INTRODUCTION
In Reinforced Concrete (RC) buildings which have been designed according
to current specifications of earthquake resistant design, the elements
are usually determined on the basis of demand strength and then the limitations
on the deflection. It seems that the heightwise distribution of these
static forces (strength and stiffness) is factually based on the elastic
vibration modes. When, these structures are subjected to severe earthquake
excitations they are expected to deform well in inelastic range and dissipate
the large seismic energy input into the structures. In order to predict
the distribution of forces and deformations in these structures under
the strong earthquake that can occur at the site, the actual performance
of structures during earthquake (hysteretic and ductility) are necessary.
Williams and Sexsmith (1995) reviewed damage based on deformation. It
is generally accepted that damage based on cycles of deformation is a
lowcycle fatigue phenomenon. Degradation is assumed to evolve by the
accumulation of plastic deformation. Karami et al. (2004) studied
the effect of the conventional lateral loading pattern (i.e., equivalent
static method) specified by the different seismic codes (Uniform Building
Code, 1997; NEHRP, 1994) on heightwise distribution of ductility demand
and drift in a number of steel shearbuilding frames. It was concluded
that the strength distribution patterns suggested by these seismic codes
do not lead to a uniform distribution of ductility and deformation in
steel shearbuilding frames subjected to catastrophic earthquake. Therefore,
the application of such conventional heightwise distribution of seismic
forces will not actually cause the best seismic performance of a structure.
Ganjavi et al. (2007) considered a number of reinforced concrete
buildings based on equivalent static loading patterns (Iranian Code of
Practice for Seismic Resistance Design of Building, 1999). They studied
the heightwise hysteretic energy, drift and damage distribution subjected
to four severe earthquakes.
In this study, three reinforced concrete frames with shear wall were
considered. The seismic loading of these frames were applied according
to equivalent static method in accordance with Iranian Code of Practice
for Seismic Design of Building (2005). The aim of this study is to investigate
the distributions of damage index, drift and hysteretic energy in height
of RC buildings with shear wall undergone strong ground motions.
EQUIVALENT STATIC LOADING PROCEDURE
In most seismic building codes (Uniform Building Code, 1997; NEHRP, 1994;
Iranian Seismic Code, 2005) the height wise distribution of lateral forces
is determined from Eq. 1:
where, w_{i} and h_{i} are the weight and height of the
ith floor above base level, respectively, N is the number of stories,
V is total base shear and k is the power that differs from one seismic
code to another.
In some provisions codes such as NEHRP1994 Code, k increases from 12
as the period varies from 0.52.5 sec. In some such as UBC1997, the force
at the top floor (or roof) computed from Eq. 1 is increased
by adding an additional force (Eq. 2), for a fundamental
period T greater than 0.7 sec. In such a case, the base shear V in Eq.
1 is replaced by vF_{i}. In this study, the value of k in
Eq. 1 base of Iranian Code of Practice for Seismic Resistance
Design of Building (2005) is taken as 1 (triangular loading pattern).
NONLINEAR MODELING
In a nonlinear analysis, the accurate choice of a hysteretic model is
crucial in predicting the correct dynamic response of the structure. The
model should be able to describe a response similar to the actual hysteretic
response of the structure. In this study IDARC 2D software has been used
to compute the response of the structures to nonlinear time history (Valles
et al., 1996). The formulations are based on macromodels in which
most of the elements are represented as a comprehensive element with nonlinear
behavior. The loaddeformation of the structure is simulated by versatile
hysteretic models, which are implemented in the program and are mainly
controlled by parameters indicating the stiffness degradation, strength
deterioration and pinching of the hysteretic loops. The damage index developed
by Park et al. (1984) has been considered in the program and is
used to estimate the accumulated damage sustained by the components of
the structure, by each story level. A global value of the damage index
can be used to characterize the damage in the entire RC frame.
PARKANGDAMAGE MODEL IN IDARC PROGRAM
ParkAng damage index (Park et al., 1984) considered in IDARC
is the most usual damage index for damage analysis of reinforced concrete
structures. The current Park and Ang threehysteretic model modified by
Kunnath et al. (1992) is as follows:
where, θ_{m} is the maximum rotation attained during loading
history, θ_{u:} is the ultimate rotation capacity of section,
θ_{r }is the recoverable rotation when unloading, M_{m}
is the yield moment and E_{m} is the dissipated energy in section.
The element damage is then selected as the biggest damage index of end
sections.
The element damage is then selected as the biggest damage index of the
end sections.
Park et al. (1987) suggested these interpretations for the damage
index:
D<0.1 
: 
No damage or localized minor cracking 
0.1 ≤ D<0.25 
: 
Minor damagelight cracking throughout 
0.25 ≤ D<0.4 
: 
Moderate damagesevere cracking, localized spelling 
0.4 ≤ D<1.0 
: 
Severe damagecrushing of concrete, reinforcement exposed 
D ≥ 1.0 
: 
Collapsed 
The two additional indices, story and overall damage indices are computed
using weighting factors based on dissipated hysteretic energy at component
and story levels, respectively:
where, DI_{i} is the damage indices and E_{i} is the
total absorbed energy by the component or the ith story.
STRUCTURAL SYSTEMS AND EARTHQUAKE EXCITATIONS
Structural systems: In present study, three reinforced concrete buildings
with shear wall, 8, 12 and 15 story frames were considered. All frames were
designed according to the equivalent lateral force procedure for a region with
relatively high seismcity (IranTehran) and for the soil type 2 (gravel and
compacted sand, very stiff clay). It was also assumed that the structures were
located in a region with relatively high seismic risk and relative design base
acceleration of A = 0.35 g. Structures have identical plan configurations and
were analyzed assuming that the floor diaphragms were sufficiently rigid under
inplane forces. Trilinear model of Takeda et al. (1970) was used in
nonlinear analyses. The viscous damping ratio was assumed to be uniformly distributed
(damping ratio = 5%). In the design of these samples a basic assumption was
considered, that a constant strength ratio (the ratio of the existing strength
to the ultimate strength) has been applied in all stories and the frames were
moment resisting with medium ductility. IDARC 2D, Ver. 6.1 (Valles and Reinhorn,
2006) Software was used for nonlinear dynamic analysis. A sample of 8 story
frame has been shown in Fig. 1. In design and analysis of
structures, Pdelta effect was considered.
Earthquake excitations: Ten observed ground motions were used
for input ground motions. Emphasis was placed on those recorded at a low
to moderate distance from the epicenter (less than 30 km), with rather
high local magnitudes (i.e., M>6). The recorded ground motions cover
a broad variety of conditions in terms of frequency content, peak ground
acceleration and velocity, duration and intensity (Table
1). In order to eliminate the influence of peak ground acceleration,
all of them were scaled to a ground acceleration of 0.35 g based Iranian
Code of Practice for Seismic Resistance Design of Building (2005).

Fig. 1: 
A sample of an 8 story frame 
Table 1: 
Characteristics of the selected ground motions 

RESULTS AND DISCUSSION
Nonlinear dynamic analyses: In order to study the heightwise
distribution of hysteretic energy and story damage indices in the frames,
walls, beams and columns were chosen as the considering elements of each
story. In this regard the average values of heightwise distribution of
hysteretic energy, drift and damage index, subjected to 10 severe earthquakes
were calculated and then compared. It should be noted the hysteretic energy
of wall, beam and column in each story has been shown as the percentage
ratio of hysteretic energy in each wall, beam and column with respect
to the total hysteretic energy in each frame.
Hysteretic energy and damage index
Walls: The amount and the form of heightwise distribution
of (DI_{wall}) and (Eh%_{wall}) in stories levels for
three 8, 12 and 15 story buildings with shear wall subjected to 10 strong
ground motions were calculated and the average values of these parameters
have been shown in Fig. 2. The qualitative distribution
of (DI_{wall}) and (Eh%_{wall}) are identical. The results
also show that the maximum values of hysteretic energy, damage indices
in 8, 12 and 15 story buildings were in the first story and the minimum
ones occurred in the last stories. By considering the mean plot of hysteretic
energy and damage indices, it can be found that the differences percentages
between maximum and minimum of (Eh%_{wall}) in 8, 12 and 15 story
frames are 99.3, 99.7 and 99.7, respectively. These values for damage
indices are 99.4, 98.8 and 98.7, respectively. According to Fig.
2, in three buildings, there is a notable difference between the maximum
and minimum values of (Eh%_{wall}) and (DI_{wall}), in
a way that the high concentration of hysteretic energy and damage indices
were observed in the first story.
Beams: Figure 3 shows the plots of damage indices
and the percentage of hysteretic energy of beams in story levels for 8,
12 and 15 story frames. The maximum average values of (DI_{beam})
and (Eh%_{beam}) for ten earthquakes in 8 story frame are observed
in the second story, while these for 12, 15 story frames occur in the
third story. Also, the average of minimum values of (Eh%_{beam})
and (DI_{beam}) for three frames occur in top stories. By considering
the average curves and amounts of (Eh%_{beam}) and (DI_{beam}),
differences percentages between maximum and minimum of (Eh%_{beam})
in 8, 12 and 15 story frames are 77.4, 99 and 99.7, respectively. These
values for damage indices are 66.1, 95.4 and 98.6, respectively.

Fig. 2: 
Effect of ground motion on heightwise distribution
of hysteretic energy and damage index of walls in 8, 12 and 15 story
buildings 

Fig. 3: 
Effect of ground motion on heightwise distribution
of hysteretic energy and damage index of beams, 12 and 15 story buildings 
Columns: Obtained results from dynamic analysis indicate that
the values of (Eh%_{column}) and (DI_{column}) in columns
of all frames in comparison to walls and beams is very small and in most
stories is close to zero and even in some stories is equal to zero. Damage
index in all columns is below 0.005, which would suggest negligible cracking
(Fig. 5).
Frames: Considering the obtained results and performed studies
in previous sections, heightwise distribution of (Eh%_{frame})
and (DI_{frame}) in 8, 12 and 15 story buildings subjected to
10 earthquakes have been shown in Fig. 4. According
to, the median values` plot of hysteretic energy and damage indices, the
maximum and minimum values of three 8, 12 and 15 story frames occurred
in the first and last story, respectively.

Fig. 4: 
Comparison of the average values of heightwise distribution
of hysteretic energy and damage index of walls, beams, columns and
frames in 8, 12 and 15 story buildings 

Fig. 5: 
Effect of ground motion on heightwise distribution
of hysteretic energyand damage index in 8, 12 and 15 story buildings 
Although, strength ratios of
stories in all frames were considered the same, the differences percentages
between the maximum and minimum of (Eh%_{frame}) in 8, 12 and
15 story buildings are 89.1, 99.1 and 99.7, respectively. These values
for damage indices are 84.7, 89.5 and 94, respectively. In addition the
amount of (Eh%_{frame}) and (DI_{frame}) for the roof
are negligible, so it can be explained that most of the elements (wall,
beam and column) in this story remain in elastic state and this story
experience the least damage compared to other stories.
Comparison of hysteretic energy and damage distribution in the walls,
beams and frames in stories levels: Here, values of (Eh%) and DI in
beams, walls, columns and frames in stories levels of each frame were
compared with each other (Fig. 4 ). It was observed
that in each three building, (Eh%) and DI of the first story was completely
affected by (Eh%_{wall}) and (DI_{wall}), while these
parameters from the 2th4th story were affected by (Eh%_{beam})
and (DI beam). This indicates that the influence of beams and walls behavior
in various stories is different and the values of (Eh%_{column})
and (DI_{column}) in all frames in comparison with beams and walls,
are very small.
Overall structural damage index (Di overall): We have previously
discussed the distribution patterns of damage index in stories based on
beams, columns and walls damage indices of each story. In order to investigate
the overall inelastic behavior of samples, overall damage indices (DI_{overall})
of all frames were calculated and then the average values of them were
plotted as shown in Fig. 6. It can be observed that
the maximum values of (DI_{overall}) occurred in 8 story building
in Manjil earthquake (DI_{overall} = 0.144). But in 12, 15 story
frames maximum amount of (DI_{overall}) was observed in Gazli
earthquake where overall damage indices are 0.109, 0.125, respectively.
Figure 6 shows that structures having different stories,
the influence of earthquakes on the structures is completely different.
It can be observed that (DI_{overall}) is lower than 0.15, i.e.,
the structures did not undergo severe damage. However, since (DI_{overall})
is only a description of general damages exerted to the structure and
does not explain the energy dissipation, drift and damage distribution
pattern in stories, it is necessary to investigate the drift and damage
indicates in stories separately.
Drift ratio in stories levels: Taking into consideration of stories
drift ratio plots, it is clear that the maximum drift ratios in all frames
occurred in the third story, whereas the minimum ones in 12 and 15 story
frames and in 8 story frame occurred in the last and first story, respectively
(Fig. 7).

Fig. 6: 
Effect of ground motion on overall damage index in 8,
12 and 15 story buildings 
According to Fig. 3 and 7, it was observed that for RC buildings with shear
wall, the way of distribution of (Eh%), DI in beams and drift in levels
of each story were relatively similar. The differences percentages between
maximum and minimum of drift ratio in 8, 12 and 15 story frames are 45.5,
73.2 and 82.6, respectively.
From the earlier described, it can be concluded that, although the average
value of overall structural damage indices of 10 earthquakes indicates
that the structures did not undergo severe damage according to Park and
Ang damage calibration. A study of drift and damage indices in stories
especially in earthquake with high intensity like Manjil and Gazli showed
that the structures underwent more damage in one or two stories. Although,
strength ratios were considered uniform in stories height, the distribution
of Eh%, DI and drift for severe strong ground motions with high intensity
were nonuniform and an intense concentration of mentioned parameters
occurred in one or two stories in walls, beams and frames. In severe earthquakes,
nonuniform distribution of damage and drift imply that considering a
matchless strength parameter in seismic loading pattern is not capable
of guaranteeing building safety.
This indicates that concurrent consideration of strength, drift and energy
parameters is necessary in an optimum seismic design. These findings have
been confirmed by the results reported by Karami et al. (2004)
and Moghaddam et al. (2005). They studied the effect of the conventional
lateral loading pattern (i.e., equivalent static method) specified by
the different seismic codes (Uniform Building Code, 1997; NEHRP Recommended
Provisions, 1994) on height wise distribution of ductility demand and
drift in a number of steel shearbuilding and concentric bracedsteel
frames. It was concluded that the strength distribution patterns suggested
by these seismic codes do not lead to a uniform distribution of ductility
and deformation in steel shearbuilding and concentric bracedsteel frames
subjected to severe earthquakes.

Fig. 7: 
Effect of ground motion on heightwise distribution
of drift in 8, 12 and 15 story buildings 
CONCLUSIONS
In this study, seismic behavior of RC buildings with shear wall based
on Iranian Seismic Code (2005) (Third edition) subjected to 10 severe
earthquakes have been investigated. The following observations and conclusions
are presented:
• 
In RC buildings with shear wall, values of hysteretic
energy and damage of columns in each story was very negligible. This
confirms strong column and weak beam discussion and indicates that
beams yield sooner than columns and experience more damage 
• 
Because of effect of shear wall in the frames, the mean of maximum
value of damage indices for 10 earthquakes was small and equaled to
0.188. This represent that structures have not been ruptured and structures
are repairable 
• 
Roof floor, of all models experienced the least damage compared
to other floors. In addition, the amount of hysteretic energy for
roof was negligible, so it can be said that most of the elements of
this story stay in elastic state and the small damage observed in
the story is only due to drift effect 
• 
A study of drift and damage indices in stories especially in earthquake
with high intensity like Manjil and Gazli showed that the structures
underwent more damage in one or two stories. Although, strength ratios
were considered uniform in stories height, the distribution of Eh%,
DI and drift for severe strong ground motions with high intensity
were nonuniform and an intense concentration of mentioned parameters
occurred in one or two stories in walls, beams and frames. In severe
earthquakes, nonuniform distribution of damage and drift imply that
considering a matchless strength parameter in seismic loading pattern
is not capable of guaranteeing building safety. This indicates that
concurrent consideration of strength, drift and energy parameters
is necessary in an optimum seismic design 