC2 at the ultimate load level. The yielding of these bars was noticed between the yield and ultimate load levels of the specimen. The bottom longitudinal bars, diagonal bars, and horizontal bars just above the opening showed larger strain levels of

greater than 1.0%, which was depicted by the strain-hard-ening behavior in the load-deflection response. The ratios of measured ultimate forces to the computed values in various ties were nearly 1.5 for Specimen RC2 with the strengthened boundaries. Although the STM adequately identified the locations of critical ties (with maximum strain levels) in the specimens, the model failed to capture the important role of anchorage bars in the load-sharing mechanism, particularly if the vertical segments of the openings were strengthened against premature local failures. The STM underestimated the forces in the ties located at the bottom of the specimen and in the bottle-shaped struts. In addition to these ties, both horizontal and vertical steel reinforcing bars around the opening were found to be critical for these specimens. Table 3 also summarizes the force carried by the steel rein-forcing bars used as ties in the SFRC specimens. Both the bottom longitudinal tensile bars and diagonal bars carried an equal proportion of forces at the failure stage, indicating a significant role of the diagonal bars in enhancing the perfor-mance of Specimen SFRC2. The steel reinforcing bars in the SFRC specimens, however, carried a smaller amount of force as compared to the RC specimens, indicating the reduction in strain demand on the reinforcing bars in the SFRC specimens due to additional tensile strength provided by the steel fibers.

SUMMARY AND CONCLUSIONSThe sufficient plastic redistribution of internal forces is

essential for a structure to sustain expected and unexpected loads and to fail in a ductile manner if overloaded. In RC members, due to the brittle nature of concrete, this redis-tribution primarily relies on the steel reinforcing bars and their layouts, in which bars are placed at locations where the concrete is overly stressed beyond its cracking strength. For typical concrete members with simple and regular geom-etries, those locations can be easily predicted by classical elastic theory. It is well known, however, that the stress pattern is highly nonlinear and deviates considerably from the classical elastic theory for RC members with significant geometric discontinuities. These members with significant geometric discontinuities and complex stress distributions under loading require considerable analyses and usually complicated reinforcement detailing. The reinforcement detailing of these concrete members based on STMs can be quite complicated and, very often, these models cannot predict the failure mechanism due to localized damages. Also, the actual stress fields in such members are typically very different from those predicted by STMs, as indicated by many experimental investigations.

This study investigates the behavior of deep beams with large openings that were designed using STMs. Two RC and two SFRC test specimens were tested under monotonically increased loads. A nearly self-consolidating SFRC mixture was used without any workability issues even with 1.5% of steel fibers by volume. Reinforcing bars in the SFRC speci-mens were required at only a few critical locations. Those bars served as “ductile links” to prevent the breakdown of the highly stressed regions before the fully plastic redis-tribution of internal forces through steel fibers. The main objectives of this study were: 1) to investigate the effect of local strengthening on the load-transferring mechanism and failure modes of test specimens; 2) to study the behavior of SFRC specimens and compare that behavior with that of the RC specimens designed using STMs; and 3) to identify the

202 ACI Structural Journal/March-April 2012

critical regions of the specimens that are not identified by STMs and to suggest the reinforcing detailing to avoid local-ized failures and enhance structural performance.

The following conclusions were drawn in this study:1. Design STMs significantly underestimate the ultimate

strengths of the test specimens. The RC specimens designed as per the STM without satisfying the requirement of secondary reinforcements as per ACI 318-08, Appendix A, provisions reached the design strength without failure.

2. The crushing of concrete that occurred in the highly stressed region over the supports was primarily due to the lack of confinement of the concrete under high axial stress. Although RC specimens designed according to STMs had

much higher strength than the design strength, these models failed to predict the locations of such local failures, where usually no special detailing is provided. The use of confining reinforcement (that is, a steel cage) in the support regions significantly improved the ultimate strength of the RC spec-imen and changed its mode of failure to a much more ductile manner. As a consequence, significant flexural action was noticed in Specimen RC2 without any local failure and the specimen showed an ultimate capacity of more than four times the design strength.

3. Both Specimens RC1 and SFRC1 (without the steel cage) showed comparable behavior. Specimen SFRC2 with the steel cage near the supports reached three times the

Table 3—Design and measured tie forces in test specimensSp

ecim

en ty

pe

Tie

No.

Stra

in g

auge

Tie

are

a, in

.2

Cal

cula

ted

tie f

orce

T

calc, k

ips

Tie forces at ultimate load Tie forces at ultimate load

Mic

rost

rain

Stre

ss, k

si

Bar

for

ce, k

ips

Tota

l for

ce T

u,

kips

T u/T

calc

Mic

rost

rain

Stre

ss, k

si

Bar

for

ce, k

ips

Tota

l for

ce T

u,

kips

T u/T

calc

RC

spe

cim

en

Specimen RC1 (Pu = 68.2 kips) Specimen RC2 (Pu = 132.1 kips)

ANC1 0.11

*

† — —4.9 —

2757.7 79.97 8.817.9 —

2 0.11 770.0 22.33 2.5 2802.3 81.27 8.9

E24

4 0.11

25.6

2000.0 58.00 6.4

20.4 0.80

4375.4 81.85 9.0

33.6 1.315 0.11 1380.0 40.02 4.4 2447.8 70.99 7.8

6 0.11 1640.0 47.56 5.2 3102.2 81.40 9.0

E197 0.11

22.0960.0 27.84 3.1

5.4 0.2515,994.3 92.00 10.1

20.0 0.918 0.11 740.0 21.46 2.4 13,520.2 90.00 9.9

E189 0.11

12.82400.0 69.60 7.7

15.8 1.2311,966.7 88.00 9.7

20.0 1.5710 0.11 2540.0 73.66 8.1 15,984.6 94.00 10.3

E8611 0.11

12.050.0 1.45 0.1

0.1 0.01‡ ‡ ‡

–1.1 –0.1012 0.11 –10.0 –0.29 –0.0 871.8 –5.19 –0.6

VT13 0.11

*30.0 0.87 0.1

6.5 —–178.9 –6.29 –0.7

–1.1 —14 0.11 2010.0 58.29 6.4 –217.0 –3.35 –0.4

E90 15 0.11 11.5 2230.0 64.67 7.1 14.2 1.23 –115.6 88.06 9.7 19.4 1.68

E10

16 0.11

25.6

1800.0 52.20 5.7

12.8 0.50

3036.5 81.30 8.9

36.4 1.4217 0.11 1570.0 45.53 5.0 5538.4 82.00 9.0

20 0.11 320.0 9.28 1.0 7723.8 84.00 9.2

E218 0.11

24.730.0 0.87 0.1

11.9 0.4811,107.1 87.00 9.6

38.2 1.5519 0.11 1830.0 53.07 5.8 10,409.9 86.50 9.5

E14 22 0.11 9.7 1210.0 35.09 3.9 7.7 0.80 1197.3 34.72 3.8 7.6 0.79

SFR

C s

peci

men

Specimen SFRC1 (Pu = 65.9 kips) Specimen SFRC2 (Pu = 96.8 kips)

ANC1 0.11

*

462.1 13.40 1.53.0

—

931.3 27.01 3.06.4

—

2 0.11 490.4 14.22 1.6 1086.1 31.50 3.5

E183 0.11 491.9 14.27 1.6

2.8675.3 19.58 2.2

5.04 0.11 389.6 11.30 1.2 897.6 26.03 2.9

DG5 0.44 ‡ ‡ ‡

—382.2 11.08 4.9

5.46 0.44 ‡ ‡ ‡ 42.5 1.23 0.5

*Instrumented bar not directly related to STM. †Damaged instrument (value not calculated). ‡Strain gauges not used. Notes: ANC is anchorage ends; DG is diagonal reinforcing bars in SFRC specimen; VT is vertical reinforcing bar in RC specimens; 1 kip = 4.45 kN; 1 ksi = 6.89 MPa; 1 in.2 = 645.16 mm2.

ACI Structural Journal/March-April 2012 203

design strength, even though most steel reinforcing bars as required by RC specimens were eliminated. The fibers serve as not only the cracking control reinforcement but also a vehicle to allow for significant internal plastic stress redis-tribution, which is an important mechanism to increase the strength of the specimens after first cracking. The distribu-tion of internal microcracking observed by AE sensors indi-cated a much wider strut developed in the SFRC specimens as compared to the RC ones.

4. A ductile plastic mechanism developed after the forma-tion of several plastic hinges in Specimen SFRC2. Further research is needed to investigate the effects of less volume fraction of steel fibers on the strength of such members.

5. The construction of RC specimens can be time-consuming and labor-intensive due to the complicated detailing of reinforcing bars in contrast to the SFRC speci-mens. Hence, replacement of conventional reinforcing bars with deformed steel fibers at a volume of 1.5% can be a feasible alternative to the current practice.

ACKNOWLEDGMENTSThe authors would like to thank G. Ramirez for providing AE equipment.

Assistance of specimen construction and testing from J.-S. Cho, N. Karki, M. Bayat, J. Lee, and J. Forteza is appreciated. Materials used in this inves-tigation were provided by V. Babakhanian at Hanson Pipe & Precast, Grand Prairie, TX. Their help is gratefully appreciated.

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204 ACI Structural Journal/March-April 2012

NOTES: