Structural Engineering and Mechanics, Vol. 41, No. 1 (2012) 43-65

43Concrete contribution to initial shear strengthof RC hollow bridge columns
Ick-Hyun Kim1a, Chang-Ho Sun1b and Myoungsu Shin2*
1

University of Ulsan, Department of Civil and Environmental Engineering,
93 Daehak-ro, Nam-gu, Ulsan 680-749, South Korea
2
Ulsan National Institute of Science and Technology (UNIST), School of Urban and Environmental
Engineering, 100 Banyeon-ri, Eonyang-eup, Ulju-gun, Ulsan 689-798, South Korea(Received April 20, 2011, Revised October 4, 2011, Accepted November 23, 2011)
Abstract. The primary objective of this study was to identify concrete contribution to the initial shear
strength of reinforced concrete (RC) hollow columns under lateral loading. Seven large-scale RC
rectangular hollow column specimens were tested under monotonic or cyclic lateral loads. The mostimportant design parameter was column length-to-depth aspect ratio ranging between 1.5 and 3.0, and theother test variables included web area ratio, hollow section ratio, and loading history. The tests showedthat the initial shear strength reduced in a linear pattern as the column aspect ratio increased, and one
specimen tested under cyclic loading achieved approximately 83% of the shear strength of the companion
specimen under monotonic loading. Also, several pioneering shear models proposed around the world, allof which were mainly based on tests for columns with solid sections, were reviewed and compared withthe test results of this study, for their possible applications to columns with hollow sections. After all, anempirical equation was proposed for concrete contribution to the initial shear strength of RC hollow
columns based on fundamental mechanics and the test results.
Keywords: hollow column; shear strength; aspect ratio; displacement ductility; axial load

1. Introduction
For reinforced concrete (RC) bridge construction, the use of hollow piers may introduce
significant benefits in comparison to piers with solid sections. A hollow section with a larger depth
and concentrated flanges carries a significantly larger sectional moment-of-inertia than solid sections
with a similar area. The use of hollow bridge piers reduces the design seismic force owing to thesmaller mass, so that it may guarantee a great savings in materials and equipment during theconstruction of such piers as well as their foundations, and may also reduce problems related to thehydration of massive concrete.
Unlike columns used in building frames that are typically designed following the weak beamstrong column philosophy for seismic resistance (Paulay and Priestley 1992), bridge columns are*Corresponding author, Assistant Professor, E-mail: msshin@unist.ac.kraProfessorbResearch Professor

44

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu ShinFig. 1 ATC-6 model (1981) for relationship between shear strength and ductility

Fig. 2 Shear flow in thin-walled tube sections: (a) rectangular and (b) circular sections (adapted from
Hartsuijker and Welleman 2007)

expected to have ductile flexural hinges at their bottoms under design-level earthquakes so as tofunction as primary sources for energy dissipation (Priestley et al. 1996). Along with thedevelopment of column hinging, brittle shear failure of bridge columns should be prevented to
avoid disastrous collapse of the superstructure. Special attention should be placed on such plastic
hinges, in that the shear strength of RC columns degrades when the flexural ductility demand
increases (ATC-6 1981). In other words, the shear performance of RC columns strongly depends on
the rate of shear strength degradation due to increasing ductility (Howser et al. 2010) as well as theinitial shear strength before the degradation, Vi, as illustrated in Fig. 1.
Differences exist between the force-resisting mechanisms of solid and hollow columns subjectedto lateral loading. The transmission of shear flow in hollow sections could be very similar to that inthin-walled tube sections (see Fig. 2), depending on the flange slenderness ratio. Also, the relatively

Concrete contribution to initial shear strength of RC hollow bridge columns

45

small thickness between the inner and outer faces of a hollow section limits the available area ofconfined concrete core, which appears related to the shear capacity of hollow columns under cyclicloads.
Numerous studies (Ang et al. 1989, Aschheim and Moehle 1992, Wong et al. 1993, Prestley et al.
1994, Xiao and Martirossyan 1998, Kowalsky and Priestley 2000, Maekawa and An 2000, Sezen
and Moehle 2004, Howser et al. 2010) proposed analytical models for evaluating the shear strengthof RC columns under seismic forces. Recently, some researchers employed the Modified
Compression Field Theory (MCFT) to estimate the deformation capacity of RC columns (Sezen
2008, Mostafaei et al. 2009), and others used a probabilistic approach (Sasani 2007) or a neuralnetwork based model (Yang 2007, Caglar 2009) for their shear behavior. However, all of them wereprimarily based on experimental tests for columns with solid sections. Only a few studies (Yeh etal. 2002, Mo et al. 2003, Mo et al. 2004, Cheng et al. 2005) have been conducted for the seismic
performance assessment or the earthquake-resistant design of RC hollow columns. Moreover, little
investigation was made on the initial shear strength of such columns; almost all hollow column tests
reported in the literature showed relatively ductile behaviour engaging plastic hinging mechanism,
before ultimate shear failure if any. Most of the studies (Mander et al. 1984, Yeh et al. 2001, Mo etal. 2003) focused on evaluating the acceptability of different lateral reinforcement details on thestandpoint of sufficient ductility under cyclic lateral loading.
Given this concern, the current study investigated the initial shear strength of RC hollow bridge
columns subjected to monotonic or cyclic lateral loads. In particular, this study focused on assessing
concrete contribution to the column shear strength, by providing no transverse reinforcement and by
imposing no axial load. It should be noted that the tests were only to investigate the initial shear
strength, so that the specimens were designed to fail in shear before reaching their flexuralstrengths. Thus, discussions related to the effect of ductility on the column shear strength (i.e.,
reduction in the shear strength due to increasing ductility) are solely based on comparisons of theshear models proposed by others.

2. Descriptions for experimental program
2.1 Specimen details and test variables
Seven approximately ¼-scale rectangular hollow column specimens were tested in this study. The
specimens represented cantilever bridge piers subjected to lateral loading (see Fig. 3). The single
most important parameter of this experimental program was column length-to-depth aspect ratio (l/h), in which l stands for the column length from the base to the loading point and h is the column
depth. The other test variables included web area ratio, hollow section ratio, and loading pattern.
The hollow section ratio was defined as the area enclosed within interior edges of a hollow section
divided by the area within exterior edges of the section. Fig. 3 illustrates plan and elevation viewsof the test specimens, and Table 1 summarizes the design details and test variables.
In all specimens, exterior dimensions of the rectangular hollow column section were kept
unchanged; 900 mm wide and 600 mm deep. Also, the specimens were reinforced with the sameamount of longitudinal bars, twenty D19, in a single layer for simple construction. No transverse
reinforcement was provided in all specimens to clearly identify the column shear strength exerted
by concrete only. In the first four specimens (H40A1.5, H40A2.0, H40A2.5, and H40A3.0), all46

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu ShinFig. 3 Dimensions and reinforcing details of specimens (units: mm)

design details were identical except the column aspect ratio (l/h) varying between 1.5 and 3.0, as
shown in Table 1; the web area ratio was equal to 0.48, and the hollow section ratio was 0.4 inthese specimens. Each of the two specimens, H40A1.5WF1.8 and H60A1.5, was intended for a
direct comparison with H40A1.5; the former had the web area ratio of 0.67, and the latter had thehollow section ratio of 0.6. The specimen H40A2.0C had completely identical design details with
H40A2.0, but was tested under reversed cyclic displacements.
The specimens were cast in their upright position, and all specimens were cast on the same day
using an identical batch. Before casting, strain gages were installed on selected longitudinal bars at
the column-footing interface. The compressive strength of concrete was 24.6 MPa, measured after
28 days since the casting, and the measured yield strength of steel for the column reinforcement
was 340 MPa.
2.2 Test setup and loading history
Fig. 4 shows a picture of the test setup. The top of the column was linked to an actuator with aswivel connector, and the bottom was restrained by (monolithically cast with) the foundation that
was anchored to the strong floor. The specimens were statically loaded in the lateral direction at theConcrete contribution to initial shear strength of RC hollow bridge columns

47

Table 1 Specimen details and test variablesSpecimen

H40A1.5

H40A2.0

H40A2.5

Exterior faces (mm)H40A3.0

H60A1.5 H40A1.5WF1.8 H40A2.0C

900 × 600Interior faces (mm)640 × 340

740 × 440

540 × 400

640 × 340

Flange thickness
(mm)

130

80

100

130

Web thickness (mm)

130

80

180

130

Gross section area,
Ag (mm2)

322,400

214,400

324,000

322,400

Longitudinal
reinforcement ratio

0.018

0.027

0.018

0.018

Hollow section ratio
(%)

40

60

Web area ratio (%)

48.4

44.8

66.7

48.4

40

Column length, l
(mm)

900

1200

1500

1800

900

900

1200

Aspect ratio, l/h

1.5

2.0

2.5

3.0

1.5

1.5

2.0

Loading pattern
Material strengths
Main test variables

Cyclicloading

Monotonic loading

Concrete compressive strength: 24.6 MPa, Steel yield strength: 340 MPa
Aspect ratio

Fig. 4 A picture of the test setup

Hollowsectionratio

Web area ratio

Loading
pattern48

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu ShinFig. 5 Loading history for specimen H40A2.0C

Fig. 6 Cracking damage at completion of testing

top of the column, by a hydraulic actuator with a 500 kN loading capacity and a ± 300 mm linear
stroke. No column axial load was applied to exclude any potential contribution of axial load to thecolumn shear strength.
Each specimen except H40A2.0C was tested under monotonic loading until it failed in shear toshow a significant strength drop larger than 20% from the maximum load. For H40A2.0C, a total oftwenty-four displacement cycles were statically applied up to 2% drift ratio as shown in Fig. 5. Twoconsecutive same-drift cycles were tested to examine strength and stiffness degradations under
repeated loading.

Concrete contribution to initial shear strength of RC hollow bridge columns

49

Fig. 7 Angle of diagonal cracks with respect to column aspect ratio

3. Summary of test results
3.1 Cracking behavior and failure mode
Fig. 6 illustrates cracking damages observed in the specimens at the completion of testing. In all
specimens, initial inclined cracks occurred at approximately 0.4 to 0.6% drift ratio, connecting to
one corner (on the opposite side of the actuator pushing the specimen) of the column base. It isnotable that the drift ratio at the onset of inclined cracks was similar in the specimens regardless ofthe varying test parameters. The crack width gradually increased to result in a couple of major
inclined cracks until the specimen failed with a significant strength drop of more than 20% of thepeak load. Fig. 6 shows only one side of each specimen that had more apparent inclined cracks. In
all specimens, no indication or behavior related to typical flexural failure was found such asconcrete spalling or reinforcement buckling near the bottom of the column; only a couple of hairline
horizontal cracks were observed in the specimens with the column aspect ratio equal to or larger
than 2. Based on these and other observations discussed later, it was concluded that all specimens
failed in shear.
The angles of the major inclined cracks measured from the horizontal line ranged approximately
between 45 and 55 degrees, as shown in Fig. 7. In general, the specimen with the higher aspectratio showed the greater crack angle. Also, the specimen with the higher web area ratio exhibitedthe greater crack angle (compare H40A1.5 vs. H40A1.5WF1.8), while the specimen with the higher
hollow section ratio had similar cracks (compare H40A1.5 vs. H60A1.5).
3.2 Overall load-displacement response
Fig. 8 illustrates the lateral load vs. drift responses of all seven specimens. The drift ratio wasdefined as the displacement at the loading level divided by the column length (l), measured fromthe column base to the loading point. The initiation of inclined cracking indicated in Fig. 8 wasdetermined by visual observation and the onset of first yielding was by strain gage data. The lateral
stiffness of the specimen became smaller as the specimen underwent more cracking damage and/or
reinforcement yielding. In all tests, the lateral strength of the specimen was limited by shear failure,

50

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu ShinFig. 8 Load-displacement responses of specimens

and suddenly dropped by more than 20% of the maximum load achieved at between 0.8 and 1.4%
drift ratio. Table 2 summarizes the maximum load (Vc, exp) reached during each test, which wasconsidered as the shear strength of the column because all seven specimens failed ultimately due toshear. The shear strength normalized by the gross section area (Ag) or the web area (bwd) was listed
together in Table 2. Also, the possible lateral strength of each specimen (Vc, flex) was calculated
assuming that a plastic hinge due to flexure would develop at the bottom of the column, as well as
the lateral load when the calculated yield moment occurred at the base (Vc, yield) (see the first andsecond rows of Table 2). In all specimens, the measured maximum load (Vc, exp) during the test was
smaller than the calculated lateral strength (Vc, flex) based on the flexural hinging mechanism; most
specimens experienced limited yielding. This was in accordance with the conclusion that all
specimens failed due to shear with very low ductility.

Concrete contribution to initial shear strength of RC hollow bridge columns

51

Table 2 Measured and calculated lateral strengths and failure modes of specimens
Specimen

H40A1.5

H40A2.0

H40A2.5

H40A3.0

H60A1.5 H40A1.5WF1.8 H40A2.0C

Flexural strength,
Vc, flex (kN)

620

464

371

310

619

616

471

Yield strength,
Vc, yield (kN)

471

338

268

224

474

463

338

Maximum load,
Vc, exp (kN)

525

445

341

259

337

522

368

Vc, exp / Ag
(MPa)

1.63

1.38

1.06

0.80

1.57

1.62

1.14

Vc, exp / bwd
(MPa)

3.37

3.05

2.34

1.78

3.76

3.33

2.53

Vc, exp / Ae*
(MPa)

2.02

1.73

1.32

1.00

1.96

2.02

1.43

Failure modeFlexureshear

Flexureshear

Flexureshear

Flexureshear

Shear

Flexure-shear Flexure-shear* Ae: Effective area equal to 0.8 Ag

Effects of the main test variables on the lateral load-drift response were analyzed in the following.
Comparing the four specimens (H40A1.5, H40A2.0, H40A2.5, and H40A3.0) with the column
aspect ratio (l/h) varied only, the specimen with the higher aspect ratio exhibited the smaller
stiffness after initial inclined cracks appeared, and ultimately reached the smaller maximum load
(Vc, exp) at the smaller drift ratio (see Fig. 8(a)). The reduction in the shear strength (Vc, exp) was
likely in part because the confinement effect of the adjacent member (i.e., footing) was lesser incolumns with higher aspect ratios (Kowalsky and Priestley 2000), and also in part because increased
normal stress due to higher bending moment interacted with shear stress against the given tensile
capacity of concrete.
The two specimens, H40A1.5 and H40A1.5WF1.8, with different web area ratios (approximately
0.48 and 0.67 respectively) but with the same gross section area (Ag), achieved similar maximum
loads (Vc, exp) in the tests. Also, the measured shear strength (Vc, exp) divided by the gross section area
(Ag) was 1.63 and 1.62 MPa in H40A1.5 and H40A1.5WF1.8 respectively, which were reasonably
close to the values estimated by some shear models proposed earlier (see Tables 2 and 4). Based onthese results, the initial shear strength of a hollow column appears to be associated more with thegross section (Ag) than the web area (bwd).
Figs. 8(c) and 8(d) compare the lateral load-drift responses of H40A1.5 and H60A1.5, with thehollow section ratio equal to 0.4 and 0.6, respectively. H40A1.5 (with the larger section area)
certainly had the greater maximum load (Vc, exp) at about 1.4% drift ratio, which was quite larger
than 0.9% in H60A1.5. However, Vc, exp normalized by Ag was similar to be 1.63 and 1.57 MPa in
H40A1.5 and H60A1.5 respectively (see Table 2), regardless of the hollow section ratio. This
supported the conclusion that the initial shear strength of a hollow column would be dependent
more on Ag than bwd. On the other hand, the percentage of strength drop after the maximum load
was lesser in H40A1.5. This was possibly because aggregate interlocking across inclined cracks wasless effective in H60A1.5 because of the smaller web thickness. However, more tests should be

52

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu ShinFig. 9 Experimental shear strength divided by Ag or 0.8 Ag

done to reach a certain conclusion on the level of the residual strength.
In this experimental program, one specimen, H40A2.0C, was tested under reversed cyclic loading
to investigate effects of different loading histories. Fig. 8(e) compares the load-drift responses of
H40A2.0 and H40A2.0C, in which design details were exactly identical. H40A2.0C achieved thesmaller maximum load (roughly 83% of that of H40A2.0) at the smaller drift ratio. This was mostly
because H40A2.0C underwent strength and stiffness degradations due to continued increase of theprincipal tensile strain after the onset of reinforcement yielding (Stevens et al. 1991).
Fig. 9 illustrates the measured shear strength (Vc, exp) normalized by the gross section area (Ag) or theeffective area (0.8 Ag for H40A2.0C only), with respect to the column aspect ratio (l/h). The normalized
shear strength (Vc, exp/Ag or Vc, exp/0.8 Ag) decreased generally in a linear proportion to the aspect ratio.
Note that, in all specimens except H40A2.0C, the gross section area, Ag, was used, while 0.8 Ag wasused as the effective area for H40A2.0C. The two different shear areas (Ag versus 0.8 Ag) were adopted
based on the findings that the shear strength of H40A2.0C was roughly 83% of that of H40A2.0.

4. Comparison of shear models with test results
Many researchers have focused on the evaluation of the shear strength of RC columns all aroundthe world, most of which were mainly based on tests of columns with solid sections. Some of thepioneering studies on this subject were reviewed and compared with the test results, for their
possible applications to columns with hollow sections. The studies reviewed in this paper include
Aschheim and Moehle (1992), Prestley et al. (1994), Xiao and Martirossyan (1998), Kowalsky andPriestley (2000), Maekawa and An (2000), Sezen and Moehle (2004), and Howser et al. (2010).
Also, two relevant design codes, ACI 318-08 (2008) for the design of new buildings and CaltransSeismic Design Criteria (2002) for the assessment and design of bridges, were investigated, whileother earlier design approaches such as in ATC-32 (1996), ATC-40 (1996), FEMA 273 (1997),
FEMA 356 (2000), and ASCE/SEI 41-06 (2006) essentially adopted the aforesaid methods.
Important design parameters that have been considered to affect concrete contribution to the column
shear strength in the previous studies and design codes are column aspect ratio (l/h), displacement
ductility (µ), axial load (P), longitudinal reinforcement ratio (ρl), size effect, and the effective area
resistant to shear. All equations introduced in the following are written in SI units.

Concrete contribution to initial shear strength of RC hollow bridge columns

53

4.1 Aschheim and Moehle (1992)
Aschheim and Moehle (1992) proposed that concrete contribution to the shear strength of an RC
column degrades when displacement ductility demand increases. In this model, the concrete
contribution (Vc) is determined byP′
Vc = 0.3 ⎛ k + ----------------⎞ fc ( 0.8Ag )⎝ 13.8Ag⎠
4–µ
k = ----------- ;
3

0≤k≤1

(1)

(2)

Here, k is the factor accounting for the aforesaid effect of increasing displacement ductility (µ). Thismodel was intended to evaluate the shear strength at plastic hinge zones, and was later adopted in
FEMA 273 (1997).
4.2 Original UCSD shear model
According to Priestley et al. (1994), the shear strength of RC columns is attributed to thefollowing three parts: contributions by concrete, transverse reinforcement, and compressive load.
They suggested that the concrete shear strength (Vc) degrades with increasing ductility as follows:′

Vc = γ fc ( 0.8Ag )(3)Here, the γ factor is taken as 0.29 when the displacement ductility (µ) is less than 2 and 0.10 whenµ is more than 4. The γ factor linearly decreases between µ equal to 2 and 4. They noted that thestrength degradation is primarily because aggregate interlocking reduces as cracks become wider.
Another unique feature of the original UCSD model was that the contribution of axial load on thecolumn shear strength was separated from the concrete contribution.
A few years later, Xiao and Martirossyan (1998) investigated the seismic performance of highstrength concrete columns, and found that concrete shear contribution in such columns degradedmore dramatically than that predicted by the original UCSD model (1994). Based on the test results,
they proposed to modify the γ factor for the case of high-strength concrete as follows:γ = 0.29

for µ ≤ 2

(4)

γ = 0.29 – 0.12 ( µ – 2 )for 2 ≤ µ ≤ 4(5)

γ = 0.05 – 0.025 ( µ – 4 )for 4 ≤ µ ≤ 6

(6)

γ=0

for µ ≥ 6

(7)

In this model, the initial concrete contribution (for µ close to 1) is identical (i.e., γ = 0.29) to that of
the original UCSD model. They noted, however, that the proposed equation was not calibrated forhigh-strength concrete columns that underwent shear failure with µ less than 4.

54

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu Shin

Recently, Howser et al. (2010) also proposed modifications to the γ factor in the original UCSD
model (i.e., the effect of ductility on the concrete shear strength), based on a numerical parametricstudy:
γ = 0.29

for µ ≤ 2

γ = 0.29 – 0.12 ( µ – 2 )for 2 ≤ µ ≤ r

γ = 0.53 – 0.095r – 0.025µ

for r ≤ µ ≤ q

γ = 0.53 – 0.095r – 0.025q

for µ ≥ q′

r = 35ρ t – 0.011fc + 3.8′

for q ≥ r

q = –144ρt + 0.03fc + 4.3
q=r

for q < r

As implied above, the numerical results well agreed with Xiao and Martirossyan (1998) for small
ductilities, while adjustments were made in this model for large ductilities.
4.3 Revised UCSD shear model
Kowalsky and Priestley (2000) proposed three revisions to the earlier UCSD shear model ofPriestley et al. (1994). The revisions account for (1) the effect of column aspect ratio and (2) the
effect of longitudinal steel ratio on the concrete shear-resisting mechanism. The concrete
contribution (Vc) to the shear strength of RC columns is defined as′

Vc = αβγ fc ( 0.8Ag )M
α = 3 – -------- ;VD

1 ≤ α ≤ 1.5

β = 0.5 + 20ρl ≤ 1
γ = 0.29 – 0.04 ( µ – 2 ) ;0.05 ≤ γ ≤ 0.29

(8)
(9)
(10)
(11)

Here, the α factor accounts for the impact of column aspect ratio represented by M/VD, where D isthe diameter of a circular column. They noted that shorter columns would have better confinementby the adjacent joints or footings. The β factor is linearly proportional to the longitudinal steel ratio(ρl) that would affect aggregate interlocking mechanism across concrete cracks, and the γ factor
stands for the degradation of concrete shear capacity with increasing displacement ductility (µ).
4.4 Maekawa and An (2000)
Maekawa and An (2000) introduced a modification factor for the current JSCE (Japanese Society

Concrete contribution to initial shear strength of RC hollow bridge columns

55

of Civil Engineers) formula for the shear strength carried by concrete (vc, JSCE), to account for the
post-yield shear capacity of RC columns. This model integrates combined effects of column aspectratio and displacement ductility as follows:
Vc = ( 1 – k ( µ – 1 ) )vc, JSCE ( bw d )(12)1
k = ------------------------2(9 – a ⁄ d)

(13)

′ 1⁄3

⋅ βp ⋅ βn ⋅ βd ⎛ a--- ≥ 2.0⎞
⎝d
⎠

(14)

′ 1⁄2

a
⋅ βp ⋅ β n ⋅ βd ⎛ --- < 2.0⎞
⎝d
⎠

(15)

vc, JSCE = 0.9 ( fc )vc, JSCE = 0.6 ( fc )Here, the modification factor expressed as 1 – k ( µ – 1 ) is limited to 1 when µ < 1 and is taken as 0
when µ > 1 + 1/k, where k is a factor accounting for the effect of column aspect ratio (a/d). It isnoted that the effect of aspect ratio is also considered in vc, JSCE.
4.5 Sezen and Moehle (2004)
Sezen and Moehle (2004) developed a comprehensive shear model for older columns having lesstransverse reinforcement, compared with columns designed following current codes. In this model,
the concrete contribution (Vc) is affected by column aspect ratio (a/d), displacement ductility (µ),
and axial load (P), and varies in proportion to the inverse of the aspect ratio, as recommended in
the ASCE-ACI Committee 426 report (1973):⎛ 0.5 f ′P ⎞Vc = k ⎜ --------------c- 1 + ---------------------⎟ 0.8Ag′⎝ a⁄d
0.5 fc Ag⎠(16)

k = 1 when µ ≤ 2, k = 0.7 when µ ≥ 6(17)Here, the k factor decreases linearly from 1 to 0.7 for µ varying between 2 and 6. Unlike in any
other models, the k factor is also multiplied to reinforcement contribution to the shear strength of
RC columns, in that concrete damage likely leads to loss of anchorage of longitudinal andtransverse reinforcement so as to degrade the truss mechanism (Sezen and Moehle 2004). Thismethod was adopted in ASCE/SEI 41-06 (2006), the most recent report for the subject of the“seismic rehabilitation of existing buildings,” which succeeded the previous editions on the same
subject, FEMA 273 (1997) and FEMA 356 (2000).
4.6 Caltrans seismic design criteria
Unlike other design codes such as ACI 318-08 (2008) and AASHTO Specifications (2002),
Caltrans Seismic Design Criteria (2002) introduced the effect of increasing displacement ductility

56

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu Shin(µ) in determining concrete contribution (Vc) to the shear strength of RC columns:′′

Vc = F1 F2 fc ( 0.8Ag ) ≤ 0.33 fc Ag
F1 = 0.08ρs fyh + 0.305 – 0.083µ ;P
F2 = 1 + ---------------- ;13.8Ag0.025 ≤ F1 ≤ 0.25

1 ≤ F2 ≤ 1.5

(18)
(19)
(20)

Here, ρs is the transverse reinforcement ratio and fyh is the yield strength of transverse steel. The
correction factor for the level of axial load, F2, is the same as that of ACI 318-08, §11.3 applying tocolumns not designed to resist seismic forces.
4.7 ACI 318-08 shear strength equation
For the design of new buildings based on ACI 318-08, the concrete contribution (Vc) is
determined considering column aspect ratio, longitudinal reinforcement ratio, and axial load by
Vu d⎞
′
bw d
Vc = ⎛ 0.16 fc + 17ρw -------⎝
Mm ⎠

(21)

4h – d )M m = Mu – Nu (-----------------8(22)Here, ρw is the longitudinal reinforcement area divided by bwd, Nu is the ultimate axial load, Vu isthe ultimate shear force, Mu is the ultimate moment, d is the effective depth of the section, and h is
the total depth of the section. The beneficial effect of compressive axial load is indirectly reflectedin Eq. (22), and the maximum moment demand, Mm, is used instead of Mu in Eq. (21) to modify theeffect of column aspect ratio, which is represented by Mm/Vud.
4.8 Comparison of various shear models
The shear models reviewed above were compared each other in terms of several major design
parameters, as summarized in Table 3. All models except for ACI 318-08 take into account theeffect of displacement ductility on the shear strength of RC columns. Also, reduction in the concrete
shear contribution due to the larger column aspect ratio is reflected in many models including therevised UCSD model, Maekawa and An (2000), Sezen and Moehle (2004), and ACI 318-08. With
respect to the effective area resistant to shear, Maekawa and An (2000) and ACI 318-08 use the
web area (bwd) of the column section, while all other models use 80% of the gross section area (Ag)to account for reduction in the shear effective area due to cracking and spalling damage near plastic
zones under reversed cyclic loading (Ang et al. 1989).
Fig. 10(a) compares the various shear models in terms of the impact of displacement ductility
demand for cases of the column aspect ratio equal to 2 as an example. In Figs. 10 and 11, thelongitudinal steel ratio is taken as that of the specimens in this study, and both the transverse steel
ratio and the axial load are taken as zero, in order to compare the concrete contribution only. With
regard to the effect of ductility demand, shear strength degradation initiates at the displacement
ductility of 1 in Aschheim and Moehle (1992) and Maekawa and An (2000), and at 2 in all theConcrete contribution to initial shear strength of RC hollow bridge columns

57

Table 3 Design parameters considered in various shear models
Ductility

Aspectratio

Aschheim & Moehle
Circular(1992)

○

×

×

○

0.8Ag

-

Priestley et al.
(1994)

Circular
Rectangular

○

×

×

×

0.8Ag

-

Xiao &
Rectangular
Martirossyan (1998)

○

×

×

×

0.8Ag

-

Priestley &Kowalsky (2000)

Circular

○

○

○

×

0.8Ag

-

Maekawa & An
(2000)

Rectangular

○

○

×

×

bwd

Size effectCaltrans (2002)

-

○

×

×

○

0.8Ag

Lateral steel
ratio

Sezen & Moehle(2004)

Rectangular

○

○

×

○

0.8Ag

-

ACI 318-08 (2008)

-

×

○

○

○

bwd

-

Shear model

Section type

Long. steel
Axial load Shear area
ratio

Remarks

Fig. 10 Comparison of shear models in terms of ductility and aspect ratio

others except ACI 318-08. On the other hand, the Caltrans model (2002) expects strength
degradation even when the ductility is less than 1 (i.e., before yield displacement) for columns withminimal transverse reinforcement. The models that do not consider the aspect ratio (Ashheim andMoehle 1992, Xiao and Martirossyan 1998, Catrans 2002), presented by dotted lines in the figures,
expect faster degradation in concrete shear strength (i.e., rapid line slopes) due to increasing
ductility in general. The strength degradation due to increasing ductility is mostly because aggregateinterlocking reduces as crack widths become wider (Priestly et al. 1994). Among the models
reviewed above, Sezen and Moehle (2004) predicts the highest residual shear strength of concrete athigh ductility demand.
Fig. 10(b) illustrates the impact of column aspect ratio for cases of the displacement ductility
equal to or less than 1. As mentioned earlier, Ashheim and Moehle (1992), Xiao and Martirossyan

58

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu Shin

Table 4 Comparison of experimental and calculated initial shear strengths
Specimen

H40A1.5 H40A2.0 H40A2.5 H40A3.0 H60A1.5 H40A1.5WF1.8 H40A2.0C

Exp. maximum load,
Vc, exp (kN) (1)

525

445

341

259

337

522

368

Shear area (2)

Ag

Ag

Ag

Ag

Ag

Ag

0.8Ag

Exp. shear strength,
τc, exp (MPa) (1)/(2)

1.63

1.38

1.06

0.80

1.57

1.62

1.43

Ratio of experimental-to-calculated (τc, exp-to-τc, cal) shear strength
based on indicated models

Shear model
Aschheim & Moehle (1992)

1.11

0.94

0.72

0.55

1.07

1.10

0.97

Xiao & Martirossvan(1998)

1.15

0.97

0.74

0.57

1.11

1.14

1.00

Priestley & Kowalsky(2000)

0.96

1.13

0.87

0.66

0.93

0.96

1.17

Maekawa & An (2000)

1.06

1.76

1.35

1.03

1.02

1.05

1.82

Caltrans (2002)

1.33

1.13

0.86

0.66

1.28

1.32

1.16

Sezen & Moehle (2004)

1.07

1.21

1.16

1.05

1.03

1.06

1.25

ACI318-08 (2008)

1.66

1.48

1.17

0.91

1.61

1.65

1.53

(1998), Catrans Seismic Design Criteria (2002) do not take into account the effect of column aspectratio. In the revised UCSD model and Maekawa and An (2000), concrete shear strength do notchange for columns with the aspect ratio more than 2. ACI 318-08 shows the smallest variation in
the concrete contribution due to the aspect ratio, while Sezen and Moehle (2004) proposed thelargest change. In general, the models that do not consider the aspect ratio give higher initial shear
strengths than the other models for larger aspect ratios than approximately 2 (see Table 4 also).

5. Evaluation of shear models based on test results
Figs. 11(a) to 11(e) compare the shear stress vs. ductility response of each specimen with thevarious shear models reviewed above. Note that the test results and analytical models in this figure
were compared in stress term (i.e., MPa units). As discussed earlier, for the specimens tested undermonotonic loading, the shear stress, τ, was determined as the lateral load, V, divided by the grosssection area, Ag. On the other hand, 0.8Ag was used as the effective shear area for H40A2.0C thatwas subjected to reversed cyclic loading. The two different effective shear areas (Ag versus 0.8Ag)
were used based on the findings that the shear strength of H40A2.0C was roughly 83% of that of
H40A2.0. The use of 0.8Ag for H40A2.0C was in accordance with most of the existing shear
models, which assumed that the confined concrete core would be effective under lateral cyclicloading (Ang et al. 1989). Also, the displacement ductility, µ, of the specimen was taken equal to 1
at the yield displacement ( ∆y ) defined in Fig. 12.
Note that each figure illustrates the entire load-drift response of the specimen with the indicatedaspect ratio (l/h), whereas the maximum load (i.e., shear strength) of the specimen is mostConcrete contribution to initial shear strength of RC hollow bridge columns

59

Fig. 11 Evaluation of shear models based on test results

meaningful for comparison with the shear models. The shear strength of the specimen wascompared with the initial parts of the models, because the specimens failed in shear before reaching
their flexural strengths at the displacement ductility slightly larger than 1. The measured shear
strength of each specimen is summarized in Table 4 in both force (Vc, exp) and stress (τc,exp) terms, inwhich the shear strength in stress term (τc,exp) is equal to the maximum value shown in Figs. 11(a)to 11(e). In addition, the ratio of measured-to-calculated initial shear strengths (τc,exp-to-τc,cal) issummarized in Table 4 and also plotted in Fig. 11(f).
For the specimens with the aspect ratio equal to 1.5 and 3.0 shown in Figs. 11(a) and 11(e),Maekawa and An (2000) and Sezen and Moehle (2004) both show good agreement with themeasured shear strengths; differences less than 7% exist between the measured and calculated

60

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu ShinFig. 12 Definitions for yield displacement (∆y) and displacement ductility (µ)

strengths (see Table 4). Note that Fig. 11(a) includes three specimens, H40A1.5, H40A1.5WF1.8,
and H60A1.5, which had the shear strength of 1.63, 1.62, and 1.57 MPa, respectively. In particular,
only the two aforesaid models give the calculated strengths larger (but very similar) than themeasured for H40A3.0. For the other specimens, Sezen and Moehle (2004) shows closer estimation
than the others as shown in Fig. 11(f). In general, the ratio of measured-to-calculated shear strengths(τc,exp-to-τc,cal) is smaller in the specimen with the larger aspect ratio (see Fig. 11(f)).
ACI 318-08 gives quite conservative estimates (larger than roughly 150% of the measured
strength) for the specimens with the aspect ratio smaller than 2, while it gives approximately a 10%
smaller estimate for H40A3.0 with the aspect ratio of 3. The ACI 318 method would seem moreconservative than shown in Fig. 11 when the measured and calculated shear strengths are comparedin force term, because the web area (bwd) used in ACI 318-08 is smaller than even 0.8Ag for the
specimens of this study. In this sense, the 10% smaller estimate for H40A3.0 appears to be in theconservative side. On the other hand, the ACI 318-08 method could be unconservative when highductility demand (more than about 4) is expected, especially for columns with large aspect ratios; inFigs. 11(d) and 11(e), the ACI 318-08 model gives much higher shear strengths than the other shear
models.

6. Proposed model for initial concrete shear strength of hollow columns
Fig. 13 illustrates an RC column under lateral loading. It may be assumed that an element
indicated in the figure is under a uniform stress condition with the shear stress, τ, the normal stressparallel to the column axis, σy, and the normal stress perpendicular to the column axis, σx. Then, theprincipal tensile stress, σ1, may be defined from equilibrium conditions as
σx + σyσ x – σ y⎞ 2 2- + ⎛ --------------σ1 = --------------- +τ
⎝ 2 ⎠
2

(23)

Here, σx can be assumed zero, which is reasonable in typical hollow columns with no confining

Concrete contribution to initial shear strength of RC hollow bridge columns

61

Fig. 13 A column element under normal and shear stresses

lateral reinforcement. Also, σy may be taken as –P/Ag (Sezen and Moehle 2004), while the effectof flexural behaviour (i.e., normal stress and bending deformation) on the concrete shear strengthis implicitly incorporated by a function of column aspect ratio. Then, inclined shear cracks would
occur when the principal tensile stress, σ1, approaches the nominal tensile strength of concrete, fct.
′

Substituting σx = 0, σy = –P/Ag, and σ1 = fct taken equal to 0.5 fc (MPa), the shear stress, τcr , atthe onset of inclined shear cracking can be expressed asP′τcr = 0.5 fc 1 + --------------------′
0.5 fc Ag(24)

Note that Eq. (24) does neither reflect the effect of column aspect ratio, nor the effect of increasing
ductility. The former is pursued in the following.
Fig. 14 compares the measured shear strength (τc,exp) with the calculated initial shear strengths(τc,cal) by the four models that account for the column aspect ratio (Maekawa and An 2000,
Kowalsky and Priestley 2000, Sezen and Moehle 2004, ACI 318 2008), for all seven hollow
specimens. For the models in Fig. 14, it is considered that the longitudinal steel ratio is the same asthat of the specimens (i.e., 0.0018), the axial load is zero, and the displacement ductility is close toone, to place the equal basis as the tests. No conclusion was attempted to be made related to theeffect of increasing ductility in this study. As discussed earlier, the Sezen and Moehle’s model
presents better estimates than the others. Nevertheless, relatively larger differences exist at the
aspect ratio of 2.0 and 2.5 between this model and the tests. In the hollow column tests, the initialshear strength reduced in a linear pattern as the column aspect ratio increased, while the strength is
proportional to the inverse of the aspect ratio in the Sezen and Moehle’s model. For the aspect ratio
larger than 3, no apparent reduction in the shear strength was found from previous studies(Leonhardt 1965, Bresler and MacGregor 1967, ASCE-ACI Committee 426 1973). Therefore, it is
proposed in this study that the initial shear strength of concrete degrades in a linear pattern (i.e.,with a negative slope) up to the aspect ratio of 3, and does not vary for the aspect ratio larger than 3.
Ang et al. (1989) found the consistency that, for columns with a certain aspect ratio, shear stresscarried by concrete at the maximum load was approximately 30% higher than shear stress at the62

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu ShinFig. 14 Effect of aspect ratio on concrete shear strength: experimental shear strengths compared with several
modelsonset of diagonal cracking. Therefore, the initial concrete shear strength (τc) of an RC hollow
column with 0 ≤ l ⁄ h ≤ 3 may be expressed as a function of τcr byP′lτc = ⎛ c1 – c2 ---⎞ 0.5 fc 1 + --------------------⎝′
h⎠
0.5 fc Ag(25)

Here, l/h is the column aspect ratio, and c 1 and c 2 are unknown constants to be determined basedon the test results. In Fig. 14, a linear regression line fitting to the test results of all seven specimens
was stated as follows:τcl------= 0.5 ⎛ 1 – 0.22 ---⎞
⎝
′
h⎠
fc

(26)

From Eq. (25) and Eq. (26) with substituting P = 0 in Eq. (25) for the tests of this study, c1 andc2 are determined to be 1.0 and 0.22, respectively.
With respect to the shear effective area for RC hollow columns subjected to cyclic lateral loading,
0.8Ag was adopted based on the comparison between the shear strengths of H40A2.0 and
H40A2.0C, as used in most of the other shear models. Based on the aforesaid findings, it is
proposed that the initial shear strength (Vc) of RC hollow columns owing to concrete only may beassessed byP′
Proposed Vc = ( α )0.5 fc 1 + --------------------- ( 0.8Ag )′0.5 fc Ag
α = 1 – 0.22 --lh
α = 0.34

for --l- ≤ 3hlfor --- ≥ 3
h

(27a)

(27b)

(27c)

Concrete contribution to initial shear strength of RC hollow bridge columns

63

It should be noted, however, that the proposed effect of column aspect ratio ( α ) is based on thelimited number of hollow column tests, due to the lack of available hollow column specimens thatfailed in premature shear mode; almost all hollow column specimens reported in literature (Yeh et al.
2002, Mo et al. 2003, Mo et al. 2004, Cheng et al. 2005) developed relatively ductile plastic hinging
before ultimate shear failure, if any. Also, the effect of longitudinal steel ratio on the concrete shear
contribution is not explicitly embodied in the proposed model due to the lack of data. Therefore,
more test data should be solicited from the research society of earthquake-resistant design.

7. Conclusions
In this study, an experimental program was conducted for seven large-scale reinforced concrete(RC) rectangular hollow columns subjected to monotonic or cyclic lateral loads, to identify concrete
contribution to the initial shear strength of such columns. Also, pioneering shear models proposed
around the world, all of which were mainly based on tests for columns with solid sections, werereviewed and compared with the test results of this study. Finally, an empirical equation was
proposed for the concrete shear contribution in RC hollow columns. The findings and conclusions
drawn based on the experimental and analytical results include the following:
1. The specimen with the higher column aspect ratio generally showed the smaller stiffness after
the initiation of diagonal cracking, and ultimately reached the smaller maximum load. The
reduction in the maximum load was likely in part because the confinement effect of the footing
was lesser in columns with higher aspect ratios, and also in part because increased normal stressdue to higher bending moment interacted with shear stress against the given tensile capacity ofconcrete.
2. The two specimens, H40A1.5 and H40A1.5WF1.8, with different web area ratios but with thesame gross section area, achieved similar maximum loads (i.e., shear strengths in force term).
Also, the two specimens, H40A1.5 and H60A1.5, with different hollow section ratios, had similar
maximum loads normalized by their gross section areas (i.e., shear strengths in stress term). Basedon these results, it was concluded that the shear strength of an RC hollow column is associatedmore with the gross section area than the web area.
3. The specimen tested under reversed cyclic loading, H40A2.0C, achieved approximately 83% of
the shear strength of the companion specimen under monotonic loading, H40A2.0. This was
mostly because H40A2.0C underwent strength and stiffness degradations due to the crossing of
diagonal cracks under reversed cyclic loading.
4. ACI 318-08 gives quite conservative design shear strengths (larger than roughly 150% of themeasured strengths) for the specimens with the aspect ratio smaller than 2. On the other hand, theACI 318-08 equation could be unconservative when high ductility demand (more than about 4) is
expected, especially for columns with large aspect ratios.
5. The Sezen and Moehle’s model presents better shear strength estimates than the other models
for the seven hollow specimens of this study. In the hollow column tests, however, the initialshear strength reduced in a linear pattern as the column aspect ratio increased, while the strengthis proportional to the inverse of the aspect ratio in the Sezen and Moehle’s model.
6. Based on the experimental and analytical results, it was proposed that the initial shear strengthof RC hollow columns owing to concrete only may be assessed by Eq. (27). It should be noted,
however, that the proposed effect of column aspect ratio is based on the limited number of hollow

64

Ick-Hyun Kim, Chang-Ho Sun and Myoungsu Shincolumn tests, due to the lack of available hollow column specimens that showed premature shear
failure.

Acknowledgements
This research was supported by Basic Science Research Program through the National Research
Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant
No. 2011-0026780). Also, this work was supported by the 2010 Research Fund of the Ulsan
National Institute of Science and Technology (UNIST), Korea. The authors would like toacknowledge continued support from their affiliations.

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