seismic reinforcement 6
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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
Contents lists available at SciVerse ScienceDirect
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.
GB50011-2010 (China) ASCE/SEI 7-10 (US) EC8 (Europe)
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
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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.
GB50011-2010 (China) ASCE/SEI 7-10 (US) EC8 (Europe)
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).
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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).
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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).
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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
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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
Interstory drift (%)
(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).
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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.
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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.
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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 )
A c c e l e r a t i o n ( g )
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
A c c e l e r a t i o n ( g )
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.
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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
Interstory drift (%)
(a) Design level earthquake (PGA=0.2g)
S t o r y l e v e l
Interstory drift (%)
(b) Collapse prevention level earthquake (PGA=0.4g)
Fig. 15. Interstory drift ratios from dynamic analysis using ground motion records.
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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.
References
[1] Ye L, Qu Z, Ma Q, Lin X, Lu X, Pan P. Study on ensuring the strong column weak
beam mechanism for RC frames based on the damage analysis in the
Wenchuan earthquake. Build Struct 2008;38(11):52–9 [in Chinese].
[2] National Standard of the People’s Republic of China, Code for seismic design of
building (GB50011-2010). China Architecture and Building Press; 2010.
[3] Kueht E, Hueste MD. Impact of code requirements in the central United States:
seismic performance assessment of a reinforced concrete building. ASCE J
Struct Eng 2009;135(4):404–13.
[4] Kim T, Kim J. Seismic demand of an RC special moment frame building. Struct
Des Tall Special Build 2009;18(10):137–47.
[5] Panagiotakos TB, Fardis MN. Seismic performance of RC frames designed to
Eurocode 8 or Greek code 2000. Bull Earthquake Eng 2004;2(2):221–59.
[6] Ile N, Reynouard JM. Non linear analysis of reinforced concrete shear wall
under earthquake loading. J Earthquake Eng 2000;4(2):183–213.
[7] Kotronis P, Ragueneau F, Mazars JA. Simplified modelling strategy for R/C walls
satisfying PS92 and EC8 design. Eng Struct 2005;27(8):1197–208.
[8] Sadjadi R, Kianoush MR, Talebi S. Seismic performance of reinforced concrete
moment resisting frames. Eng Struct 2007;29(9):2365–80.
[9] Arturo TC, Hector CA, Jose Luis LA, Gonzalo GA. Seismic behavior of code-
designed medium rise special moment-resisting frame RC buildings in soft
soils of Mexico city. Eng Struct 2008;30(12):3681–707.
[10] Mehanny SSF, EI Howary HA. Assessment of RC moment frame buildings in
moderate seismic zones: evaluation of Egyptian seismic code implications and
system configuration effects. Eng Struct 2010;32(8):2394–406.
[11] Yang SS, Hao XQ, Qin R. Evaluation and study for earthquake resistant
capability of reinforced concrete frame structure. Earthquake Eng Eng Vib
2005;25(5):80–4 [in Chinese].
[12] Ye LP, Lu XZ, Ma QL, Wang XL, Miao ZW. Seismic nonlinear analytical models,
methods and examples for concrete structures. Eng Mech 2006;23(2):131–40
[in Chinese].
[13] Li YM, Wu XP, Wei F, Bai SL. Comparison between seismic performances of RC
frames designed according to Chinese and European Codes. J Earthquake EngEng Vib 2007;27(6):82–7 [in Chinese].
[14] Ou JP, Li H, Wu B, Guo AX. Earthquake engineering disaster and fortification:
analysis and comparison of seismic design code. Lessons from Wenchuan
earthquake and strategies for post-earthquake reconstruction and
retrofit. China Architecture and Building Press; 2008.
[15] ASCE. Minimum design loads for building and other structures (ASCE/SEI 7–
10). American Society of Civil Engineers; 2010.
[16] Eurocode 8: Design of structures for earthquake resistance Part 1: General
rules, seismic actions and rules for buildings. European Committee for
Standardization; 2003.
[17] ICC. International building code (IBC 2012). International Code Council; 2011.
[18] Building Seismic Safety Council, NEHRP recommended seismic provisions for
new buildings and other structures (FEMA P-750). Washington, DC: Building
Seismic Safety Council, National Institute of Building Sciences; 2009.
[19] National Standard of the People’s Republic of China, Code for design of
concrete structures (GB50010-2002). China Architecture and Building Press;
2002.
[20] ACI Committee 318. Building code requirements for structural concrete and
commentary (ACI 318-08). Farmington (MI): American Concrete Institute(ACI); 2008.
Table 8
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
88 H. Duan, M.B.D. Hueste / Engineering Structures 41 (2012) 77–89
7/21/2019 seismic reinforcement 6
http://slidepdf.com/reader/full/seismic-reinforcement-6 13/13
[21] Elnashai AS, Papanikolaou V, Lee DH. ZEUS-NL user manual. Urbana, IL: Mid-
America Earthquake Center, Univ. of Illinois at Urbana–Champaign; 2004.
[22] Erberik MA, Elnashai AS. Fragility analysis of flat-slab structures. Eng Struct
2004;26(7):937–48.
[23] Jeong SH, Elnashai AS. Analytical assessment of an irregular RC frame for full
scale 3D pseudo-dynamic testing Part I: Analytical model verification. ASCE J
Struct Eng 2005;9(1):95–128.
[24] Hueste MD, Bai JW. Seismic retrofit of reinforced concrete flat-slab structures:
Part I – Seismic performance evaluation. Eng Struct 2007;29(6):1165–77.
[25] Barron JM, Hueste MD. Diaphragm effects in rectangular reinforced concrete
buildings. ACI Struct J 2004;101(5):615–24.
[26] Mander JB, Priestley MJ, Park R. Theoretical stress–strain model for confined
concrete. J Struct Eng 1988;114(8):1804–26.
[27] ASCE. Seismic rehabilitation of existing buildings (ASCE/SEI 41-06). American
Society of Civil Engineers (ASCE); 2007.
[28] Abrahamson NA. Non-stationary spectral matching program RSPMATCH –
user manual; 2008.
[29] Antoniou S, Pinho R. Advantages and limitations of adaptive and non-adaptive
force-based pushover procedures. J Earthquake Eng 2004;8(4):497–522.
[30] Mwafy AM, Elnashai AS. Static pushover versus dynamic analysis of R/C
buildings. Eng Struct 2001;23(5):407–24.
H. Duan, M.B.D. Hueste/ Engineering Structures 41 (2012) 77–89 89