INTRODUCTION
Seismic response of steel frame buildings has been analyzed under the cyclic load of earthquake due to strong ground motion during some previous studies (Fragiacomo et al., 2004). The results show that the strength is an insufficient criterion for seismic design because most of the structures in strong earthquakes are yielded and entered in the plastic area. Performance based design is a much more comprehensive design method in which the design criteria is based on performance goals. Performance goal can be regarded as fair and to the point criteria of seismic performance of structures such as lateral deformations, lateral displacements of story, element ductility and element loss index in comparison to specific criteria of earthquake hazard. In other words, with combination of earthquake level and building performance level a performance goal is formed (Grecca et al., 2004). The base of making building code according to performance design in 1992 by decision making group SEAOC was expanded in VISION 2000 (SEAOC, 1995) committee and it was ordered to do this job before 2000 but nothing special was done except some limited activities. The cause of forming this committee was the 8 billion dollar loss from Loma Prieta earthquake in 1989. In Northridge earthquake in January 1994 with magnitude of 6.7 Richter around 20 billion dollar loss occurred. Following this accident during one year, VISION 2000 committee gave some suggestions on the performance based design. The report of the committee was published in 1995 which included full earthquake engineering problems in the field of performance based design (Bertero, 1995). In 1997 Bertero (1997) reexamined the instructions of SEAOC for new buildings and NEHRP for seismic retrofitting of existing building (FEMA, 273, 1997) Therefore a primary source was prepared in relation to performance based design which included suggestions and guidelines for designing and retrofitting of buildings.
MATERIALS AND METHODS
To do this research, at first Probabilistic Seismic Hazard Analysis (PSHA) in 2 hazard levels has been done in the center of Tehran. Following this, three 3D models including three common 5, 10, 15story buildings were selected and were designed and typically formed based on 2800 Standard (Standard No. 2800, 2005) using ETABS software. The selected rehabilitation goal used for the controlling of these buildings is fair according to Seismic Rehabilitation Code for Existing Buildings in Iran (IIEES, 2002) (which is based on FEMA reports). This has been done using the four main analysis methods (Linear Static, Linear Dynamic, Nonlinear Static and Nonlinear Dynamic Analyses) in SAP2000 software. Finally the results have been summarized and concluded.
DIFFERENT METHODS OF STRUCTURAL ANALYSIS
There are four types of analysis in Seismic Rehabilitation Code for Existing
Buildings in Iran (IIEES, 2002) which are as followings:
• 
Linear static analysis 
• 
Linear dynamic analysis 
• 
Nonlinear static analysis 
• 
Nonlinear dynamic analysis 
Linear static analysis: In this method, the Pseudo lateral load of earthquake
is selected in a way that its base shear is equal to the base shear according
to Eq. 1. The amount of base shear in this method is selected
in a way to have the maximum deformation of structure with the predicted hazard
level earthquake.
V = C_{1}C_{2}C_{3}C_{m}S_{a}W 
(1) 
Where:
W 
= 
Total dead load and anticipated live load 
S_{a} 
= 
Spectral response acceleration, at the fundamental period and damping
ratio of the building in the direction under consideration 
C_{1} 
= 
Modification factor to relate expected maximum inelastic displacements
to displacements calculated for linear elastic response 
C_{2} 
= 
Modification factor to represent the effect of stiffness degradation and
strength deterioration on maximum displacement response 
C_{3} 
= 
Modification factor to represent increased displacements due to dynamic
PΔ effects 
C_{m} 
= 
Modification factor to have impact for higher modes 
Distribution of lateral force on building height based on the base shear force,
height and weight of the stories are:
In which, Where, F_{i} is the force on the story i, W weight of the
story i and h height of the story i from the base level and the amount of K
equals to:
Where:
K 
= 
1.0 for T<=0.5 sec 
K 
= 
2.0 for T>=2.5 sec 
Where:
T 
= 
The fundamental period of the building in the direction under
consideration 
Linear dynamic analysis: Linear dynamic analysis can be done with two
methods; response spectrum or timehistory analysis. Special assumptions of
this method in the limit of linear behavior are:
• 
Structural behavior can be calculated with a linear combination
from different vibrational modes of structure which are independent of each
other 
• 
Period of structure in each mode is constant during earthquake 
As mentioned before response spectrum method has been used in this research.
The amount of vibration modes in response spectrum method should be selected
in a way that the total percent of contribution of effective mass for each direction
excitation in selected modes be at least 90%. In addition in each direction
at least three primary modes of vibration and all modes which have more than
0.4 sec time period should be considered. To do this analysis, obtained spectrum
from probabilistic seismic hazard analysis was used.
Nonlinear static analysis: In this method, the mathematical model of
the building is subjected to monotonically increasing lateral forces or displacements
until either a target displacement (Eq. 4) is exceeded or the
building collapses (for structures with rigid diaphragms) (IIEES, 2002).
Where:
T_{e} 
= 
The effective fundamental period in the direction under consideration 
S_{a} 
= 
Spectral response acceleration, at the fundamental period and damping
ratio of the building 
C_{0} 
= 
Modification factor to relate spectral displacement and likely building
roof displacement 
C_{1} 
= 
Modification factor to relate expected maximum inelastic displacements
to displacements calculated for linear elastic response 
C_{2} 
= 
Modification factor to represent the effect of hysteretic shape on the
maximum displacement response 
C_{3} 
= 
Modification factor to represent increased displacements due to dynamic
PΔ effects 
In this research 2 types of lateral load distribution were used on structures
(IIEES, 2002):
• 
Distribution type I: Distribution corresponding to
lateral forces derived from linear spectrum dynamic analysis. 
• 
Distribution type II: Uniform distribution, in which lateral forces
is calculated corresponding to the mass distribution at each floor level,
like Eq. 5: 
Where:
F_{i} 
= 
The force on level i 
W_{i} 
= 
Weight of level i 
V 
= 
Base shear force 
Nonlinear dynamic analysis: In this method, the structure response is
calculated regarding nonlinear behavior material and geometrically nonlinear
behavior of structures. In this method, it is supposed that stiffness and damping
matrix can be changed from one step to another but is constant in each time
step. The response of model under the earthquake acceleration is calculated
using numerical method.
Nonlinear dynamic analysis is the most accurate method which is used for the
structural analysis. In fact the main goal in this method is to solve differential
equation of dynamic equilibrium of motion (Eq. 6). Nonlinear
dynamic analysis is done with 2 general methods of Direct Integration and Modal
Analysis (Bathe, 1996). Direct Integration includes different methods such as
Houbolt, Central Difference, Wilson θ and Newmark. In this research Direct
Integration Method (Wilson θ and Newmark) has been used.
Where:
K, C, M 
= 
Stiffness, damping and mass matrixes, respectively 

= 
Displacement, velocity and acceleration vectors, respectively 
r(t) 
= 
External force vector (Clough and Penzin, 1993) 
STUDIED MODELS
Three symmetric and regular 5, 10, 15 story steelbraced buildings have been
selected. The ratio of their height to width varies from 1.5 to 3 and is regarded
as common buildings. It is good to note that these three models are 3D and all
the processes of analysis, design and evaluation are done using these 3D models.
For each model:
• 
Bay width for each direction is 4 m 
• 
The height of first story is 3.8 m and the rest are 3.2 m 
• 
Cross brace system is used (Because of wide usage) 
The type of building is residential with average importance located in the
center of Tehran. In all models the resistance system against lateral loads
in both directions are braced frame. In order to tolerate the gravity loads
of the stories, oneway slab system is used for floors. Plans and 3D elevations
of the buildings under study are shown in Fig. 1 and 2,
respectively:
MATERIAL SPECIFICATIONS AND ELEMENT SECTIONS
Specification of the material is stated as:
F_{y} = 235 Mpa, F_{u} = 392 Mpa,
E = 2* 10^{5} Mpa, v = 0.3 
Box and 2IPE, IPE and Box sections, according to DIN Standard, are chosen for
columns, beams and bracings, respectively.
DESIGNING AND ANALYSIS SOFTWARE
In order to make and design the assumed models, ETABS ver8.5.4 (Computers and
Structures, Inc., 2004) has been used (the members of the all primary models
were typically formed after being designed). Then the models were transferred
to SAP2000 ver9.1.6 (Computers and Structures, Inc., 2005) and the four mentioned
analysis were done by this program.

Fig. 1: 
Plans of studied buildings, a 5story, b 10story and c 15story
(thick line: bracing) 

Fig. 2: 
3D elevations of studied buildings 
LOADING AND DESIGNING BASED ON 2800 STANDARD
Gravity loading of mentioned buildings is based on National Building Code for
Structural Loadings (Iranian, 2004) and the lateral loading is based on 2800
Standard (Standard No. 2800, 2005). Dead and live area loads and lateral wall
loads in the stories are 700, 200 and 800 kgf m^{2}, respectively and
in the roof are 600, 150 and 250 kgf m^{2}, respectively. To consider
the effect of earthquake loading according to 2800 Standard (Standard No. 2800,
2005), static equivalent loading method is used. Seismic parameters values are
mentioned below:
• 
Base Design Acceleration: A = 0.35 g 
• 
Soil Type: Type II (T_{soil} = 0.5 sec) 
• 
Importance Factor: I = 1 
Design Code AISCASD89 which is supported by the aforementioned program has
been used for designing members. Specific criteria for steelbraced framed buildings
which are earthquake resistant according to 2800 Standard (Standard No. 2800,
2005) and Iranian National Building code (Iranian, National Building Code for
Steel Structures, 2004) are stated as below:
• 
Controlling the least slenderness of bracing members 
• 
Reduction of allowed compressive stress in bracing members 
• 
Controlling of columns in load combinations stated below 
a 
Axial pressure 
P_{DL} + 0.8 P_{LL}+2.8 P_{E} <= P_{SC} 
b 
Axial tension 
0.85 P_{DL} + 2.8 P_{E} <= P_{ST} 
PROBABILISTIC SEISMIC HAZARD ANALYSIS (PSHA)
As mentioned earlier, probabilistic seismic hazard analysis in center of Tehran
in two hazard levels 1 and 2 has been done. This caused seismic evaluation of
buildings to occur for these 2 hazard levels. Hazard level 1 is determined based
on 10% earthquake probability of accedence in 50 years (return period = 475
years). Hazard level 2 is determined based on 2% earthquake probability of accedence
in 50 years (return period = 2475 years). In Fig. 3 the obtained
design spectra are shown.

Fig. 3: 
Design spectra based on PSHA (Hazard levels 1 and 2) and 2800
standard 
APPROPRIATE ACCELEROGRAMS AND SCALING PROCESS
Selecting appropriate accelerograms: In this research 7 accelerograms
(Table 1) have been used for the nonlinear dynamic analysis
and as a result their average response value can be used to control the deformations
and internal forces. The accelerograms which are used for nonlinear dynamic
analysis should have at least matching specifications with the site of the structure.
These specifications include PGA, frequency contents, duration and harmony with
design spectra (Lestuzzi et al., 2004). In order to use the accelerograms
in nonlinear dynamic analysis, the spectrum of this accelerogram should be as
much as possible in harmony with design spectrum of the site. In fact before
using the accelerograms, they should be scaled.
Scaling accelerograms: In this research by using spectrum scaling method, accelerograms have been scaled. In this method the maximum acceleration of each accelerograms is scaled to 1 g. Then the response of SingleDegreeOfFreedom (SDOF) system is calculated versus these records. Area under this spectrum is obtained between periods of 0.1 and 3 sec. The area under site spectrum curve between the two periods is calculated. By multiplying scaled accelerogram to 1 g by the ratio of site spectrum area over accelerogram spectrum area and finally by site design acceleration, the scaled accelerogram is obtained. In this method the energy of accelerograms is harmonized with design spectrum (Lestuzzi et al., 2004).
DISCUSSION
Designed models using 2800 Standard (Standard No. 2800, 2005), are analyzed
based on Seismic Rehabilitation Code for Existing Buildings (IIEES, 2002), using
four methods including Linear Static, Linear Dynamic, Nonlinear Static and Nonlinear
Dynamic procedures. The selected rehabilitation goal for this research is fair
(Life Safety in Hazard Level 1 + Collapse Prevention in Hazard Level 2). In
nonlinear static analysis two types of load distributions (Types I and II) are
implemented on the structures. In linear dynamic analysis, the spectrum method
and in nonlinear dynamic analysis, the timehistory method has been used.
Table 1: 
Accelerograms and the utilized scale coefficients in nonlinear
dynamic analysis 

Table 2: 
Loading details according to linear static method 

Table 3: 
The results of linear static analysis, percentage of the members
which do not satisfy the acceptance criteria 

Linear static method: Assumed models with the shown forces in Table
2 are loaded and then evaluated. Acceptance criteria were implemented according
to Seismic Rehabilitation Code for Existing Buildings (IIEES, 2002), the summary
is stated as:
• 
Deformationcontrolled actions in primary and secondary components
and elements shall satisfy the equation: 
• 
Forcecontrolled actions in primary and secondary components
and elements shall satisfy the equation: 
General assumptions are used in evaluating all models which are stated as:
• 
Knowledge factor: K = 1 
• 
Rehabilitation goal: Fair 
The results of this evaluation are shown in Table 3. According
to this method all bracing members (deformationcontrolled) have satisfied the
acceptance criteria but lack of acceptance of this criteria is visible in some
percentage of columns (forcecontrolled).
Table 4: 
The values of parameters used in linear dynamic analysis 

Table 5: 
The results of linear dynamic analysis, percentage of the
members which do not satisfy the acceptance criteria. 

Table 6: 
Needed parameters for nonlinear static analysis, distribution
type I 

Linear dynamic method: Assumed models were analyzed and evaluated with
spectrum obtained from PSHA. The values of parameters used in linear dynamic
analysis are shown in Table 4. Acceptance criteria are implemented
according to Clause (101).
The results of this evaluation are shown in Table 5. According
to this method all bracing members (deformationcontrolled) have satisfied the
acceptance criteria but lack of acceptance of this criteria is visible in some
percentage of columns (forcecontrolled).
Nonlinear static method: Assumed models were analyzed and evaluated
by nonlinear static method (Target Displacement Method). In Table
6 and 7 needed parameters for nonlinear static analysis
are shown.
For modeling the stiffness of members in nonlinear static method, the principles
of Seismic Rehabilitation Code for Existing Buildings (IIEES, 2002) are used.
For modeling forcedeformation curve of members which is shown in Fig.
4, values of a, b, c shown in Table 8 are used. Strainhardening
of components is accounted according to the slope of 3% of the elastic slope.

Fig. 4: 
Generalized forcedeformation relation for steel elements
or components (FEMA 356, 2000) 
The results of this evaluation are shown in Table 9. As it
is shown, some percentage of bracing members (deformationcontrolled) and columns
(forcecontrolled) have not satisfied acceptance criteria. Also 5story building
in Hazard Level 2 experienced instability.
Table 7: 
Needed parameters for nonlinear static analysis, distribution
type II 

Table 8: 
Modeling parameters and acceptance criteria of bracing members
in nonlinear static analysis 

Table 9: 
The results of nonlinear static analysis, percentage of the
members which do not satisfy the acceptance criteria 

Table 10: 
The results of nonlinear dynamic analysis, percentage of
the members which do not satisfy the acceptance criteria 

Nonlinear dynamic method: Assumed models were analyzed and evaluated
using seven mentioned accelerograms and direct integration method. Description
and attribution of nonlinear hinges of bracing members is like Table
8. The results of this evaluation are shown in Table 10.
As it is visible, some percentage of bracing members (deformationcontrolled)
and columns (forcecontrolled) have not satisfied the acceptance criteria. Instability
of different buildings against some earthquakes is visible in the both hazard
levels.
CLASSIFICATION OF RESULTS
To reach a better understanding and also integration of analysis, the results
of 4 types of analyses are presented for comparison in a curve form from Fig.
58.

Fig. 5: 
Comparison of results accuracy obtained from 4 types of analyses,
bracing members (HL1) 

Fig. 6: 
Comparison of results accuracy obtained from 4 types of analyses,
columns (HL1) 

Fig. 7: 
Comparison of results accuracy obtained from 4 types of analyses,
bracing members (HL2) 
In these curves:
LSP 
= 
Shows linear static analysis 
LDP 
= 
Shows linear dynamic analysis 
NSP 
= 
Shows nonlinear static analysis 
NDP 
= 
Shows nonlinear dynamic analysis 

Fig. 8: 
Comparison of results accuracy obtained from 4 types of analyses,
columns (HL2) 
And vertical axis shows the percentage of members which have not satisfied
acceptance criteria (failed members).
CONCLUSION
The accuracy of linear analysis (static and dynamic) in evaluation of the bracings is very low and not reliable.
In evaluation of the columns, the results of linear static analysis is closer to reality than linear dynamic and nonlinear static analyses.
In general, the results of nonlinear static analysis have more accuracy and are more reliable than linear static and linear dynamic analysis.
Nonlinear static analysis in the evaluation of 15story building has less accuracy than 5 and 10story buildings.
(This may be due to lack of contribution of higher modes effects in load distribution
pattern used in nonlinear static method. Because in tall buildings higher modes
have substantial effect, it is recommended that for tall buildings, MPA method
(Chopra and Goel, 2002) be used in nonlinear static analysis).
According to nonlinear dynamic analysis for the models designed based on 2800 Standard, the following results have been obtained:
5story building
Hazard level 1: More than 65% of members do not satisfy the acceptance criteria.
Hazard level 2: The structure experienced instability.
10Story building
Hazard level 1: Around 60% of members do not satisfy the acceptance criteria.
Hazard level 2: Around 80% of members do not satisfy the acceptance criteria.
15Story building:
Hazard level 1: Around 45% of members do not satisfy the acceptance criteria.
Hazard level 2: The structure experienced instability.
ACKNOWLEDGMENT
The authors would like to thank Mr. Hadi Hamidi for his great help in translating the text.
NOTATIONS
C 
= 
Damping Matrix 
C_{0} 
= 
Modification factor to relate spectral displacement of an equivalent SDOF
system to the roof displacement of the building MDOF system calculated 
C_{1} 
= 
Modification factor to relate expected maximum inelastic displacements
to displacements calculated for linear elastic response 
C_{2} 
= 
Modification factor to represent the effects of pinched hysteretic shape,
stiffness degradation and strength deterioration on the maximum displacement
response 
C_{3} 
= 
Modification factor to represent increased displacements due to PΔ
effects 
C_{m} 
= 
Effective mass factor to account for higher mode mass participation effects 
E 
= 
Modulus of elasticity 
F_{i} 
= 
Lateral load applied at floor level i 
F_{y} 
= 
Yield strength of the material 
F_{u} 
= 
Tensile strength of the material 
K 
= 
Stiffness matrix 
M 
= 
Mass matrix 
P_{DL} 
= 
Axial force in member, due to dead load, 
P_{E} 
= 
Axial force in member, due to earthquake 
P_{LL} 
= 
Axial force in member, due to live load 
P_{SC} 
= 
Column axial load capacity, compression 
P_{ST} 
= 
Column axial load capacity, tension 
Q 
= 
Generalized force in a component 
Q_{CE} 
= 
Expected strength of the component or element at the deformation level
under consideration for deformationcontrolled actions 
Q_{CL} 
= 
Lowerbound strength of a component or element at the deformation level
under consideration for forcecontrolled actions 
Q_{UD} 
= 
Deformationcontrolled design action due to gravity loads and earthquake
loads 
Q_{UF} 
= 
Forcecontrolled design action due to gravity loads in combination with
earthquake loads 
S_{a} 
= 
Spectral response acceleration (g) 
T 
= 
Fundamental period of the building in the direction under consideration 
T_{0} 
= 
Period at which the constant acceleration region of the design response
spectrum transitions to the constant velocity region 
T_{e} 
= 
Effective fundamental period of the building in the direction under consideration 
V 
= 
Pseudo lateral load 
W 
= 
Effective seismic weight of a building including total dead load and applicable
portions of other gravity loads 
h_{i} 
= 
Height from the base to floor level i 
h_{j} 
= 
Height from the base to floor level j 
g 
= 
Acceleration of gravity 
k 
= 
Knowledge factor 
m 
= 
Component or element demand modifier (factor) to account for expected
ductility associated with this action at the selected Structural Performance
Level 
r(t) 
= 
External forces vector 
u(t) 
= 
Displacement vector 
u(t) 
= 
Velocity vector 
u(t) 
= 
Acceleration vector 
w_{i} 
= 
Portion of the effective seismic weight W located on or assigned to floor
level i 
w_{j} 
= 
Portion of the effective seismic weight W located on or assigned to floor
level j 
Δ 
= 
Generalized deformation 
θ 
= 
Generalized deformation, radians 
δ_{t} 
= 
Target displacement 
v 
= 
Poisson`s ratio 