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Seismic performance of a reinforced concrete frame building in China

Haijuan Duan a,⇑, Mary Beth D. Hueste b

a Department of Civil Engineering, Shanghai Jiaotong University, Shanghai, Chinab Zachry Department of Civil Engineering, Texas A&M University, College Station, TX, USA

a r t i c l e i n f o

Article history:

Received 12 November 2010

Revised 16 March 2012

Accepted 17 March 2012

Available online 24 April 2012

Keywords:

Reinforced concrete frame

Seismic performance

Push-over analysis

Time-history analysis

a b s t r a c t

This paper investigates the seismic performance of a multi-story reinforced concrete frame building

designed according to the provisions of the current Chinese seismic code (GB50011-2010). A typical

five-story reinforced concrete frame building is designed. Seven natural earthquake acceleration records,

selected and adjusted for compatibility with the adopted design spectrum, are used. The frame structure

is evaluated using both a nonlinear static (push-over) analysis and nonlinear dynamic time-history anal-

ysis. The assessment of seismic performance is based on both global and member level criteria. According

to the numerical results, the building frame designed by GB50011-2010 provides the inelastic behavior

and response intended by the code and satisfies the interstory drift and maximum plastic rotation limits

suggestedby ASCE/SEI 41-06. However, thepush-over analysis indicated the potential for a soft first story

mechanism under significant lateral demands. Design recommendations are provided to help ensure the

preferred strong-column, weak-beam damage mechanism.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

Earthquakes are among the major natural hazards impacting ci-vil infrastructure. During recent earthquakes, such as the 1994

Northridge earthquake in the United States (US), the 1995 Kobe

earthquake in Japan, the 1999 Chi-Chi earthquake in Taiwan, and

the 2008 Wenchuan earthquake in China, many reinforced con-

crete (RC) frame structures experienced substantial damage. Ye

et al. [1] noted the absence of the preferred strong-column,

weak-beam damage mechanism in typical RC frames that were

damaged in the Wenchuan earthquake. Most building structures

in China are normally low- to medium-rise RC frames. If another

severe earthquake like the 2008 Wenchuan earthquake occurs,

the damage or collapse of not only general commercial buildings,

but also public service buildings such as hospitals and schools,

could result in a very large loss of life and economic losses.

The current Chinese code, National Standard of the People’sRepublic of China, Code for Seismic Design of Building (GB50011-

2010) [2], recommends a linear static procedure for analysis and

design. However, buildings designed for a seismic force reduced

by the response modification factor are intended to behave inelas-

tically when they are subject to a design-level earthquake. A build-

ing should have enough strength and ductility to avoid collapse

during a severe earthquake. An inelastic dynamic analysis can be

used to evaluate the safety of a structure designed according to

the current seismic design code.Research on the seismic performance of RC structures designed

by current design codes includes several studies focused on US and

European buildings. Kueht and Hueste [3] conducted a numerical

investigation on the seismic performance of a four-story RC frame

designed based on the 2003 International Building Code (IBC), a lo-

cally amended version of the 2003 IBC, and the 1999 Standard

Building Code. Kim and Kim [4] studied the seismic demand of a

RC special moment-resisting frame designed by IBC 2003. Panagi-

otakos and Fardis [5] evaluated the performance of RC buildings

designed with Eurocode 8. Ile and Reynouard [6] proposed a con-

stitutive model for predicting the cyclic response of RC structures

using a smeared crack approach with orthogonal fixed cracks. Kot-

ronis et al. [7] proposed a simplified modeling strategy for RC walls

based on Bernoulli multilayered beam elements and the principlesof damage mechanics and plasticity. The strategy was used to sim-

ulate the nonlinear behavior of two RC wall specimens designed

according to the French code PS92 and the Eurocode 8, respec-

tively. There have also been several studies on the seismic perfor-

mance of RC frames in other countries. Studies by Sadjadi et al. [8],

Arturo et al. [9] and Mehanny and EI Howary [10] focus on RC

frames designed based on the National Building Code of Canada,

Mexico Federal District Code and Egyptian seismic code (ECP

201), respectively.

Only limited studies [11,12] have been conducted to investigate

the seismic performance of typical RC building frames designed

based on the Chinese code (GB50011-2010). Li et al. [13] analyzed

0141-0296/$ - see front matter 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2012.03.030

⇑ Corresponding author. Address: Department of Civil Engineering, Shanghai

Jiaotong University, 800 Dongchuan Road, Shanghai 200240, China. Tel.: +86 21

34207985.

E-mail addresses: [email protected] (H. Duan), [email protected] (M.B.D.

Hueste).

Engineering Structures 41 (2012) 77–89

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Engineering Structures

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the seismic performance of RC frames designed according to

Chinese and European Codes. Ou et al. [14] reported that compared

with developed countries, China’s current seismic fortification cri-

terion is low. In addition, reinforcement detailing practices and

construction in China are different from that of the US and Europe.

The objective of this study is to investigate the seismic perfor-

mance of a RC frame designed according to the Chinese code

(GB50011-2010) using nonlinear static and dynamic analysis. The

results are presented in terms of key response parameters, includ-

ing interstory drift, base shear versus building drift, and plastic

rotation. The structural response is assessed to determine the over-

all safety of the structure under seismic demands.

2. Code comparison

Before evaluating the seismic performance of a multi-story

reinforced concrete frame building designed according to Chinese

seismic code GB50011-2010, a comparison was made between

the Chinese Code (GB50011-2010) [2], US Standard Minimum De-

sign Loads for Building and Other Structures (ASCE/SEI 7-10) [15],and Eurocode 8: Design of Structures for Earthquake Resistance

(EC8) [16]. ASCE/SEI 7-10 is referenced by the International Build-

ing Code (IBC 2012) (ICC 2012) [17] for seismic loading criteria.

Similarities and differences related to seismic demand criteria, site

classification, horizontal seismic actions, and structural factors are

discussed below.

The seismic ground motion criteria prescribed by the selected

codes and standard are shown in Table 1. GB50011-2010 contains

three levels of seismic design criteria, while ASCE 7-10 and EC8

contain two levels. The Chinese and European codes have the same

design return period of 475 years, while the design earthquake

ground motion in ASCE/SEI 7-10 is taken as 2/3 of the risk-targeted

maximum considered earthquake (MCER ) ground motion.

The base shear equations for the Chinese code, European code,and US standard are provided in Table 2. In GB50011-2010, the

base shear calculation can be used for shorter structures (below

40 m high) that are vertically regular (mass and stiffness evenly

distributed in vertical direction). The earthquake affecting coeffi-

cient is determined by seismic intensity, site classification, peak

acceleration and damping ratio. As regards EC 8, contains design

ground acceleration on type A site type and behavior factor q.

Structural factors are used to account for the anticipated non-

linear response of a structure, associated with the material, the

structural system and the design procedures. The response modifi-

cation factor (ASCE/SEI 7-10) and behavior factor (EC8) are in-

tended to reduce the forces obtained from a linear analysis to

account for nonlinearity. There is no nonlinear response modifica-

tion factor applied to the seismic demand in GB50011-2010.

Rather, an adjustment factor is used to account for ductility in

the seismic capacity of a structural component. The response mod-

ification factor R in ASCE/SEI 7-10 accounts for the damping, over-

strength and ductility inherent in the structural system. The value

of R varies for different types of building systems. In EC 8 the value

of the behavior factor q is given for various materials and structural

systems according to the relevant ductility classes. Table 3 pro-

vides a comparison of these structural factors intended to accountfor nonlinear response under seismic demands.

3. Case study building

3.1. Building description

A five-story RC office building was considered in this study. The

building has three bays in the North–South (N–S) direction and five

bays in the East–West (E–W) direction. The building contains inte-

rior and exterior moment frames in both directions. The total

building height is 17.8 m, with a first story height of 4.6 m and

3.3 m story heights for the upper stories. The plan and elevation

views of the five-story building are shown in Fig. 1. It is notedthat the layout shown is very typical of low-rise office buildings

Table 1

Seismic ground motion criteria.

GB50011-2010 (China) ASCE/SEI 7-10 (US) EC8 (Europe)

Level Probability of

exceedance in

50 years (%)

Return

period

(years)

Level Probability of exceedance

in 50 years

Return period

(years)

Level Probability of

exceedance

Return period

(years)

Rare earthquake 2–3% 2000 MCER 2%a 2500a NA NA NA

No collapse

Design earthquake 10% 475 Design earthquake 2/3 MCER a Varies No collapse 10% in 50 y ears 475

Repairable

Frequent earthquake 63.2% 50 NA NA NA Damage limit 10% in 10 years 95

No damage

a Most regions of the US use a 2% in 50 years uniform probability of exceedance to define the MCER event. In regions of high seismicity, MCER ground motions are

determined by deterministic methods based on characteristic earthquakes. In these cases, the median ground motion estimated for the characteristic event is multiplied by

1.5 [18].

Table 2

Horizontal seismic base shear expressions.


F EK ¼ T g

T

cg2amaxGEK

E h ¼ qS DS R=I e

W F b = S d(T 1)mk

F EK = design base shear E h = horizontal seismic load effect F b = design base shearT g = characteristic site period q = redundancy factor S d = design spectrum at period T 1T = fundamental period of vibration of

the building

S DS = design spectral response acceleration parameter in

the short period range

T 1 = fundamental periodof vibrationof building for lateral motion

in direction considered

c = attenuation index R = response modification factor m = total mass of the building

g2 = damping adjustment coefficient I e = occupancy importance factor k = correction factor

amax = maximum of earthquake

affecting coefficients

W = effective seismic weight

GEK = equivalent gravity loads

78 H. Duan, M.B.D. Hueste / Engineering Structures 41 (2012) 77–89



in China, where a long corridor runs through the center of the floor

plan parallel to the long direction of the building. This creates

frames in the transverse direction that are composed of longer

exterior bays with a more narrow interior bay, as shown in Fig. 1.

The RC frame is designed to be located in Wenchuan, Sichuan

province, in Southwest China. The structure was designed accord-

ing to the requirements of the Chinese code for seismic design of

buildings (GB50011-2010) with design peak ground acceleration

(PGA) of 0.2 g . A Class II soil was used, which corresponds to a rock

or stiff soil site having an equivalent shear wave velocity of 250–500 m/s and a site soil layer thickness greater than 5 m

(GB50011-2010). Earthquake loading was combined with gravity

loading G + 0.5Q , where G denotes permanent actions, which in-

clude exterior walls, interior light partitions, and superimposed

dead load. Exterior walls and interior light partitions are taken as

2.0 kN/m2 and 1.0 kN/m2, respectively. Superimposed dead load

is 0.75 kN/m2. Q is the live load required by the code for civil build-

ings (2.0 kN/m2).

The design of the structural concrete members follows the Na-

tional Standard of the People’s Republic of China, Code for Design of

Concrete Structures (GB50010-2002) [19]. Fig. 2 summarizes mem-

ber dimensions and reinforcement details for selected elements of

a typical frame in the transverse direction. The slab is 120 mm

thick. In the transverse direction, the beams of the longer exteriorbays are 300 600 mm, while the interior short bay beams are

300 400 mm. All columns are 600 600 mm in cross-section.

Although it is more typical in the US to maintain the same beam

depth within a frame, this difference in beam depth is common

in China, and was utilized to be more representative of typical

Chinese design and construction practices.

The compressive strength of the concrete in the frame is

23.4 MPa, where the design steel yield strength is 380 MPa and

300 MPa for the longitudinal and hoop reinforcement, respec-

tively. Reinforcement layouts were identical in beams and col-

umns at all story levels. The beam top and bottom longitudinaland hoop reinforcement are shown in Fig. 2. Two top bars are

cut off at 1650 mm from the column face at both span ends.

The column hoop reinforcement consists of 8 (8 mm-diameter)

bars. The spacing of the column hoop reinforcement is 200 mm

and decreases to 100 mm adjacent to the beam-column joints

(see Fig. 3). As defined by GB50010-2002 [19], the length of the

region requiring the closer spacing is 1500 mm from each joint

face for the first floor and 500 mm from each joint face for the

upper stories.

3.2. Column-to-beam strength ratios

The sizes of the columns were determined based on the applica-

tion of capacity design at the joints, adopted by Chinese code(GB50011-2010) [2], which imposes the requirement that:

Table 3

Nonlinear response modification factors.


Category Response

modification

factor (R)

Category Behavior

factor (q)

No special factor to account for effect of ductility on seismic demand. A

seismic adjustment coefficient accounting for ductility is applied to the

structural capacity

Special reinforced

concrete moment

frames

8 High ductility 4.5au/a1a

Intermediate

reinforced concrete

moment frames

5 Medium ductility 3.0au/a1a

Ordinary reinforced

concrete moment

frames

3 Multi-stor y, multi-bay fr ames or

frame – equivalent dual structures:

au/a1a = 1.3

a a1: multiplier of the horizontal seismic design action which, while keeping constant all other design actions, corresponds to the point where the most strained cross-

section reaches its plastic resistance; au: multiplier of the horizontal seismic design action which, while keeping constant all other design actions, corresponds to the point

where a number of sections, sufficient for the development of overall structural instability, reach their plastic moment of resistance. Factor au may be obtained from a

nonlinear static (pushover) global analysis [16].

7200 7200 7200 7200 7200

7 2 0 0

7 2 0 0

2 4 0 0

3 3 0 0

3 3 0 0

3 3 0 0

3 3 0 0

4 6 0 0

7200 2400 7200

(b) Elevation(a) Plan

Fig. 1. Plan and elevation of case study building (unit: mm).

H. Duan, M.B.D. Hueste/ Engineering Structures 41 (2012) 77–89 79



XM c P 1:2

XM b ð1Þ

where PM c is the sum of moments at the center of the joint, corre-

sponding to the resistance of the columns framing into the joint,and

PM b is the sum of moments at the center of the joint, corre-

sponding to the resistance of the flexural strength of the beams

not including the slab in tension framing into a joint.

ACI 318 [20] stipulates a strong-column weak-beam design

strategy to prevent story mechanisms from forming. In the vertical

plane of the frame considered, the sum of the nominal flexural

strength of the columns at the face of the joint is required to be

at least 1.2 times the sum of the nominal flexural strength of the

beams described in Eq. (2)

XM nc P 1:2

XM nb ð2Þ

where P

M nc is the nominal flexural strength of the columns fram-

ing into the joint for the factored axial load consistent with the lat-eral force direction, and

PM nb is the sum of the nominal flexural

strength of the beams including the slab in tension framing into a

joint in a plane.

For this case study building, the column-to-beam strength ra-

tios for the first story are 1.66 and 1.18, according to GB50011-2010 and ACI 318, respectively. While the design meets the

requirements of GB50011-2010, it is slightly below the require-

ment of ACI 318.

4. Analytical model and collapse criteria

4.1. Modeling approach

The finite element (FE) structural analysis program ZEUS-NL

was used to perform the eigenvalue, push-over and nonlinear dy-

namic analyses. ZEUS-NL was developed by Elnashai et al. [21].

The program can be used to model two- and three-dimensional

steel, RC, and composite structures under static and dynamic load-ing, taking into account the effects of geometric nonlinearities and

4φ25

φ25

φ

φ8@200

φ8@2φ20

2φ20

φ @

φ @200

4φ20

4φ20

4φ20

4φ20

4φ202φ20

2φ20

Fig. 2. Frame elevation and member cross-sections (dimensions in mm, @ is used between stirrup size and spacing).

1650

950

1650

9504700 1200

LC

φ8@100 φ8@200 φ8@100 φ8@100

Fig. 3. Typical beam detailing (dimensions in mm, @ is used between stirrup size and spacing).




material inelasticity. A layered fiber approach is used for the non-

linear analysis of RC structures where the member cross-sections

are divided into fibers that monitor the confined concrete section,

the unconfined concrete cover, and the reinforcement. A typical RC

rectangular cross-section is shown in Fig. 4. This approach allows

prediction of the spread of inelasticity within the member cross-section and along the member length. The ZEUS-NL program has

been used successfully to investigate the seismic vulnerability of

concrete structures [22–24].

The appropriate development and analysis of a nonlinear FE

model for seismic analysis of a multi-story RC structure can be a

time-consuming task. A two-dimensional model using half of the

building was chosen for this study, taking into account the sym-

metrical configuration of the case study building. One exterior

frame and two interior frames, parallel to the short (N–S) direction

of the building, were linked with rigid truss elements at each level

so that only lateral forces and displacements are transmitted be-

tween frames. The overall geometry of the frame model for the

N–S direction is shown in Fig. 5. A similar model was developed

for the E–W direction. The modeling approach assumes rigid dia-phragm behavior, which is reasonable for a rectangular RC building

floor plan with an aspect ratio less than 3:1 [25].

Beams and columns were modeled using the two-dimensional

cubic elastic–plastic beam-column element. The columns were

modeled using a fixed base condition. Rigid end zones were used

for beam-column joint modeling. Fig. 6 shows the overall node

geometry for a typical frame and a zoomed in view of a typical

bay and story within the frame. Each beam is divided into ten

sub-elements. A node is provided at each column face, and two

additional nodes are located near each column face to refine the

model within the critical sections. Three additional nodes are used

to apply the seismic dead load along the span length. Each column

is divided into six sub-elements.The cross-sectional shape, dimensions, reinforcement area, and

bar locations for the RC column and beam members were defined

using the ‘‘RC rectangular section’’ and ‘‘RC T-section’’ section

types, respectively. To compute the element forces, the stress–

strain relationship for each monitoring area is computed by

numerical integration at the two Gauss points. The effective slab

width participating in beam deformation is taken as one fourth

of the span of the structural member (ACI 318) [20].

The constitutive material models for steel and concrete are

shown in Fig. 7. The bilinear elastic–plastic material model with

kinematic strain-hardening (stl1) was used for the steel reinforce-

ment and rigid truss elements. Three parameters are required for

the stl1 model: Young’s modulus (E ), yield stress (r y), and a

strain-hardening coefficient (l). In this study, E and l are assumedas 210 GPa and 0.02, respectively. The yield stresses for the longi-

tudinal and hoop reinforcement are 360 and 300 MPa, respectively.

The concrete material was represented by the uniaxial constant

confined model (conc2), shown in Fig. 7b. For the conc2 model,

four parameters are required: compressive strength ( f 0c ), tensile

strength ( f t ), maximum strain (eco) corresponding to ( f 0c ), and a con-

finement factor (k). The values of f 0c , f t and eco are 23.4 MPa,

Unconfined

concretes fibresConfined

concretes fibres Steel fibres

Fig. 4. Decomposition of a RC rectangular section [21].

Fig. 5. N–S model of case study building (units in mm).




2.34 MPa and 0.002 respectively. The confinement effect is taken

into account using the model proposed by Mander et al. [26],

where the confinement factor k represents the ratio of the confined

concrete compressive strength to the unconfined concrete com-

pressive strength. The value of k depends on the transverse and

longitudinal reinforcement, concrete strength, and memberdimensions and can have a significant effect on the post-yield con-

crete behavior. The value of k can range from 1.0 to 1.17, where 1.0

represents an unconfined section. The value of k for the beams and

columns in the study building are shown in Table 4. For the rigid

connections, the values of the Young’s modulus and yield strength

were chosen to be very large to create a rigid zone and prevent

yielding. The seismic masses for the frames were lumped at the

beam-column joints based on the tributary dimensions.

4.2. Failure criteria

Both global-level and member-level limits were used to evalu-

ate the possibility of exceeding a particular performance level

within each story, as well as in each member. Seismic performancecriteria were based on the ASCE/SEI 41-06 standard [27]. Three

performance levels [Immediate Occupancy (IO), Life Safety (LS)

and Collapse Prevention (CP)] are used for seismic evaluation in

ASCE/SEI 41-06. The case study building was evaluated to deter-

mine if the expected seismic response was acceptable for the three

selected performance levels. For the global-level evaluation, maxi-

mum interstory drifts from the nonlinear analysis were compared

to the suggested limiting interstory drift values. A member-level

evaluation using ASCE/SEI 41-06 plastic rotation limits was also

performed to provide a more detailed assessment of structuralbehavior and seismic performance.

Fig. 6. N–S model of case study building – typical frame geometry and details of frame members.

Strain

Stress

E

µEσy

Stress

Compressive Strain

f c

εcof t

(a) Steel (b) Concrete

Fig. 7. Constitutive material models [21].

Table 4

Confinement factors for columns and beams.

f 0c (MPa) Hoop spacing (mm) Confinement factor, k

Column

23.4 100 1.17

23.4 200 1.08

Beam

23.4 100 1.15

23.4 200 1.07




5. Push-over analysis

5.1. Global response

Push-over analysis is a series of incremental nonlinear static

analyses carried out to examine the lateral deformation and dam-

age pattern of a structure into the inelastic range of behavior. The

lateral load distribution applied in the push-over analysis is impor-

tant because different lateral load patterns may yield different

load–displacement relationships. Both uniform and inverted trian-

gular lateral load patterns were used for the push-over analyses in

this study. The uniform pattern uses equal lateral loads at each

story, while the inverted triangular pattern represents the first

mode shape and is based on the seismic load distributionprescribed in the building code [2]. For the case study building,

the inverted triangular load pattern was distributed over the build-

ing height as follows: 0.35 (roof level), 0.26 (4th level), 0.19 (3rd

level), 0.13 (2nd level), and 0.06 (1st level).

Push-over capacity curves, such as base shear versus roof dis-

placement, provide lateral load–displacement envelopes that rep-

resent the global structural response. Capacity curves for the

building in the N–S and E–W directions are presented in

Fig. 8a and b, respectively. For these curves, the base shear is

normalized with respect to the total seismic weight of the frame.

The building drift BD is defined as the roof displacement DR normal-

ized with respect to the total height of the frame H (BD =DR/H ).

The solid line type corresponds to the triangular lateral load dis-

tribution, while the dashed line corresponds to the uniform lat-

eral load pattern. The circular markers indicate the occurrenceof an ASCE/SEI 41-06 CP plastic rotation limit being exceeded

0

5

10

15

20

25

30

Building Drift (%)

Triangular

Uniform

Exceedance ofPlastic Rotation

0

5

10

15

20

25

30

0 1 2 3 4 5 0 1 2 3 4 5

B a s e

s h e a r / W e i g h t ( % )

B a s e

s h e a r / W e i g h t ( % )

Building Drift (%)

Triangular

Uniform

Exceedance ofPlastic Rotation

(a) N-S (transverse) (b) E-W (longitudinal)

Fig. 8. Push-over analysis results.

S t o r y l e v e l

Interstory drift (%)

S t o r y l e v

e l


(a) 0.25% - 1% Building Drift (N-S) (b) 1.5%-3% Building Drift (N-S)

S t o r y l e v e l

S t o r y l e v e l

Interstory drift (%) Interstory drift (%)

(c) 0.25% - 1% Building Drift (E-W) (d) 1.5%-3% Building Drift (E-W)

Fig. 9. Interstory drifts at different building drifts from push-over analysis (Tr., Un., and BD indicate triangular load pattern, uniform load pattern, and building drift,

respectively).




at some location in the frame system. This can be compared to

the more detailed member-level response provided in the next

section.

Some variations can be observed when comparing the capacity

curves for the two load patterns. The push-over analysis using theuniform lateral load pattern yielded a higher initial stiffness and

base shear capacity compared with the triangular lateral load pat-

tern. In other words, for the same base shear force, the uniform

load pattern had a lower roof displacement. This is due to differ-

ences in the lateral displacement at the upper stories, where the

triangular load pattern resulted in higher displacements for build-ings drifts below about 2.5%.

Rigid Link

5 3

10 8

17 11 10

13

9 6

1114

16

4

7

11

2

4

12

2

5

7

2

1

5 2 2 2

8

4

2 7

1 2 2

10

10

212

4

4

7 3 1 2

12 9 1213

15

414

2 9

10

(a) Triangular lateral load pattern (N-S)

Rigid Link

3 3

9 3

7

8

2

45

5

7

2

1

5 2 2 2

8

4

2

1 2 2

8

10

212

4

4

6 1 5

8

2 9

2

7

2

1 1 1

(b) Uniform lateral load pattern (N-S)

7 124

4 8 7

314 121614 7

4

11

159 18

7 1048413

1

11

12 17 15

106

8

3

5

89 6

17 18 19

5 2 1 3 38

8

16

11

Rigid Link

138

14 147 13

65 9

(c) Triangular lateral load pattern (E-W)

7 12344

79

911 1216151414 15 148 810 12 10

13 8

8 5

8 710489

11

6 9

15

5 5 4

17 10

4 7 6 6 685 8

3

Rigid Link

3

(d) Uniform lateral load pattern (E-W)

Fig. 10. Sequence of exceedance of ASCE/SEI 41-06 CP plastic rotation limits during push-over analysis.




When compared to the transverse (N–S) direction, the push-

over curve for the longitudinal (E–W) direction shows a slightly

higher initial stiffness and strength. For the triangular load pattern,

the first exceedance of plastic rotation limits occurred at base

shear ratios of 23.4% and 26.8% for the N–S and E–W direction,

respectively. The corresponding building drift ratios are 0.86%

and 0.78% for the N–S and E–W direction, respectively.

The interstory drift ratio is critical for a seismic performance

evaluation because it is directly related to level of structural dam-

age. Interstory drift IDR is computed as the difference in lateral dis-placement (Di Di1) between two adjacent floor levels

normalized by the corresponding story height hi

[IDR = (Di Di1)/hi]. Interstory drifts of the frames at different

building drifts are shown in Fig. 9. ASCE/SEI 41-06 suggests typical

limits of 2% interstory drift associated with Life Safety (LS) perfor-

mance level and 4% interstory drift for Collapse Prevention (CP)

performance. These values are appropriate for well-detailed RC

frames [27].

The magnitude and distribution of interstory drift for the N–S

and E–W directions are very similar. As shown in Fig. 9a and c,

the interstory drift distribution is almost uniform when the build-ing drift is below0.5% because the behavior is primarily elastic. The

first and second stories exhibit significant interstory drifts com-

pared to the upper stories when the building drift is above 0.5%.

As expected, the uniform load pattern leads to a more distinct soft

story behavior at the first story, particularly in the transverse (N–S)

direction. Fig. 9b and d show that the interstory drifts of the first

story exceed that of the upper stories in both directions. This indi-

cates the first story has the potential to act as a soft story under

significant lateral demands.

5.2. Member-level performance

According to ASCE/SEI 41-06 [27], the plastic rotation limits for

the LS performance level for the case study building are 0.020 radi-ans (beams) and 0.015 radians (columns). For the CP performance

level, the limits are 0.025 radians (beams) and 0.020 (columns).

Fig. 10a–d illustrates the sequence and locations where the CP

plastic rotation limits are exceeded in the beams and columns,

for the triangular and uniform load patterns, respectively. The

numbers in these figures indicate the sequence in which the corre-

sponding member CP plastic rotation limit is exceeded. In some

cases, more than one member exceeded the CP limit in the same

time step, and so multiple locations are labeled with the same

number.

The frame elevations provide insight into the expected locations

of inelastic rotation for this structure under lateral loading in both

the N–S and E–W directions. As shown in Fig. 10a–d, the locations

where the CP plastic rotation limits are exceeded are concentratedin the first and second stories. As was mentioned earlier, the inter-

story drift profiles indicate that the RC frame has a soft first story

failure mechanism at collapse. It is important to note that while

the code (GB50011-2010) aims to achieve a strong-column

weak-beam behavior, in terms of actual response, a significant

number of column hinges occur. In most cases, for the transverse

(N–S) direction, the beam plastic rotations for the shallow interior

beams appear first as compared to the deeper exterior beams.

6. Nonlinear dynamic analysis

6.1. Building direction

Additional analysis was conducted in the transverse (N–S)direction to assess the structural performance of the building

Table 5

Selected earthquake records.

Earthquake Station EQ ID Date Magnitude PGA( g ) Duration(s)

Imperial Valley EI Centro CETO 05/19/1940 7.0 0.2142 53.46

Kobe JMAa KOBE 01/17/1995 6.9 0.8300 49.98

Northridge Nordhoff Fire NRDG 01/17/1994 6.7 0.3442 59.98

Kern Country Taft, Lincoln School TAFT 07/21/1952 7.7 0.1557 54.38

San Fernando Orion Blvd. SANF 02/09/1971 6.6 0.2547 59.48

Landers Barstow LADR 06/28/1992 7.3 0.1320 40.00Tangshan aftershock Tianjing TIAN 11/05/1976 7.1 0.1450 19.19

a Japanese Meteorological Agency.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

S p e c t r a A

c c e l e r a t i o n ( g )

Period (s)

CODE

CETO

KOBE

NRDG

TAFT

SANF

LANR

TIAN

Fig. 11. Response spectra of the original earthquake records (scaled to 0.4 g ) and

target design spectrum.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

S p e c t r a A c c e l e r a t i o n ( g )

Period (s)

CODE

CETO

KOBE

NRDG

TAFT

SANF

LANR

LOMA

Fig. 12. Response spectra of the matched earthquake records and target design

spectrum.




under dynamic loading. This building direction was of particular

interest because of the relatively unique configuration, including

the shorter middle span with shallower beams.

6.2. Seismic input

Choosing ground motion records for dynamic analysis can be

challenging, especially when studying a location where seismichazard data are not available. In general, the selection of ground

motion records is based on two criteria. One is the geophysical sit-

uation and the other is ground motion parameters. Therefore, the

soil type for the selected ground motions should be similar to

the soil at the building site. In addition, the response spectra of

the selected records should match the target design spectrum.

The selection of ground motion data was carried out in this

study by considering the two criteria discussed above. Seven natu-

ral ground motion records were chosen by considering following

three conditions: (1) a minimum event magnitude of six was se-

lected to represent a high magnitude event (the Richter magnitude

scale, also known as the local magnitude (M L) scale, assigns a singlenumber to quantify the amount of seismic energy released by an

earthquake), (2) a rock or stiff soil site was needed for consistency

with the soil type of the region where the case building is located,

and (3) a peak ground acceleration (PGA) larger than 0.1 g was de-

sired for consistency with the design earthquake. The main charac-

teristics of the input motion used are summarized in Table 5.

The selected ground motion records were scaled to different

maximum PGA levels (0.2 g and 0.4 g ) to produce design and rare

earthquakes based on the requirementsof the Chinese code for seis-

mic design of buildings (GB50011-2010). According to the Chinese

code, a PGA of 0.2 g corresponds to earthquakes having probability

of exceedance of about 10% in 50 years, and a PGA of 0.4 g corre-

sponds to a probability of exceedance of about 2% in 50 years.

The response spectra for the seven selected records, scaled to aPGA of 0.4 g , and the target design spectrum are shown in Fig. 11.

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 10 20 30 40 50 60

Time (s)

0 10 20 30 40 50 60

Time (s)

0 10 20 30 40 50 60

Time (s)

Matched

Original

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 10 20 30 40 50 60

Time (s)

Matched

Original

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

A c c e l e r a t i o n ( g ) Matched

Original

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 10 20 30 40 50 60

A c c e l e r a t i o n ( g )



Time (s)

Matched

Original

EBOKOTEC

NRDG TAFT

-0.6

-0.4

-0.20.0

0.2

0.4

0.6

A c c e l e r

a t i o n ( g ) Matched

Original

-0.6

-0.4

-0.20.0

0.2

0.4

0.6

0 10 20 30 40 50 60

A c c e l e r a

t i o n ( g )

Time (s)

Matched

Original

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 10 20 30 40 50


Time (s)

Matched

Original

SANF LADR

TIAN

Fig. 13. Time histories of original scaled ground motion records and matched records.

0

5

10

15

20

25

30

0 1 2 3 4 5

B a s e s h e a r / W e i g h t ( % )

Building Drift (%)

Triangular

Uniform

CETO

KOBE

NRDG

TAFT

SANF

LADF

TIAN

Fig. 14. Comparison of push-over analysis and maximum response from dynamic

analysis.




The RSPMATCH [28] program was used to match the ground mo-

tions to the target design spectrum. The fundamental period of

the building determined from ZEUS-NL analysis is 0.65 s. The

adjustment with RSPMATCH is performed in two steps. In the first

step, each record is modified to match the target spectrum within

the period range between 0 and 1 s. In the second step, wavelets

are introduced to match the target spectrum within the entire per-

iod range between 0 and 4 s. The response spectra for the seven

matched ground motions and the target design spectrum are

shown in Fig. 12. The response spectra in Figs. 11 and 12 are for

5% damping. The seven ground motions, scaled to a PGA of 0.4 g ,

and their corresponding matched acceleration time-histories are

provided in Fig. 13.

6.3. Global response

Using the seven earthquake records developed with the spectral

matching software, dynamic nonlinear response analysis was per-

formed for the case study building. Each of these records was ap-

plied with increasing ground motion intensity. In this study, the

intensity measure was considered as the spectral acceleration at

the fundamental period. The base shear, as well as the buildingdrift and interstory drift, were examined.

In dynamic analysis, the maximum displacement does not nec-

essarily coincide with the peak base shear. A special procedure is

required to extract these parameters from the dynamic analysis re-

sults. As suggested by Antoniou and Pinho [29], the dynamic anal-

ysis envelopes consist of the locus of maximum displacement

versus corresponding base shear (i.e., peak base shear within a

±0.5 s interval of the instant of maximum displacement

occurrence).

The dynamic response of the structure is compared with the

push-over curves in Fig. 14. The dynamic response indicates rela-

tively low dispersion between the results from the seven earth-

quake records. The trend of the push-over curves provides a good

estimate of the maximum dynamic response up to approximately1.5–2.0% building drift, after which the dynamic base shear ratio

tends to be underestimated by the push-over response. The basic

reason is that the static nonlinear (push-over) analysis does not ac-

count for higher mode effects. Mwafy and Elnashai [30] also ob-

served that push-over analysis achieved a conservative prediction

of capacity.

Tables 6 and 7 provide a summary of the maximum building

and interstory drifts, along with the maximum base shear ratio

(base shear divided by building weight) for each of the adjusted

ground motion records. The interstory drifts for the design earth-

quake (PGA = 0.2 g ) and collapse prevention earthquake (PGA =

0.4 g ) are shown in Fig. 15a and b, respectively.

As seen in the tables and figures, the median interstory drift val-

ues for the design level earthquake (PGA = 0.2 g ) are less than the

ASCE/SEI 41-06 global-level limit of 2% for LS. For the collapse pre-

vention level earthquake (PGA = 0.4 g ), the median interstory drift

values are much less than the ASCE/SEI 41-06 global-level CP limit

of 4%. Therefore, the case study building meets the recommended

Basic Safety Objective (BSO) of LS performance for the design event

and CP performance for the rare event based on a general global-le-

vel evaluation using the suggested drift limits.

6.4. Member-level performance

Plastic rotation limit criteria for the ASCE/SEI 41-06 member

evaluation of RC frames is provided for each performance level

based on member reinforcement ratio, confinement, and shear de-

mand-to-strength ratio for beam and columns controlled by flex-ure. The ASCE/SEI 41-06 plastic rotation limits for beams and

columns and maximum plastic rotations are summarized in

Table 8.

As shown in Table 8, the first and second story column plasticrotations are approaching the corresponding LS limit for the

Table 6

Summary of maximum drift and base shear ratio (design level earthquake,

PGA = 0.2 g ).

Ground

motion

Max. building

drift (%)

Max. base shear

ratio (%)

Max interstory

drift (%)

CETO 0.410 25.2 0.93

KOBE 0.404 19.8 0.93

NRDG 0.450 25.6 1.13

TAFT 0.401 23.8 0.78SANF 0.450 21.2 0.75

LADR 0.522 25.1 0.96

TIAN 0.466 21.1 0.73

Median 0.450 23.8 0.93

Table 7

Summary of maximum drift and base shear ratio (collapse prevention level

earthquake, PGA = 0.4 g ).

Ground

motion

Max. building

drift (%)

Max. base shear

ratio (%)

Max interstory

drift (%)

CETO 0.740 27.09 1.61

KOBE 0.843 21.30 1.56

NRDG 1.100 26.53 2.17

TAFT 0.706 24.59 1.09

SANF 0.843 23.45 1.82

LADR 1.275 26.22 1.65

TIAN 0.820 24.10 1.74

Median 0.843 24.59 1.65

S t o r y l e v e l


(a) Design level earthquake (PGA=0.2g)

S t o r y l e v e l


(b) Collapse prevention level earthquake (PGA=0.4g)

Fig. 15. Interstory drift ratios from dynamic analysis using ground motion records.




collapse prevention event. However, the median maximum re-

sponse values do not exceed the LS and CP beam and column plas-

tic rotation limits for the rare (collapse prevention) earthquake.

Therefore, the case study building meets the suggested BSO.

7. Summary and conclusions

This study evaluated the seismic performance of a five-story RC

frame building designed according to the provisions of the current

Chinese code, National Standard of the People’s Republic of China ,

Code for Seismic Design of Building (GB50011-2010) [2]. Both non-

linear static and dynamic analyses were used to evaluate the build-

ing. Seven natural earthquake acceleration records were selected

and adjusted for compatibility with the target design spectrum.

The criteria used in ASCE/SEI 41-06 were referenced for the seismic

performance evaluation. The observation and conclusions of the

study were summarized as follows:

1. The push-over analysis provided a useful tool for identifying the

locations that are likely to be subjected to large inelastic defor-

mation. This information is not only useful for evaluating the

seismic performance of the structure, but could also be helpful

for selecting seismic details that are more suitable for with-

standing the expected inelastic deformations.2. Both GB50011-2010 and ACI 318-08 require that the column-

to-beam strength ratio be at least 1.2. However, the Chinese

code differs in that it does not include the slab in computing

the flexural strength of the beams. While the case study build-

ing design meets the requirements of GB50011-2010, it is

slightly below the requirement of ACI 318. As such, the design

is less prone to provide the preferred strong-column, weak-

beam damage mechanism. The push-over analysis indicated

that the case study building has the potential for a soft first

story failure mechanism at building drifts of 2–3%.

3. The dynamic analysis of the structure to the scaled ground

motions indicated that the seismic response of the case study

building met the ASCE/SEI 41-06 recommended Basic Safety

Objective (BSO) of LS performance for the design earthquake(10% in 50 year hazard level) and CP performance for the col-

lapse prevention earthquake (2% in 50 year hazard level).

4. The push-over analysis indicated the potential for a soft first

story mechanism; however, the drift and plastic rotation

demands from the dynamic analysis did not indicate a risk of

collapse for the collapse prevention (rare) earthquake. Never-

theless, it is noted that the availability of recorded ground

motions in this area is very limited. Therefore, it is recom-

mended that a strong-column weak-beam design requirement

consistent with ACI 318 be implemented into the Chinese seis-

mic code provisions to reduce the risk of collapse under

extreme seismic events.

5. Although the analysis has been conducted for a particular RC

frame building, the observations provide insight relevant tosimilar structures in China. Future work is aimed at evaluating

this and similar structures for Chinese ground motions when

they become available, as well as considering additional model-

ing approaches to help address the complex nonlinear behavior

of RC building elements and systems.

Acknowledgment

Project Sponsored by the Scientific Research Foundation for the

Returned Overseas Chinese Scholars, State Education Ministry.

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Member-level evaluation (PGA = 0.4 g ).

Story level Beam rotation (rad) Column rotation (rad)

ASCE 41 limits Median max. plastic rotation ASCE 41 limits Median max. plastic rotation

LS CP LS CP

1 0.02 0.025 0.0121 0.015 0.02 0.0128

2 0.02 0.025 0.0105 0.015 0.02 0.0115

3 0.02 0.025 0.0046 0.015 0.02 0.00364 0.02 0.025 0.0024 0.015 0.02 0.0025

5 0.02 0.025 0.0016 0.015 0.02 0.0017




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seismic reinforcement 6

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