seismic design proposal based on a study on rc columns and

Fédération Internationale du Béton Proceedings of the 2nd International Congress June 5-8, 2006 – Naples, Italy ID 9-31 Session 9 – Seismic evaluation of concrete structures

Seismic Design Proposal Based on a Study on RC Columns and Frame Sub-assemblage Bechtoula, H., Sakashita, M., Kono, S., Fumio, W. Department of Architecture and Architectural Engineering, Kyoto University, Nishikyo, Kyoto 615-8540, Japan INTRODUCTION A few researchers have experimentally studied the effects of variable axial loads on reinforced concrete columns [1, 2]. Recently, Asad et al. [3] carried out a test on six large-scale reinforced concrete circular columns. Experimental evidence revealed the significant effects of the magnitude and loading pattern of axial force on the seismic behavior of columns. They suggest that analytical tools, such as plastic hinge models, need to be modified to account for the effects of varying axial load. Due to effect of such important vertical ground motion, near-fault earthquake, the axial load on a column may vary considerably. It is quite possible that the hysteretic characteristics of the columns, which include stiffness, strength, ductility and energy dissipation are influenced by the axial load history. Hence, the objectives of the research described in this paper were to 1) experimentally and analytically address the problems associated with the performance of reinforced concrete cantilever columns subjected to various loading patterns in both lateral and vertical directions, 2) evaluate other parameters that may influence the seismic performance of a column such as the interaction between columns, beams and joints during cyclic loadings. This paper also addresses a lack of data on the behavior of reinforced concrete cantilever columns and frame sub-assemblage subjected to lateral load under varying axial load. Keywords: reinforced concrete, column, frame, crack, damage, beam elongation MATERIAL CHARACTERISTICS AND TEST SETUP Cantilever Columns Eight large-scale and eight small-scale cantilever columns with square cross-sections were tested at Kyoto University under quasi-static unidirectional and bi-directional displacement-controlled horizontal loads with various axial loads patterns. All specimens were designed to fail in flexure, based on the Japanese design guidelines [4]. Three hydraulic jacks applied orthogonal horizontal displacements at the top of the cantilever, as shown in Fig. 1. Specimen dimensions and test variables are listed in Tab. 1. Three horizontal displacement patterns were used: linear reversed cyclic (LC), circular cyclic (CC), and square cyclic (SC). Specimens were loaded with 2 cycles at each of the following drifts: ±0.25%, ±0.5%, ±1%, ±1.5%, ±2%, ±3% and ±4%. The one exception to this loading scheme is specimen L2NVC, which was loaded with 4 cycles instead of 2 cycles at each drift. Concrete compressive strength as well as the longitudinal and transverse steel reinforcement characteristics are shown in Tab. 1. Frame Sub-assemblage Besides the sixteen cantilever RC cantilever columns, four sub-assemblage frames were also tested. Two of these frames called small-scale frames, represented the lower up to the mid height of the third story of an eleven-story reinforced concrete frame-building prototype. The specimens were scaled to 1/3 to fit the loading system. The cross section of the columns was 270 mm by 270 mm and the beam cross-section measured 180 mm by 270 mm. The heights of the first and second story were 765 and 840 mm, respectively, and the beam span length was 1800 mm. The other two frames called large-scale frame were

Proceedings of the 2nd Congress Session 9

June 5-8, 2006 – Naples, Italy Seismic evaluation of concrete structures

2

scaled to 1/2, and also represented the lower up to the mid height of the second story of an eleven-story reinforced concrete building. The cross section of the column was 500 mm by 500 mm and 300 mm by 500 mm for beams. The height of the first story was 2000 mm and the beam span length was 3000 mm. Axial load variation in columns and shear reinforcement ratio in columns were the test variables for the small and the large-scale frame, respectively, as it will be discussed later. All frames were designed with the 1999 Japanese design guidelines [4]. Small-scale frames were cycled to the following frame drift percentage: 0.25± , 0.35± , 0.45± , 0.55± ,

0.75± , 1.25± , 1.50± , 2.00± , 3.00± , 4.00± . Beyond 1.50%± , frames were loaded with two cycles instead of one cycle for each drift measured at the second story. Large-scale frames were loaded to the following drift percentage: 0.10± , 0.20± , 0.40± , 0.70± , 1.00± ,

2.00± , 3.00± and 4.00± . Two cycles were used for each prescribed drift except for the first value where only one cycle was used. As an example, Fig. 2 shows the test setup for the large-scale frame, whereas Tab. 2 and Tab. 3 summarize the material characteristics and test variables for the small and large-scale frames, respectively.

Eleva tion

Plan

Spec imen Loadc ell Universa l

joint

Reac tionframe

500kNJac k

Loadc ell

500kNJac k

Spec imen

Loadc ell

2000kNJac k

Fig. 1. Loading system for the small-scale column

Tab. 1. Material characteristics and test variables for the cantilever columns

Column width D (mm)

Shear span L (mm)

Concrete strength f'c (MPa)

Longitudinal rebar (ratio)

[Fy]

Shear rebar

(ratio) [Fy]

Axial force (axial force

level in f'cD2)

Slope in normalized moment-

axial force relation

Lateral loading

directions

1 D1N3 Constant (0.3)2 D1N6 Constant (0.6)3 D2N3 Constant (0.3)4 D2N6 Constant (0.6)5 D1NVA 1.396 D1NVB 2.797 D2NVA 1.048 D2NVB 1.669 L1D60

10 L1N6011 L1NVA12 L2NVA Bi (CC)13 L1N6B Uni (LC)14 L2N6B15 L2NVB16 L2NVC

No Specimen designation

specimen configuration Test variables

250

242

600

12-D13 2.44%

461MPa

12-D25 1.69%

388MPa

26.812-D13 2.60%

467MPa

Φ4@40 0.52%

604MPa

560

625

1200

37.6

39.2

32.212-D25 1.94%

388MPa

Φ4@40 0.50%

485MPa

D13@100 0.85%

524MPa

D13@100 0.91%

524MPa Varied (0-0.6)

0

0

2.47

0

3.36

Varied (0-0.6)

Constant (0.6)

Varied (0-0.6)

Constant (0.6)

Bi (SC)

Uni (LC)

Uni (LC)

Bi (CC)

Uni (LC)

Bi (CC)



3

800

800

500

1750

250

500 500 500500500500500 500 500 500 500 500 500 500

3000

50

590

300

4000

500

500

500

500

500

500

500

500

500

500

500

250

140

1347

5727

3350

2000 kN jack

Load cell

Load cells

8000 kN jack

Anchor disc

Anchor disc

Reaction wall

High strength bars

Trumpet sheath

500x500mm column

300x500mm beam

1000 kN jack

Load cell

sheath for prestressed tendons

Universal pins

Foundation

Reaction wall

EASTWEST

Fig. 2. Test setup for the large-scale frames

Tab. 2. Material characteristics and test variables for the small-scale frames

Frame designation

Material

SN30

SN50

31.0 MPa

Column 12D16

(3.27%) Fy=346 MPa

Beam 8D13

(2.08%) Fy = 332 MPa

Concrete strength

Longitudinal steel

Test variable -Axial load-Max. Tension

N/f'cD2

Column 4D6@50 (0.94%) Beam

2D6@80 (0.44%)

Fy = 394 MPa

0.3

0.5

0.1

0.2

Shear rebarMax. Comp.

N/f'cD2

Tab. 3. Material characteristics and test variables for the large-scale frames

Axial load

Max. Comp. 0.6

Min. Comp. 0.05

Test variable -Column shear

rebar-

Beam 2D10@100

(0.47%) Fy = 378 MPa

4D13@100 (1.0%)

Fy=377MPa

2D13@100 (0.5%)

Fy=377MPa

Shear rebar N/f'cD2Frame

designation

Material

LN60

QN60

36.0 MPa

Column 12D25

(2.43%) Fy=323 MPa

Beam 8D22

(2.06%) Fy = 378 MPa

Concrete strength

Longitudinal steel



4

EXPERIMENTAL RESULTS Cantilever Columns Load-Drift Relationships Since shear failure was precluded during design, all specimens showed ductile behavior. A small difference was observed between the envelope curves of the first-cycles and second-cycles for specimens under a unidirectional load. However, as illustrated in Fig. 3 (a), a large difference was observed for the specimens under bi-directional load, even with a moderate axial load, 20.3 cD f ′ . Fig. 3 (b) shows the normalized horizontal load versus the drift relationship for column L2NVC, which was loaded with four cycles at each prescribed drift. Under high axial load corresponding to the negative drift, a large drop in the normalized horizontal load was observed from the first-cycle to the fourth-cycle envelope curve. However, under a low axial load corresponding to the positive drift, difference was minimal between the second, third and fourth-cycle envelope curves. In the negative drift of the NS direction, L2NVB and L2NVC showed at 3% drift 20% and 50% reduction in the maximum load carrying capacity, respectively. This difference is due to the effect of number of cycles applied during the loading, since this was the unique difference between L2NVB and L2NVC.

EW envelope curve for D2N3 specimen

-1.5

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift (% )

Nor

mal

ized

hor

izon

tal l

oad

(Q/Q

max

)

First cycleSecond cycle

NS envelope curve for L2NVC specimen

-1.5

-1

-0.5

0

0.5

1

1.5

-4 -3 -2 -1 0 1 2 3 4

Drift (% )

Nor

mal

ized

hor

izon

tal l

oad

(Q/Q

max

)

First cycleSecond cycleThird cycleFourth cycle

(a) D2N3 (b) L2NVC Fig. 3. Normalized load-drift relationships

Axial Strain-Normalized Curvature Relationships Axial deformations of the column were measured over a length equal to the column depth.

D1N3

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.04 -0.02 0 0.02 0.04

Normalized curvature D*Φ ew

Axi

al s

train

(%)

D1N6

-2

-1.5

-1

-0.5

0

0.5

-0.04 -0.02 0 0.02 0.04

Normalized curvature D*Φ ew

Axi

al s

train

(%)

(a) D1N3 (b) D1N6

Fig. 4. Axial strain variation



5

Columns under high axial load, either under unidirectional or bi-directional horizontal loads, showed shortening throughout the test as illustrated in Fig. 4 (b). However, D1N3 under unidirectional horizontal load and moderate axial load showed both shortening and elongation during every cycle as shown in Fig. 4 (a). Whereas, D2N3 under bi-directional horizontal load and moderate axial load showed only shortening during testing. It can be concluded that, there is a transition zone between 0.3 and 0.6 normalized axial load where the columns transit from tensile and compressive strains to only compressive strains under lateral loading due to the large damage that occurs in concrete. Based on this result and considering retrofit concerns, we suggest lowering the maximum normalized axial load below the current value, 0.67, suggested by the Japanese design guidelines, especially for strategic buildings that must be functional after an earthquake. Axial Load Redistribution While Damage Progress After cracks started to propagate at the column base, the total axial load carried by the vertical reinforcement bars started to shift toward the tension side. As a consequence, concrete carried additional vertical load in order to equilibrate the applied axial load. The axial force in each vertical reinforcement bar was computed using Nakamura’s steel model [5] using the strain recorded along the longitudinal reinforcement during the test. Theoretically if we consider a perfect bond, elastic range, load carried by the vertical reinforcement bars and by the concrete can be computed as follow:

1 111 1

c ss

sc

c

N N and N NAAAA

ηη

= =+ +

(1)

where, , ,c sN N N are, the total applied axial load, axial load carried by concrete and axial load carried by

steel, respectively. c sA and A are the gross sections of concrete and steel, respectively. η is the ratio between the steel and the concrete Young’s modulus.

D1N3: Nakamura

-1200

-1000

-800

-600

-400

-200

0

200

400

600

0 2 4 6 8 10 12 14 16

Cumulative cycles

Verti

cal l

oad

(KN

)

Total Steel Concre te

D1N3: Dodd

-1200

-1000

-800

-600

-400

-200

0

200

400

600

0 2 4 6 8 10 12 14 16

Cumulative cycles

Verti

cal l

oad

(KN

)

Total Steel Concrete

(a) Nakamura model (b) Dodd model Fig. 5. Comparison between Nakamura and Dodd’s steel models for D1N3

As an example, applying Eq. (4) to the small-scale D1N3 under constant axial load,

0.3 706c gN f A kN′= = , the concrete and steel contribution was found to be,

569 137c sN kN and N kN= = which match very well with the axial load computed using the reading from the strain gauges at the column base for a cumulative cycles less than 4 as shown in Fig. 5 (a).



6

To confirm our results given by Nakamura’s model, Larry Dodd’s steel model [6] was applied for the same specimens. As an example, the results using Dodd’s model for D1N3 is shown in Fig. 5 (b) which agree well with the previous result found using Nakamura’s model and shown in Fig. 5 (a). Hence, it is recommended that enough confinement should be provided at the plastic hinge regions of the columns in order to give the concrete the ability to sustain such high axial load. Otherwise, crushing of concrete followed by a brittle failure may occur before reaching the flexural strength. Frame Sub-assemblage Load-Drift Relationships The load-drift relationship for small-scale frames, showed a slight difference between the two frames in term of peak load and the loading and unloading stiffness. This can be seen through Fig. 6 (a) where load-drift curves for the entire frames are shown.

Entire frame

-250

-200

-150

-100

-50

0

50

100

150

200

250

-6 -4 -2 0 2 4 6 8 10

Drift D/H (% )

Shea

r for

ce Q

(KN

)

SN30SN50

LN60 Frame

-800

-600

-400

-200

0

200

400

600

800

-6 -4 -2 0 2 4 6

Drift (% )

Shea

r for

ce (K

N)

(a) Small-scale frames (b) Large-scale LN60

Fig. 6. Load-drift relationships for the small-scale frames

The maximum drift reached for SN30 an SN50 were 6.08% and 7.09%, respectively. The tests were terminated due to the lack of enough space between the top jack that applied the axial load to the south column and an existing loading steel frame. It was observed that the total shear force was not distributed evenly to the column bases. This is due to the stiffness variation during the test as a result of the axial load variation. Fig. 6 (b) shows the load drift relationships for large-scale frames LN60 as an example. LN60 with high shear reinforcement, 1%, showed a stable hysteresis curve until 4% drift. Whereas, QN60 with low shear reinforcement, 0.5%, lost more than 30% of its horizontal load carrying capacity at the second cycle of 2% drift just before the shear failure.

-1

-0.5

0

0.5

1

-6 -4 -2 0 2 4 6

Drift (% )

Mea

n St

rain

(%)

1FNC-SN50 k=2.0D1NVA k=1.39D1NVB k=2.79

1FNC

D1NVA

-1

-0.5

0

0.5

1

1.5

-6 -4 -2 0 2 4 6

Drift (% )

Mea

n St

rain

(%)

1FSC-SN50 k=2.0D1NVA k=1.39D1NVB k=2.79

1FSC

D1NVA

(a) First story north column (b) First story south column

Fig. 7. Comparison of axial strain of the cantilever and the first story columns of SN50



7

Comparison Between the Cantilever Column and the Frame Column Axial Strains Mean strains of the first story column of the small-scale frames were much higher than those for cantilever columns D1NVA and D1NVB, especially for columns under high axial load of SN50 as illustrated in Fig. 7. Even though the normalized compressive axial load applied to columns, / g cN A f ′ , was 0.5 for SN50 and

0.6 for the cantilever columns, the axial strain of the first story north column of SN50, 1FNC-SN50, under compression at 3% drift was more than three times larger than those of D1NVA and D1NVB. It can be concluded that this large difference in axial strain variation cannot be grasped while testing a single isolated column. Hence, it is important to test an entire frame or sub-structure in order to reflect and assess the real situation that a column may be subjected to during a real earthquake. Shift of the Contraflexure Point at Columns Fig. 8 shows the curvature distribution along the beam length at maximum drifts for LN60. It can be observed that beyond 2% of the positive drifts, curvatures at the beam-ends were nearly two times the ones recorded during the negative drifts. This increase in the curvature distribution was found to be directly linked to the shift of contraflexure point at columns as illustrated in Fig. 9 (a). It is well known that curvature distribution, ( )xφ , and bending moment distribution, ( )M x , at any section of the frame-member are related to each other by:

( ) ( )EI x M xφ = (2) where E and I are the Young’s modulus and moment of inertia of the considered element. Moment at a section distant from the left side of the beam by a distance of “ x ”, as shown in Fig. 9 (a), can be written as:

2( ) / 4A A AM x V h QH N x R x= + − + (3) Near the left side edge of the beam, the third and fourth terms of the right side of Eq. (3) can be neglected since the value of “ x ” is very small, hence, Eq. (3) can be rewritten as:

2( ) / 4AM x V h QH= + (4)

LN60 frame curvature distribution along beam length at maximum drift

-3

-2

-1

0

1

2

3

0 500 1000 1500 2000 2500

Zone location from west column internal face (mm)

Cur

vatu

re 1

0-4

(1/m

m)

+4% Drift+3% Drift+2% Drift+1% Drift+0.4% Drift

LN60 frame curvature distribution along beam length at maximum drift

-3

-2

-1

0

1

2

3

0 500 1000 1500 2000 2500

Zone location from west column internal face (mm)

Cur

vatu

re 1

0-4

(1/m

m)

-4% Drift-3% Drift-2% Drift-1% Drift-0.4% Drift

(a) Positive cycles (b) Negative cycles

Fig. 8. Curvature distribution along the beam length of LN60

The increase of curvature at beam is due to the increase of bending moment given in Eq. (4), as a consequence of the increase in the level arm of the shear force at column, h . Shift of the contraflexure points at columns were evaluated using the experimental recorded bending moment at beam edge, the applied horizontal load and the column shear force. Fig. 9 (b) shows the variation of the contraflexure point at the west column of LN60. It was found that only in the west column under the positive cyclic loading that the contraflexure point, h , shifted from negative value to positive value, showing that the contraflexure point was



8

shifted into the column as illustrated in Fig. 9 (a), which explain the differnce in values of the curvature distribution shown in Fig. 8. The contraflexure point varied from –0.8 m to +0.2 m, which means that the level arm of the column shear force, AV , varied around 1 m. Shift of the lever arm toward column base, is due mainly to the degradation and damage of the lower part, plastic hinge region, of the columns.

Q/2

NA

VA

RA

Q/2

NB

xH /22

:Redistribution of bending moment diagram

:New location of contraflexure point

h

West column East column

Positive drift

West column LN60

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0 1 2 3 4

Drift (% )

Con

trafle

xure

poi

nt, h

(m)

(a) Moment redistribution (b) Variation of the contraflexure point

Fig. 9. Variation of the moment redistribution due to the shift of the contraflexure point

Effect of the lever arm variation on the seismic performance of the plastic hinge region cannot be captured by a cantilever column test, since the point of the application of the horizontal load is kept constant along the test. To take this effect into account, it is suggested that double flexure column test should be carried out instead of a single curvature column test, cantilever column. ANALYTICAL RESULTS The analytical results for the sixteen RC cantilever columns can be found elsewhere [8]. Due to the copyright this part will not be shown here, however, the readers are welcome to consult this reference for more details. Frames Sub-assemblage Prediction of the Load-drift Relationships The envelope curve of the load-drift relationship was calculated using the pushover analysis option in the nonlinear SAP2000 program [9]. Columns and beams were modeled with a beam element as shown in Fig. 10 (a). Plastic hinges where introduced at the end of each element having the characteristics recommended by the Japanese design guidelines [4]. The pushover analysis was carried step by step, by incrementing the horizontal force until a collapse mechanism is reached. Tab. 4. Comparison between SAP2000 and the test results for the small-scale frames

Positive Negative Positive NegativeSN30 0.846 0.877 0.963 0.998SN50 0.838 0.862 0.897 0.923

Q-analysis/Q-experimental (Without rigid zone)

Q-analysis/Q-experimental (With rigid zone)Frame

identification



9

Tab. 5. Comparison between SAP2000 and the test results for the large-scale frames

Positive Negative Positive Negative Positive NegativeLN60 709.00 -709.00 717.37 -717.37 1.01 1.01QN60 709.00 -662.90 709.19 -709.19 1.00 1.07

Specimen Experimental (kN) Analytical -SAP-(kN) Analy./Exp.

Rigid zoneFixed supportBeam hingeColumn hinge

SN30 frame

-250

-200

-150

-100

-50

0

50

100

150

200

250

-6 -4 -2 0 2 4 6

Drift Ratio, D/H (% )

Bas

e Sh

ear,

Q (K

N)

SAP2000: Without R.ZoneSAP2000: With R.ZoneExperimental: SN30 frame

(a) Model for the small-scale frames (b) Experimental and analytical results for SN30

Fig. 10. Model and analytical results using SAP2000

In the first trial beams and columns were modeled using the beam-element ignoring the beam-column joint panel. This trial gave a lower envelope curve compared to the experimental one. The ratios between the analytical to the experimental results, in term of peak load for positive and negative cycling, varied between 84 to 88%. The model was ameliorated by inserting rigid zones at the beam-column joints. The envelope curve of the second trial was improved considerably for both frames. In this case the ratios, defined above, varied between 90 to 100%. A comparison between the experimental and analytical peaks is given in Tab. 4. The experimental cyclic loading loops and the analytical envelope curves for the two models are shown in Fig. 10 (b) for SN30 as an example. It is clear from the figure that the analytical envelope curves using the rigid-zones fit quite well with the experimental hysterisis curves. Pushover analysis was also carried out for large-scale frames, LN60 and QN60. As for the small-scale frame, a good prediction was found for the large-scale frames. Tab. 5 compares the experimental and analytical peak loads. The analytical peak loads varied between 100 to 107% of the experimental ones, which is quite acceptable. Proposed method for prediction the Axial load in Beams In design practice, beams in a RC moment resisting frame building are designed under shear and bending moment only. However, axial load exists in reality due to the elongation of plastic hinge regions as discussed previously. Here after, a simple method for computing the probable axial compression force that may be developed in beams is proposed. Using Fig. 11 (a), the shear force 1N at column 1 can be determined using the beam shear force, bV , and

the beam axial load, bN , as follows:

( )1 2 21 1 2 2

1b bN h N M

h hα

α α= −

+ (5)



10

where, 1h and 2h are the height of the first story and second story, respectively. 1 1hα and 2 2hα are the distances from the center of the considered beam-column joint to the column’s contraflexure points that can be determined by any kind of software. bM is the beam moment at beam-column joint defined as

b bM V L= , where L can be taken as half of the beam span length. Moments at the top of column 1 is found to be equal to:

( )1 11 1 1 1 2 2

1 1 2 2b b

hM N h h N Mh hαα α

α α= = −

+ (6)

Solving the axial load in beam, bN , from Eq. (6) we get:

1 1 2 21

2 2 1 1

1b b

h hN M Mh h

α αα α

+= +

(7)

Using Eq. (7) for the case of LN60 and taking bM as the maximum flexural strength of the beam, the beam

axial load was found to be 238bN kN= . The values of iα and iM can be evaluated using the moment

distribution of the frame computed using any kind of frame analysis program. In our case, 2α was taken

equal to 0.6 and the top moment of the first story 1M was taken equal to zero, as found using the nonlinear SAP2000. The maximum axial load recorded by the load cell at mid-span of the beam during the test was

237lcN kN= , which is exactly as the value computed using Eq. (7). The axial compression force in beam was around 33% of the frame horizontal load carrying capacity. Presence of axial load in beams may lead to joint failure since, generally, during design phase beam are designed only for shear and bending. Damage can be important for “T” shape and “L” shape beam-column joints. In the contrary, for the cross shape “+”, the presence of axial load will act as a confinement for the beam column joint.

L

α2

2hα

11h

Ν1

Ν2

Νb

Vb

Contraflexure points

Beam

column 2

column 1

Μb

Μ1

Μ2

Column

Column

Beam

Beam column joint

Vj

T

'sC'cC

Vc

Nb

(a) Acting forces at frame substructure (b) Components acting at the ‘T” shape beam-column joint

Fig. 11. Forces acting at different elements and joint of a RC “T” shape junction

Fig. 11 (b) shows the different forces acting at a “T” shape beam-column joint. The definition of joint shear,

jV , as given in Eq. (8) was introduced by Hanson et al. [10], and is widely accepted and used nowadays. The joint shear means an internal force acting on the free body cut at the horizontal line at the mid height of the joint core as illustrated in Fig. 11 (b).



11

j s c c cV C C V T V′ ′= + − = − (8) In Eq. (11), cC′ is the concrete compressive force, sC′ is the compressive force carried by the top

reinforcement and T is the tensile force carried by the lower reinforcement. Eq. 8 was derived without axial force acting in beam. However, tested frame showed clearly the presence of axial load in beams, bN . We suggest that Eq. 8 should be modified in order to take into account the real applied forces near the beam-column joint connection. Hence, Eq. (8) can be rewritten as:

j s c b cV C C N V′ ′= + + − (9) where the beam axial load, bN , can be evaluated using the proposed equation, Eq. (7). To avoid the formation of plastic hinge in columns, many codes suggests that the flexural strength ratio at joint, defined as the ratio between the sum of the moments of the columns, cM∑ , to the sum of the

moments of beams, bM∑ , framing into the joint, should be larger than unity. As an example the ACI code [11] suggests that the ratio should be larger than 1.20. For the large-scale frame, the generated axial force at mid-span of the beam, reduced the flexural strength ratio at joint of about 14%. This amount of reduction is very important and can lead to the formation of plastic hinge in columns before beams. CONCLUSIONS To assess the seismic performance of the plastic hinge region of reinforced concrete columns, sixteen cantilever columns and four frame sub-assemblage were tested under various axial and lateral loading patterns. The main conclusions of this experimental and analytical investigation are as follows:

1. Axial load intensity had a small effect on the envelope curve of the second-cycle of the load-displacement relation for specimens under a unidirectional horizontal load with a constant or variable axial load. However, specimens under bi-directional horizontal loads, showed a large difference between the first and the second envelope curves. Also it was observed that damage, concrete spalling and buckling, was more pronounced for large-scale columns than for small-scale columns.

2. The type of loading, unidirectional or bi-directional, and axial load intensity had an influence on the axial strain variation, elongation/shortening. From the experimental results and as for a retrofitting point of view, it is suggested to lower the maximum normalized axial load suggested by the Japanese design guidelines, 067, to a lower value especially for strategic building that must be functional after a strong earthquake.

3. Axial strain for the first story columns were higher than those of the cantilever columns even though the axial load was more important for the case of the cantilever column than in the frame. This is due to the complex interaction between the beam, column and the joint.

4. The envelope curves of the load-drift relationship for the frames were predicted with a good accuracy using a pushover analysis with the plastic hinge characteristics for beams and columns as suggested by the Japanese design guidelines.

5. It is suggested that double curvature column should be tested instead of single curvature column test, cantilever column, in order to take into account the shift of the Contraflexure point.

6. The joint shear force and the flexural strength ratio at a joint have to be assessed by taking into account the probable axial loads that can be generated in beams. The beam axial load is due to the beam elongation as a consequence of the damage that occurs at the beam plastic hinge regions.

REFERENCES 1. Abrams D. P. Influence of axial force variation on flexural behavior of reinforced concrete columns. ACI

structural journal, V.84 No.3 1987, 246-254. 2. Benzoni G., Ohtaki T., Priestley M. j. N., and Seible F. Seismic performance of reinforced concrete

columns under varying axial load. Proceeding of the fourth caltrans seismic research workshop, California department of transportation, Sacramento, California 1996.



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3. Asad E., and Yan X. Behavior of reinforced concrete columns under variable axial loads. ACI structural journal, V.101 No.1 2004, 124-132.

4. Architecture Institute of Japan AIJ, Design guidelines for earthquake resistant reinforced concrete buildings based on inelastic concept 1999.

5. Yokoo Y. and Nakamura T. Non-stationary hysteresis uniaxial stress-strain relations of wide-flange steel: Part II-Empirical formulae, Transactions of the Architectural Institute of Japan, AIJ, No.260, October 1977, pp.71-82.

6. Larry L. Dodd The dynamic behavior of reinforced-concrete bridge piers subjected to New Zealand seismicity, PhD thesis, Department of Civil Engineering University of Canterbury Christchurch, New Zealand, report 92-04, ISSN 0110-3326, June 1992.

7. Kono S., Bechtoula H., Kaku T., Watanabe F. Damage assessment of RC columns subjected to axial load and bi-directional bending. Proceedings of Japan Concrete Institute, JCI, Vol.24 No.2 2002, pp.235-240.

8. Bechtoula H., Kono S. and Fumio W. Experimental and Analytical Investigations of Seismic Performance of Cantilever Reinforced Concrete Columns Under Varying Transverse and Axial loads, Journal of Asian Architecture and Building Engineering, JAABE vol.4 no.2 November 2005, pp.467-474.

9. SAP2000, linear and nonlinear static and dynamic analysis and design of three-dimensional structures, Integrated Finite Elements Analysis and Design of Structures, a product of Computer & structures, Inc., Version 8.0, June 2002.

10. Hanson, Norman W. and Harold W. Connor: Seismic Resistance of Reinforced Concrete Beam-Column Joint, Journal of the Structural Division, Vol. 93, ST5, Oct.1967, pp.533-560.

11. American Concrete Institute Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02), Reported by ACI Committee 318.

seismic design proposal based on a study on rc columns and

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