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ACI Structural Journal/March-April 2013 307

Title no. 110-S27

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 110, No. 2, March-April 2013.MS No. S-2011-134.R1 received June 5, 2011, 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 January-February 2014 ACI Structural Journal if the discussion is received by September 1, 2013.

Drift Capacity of Concrete Columns Reinforced with High-Strength Steelby Jeffrey M. Rautenberg, Santiago Pujol, Hooman Tavallali, and Andres Lepage

The use of high-strength steel bars with a yield stress of 80 ksi (550 MPa) or more as reinforcement for concrete columns has the potential to reduce steel congestion and lower construction costs. Current standards prohibit the use of these steels for most applica-tions by imposing upper limits on yield stress. In this study, those limits are reconsidered for columns resisting lateral loads induced by earthquakes.

Eight columns were tested under displacement reversals. Columns reinforced longitudinally with high-strength steel (Grades 80 to 120) had drift capacities between 4 and 8%. The drift capacities of these columns were comparable to the drift capacities of similar columns reinforced with Grade 60 steel. Columns with high-strength steel dissipated less energy than comparable columns with Grade 60 steel, but numerical analyses indicate that multi-story moment-frame buildings with columns reinforced with high-strength steel are not likely to experience consistently larger drifts than buildings with columns reinforced with Grade 60 steel.

Keywords: cyclic tests; deformation capacity; displacement reversals; earthquake; high-strength reinforcement; seismic.

INTRODUCTIONThe use of high-strength steel bars as reinforcement

in concrete elements has the potential to reduce problems associated with concrete placement and reduce costs associ-ated with the shipment and placement of reinforcing steel. These cost savings are expected to be nearly proportional to the increase in the design yield stress of the reinforcement. The term “high-strength steel” as used herein refers to steel having a nominal yield stress of 80 ksi (550 MPa) or more and an elongation at rupture of at least 7%. Building codes in the United States have limited the nominal yield stress of the reinforcement since 1963,1 when the limit was set at 75 ksi (520 MPa). The maximum nominal yield stress permitted by ACI 318-112 varies depending on the application, but for longitudinal reinforcement in members resisting earthquake-induced forces, the limit is set at 60 ksi (410 MPa). This limit was established based on tests of beams3 and concentrically loaded columns.4,5 The limit is reconsidered herein on the basis of theoretical and experimental evidence.

Columns in frames resisting seismic loads are typically designed with the intent that the longitudinal reinforcement in tension yields before the concrete in compression reaches its limiting strain (that is, the columns are subjected to axial loads below the balanced point). It is in these columns that increasing the yield stress of the steel would be advanta-geous because less steel would be required to resist the same bending moment.

The use of high-strength steel reinforcement requires the consideration of three issues:

1. Crack widths during service conditions;2. Drift capacity; and3. Reduction in flexural stiffness.

The first issue—crack widths during service conditions—may control the design of beams, but it seldom controls the design of columns. The second issue—computing the lateral drift capacity of a column resisting cyclic lateral loads—requires careful study and is the focus of the experimental investigation reported herein. Investigation of the third issue is motivated by the fact that a column with high-strength steel is more flexible after cracking than a column reinforced with a larger amount of conventional steel. This reduction in stiffness is accompanied by an increase in the displacement at yield (which may translate into a reduction in the ratio of maximum displacement to yield displacement) and a reduc-tion in hysteretic energy dissipation. The effect of this issue on the seismic response of frames was investigated through a series of numerical analyses.

SCOPEThe results from tests on eight columns and a series of

numerical simulations are presented in this paper. The columns tested were designed to investigate the effects of using steel bars conforming to either ASTM A1035/A1035M-09 Grade 1206 (nominal yield stress of 120 ksi [830 MPa]) or ASTM A706/A706M-09b Grade 807 (nominal yield stress of 80 ksi [550 MPa]) as longitudinal reinforce-ment. Grade 60 (nominal yield stress of 60 ksi [410 MPa]) steel bars were used to fabricate hoops for transverse reinforcement. All reinforcement details were chosen to meet the provisions required for special moment frames described in Chapter 21 of ACI 318-11.2 This study focused on columns, so the use of high-strength steel in walls, beams, joints, and other structural elements was not addressed.

The test results were used to calibrate numerical tools for investigating the effects of using high-strength steel bars as longitudinal reinforcement in the columns of multi-story moment-resisting frame buildings. Hypothetical buildings with three to 20 stories were modeled and nonlinear dynamic analyses were conducted to estimate their responses to 24 strong ground motions.

RESEARCH SIGNIFICANCEThe use of high-strength steel bars for reinforcement in

concrete columns offers the opportunity to reduce construc-tion costs and ease concrete placement.

The available literature on the use of high-strength reinforcement predominantly focuses on beams, columns

308 ACI Structural Journal/March-April 2013

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

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, Reinforced Concrete Columns, and 445, Shear and Torsion.

ACI member Hooman Tavallali is an Engineer at LERA in New York. He received his BSc in civil engineering from Shiraz University, Shiraz, Iran; his MSc in civil engineering from Sharif University of Technology, Tehran, Iran; and his PhD in archi-tectural engineering (structures) from Pennsylvania State University, University Park, PA, in 2003, 2005, and 2011, respectively.

ACI member Andres Lepage is an Assistant Professor in the Department of Architec-tural Engineering at Pennsylvania State University. He is a member of ACI Committees 335, Composite and Hybrid Structures; 374, Performance-Based Seismic Design of Concrete Buildings; and 375, Performance-Based Design of Concrete Buildings for Wind Loads, and ACI Subcommittee 318-H, Seismic Provisions.

with circular cross sections, bond, and corrosion resis-tance.8-12 Prior studies have not investigated the cyclic response of tied columns with rectangular cross sections reinforced longitudinally with ASTM A706/A706M Grade 80 or ASTM A1035/A1035M Grade 120 steel bars.

MOMENT-CURVATURE ANALYSESThe section of a column reinforced with Grade 60 steel

has approximately the same flexural capacity and ulti-mate curvature as a section reinforced with half as much Grade 120 steel. This relationship is best illustrated through an example. Consider the cross sections shown in the inset drawings in Fig. 1. Section A is reinforced with Grade 60 steel and Section B is reinforced with Grade 120 steel. Assume that the compressive strength of the concrete is 6000 psi (41 MPa), the stress-strain curve for Grade 60 steel is elasto-plastic, and the stress-strain curve for Grade 120 steel is defined by Eq. (1)13 and shown in Fig. 2. The stress-strain behavior of the concrete in compression is assumed to follow the relationship proposed by Hognestad,14 with the maximum usable strain in compression set equal to 0.004. Both sections are assumed to resist a concentrically applied axial load of 0.2fc′Ag.

( )1

1

1s s s u

C Cs

Af E A fB

− = e ⋅ + ≤ + e

(1)

where fs is the stress in the steel; Es is the elastic modulus of steel (29,000 ksi [200 GPa]); es is the strain in the steel; A = 0.0015; B = 175; C = 2.0; and fu is steel strength (170 ksi [1170 MPa]).

Computed moment-curvature relationships for the two sections described previously are shown in Fig. 1. Before cracking, the gross section properties control the behavior and the two column sections have nearly identical responses. After cracking, the section reinforced with high-strength steel has a lower stiffness, but the sections have approxi-mately the same moment capacity and ultimate curvature. These results indicate that, in terms of strength and curvature capacity, the use of high-strength reinforcing bars may not lead to detrimental consequences. Nevertheless, displace-ment capacity, rather than curvature capacity, is a better indi-cator of damage, and to extrapolate theoretical estimates of curvature capacity to displacement capacity requires support from experimental data.

EXPERIMENTAL PROGRAMResearchers15-19 have proposed methods to estimate the

drift capacity of reinforced concrete elements based on moment-curvature relationships. These methods have been calibrated primarily using results from members reinforced with Grade 60 (or similar) steel bars. The use of these methods for elements reinforced with steel bars of a different grade needs to be vetted using test results. Eight specimens were tested to provide physical evidence for estimating the drift capacity of columns reinforced with high-strength steel. Photographs, reports, and test data are available at NEES.20

Specimen descriptionEight specimens were tested under lateral displacement

reversals. The dimensions of the specimens are shown in Fig. 3. Each specimen consisted of two cantilevered columns joined by a central loading stub. The shear span-to-effective depth ratio (a/d) for all columns was 3.

Figure 3 shows a typical layout of reinforcing steel. Spec-imens were reinforced in the longitudinal direction with either four or six deformed steel bars with diameters ranging

Fig. 1—Computed moment-curvature relationships of sections reinforced with Grade 60 (Section A) and Grade 120 steel (Section B) for an axial load of 0.2fc′Ag. (Note: 1 in. = 25.4 mm.)

Fig. 2—Measured and idealized stress-strain curves for longitudinal reinforcement.


from 5/8 to 7/8 in. (16 to 22 mm). Reinforcement ratios rg ranged from 1.1 to 3.3%. Transverse reinforcement in all specimens was Grade 60 and consisted of 3/8 in. (10 mm)

diameter deformed-bar hoops fabricated in accordance with current provisions for the design of special moment-resisting frames.2 The hoops were spaced at 2.5 in. (64 mm), which resulted in a transverse reinforcement ratio rv of 1%. The specimens were labeled with a series of numbers and letters (that is, CC-3.3-10). The first letter is used to identify the nominal yield stress of the longitudinal reinforcement (C = 60 ksi [410 MPa], H = 80 ksi [550 MPa], and U = 120 ksi [830 MPa]). The second letter is used to identify the nominal yield stress of the transverse reinforcement (C = 60 ksi [410 MPa]). The numbers after the first hyphen are used to identify the longitudinal reinforcement ratio as a percentage of the gross cross-sectional area of the column (As/Ag). The numbers after the second hyphen represent the applied axial load as a percentage of the product of the measured concrete cylinder compressive strength and the gross cross-sectional area (P/fc′Ag).

Test setup and instrumentationSpecimens were tested lying horizontally (Fig. 4) and were

supported by greased wooden blocks. Lateral load was applied using a double-acting 175 kip (775 kN) hydraulic actuator. The lateral load was measured with a 150 kip (670 kN) load cell. The axial load was applied using an external post-tensioning system consisting of four high-strength threaded Fig. 3—Typical layout of reinforcing steel, in. (mm).

Fig. 4—Typical test setup. (Note: 1 in. = 25.4 mm; 1 ft = 0.3048 m; 1 kip = 4.45 kN.)


rods, two reaction blocks, and four 60 kip (270 kN) hydraulic rams (Fig. 4). The rams were connected in parallel through a manifold and were controlled with a hydraulic hand pump and a pressure regulator. Axial load was measured using two 50 kip (220 kN) capacity load cells and was kept nearly constant through the duration of each test. Displacements were measured at the column supports and on either side of the central stub using an array of eight linear variable differ-ential transformers (LVDTs). Measured displacements were corrected to account for displacements related to rigid-body motion caused by deformations of the supports.21

Material propertiesAll specimens were cast horizontally using ready mixed

concrete made with Type I portland cement. The target compressive strength of the concrete was 6000 psi (41 MPa). Actual compressive strengths ranged from 5200 to 7850 psi (36 to 54 MPa) (Table 1). These values were obtained from compression tests of standard concrete cylinders.22 Stress-strain relationships for the longitudinal (Fig. 2) and trans-verse reinforcing bars were obtained from standard tensile tests.23 Three coupons from each heat of steel were tested in tension. The average measured properties of each heat of steel used as longitudinal reinforcement are summarized in Table 1. The nominal yield stress of all transverse reinforce-ment was 60 ksi (410 MPa) with an average measured yield stress of 64 ksi (440 MPa).

Test variablesControlled test variables included nominal yield stress of

the longitudinal reinforcement (60, 80, and 120 ksi [410, 550, and 830 MPa]); applied axial load (0.10 and 0.20 fc′Ag); and maximum applied shear stress (5 and 6 √fc′ psi [0.4 and 0.5 √fc′ MPa]). Properties of specimens were chosen to form groups of two or three specimens having only one variable among them. The comparison groups and brief descriptions of the variables investigated are shown in Table 2.

EXPERIMENTAL RESULTSHysteretic response

During testing, the plastic deformations concentrated in one of the two columns in each test assembly because rota-

tions of the central stub were not restrained. The column with consistently higher drift ratios (defined as the lateral deviation of the pinned end relative to a tangent to the central stub divided by the shear span) in each test was identified as the controlling column. The loading protocol24 applied to the controlling column is shown in Fig. 5. Two cycles were applied at each drift target up to a drift ratio of 5%, after which the specimens were loaded monotonically. The measured shear versus drift ratio curves for the control-ling column in each of the eight test assemblies are shown in Fig. 6; the letters “S” and “N” identify the controlling column (North or South). Figure 7 shows photographs of each specimen at the peak displacement of the first excur-sion to a drift ratio of 4%, with N to the right.

All columns retained their integrity, their capacity to resist axial load, and a large fraction of their capacity to resist lateral loads at drift ratios of at least 4%. Specimens reinforced with high-strength steel had yield drift ratios (defined as the drift ratio at which the longitudinal reinforce-ment in tension reached its yield strain) up to 90% larger than specimens reinforced with Grade 60 steel (Table 3). This difference translated into a reduction in hysteretic energy dissipation. The effects of the reduced energy dissipation on building drift are discussed in the section describing the analytical investigation.

Failure mechanismsSpecimen UC-1.6-10 failed at a drift ratio in excess of

8%, when fracture of a bar in tension caused a loss in lateral load-carrying capacity. In the other seven specimens, loss in lateral load-carrying capacity was initiated by buckling of the longitudinal reinforcement in compression. In Speci-mens CC-3.3-20, HC-2.2-20, UC-1.6-20, and UC-1.1-20, bars buckled at drift ratios near zero after deterioration of the concrete caused by cycles in the inelastic range of response. The buckling of the reinforcement at drift ratios near zero is attributed in part to the fact that, at low drift ratios, cracks that had formed earlier in testing were still open. The combi-nation of the cracks being open and the deterioration of the concrete caused a loss of lateral support and an increase in the fraction of the axial load resisted by the reinforcement, which led to a higher susceptibility to bar buckling.

Table 1—Selected properties of eight test specimens

Specimen

Longitudinal reinforcement

fc′, psi (MPa) P, kips (kN) P/fc′AgASTM standard Quantity*db, in. (mm) rg, %

fy†, ksi

(MPa)fu, ksi (MPa)

eu (200 mm), %

CC-3.3-10A706/A706M

Grade 606 7/8 (22) 3.3

66(455)

94(648)

23.45200(36)

65(290)

0.11

HC-2.2-10A706/A706M

Grade 804 7/8 (22) 2.2

83(572)

118(814)

14.07750(53)

84(375)

0.10

UC-1.6-10A1035/A1035M

Grade 1204 3/4 (19) 1.6

133(917)

168(1160)

8.65300(37)

64(285)

0.11

CC-3.3-20A706/A706M

Grade 606 7/8 (22) 1.6

64(441)

92(634)

20.37800(54)

169(750)

0.20

HC-2.2-20A706/A706M

Grade 804 7/8 (22) 2.2

83(572)

118(814)

14.07850(54)

170(755)

0.20

UC-1.6-20A1035/A1035M

Grade 1204 3/4 (19) 1.6

133(917)

168(1160)

8.66300(43)

140(620)

0.21

CC-2.4-20A706/A706M

Grade 606 3/4 (19) 2.4

65(448)

91(627)

16.45250(36)

108(480)

0.19

UC-1.1-20A1035/A1035M

Grade 1204 5/8 (16) 1.1

134(924)

165(1140)

9.05350(37)

116(515)

0.20

*Specimens with six longitudinal reinforcing bars had two equal layers of three bars each. †Based on 0.2% offset method for Grade 120 steel. Note: 1 mm = 0.0394 in.


Drift capacityLateral drift capacity has been defined in different ways by

different researchers.19,25 Drift capacity is defined herein as the maximum lateral drift a column has reached before one of the following two conditions is met:

1. The peak lateral-load resistance in a given cycle is less than 50% of the peak load reached in any previous cycle; or

2. The peak lateral load reached in the first cycle applied at a displacement amplitude is less than 80% of the peak load reached in the first cycle applied at the previous amplitude.

This definition of drift capacity is adopted herein because the P-D effect may cause a reduction in lateral-load-carrying capacity that is not necessarily associated with a loss in the integrity of the column.

Shear forces and drift ratios at yield, maximum measured shear forces, and drift capacities based on the criteria described previously are shown in Table 3. Figure 8(a) shows the drift capacity of the columns plotted against the measured yield stress of the longitudinal reinforcement. Each series represents one of the first three comparison groups shown in Table 2. The drift capacities of columns

reinforced with high-strength steel are lower than the drift capacities of columns reinforced with Grade 60 steel in all three series. The decrease in drift capacity related to the use of high-strength steel ranges from 10 to 50%. However, in the comparison group in which there is a 50% reduction (dotted line in Fig. 8(a)), Specimen CC-2.4-20 (reinforced with Grade 60 steel) failed during the mono-tonic push after all drift cycles in the loading protocol had been completed, while Specimen UC-1.1-20 (reinforced with Grade 120 steel) failed during one of the displacement cycles. Pujol et al.26 observed that “column drift capacity is sensitive to displacement history,” so it is difficult to compare results from those two specimens directly. For the other comparison groups, the columns with high-strength

Table 2—Description of comparison groups

Specimens being compared Variable Constants

CC-3.3-10HC-2.2-10UC-1.6-10

Yield stress of longitudinal steel:(60, 80, or 120 ksi)

Maximum applied shear stress: (6√fc′ psi)Axial load ratio: (0.10fc′Ag)

CC-3.3-20HC-2.2-20UC-1.6-20

Yield stress of longitudinal steel:(60, 80, or 120 ksi)


CC-2.4-20UC-1.1-20

Yield stress of longitudinal steel:(60 or 120 ksi)


CC-3.3-10CC-3.3-20

Applied axial load ratio:(0.10 or 0.20fc′Ag)

Maximum applied shear stress: (6√fc′ psi)Yield stress of longitudinal steel: (60 ksi)

HC-2.2-10HC-2.2-20



UC-1.6-10UC-1.6-20



CC-3.3-20CC-2.4.20

Maximum applied shear stress:(5 or 6√fc′ psi)

Yield stress of longitudinal steel: (60 ksi)Axial load ratio: (0.20fc′Ag)

UC-1.6-20UC-1.1-20

Maximum applied shear stress:(5 or 6√fc′ psi)

Yield stress of longitudinal steel: (120 ksi)Axial load ratio: (0.20fc′Ag)

Notes: √fc′ psi = 1/12 √fc′ MPa; 1 ksi = 6.9 MPa.

Fig. 5—Loading protocol applied to each test specimen.

Table 3—Measured yield and ultimate shear forces and drift ratios for test specimens

SpecimenVy, kips

(kN) qy, %Vu

*, kips (kN)

vu*, √fc′ psi (MPa) qu

†, %

CC-3.3-1045.7 (203)

0.946.3 (206)

6.0 (0.49) 10.0

HC-2.2-1043.1 (192)

1.045.5 (202)

4.8 (0.40) 7.0

UC-1.6-1042.3 (188)

1.748.0 (214)

6.1 (0.51) 8.0

CC-3.3-2058.0 (258)

0.960.0 (267)

6.3 (0.52) 5.0

HC-2.2-2052.5‡ (234)

1.054.7‡ (243)

5.7 (0.47) 4.0

UC-1.6-2047.0 (209)

1.551.3 (228)

6.0 (0.50) 4.5

CC-2.4-2041.0 (182)

0.941.6 (185)

5.3 (0.44) 8.0

UC-1.1-2034.1 (152)

1.437.0 (165)

4.7 (0.39) 4.0

*Based on maximum measured shear force at any point during testing. †Drift capacity as defined herein. ‡Estimated because of malfunction in data acquisition equipment.


Fig. 6—Measured shear versus drift ratios. (Note: 1 ksi = 6.9 MPa; 1 in. = 25.4 mm.)


steel reinforcing bars had drift capacities that were approxi-mately 80% of the drift capacities of comparable columns reinforced with ASTM A706/A706M Grade 60 steel bars.

Comparison to tests conducted by othersA database of 53 columns tested by other researchers27-39

was compiled using data published by Berry and Eberhard.40 The columns were chosen to have similar properties to the columns tested in this study. The columns considered had:• Rectangular cross sections with rectangular hoops;• Concrete compressive strengths between 3000 and

13,000 psi (21 and 90 MPa);• Axial load ratios between 0.05 and 0.30;• a/d between 3.0 and 5.0; and• Reinforcing details that precluded shear and bond failures.

The drift capacity of each of the columns in the database was determined using the criteria introduced previously and is plotted in Fig. 8(b) as a function of the measured yield stress of the longitudinal reinforcement. From this plot, it can

Fig. 7—Photographs of test specimens at first excursion to drift ratio of 4%.

be concluded that the drift capacities of columns reinforced with high-strength steel ranged from 4 to 8% and are compa-rable to drift capacities of similar columns reinforced with conventional steel.

The “reinforcement buckling ratio” (ℜ) is introduced herein to quantify the vulnerability of the longitudinal reinforcement to buckling

e

PP

ℜ = (2)

( )2

21 0.7

barsNs i

ei

E IP

s=

p= ∑ (3)

where P is the applied axial load; Pe is the total buckling load of the longitudinal reinforcement assuming pin-fixed end condi-tions and an unbraced length equal to the spacing of the trans-verse reinforcement; Nbars is the total number of longitudinal reinforcing bars in the cross section; Es is the elastic modulus of steel reinforcement; Ii is the moment of inertia of the i-th reinforcing bar in the cross section about its own centroidal axis; and s is the spacing of transverse reinforcement.

Fig. 8—Drift capacity versus yield stress of longitudinal reinforcement for: (a) test specimens; and (b) columns from database.27-39


Figure 9 shows the relationship between the reinforcement buckling ratio ℜ and drift capacity for the 53 columns in the database27-39 and the eight columns tested in this study. The data suggest that an increase in the reinforcement buckling ratio is generally associated with a decrease in drift capacity. An increase in the reinforcement buckling ratio can result from the use of smaller or fewer longitudinal reinforcing bars. Therefore, the reduction in required reinforcement associated with an increase in yield stress for constant spacing of the transverse reinforcement may lead to lower drift capacities.

ANALYTICAL INVESTIGATIONOverview

The experimental results show that columns reinforced longitudinally with Grade 120 steel dissipated less energy through hysteresis than columns reinforced with twice as much Grade 60 steel. The reason for the lower energy

dissipation is the reduction in post-cracking stiffness. The question addressed herein is: If a multi-story moment-frame building has columns reinforced with high-strength steel, does the reduced post-cracking stiffness lead to a consistent increase in displacement demand?

Eight hypothetical buildings were modeled using a soft-ware package for nonlinear dynamic analysis (LARZ41-43). Half of the models represented building frames with all members reinforced longitudinally with Grade 60 steel. The other half of the models represented building frames with columns reinforced with Grade 120 steel and beams reinforced with Grade 60 steel.

Building modelsEach of the two model sets included building frames with

three, six, 12, and 20 stories (Fig. 10). The model sets were designated “C” or “H,” where “C” refers to frames with conventional steel (Grade 60) and “H” refers to frames with high-strength steel (Grade 120) in the columns. All models were assumed to have beams reinforced with Grade 60 steel.

All models had the same floor plan, with four bays in the direction of applied ground motion and three in the perpen-dicular direction. Columns were spaced in both directions at 24 ft (7.3 m) and all story heights were 12 ft (3.7 m). Column sizes varied both from model to model and within each model (Fig. 10), but models in Set C had identical column sizes to those in the comparable models from Set H. Columns were sized so that the axial loads related to gravity effects were mostly between 0.10 and 0.20fc′Ag for inte-rior columns (buildings were assumed to weigh 150 lb/ft2 [7.2 kN/m2] per floor). All columns in a given story were the same size. Column sections were assumed to be square with three layers of reinforcement (Fig. 10). All beams were assumed to have T-shaped cross sections with the same cross-sectional dimensions and material properties (Fig. 10). Strong-column, weak-beam design requirements, as speci-fied in ACI 318-11,2 were not satisfied at every joint. This

Fig. 9—Drift capacity versus reinforcement buckling ratio for all columns considered.

Fig. 10—Typical elevations and cross sections used in building models, in. (mm).


caused a relative increase in column end rotations, which may amplify the effect of the change in post-cracking stiff-ness of the columns.

Grade 60 steel was assumed to have an elasto-plastic stress-strain curve and Grade 120 steel was assumed to follow the stress-strain curve defined by Eq. (1), as shown in Fig. 2. Concrete was assumed to follow the stress-strain curve proposed by Hognestad14 with a compressive strength

Table 4—Initial periods and base shear strength coefficients of building models

Number of stories C or H* To†, seconds Cy

‡

3C

0.50.27

H 0.28

6C

0.90.21

H 0.22

12C

1.50.12

H 0.13

20C

2.30.09

H 0.09*C refers to building models with conventional (Grade 60) longitudinal reinforcement in columns; H refers to models with high-strength (Grade 120) longitudinal reinforcement in columns. All beams are reinforced with conventional longitudinal steel. †Initial period based on gross cross-sectional properties and elastic modulus of concrete equal to 4000 ksi (28 GPa). ‡Base shear strength coefficient determined from limit analyses using triangular lateral-load distribution.

Table 5—Twenty-four strong-motion records used in dynamic analyses

Location45 DateEpicentral distance,

miles (km) Magnitude DirectionPeak ground

acceleration, gPeak ground velocity, in./s

(cm/s)

Long Beach, CA March 10, 1933 0.5 (0.8) 6.4NS 0.197 11.6 (29.4)

EW 0.159 6.5 (16.5)

El Centro, CA May 18, 1940 7.6 (12.2) 6.9NS 0.348 13.2 (33.5)

EW 0.214 14.5 (36.9)

San Fernando, CA February 9, 1971 2.2 (3.5) 6.6S16E 1.171 44.7 (113.5)

S74W 1.076 22.7 (57.6)

Tabas, Iran September 16, 1978 —* 7.4NS 0.932 43.9 (111.6)

EW 0.881 39.4 (100.0)

Llolleo, Chile March 3, 1985 62.8 (101.0) 7.8N70E 0.177 —*

N20W 0.133 —*

Mexico City September 19, 1985 23.8 (38.3) 8.1EW 0.143 —*

NS 0.142 —*

Loma Prieta, CA October 17, 1989 1.7 (2.8) 7.0EW 0.479 18.7 (47.5)

NS 0.630 21.8 (55.3)

Northridge, CA January 17, 1994 8.0 (12.9) 6.7NS 0.477 24.1 (61.2)

EW 0.364 12.2 (31.1)

Kobe, Japan January 16, 1995 0.6 (1.0) 6.9NS 0.821 —*

EW 0.599 —*

Izmit, Turkey September 13, 1999 18.0 (29.0) 5.8NS 0.196 —*

EW 0.144 —*

Chi Chi, Taiwan September 20, 1999 7.1 (11.4) 7.6EW 1.010 —*

NS 0.432 —*

Duzce, Turkey November 12, 1999 4.4 (7.1) 7.1NS 0.728 —*

EW 0.822 —*

*Not reported.

equal to 5000 psi (34 MPa), modulus of rupture equal to 7.5 √fc′ psi (0.62 √fc′ MPa), and elastic modulus equal to 4000 ksi (28 GPa).

A moment-curvature relationship was generated for each member, and simplified trilinear moment-curvature relation-ships were used as input for the modeling software.21 The first break point in the relationship represents flexural cracking and the second break point represents yielding of the longi-tudinal reinforcement. Beam-column joints were assumed rigid, but additional deformations due to bond slip were accounted for.21

The natural period To of each model was based on the gross section properties and was computed using SAP2000 v.14.0.044 (Table 4). Because the dimensions of the structural elements in the models from Set C were the same as those from Set H, the computed initial stiffnesses and natural periods were the same (for a given number of stories).

The base shear strength of each model was computed assuming a triangular lateral-load distribution increasing from zero at the ground level to a maximum at the roof. The total lateral load required to cause the weakest flexural mechanism was normalized with respect to the weight of the structure to obtain the base shear strength coefficient Cy reported in Table 4. Figure 11 shows the load-deflection curves computed for the eight building models. It can be observed that the effect using high-strength steel in columns on the overall load-deflection curve decreases as the number of stories increases. This is because a relatively larger


number of hinges form in the beams and slabs in the taller buildings than in the shorter buildings.

Strong ground motionsNumerical analyses were performed on each of the eight

building models to estimate their response to 24 unscaled strong-motion acceleration records45 (Table 5). The records were chosen to encompass a wide array of soil conditions and frequency contents.

Computed roof driftsFor each analysis, the maximum computed roof displace-

ment was normalized with respect to the height of the struc-ture to obtain the maximum mean drift ratio.

Figure 12 shows a comparison between the maximum computed mean drift ratio for models from Set C (d60) and the maximum computed mean drift ratio for models from Set H (d120). The average ratio of roof drifts for comparable models was 1.03 with a coefficient of variation of 0.14. Considering the assumptions and approximations inherent to modeling the response of structures to strong ground motions, this increase of 3% is well within the tolerance of

Fig. 11—Base shear coefficient versus mean drift ratio for eight building models. (Note: 1 ksi = 6.9 MPa.)

Fig. 12—Comparison of maximum computed mean drift ratios in models with Grade 60 steel (d60) and models with Grade 120 steel (d120) in columns.

what engineers are able to reliably predict and is regarded as inconsequential. These results indicate that multi-story frame buildings with columns reinforced longitudinally with high-strength steel are not likely to experience consistently higher drift ratios than buildings with columns reinforced with twice as much Grade 60 steel.

CONCLUSIONSBased on results from laboratory tests of specimens

detailed to avoid shear and bond failures and numerical simu-lations of moment-resisting frame buildings, the following conclusions are made:

1. Laboratory tests indicated that the drift capacities of columns reinforced with Grade 80 or Grade 120 longitudinal reinforcement were comparable to the drift capacities of columns reinforced with Grade 60 steel. All columns tested had lateral drift capacities between 4 and 8%.

2. Numerical simulations indicated that under strong ground motion, the models of frame buildings with columns reinforced with Grade 120 longitudinal steel did not produce roof drifts consistently larger than the roof drifts computed for models of buildings with columns having twice as much Grade 60 longitudinal reinforcement.

ACKNOWLEDGMENTSThe authors would like to acknowledge the generous funding and dona-

tions provided by Pennsylvania State University, the Concrete Reinforcing Steel Institute, MMFX Technologies, the Neturen Corporation, and Kenny Construction Company.

NOTATIONAg = gross cross-sectional area of columnAs = cross-sectional area of longitudinal reinforcementAv = cross-sectional area of transverse reinforcementa = shear spanb = width of sectiond = effective depth to reinforcement in tensionfc′ = concrete compressive strengthfu = steel tensile strengthfy = yield stress of longitudinal reinforcementfyv = yield stress of transverse reinforcementVu = maximum measured shear forceVy = measured shear force at yield of longitudinal reinforcement in tensionvu = Vu/Ag, maximum shear stresseu = fracture elongation in 8 in. (200 mm) gauge lengthqu = drift capacity as defined hereinqy = measured drift ratio at yield of longitudinal reinforcement in tensionr = reinforcement ratio of bottom bars in T-beamsr′ = reinforcement ratio of top bars in T-beamsrg = longitudinal reinforcement ratio for columns based on gross

cross-sectional arears = reinforcement ratio of bottom bars in slabr′s = reinforcement ratio of top bars in slabrv = Av/(bs), transverse reinforcement ratio

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