The introduction of an eccentricity in this system results in a geometric nonlinearity behavior. The midpoint of the diagonal member is connected to the corner joint using a brace member with a relatively low stiffness, thus forming a threemember bracing system in each braced panel. An iterative method of analysis has been developed to study the nonlinear loaddeflection behavior of ODBS. The results indicate that the loaddeflection behavior of this system follows a nonlinear stiffnesshardening pattern with two yielding points, which reflect the tensile failure of different bracings; the present study aims to investigate the efficiency of applying offdiagonal steel braces to reinforced concrete frames. To achieve this, three types of 2story, 6story, and 15story structures without and with Xbracing and offcenter bracing systems were modeled using SAP2000 software, and for micromodeling ANSYS software was used to achieve finite element results for an exact comparison between various retrofitting systems. The results showed that the structures strengthened by toggle bracing system revealed better behavior for low oscillation periods. Moreover, this type of bracing system is quite suitable for 10story structures but not for higher ones. Its main problem, which requires special contrivances to solve, is the existence of a soft ground floor.
The earthquake catastrophe is one of the primary reasons for destruction of buildings, engineering infrastructures, and social systems [
Nowadays, the use of reinforced concrete structures increases in Iran. Factors such as availability of required materials, simpler construction procedure, and possibility for creation of larger spaces persuade designers and engineers to employ this system [
The present study mainly aims to investigate the effect of high ductility of the ODBS braced frame as well as the way of damping the oscillations transmitting to the upper levels which have been strengthened with steel Xbracing system. To achieve this, different frames should be modeled and the seismic behavior of each one should separately be investigated and compared to one another. On this basis, we will firstly model severalstory frames with only its first story frame strengthened by ODBS system and the upper stories braced with Xbrace system. Then, another frame strengthened by Xbracing system in all stories will be modeled and compared to the former frame.
Another goal of this study is to research the reduction in the impact loads originated when changing the oscillation mode of structure. As it is known to us, a considerable impact load is exerted on bracing components if the direction of forces changes and components stretch under the influence of components’ buckling caused by pressure [
The idea of steel bracing system application to reinforced concrete buildings was first suggested for seismic strengthening of concrete buildings. From the viewpoint of both research and application, this idea has been very prevalent during past two decades because of the simplicity of its implementation and its relatively lower cost compared to shear wall. For example, Sugano and Fujimura performed a series of experiments on a model of onestory frame which had been strengthened through various methods. They examined the frame samples with X and KShape bracing systems and compared them to the samples strengthened by concrete and masonryinfilled walls. They aimed to determine the effect of each of these systems on enhancement of inplane strength and ductility of the samples [
A model of twospan second stories reinforced concrete frame with a scale of 1 : 3 was chosen to represent the seismic weaknesses of the structures of this type. The strengthened frame was exposed to lateral and gravity loadings and its displacements were allowed to increase by one fiftieth of the frames’ original height (allowable drift). The strengthened inside frame by a ductile steel bracing demonstrated considerably better behavior than the preliminary reinforced concrete frame [
In 1999, the direct internal use of steel bracing system in concrete frame was studied in laboratory. Experiments were carried out on five onespan onestory frame samples with a scale of 1 : 2.5. Two of them had no bracing system but the other three samples were strengthened by Xbracing systems with different component connectors including bolt and nut, cover of RC column, and plates placed in concrete. The prepared frames were exposed to constant gravity and lateral cyclic loadings. Results showed, depending upon various component connectors, the bracing system considerably increases the equivalent stiffness of the frame and notably changes its behavior. When the bracing connector is implanted inside concrete, the performance of frame gets even better and further energy is absorbed. Generally, experiments demonstrated that bracing tolerates a major part of lateral load in reinforced concrete frame [
Dynamic behavior of the concrete buildings strengthened with concentric bracing systems has been investigated by AbouElfath and Ghobarah. A threestory building was dynamically analyzed with various earthquake records and the effect of steel bracing system on building as well as the effect of bracing system distribution throughout frames’ height was studied. This study on the placement of braces investigated the seismic performance, relative and total drift of floor, and destruction index to show the effect of this type of bracing systems [
Maheri and Akbari first reviewed previous studies on strengthening by steel bracing systems and then investigated three models including a simple frame, a frame strengthened with Xbracing, and a frame strengthened with knee bracing system under lateral load until failure stage. They found that ductility of RC frame considerably increases when using knee bracing system [
In 1995, Moghaddam and Estekanchi modeled and tested offcentre bracing systems in steel frames for the first time. Later in 1999, they analyzed the seismic behavior of offdiagonal bracing system. They confirmed that this system’s behavior resembles that of seismic isolators and plays a considerable role in reduction of seismic forces [
Macromodeling method was used to analyze the nonlinear behavior of reinforced concrete frame strengthened by steel bracing system (macroelement by lowest accuracy related to micromodeling elements). The model was calibrated using existing laboratory work results and then a larger number of floors and openings were analyzed. The SAP2000 software was employed to model the reinforced concrete frame braced with ODBS system. Dynamic time history analysis was done on the concrete frames with more floors and openings. Dynamic time history analysis using earthquake accelerograms is one of the methods suggested by most regulations to investigate the seismic behavior of structures. This study used three accelerograms of Naghan, Tabas, and El Centro. Their general characteristics are listed in Table
Characteristics of the selected accelerograms.
Records  Duration (s)  PGA m/sec^{2}  Time Step (s)  Country of event  Date of event  Station  Position  Longitude  Latitude 

components  
Tabas  50  3.42  0.01  Iran 

Deyhook  33.3′N, 57.52′E  3.27  4.10 
Naghan  5  7.09  0.001  Iran 

Central  31.98′N, 50.68′E  7.61  7.61 
El Centro  53.7  3.49  0.01  USA 

E06 array  32.44′N, 115.3′W  3.35  4.03 
The various maximum ground acceleration after scaling is set to 0.3 g. Three groups of records are selected based on two parameters: the closest distance to a fault rupture surface [greater than 50 km (far field) and nearer than 10 km (near fault)] and the moment magnitude in every scales [
Since the characteristics of these earthquakes are different from other places, they have to be scaled to one scale before using them for nonlinear dynamic analyses of the studied models. To scale accelerograms using UBC97 method, the values of natural oscillation period were firstly calculated for our three models. These three models included the models with three spans and 2, 6, and 15 floors. Models were divided into three groups of short, medium, and tall buildings and their natural period was considered to be in three categories of short, medium, and long periods [
Two, six, and fifteenstory models by various load bearing systems. (a) Twostory models and (b) sixstory models and (c) fifteenstory models. All models have 3 m height of stories and 4 m length of spans.
Twostory models of flexural frame (A), XSteel (B), and offdiagonal bracing system (C)
Sixstory models of flexural frame without bracing system (A), with XSteel bracing system (B), and with offdiagonal steel bracing system (C)
Fifteenstory models of flexural frame without bracing system (A), with XSteel bracing system (B), and with offdiagonal steel bracing system (C)
Offdiagonal bracing system schematic models and forcedisplacement diagram by ductile behavior.
Convergence of SAP2000 numerical and experimental results on calibration process.
Time history analysis should be performed according to previous accelerogram multiplied by modified scaled factor. Simulated accelerograms should be done according to peak ground acceleration of the region. Seismic hazard of the region could clear the quantity of PGA according to related seismic manuals. Details of scale factors are in Table
Accelerograms scale factors to modify structural base shear: (a) flexural RC frame and (b) Xbraced RC frame and (c) ODBSbraced RC frame.
Models  Records  

Tabas  Naghan  El Centro  
2story  0.578  1.083  1.35 
6story  0.756  1.31  1.617 


15story  0.881  1.65  1.78 
Models  Records  

Tabas  Naghan  El Centro  
2story  0.431  0.954  1.21 
6story  0.699  1.18  1.543 


15story  0.722  1.51  1.59 
Models  Records  

Tabas  Naghan  El Centro  
2story  0.529  0.998  1.316 
6story  0.709  1.237  1.608 


15story  0.807  1.6  1.67 
A rectangular building with dimensions of 15 m × 25 m was chosen for frames. Dead loads which equaled 60 kN·m^{−2} and live loads which were 20 kN·m^{−2} for floors and 15 kN·m^{−2} for ceiling were considered to uniform linearly be 300 kN·m^{−1} for dead loads and 100 and 75 kN·m^{−1} for live loads of floors and ceiling, respectively. The effect of wind and other similar effects were neglected. Tables
Sections characteristics and component properties of the twostory frame modeled for static and dynamic nonlinear analysis.
Components  Floor  Type  Dimensions 
Bars and stirrups  Hinges  Acceptance criteria/type 

Beams  First floor  Rectangular 
3 Ø 18 
Flexural 
0.01 rad  
Second floor  Rectangular 
3 Ø 16 
Flexural 
0.01 rad  


Columns  First floor  Rectangular 
8 Ø 18 
Flexural + axial 
0.012 rad  
Second floor  Rectangular 
8 Ø 16 
Flexural + axial 
0.012 rad  


Braces  First floor  X  Box 
—  Axial 
7 
Second floor  Box 
—  Axial 
7 

First floor  ODBS 

—  Axial 
7  
Second floor 

—  Axial 
7 
Sections characteristics and component properties of the sixstory frame modeled for static and dynamic nonlinear analysis.
Components  Floor  Type  Dimensions 
Bars and stirrups  Hinges  Acceptance criteria/type 

Beams  First and second floors  Rectangular 
4 Ø 18 
Flexural 
0.01 rad  
Third and fourth floors  Rectangular 
4 Ø 16 
Flexural 
0.01 rad  
Fifth and sixth floors  Rectangular 
3 Ø 16 
Flexural 
0.01 rad  


Columns  First and second floors  Rectangular 
12 Ø 20 
Flexural + axial 
0.012 rad  
Third and fourth floors  Rectangular 
8 Ø 20 
Flexural + axial 
0.012 rad  
Fifth and sixth floors  Rectangular 
8 Ø 18 
Flexural + axial 
0.012 rad  


Braces  Second and third floors  X  Box 
—  Axial 
7 
Fourth, fifth, and sixth floors  Box 
—  Axial 
7 

First floor  ODBS  Components 1 and 2: 
— 
Axial 
7 

Component 3 
9 
Sections characteristics and properties of the fifteenstory concrete frame with X and offdiagonal bracing systems for nonlinear analysis.
Components  Floor  Type  Dimensions 
Bars and stirrups  Hinges  Effective inertia 

Beams  First, second, and third floors  Rectangular 
7 Ø 20 
Flexural 
0.01 rad  
Fourth, fifth, sixth, and seventh floors  Rectangular 
8 Ø 22 
Flexural 
0.01 rad  
Eighth, ninth, tenth, and eleventh floors  Rectangular 
7 Ø 18 
Flexural 
0.01 rad  
Floors from twelve to fifteen  Rectangular 
6 Ø 18 
Flexural 
0.01 rad  


Columns  First floor and second floor  Rectangular 
44 Ø 25 
Flexural + axial 
0.012 rad  
Floors from three to six  Rectangular 
36 Ø 25 
Flexural + axial 
0.012 rad  
Floors from seven to eleven  Rectangular 
28 Ø 22 
Flexural +axial 
0.012 rad  
Floors from twelve to fifteen  Rectangular 
20 Ø 22 
Flexural + axial 
0.012 rad  


Braces  Floors from one to four  X  Box 
—  Axial 
7 
Floors from five to nine  Box 
—  Axial 
7 

Floors from ten to fifteen  Box 
—  Axial 
7 

First floor  ODBS  Components 1 and 2: 
—  Axial 
9 
Calibration of obtained results in SAP2000 is performed for flexural frame and Xbracing systems according to previous experimental investigation by Maheri and Ghaffarzadeh in laboratory of Shiraz university [
According to Figure
To perform nonlinear static analysis for various models, reinforced concrete beams and columns action are in LifeSafety performance level according to FEMA356 and ATC40. Also components of steel bracing system (all components of Xbracing and 1st and 2nd components of ODBS bracing system) were analyzed through LifeSafety performance level. For third member of ODBS, the Collapse Prevention performance level is used.
Table
The values of maximum relative drifts of floors obtained for two, six, and fifteenstory frames of flexural type, strengthened with Xbracing system type and strengthened with offdiagonal bracing system type undergoing the earthquakes of Naghan, Tabas, and El Centro (from left to right).
Floor  (Interstory drift) (cm) (Naghan/Tabas/El Centro)  

Xbracing system  
2ST  6ST  15ST  
1  0.25  0.16  0.21  0.62  0.6  1.4  0.95  0.6  0.8 
2  0.1  0.09  0.12  0.7  0.83  1.71  0.9  0.45  0.4 
3  0.8  1.15  1.93  0.75  0.39  1.00  
4  1.45  2.41  1.68  1.47  0.51  1.1  
5  0.72  1.52  0.79  1.68  1.41  2.1  
6  0.51  0.89  0.46  1.93  1.50  2.6  
7  0.76  0.95  3.01  
8  0.93  2.1  1.76  
9  0.81  2.05  2.51  
10  0.75  2.5  1.12  
11  0.6  1.63  0.93  
12  0.72  0.95  0.81  
13  0.58  0.71  0.6  
14  0.49  0.45  0.48  


15  0.33  0.2  0.23 
Floor  (Interstory drift) (cm) (Naghan/Tabas/El Centro)  

Offdiagonal bracing system  
2story  6story  15story  
1  0.4  0.28  0.35  2.75  1.9  2.6  5.1  3.1  4.93 
2  0.24  0.12  0.2  1.76  1.24  2.1  1.9  2.03  3.1 
3  0.85  0.43  0.6  1.71  1.47  2.08  
4  1.46  1.05  1.4  1.63  1.2  1.43  
5  0.77  0.52  0.7  1.04  0.98  1.76  
6  0.68  0.3  0.5  0.98  0.8  1.45  
7  1.45  0.77  2.5  
8  2.53  0.63  0.23  
9  0.8  1.51  0.2  
10  0.71  2.33  1.49  
11  0.7  1.51  0.7  
12  0.62  1.06  0.32  
13  0.41  0.43  0.11  
14  0.28  0.41  0.1  


15  0.14  0.32  0.06 
Floor  (Interstory drift) (cm) (Naghan/Tabas/El Centro)  

(flexural)  
2story  6story  15story  
1  0.3  0.2  0.27  2.95  1.68  2.93  1.4  0.07  0.9 
2  0.18  0.1  0.19  1.05  1.98  2.85  3.1  0.51  1.8 
3  2.48  1.85  2.33  2.4  1.7  1.93  
4  1.49  1.08  1.45  2.1  0.61  3.91  
5  1.2  0.9  1.21  1.9  0.53  2.85  
6  0.8  0.58  0.86  1.85  0.42  2.7  
7  1.61  0.43  2.53  
8  1.42  0.94  1.98  
9  1.23  0.83  1.45  
10  1.2  0.9  2.9  
11  2.31  3.4  1.95  
12  1.86  1.95  1.43  
13  1.03  1.08  1.32  
14  0.68  0.81  1.11  


15  0.34  0.71  0.95 
After performing dynamic nonlinear analyses by scaled earthquakes, the drifts of different nodes in numerous time steps were investigated for each of the described models. The results obtained for each of the columns listed in Table
According to Table
The tolerance towards drift is limited for El Centro earthquake and both floors have almost the same amount of drift, while the tolerance for Naghan earthquake is something between those for Tabas and El Centro earthquakes; that is, the amount of drift for twostory sample increases in the sequence of El Centro earthquake < Naghan earthquake < Tabas earthquake. According to the results obtained for sixstory building, it is obvious that the greatest amount of drift occurs in lower floors for intense earthquakes like Tabas earthquake and in higher floors for the earthquakes of medium intensity but longer duration like El Centro earthquake. For sixstory building, the amount of drifts in different floors of flexural frame is almost the same and does not vary considerably. Nonetheless, Xbracing system decreases the drift of lower floors and ODBS decreases that of second, third, and fourth floors. The result is that the offdiagonal braces act similar to seismic isolators. The criterion for performance of ODBS as seismic isolators is the entrance of concrete and steel construction materials into nonlinear or postelastic region. Therefore, a considerable drift is absorbed by first floor and the drifts of upper floors are balanced to a great degree. In fifteenstory flexural frame samples, the maximum amount of drift belongs to third and fourth floors, while the minimum drift in ODBS system was observed along first, eighth, and fifteenth floors. The reason is the greater number of oscillation modes in taller buildings. Therefore, the highperiod earthquakes such as Tabas earthquake have greater effect on fifteenstory tall buildings and result in the maximum drifts. For the earthquakes of higher oscillation period and PGA, like El Centro earthquake, the maximum relative deformations occur for fourth and eleventh floors. The earthquakes like Naghan earthquake, which have lower oscillation period, have smaller effect on fifteenstory building which possesses a great natural period and hence the amount of relative deformation for its floors is smaller. Considering the reducing effect of Xbracing system on structure period, this system intensifies the effect of lowoscillationperiod earthquakes, such as Naghan earthquake, on floors’ relative drift. Nevertheless, the relative drift of a fifteenstory concrete building braced with Xbracing system is generally smaller than that of a flexural frame. In the case of ODBS, the effect of bracing system on drift of a fifteenstory concrete structure is a considerably reducing effect for the floors from second to eighth but a negligible effect for the floors from ninth to fifteenth and the ratio obtained for flexural frame and Xbraced frame is also obtained here. Eventually, the effect of various steel bracing systems on concrete flexural structure is related to the formation of plastic hinges in flexural frame and steel bracing system components. Adding the Xbracing system to concrete flexural frame, the formation of hinges in steel components is restricted and the possibility of formation of plastic hinges in beam components, especially in concrete frame column, will be weak.
Adding the ODBS to concrete flexural frame, not only is the formation of more plastic hinges in components of beam and column, but also the systems ductility increases specially for three to tenstory structures, as a result of producing axial plastic hinges of ODBS components. Considering the design of frame sections based on linear static analysis, a limited number of plastic hinges are formed in flexural frame and all of the members will not be able to produce plastic hinges, but when the steel offdiagonal bracing system is added to flexural frame, increasing the rotational capacity of RC members and also increasing the number of composed plastic hinge are some indices of increased ductility of ODBS braced RC flexural frame. Many results are generated along this analysis, in ODBS braced RC frame before performing any damages, the third member of this system has been rotated and deflected near the plastic limit. In this hand, the initial sever vibrations have been damped through the flexibility of ODBS system and also its members elongation and energy absorption. Figure
The sequence of formed plastic hinges in various sixstory reinforced concrete frames under equivalent Tabas general response spectrum: (a) the flexural frame (left), (b) retrofitted frame by Xbracing system (center), and (c) retrofitted frame by ODBS.
Flexural frame
Xbraced frame
ODBS braced frame
Contour shape of plastic hinges is indicated in Figure
Acceptance criterion for flexural frame of LS level is 0.02 for primary components and also the acceptance criteria for ODBS braced frame of CP level are 0.025 and 0.05 for primary and secondary components, respectively. A more detailed scrutinizing of the results reveals that the hinges formed in ODBS system endure the maximum deformation and earn the structure a very high performance level along ductile behavior. In addition, the more performance levels of plastic hinges are gathered in the structure, so by this level of ductility, the structure will absorb more quantity of energy. These results are deduced based on nonlinear dynamic step by step analyses. The time steps for this analysis is considered less than
According to Fema356, the plastic rotation of mentioned beams and columns of flexural frame is 0.025 rad and 0.02 rad, the plastic rotation of mentioned beams and columns of flexural frame is 0.025 rad and 0.02 rad, respectively. These quantities are 0.05 rad 0.03 rad in the system like ODBS by high ductility and therefore the structural damage can be prevented to a great extent. This is why the structure’s ductility and its capacity of energy absorption decrease considerably when the structural performance is limited to the formation of first crack [
Also in micromodeling phase the flexural RC frame was designed according to ACI concrete manual. In all modeling specimens main RC frame is flexural and these bracing systems are added to the main flexural frame. ANSYS scale modeling is 2/5 because that in experimental models used the same scale factor for geometry characteristics (Figure
Beam and column and sections’ details, reinforcement of flexural RC frame, and also other composed frames and steel bracing sections that are considered for analytical calibration [
For the braced RC frames, two,
The beamcolumn joint of the moment frame was transversely reinforced with two 6 mm steel wires in accordance with the special seismic provisions of the ACI code (ACI Committee Manual, 31802). For the braced frame, the stirrups of the column were continued in the joint resulting in one 6 mm wire in the joint area. It can be observed that the strains in the one 6 mm wire of the braced frame were about 40% those of the two 6 mm wires of the ductile moment frame. Thus, the use of braced frames is expected to eliminate the undesirable shear failure of beamcolumn joints without the need for any special joint detailing [
According to Figure
Values of the maximum drift of floors (regardless of drift limitations), ductility, and
Model 











(flexural RC frame) 
0.0173  0.0665  0.0112  0.067  17272  4500  2875  1740  3.84  9.92 
(Xbraced frame) 
0.0103  0.0390  0.0058  0.0547  33034  12200  9147  5480  2.69  6.04 
(ODBSbraced frame) 
0.0125  0.1101  0.0082  0.0781  26177  7800  5032  3012  9.58  23.20 
((a), (b), (c)) Pushover diagrams in various types of (a) only RC flexural frame and (b) X Steel braced RC flexural and (c) ODBS steel braced RC flexural frame (plus results of simulated models in ANSYS).
Forcedisplacement curve of flexural frame and deformed shape and sum of elastic and plastic strain contour
Forcedisplacement curve of Xbraced frame and deformed shape and sum of elastic and plastic strain contour
Forcedisplacement curve of ODBS steel braced frame and deformed shape and sum of elastic and plastic strain contour
Response modification factor evaluation along pushover curve and its equivalent bilinear EPP curve.
Concrete and steel are the two constituents of RC braced frame. Among them, concrete is much stronger in compression than in tension (tensile strength is of the order of onetenth of compressive strength). While its tensile stressstrain relationship is almost linear, the stressstrain relationship in compression is nonlinear from the beginning. But for specification of nonlinear geometry of ODBS, concrete nonlinearity is added to material nonlinearity in this paper. Only steel nonlinearity for third member of ODBS is considered in this paper’s analysis. Steel, on the other hand, is linearly elastic up to a certain stress (called the proportional limit) after which it reaches yield point (
In this research the WillamWarnke, the yield and failure criteria, is considered for concrete model behavior. Also, since the SAP2000 assumption applies the DruckerPrager criteria for concrete material modeling and its behavior, both of mentioned criteria’s are considered in analysis of models. By this method, the analytical comparison of applied criteria’s is done.
In steel material modeling, the bilinear curve of behavior is used. This model is included in two parts, linear and elastoplastic behavior. The elasticity modulus is
Definition for materials behavior (concrete in left and steel in right) and nonlinearity for numerical analysis assignments in form of forcedisplacement curve.
((a), (b)) ODBS and Xbraced deformed RC frames modeling in ANSYS (the model is under lateral incremental and gravitational loads for pushover analysis).
ODBS frame (deformed shape)
Xbraced frame (deformed shape)
Nonlinear static procedures use equivalent SDOF structural models and represent seismic ground motion with response spectra. Story drifts and component actions are related subsequently to the global demand parameter by the pushover or capacity curves that are the basis of the nonlinear static procedures. Nonlinear dynamic analysis utilizes the combination of ground motion records with a detailed structural model and therefore is capable of producing results with relatively low uncertainty. In nonlinear dynamic analyses, the detailed structural model subjected to a groundmotion record produces estimates of component deformations for each degree of freedom in the model and the modal responses are combined using schemes such as the sum of squares square root.
In nonlinear dynamic analysis, the nonlinear properties of the structure are considered part of a time domain analysis. This approach is the most rigorous and is required by some building codes for buildings of unusual configuration or of special importance. However, the calculated response can be very sensitive to the characteristics of the individual ground motion used as seismic input; therefore, several analyses are required using different ground motion records to achieve a reliable estimation of the probabilistic distribution of structural response.
Since the properties of the seismic response depend on the intensity, or severity, of the seismic shaking, a comprehensive assessment calls for numerous nonlinear dynamic analyses at various levels of intensity to represent different possible earthquake scenarios. This has led to the emergence of methods like the incremental dynamic analysis [
Complete comparisons of the studied Retrofitted Frames in ANSYS (version10) software with the micromodeling structural element indicate that ODBS steel bracing RC frame has two yielding points that were related to main RC flexural frame and third steel member of ODBS. It is so useful for structures that are under impact loads and loads by high velocity specifically according to Figure
The main flexural RC frame is calibrated by results of experimental modeling of the same flexural frame and Xbraced frame that were constructed in laboratory [
According to Figure
((a), (b)) Comparison of flexural and Xbraced deformed frames pushover curves for calibration models obtained from ANSYS software results.
Flexural frame calibration
Xbraced frame calibration
According to Figure
Figure
Comparison of flexural, Xbraced, and offdiagonal bracing deformed frames for structural behavior in terms of various analysis software (ANSYS in left and SAP2000 in right).
Comparison between shown results in Figure
Also to optimize eccentricity ratio according to Figure
The values of maximum response of structural frames along various eccentricities.
El Centro timehistory accel. loading  General characteristics  

Models and numbers  Max. ecc. 
Max. acc. 
Max. vel. 
Max. displ. 
Initial stiffness 
Period 

ODBS (p0)  0.00  0.342  46.08  3.93  491.78  0.47  2.83 
ODBS (p1)  0.1  0.261  40.14  4.67  315.59  0.59  2.49 
ODBS (p2)  0.2  0.175  37.72  5.10  158.51  0.83  2.31 
ODBS (p3)  0.3  0.073  33.30  6.06  77.49  1.19  2.1 
ODBS (p4)  0.4  0.034  34.71  6.81  37.77  1.71  1.7 
ODBS (p5)  0.5  0.028  36.95  6.22  17.36  2.52  1.6 
ODBS (p6)  0.6  0.023  38.71  6.16  6.50  4.12  1.3 
ODBS (p7)  0.7  0.018  40.08  6.00  1.23  9.48  1.1 


Xbracing  —  0.581  78.35  2.04  894.39  0.39  2.96 
Variation of stiffness by different eccentricity ratio in offdiagonal bracing system.
((a), (b)) Maximum acceleration versus eccentricity ratio under El Centro, Tabas, and Naghan Earthquakes (a) and ductility assessment of various eccentricities in form of pushover curves (b).
Maximum Acceleration
Ductility Assessment
After performing pushover analysis and results of deformations along shear force, many parameters have been recorded. Ductility and factor of behavior (response modification factor (
Effect of lateral force will decrease when the factor of behavior is increased in a structure. Also frame resistance was optimized in offdiagonal bracing system related to flexural frame.
The dynamic behavior of the mentioned frames under three records (the earthquake records considered in this research are Tabas, Naghan, and El Centro whose peak ground accelerations are 0.93 g, 0.72 g, and 0.35 g, resp.) of Tabas, Naghan, and El Centro has been studied. Each typical 4bay frames with different stories (2, 6, and 15) has been adopted accordingly. Structural response for each frame versus eccentricity ratio was determined and the optimum eccentricity value is obtained comparing each other. The effect of the parameters such as period time of vibration, initial stiffness, and displacement at first yield point compares various eccentricity ratios. Optimum eccentricity was around
Also the dynamic behavior of the 6story frames retrofitted by offdiagonal bracing system under three records of Tabas, Naghan, and El Centro has been compared for optimizing normalized eccentricity ratio. Overall result related to several eccentricities has been shown in Figure
In next step, the dynamic time history analysis was applied on single offdiagonal braced frame. Acceleration excitation was exerted on joint1 at the base level of ODBS retrofitted frame and then joint2 response at floor level of frame was monitored (Figure
Excitation and response ODBS frame accelerations of El Centro time history analysis.
Another investigation of ODBS is about its dynamic behavior under various earthquakes. Many difference ratios in 15story drift are shown in Figure
Difference ratio of (a) flexural frame and (b) Xbraced and (c) ODBS braced frame stories drift (cm) under various earthquakes.
Flexural frame
Xbraced frame
ODBS braced frame
Performing dynamic analyses on various models, hysteresis behavior curves were obtained for the studied models. Results showed that as the structure period increases the energy absorption capacity also rises [
Application of ODBS to tall buildings weakens ground floor columns; that is, in the case of using ODBS which offers no resistance to column’s stretch and pressure forces on foundation, all the above forces are transmitted through columns. Thus, to achieve a suitable performance of ODBS in tall buildings, the ground floor columns should be strengthened through special design of the columns and beams with specific flexural connections. Modification of ground floor columns and creation of special flexural frame with special flexural connections prevent the formation of soft story on ground floor of tall buildings. The above studies on fifteenstory building, which was designed based on linear static analysis, were carried out based on Naghan and El Centro earthquakes which caused greater destruction in ground floor columns.
In addition, plastic hinges did not form in most of the beams, columns, and Xbraces of upper floors and before the ODBS system could show its efficiency in making tall buildings ductile, ground floor columns transformed to mechanism and reduced the efficiency of entire system energy absorption. By neglecting PΔ effects and MP interactions, the model will continue its efficiency at various performance levels. As a general result, the different stiffness of floors is proportional to each floor’s shear absorption level. Considering the drift and energy absorption potentials of various floors, the stiffness of each floor should be controlled.
Eventually, nonlinear dynamic analyses of flexural frame, Xbracing system frame, and steel ODBS frame revealed a greater ductility for the frame strengthened by ODBS system. The effect of ODBS system on concrete buildings up to tenstory is desirable but not considerable for taller structures. The height of a building will be acceptable only when the structure’s basic oscillation on first mode can cause basic shear and the amount of this shear is at least 40 percent of the final shear of the structure. If the number of floors is greater, ODBS system will not be suitable for reinforced concrete frame and may result in undesirable consequences. Structure underwent three accelerations which were different in intensity, period, and oscillation range and their responses to each case were investigated. The findings demonstrate that application of ODBS is suitable for the structures which undergo lowoscillationperiod earthquakes. ODBS itself does not possess a considerable lateral strength but when combining with concrete flexural frame system, the strength of entire system rises by 10 to 45 percent. This effect is because of the behavioral nature of ODBS system so that when composed to stretching, its components start to form an internal force that helps the system to tolerate the stretch. As a result, an extra strength of about 10 to 45 percent is earned when concrete frame is strengthened by steel ODBS system.
The author declares that there is no conflict of interests regarding the publication of this paper.
The author would like to express his deep gratitude to Professor Mahmoud Reza Maheri, Professor Abdolrasoul Ranjbaran, and Professor Seyed Ahmad Anvar, for their patient guidance, enthusiastic encouragement, and useful critiques of this research work in Shiraz University. The author would also like to thank Dr. Hamid Seyedian, for his advice and assistance in keeping his progress on schedule. He would also like to extend his thanks to the technicians of the laboratory of the structural department of Aisan Disman Consulting Engineers for their help in offering him the resources in running the program. Finally, he wishes to thank Roza for her support and encouragement throughout his study.