9 Evaluation Of The Seismic Performance Of A 3story Ordinary Moment Resisting Concrete Frame

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2004; 33:669–685 (DOI: 10.1002/eqe.367)

Evaluation of the seismic performance of a three-story ordinary moment-resisting concrete frame Sang Whan Han1; ∗; † , Oh-Sung Kwon2 and Li-Hyung Lee1 1 Department 2 Department

of Architectural Engineering; Hanyang University; Seoul 133-791; Korea of Civil and Environmental Engineering; University of Illinois at Urbana-Champaign; Urbana; IL 61801; U.S.A.

SUMMARY This study focuses on the seismic performance of Ordinary Moment-Resisting Concrete Frames (OMRCF) designed only for gravity loads. For this purpose, a 3-story OMRCF was designed in compliance with the minimum design requirements in the American Concrete Institute Building Code ACI 318 (1999). This model frame was a regular structure with
exure-dominated response. A 1=3-scale 3-story model was constructed and tested under quasi-static reversed cyclic lateral loading. The overall behavior of the OMRCF was quite stable without abrupt strength degradation. The measured base shear strength was larger than the design base shear force for seismic zones 1, 2A and 2B calculated using UBC 1997. Moreover, this study used the capacity spectrum method to evaluate the seismic performance of the frame. The capacity curve was obtained from the experimental results for the specimen and the demand curve was established using the earthquake ground motions recorded at various stations with dierent soil conditions. Evaluation of the test results shows that the 3-story OMRCF can resist design seismic loads of zones 1, 2A, 2B, 3 and 4 with soil types SA and SB . For soil type SC , the specimen was satisfactory in seismic zones 1, 2A, 2B and 3. For soil type SD , the OMRCF was only satisfactory for seismic zones 1 and 2A. Copyright ? 2004 John Wiley & Sons, Ltd. KEY WORDS:

concrete structures; performance evaluation; base shear; capacity spectrum method

1. INTRODUCTION During the recent earthquakes, such as the 1994 Northridge earthquake in the U.S.A., the 1995 Kobe earthquake in Japan, and the 1999 Chi-Chi earthquake in Taiwan, many concrete frame structures experienced substantial damage. Older low- to mid-rise concrete buildings were particularly vulnerable to those earthquakes. The seismic performance of concrete buildings during such earthquakes generally depends on reinforcement details, building shape, applied design provisions, etc. Insucient details can cause unexpected structural failure during a large earthquake event. ∗ Correspondence

to: Sang Whan Han, Department of Architectural Engineering, Hanyang University, Seoul 133791, Korea. [email protected]

† E-mail:

Copyright ? 2004 John Wiley & Sons, Ltd.

Received 3 December 2002 Revised 29 July 2003 Accepted 8 October 2003

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Most low-rise buildings in low-to-moderate seismic zones, and older buildings in high seismic zones have been designed primarily for gravity loads. Because such buildings have less stringent details than those required in a high seismic zone (e.g. strong column–weak beam requirements need not be considered), the buildings may behave in a brittle manner during a large earthquake event. In these cases story mechanisms can develop. Current design provisions, such as ACI 318 (2002) [1], dene three types of moment frames: Ordinary Moment Resisting Concrete Frame (OMRCF), Intermediate Moment Resisting Concrete Frame (IMRCF), and Special Moment Resisting Concrete Frame (SMRCF). OMRCF is the most popular type of moment frame in low-to-moderate seismic zones. This study focuses on OMRCF for which the detail and design requirements are less stringent than IMRCF and SMRCF. The details of OMRCF are dierent from those of IMRCF and SMRCF as follows: (1) Strong column–weak beam requirements need not be satised, which may result in story failure mechanisms during a large earthquake event. (2) Column splices can be placed just above slabs that are likely plastic hinge locations during a large earthquake loading. (3) The spacing limits for column ties and beam stirrups of OMRCF are large. (4) No transverse shear reinforcement is required at interior beam–column joints, and minimal reinforcement is required at exterior joints. (5) Discontinuous
exural reinforcement can be placed in a beam. This study investigates the seismic behavior of moment frames designed only for gravity loads (1.4D + 1.7L), and detailed by the requirements for OMRCF in ACI 318 (1999) [1]. For this purpose, a 1=3-scale 3-story OMRCF oce building was constructed and tested. In this study, the Capacity Spectrum Method (CSM) was used to evaluate the seismic performance of the OMRCF. This method requires both the capacity and demand curves to nd a performance point. This point is treated as the seismic demand of a structure (ATC-40, 1996) [2]. In this study, the capacity curve was determined from the experimental result of the OMRCF structure. The demand spectrum was determined from the ground motion acceleration of 30 earthquakes, recorded at the SB , SC and SD soil sites. The accelerations were scaled to conform to the design spectrum in seismic zones 1, 2A, 2B, 3 and 4, as classied in the UBC [3].

EXPERIMENTAL PLAN Design of OMRCF In this study a 3-story oce building was considered. The building was assumed to have 3 bays in the E–W direction and 4 bays in the N–S direction. The story height was 3:5 m and the width of each bay was 5:5 m. The total building height was 10:5 m. Figure 1 shows the dimensions of the building. Table I shows the design loads used in the building design. The specied compressive strength of concrete (fc
) and yield strength of reinforcement (fy ) are assumed to be 23:5 MPa (240 kgf =cm2 ) and 392 MPa (4000 kgf =cm2 ), respectively. Structural analysis for member design was carried out using the commercial software SAP2000 [4]. Only gravity loads were considered for the design in this study. As this study is aimed at Copyright ? 2004 John Wiley & Sons, Ltd.

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550cm

550cm

THREE-STORY ORDINARY MOMENT-RESISTING CONCRETE FRAME

All Columns 33cm x 33cm

550cm

All Beams 25cm x 50cm

550cm

183cm 183cm

Test Specimen

550cm

(a)

550cm

550cm

Beam (25cm x 50cm)

550cm

550cm

(b)

350cm

350cm

Column (33cm x 33cm)

350cm

Slab(15cm)

550cm

Figure 1. Plan and elevation of prototype structure: (a) plan; and (b) elevation.

Table I. Design loads. Category

Loads

Value (N=m2 )

Dead load

Slab and roof Ceiling Interior partition Electric and water Total slab dead load 1st, 2nd, and roof 1:4D + 1:7L

3530 441 981 245 5200 2450 11400

Live load

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S. W. HAN, O.-S. KWON AND L.-H. LEE

517cm 210cm

54cm

A

254cm

B

CL C

C

2 -D19

3 -D19

2 -D19 A

B

50cm 35cm 15cm

11-D10 @200mm

C

13-D10 @200mm

C

13-D10 @200mm

2-D19

3-D19

D10 2-D19

D10 2-D19

2-D19

25cm

A-A

B-B

C-C

Figure 2. Rebar layout for beams of prototype structure.

existing structures that were built based on the previous code, ACI 318 (1999) [1], the load combination of 1.4D + 1.7L was used to design the frame. The slab was designed using the direct design method according to Section 13.6 of ACI 318 (1999) [1]. Cross-sections of the columns and beams were assumed to be 33 × 33 (cm2 ) and 25 × 50 (cm2 ), respectively. Beam and column details followed the design procedure for the ordinary moment frame in ACI 318 (1999) [1]. The design result of the beams in the prototype 3-story frame is given in Figure 2. Columns of the prototype structure are shown in Figure 3.

Experimental model layout The prototype frame was reduced to a 1=3-scale model due to experimental space constraints. The test specimen represented an inner column strip along the E–W direction of the prototype structure (see Figure 1(a)). The material size used in the 1=3-scale model specimen, such as maximum size of aggregates and reinforcement, were also reduced. This study attempted to make the material properties of the reduced-scale model identical to those of the prototype model. As materials used in a 1=3-scale model specimen are almost similar in strengths and modulus of elasticity as those of the prototype building, the similitude law of true replica was applied to reduce the prototype model. Copyright ? 2004 John Wiley & Sons, Ltd.

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3-D10 @150mm

50cm

8-D10 @300mm

8-D10 @300mm

3-D10 @150mm 3-D10 @150mm

50cm

8-D10 @300mm

8-D10 @300mm

300cm

3-D10 @150mm 3-D10 @150mm

3-D10 @150mm 3-D10 @150mm

50cm Y

Y

Y

9-D10 @300mm

4-D10 @150mm

3-D10 @150mm

300cm

3-D10 @150mm 3-D10 @150mm

673

Y

9-D10 @300mm

300cm 18.5cm

4-D10 @150mm 4-D19

33cm

D10

33cm

Figure 3. Rebar layout for columns of prototype structure.

Material properties For concrete, based on trial mixes from various recipes, a design mix was established for a 28-day target strength of 24 MPa, with a slump of 18 cm, and maximum aggregate size of 13 mm. Cylinder specimens with a diameter of 10 cm and a height of 20 cm were cured near the model specimen in the laboratory. The measured strength was 29 MPa at 28 days. The reinforcing bars used in the prototype building were D10 (10 mm diameter) and D19 (19 mm diameter), with yield strengths (fy ) of 294 MPa and 392 MPa and cross-sectional rebar areas (Ab ) of 0:713 cm2 and 2:87 cm2 , respectively. In order to satisfy the similitude law for both yield and ultimate strength of rebar, D19, which was used for longitudinal reinforcement in the prototype building, was replaced by D6 with a cross-sectional area of 0:316 cm2 and a diameter of 6:35 mm in the 1=3-scale model specimen. A H3:3 mm wire with a cross-sectional area of 0:086 cm2 and a yield strength of 345 MPa was used in the model specimen for replacing D10 bars for lateral reinforcement in the prototype frame. Reinforcement for slabs in the model specimen was a 5 cm square wire mesh composed of H3:2 mm wire with yield strength of 461 MPa. Copyright ? 2004 John Wiley & Sons, Ltd.

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Mass similitude For proper modeling of gravity loads, mass similitude must be satised. Given the scale factor for geometric length as
, the scaling factor for material volume becomes
3 . Required and provided masses of the model are: mreq m = mp ·

1
2

mprov m = mp ·

1
3

where mreq m = required mass of the test model mprov m = provided mass of the test model mp = mass of the prototype structure
= scale factor = 3 The provided mass is less than required. To correct this dierence, an additional mass is required as much as m shown below: 
2 1 1 − = mp = 2mprov m = mp · m
2
3 27 Therefore, the additional required mass is twice the mass of the model. To compensate for the dierence in required and provided gravity loads additional weight was placed on the model using concrete blocks. These blocks were mounted at the one-sixth point of the span length of the beam to simulate the shear forces and moments at ends of the beam induced by gravity loads. Figure 4 shows the test specimen with concrete block arrangements on slabs. Loading and test set-up The experimental set-up of the test specimen is shown in Figure 4. A guide frame was placed on each side of the test specimen to prevent out-of-plane movement and instability of the specimen. The specimen was subjected to a quasi-static reversed cyclic loading controlled by drift given in Figure 5. In this gure, the roof drift ratio, Dr , denotes the ratio of the roof displacement (D3 ) to the height of a structure (H ). Drift loads were applied at the roof by a hydraulic actuator xed on the reaction wall, and the force induced by this drift at the roof (F3 ) was measured. Forces F1 and F2 to be applied at the 1st and 2nd
oors, respectively, were calculated from F3 , the measured force, as 1=3 and 2=3 of F3 . The ratios for F1 =F3 and F2 =F3 were kept constant, (i.e. 1=3 and 2=3, respectively) throughout the test. Horizontal displacements of the specimen were measured with linear potentiometers placed at each level. In addition, 12 pairs of potentiometers were installed to measure the average curvatures at beam and column sections. Potentiometers were located at 1=2 of the beam depth from the face of the column, and instrumented column sections were located at 1=2 of the column depth from the face of a beam. Copyright ? 2004 John Wiley & Sons, Ltd.

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675

Figure 4. Test set-up of 1=3-scale model specimen.

6%

Roof Drift, Dr

4% 2% 0% 0 -2%

2

4

6

8

10

12

14

-4% -6%

Number of Cycles

Figure 5. Loading history.

TEST RESULTS AND OBSERVATIONS Cracks and failure mode The test specimen was observed after each cycle to assess safety concerns. During the observation after the rst cycle with roof drift ratio of 0.5%, the rst crack was found. Cracks were found at both ends of all columns and beams in the rst and second story. In the third story, cracks were observed at the lower ends of all columns and interior beam ends. At a roof drift ratio of 2.5%, shear cracks were observed at the exterior joint of the rst
oor, where the transverse beam meets the longitudinal beam. At a roof drift ratio of 3.0%, the crack widths at the upper ends of the rst-story columns became wider, while slight concrete crushing was observed at the lower ends of the columns in the same story. The test was terminated at a roof drift ratio of 5.5% where lateral strength deteriorated to 67% of the maximum strength. Copyright ? 2004 John Wiley & Sons, Ltd.

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Figure 6. Damage patterns in the model.

0.20

Hu =0.157 Base shear coefficient (V/W)

0.15

0. 8 Hu

0. 75 Hu 0.10 0.05 0.00

∆ max

6

-0.05

∆ y ∆ u =0.015

-0.10 -0.15 -0.20 -0.06

-0.04

-0.02

0

0.02

0.04

0.06

Roof drift ratio(∆/H)

Figure 7. Roof drift ratio and base shear coecient relation.

After testing, the columns in the rst and second story were damaged. Cover concrete was lost and reinforcements were exposed at the column ends in the rst-story (see Figure 6). Hysteretic performance The hysteretic loops (measured base shear force coecient (V=W ) versus roof drift ratio (=H )) are shown in Figure 7. The hysteresis loops shown in the gure were quite stable. Copyright ? 2004 John Wiley & Sons, Ltd.

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+

-

Loading Direction 0.2

0.2

-0. 0002

-0 .0002 0.0002

0.0002 0.2

-0.2

0.2

0.2

-0 .2 -0. 0002

0.0002

Beam lef t- end -0. 2 -0. 0002

0.2

2nd story Col. Bot.

0.0002

-0 .0002

2nd story Col. Bot.

0.2

0.0002

Beam right - end -0. 2

-0. 0002 0.0002

0.0002

Beam left-end -0. 2

-0.0002

1st story Col. Top -0.2

1st story Col. Top -0.2

0.2

0.2

-0. 0002 0.0002 -0.2

1st story Col. Bot.

-0 .0002

0.0002 -0.2

1st story Col. Bot.

Note that the abscissa is curvature of members (rad/mm) and the ordinate is base shear coefficient.

Figure 8. Base shear force versus curvature measured at discrete locations.

The model behaved almost elastically until ±0:5% roof drift level. As the drift level increased, the stiness degradation in the loading curves became larger. At the 2nd cycle of a large drift amplitude (¿1:8%), signicant stiness degradation was observed while strength degradation was relatively small. Even though the structural damage was severe at the roof-drift ratio of 5.5%, hysteretic loops were still stable without abrupt degradation of strength or energydissipation capacity. Figure 8 shows the hysteretic curves (base shear vs curvature) of the beams and columns at the exterior and interior joints at the 1st
oor. In Figure 8, the axis scales are set equal to facilitate comparisons. In the exterior joints, damage was distributed to the exterior beam and column. Exterior columns did not experience as severe inelastic excursion as interior columns, whereas the exterior beam experienced large inelastic excursion. Considerable cracks were found at the exterior beam, while the
exural cracks at the exterior columns were minor compared with the interior columns. Owing to the slab eect, the hysteretic curves at the exterior joints were not symmetric (see Figure 8). In the negative loading the reinforcement in the slab acted as tensile reinforcement, so that the beam moment capacity became larger. The slab contribution to the beam moment capacity, however, was minor in the positive loading direction. For the positive loading direction the damage is therefore concentrated in the beams, whereas exterior Copyright ? 2004 John Wiley & Sons, Ltd.

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columns behaved almost in the elastic range. In the negative loading direction the damage was distributed among the beams and columns. For the interior joint, the hysteretic curves of the beams and columns were symmetric. Columns behaved in the inelastic range whereas beams almost remained in the elastic range. This phenomenon can be explained by calculating the strength (moment capacity) ratio between the beams and columns at a joint. At the interior joint, the summation of nominal moment capacities of the columns was 2 × 2:4 kN · m = 4:8 kN · m, while the summation of those of the beams was 2 × 3:4 kN · m = 6:8 kN · m, where the slab is disregarded and the positive moment capacity is used in the calculation for brief explanation. The ratio of the moment capacities of beams to columns is 1.44, which means the columns are weaker than the beams (strong beam–weak column). Therefore, when a large earthquake occurs, columns are more vulnerable than beams at interior joints. At the exterior joint, however, the ratio is 0.72 (3:41=4:73), which is treated as strong column–weak beam. Maximum base shear force and energy dissipation The maximum base shear force from the quasi-static test was 0:16W , where W was the total weight of the model. This shear force was attained at a roof drift ratio (u ) of 0.015 (see Figure 7). The design base shear for a similar structural layout in seismic zone 2A can be calculated as the following according to the UBC [3]. V=

(0:15) · (1:0) Cv I W= = 0:10W RT (3:5) · (0:43)

where Cv is the seismic coecient. For soil type SB and seismic zone 2A, Cv is 0.15. I is the seismic importance factor; for a standard occupancy structure I is 1.0. R is the response modication factor; for an OMRCF building R is 3.5. T is the natural period of the building; for the prototype building T was 0:43 sec based on the UBC [3]. Using the above equation the design base shears for other seismic zones (1, 2B, 3 and 4) was determined to be 0:05W , 0:13W , 0:20W and 0:27W , respectively. The 3-story OMRCF designed only for gravity load, therefore, had a base shear strength larger than the design base shear required for seismic zones 1, 2A and 2B. The prototype structure was designed using the ACI 318 (1999) code [1] in which the load combination for gravity force is 1.4D + 1.7L. In the recent revision of ACI 318 (2002) [1], the load combination has changed to 1.2D + 1.6L which results in smaller section dimensions than those of a structure designed with the previous code. Thus the lateral resistant capacity of those structures could be smaller than the structures designed with the previous code. As some other provisions, such as maximum and minimum reinforcement ratio, have also changed in ACI 318 (2002), it requires more thorough study to conclude the eect of code change on the lateral resistance capacity of OMRCF. Yield drift was obtained from a bilinear representation of base shear coecient vs roof drift ratio curve (Figure 7), where the secant line is drawn from origin to the 0:75Hu point in the gure. From Figure 7, a yield drift ratio of 0.005 was determined. The maximum drift ratio (max ) was approximated as the drift ratio corresponding to the strength deteriorated by 20% of the maximum strength (0:8Hu ). From Figure 7, the maximum drift ratio was determined to be 0.04. Copyright ? 2004 John Wiley & Sons, Ltd.

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100

6%

Dissipated energy (%)

3rd story 80

2nd story

40%

1st story 60 40

54%

20 0 1

6

11

16

21

Number of cycles

Figure 9. Cumulative dissipated energy in each cycle.

The energy dissipation is known to be the most eective index for indicating the seismic energy absorption capacity of a structure. Figure 9 shows the cumulated dissipated energy that is calculated based on the applied external forces and story displacements. From Figure 9 it is shown that 54% of the total energy was dissipated at the rst story and 40% was dissipated at the second story. According to Figure 9 most of the inelastic deformations occurred at the rst and second stories, while the third story behaved mainly in the elastic range. Seismic performance evaluation In this study, the capacity spectrum method (CSM) was used to evaluate the seismic performance of the 3-story OMRCF. The capacity spectrum method is a non-linear static procedure that provides a graphical representation of the global force–displacement capacity curve of the structure (i.e. pushover) and compares it to the response representations of the earthquake demands. It is a useful tool in the evaluation and retrot design of existing concrete buildings. The capacity spectrum method uses the intersection of the capacity (pushover) curve and a reduced response spectrum to estimate the maximum displacement. Thus, the method needs to determine the capacity of the structure and the seismic demands. The performance of the structure is evaluated in view of global response and component response. The response limit for the given performance goal is specied in ATC-40(1996) [2] and FEMA 273(1997) [5]. The capacity of a structure can be determined from either non-linear analysis or experiment. As there exist many uncertainties and assumptions in modeling concrete structures for analytical study, the analysis result could result in signicant error. In this study, the capacity of the structure was determined from the experimental result of the 3-story OMRCF structure. The demand spectrum was determined from the ground motion accelerations of 30 earthquakes in Table II, recorded at the SB , SC and SD soil sites. Ground accelerations having a response spectrum similar to the design response spectrum were selected. The accelerations were scaled to conform to the design response spectrum in each seismic zone (1, 2A, 2B, 3 and 4) as classied in the UBC [3]. Copyright ? 2004 John Wiley & Sons, Ltd.

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Table II. Earthquake catalog. No.

Event name

Station name

Date

Comp

PGA

(a) Soil Type SB 1 Michoacan 2 Helena 3 Kern County 4 Mammoth Lakes 5 Borrego Min 6 Mammoth Lakes 7 San Fernando 8 Imperial Valley 9 San Fernando 10 Whittier

Calete De Campo Federal Bldg, Helena Taft Long Valley Dam, Bed Rock SCE Power Plant, San Onofre Long Valley Dam Cal. Tech. Seism. Lab. El Centro Santa Felicia Dam(Outlet) Pacoima-Kagel Canyon

21=08=85 31=10=35 21=07=52 25=05=80 08=04=68 25=05=80 09=02=71 18=05=40 09=02=71 01=10=87

N90W EW N21E 90 N33E 90 EW NS S08E 90

0.083 0.145 0.156 0.137 0.041 0.474 0.192 0.318 0.217 0.158

(b) Soil type SC 1 Whittier Narrows 2 Whittier Narrows 3 Landers 4 Landers 5 Landers 6 San Fernando 7 San Fernando 8 Northridge 9 Northridge 10 Northridge

Mt. Gleason Ave. Kagel Canyon Ave. N. Figueroa St. Mel Canyon Rd Willoughby Ave. Water and Power Building South Olive Ave. Mel Canyon Rd S. Alta Dr. N. Figueroa St.

01=10=87 01=10=87 28=06=92 28=06=92 28=01=92 09=02=71 09=02=71 17=01=94 17=01=94 17=01=94

S90W N45E N58E N90E S00E S40W S37W S00E N00E N32W

0.098 0.12 0.028 0.030 0.024 0.172 0.196 0.026 0.074 0.158

Colima Rd Palma Ave. Del Amo Blvd Manhattan Beach Blvd Willoughby Ave. S. Orange Ave. Water St. Colima Rd Sunset Blvd Via Tejon

01=10=87 01=10=87 28=06=92 28=06=92 28=01=92 09=02=71 09=02=71 17=01=94 17=01=94 17=01=94

S90W N40W N58E N90E N90W S40W N38E S00E N00E N32W

0.046 0.045 0.054 0.158 0.250 0.065 0.111 0.197 0.036 0.025

(c) Soil type SD 1 Landers 2 Landers 3 Landers 4 Northridge 5 Northridge 6 Northridge 7 Whittier 8 Whittier 9 Whittier 10 San Fernando

Capacity spectrum As the experiment was conducted using a 1=3-scale model, the roof drift–base shear relationship of a full-scale structure should be scaled from the test results shown in Figure 7. FEMA 273 [5] recommends that a smooth ‘backbone’ curve can be drawn through the intersection of the rst cycle curve for the i-th deformation step with the second cycle curve of the (i − 1)-th deformation step, for all i steps. In this study, however, note that the capacity curve from the scaled load–deformation relationship was taken by connecting the plateaus of each cycle, as shown in Figure 7. The measured capacity curve needed to be converted into a spectral displacement and spectral acceleration. This conversion required the dynamic properties of the structure. To Copyright ? 2004 John Wiley & Sons, Ltd.

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681

Table III. Modal participation factor and modal mass factor of prototype structure.

Roof 2nd Story 1st Story  PFRF am

W=g (t)

1

(W=g) × 1

(W=g) × 21

58.3 60.1 60.1 178.5

1.000 0.747 0.335 –

58.3 44.9 20.1 123.3

58.3 33.6 6.8 98.7

1.25 0.86

Where W=g = mass of structure, 1 = 1st mode shape, PFRF = modal participation factor at roof, and am = eective mass coecient

identify the dynamic properties of the structure, modal analysis was conducted using the commercial software SAP2000 [4]. Because micro-cracking is present in reinforced concrete members, the stiness of the members was reduced as specied in the ATC-40 document. For columns and beams, reduction factors of 0.7 and 0.5 were used, respectively. Also, the natural period of the specimen was measured using a snap-back test. The 1st modal natural period of the specimen (1=3-scale model) was measured as 0:32 sec. Since the scale of the structure is 1=3, the stiness reduces to 1=3. Also, as additional mass was placed√to adjust the mass to be 1=9 of the original structure, the structural period was reduced to 1= 3 of the original structure. To convert the period√of the test specimen to that of the prototype model, the measured period was multiplied by 3, resulting in 0:55 sec, which is 4.3% less than the period from eigenvalue analysis using SAP2000 [4]. Thus, it was assumed that the analytical model represented the dynamic property of the test specimen. The modal analysis results, the corresponding modal participation factors, and the modal mass factors are given in Table III. The capacity curve was converted using modal analysis and is shown in Figure 10. Demand spectrum In this study, the seismic performance of a given structure was evaluated using the design level and maximum earthquakes of zones 1, 2A, 2B, 3 and 4, as dened in the UBC [3]. The structure is assumed to be located on soil sites SB , SC and SD . The earthquake accelerations recorded at each soil site were scaled to make their eective peak acceleration (EPA) close to the design earthquake (DE) and the maximum considered earthquakes (MCE). The selected ground acceleration data are given in Table II. Calculation procedure of performance point This study adopted the procedure developed by Chopra and Goel [6]. The steps for calculating the performance point in this study are brie
y summarized below. (1) Assume that the performance point is on the capacity curve. Then make bilinear representation of the capacity curve, which has the same initial stiness and energy dissipation as that of the original capacity curve (Figure 10(a)). (2) Generate a response spectra for single-degree-of-freedom system using either eective damping (ATC-40 [2]) or constant ductility (Chopra and Goel [6]). Calculate the median and standard deviation values of spectral acceleration and spectral displacement for Copyright ? 2004 John Wiley & Sons, Ltd.

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Spectral Acceleration (g)

0.50 Bilinear representation of capacity curve α =0.0975, µ =3.367

0.40 0.30

Capacity curve measured from the experiment

0.20 0.10

Assumed performance point Sd = 10 cm

Equal area

dpi

0.00 0

5

10

(a)

15 SD (cm)

20

25

30

Spectral Acceleration (g)

0.50 Seismic demand on SDOF system with α =0.0975, µ =3.367

0.40 0.30

Calculated performance point Sd=7.538 (Err= 24.6%)

0.20

Assumed performance point Sd = 10 cm

0.10 di

0.00 0

5

dpi

10

(b)

15 SD (cm)

20

25

30

Spectral Acceleration (g)

0.50 Seismic demand on SDOF system with α =0.15, µ =3.08

0.40 0.30

Calculated performance point Sd=8.79 (Err = -3 .38 %)

0.20

Assumed performance point Sd = 8.5 cm Bilinear representation α=0.15 ,

0.10 0.00 0

(c)

5

10

15 SD (cm)

20

25

30

Figure 10. Procedures for nding performance point: (a) bilinear representation of capacity spectrum and assumed performance point; (b) demand spectrum and calculated performance point; and (c) nal performance point after iteration.

each period. Then superimpose the capacity curve and demand curve. The intersection point of the two curves is the calculated performance point (Figure 10(b)). (3) The performance point lies between the assumed performance point and the tentative performance point. Follow steps (1) and (2) again. (4) Repeat steps (1) and (2) until the error between the assumed performance point (dpi ) and tentative performance point (di ) is less than 5%, as shown in Figure 10(c) (i.e. 0:95dpi 6di 61:05dpi ). For each consecutive iteration, take a new assumed performance point between the last assumed performance point and the calculated performance point. Copyright ? 2004 John Wiley & Sons, Ltd.

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THREE-STORY ORDINARY MOMENT-RESISTING CONCRETE FRAME

Table IV. Maximum story drift at performance points (%). Earthquake

Site condition

Zone 1

Zone 2A

SB SC

0.41 0.50

0.81 0.78

SD

0.86

SB

Design earthquake

Maximum earthquake

Seismic zone Zone 2B

Zone 3

Zone 4

0.95 1.35

1.56 1.76

1.96 2.16

1.56

2.16

3.36

*

0.67

1.08

1.56

2.16

2.36

SC

0.66

1.35

1.96

3.96

4.16

SD

1.08

3.16

4.56

*

*

Note that the shaded area does not meet the performance criteria in ATC-40.

When the iterations for the performance point converge, the maximum structural displacement expected for the demand earthquake ground motion is thus identied. Performance evaluation From the structural capacity and seismic demand, roof drift was calculated using CSM. The displacements of each story at the performance points were found using the experimental result. The maximum story drift ratios for each performance point are given in Table IV and Figure 11. The ATC-40 document [2] species that the structural displacement should satisfy both the life-safety limit for design earthquakes, and the structural stability limit for maximum considered earthquakes. The response limits are dened in view of both global responses and component responses. The component response criteria are not checked in this study, as the member forces could not be measured from this experiment. In ATC-40, the global response limit, the inter-story drift is 0.02 for the life-safety level and 0:33V=P for the structural stability limit, which is approximately 0.04. Table IV shows that the OMRCF designed only for gravity loads can sustain the seismic load of every seismic zone with soil condition SB , of zones 1, 2A, 2B and 3 with soil condition SC , and of zones 1 and 2A with soil condition SD . As the seismic demand of soil condition SA is smaller than that of soil condition SB , it can be inferred that the OMRCF designed for gravity loads also sustain the seismic load of every seismic zone with soil condition SA . The UBC [3] species that only structures in seismic zone 1 can be designed with OMRCF detail.

CONCLUSIONS This study investigated the seismic performance of the 3-story OMRCF designed only for gravity loads and specied by the requirements for OMRCF. The test for this study was conducted using a 1=3-scale model specimen for the quasi-static cyclic loading. This study adopted the capacity spectrum method to carry out seismic performance evaluation of this 3-story OMRCF. Because the results of this study were obtained for the case of a 3-story OMRCF structure that had a regular shape with a response dominated by
exural behavior, Copyright ? 2004 John Wiley & Sons, Ltd.

Earthquake Engng Struct. Dyn. 2004; 33:669–685

684

S. W. HAN, O.-S. KWON AND L.-H. LEE

Story Drift (DE, Site SB)

3

Story Drift (MCE, Site SB)

3

Life safety limit

Structural stability limits 2

Story

Story

2 Zone 1 Zone 2A

1

Zone 1 Zone 2A

1

Zone 2B

Zone 2B Zone 3

Zone 3

Zone 4

Zone 4

0

0

0.01

(a)

0.02

0.03

0.04

0

0.05

0

0.01

Story Drift (DE, Site SD)

3

0.02

0.03

0.04

0.05

Story drift

Story drift

Story Drift (MCE, Site SC)

3

Life safety limit

Structural stability limits 2

Story

Story

2 Zone 1

Zone 1

Zone 2A

1

Zone 2A Zone 2B Zone 3

1

Zone 2B Zone 3 Zone 4

Zone 4

0

0

0

0.01

(b)

0.02

0.03

0.04

0.05

0

0.01

Story drift

0.04

0.05

0.04

0.05

Story Drift (MCE, Site SD)

3

Life safety limits

Structural stability limits

2 Story

Story

2

Zone 1

1

1

Zone 2A

Zone 1 Zone 2A

Zone 2B

Zone 2B

Zone 3

0

0

0

(c)

0.03

Story drift

Story Drift (DE, Site SC)

3

0.02

0.01

0.02

0.03

0.04

Story drift

0.05

0

0.01

0.02

0.03

Story drift

Figure 11. Global structural responses at performance point against design earthquake (DE) and maximum credible earthquake (MCE): (a) site condition, SB ; (b) site condition, SC ; and (c) site condition, SD .

care must be taken when extrapolating the results of this study to other OMRCFs as many such structures have experienced shear failures during recent earthquakes. The ndings from this study are as follows. (1) The OMRCF structure showed a stable energy dissipation capacity without abrupt strength deterioration, even though the structure was designed for gravity loads only and specied for the requirements of OMRCF. Copyright ? 2004 John Wiley & Sons, Ltd.

Earthquake Engng Struct. Dyn. 2004; 33:669–685

THREE-STORY ORDINARY MOMENT-RESISTING CONCRETE FRAME

685

(2) At the nal loading stage, interior columns in the 1st story were severely damaged, while beams had not experienced any apparent damage. At the exterior joints of the 1st story, damage was distributed to exterior columns and beams. This shows that interior joints have the mechanisms of a weak column–strong beam, whereas exterior joints have that of a strong column–weak beam in the investigated OMRCF. This could be referred to as a hybrid failure mechanism. (3) The maximum lateral strength of the frame was 0:16W , which occurred at a roof drift ratio of 0.015. The expected base shears of the building designed with the UBC [3] and ACI 318(1999) [1] for seismic zones 1, 2A and 2B for soil type SB were 0:05W , 0:10W and 0:13W , respectively. Thus the OMRCF designed only for gravity loads had a base shear strength larger than the unfactored base shear strength required in seismic zones 1, 2A and 2B. (4) The yield roof drift ratio of the test model was 0.005. The maximum roof drift ratio was 0.04, which was obtained at a strength deteriorated up to 80% of the maximum lateral strength. (5) From the results of the capacity spectrum method, it was shown that the OMRCF designed only for gravity loads could therefore sustain the seismic load of every seismic zone with soil condition SA and SB , zones 1, 2A, 2B and 3 with soil condition SC , and zones 1 and 2A with soil condition SD . Note that the results were obtained using a 3-story regular OMRCF structure that was governed mainly by
exure. Thus, caution is needed when trying to extrapolate the results to other OMRCF structures. REFERENCES 1. American Concrete Institute. Building code requirements for reinforced concrete, ACI 318-99,02, Detroit, Michigan, 1999 and 2002. 2. Applied Technology Council. ATC-40: Seismic Evaluation and Retro
t of Concrete Buildings, vols. 1 and 2, California Seismic Safety Commission, No. SSC 96-01, Nov. 1996. 3. International Conference on Building Ocials, Uniform Building Code (UBC), Whittier, California, 1997. 4. Computers and Structures Inc., SAP2000, Berkeley, California, 1997. 5. Building Seismic Safety Council, NEHRP Guidelines for the Seismic Rehabilitation of Buildings (FEMA Publication 273), 1997 Edition, Federal Emergency Management Agency. 6. Chopra AK, Goel RK. Capacity-Demand-Diagram Methods for Estimating Seismic Deformation of Inelastic Structures: SDF Systems, Report No. PEER-1999=02, Pacic Earthquake Engineering Research Center, University of California, Berkeley, 1999.

Copyright ? 2004 John Wiley & Sons, Ltd.

Earthquake Engng Struct. Dyn. 2004; 33:669–685