aci seismic behavior of shear dominated

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ACI Structural Journal/July-August 2009 445  ACI Structura l Journal , V. 106, No. 4, July-August 2009. MS No. S-2007-377 received November 12, 2007, and reviewed under Institute publication policies. Copyright © 2009, American Concrete Institute. All rights reser ved, inclu ding the making of copies unless permission is obtain ed from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the May-June 2010 AC I S tru ctu ral Jou rna l  if the discussion is received by January 1, 2010. A CI STR UCTURAL JOURNAL TECHNI CAL P APER The most important consideration for structures in seismically active cold regions is the danger of brittle failure due to a combination of extreme cyclic load reversals and very low temperatures. To identify the effect of low temperatures on the seismic behavior of shear-dominated columns, two pairs of reinforced concrete squat columns were tested under cyclic load reversals while subjected to freezing (–36 °C [–33 °F]) and room temperatures (22 °C [72 °F]). It was found that cold specimens exhibited an increase in the shear strength and elastic stiffness. Existing models for assessment and design of shear strength were evaluated based on the experimental results obtained. It is concluded that current models are conservative for low temperature conditions even if the appropriate low temperature material properties are used. Keywords: column; ductility; seismic; strength; temperature. INTRODUCTION Past research 1,2  has shown that reinforced concrete (RC) columns subjected to cyclic reversals and low temperatures undergo a gradual increase in strength and stiffness that is sometimes coupled with a reduction in displacement capacity. All the units tested in the past, 1,2  however, were flexurally dominated. Therefore, not much can be said regarding the effect of low temperatures and cyclic loads on the shear strength of RC columns. Note that due to its brittle nature, shear is regarded as a mode of failure that should be avoided in RC design. 3  To determine the effect of low temperatures on the seismic behavior of shear-dominated RC columns, two pairs of squat columns where tested under reversed cyclic loading. The only variable between columns of the same pair was the temperature of the specimen during testing: one of the columns was tested at room temperature (22 °C [72 °F]) while the other was tested at –36 °C (–33 °F). Differences between each pair of columns were the ratios of transverse and longitudinal reinforcement, which were designed with the aim of achieving shear failures at low levels of ductility (brittle shear failure) and high levels of ductility (ductile shear failure). RESEARCH SIGNIFICANCE Many moderate to high seismic zones are located in regions where temperatures may drop to levels that may have an adverse effect on the ductility of the constituent materials and structural member. In the U.S., for example, Alaska is by far the coldest and one of the most highly active seismic regions. To the authors’ knowledge, however, this is the first large-scale testing program aimed to identify the effect of low temperatures on the seismic behavior of shear- dominated RC columns. Results presented in this paper will hopefully be of value in the seismic design and assessment of RC structures in cold regions. THEORETICAL SHEAR STRENGTH The test units were designed to fail by shear at different levels of ductility. Theoretical strengths were calculated using the revised UCSD shear model. 4  The original UCSD model included the degradation of concrete strength with ductility, whereas the effect of axial load is accounted for separate from the concrete contribution to shear strength. The revised model also accounts for the effect of concrete compression zone on the mobilization of transverse steel and the influence of the aspect ratio and the longitudinal steel ratio on the strength of the concrete shear-resisting mechanism. The shear strength capacity of the member is expressed as the sum of three separate components, as shown in Eq. (1), where V s  represents the shear capacity attributed to the steel truss mechanisms, V c  represents the strength of the concrete shear-resisting mechanism, and V  p  represents the strength attributed to the axial load V  = V s  + V c  + V  p (1) The shear resistance provided by the transverse reinforcement truss mechanism depends on the yield stress of the transverse reinforcement and the number of layers of transverse reinforcement crossed by the flexure-shear crack. For a circular column with circular hoops or spirals, the contribution of the transverse reinforcement to the column shear strength is given by (2) where clb is the cover to the longitudinal bar, c is the depth of the neutral axis, θ is the angle of the flexure-shear crack (for assessment of existing structures, a value of θ = 30 degrees is recommended); and A sp , d sp ,  f  yh , and s are the cross section area, diameter, yield stress, and spacing of the transverse reinforcement, respectively. The main component of the concrete shear-resisting mechanism is provided by the aggregate interlock between the rough flexure-shear cracks. In plastic hinge regions, the strength of aggregate interlock reduces as the flexure-shear cracks widen with increasing ductility. The strength is also dependent on the aspect ratio (  M  / VD) and the ratio of longitudinal reinforcement ρ l . Equations (3) through (6) are used to calculate the strength of the concrete shear- resisting mechanism. V s π 2 -- -  A sp  f  yh  D cl b d sp c + s ------- --------- -------- -------- ------- -cot  θ ( ) = Title no. 106-S42 Seismic Behavior of Shear-Dominated Reinforced Concrete Columns at Low Temperatures by Luis A. Montejo, Mervyn J. Kowalsky, and Tasnim Hassan

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ACI Structural Journal/July-August 2009 445

 ACI Structural Journal, V. 106, No. 4, July-August 2009.MS No. S-2007-377 received November 12, 2007, and reviewed under Institute

publication policies. Copyright © 2009, American Concrete Institute. All rightsreserved, including the making of copies unless permission is obtained from the copyrightproprietors. Pertinent discussion including author’s closure, if any, will be published in theMay-June 2010 ACI Structural Journal if the discussion is received by January 1, 2010.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

The most important consideration for structures in seismically

active cold regions is the danger of brittle failure due to acombination of extreme cyclic load reversals and very lowtemperatures. To identify the effect of low temperatures on theseismic behavior of shear-dominated columns, two pairs of reinforced concrete squat columns were tested under cyclic

load reversals while subjected to freezing (–36 °C [–33 °F]) and room temperatures (22 °C [72 °F]). It was found that cold specimens exhibited an increase in the shear strength and elastic stiffness. Existing models for assessment and design of 

shear strength were evaluated based on the experimental resultsobtained. It is concluded that current models are conservative for low temperature conditions even if the appropriate low temperaturematerial properties are used.

Keywords: column; ductility; seismic; strength; temperature.

INTRODUCTIONPast research1,2 has shown that reinforced concrete (RC)

columns subjected to cyclic reversals and low temperaturesundergo a gradual increase in strength and stiffness that issometimes coupled with a reduction in displacementcapacity. All the units tested in the past,1,2 however, wereflexurally dominated. Therefore, not much can be saidregarding the effect of low temperatures and cyclic loads onthe shear strength of RC columns. Note that due to its brittle

nature, shear is regarded as a mode of failure that should beavoided in RC design.3  To determine the effect of lowtemperatures on the seismic behavior of shear-dominatedRC columns, two pairs of squat columns where tested underreversed cyclic loading. The only variable between columnsof the same pair was the temperature of the specimen duringtesting: one of the columns was tested at room temperature(22 °C [72 °F]) while the other was tested at –36 °C (–33 °F).Differences between each pair of columns were the ratios of transverse and longitudinal reinforcement, which weredesigned with the aim of achieving shear failures at lowlevels of ductility (brittle shear failure) and high levels of ductility (ductile shear failure).

RESEARCH SIGNIFICANCEMany moderate to high seismic zones are located in

regions where temperatures may drop to levels that mayhave an adverse effect on the ductility of the constituentmaterials and structural member. In the U.S., for example,Alaska is by far the coldest and one of the most highly activeseismic regions. To the authors’ knowledge, however, this isthe first large-scale testing program aimed to identify theeffect of low temperatures on the seismic behavior of shear-dominated RC columns. Results presented in this paper willhopefully be of value in the seismic design and assessmentof RC structures in cold regions.

THEORETICAL SHEAR STRENGTHThe test units were designed to fail by shear at different

levels of ductility. Theoretical strengths were calculatedusing the revised UCSD shear model.4 The original UCSDmodel included the degradation of concrete strength withductility, whereas the effect of axial load is accounted forseparate from the concrete contribution to shear strength.The revised model also accounts for the effect of concretecompression zone on the mobilization of transverse steel andthe influence of the aspect ratio and the longitudinal steelratio on the strength of the concrete shear-resisting mechanism.The shear strength capacity of the member is expressed as thesum of three separate components, as shown in Eq. (1),where V s  represents the shear capacity attributed to thesteel truss mechanisms, V c  represents the strength of theconcrete shear-resisting mechanism, and V  p represents thestrength attributed to the axial load

V  = V s + V c + V  p (1)

The shear resistance provided by the transverse reinforcementtruss mechanism depends on the yield stress of the transversereinforcement and the number of layers of transversereinforcement crossed by the flexure-shear crack. For a circularcolumn with circular hoops or spirals, the contribution of the

transverse reinforcement to the column shear strength is given by

(2)

where clb is the cover to the longitudinal bar, c is the depthof the neutral axis, θ is the angle of the flexure-shear crack (for assessment of existing structures, a value of θ = 30 degreesis recommended); and Asp, d sp, f  yh, and s are the cross sectionarea, diameter, yield stress, and spacing of the transversereinforcement, respectively.

The main component of the concrete shear-resistingmechanism is provided by the aggregate interlock between

the rough flexure-shear cracks. In plastic hinge regions, thestrength of aggregate interlock reduces as the flexure-shearcracks widen with increasing ductility. The strength is alsodependent on the aspect ratio ( M  / VD) and the ratio of longitudinal reinforcement ρl. Equations (3) through (6)are used to calculate the strength of the concrete shear-resisting mechanism.

V sπ2--- Asp f  yh

 D clb d sp c–+–

s----------------------------------------cot  θ( )=

Title no. 106-S42

Seismic Behavior of Shear-Dominated Reinforced Concrete

Columns at Low Temperatures

by Luis A. Montejo, Mervyn J. Kowalsky, and Tasnim Hassan

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ACI Structural Journal/July-August 2009446

(3)

(4)

(5)

(6)

In Eq. (4), µ f  is the ductility ratio based only on flexuraldeformations. For columns in single curvature, M  / VD = L /  D,where L is the cantilever length and D is the column diameter.

The shear component V  p , due to the axial load P, isexpressed as the horizontal component of the diagonalcompression strut that forms between the ends of the column.For columns in single curvature, it is calculated using

(7)

V c   αβγ  f c′ 0.8 Ag( )=

0.05   γ 0.37 0.04µ f  0.29≤–=≤

1   α 3  M VD-------- 1.5≤–=≤

β 0.5 20ρt  1≤+=

V  p P D c–2 L

------------- P 0>=

Equations (1) through (7) are given in SI units as presented bythe authors.4 Note that these equations are to be used for theassessment of the shear strength of existing structures. For thedesign of new structures, a more conservative approach is used:the axial load component is reduced by 15%, the angle of theflexure-shear crack is incremented to 35 degrees, and a shearstrength reduction factor of 0.85 is applied. Figure 1 illustratesthe assessment of shear strength according to the revised UCSDmethod; the point of shear failure, if any, is given by theintersection between the force-displacement response and the

shear strength envelope (Eq. (1)).

EXPERIMENTAL PROGRAMThe test matrix is presented in Table 1 and the geometric

properties of the test units are shown in Fig. 2. For all fourcolumns, the cantilever length was 762 mm (30 in.) and thediameter was 419 mm (16.5 in.), that is, all the columns havea moment-to-shear ratio of 1.8. Longitudinal and transversesteel were designed to ensure shear failure at different levelsof ductility. The ductile shear units (DSH-87A and DSH-87C)were reinforced with eight No. 7 bars and a No. 3 spiralspaced at 102 mm (4 in.). The brittle shear units (BSH-89Aand BSH-89C) were reinforced with eight No. 9 bars andNo. 3 spiral spaced at 145 mm (5.7 in.). The last letter in the

name of each unit indicates if the test was performed atambient (DSH-87A and BSH-89A) or cold (DSH-87C andBSH-89C) temperature.

Test setupThe test setup is presented in Fig. 3. The columns were

tested inside of an environmental chamber that is equippedto lower the temperature to a desired level and maintain itduring testing of the specimen. Due to the space constraintsof testing inside an environmental chamber, the columnswere tested in a horizontal position. Four D 35 mm (1-3/8 in.)post-tensioning bars were placed through the column footingand the strong floor to anchor the specimen. Each bar waspost-tensioned to 400 kN (90 kips). Lateral load was applied

using an actuator with a capacity of 500 kN (112 kips). Anextension was designed to transmit the force from theactuator to the specimen inside the environmental chamber.Two hydraulic jacks were used to apply the axial load; both jacks were connected in parallel to a single pump todistribute the pressure uniformly to both sides of thecolumn. A constant pressure valve maintained constant axialload during testing to within ±10% of the applied load.

 ACI member Luis A. Montejo  is a Structural Engineer at Bechtel Corporation,

Frederick, MD. He received his BS from the Universidad Del Valle, Cali, Colombia;

his MS from the University of Puerto Rico at Mayagüez, Mayagüez, Puerto Rico;

and his PhD from the Department of Civil, Construction, and Environmental Engi-

neering at North Carolina State University, Raleigh, NC, in 2008. His research

interests include structural and geotechnical earthquake engineering and engineering

seismology.

 ACI member Mervyn J. Kowalsky is an Associate Professor in the Department of Civil, Construction, and Environmental Engineering at North Carolina State University.

 He is a member of ACI Committees 213, Lightweight Aggregate and Concrete;

341, Earthquake-Resistant Concrete Bridges; 374, Performance-Based Seismic Design of Concrete Buildings; and Joint ACI-ASCE-TMS Committee 530, Masonry

Standards Joint Committee. His research interests include earthquake engineeringand seismic design of concrete and masonry structures.

Tasnim Hassan is an Associate Professor in the Department of Civil, Construction,

and Environmental Engineering at North Carolina State University. He received his

 BS from Bangladesh University of Engineering and Technology, Dhaka, Bangladesh;

his MS from the University of Arizona, Tucson, AZ; and his PhD from the University

of Texas at Austin, Austin, TX. His research interests include solid mechanics, fatigue

and failure of steel and concrete structures, and constitutive modeling.

Fig. 2—Geometric properties on test units.

Fig. 1—Assessment of shear strength.

Fig. 3—Test setup and instrumentation.

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ACI Structural Journal/July-August 2009 447

InstrumentationTemperature variations inside the specimen were monitored

with three imbedded thermocouple wires placed in the twomain longitudinal bars and the section core (refer to inset inFig. 4). Temperatures reported in Table 1 are the average of the temperatures recorded during the test by the threethermocouples. All applied loads were measured bycalibrated load cells. Axial loads reported in Table 1 are theaverage of the summation of the values recorded by the loadcells placed in each of the two bars used to apply the axial

load. Deflections at the point of lateral load application andintermediate column deflections were recorded by stringpotentiometers. Linear potentiometers were installeddiagonally, horizontally, and vertically as shown in Fig. 3.This enabled computation of the column shear and flexuredeformation components. Strains in the longitudinal andtransverse reinforcement were monitored by means of electrical resistance strain gauges.

Material propertiesAll four columns were cast from the same batch of 

concrete. Table 2 shows the concrete compressive strengthsat different ages and temperatures. To determine theconcrete compressive strength at low temperatures, concrete

cylinders with an imbedded thermocouple wire were placedinside the environmental chamber during the testing of thecold specimens and tested after the column itself was tested.As the cylinders were tested outside the chamber, however,the temperature in the cylinders gradually increased duringthe tests. Compressive strength at the desired temperature

was then extrapolated using the equation proposed byBrowne and Bamforth5

(8)

0 °C (32 °F) > T  > –120 °C (–184 °F)

where w  is the concrete moisture content. For example, if  f c′(20 °C [68 °F]) = 27.6 MPa (4 ksi) and f c′ (–26 °C [–15 °F]) =34.5 MPa (5 ksi), then using Eq. (8), w = 3.2% and thecompressive strength at the average temperature of thecolumn during the test is estimated to be f c′(–36 °C [–33 °F]) =27.6 – (–36)(3.2)/12 = 37.2 MPa (5.4 ksi).

Tension tests were performed on the longitudinal andtransverse steel at room temperature. Figure 5 shows theresults obtained for the longitudinal bars. It is seen that, eventhough both sizes of bars used (No. 7 and No. 9) weremarked to be of the same type (ASTM A615), the stress-strain behavior is quite different. Figure 6 shows the resultsobtained for the ASTM A706 spirals; note that there is no definedyield plateau for the spirals as they have been previously deformedpast the onset of strain hardening in the forming process. Forpurposes of analysis, the yield stress of the spirals was estimated to

be equal to the maximum tensile stress divided by 1.4. Table 3shows the key properties obtained during the tests. Lowtemperature strengths were estimated to be ~11% larger than thatexhibited at room temperature.1

Testing procedureThe cooling process of the cold specimens was started

26 hours before the application of the lateral load. Duringthis time and through the entire test, the ambient temperature

 f c′ T ( )  f c′ 20 °C 68 °F[ ]( ) Tw 12 ⁄ –=

Table 1—Test matrix

UnitTemperature,

°C (°F) BehaviorLongitudinal

steel/ratioTransversesteel/ratio

Axialload/ratio

DSH-87A 22 (72) Ductileshear

8 No. 72.2%

No. 3 at102 mm (4 in.)

0.8%

142 kN(32 kips)

3.7%

DSH-87C –36 (–32)Ductileshear

8 No. 72.2%

No. 3 at102 mm (4 in.)

0.8%

130 kN(29 kips)

2.5%

BSH-89A 22 (72)Brittleshear

8 No. 93.8%

No. 3 at145 mm (5.7 in.)

0.6%

135 kN(30 kips)

3.5%

BSH-89C –36 (–32)Brittleshear

8 No. 93.8%

No. 3 at145 mm (5.7 in.)

0.6%

135 kN(30 kips)

2.6%

Fig. 4—Temperature variations during testing of DSH-87C.

Table 2—Concrete properties

Days after casting Average strength, psi Temperature, °C (°F)

7 2965 ~23 (74)14 3960 ~23 (74)

21 4000 ~23 (74)

28 4045 ~23 (74)

250 (DSH-87A test day) 3985 ~23 (74)

265 (BSH-89A test day) 4000 ~23 (74)

274 (DSH-87C test day) 4845 –26 (–15)

286 (DSH-89C test day) 5040 –26 (–15)

287 (DSH-89C warm test) 3990 ~23 (74)

Warm test prediction 4000 ~23 (74)

Cold test prediction (Eq. (8)) 5400 –36 (–32)

Note: 1 MPa = 145 psi.Fig. 5—Stress-strain relation for longitudinal reinforcement.

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448 ACI Structural Journal/July-August 2009

inside the environmental chamber was set to –40 °C (–40 °F).Figure 4 shows the temperature variations recorded duringthe testing of DSH-89C. Although the core of the columnwas ~3 °C (5 °F) warmer than the longitudinal bars, it is seenthat temperatures remained constant during the test. Similarresults were obtained for BSH-89C.

Each pair of identical columns was subjected to the samelateral displacement pattern of increasing magnitude. Theload protocol consisted of an initial load control stage,followed by displacement control cycles after the theoretical

force to cause first yield of the longitudinal bars was reached.As shown in Fig. 7, three complete cycles of displacement atductility factors of µ =1, 1.5, 2, 3, 4, 6, and 8 were imposed,unless the column failed earlier. The displacement ductilityratio µ is calculated as the ratio between the displacement ∆and the equivalent yield displacement ∆ y of the column. Theequivalent yield displacement is determined by extrapolationof the average of the displacements recorded in eachdirection (∆′ y1  and ∆′ y2) at the theoretical lateral force levelrequired for first yield of the longitudinal bars, F  y′ , to theideal flexural capacity F n (defined as the force at which thecover concrete reaches a compression strain of 0.004), thatis, ∆ y = 0.5(∆′ y 1 + ∆′ y 2)(F n / F ′ y ).

TEST RESULTSForce-displacement responseThe measured lateral force-displacement hysteresis loops

for the four column tests are displayed in Fig. 8. Also shown

Table 3—Reinforcing steel properties

Description

Measured at room temperature Estimated for –38 °C (–37 °F)

Yield strength, MPa (ksi) Ultimate strength, MPa (ksi) Yield strength, MPa (ksi) Ultimate strength, MPa (ksi)

Longitudinal bars No. 9 558 (81) 703 (102) 627 (91) 778 (113)

Longitudinal bars No. 7 442 (64) 675 (98) 490 (71) 741 (108)

Spiral 469 (68) 655 (95) 524 (76) 723 (105)

Fig. 6—Stress-strain relation for transverse reinforcement.

Fig. 7—Load protocol applied to test specimens. Fig. 8—Hysteretic loops from column tests.

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ACI Structural Journal/July-August 2009 449

Fig. 9—Average first cycle envelopes. Fig. 10—Average envelope for each of three cycles.

in this figure are the theoretical lateral force level corre-sponding to first yield of longitudinal reinforcement F ′ y  andto the ideal flexural capacity F n calculated using the appropriatetemperature-dependent material properties. It is seen that thecold ductile shear specimen DSH-87C (Fig. 8(b)) exhibitedstable hysteretic loops up to the first cycle of µ8, whereas thecompanion room temperature specimen DSH-87A (Fig. 8(a))failed after the first cycle at µ6, that is, the cold specimenwas able to sustain cyclic deformations 33% larger than thewarm unit. The envelopes to the hysteretic response were

obtained for each of the first, second, and third cycle of loading. In each case, the envelope was obtained by averagingthe responses in each direction of loading. If the average firstcycle envelopes are compared (Fig. 9(a)), it is noticed thatthe cold unit exhibited an average increase of 20% in thelateral strength and 56% in the elastic stiffness whencompared to the room temperature unit. Also from Fig. 9(a), itis seen that strength degradation associated with increasinglevels of lateral demand started at ductility 3 for both specimens.If the average envelope for each of the three cycles iscompared (Fig. 10(a)), however, it is noticed that strengthdegradation over repetitive cycles at the same level of ductilityis more severe in the warm unit compared to the cold unit.

Before analyzing the results shown in Fig. 8(c) and (d) for

the brittle shear columns (BSH-89A and BSH-89C), it isimportant to mention that during testing of the cold unitBSH-89C, the maximum load capacity of the actuator (500 kN[112.5 kips]) was reached at ~µ1.5. After three cycles at~µ1.5, strength degradation was minimal and the test wasstopped. To verify that the increase in strength was effectivelydue to the cold temperature effect (and not perhaps to aninitial larger concrete strength in this column) the test wascontinued the next day at room temperature (shown as dottedline in Fig. 8(d)). The column was first subjected to one morecycle at µ1.5, and the recorded lateral load was 414 kN

(93 kips). After this cycle, the specified load protocol wasfollowed. Comparison of the average first peak envelopes(Fig. 9(b)) show that up to µ1.5 (when the cold test wasstopped), the cold unit exhibited an increase in the shearstrength of 32% when compared to the room temperatureunit. An increase of 35% in the elastic stiffness at lowtemperatures is also noticed from Fig. 9(b). Also, up to µ1.5strength degradation over repetitive cycles at the same levelof ductility was found to be more severe in the warm unit(Fig. 10(b)).

Column curvatures and equivalent plastichinge lengths

Using results from linear potentiometers mounted on theextreme tension/compression faces of the column (Fig. 3),average curvatures over the potentiometer gauge lengthswere obtained by dividing the rotation indicated in thepotentiometers by the gauge length. Note that the averagecurvatures measured in this manner include bar slipdeformations in addition to flexural deformations as acomponent due to strain penetration was included in thegauge length of the bottom cell. Typical results are presentedin Fig. 11(a) and (b) in the form of curvature profiles. Alsoshown in these figures are theoretical curvature distributions

for first yield of the longitudinal reinforcement (φ y′ ). It isseen that curvature distributions were not affected by thetemperature of the specimen during the test.

Using the curvatures calculated from the linear potentiometerdata, an equivalent plastic hinge length can be defined byassuming that the post-yield deformation of the column isachieved by the formation of a plastic hinge of length  L p atthe base. Values of L p are calculated separately for the pulland push directions, and the average values are displayed in

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450 ACI Structural Journal/July-August 2009

Fig. 12. It is seen that L p did not change when the temperature inthe specimen was dropped to –36 °C (–33 °F). Note that inthe case of BSH-89C, the only value of  L p obtained at lowtemperature is that at µ1.5 (as mentioned previously, the coldtest was stopped at µ1.5 as the actuator reached its maximum

load capacity); all other values were obtained at roomtemperature conditions. Note that a reduction in the equivalentplastic hinge length was observed in prior flexurally dominatedRC columns tested at sub-freezing temperatures,1,2 and thisreduction was identified as the main factor for the cold RCcolumns having a reduced displacement capacity whencompared to RC columns tested at room temperatures. It isbelieved that such a reduction was not observed in the shear-dominated members tested at low temperatures because thecontribution of shear-induced deformation into the total

measured deflection was quite considerable (~30%),whereas it was negligible for the flexural members. Also, thereduced clear length of the column caused the shear and flexuralcracks to cover the entire length of the column (Fig. 13 and14), leaving no space for a possible reduction in the spreadof plasticity of the columns tested at low temperatures.

Dissipative propertiesArea-based equivalent viscous damping σ( AB) is calculated

for each force-displacement hysteresis loop followingJacobsen’s approach6

(9)

where Aloop is the area inside each loop, and A RPP is the areaof a rigid, perfectly-plastic member with the same maximumstrength and the same maximum displacement in each directionas the actual member. Damping values obtained using Eq. (9)need to be corrected before they can be used in directdisplacement-based design,7 as they may overestimate theeffective equivalent viscous damping for systems with highenergy absorption. Appropriate levels of ξ have been calibratedfor different hysteretic rules to give the same peak displacementsas the hysteretic response using inelastic time history analysesITHA.8,9  Correction factors to be applied to ξ( AB) arecalculated using Eq. (10).2,7 The results obtained for ξ in the

first cycle at each level of demand are displayed in Fig. 15.It is seen that the differences between the ξ( AB) obtained forthe cold and room temperature are minimal and that differences

ξ  AB( ) 2

π--- Aloop

 A RP P

------------=

Fig. 11—Curvature profiles.

Fig. 12—Equivalent plastic hinge lengths. Fig. 13—Condition of DSH units atµ 2.

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ACI Structural Journal/July-August 2009 451

vanish when the design values are compared. Shown indashed lines in these figures are the design damping valuesproposed by Dwairi and Kowalsky8 for bridge columns(Eq. (11)). It is seen that values obtained from Eq. (11) canbe used in the case of shear-dominated columns.

(10)ξdesign

ξ  AB( )--------------- 0.53µ 0.8+( )ξ  AB( )   µ 40 0.4+ ⁄ ( )–

=

(11)

Strains on transverse reinforcementEach unit was instrumented with 12 strain gauges placed

on the transverse reinforcement at three different levels toallow the generation of strain profiles. Only a subset of thesestrain gauges worked properly during the testing of the coldspecimens, presumably due to the severe freezing conditionsthey were exposed to. Because not enough data were available

to generate strain profiles for the cold units, comparison of the strains induced in the transverse reinforcement in thecold and room temperature units is carried out based on strainhistories as shown in Fig. 16. Strains presented in Fig. 16 wererecorded by strain gauges placed on the transverse reinforcement

ξdesign 50  µ 1–

πµ------------

=

Fig. 15—Area-based (AB) and design hysteretic damping. Fig. 16—Shear-induced strain responses.

Fig. 14—Condition of BSH units at µ 1.5.

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452 ACI Structural Journal/July-August 2009

at the side of the column (refer to inset in the figure) ~270 mm

(10.6 in.) and 50 mm (2 in.) from the column base for theDSH-87 and BSH-89 units, respectively. The strains shown

in Fig. 16 can be considered to be mostly shear-inducedstrain because of the strain gauge location at the midcolumndepth. For both type of units, it can be noticed that strains onthe transverse reinforcement are activated earlier on theroom temperature specimens, which implies that theconcrete at low temperatures was able to sustain larger shearstresses. This can also be inferred by examining the condition of the specimens when subjected to the same level of lateraldemand in Fig. 13 and 14. It is seen that at the same level of lateral displacement there is more damage induced in the

concrete of the room temperature specimen than in cold testunit. These observations will be corroborated in the nextsection when the contribution of the concrete component tothe total shear strength of the columns is calculated.

Shear strength componentsThe total shear V s carried by the transverse steel is usually

calculated from the hoop strains measured at differentheights of the column. As mentioned previously, themajority of strain gauges placed on the transverse steel of thecold units did not work properly. Therefore, average strainsin the spirals were calculated from the shear deformationsmeasured in the specimen and then used to calculate V s at adifferent level of lateral demand during the test. The axial

load contribution to shear strength, V  p, is calculated usingEq. (7); the neutral axis depth at different levels of lateraldemand is obtained from a moment-curvature analysis. Theconcrete contribution V c is then obtained by subtracting fromthe total shear the other two components (V s and V  p). Resultsobtained are displayed in Fig. 17. Shown in this figure arealso the shear force at which inclined flexure-shear crackingwas first observed (V cr ) and the shear strength provided bythe concrete according to Eq. (3) using correspondingtemperature-dependent material properties. It is seen that theconcrete contribution V c  is largely increased in the unitstested at sub-freezing temperatures, and peak contributionsincreased by 30% and 34% in the DSH and BSH units,respectively. The predicted V c is in close agreement with that

exhibited by the room temperature units; however, itunderestimates the improvement in the concrete shear-resisting mechanism at low temperatures, although lowtemperature material properties were used for the prediction.Whereas the close agreement with the theoretical model maysimply be coincidental, it is important to note that the relativeincrease in the strength of the concrete shear-resistingmechanism at low temperatures is larger than that expectedfrom the improvement in the compressive strength.

COMPARISON WITH PREDICTIVE MODELSThe shear strength envelopes for the four units were calculated

using the computer code  CUMBIA10  and the appropriatetemperature-dependent material properties, and plotted inFig. 18. Also shown in this figure are the predicted force-displacement response calculated using the equivalentplastic hinge method7 and the average first peak envelopeFig. 17—Column shear capacity components versus ductility.

Table 4—Experimental and design shear strengths

Unit T , °C (°F) V exp, kN (kips) V a, kN (kips) V d 1, kN (kips) V d 2, kN (kips) V exp / V a V exp / V d 1 V exp / V d 2

DSH-87A +22 (+72) 297 (66.7) 288 (64.7) 162 (36.3) 202 (45.4) 1.03 1.84 1.47

DSH-87C –36 (–33) 356 (80) 325 (73) 181 (40.7) 229 (51.5) 1.10 1.97 1.55

BSH-89A +22 (+72) 387 (87) 363 (81.6) 238 (53.4) 261 (58.7) 1.07 1.63 1.48

BSH-89C –36 (–33) 500 (112) 416 (93.5) 271 (60.9) 299 (67.2) 1.20 1.84 1.67

Note: V exp is experimental shear strength; V d 1 is AASHTO design shear strength11; V a and V d 2 are UCSD revised model assessment and design shear strength,9 respectively.

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ACI Structural Journal/July-August 2009454

displacement capacity. In the case of the ductile shear units,the cold specimen sustained cyclic deformations 33% largerthan the warm unit. The brittle shear cold test units could notbe tested to failure because the maximum load of the actuatorwas reached. Nonetheless, based on the informationcollected up to µ1.5 and the condition of the specimen at thispoint, a similar behavior can be anticipated. The reduction atlow temperatures in the displacement capacity of the flexural-dominated columns was attributed mainly to a reduction inthe spread of plasticity and the equivalent plastic hinge

length of the cold flexural units; however, for the shear-criticalmembers, the increased shear capacity allowed for a largerlateral displacement before failure.

The increase at low temperatures in the displacementcapacity of the shear-dominated columns can be explainedby the increase at low temperatures of the shear strength(>20% at –40 °C [–40 °F]), which is larger than the increasein flexural strength (~15% at –40 °C [–40 °F]).1,2 The shearstrength envelope at low temperatures is then shifted upwardby a greater proportion than the force-displacement response(Fig. 1), thus delaying the onset of shear failure.

CONCLUSIONSThis paper presented the results from the reversed cyclic

testing of four shear-dominated columns subjected to room(22 °C [72 °F]) and low (–36 °C [–33 °F]) temperatureconditions. Specimens tested at low temperatures exhibitedan increase in its shear strength; the amount of this increasewas larger in the brittle shear units (32%) than in the ductileshear units (20%).

Even though it has been shown that flexural strengthincreases at low temperatures,1,2  thus resulting in anincreased shear demand, the shear capacity increases at aneven higher proportion, thus delaying the onset of shearfailure at low temperatures.

Specimens tested at low temperatures also exhibited anincrease of 56% (ductile units) and 35% (brittle units) in the

elastic stiffness. A slight reduction in the strength degradationover repetitive cycles at the same level of ductility wasnoticed when the specimens were tested at low temperatures.No major changes were noticed in the dissipation propertiesof the specimens tested at low temperatures.

The observed increase in shear strength of the columnstested at low temperatures was expected, as past research hasshown mechanical properties of plain concrete and reinforcingsteel to improve at low temperatures.1 Current availablemodels4,11 for assessment and design of shear strength in RCcolumns under seismic actions are conservative when thecolumns are exposed to sub-freezing temperatures, even if 

the increase in concrete compressive strength and steel yieldstress due to low temperatures are taken into account. It wasshown that the assessment shear model4  was mainlyunderpredicting the contribution of the concrete shear-resisting mechanism, presumably because the concretetensile and fracture properties are not taken directly intoaccount by the method but through the compressive strength;however, past research1 has shown tensile strength and fractureproperties to improve at low temperatures in a proportion evenlarger than is the case for the compressive strength.

ACKNOWLEDGMENTSThe research described in this paper was funded by the Alaska Department of 

Transportation (AKDOT). The effective feedback from E. Marx of AKDOT ismuch appreciated. The experimental program was carried out at the ConstructedFacilities Laboratory (CFL) at North Carolina State University and benefitedfrom the support of the entire technical staff at CFL. Special thanks are extendedto CFL Technician J. Atkinson for his continuous support during the constructionand testing of the specimens. The authors also want to thank the reviewers fortheir thoughtful comments, which improved the quality of the paper.

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of Flexural Dominated Reinforced Concrete Bridge Columns at LowTemperatures,”  Journal of Cold Regions Engineering, ASCE, V. 23, No. 1,Mar. 2009, pp. 18-42.

2. Montejo, L. A.; Sloan, J. E.; Kowalsky, M. J.; and Hassan, T., “CyclicResponse of Reinforced Concrete Members at Low Temperatures,” Journal

of Cold Regions Engineering, ASCE, V. 22, No. 3, Sept. 2008, pp. 79-102.3. Paulay, T., and Priestley, M. J. N., Seismic Design of Reinforced 

Concrete and Masonry Buildings, John Wiley & Sons, Inc., New York,1992, 713 pp.

4. Kowalsky, M. J., and Priestley, M. J. N., “Improved Analytical Modelfor Shear Strength of Circular Reinforced Concrete Columns in SeismicRegions,” ACI Structural Journal, V. 97, No. 3, May-June 2000, pp. 388-396.

5. Browne, R. D., and Bamforth, P. B., “The Use of Concrete forCryogenic Storage: A Summary of Research Past and Present,” 1stInternational Conference on Cryogenic Concrete, New Castle, 1981,pp. 135-166.

6. Jacobsen, L. S., “Steady Forced Vibrations as Influenced byDamping,” ASME Transactions, V. 52, No. 1, 1930, pp. 169-181.

7. Priestley, M. J. N.; Calvi, G. M.; and Kowalsky, M. J.,  Direct 

 Displacement Based Seismic Design of Structures, IUSS Press, Pavia, Italy,2007, 721 pp.

8. Dwairi, H., and Kowalsky, M. J., “Equivalent Viscous Damping inSupport of Direct Displacement Based Design,”  Journal of Earthquake

 Engineering, V. 11, No. 4, 2007, pp. 512-530.9. Grant, D. N.; Blandon, C. A.; and Priestley, M. J. N., “Modeling

Inelastic Response in Direct Displacement Based Design,” Report  2005/03,IUSS Press, Pavia, 2005, 104 pp.

10. Montejo, L. A., and Kowalsky, M. J., “CUMBIA—Set of Codes forthe Analysis of Reinforced Concrete Members,” CFL Technical Report No. IS-07-01, Department of Civil, Construction and EnvironmentalEngineering, North Carolina State University, Raleigh, NC, 2007, 43 pp.

11. Association of State Highway and Transportation Officials(AASHTO), “Guide Specifications for LRFD Seismic Bridge Design,”

 NCHRP Project  20-07, Task 193, National Cooperative Highway ResearchProgram, Transportation Research Board, 2007, 231 pp.