Concrete Beams Reinforced with High-Strength Steel Subjected to ...

1037ACI Structural Journal/September-October 2014

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

The use of concrete members reinforced with high-strength steel bars (with a yield strength greater than 80 ksi [550 MPa]) in earthquake-resistant structures has been limited by the U.S. building codes since the introduction of strength design in 1963. This inves-tigation aimed to reexamine that limit by providing benchmark data for studying the cyclic response of concrete beams reinforced with steel bars having yield strengths approaching 100 ksi (690 MPa).

Seven specimens were subjected to large transverse displace-ment reversals: three specimens were reinforced with conventional steel bars (Grade 60 [415]) and four specimens were reinforced longitudinally with high-strength steel bars (Grade 97 [670]). All transverse reinforcement was Grade 60. Other experimental vari-ables were: volume fraction of steel-hooked fibers (Vf = 0 or 1.5%), spacing of transverse reinforcement (s = d/4 or d/2), and ratio of compression-to-tension longitudinal reinforcement (ρ′/ρ = 0.5 or 1). The nominal concrete compressive strength was 6000 psi (41 MPa).

Test beams reinforced with Grade 97 (670) steel bars had cyclic drift ratio capacities in excess of 5%, comparable to the deforma-tion capacities of similar beams reinforced with conventional bars. The evidence presented shows that the use of high-strength steel (Grade 97 [670]) as longitudinal reinforcement is a viable option for earthquake-resistant construction.

Keywords: advanced high-strength steel; crack width; cyclic test; defor-mation capacity; earthquake; high-performance fiber-reinforced concrete; seismic; ultra-high-strength steel.

INTRODUCTIONFor many years, the design of reinforced concrete (RC)

structures for seismic applications in the United States has been dominated by the use of deformed steel bars with specified yield strength fy of 60 ksi (415 MPa). The use of steel bars with fy greater than 60 ksi (415 MPa) could allow designers to reduce the amount of required reinforcement, leading to savings on material, shipping, and handling costs. A reduced amount of reinforcement also facilitates concrete placement and improves construction quality.

The limitations on fy of reinforcing steel can be traced back to the requirements of the 1956 ACI code (ACI 318-561), where a limit on fy of 60 ksi (415 MPa) was specified. This limit was increased to 75 ksi (515 MPa) in 1963 (ACI 318-632) provided that full-scale beam tests were conducted to demonstrate that the average crack widths at service load levels did not exceed 0.015 in. (0.38 mm). Later, the 1971 version (ACI 318-713) relaxed the limit on fy to 80 ksi (550 MPa) to continue accommodating the highest strength covered by contemporary ASTM standards, but the limit on fy for seismic applications remained at 60 ksi (415 MPa).

After the introduction of ASTM A10354 Grade 100 (690) in 2004 and its acceptance as confining reinforcement in

the 2005 ACI code (ACI 318-055), there has been growing interest in the use of high-strength reinforcing bars.

Steel with yield strength above 80 ksi (550 MPa) and elongation at fracture of at least 6% is currently produced commercially and often referred to as advanced high-strength steel or ultra-high-strength steel (ISSI6; ASTM A10117).

In 2007, ACI Innovation Task Group 6 was formed to develop a design guide for the use of ASTM A1035 Grade 100 (690) steel bars for structural concrete. The task group completed the document ACI ITG-6R-108 in 2010 and recommended design criteria for beams, columns, slab systems, walls, and footings of buildings located in low seismic design categories A, B, or C (excluding D, E, and F).

In 2009, ASTM A7069 introduced Grade 80 (550) rein-forcement but ACI 318-1110 continued limiting fy for flex-ural and shear reinforcement to 60 ksi (415 MPa) for seismic applications.

To make effective use of the high yield strengths of newly developed high-strength steel bars, the deformability of conventional concrete may need to be increased. High deformation capacities in RC members are achieved with the use of closely spaced transverse reinforcement11 and/or high-performance fiber-reinforced concrete (HPFRC).12

A collaborative experimental program between The Pennsylvania State (Penn State) University and Purdue University was aimed at studying concrete frame members (RC and HPFRC) reinforced with high-strength steel bars and subjected to reversed cyclic loading. Beam tests were conducted at Penn State by Tavallali13 and column tests were conducted at Purdue by Rautenberg14 and Rautenberg et al.15 This paper reports on the experimental data obtained from the beam tests.

The Penn State research program mainly addresses four major issues on the performance of beams reinforced with high-strength steel bars: hysteretic response under displace-ment reversals, strains in longitudinal and transverse rein-forcing bars along member length, changes in flexural stiff-ness with increased displacement demands, and crack widths at service load levels.

RESEARCH SIGNIFICANCEEarthquake-resistant design of RC structures often leads

to heavy and congested reinforcement cages, which can impose construction problems, delays, and additional costs.

Title No. 111-S87

Concrete Beams Reinforced with High-Strength Steel Subjected to Displacement Reversalsby Hooman Tavallali, Andres Lepage, Jeffrey M. Rautenberg, and Santiago Pujol

ACI Structural Journal, V. 111, No. 5, September-October 2014.MS No. 2012-246.R2, doi: 10.14359/51686967, was received November 23, 2013,

and reviewed under Institute publication policies. Copyright © 2014, 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 ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.

1038 ACI Structural Journal/September-October 2014

These issues may be resolved with the use of high-strength steel bars because the structures would require reduced amounts of reinforcement.

Available literature on the use of high-strength steel bars as flexural reinforcement has focused predominantly on non-seismic applications.8 To date, there is no evidence in the United States of any structure that has been built or reha-bilitated using high-strength steel bars as primary longitu-dinal reinforcement (in RC or HPFRC applications), taking advantage of yield strengths in excess of 80 ksi (550 MPa). In addition, prior research initiatives in the United States have not investigated the response to reversed cyclic loading of beams reinforced longitudinally with such high-strength steel bars. This study seeks to address this gap.

EXPERIMENTAL INVESTIGATIONThe research program described in this paper involved

testing seven specimens (Table 1). The specimens consisted of two beam elements connected to a central stub (Fig. 1). Each beam element was intended to represent a beam canti-levered from the central stub. The overall length of each specimen was 88 in. (2240 mm), consisting of two 36 in. (914 mm) long beam elements and a 16 in. (406 mm) long central stub. The ends of the cantilevered beams were supported by rollers located 24 in. (610 mm) away from the face of the central stub. The end rollers reacted against supports capable of carrying reactions in the two directions of loading. The space between the top and bottom rollers was such that there was always a small gap (approximately 1/8 in. [3 mm]) to allow horizontal movement of the spec-

imens. All beams had the same cross-sectional dimensions, with an overall depth h of 10 in. (254 mm), a width b of 16 in. (406 mm), and an effective depth d of approximately 8 in. (203 mm). All beams were proportioned to have nearly identical flexural strength. Dimensions and reinforcement layouts were chosen so that the maximum induced shear stress (V/bd) approached 6 ′fc psi[ ] (0.5 ′fc MPa[ ]), a value on the high end of what is permitted in Chapter 21 of ACI 318-1110 for moment-frame beams. Transverse rein-forcement was provided to resist shear, confine the concrete core, delay buckling of the longitudinal reinforcement, and enhance the bond between the concrete and the longitudinal bars. Specifically, the amount of transverse reinforcement was designed to prevent a non-ductile failure before devel-opment of flexural strength.

The experimental variables considered were the yield strength of the longitudinal reinforcement (Grade 60 [415] or Grade 97 [670]), the volume fraction of steel-hooked fibers (0% for RC specimens or 1.5% for HPFRC speci-mens), spacing of transverse reinforcement (s = d/4 or d/2), and ratio of compression-to-tension longitudinal reinforce-ment (ρ′/ρ = 0.5 or 1). The controlled parameters included nominal compressive strength of concrete (fc′ = 6000 psi [41 MPa]), nominal yield strength of transverse reinforce-ment (fyt = 60 ksi [415 MPa]), and shear span-to-effective depth ratio (a/d = 3). Chapter 21 of ACI 318-1110 requires that beams of special moment-resisting frames comply with ℓ/d ≥ 4, where ℓ refers to the total clear span of the beam. Assuming an inflection point at midspan, the selected value of a/d = 3 corresponds to ℓ/d = 6.

All transverse reinforcement consisted of No. 3 (9.5 mm) Grade 60 (415) rectangular hoops compliant with Chapter 21 of ACI 318-11.10 The HPFRC specimens had 1.5% volume fraction of steel-hooked fibers added to the same concrete mixture that was used to cast the non-fiber RC speci-mens. The fibers had a nominal tensile strength of 335 ksi (2300 MPa), a length-to-diameter ratio of 80, and a length of 1.2 in. (30 mm). The maximum aggregate size of the concrete mixture was limited to 1/2 in. (13 mm)—less than half the fiber length.

Table 1—Description of test specimens

Specimen* fc′, ksi (MPa)

Longitudinal reinforcement Transverse reinforcement

db, in. (mm) fy†, ksi (MPa) fu, ksi (MPa) εsu, % Total bars‡ db, in. (mm) fyt

†, ksi (MPa)

No. 1 CC4-X 6.0 (41) 7/8 (22) 65 (448) 98 (676) 16 8 3/8 (9.5) 68 (469)

No. 2 UC4-X 6.2 (43) 0.7 (18)§ 97 (669) 117 (807) 10 8 3/8 (9.5) 68 (469)

No. 3 UC4-F 6.4 (44) 0.7 (18)§ 97 (669) 117 (807) 10 8 3/8 (9.5) 68 (469)

No. 4 UC2-F 5.9 (41) 0.7 (18)§ 97 (669) 117 (807) 10 8 3/8 (9.5) 68 (469)

No. 5 CC2-F 5.8 (40) 7/8 (22) 65 (448) 98 (676) 16 8 3/8 (9.5) 68 (469)

No. 6 CC4-X$ 6.2 (43) 7/8 (22) 65 (448) 98 (676) 16 6 3/8 (9.5) 68 (469)

No. 7 UC2-F$ 6.2 (43) 0.7 (18)§ 97 (669) 117 (807) 10 6 3/8 (9.5) 68 (469)

*Specimen designation is based on the following symbols: CC is conventional Grade 60 (415) longitudinal and transverse reinforcement; UC is ultra-high-strength Grade 97 (670) longitudinal and conventional Grade 60 (415) transverse reinforcement; 4 is d/s = 4, where d is effective depth and s is spacing of transverse reinforcement; 2 is d/s = 2; X is RC without fibers (RC specimen); F is HPFRC specimen with Vf = 1.5% of steel-hooked fibers; $ is specimen with asymmetrical reinforcement (ρ′/ρ = 0.5).†Defined using 0.2%-offset method.‡Specimens No. 1 to 5 had four top bars and four bottom bars. Specimens No. 6 and 7 had two top bars and four bottom bars.§Threaded bars comply with ICC-ES AC 237.17

Fig. 1—Geometry of typical specimen. (Note: Dimensions in inches; 1 in. = 25.4 mm.)


MaterialsAll specimens were cast using ready mixed concrete

provided by a local supplier. The target compressive strength of concrete was 6000 psi (41 MPa). Actual compressive strengths were obtained from compression tests of standard 4 x 8 in. (102 x 203 mm) concrete cylinders16 (Table 1).

Grade 97 (670) reinforcing bars met the performance requirements of ICC-ES AC 237.17 All Grade 60 (415) steel bars comply with ASTM A706. Stress-strain relationships for the longitudinal reinforcing bars were obtained from standard tensile tests18 (Fig. 2). The measured steel proper-ties are summarized in Table 1.

Test setup and instrumentationThe general specimen configuration and dimensions are

shown in Fig. 1, and the typical test setup is shown in Fig. 3. The drift ratio history applied to each specimen follows the protocol of FEMA 46119 (Fig. 4) with the addition of a monotonic final push. The drift ratio (or effective beam rotation) was defined as the ratio of transverse displacement to shear span, corrected for the rotation of the central stub. This definition of drift ratio closely corresponds to the inter-story drift ratio of modern multi-story frames (designed with columns stronger than beams), where inelastic action occurs predominantly in the beams.

Two cycles at each drift target were applied to the stub at increasing amplitudes. After completing the second cycle at a drift ratio of 5%, specimens were subjected to monotoni-cally increasing displacements until failure of the specimen (defined herein as the state where the capacity of the spec-imen dropped by more than 25%) or to the maximum avail-able stroke of the load actuator.

Specimens were instrumented to measure displacements, forces, and strains. Displacements were measured at the roller supports and at the stub-beam interfaces using a redun-dant system of eight linear potentiometers. The drift ratios assigned to each cantilever beam account for the rotation of the central stub and rigid-body motions caused by deforma-tion of the supports. The transverse force applied through the central stub was measured using a custom-made load cell. Selected longitudinal and transverse reinforcing bars were also instrumented with strain gauges, which were contin-ually monitored throughout each test. These strain gauges were attached to the reinforcement cage at locations shown in Fig. 5 (symmetrical with respect to the central stub). For more details on the test setup, instrumentation, and measure-ments, refer to Tavallali.13

EXPERIMENTAL RESULTS

Measured shear versus drift ratioDuring cycles at drift ratios not exceeding 1%, the beam

elements on either side of the central stub experienced similar drift ratios. With yielding of the longitudinal reinforcement

Fig. 2—Representative tensile properties of reinforcing bars.

Fig. 3—Typical test setup.

Fig. 4—Loading protocol, after FEMA 461.19

Fig. 5—Position of strain gauges on reinforcing cage. (Note: Dimensions in inches; 1 in. = 25.4 mm.)


at larger drift ratios, the central stub rotated and the drift ratio of one beam became larger than the drift ratio of the beam on the opposite side of the central stub. The beam with the larger drift ratio was used to control the loading protocol of Fig. 4. The measured shear force versus drift ratio curves of the controlling beams are shown in Fig. 6.

Photographs in Fig. 7 show each specimen at the second excursion to a drift ratio of +5%. All beams success-fully completed the loading protocol and exhibited stable hysteretic response. At the end of the cyclic portion of the loading protocol, each specimen was loaded monotonically (final push). During the final push (not shown in Fig. 6), all

test specimens attained drift ratios in excess of 10%. This amount of deformation greatly exceeds the required drift ratio demands in practical design of structures.

Maximum measured shear forces and drift ratios are summarized in Table 2. All specimens were designed to have nearly identical flexural strength (neglecting the effect of fibers). Therefore, all specimens had nearly the same ρfy. The average of the maximum applied shear for the three RC specimens was 55 kip (245 kN) while the average value obtained for the four HPFRC specimens was 64 kip (285 kN). The increase in strength is attributed to the fibers.

Fig. 6—Shear versus drift ratio for controlling beams.


The testing apparatus allowed the application of drift ratios up to approximately 15%, depending on how much the central stub rotated in each test. In all specimens rein-forced with Grade 60 (415) bars, the limits of the testing apparatus were reached prior to failure of the specimen. In Specimen UC4-X with Grade 97 (670) longitudinal rein-forcement, failure occurred at a drift ratio above 15% due to fracture of the longitudinal reinforcement. In HPFRC specimens reinforced with high-strength steel, the addition

of fibers resulted in fracture of the longitudinal bars at an average drift ratio of 11%. It was observed that the use of HPFRC resulted in curvature concentration and accumula-tion of strains over a shorter distance (that is, shorter “plastic hinge” length). Additional details on strain and curva-ture distribution along the length of the test specimens are provided by Tavallali.13

None of the specimens failed in shear. The footnotes in Table 2 indicate that using the traditional shear strength model

Fig. 7—Photographs of specimens at second excursion to 5% drift ratio.


in ACI 318 code, where Vn = Vc + Vs, transverse reinforce-ment spaced at d/4 was sufficient to carry the applied shear, assuming that the shear strength attributed to the concrete Vc was zero (in accordance with Chapter 21 of ACI 318-1110). The three HPFRC specimens (UC2-F, CC2-F, and UC2-F$), were constructed with hoops spaced at d/2 (twice the spacing of hoops used in other specimens). For the same formulation of shear strength (Vn = Vc + Vs), HPFRC specimens attained values of Vc as high as 4 0 33′ ′( )f bd f bdc c psi] MPa][ . [ .

The hysteretic response of Specimens CC4-X (with conventional reinforcement bars) and UC4-X (with high-strength reinforcement bars) are compared in Fig. 8. In general, both specimens exhibited similar behavior. During cycles exceeding 1.5% drift ratios, Specimen CC4-X showed a slight gain in strength while Specimen UC4-X had a nearly flat shear versus drift response. This difference is attributed to the deviations in the stress-strain relationships of the longi-tudinal reinforcement (Fig. 2). Both specimens exhibited stable hysteretic response but the hysteretic loops of UC4-X were slightly narrower than those of Specimen CC4-X.

A direct comparison between the measured response of Specimens CC4-X and UC4-F is shown in Fig. 9. It is

observed that the addition of fibers in Specimen UC4-F led to hysteresis loops that were nearly as wide as those obtained for Specimen CC4-X. Fibers were also effective in increasing the peak strength of the beam up to a drift ratio of approximately 3%. However, in the subsequent cycles after reaching the peak strength, the strength was reduced to nearly the same strength of Specimen UC4-X (without fibers). The drop in strength is due to fiber pullout. This type of behavior was also observed in the other two HPFRC specimens (UC2-F and UC2-F$) reinforced with Grade 97 (670) steel bars. Note that Specimen CC2-F reinforced with Grade 60 (415) steel bars was able to maintain the peak strength, even at cycles above 3% drift ratio. A plau-sible explanation is that strain hardening characteristics of ASTM A706 bars compensated the strength drop caused by fiber pullout.

Measured strains in longitudinal and transverse reinforcement

Longitudinal and transverse reinforcing bars were instrumented with electrical resistance strain gauges (Fig. 5). Measured strains in the longitudinal bars of

Table 2—Maximum measured drift and shear

Specimen Maximum drift, %Maximum shear Vmax,

kip (kN)

vV

bdmaxmax=

*

vV V

bdcs=

−max

*†

′fc ,psi (MPa) ′fc ,psi (MPa)

No. 1 CC4-X >15 55 (245) 5.5 (0.46) 0.0 (0.00)

No. 2 UC4-X >15 53 (236) 5.3 (0.44) 0.0 (0.00)

No. 3 UC4-F 12 64 (285) 6.3 (0.52) 0.4 (0.03)

No. 4 UC2-F 11 61 (271) 6.2 (0.52) 3.2 (0.27)

No. 5 CC2-F >15 69 (307)‡ 7.1 (0.59) 4.0 (0.33)

No. 6 CC4-X$ >15 56 (249) 5.6 (0.47) 0.0 (0.00)

No. 7 UC2-F$ 11 60 (267) 6.0 (0.50) 3.0 (0.25)

*Shear stress expressed in terms of √fc′, where fc′ refers to values in Table 1; b = 16 in.; d = 8 in.†vc is shear stress attributed to concrete assuming contribution of transverse steel reinforcement is given by Vs = Avfytd/s, where Av = 0.22 in.2 For values of fyt and d/s, refer to Table 1.‡Maximum shear occurred during monotonic final push.

Fig. 8—Comparison of measured response, Beams CC4-X north and UC4-X south.

Fig. 9—Comparison of measured response, Beams CC4-X north and UC4-F south.


Specimens CC4-X, UC4-X, and UC4-F are shown in Fig. 10 (for the beams controlling the loading protocol). The strains measured during the tests assume a zero initial steel strain.

The strain versus drift ratio curves in Fig. 10, for Spec-imens CC4-X and UC4-X, indicate that yielding of the longitudinal reinforcement occurred at a distance of 0, 4, and 8 in. (0, 102, and 203 mm) from the face of the central stub. Upon yielding, there was a significant increase in the tensile strain associated with a very small increase in drift. The measured data suggest that the plastic region in both specimens (CC4-X and UC4-X) extended more than 8 in. (203 mm) or d away from the critical section. It is important to note that the apparent yield point for Specimen CC4-X, based on the shear versus drift curves (Fig. 6), occurred at a drift ratio of approximately 1%. This value is lower than the one obtained from the strain gauge readings in the bottom bar at the face of stub (Fig. 10(a)). This discrepancy may be explained by several factors, most notably the influence of

crack locations on strain gauge readings and the presence of an initial strain due to the effects of shrinkage.20

Two distinctive characteristics were observed in the strain versus drift ratio curves of HPFRC specimens (Fig. 10(c)). First, the measurements from strain gauges at 8 in. (203 mm) away from the face of stub indicate that the reinforcement had a nearly linear response at that section throughout the cyclic test. This suggests that unlike Specimens CC4-X and UC4-X, the plastic hinge region in Specimen UC4-F extended less than 8 in. (203 mm) or d. Second, the strain gauge at the face of stub in UC4-F reached 5% strain in the first cycle to a drift ratio of 5% compared to the 3.5% strain reached in Specimen UC4-X during the same cycle. These measurements, consistent with visual observations, indi-cate that adding fibers resulted in concentration of plastic curvature in a smaller region. The strain measurements at 4 in. (102 mm) away from the face of the stub suggest that the plastic hinge region extended more than d/2. Measured longitudinal strains in Specimen UC2-F and UC2-F$ were

Fig. 10—Measured strain in longitudinal reinforcing bars versus drift ratio.


similar to those in Specimens UC4-F while the strains in Specimen CC4-X$ was similar to those in Specimen CC4-X. The response characteristics of Specimen CC2-F based on strain measurements is not presented because multiple strain gauges malfunctioned.

The first four hoops near the central stub were instrumented in specimens with hoops spaced at d/4 (Fig. 5). In specimens with hoops at d/2, the first two hoops were instrumented. All specimens had the first hoop placed at 1 in. (25 mm) away from the face of stub. A sampling of measured hoop strains is shown in Fig. 11.

The measured hoop strains were generally higher in the RC specimens than in the HPFRC specimens. Maximum strain measurements did not exceed 0.4%, even during the final cycles of the test. For these strain values, the location of an inclined crack greatly influenced gauge readings and not always the maximum hoop strain occurred in the first hoop.

The HPFRC specimens, CC2-F, UC2-F, and UC2-F$ with hoops spaced at d/2 showed hoop strains slightly higher than in Specimen UC4-F with hoops spaced at d/4 (Fig. 11). However, the measured strains in HPFRC specimens (with hoops at d/2) did not exceed the values obtained for RC specimens (with hoops at d/4). HPFRC specimens with reduced amount of transverse reinforcement resisted higher shear than the RC specimens, suggesting that higher stresses may be attributed to the vc term based on the shear-strength model of the ACI 318 code, as indicated in the last column of Table 2.

Stiffness reductionsTo study the influence of using a reduced amount of high-

strength steel reinforcement and the presence of fibers on the stiffness of concrete beams, several stiffness measures were calculated at various stages of the tests.13 In this section, observations are presented regarding the effective initial stiffness ky and the unloading stiffness ku. Both ky and ku have strong influence on the nonlinear seismic response of RC members.21 All stiffness calculations were based on the measured shear versus drift curves.

The effective initial stiffness ky refers to the secant stiff-ness that is associated with first yield of the longitudinal reinforcement based on the strain gauge readings (the yield strain was defined using fy/Es, where fy was based on the values reported in Table 1). Beams with high-strength steel reinforcement had a lower initial stiffness because of the reduced amount of reinforcement and the higher strain required to yield the reinforcement. Careful inspection of Fig. 6, combined with the data presented in Fig. 10, suggests that ky in RC specimens with Grade 97 (670) steel bars was approximately three-quarters (3/4) of the stiffness of speci-mens with Grade 60 (415) steel bars. On average ky in RC specimens was approximately seven-eighths of the stiffness of the companion HPFRC specimens.

The unloading stiffness ku is a measure of the effective stiffness after large inelastic cyclic deformations. It refers to the secant stiffness measured from the maximum drift of a loading cycle to the point of zero shear force. In loading cycles before flexural yielding (typically cycles No. 1 to No. 14, with target drift ratios of 0.15 to 1%), the unloading

stiffness exhibited a nearly constant value for a given spec-imen. In cycles beyond flexural yielding (cycles No. 15 to No. 24, with target drift ratios of 1.5 to 5%), the unloading stiffness decreased with increasing drift (Fig. 12). These observations are in agreement with the general hysteresis rules presented by Takeda et al.22 for the response of RC members subjected to load reversals.

The unloading stiffness of RC specimens with high-strength reinforcement was approximately four-fifths of that for RC specimens with conventional reinforcement (Fig. 12). In contrast, the unloading stiffness in RC specimens with conventional reinforcement was generally slightly lower than that for HPFRC specimens with high-strength rein-forcement (Fig. 12).

Independent of all test variables, it was observed that measured stiffnesses decreased with increasing numbers of applied displacement cycles, even in successive cycles that reached an identical drift ratio.

Measured crack widthsFor many years, concrete members were designed based

on working stress design and the use of Grade 40 (275) rein-forcement. Crack control was seldom a primary design crite-rion. With the introduction of strength design provisions in ACI 318-632 and the use of higher grades of reinforcement, higher tensile stresses occurred during service conditions. The higher stresses typically led to wider cracks and the need for crack control. The occurrence of wider cracks may not be aesthetically acceptable, may lead to leakage problems, and may potentially increase the possibility of corrosion of the reinforcing bars.

In versions of the ACI 318 code before 1999, provisions were given for distribution of longitudinal reinforcement based on a calculated maximum crack width of 0.016 in. (0.41 mm). Current version of ACI 318 code10 controls crack width indirectly by limiting the maximum spacing of longi-tudinal bars.

Crack widths were measured in the test specimens at each peak (positive and negative) of the loading protocol. For meaningful crack width comparisons, an arbitrary reference service load was defined as the load corresponding to 60% of the nominal strength of the control Specimen CC4-X. For a nominal flexural strength of CC4-X equal to 110 k-ft (149 kN-m), the shear force defining the reference service load was taken as 33 kip (147 kN). The reader is reminded that all specimens were designed to have the same flex-ural strength. For RC beams where a large fraction of the required reinforcement is due to seismic loads, crack widths due to gravity loads should not be a concern.

The maximum crack widths reported in Fig. 13 corre-spond to measurements at the first peak of the cycle where the assumed service load level was reached. For the crack widths shown in Fig. 13, shear forces were 33 kip ± 3 kip (147 kN ± 13 kN). Using high-strength steel bars (Specimen UC4-X) generally resulted in increased crack widths. A comparison of the maximum measured crack width in Specimen UC4-X with that of Specimen CC4-X (Fig. 13) indicates that the crack width is nearly proportional to the specified yield strength of the longitudinal reinforcement.


The addition of fibers (Vf = 1.5%) dramatically reduced the maximum width of both flexural and shear cracks (refer to UC4-F, UC2-F, and UC2-F$ in Fig. 13). On average, the addition of fibers reduced the crack sizes by more than 50%.

The HPFRC specimens with Grade 97 (670) reinforcement showed that maximum crack widths did not exceed the crack widths of Specimen CC4-X. Crack widths for Spec-imen CC2-F were not recorded.

Fig. 11—Measured hoop strain versus drift ratio.


CONCLUSIONSBased on the test results presented for RC and HPFRC

beams and within the scope of parameters defined in this paper, the following conclusions are drawn:

1. Replacing conventional Grade 60 (415) longitudinal steel bars with reduced amounts of Grade 97 (670) high-strength steel bars provided nearly identical flexural strength and did not decrease the usable deformation capacity. The tested beams exhibited stable hysteretic response to cycles of 5% drift.

2. Lower spread of plasticity was observed in HPFRC beams than in RC beams. In RC beams with a shear-span ratio of 3 and reinforced using either Grade 60 (415) or Grade 97 (670) steel bars, yielding of the longitudinal reinforcement extended to a distance greater than d away from the critical section at drift ratios in excess of 3%. In HPFRC beams, yielding of the longitudinal reinforcement extended to a distance between 0.5d and d away from the critical section.

3. During cyclic displacements between drift ratios of 1.5 and 5%, the unloading stiffness of RC beams with Grade 60 steel bars was nearly 20% higher than that of RC beams with Grade 97 bars. At drift ratios near 1.5%, the unloading stiff-ness of HPFRC beams with Grade 97 steel bars was approx-imately 10% higher than that of RC beams with Grade 60 bars. This difference gradually reduced with increased drift ratios.

4. At 60% of the nominal flexural strength (chosen as service level load), maximum crack widths in RC beams reinforced with Grade 60 (415) steel bars were smaller than in RC beams reinforced with Grade 97 (670) bars. In RC beams (with constant ρfy), crack widths were observed to be approximately proportional to the specified yield strength of the longitudinal reinforcement. The maximum crack widths in HPFRC beams reinforced with Grade 97 steel bars were generally smaller than in RC beams reinforced with Grade 60 bars.

These findings suggest that high-strength reinforce-ment with yield strength in excess of 80 ksi (550 MPa) is a viable option for frame members in earthquake-resistant construction. Further experimental studies using full-scale

moment frames are needed to evaluate the influence of other variables not included in this study, among them: (a) the required spacing of transverse reinforcement (other than s = d/4) to prevent buckling of the longitudinal reinforce-ment; (b) the required anchorage length of longitudinal bars passing through the beam-column joint; and (c) the effects of reduced stiffness and hysteresis on the nonlinear seismic response of concrete frames reinforced with high-strength steel bars.

AUTHOR BIOSACI member Hooman Tavallali is a Practicing Engineer in the Greater Los Angeles area, CA. He received his BS from Shiraz University, Shiraz, Iran, in 2003; his MS from Sharif University of Technology, Tehran, Iran, in 2005; and his PhD from The Pennsylvania State University, University Park, PA, in 2011.

ACI member Andres Lepage is an Associate Professor in the Department of Civil, Environmental and Architectural Engineering at the University of Kansas, Lawrence, KS. He is a member of ACI Committees 335, Composite and Hybrid Structures; 374, Performance-Based Seismic Design of Concrete Buildings; 375, Performance-Based Design of Concrete Build-ings for Wind Loads; and ACI Subcommittee 318-H, Seismic Provisions (Structural Concrete Building Code).

ACI member Jeffrey M. Rautenberg is a Project Engineer at Wiss, Janney, Elstner Associates, Inc., Emeryville, CA. He received his BS, MS, and PhD in civil engineering from Purdue University, West Lafayette, IN, between 2004 and 2011. He is a member of ACI Committee 374, Performance-Based Seismic Design of Concrete Buildings.

ACI member Santiago Pujol is an Associate Professor of civil engineering at Purdue University. He is a member of ACI Committee 314, Simplified Design of Concrete Buildings, and Joint ACI-ASCE Committees 441, Rein-forced Concrete Columns, and 445, Shear and Torsion.

ACKNOWLEDGMENTSThe major source of funding for this project was provided by the Depart-

ment of Architectural Engineering, College of Engineering, of The Penn-sylvania State University. The authors would also like to express their grat-itude to SAS Stressteel, Inc., for partial financial support and to P. Kremer for his technical support in the Architectural Engineering Laboratory. Special thanks to Bekaert Corporation for donating the steel-hooked fibers used in this project.

NOTATIONAv = cross-sectional area of transverse reinforcementd = effective depth to reinforcement in tensiondb = diameter of reinforcing barEs = modulus of elasticity of steel, taken as 29,000 ksi (200,000 MPa)fc′ = concrete compressive strengthfu = steel tensile strengthfy = yield strength of longitudinal reinforcement

Fig. 12—Comparison of unloading stiffness, Beams CC4-X north, UC4-X south, and UC4-F south.

Fig. 13—Comparison of maximum measured crack width at service load level.


fyt = yield strength of transverse reinforcementVf = volume fraction of fibersVmax = maximum measured shear forcevc = shear stress attributed to concretevmax = maximum shear stressεsu = steel fracture strain measured in 8 in. (203 mm) gauge lengthρ = reinforcement ratio of bottom bars in beamsρ′ = reinforcement ratio of top bars in beams

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NOTES:

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