Shear Strength and Capacity Protection of RC Bridge Columns

Jae-Hoon Lee, Seong-Hyun Ko, and Jin-Ho Choi

ABSTRACT

The most bridge seismic design specifications contain capacity protection provisions explicitly or implicitly. The capacity protection is normally related with slenderness effect of the columns, force transfer in connections between columns and adjacent elements, and shear design of columns. It intends to prevent brittle failure of the structural components of bridges, so that the whole bridge system may show ductile behavior and failure during earthquake events. One of the important capacity protections is the shear design of columns. This paper presents test results of 4 full scale circular column specimens, which show shear related behavior under cyclic lateral load with constant axial force. The test variables are aspect ratio(1.825%, 2.5%, 4.0%), transverse steel configuration(with or without crossties), and longitudinal steel ratio(1% and 2%). Volumetric ratio of transverse hoop of all the columns is 0.0023 in the plastic hinge region. It corresponds to 24% of the minimum requirement of confining steel by Korean Bridge Design Specifications, which represent existing columns not designed by the current seismic design specifications or designed by limited ductility concept. The columns showed flexural failure or flexure-shear failure depending on the test variables. The test results are compared with shear strength equations adapted by the bridge seismic design specifications or guidelines such as AASHTO, CALTRANS, NCHRP 12-49, Standard New Zealand, etc. and proposed by other researchers. And also, researches by the Korea Earthquake Engineering Research Center(KEERC) related to capacity protection of bridge columns are briefly introduced. INTRODUCTION

Seismic design for capacity protection intends to prevent brittle failure of the structural

components of bridges, so that the whole bridge system may show ductile behavior and failure during earthquake events. It may provide the least guarantee to mitigate human casualties and serious property damages. Therefore, the most bridge seismic design specifications contain capacity protection provisions, explicitly or implicitly. The capacity protection is normally related with slenderness effect of the columns, force transfer in connections between columns and adjacent elements, and shear design of columns. One of the important capacity protections is the shear design of columns. The bridge columns should be designed so that shear failure be prohibited to insure ductile behavior. _____________ Jae-Hoon Lee, Korean Earthquake Engineering Research Center (KEERC), Yeungnam University, Gyongsan City, 712-749, KOREA Seong-Hyun Ko, Department of Civil and Environmental Engineering , Yeungnam University, Gyongsan City, 712-749, KOREA Jin-Ho Choi, Department of Civil and Environmental Engineering , Yeungnam University, Gyongsan City, 712-749, KOREA

Failure mode of reinforced concrete column is mostly dependent on aspect ratio, relative steel amount of longitudinal reinforcement and transverse reinforcement, and reinforcement details. It is well known that the reinforced concrete columns with the aspect ratio between 1.5 and 2.5 show shear related behavior. Recently, the aspect ratio of bridge columns in Korea were investigated and reported that approximately 37% of the bridge columns have less than 3.0 of aspect ratio. These columns are expected to show shear or flexure-shear behavior. In order to investigate shear related column behavior under seismic loads, experimental test of 4 full scale circular column specimens was conducted. The test results are compared with shear strength equations adapted by the bridge seismic design specifications or guidelines such as AASHTO, CALTRANS, NCHRP 12-49, Standard New Zealand, etc. and proposed by other researchers. This paper also briefly introduces the researches by the Korea Earthquake Engineering Research Center(KEERC) related to capacity protection of bridge columns. CAPACITY DESIGN Capacity Protection

The object of capacity protection is to guarantee ductile behavior and failure of the bridge columns, preventing abrupt brittle failure. To insure this behavior, the column itself and the adjacent elements should not fail abruptly until the columns provide full plastic rotation capacity. Consideration of Preventing Brittle Failure

Brittle behavior of the columns is normally related with slenderness effect of the columns, force transfer in connections between columns and adjacent elements, and shear design of columns. Slenderness Effect

Secondary moment, i.e. P-∆ moment, is produced in slender columns. This length effect of columns may result in brittle failure. As the slenderness ratio of the column increases, the P-∆ moment increases. The increased P-∆ moment results in decreasing lateral force capacity of the columns. It may cause brittle failure due to instability. Therefore, the most bridge seismic design specifications contain the provisions for slenderness effect, explicitly or implicitly. Connections

The force produced by the mass and the acceleration of bridge superstructure should be transferred to the ground without brittle failure of any structural component. One of the critical components is the connection between column and adjacent element. Therefore, the most bridge seismic design specifications contain the related provisions, explicitly or implicitly. Two types of design approaches are normally adopted in the bridge seismic design specifications, either or both. The first approach is to use reduced response modification factor for connection. Half the response modification factor of the columns is normally adapted for connections, foundations, and piles. It results in increasing seismic demand for the elements. The second approach is to use the flexural overstrength of the column which is the maximum feasible force transferred from the columns.

∆ u ∆

Elastic Analysis

effE I

V

Design Capacity

Nominal Capacity

OverstrengthCapacity

el

V

Vplo

Shear Failure

The bridge column itself also should not fail abruptly until the column provides full plastic rotation capacity. It means that shear failure of the column should be prevented to result in ductile flexural failure. Therefore, the most bridge seismic design specifications contain the related provisions, explicitly or implicitly. SHEAR DESIGN OF REINFORCED CONCRETE BRIDGE COLUMNS Demand for Shear Design

To ensure that inelastic deformations occur only in designated and properly detailed plastic end regions, it is necessary to determine the maximum feasible moment capacity of the plastic hinges and to design the rest of the structure for the actions corresponding to gravity loads plus this flexural overstrength. The capacity design concept is commonly used in the seismic design specifications such as AASHTO, CALTRANS, EC 8-part 2, and New Zealand Code. As the design flexural strength is the lowest reliable strength, actual ultimate flexural strength of the member is always larger than the design strength. Therefore, in order to avoid shear failure and secure the ductile flexural failure of the member, a larger flexural strength than the design strength or the nominal strength should be used to determine the demand for shear design. The corresponding shear force to the maximum feasible flexural strength is used as the design load. Some seismic design codes prescribe that the design shear force Vu shall be the lesser of the shear forces resulting from plastic hinging or calculated elastic seismic forces in columns. Even though using the calculated elastic seismic forces Vel as the design shear force may result in conservative design in most case, it may not be rational, considering the actual behavior and capacity of the columns as shown in Figure 1.

(a) Lateral force capacity (b) Flexural strength Figure 1. Maximum feasible strength

The overstrength of column section is the strength taking into account all possible factors that

may contribute to strength exceeding the nominal value. For a confined column, the following factors contribute to the overstrength:

1) Compression strength enhancement of the concrete due to its confinement. 2) Additional strength enhancement of steel due to strain-hardening at large deformations. 3) Steel strengths greater than the specified yield strength.

P

M

Design Capacity

Nominal Capacity

Overstrength Capacity

M opl

Pu

4) Concrete compressive strength greater than the specified yield strength due to its aging effect. 5) Additional reinforcement placed for construction and otherwise unaccounted for in calculations.

The flexural overstrength may be obtained by moment-curvature analysis considering the above

factors or by simplified constant overstrength factor. The moment overstrength of a column section is related to the nominal flexural strength. It is convenient to express the overstrength of a member in flexure at a specified section in terms of the nominal flexural strength. The overstrength equations or the overstrength constant to calculate the maximum feasible strength are different in each code.

The Korea Earthquake Engineering Research Center(KEERC) conducted an analytical research on overstrength factor in 2002(Lee, 2003). This research continues in 2004 to provide reasonable overstrength factor considering Korean construction circumstances. It has searched material strength of old bridge columns in Korea. Total 5,336 data of concrete compressive strength were surveyed using nondestructive test and compared with the design characteristic strength as shown in Figure 2. Based on these data and the data for steel strength, the overstrength factor will be re-evaluated to propose to the Korean Bridge Design Specifications(2000) for future revision of seismic design specifications.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50 60 70 80 90 100Age(years)

fcu/f c

k

Figure 2. Concrete compressive strength ratio of old bridge columns in Korea

Capacity for Shear Design

The shear strength of reinforced concrete members under inelastic loading is affected by a number of parameters: applied shear stress level, level of imposed ductility, level of axial compression force, aspect ratio, transverse steel ratio, and longitudinal steel ratio. The proposed shear strength equations by the design codes or researchers adopted one or more factors among those parameters. The shear strength equations introduced here in are presented in SI unit and the shear strength by transverse steel Vs presented here in is for circular sections.

AASHTO

The AASHOTO Standard Specifications(2002) adapted the following equations based on 45 degree truss model in determination of the nominal shear strength of reinforcement concrete columns.

scn VVV += (1)

( )dbA

PfV w

g

cc ⎟

⎟⎠

⎞⎜⎜⎝

⎛+=

141

6'

(2)

( )dbf

V wc

c 6'

= (3)

( )dbf

AfPV w

c

gcc 6

''

10⎟⎟⎠

⎞⎜⎜⎝

⎛= (4)

sdfA

V yhvs = (5)

πrDDd +=

2 (6)

where, Av = cross-sectional area of transverse steel, fyh = yield strength of transverse steel, D = column diameter, Dr = diameter of the circle passing through the center of the longitudinal steel, and s = vertical distance between transverse hoops.

For non-seismic design, either Eq.(2) or Eq.(3) is used for concrete contribution, depending on axial load effect. For seismic design, either Eq.(2) or Eq.(3) is also applied to the plastic hinge region. However, if the axial load ratio is less than 0.1, Vc is linearly decreased from Eq.(2) or Eq.(3) to zero as the axial load ratio decreased. In this case, Eq.(4) is to be used. The transverse steel contribution Vs is determined by Eq.(5). For circular columns, bw shall be the diameter and d need not be less than the distance from the extreme fiber to the centroid of the tension reinforcement in the opposite half of the member. Therefore, Eq.(6) is used for the circular sections. CALTRANS

CALTRANS(2001) adapted the following equations based on 45 degree truss model in determination of the nominal shear strength of reinforcement concrete columns. CALTRANS defines Vc differently by classifying inside the plastic hinge zone and other zone. In Vc determination for the plastic hinge zone, displacement ductility factor is used to factor 1 in Eq.(10). For circular columns, Eq.(12) is used considering resistance direction of the circular transverse steel. In this equation, Asp is the area of spiral and Dsp is the core diameter of circular column

scn VVV += (7)

ecc AV υ= (8) ccc ffFactorFactor '33.0'21 ≤××=υ (9)

dyhs f

µρ

083.0305.05.12

FACTOR1 −+= (10)

FACTOR2 = gA

p8.13

1+ (11)

sDfA

V spyhsps 2

π= (12)

Aschheim and Moehle

Aschheim and Moehle(1992) suggested Eq. (13) ~ (16) to compute the nominal shear strength of reinforced concrete columns. Considering displacement ductility and the effect of compression, Vc is calculated by Eq. (14) and (15) for the plastic hinge zone. In Eq.(14), Ae is effective shear area and 0.8Ag is used as Ae for circular sections. The shear strength of reinforcement Vs is calculated by Eq. (16) based on 30 degree truss model, and 0.8 D is used as d for circular columns.

scn VVV += (13)

ecg

c AfA

PkV '14

3.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛+= (14)

13

40 ≤−=≤ ∆µk (15)

°= 30cot2 s

dfAV yhsp

sπ (16)

Priestley et al.

Priestley et al.(1996) proposed Eq. (17) ~ (22) to calculate the nominal shear strength of reinforced concrete columns for design purpose. Considering the effect of displacement ductility, Vc is calculated by Eq.(18) and (19) for the plastic hinge zone. The shear strength of reinforcement Vs is calculated by Eq. (20) based on 35 degree truss model for circular columns. The axial load effect is considered by Eq.(21).

scn VVV += (17)

ecc AfkV '= (18)

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

=≤−−=≤≤

==−−=≤≤

=≤

∆

∆∆

∆

∆∆

∆

042.0:8)4(0125.0083.0:84

083.0:4)2(0835.025.0:42

25.0:2

kk

kk

k

µµµ

µµµ

µ

(19)

35cot2 s

DfAV spyhsp

sπ= (20)

LD

ppV cp 2

85.0tan85.0 == α (21)

ATC/MCEER Joint Venture

ATC/MCEER Joint Venture(2001) suggested seismic design guidelines for AASHTO-LRFD, based on NCHRP 12-49(2001). Eq.(22) through (28) are used for nominal shear strength calculation for the plastic hinge zone. In determination of fixity factor Λ in Eq.(23) and (27) which is the coefficient for boundary condition, 2.0 is applied in case of both end fixed. In case of one end fixed

and other end free such as cantilever, 1.0 is applied. In Eq.(24), D’ is pitch circle diameter of the longitudinal steel in circular column, which is the same as Dr in Eq.(6). The crack angle θ is determined by Eq.(27) considering the transverse steel and the longitudinal steel, and used for Vs calculation. The shear strength of reinforcement Vs is calculated by Eq. (26) for circular columns. The axial load effect is considered by Eq.(23).

scpn VVVV ++= (22)

αtan2

PVpΛ= (23)

LD'tan =α (24)

dbfV wcc '05.0= (25)

θπ cot2 s

dfAV yhsp

s = (26)

α

ρρθ tan

6.1tan

25.0

≥⎟⎟⎠

⎞⎜⎜⎝

⎛

Λ=

gt

vv

AA

(27)

sp

spsv sD

A22

==ρρ (28)

Standard New Zealand

Standard New Zealand(1995) adapted the following equations based on 45 degree truss model for

the nominal shear strength of reinforcement concrete columns. In determination of Vc for the plastic hinge zone, the longitudinal steel amount and the axial load effect are considered. However, the axial load effect is applied only if the axial load ratio exceeds 0.1 as shown in Eq.(30). Therefore, in case that the axial load ratio is less than or equal to 0.1, the concrete contribution to shear strength is ignored. In consideration of the longitudinal steel, the last terms in Eq.(32) is applied to the circular columns, where Ast is the area of longitudinal steel and Ac is the area of column section. The shear strength of reinforcement Vs is calculated by Eq. (33) for circular columns.

Scn VVV += (29)

dbAf

PfvV wgc

cbc ⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1.0

''4 (30)

wb pv 1007.0 += (31)

c

st

w

tenssw A

Adb

Ap 5.0, == (32)

sDfA

V spyhsps 2

π= (33)

EXPERIMENT OF COLUMNS Column Specimens

Four large seize circular column specimens were tested under cyclic lateral load with constant axial force(Chung, Lee, and Kim, 2001). The objective of the test was to investigate shear strength and capacity of circular columns with variables of longitudinal steel ratio and aspect ratio(span-depth ratio). The axial load ratio was 0.07 based on concrete compressive strength and cross sectional area. Details and variables of the column specimens are shown in Table 1, Figure 3, and Figure 4. All the column specimens had a 1200mm diameter cross-section and D19 and D10 bars were used as longitudinal reinforcement and transverse reinforcement, respectively. In addition to the circular ties, crossties were used for MS-HT4 series columns as shown in Figure 3. Perfect hoops by use of couplers were used for MD-HT60N-L2 column.

Material tests were carried out to determine the actual mechanical properties of concrete and steel. The concrete compressive strength by 100 X 200 mm cylinder was 24.8 MPa at the time of loading test. Yield strength of the reinforcement was measured to be 343 MPa for D19 reinforcement and 373 MPa for D10 reinforcement.

Table 1. Variables of specimens and material properties

Transverse hoop tie in plastic hinge Specimens

Shear Span (mm)

Aspect ratio Volumntric ratio

(%) Spacing

(mm)

Longitudinal steel ratio (%)

MS-HT4-N-L2 4800 4.0 0.23 115 1.02 MS-HT4-N-FS 3000 2.5 0.23 115 1.02 MS-HT4-N-SH 2190 1.825 0.23 115 1.02 MD-HT6-N-L2 4800 4.0 0.23 115 2.03

Figure 3. Column specimens

22@

150=

3300

180

plas

tic h

inge

reg

ion

(cro

ss ti

e

)

10@

115=

1150

4@11

5=46

0

배근구간

3@20

0=60

0

1210

2400

800

4800

310

100

620

1200 1060

1200

70

10@

150=

1500

4@11

5=46

018

0

배근구간

10@

115=

1150

plas

tic h

inge

reg

ion

(cro

ss ti

e

)

1210

2400

800

3000

310

620

100

3@20

0=60

0

1200 1060

1200

70

plas

tic h

inge

reg

ion

(cro

ss ti

e

)

2400

2190

800

100

62031

0

8@15

0=12

00

1210

10@

115=

1150

180

4@11

5=46

0

배근구간

1060

1200

1200 70

22@

150=

3300

180

plas

tic h

inge

reg

ion

(cro

ss ti

e

)

10@

115=

1150

4@11

5=46

0

배근구간

3@20

0=60

0

1210

2400

800

4800

310

100

620

1200 860

1200

(a) MS-HT4-N-L2 (b) MS-HT4-N-FS (c) MS-HT4-N-SH (d) MD-HT6-N-L2

(a) MS-HT4 series (b) MD-HT6-N-L2 Figure 4. Configuration of transverse steel

Test Results Lateral Force-Displacement Relationships

Hysteresis relationships of the column specimens are presented in Figure 5. As shown in the figures, different failure modes were observed that might be dependent on the shear span-to-depth ratio and the relative steel amount of longitudinal reinforcement and transverse reinforcement.

① Initial crack ② Longtudinal steel yield ③ Crack propagation ④ Initial spalling ⑤ Longtudinal steel fracture

(a) MS-HT4-N-L2

Figure 5. Load-displacement relationship

① Initial crack ② Longtudinal steel yield, Initial shear crack ③ Initial spalling ④ Confining steel fracture ⑤Longtudinal steel fracture

(b) MS-HT4-N-FS

� Initial crack � Longtudinal steel yield � Initial spalling � Initial shear crack � Confining steel fracture

(d) MD-HT6-N-L2

� Initial crack � Longtudinal steel yield � Initial shear crack � Initial spalling

(c) MS-HT4-N-SH

250 mm

D10

1060

mm

D10

coupler

1060

mm

0

400

800

1200

1600

2000

2400

2800

0 1 2 3 4 5

MS-HT4-N-L2

0 2401921449648Displacement [mm]

Late

ral F

orce

[kN

]

Drift Ratio [%]

CALTRANS

Priestley et al

ATC/MCEER

New Zealand

AASHTO(Seismic)

AASHTO(Non-seismic)

Test

Aschheim& Mohel

0

400

800

1200

1600

2000

2400

2800

0 1 2 3 4 5

Displacement [mm]0

Late

ral F

orce

[kN

]

Drift Ratio [%]

MS-HT4-N-FS

30 60 90 120 150

CALTRANS

Priestley et al

ATC/MCEER

New Zealand

AASHTO(Seismic)

AASHTO(Non-seismic)

Test

Aschheim& Mohel

0

400

800

1200

1600

2000

2400

2800

0 1 2 3 4 5

Displacement [mm]0

Late

ral F

orce

[kN

]

Drift Ratio [%]

CALTRANS

Priestley et al

ATC/MCEER

New Zealand

AASHTO(Seismic)

AASHTO(Non-seismic)

MS-HT4-N-SH

21.9 43.8 65.7 87.6 109.5

Test

Aschheim& Mohel

0

400

800

1200

1600

2000

2400

2800

0 1 2 3 4 5

0 2401921449648

MD-HT6-N-L2

Displacement [mm]

Late

ral F

orce

[kN

]

Drift Ratio [%]

CALTRANS

Priestley et al

ATC/MCEER

New Zealand

AASHTO(Seismic)

AASHTO(Non-seismic)

Test

Aschheim& Mohel

Failure of Column Specimens

MS-HT4-N-L2 column(M/VD=4.0) showed typical flexural failure and MS-HT4-N-FS (M/VD=2.5) and MS-HT4-N-FS(M/VD=1.825) columns showed flexure-shear failure due to reinforcement fracture or degradation of shear capacity. In spite of the same aspect ratio of 4.0 as MS-HT4-N-L2, the column specimen MD-HT6-N-L2 eventually presented flexural-shear failure due to shear cracks and transverse steel fracture after formation of plastic hinge. The flexural-shear failure of MD-HT6-N-L2 column can be investigated from the fact that flexural capacity increases compared with MS-HT4-N-L2 column with the equal shear capacity. SHEAR STRENGTH EVALUATION

Theoretical shear strength for the column specimens are calculated by AASHTO(2000), CALTRANS(2001), ATC/MCEER(2001), Standard New Zealand(1995), and the proposed equations by Ascheim and Moehle(1992) and Priestley et al.(1996). Figure 6 shows the experimentally obtained lateral load-displacement envelopes and the predicted shear capacity by each equation.

(a) MS-HT4-N-L2 (b) MS-HT4-N-FS

(c) MS-HT4-N-SH (d) MD-HT6-N-L2

Figure 6. Comparison of experimental result and predicted shear strength

In comparison of the calculated shear strength at ultimate deformation and test result, all the

predicted strength for MS-HT4-N-L2 column, except Standard New Zealand, are greater than the test result which showed flexural failure. For MS-HT4-N-FS column with aspect ratio of 2.5, which also showed flexure-shear failure, CALTRANS and Standard New Zealand predict lower strength than the test result. For MS-HT4-N-SH column with aspect ratio of 1.825, which showed flexure-shear failure, the AASHTO equations for seismic design, the ATC/MCEER equations, the equations by Ascheim and Moehle, and the equations by Priestley et al. predict reasonably accurate strength compared with the test result. For MD-HT6-N-L2 column with aspect ratio of 4.0 but 2 % of longitudinal steel ratio, which showed flexure-shear failure, the proposed equations by Preistley et al. predicts the best fit for the test result. The Standard New Zealand predicts conservatively lower strength than all the other methods and test results. This is because that the concrete contribution to shear strength is ignored when the axial load ratio is less than 0.1, which may be for design purpose. CONCLUSION

Four large size circular column specimens were tested under cyclic lateral load with constant axial force. Different failure modes were observed according to the aspect ratio and the relative steel amount of longitudinal reinforcement and transverse reinforcement. The test results are compared with the theoretical shear strength at ultimate deformation. The accuracy of each method for shear strength prediction also depends on the aspect ratio and the relative steel amount of longitudinal reinforcement and transverse reinforcement. ACKNOWLEDGEMENT

This research was supported by the Korea Earthquake Engineering Research Center(KEERC) and the Korea Bridge Research Center(KBRC). REFERENCES AASHTO, 2000, “Standard Specifications for Highway Bridges,”�American Association of State Highway and Transportation Officials, 17th ed., Washington, D.C., USA. AASHTO, 2002, “LRFD Bridge Design Specifications,”�American Association of State Highway and Transportation Officials, 2nd ed., Washington, D.C., USA. Aschheim, M. and Moehle, J. P., 1992, “Shear Strength and Deformability of RC Bridge Columns Subjected to Inelastic Cyclic Displacement,”�Report No. UCB/EERC 92/04, Earthquake Engineering Research Center, University of California at Berkeley, USA. ATC/MCEER Joint Venture, 2001, “Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Part I : Specifications,”�ATC-49a and MECCR-02-SP01, USA. CALTRANS, 2001, “Caltrans Seismic Design Criteria,� Version 1.2,” California Department of Transportation, Sacramento, USA. Chung, Young-Soo, Lee, Jae-Hoon, and Kim, Jae-Kwan, 2001, “Experimental Research for Seismic Performance of

Existing Reinforced Concrete Piers,”�Research Report, Highway and Transportation Technology Institute, Korea Highway Corporation , 397 pp. Korean Ministry of Construction & Transportation, 2000, “Bridge Design Specifications.” Lee, Jae-Hoon, Son, H. S., and Han, S. Y., 2003, “Reinforcement Details and Design strength of Bridge Columns in Moderate Seismicity Regions (Overstrength Factor for Capacity Design),” KEERC 2002 Annual Report, Korea Earthquake Engineering Research Center, Seoul National University, Korea, pp.105�120. NCHRP 12-49, 2001, “Comprehensive Specifications for the Seismic Design of Bridges,” Revised LRFD Design Specifications (Seismic Provisions),�3rd Draft, USA. Standard New Zealand, 1995, “Design of Concrete Structures,”� NZS 3101, Wellington, New Zealand. Priestley, M. J. N., Seible, F., and Calvi, G. M., 1996, “Seismic Design and Retrofit of Bridges,”� John Wiley & Sons, Inc., New York, 686 pp.