The Structural Design Of Tall And Special Buildings (wiley) s1x4j

THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS Struct. Design Tall Spec. Build. (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/tal.751

Comparison of nonlinear behavior of steel moment frames accompanied with RC shear walls or steel bracings Hamed Esmaeili1*,†, Ali Kheyroddin1, Mohammad Ali Kafi1 and Hamed Nikbakht2 1 Faculty of Civil Engineering, Semnan University, Semnan, Iran Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

2

SUMMARY In this paper, the seismic behavior of dual structural systems in forms of steel moment-resisting frames accompanied with reinforced concrete shear walls and steel moment-resisting frames accompanied with concentrically braced frames, have been studied. The nonlinear behavior of the mentioned structural systems has been evaluated as, in earthquakes, structures usually enter into an inelastic behavior stage and, hence, the applied energy to the structures will be dissipated. As a result, some parameters such as ductility factor of structure (m), over-strength factor (Rs) and response modification factor (R) for the mentioned structures have been under assessment. To achieve these objectives, 30-story buildings containing such structural systems were used to perform the pushover analyses having different load patterns. Analytical results show that the steel moment-resisting frames accompanied with reinforced concrete shear walls system has higher ductility and response modification factor than the other one, and so, it is observed to achieve suitable seismic performance; using the first system can have more advantages than the second one. Copyright © 2011 John Wiley & Sons, Ltd. Received 2 August 2011; Accepted 3 November 2011 KEYWORDS:

dual system; steel moment-resisting frame; shear wall; steel bracing; reinforced concrete; seismic behavior

1. INTRODUCTION As extensive areas in Iran, especially the populated cities, are located on the critical seismic zones and they have high vulnerability to destruction, the study of seismic behavior of structural systems is of great importance. Today, reinforced concrete (RC) shear walls or steel bracings are used widespread as a main load-carrying system in tall buildings, for different reasons such as increase of energy dissipation and its ability to resist lateral displacements of tall buildings that have moment-resisting frames. Therefore, the recognition of the seismic behavior of the dual structural systems and figuring out their advantages can be helpful to structural engineers in selecting a proper system for structures that are being designed. Studying the behavior of building structures as subjected to severe earthquake ground motions reveals that this type of structures can exhibit enough strength, due to the nonlinear behavior of materials and possibility of sufficient deformations of the structures. These structures absorb the applied energy and will dissipate it via tolerating great displacements in nonlinear seismic behavior. Nonlinear time history analysis of a detailed analytical model is perhaps the best option for the estimation of deformation demands. However, because of many uncertainties associated with the site-specific excitation as well as uncertainties in the parameters of analytical models, in many cases, the effort associated with detailed modeling and analysis may not be justified and feasible (Hajirasouliha and Doostan, 2010). In current years, nonlinear static analyses have earned a great deal of research attention within the earthquake engineering community. Their main purpose is to demonstrate the nonlinear capacity of a structure when subjected to horizontal loading with a reduced computational attempt with respect *Correspondence to: Hamed Esmaeili, Faculty of Civil Engineering, Semnan University, Semnan, Iran. † E-mail: [email protected] Copyright © 2011 John Wiley & Sons, Ltd.

H. ESMAEILI ET AL.

to nonlinear dynamic analyses. Pushover methods are particularly shown for assessing existing structures (frequently not originally designed with seismic criteria in mind), when the employment of linear elastic methods, typical in new design situations, tends to be unsuitable. For these goals, many codes and guidelines (e.g. Eurocode 8, 2005; ATC-40, 1996; FEMA-356, 2000) propose the use of nonlinear static methodologies to evaluate structural behavior under seismic movement (Ferracuti et al., 2009). To assess the seismic performance of the structures, three various nonlinear static analyses are used, each of which contains a constant load pattern. These approaches are pushover analyses with load patterns proportionate to uniform and reverse triangular displacements of structures, and modal pushover analysis (MPA).

2. REVIEW OF THE LATEST RESEARCHES In general, numerous studies in forms of analytical and experimental works have been implemented on the mentioned structural systems. Most important results of which are as follows: A series of experimental programs including two-story specimens was developed to recognize the cyclic behavior of the composite structural systems. This study shows that the lateral shear force tolerate via compressive strut of wall and shear studs (Tong, 2001). Tong et al. (2005) presented an experimental study on the cyclic behavior of a composite structural system consisting of partially restrained steel frames with RC infill walls. The one-bay, two-story test specimen was built at one-third scale. The study shows that this system has the potential to offer strength appropriate for resisting the forces from earthquakes and stiffness adequate for controlling drift for low-rise to moderate-rise buildings located in earthquake-prone regions. As a basis of many studies, structural frames with infill s are typically providing an efficient method for bracing buildings (Jung and Aref, 2005). The presence of infills can also have a significant effect on the energy dissipation capacity (Decanini et al., 2002). In common practice, steel bracing system is used to increase the lateral load resistance of steel structures. Steel moment-resisting frame structures possess high strength and significant ductility, thus are effective structural forms for earthquake-resistant designs. However, the load-carrying efficiency of such designs is limited when an earthquake induces large story drift because of the lower structural stiffness of the steel frames (Hsu et al., 2011). Over-strength, ductility and response modification factors of buckling-restrained braced frames were evaluated by Asgarian and Shokrgozar (2009). To do so, buildings with various stories and different bracing configurations including diagonal, split X and chevron (V and inverted V) bracings were considered. In this article, seismic response modification factor for each of bracing systems has been determined separately, and tentative values of 8.35 and 12 has been suggested for ultimate limit state and allowable stress design methods, respectively. The over-strength, ductility and response modification factors of special concentric braced frames and ordinary concentric braced frames were evaluated by performing pushover analysis of model structures with various stories and span lengths (Kim and Choi, 2005). The results were compared with those from nonlinear incremental dynamic analyses. The results of incremental dynamic analysis generally matched well with those obtained from pushover analysis. A significant aspect in the design of steel braced RC frames is the level of interaction between the strength capacities of the RC frame and the bracing system. Maheri and Ghaffarzadeh (2008) conducted an experimental and numerical investigation to evaluate the level of capacity interaction between the two systems. It was found that the capacity interaction is primarily due to the connections over-strength and also the number of braced bays and the number of frame stories recognized.

3. SEISMIC BEHAVIOR OF STRUCTURES 3.1. The ductility of structures As a general rule, it is possible to replace the ideal bilinear elasto-plastic diagrams with the base shear–displacement curves of structures (Figure 1). The ductility factor in single degree-of-freedom Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

COMPARISON OF NONLINEAR BEHAVIOR OF STEEL MOMENT FRAMES

(SDOF) systems is a proportion of maximum lateral displacement to the yielding lateral displacement of structures. Δ max m¼ (1) Δy In fact, the ductility factor explains to what extent the structure enters when in nonlinear state. There is no accurate definition for the ductility factor of multiple degrees-of-freedom structures. In some provisions, yielding is assumed to have been simultaneous, although not precise (Wakabayashi, 1986). Meanwhile, the relation between the base shear and displacement is not an elastic–perfectly plastic equation. With consideration to Figure 1, an idealization in definition of the ductility factor is accepted. 3.2. Response modification factor Seismic codes consider a reduction in design loads, taking advantage of the fact that the structures possess significant reserve strength (over-strength) and capacity to dissipate energy (ductility). The over-strength and the ductility are incorporated in structural design through a force reduction or a response modification factor. This factor represents ratio of maximum seismic force on a structure during specified ground motion if it was to remain elastic to the design seismic force. Thus, actual seismic forces are reduced by the factor ‘R’ to obtain design forces. The basic flaw in code procedures is that they use linear methods but rely on nonlinear behavior (Kim and Choi, 2005). As it is shown in Figure 1, usually, real nonlinear behavior is idealized by a bilinear elasto–perfectly plastic relation. The yield force of structure is shown by Vy and the yield displacement is Δy. In this figure Ve or Vmax correspond to the elastic response strength of the structure. The maximum base shear in an elasto perfectly behavior is Vy (Uang, 1991). The ratio of maximum base shear considering elastic behavior Ve to maximum base shear in elasto perfectly behavior Vy is called force reduction factor, Rm ¼

Ve Vy

(2)

The over-strength factor is defined as the ratio of maximum base shear in actual behavior Vy to the first significant yield strength in structure Vs, Vy RS ¼ (3) Vs To design for allowable stress method, the design codes decrease design loads from Vs to Vw. This decrease is done by allowable stress factor, which is defined as (Asgarian and Shokrgozar, 2009):

Figure 1. General structure response (Uang, 1991). Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

H. ESMAEILI ET AL.

Y¼

VS VW

(4)

The response modification factor, therefore, s for the ductility and over-strength of the structure and for the difference in the level of stresses considered in its design. It is generally expressed in the following form, taking into s the aforementioned conceptions (Asgarian and Shokrgozar, 2009), R¼

Ve Ve Vy VS ¼ ¼ Rm RS Y VW Vy VS VW

(5)

3.3. The relation between the force reduction factor, the ductility factor and the period of structure The force reduction factor (Rm) is related to many parameters of which many are correlated to characteristics of the structural system and some of them are independent from the structure and are related to the other parameters such as respected loading (the time history of earthquake). Rm will be correlated to a set of factors, especially the ductility factor of structure and its performance characteristics in the nonlinear state, if we consider a specific earthquake for a particular place. Therefore, the first step in determining force reduction factor is specifying the relation between it and the capacity of the ductility of structure. Multiple factors are known that affluence on the relation between Rm and m, such as materials, period of system, damping, P Δ effects, the load–deformation model in the hysteresis loops and type of the soil that exists in the site. If we consider this assumption that the ductility in the structures with short period is the same as those that have longer periods, then smaller Rm is obtained. Also, New Mark and Hall (1982) suggested the following equations for calculation of the force reduction factor of structures:

Rm ¼ 1

Rm ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2m 1

Rm ¼ m

T < 0:125 s

0:125 s < T < 0:5 s

0:5 s < T

(6)

(7)

(8)

3.4. The conversion coefficient of linear to nonlinear displacement (Cd) It’s clear that the structural damages are normally originated from excessive deformations of the structure. Therefore, with regard to the effective parameters on seismic design of a structure, the discussion about assessment and accurate prediction of displacement and monitoring of them are the most important aims in seismic design of a structure. The Cd coefficient can be calculated as follows: Cd ¼

Δmax Δmax Δy ¼ ¼ m Rs ΔS Δy Δs

(9)

4. DESIGN OF THE STRUCTURAL MODELS IN THIS STUDY In this study, two structural models are used for specifying the trend of this research, defines as follows: Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

COMPARISON OF NONLINEAR BEHAVIOR OF STEEL MOMENT FRAMES

(1) Model A: A 30-story building in the form of special steel moment-resisting frame accompanied with special RC shear wall. (2) Model B: A 30-story building in the form of special steel moment-resisting frame accompanied with concentrically steel braced frames (X-braces). The height of the all stories is 3.5 m. Both of them have a residential application. Therefore, a floor dead load, an equivalent partition load and a live load for each story of values 200 kg/m2, 650 kg/m2 and 150 kg/m2 (1961 N/m2, 6374 N/m2 and 1471 N/m2), respectively, are applied. Also, the structural system of the floor is composite of RC slabs and steel secondary beams. The steel material used in the sections of the structural is of ST37 type with yielding strength of 2400 kg/cm2 (235 359 600 N/m2) and ultimate strength of 3700 kg/cm2 (362 846 050 N/m2). The compressive strength of concrete material, f ′ c , used in the shear walls is 300 kg/cm2 (29 419 950 N/m2). American Institute of Steel Construction Specification (AISC, 2005) and American Concrete Institute Requirements (ACI Committee 318, 2008) were used to design steel and shear wall, respectively. Also, in order to calculate earthquake load, the spectrum dynamic method was used. The equation suggested by Kheyroddin (2006) was used to determine the thickness and the number of required shear walls. 2 r min ¼

hw lw

835 þ 205 hlww

(10)

In which, rmin is the minimum wall-area-to-story-area ratio, hW is the total wall height and lW is the wall length (average shear wall lengths present in building plan). The plans of the structures, the direction of the girders and secondary beams, and the location of shear walls and bracings are shown in Figures 2 and 3. In the design process of these structures, it has been tried that moment frame tolerate 25% of earthquake forces in addition to bearing gravity load. The thicknesses of the shear walls for each story are shown in Table 1, and the sizes of the steel braces for each story are shown in Table 2. With regard to the design of the structures, box-shaped and I-shaped sections are obtained for section area of columns and beams, respectively.

5. NONLINEAR ANALYSIS 5.1. Existing pushover analysis methods During a pushover analysis, a frame structure is subjected to gravitational loads and horizontal loads applied at each story, with the latter being incremented up to failure. Ideally, the distribution of horizontal loads should approximate the inertia forces that are generated in the structure during an earthquake. Conventional pushover procedures adopt an invariant load pattern during the analysis, and according to a number of codes and guidelines, at least two different force distributions must be considered, uniform and proportional to the first modal shape. The invariant load pattern is one of the most significant limitations of traditional methods because the actual inertia force distribution changes continuously during seismic events as a result of higher mode contribution and structural degradation, which modifies the stiffness of individual structural elements and, consequently, of the structure as a whole. A procedure that proposed by Chopra and Goel (2003) is MPA, whereby a series of independent pushover analyses are carried out, considering different horizontal load patterns for each modal shape. According to the authors, it is sufficient to consider the first two or three modal shapes. Results in of capacity curves for various modal shapes are transformed in capacity curves for equivalent SDOFs, one for each mode. Seismic demands are separately evaluated for each SDOF and finally combined by the square-root-of-the-sum-of-the-squares method. A common drawback of this method is the mode superposition of results obtained from nonlinear pushover analyses carried out separately, for various modes. The method neglects the interaction amongst the modes, with modal superposition being performed just as in elastic modal analysis. Accordingly, capacity curves typically overestimate base shear values (Hernandez-Montes et al., 2004). On the basis of an analytical work that is conducted by Mortezaei et al. (2009), it is shown that nonlinear static procedures based on invariant load vectors using elastic modal properties cannot capture Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

H. ESMAEILI ET AL.

Figure 2. The structural plan of the model A.

Figure 3. The structural plan of the model B. Table 1. The thickness of the shear walls in the Model A. Story

1–2

3–6

7–9

10–12

13–15

16–18

19–21

22–24

25–27

28–30

Thickness (mm)

650

600

500

500

450

400

350

300

250

200

25–27

28–30

Table 2. The sizes of the steel braces in the Model B. Story

1–2

3–6

7–9

10–12

13–15

16–21

22–24

Sizes of braces 2UNP300 2UNP280 2UNP260 2UNP240 2UNP220 2UNP200 2UNP180 2UNP160 2UNP140 Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

COMPARISON OF NONLINEAR BEHAVIOR OF STEEL MOMENT FRAMES

the changes to the dynamic modes resulting from inelastic action. The variation of inertial forces must be considered in static procedures that attempt to reproduce inelastic dynamic response. 5.2. Nonlinear modeling of the structures In order to assess the seismic behavior of selected buildings, we have conducted a series of nonlinear static analysis. The designed structures have been used by importing into PERFORM-3D (Computers and Structures Inc., 2006a) software to create a nonlinear model. After a preliminary design of the structures, the nonlinear model of the following elements, force–deformation relationship and deformation capacities in PERFORM-3D has been developed. There are a number of different ways to model inelastic beams and columns in PERFORM. At one extreme are finite element models using fiber sections. At the other extreme are chord rotation models that consider the member as a whole and essentially requires one to specify only the relationship between end moment and end rotation. In between these extremes are a number of other models. In this study, the chord rotation model for beams and columns has been selected. The basic model is shown in Figure 4. This is a symmetrical beam with equal and opposite end moments and no loads along the beam length. To use this model, one has to specify the nonlinear relationship between the end moment and end rotation. An advantage of this model is that FEMA-356 gives specific properties, including end rotation capacities (Mohammadjafari and Jalali, 2009). Figure 5 shows a PERFORM frame compound component for the chord rotation model. The key parts of this model are the FEMA beam components. These are finite length components with nonlinear properties. The model has two of these components for cases where the strengths are different at the two ends of element. PERFORM allows to specify different strength for two components and also different lengths to consider cases where the inflection point is not at mid-span (Mohammadjafari and Jalali, 2009). For modeling the braces, the Simplr Bar element is used, and parameters in Tab. 5–6 of FEMA-356 are implemented to model this element in the software. An example of the F–D relationship of Simplr Bar element is shown in Figure 6. To make the RC shear wall sections, defining the linear and nonlinear characteristics of its materials (concrete and steel bar) are necessary. As it is shown in Figure 7, the stress–strain curve of concrete is selected in the form of trilinear with strain hardening; and its tension strength is ignored. The modulus of elasticity, EC is assumed to be

Figure 4. Chord rotation model.

Figure 5. Basic components for chord rotation. FEMA, Federal Emergency Management Agency.

Figure 6. Modeling of the behavior of bracing in Copyright © 2011 John Wiley & Sons, Ltd.

PERFORM.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

H. ESMAEILI ET AL.

Figure 7. Nonlinear properties of concrete. 261 540 kg/cm2 (2.56*1010 N/m2). The strain of ultimate strength of concrete, eL, is taken 0.003 (Kheyroddin, 2008), and the strain of crushing limit of concrete, eCU, is taken 0.005. As it is seen in Figure 7, the strain of yielding strength of concrete, eY, is taken 0.002; then, the ratio of initial modulus of elasticity to secondary modulus of elasticity is specified to 0.402. The stress–strain relationship of steel bar is supposed to be bilinear (elastic–perfectly plastic). The modulus of elasticity, ES, is taken 2 100 000 kg/cm2 (2.06*1011 N/m2), and the ultimate strain, eSU, is taken 0.05 (Kheyroddin, 2008). Also, its yielding strength, FY, is 4000 kg/cm2 (392 266 000 N/m2). 5.3. Nonlinear analysis of the models In this study, three nonlinear static analysis approaches are used for each model, which are described in the following. So, six pushover analyses have been performed. The center of mass at the roof level is selected as a control point of the displacement of structure in all analysis. Thus, the relative lateral displacement (drift) of the roof is used as a reference relative to lateral displacement, for plotting the capacity curves of the structures and for interpretation of the results obtained from these analyses. During application of these analyses, two approaches have been used to regulate the drift of structure. The first criterion is the limitation of reference drift and inter-story drift for the structure, which is 2% on the basis of Tab. C1-3 of FEMA-356 and Standard No.2800 (2007) (Table 3). Consequently, the analysis will be stopped when these drifts exceed from the mentioned limit. The second criterion for finishing the analysis is when the deformation capacity of each element is reached. 5.3.1. Uniform nonlinear static procedure To perform a static pushover analysis, you must specify the distribution of horizontal loads over the structure height. The current version of PERFORM-3D (Computers and Structures Inc., 2006b) allows fixed distributions only (i.e. you cannot consider ‘adaptive’ load distributions that depend on the deflected shape). As will be explained later, you can specify load distributions using nodal load patterns, or you can specify loads on the basis of the structure mass and a deflected shape. One of the most difficult issues for pushover analysis is choosing the pushover load distribution. During an actual earthquake, the effective loads on a structure change continuously in magnitude, distribution and direction. The distribution of story shears over the height of a building can thus change substantially with time, especially for taller buildings where higher modes of vibration can have significant effects. In a static pushover analysis, the distribution and direction of the loads are fixed, and only the magnitude varies. Hence, the distribution of story shears stays constant. To for Table 3. The structural properties of model A and model B in linear design stage. Type of model

T1 (s)

R

V (kN)

Δx (mm)

Δy (mm)

Max drift X

Max drift Y

Model A Model B

2.84 3.066

11 9

11 576 10 791

200 229.6

193.1 212.6

0.0027 0.003

0.0026 0.0028

T1 is the natural period of the structure. R is the response modification factor of the structure. V is the base shear of the structure. Δx and Δy are the displacements at roof level of the structure in the X and Y directions, respectively. Max drift X and max drift Y are the maximum drifts of the structure in the X and Y directions, respectively. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

COMPARISON OF NONLINEAR BEHAVIOR OF STEEL MOMENT FRAMES

different story shear distributions, to consider a number of different pushover load distributions is necessary. One option in FEMA-356 is to use uniform and triangular distributions over the building height. Note that a uniform distribution usually corresponds to a uniform acceleration over the building height so that the load at any floor level is proportional to the mass at the floor. In fact, to access this load pattern in the software, a procedure is performed for loading on the basis of uniform displacement pattern over the building height. Then, in loading step, the software calculates the necessary force proportioned to the created displacement. 5.3.2. Triangular nonlinear static procedure The difference between this procedure and the previous one is in their load pattern: in this procedure, the inverted triangular profile is used for displacement-based load pattern of story masses, based on FEMA-356. Therefore, the imposed displacement and, hence, the acceleration will not be uniform over the building height. 5.3.3. Modal pushover analysis Load distributions can be based on the structure mode shapes. For a low-rise structure that is dominated by its first mode response, a load distribution based on the first mode may be reasonable. Also, considering the higher modes is important for a structure with significant higher mode responses (medium-rise and high-rise buildings). In this study, the three first mode shapes in the X-direction of structural plan (see Figures 2 and 3) are selected to perform of modal pushover analyses. The capacity curves of models A and B, which are acquired from the aforementioned pushover procedures, are converted to the ideal bilinear diagrams, which are shown in Figures 8 and 9, respectively. Also, the values of VS, VY, VU, ΔY and ΔU, which are obtained from the analyses, and the value of VW,

Figure 8. The ideal bilinear diagrams of the pushover analyses for model A. UNSP, uniform nonlinear static procedure; TNSP, triangular nonlinear static procedure; MPA, modal pushover analysis.

Figure 9. The ideal bilinear diagrams of the pushover analyses for model B. UNSP, uniform nonlinear static procedure; TNSP, triangular nonlinear static procedure; MPA, modal pushover analysis. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

H. ESMAEILI ET AL.

which is specified in preliminary design stage, are represented in Table 4. Therefore, seismic parameters have been calculated by using the equations, which are defined in Section 3, as indicated in Table 5. Also, the averages of the aforementioned values are determined that are shown in following tables. At the end, the mean of capacity curves of models A and B are shown in Figure 10. As it observed from analytical results, the parameters obtained from MPA such as ductility factor (m), force reduction factor (Rm) and response modification factor (R) for the mentioned structures will be larger than the same parameters gained from other pushover approaches. This behavior can reveal the importance and, hence, the effect of higher mode shapes of the structure in tall buildings. Considering the capacity curves in Figure 10, it is clear that the energy dissipation of the structural system in model A is greater than that of model B. Also, the mean value of response modification factor (R) for model A is bigger than the same parameter of model B. Therefore, structures with shear walls have better seismic behavior rather than structures with steel X-bracings. To evaluate combined behavior and interaction of RC shear wall with steel moment-resisting frame and comparison of that with concentrically braced frame system, the percent of shear absorption of Table 4. The structural properties of models A and B in nonlinear analysis stage. Type of analysis

VW (kN)

VS (kN)

VY (kN)

VU (kN)

ΔY

ΔU

Model A

UNSP TNSP MPA Mean

11 576

27 125 18 080 30 784 25 329

44 047 31 294 49 737 41 692

47 628 35 551 52 660 45 283

0.00463 0.00468 0.00430 0.00454

0.01768 0.01678 0.01757 0.01734

Model B

UNSP TNSP MPA Mean

10 791

26 301 19 443 27 939 24 564

37 719 26 291 40 417 35 385

38 416 29 734 42 585 36 915

0.00486 0.00513 0.00426 0.00475

0.01759 0.01800 0.01540 0.01700

Type of model

UNSP, uniform nonlinear static procedure; TNSP, triangular nonlinear static procedure; MPA, modal pushover analysis.

Table 5. The seismic parameters of models A and B. Type of analysis

m, Rm

RS

Y

R

Cd

Model A

UNSP TNSP MPA Mean

3.82 3.58 4.08 3.82

1.62 1.73 1.62 1.65

2.34 1.56 2.66 2.19

14.53 9.68 17.58 13.78

6.20 6.20 6.60 6.29

Model B

UNSP TNSP MPA Mean

3.62 3.50 3.61 3.58

1.43 1.44 1.45 1.44

2.44 1.80 2.59 2.28

12.65 9.10 13.52 11.74

5.19 5.05 5.22 5.15

Type of model

UNSP, uniform nonlinear static procedure; TNSP, triangular nonlinear static procedure; MPA, modal pushover analysis.

Figure 10. The mean of capacity curves of the Model A and Model B. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

COMPARISON OF NONLINEAR BEHAVIOR OF STEEL MOMENT FRAMES

these models has been studied in this paper. The meaning of the percent of shear absorption is the ratio of shear quantity that is endured by the columns of frame or brace in each story to the total shear absorbed in that story. Figures 11 and 12 indicate the quantity of shear absorbed by moment-resisting frames and RC shear walls in model A and quantity of shear absorbed by moment-resisting frames with steel bracing in model B in of the average of various analytical methods applied in this study in levels of yield and ultimate strength of structure. As it is observed in these figures, in system with shear wall, major part of transferring lateral force in the middle and lower stories is tolerated by RC shear wall, and contribution of shear absorbed by

Figure 11. The interaction curves of the Model A and Model B for mean state of different analysis methods in level of yield strength of structure.

Figure 12. The interaction curves of the Model A and Model B for mean state of different analysis methods in level of ultimate strength of structure. Copyright © 2011 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

H. ESMAEILI ET AL.

moment-resisting frames gradually has increased in higher stories. In addition, in both levels of yield and ultimate strength, negative shear has been created in the last story, indicating that shear wall relies to the steel moment-resisting frame, but in braced systems, a main part of this process in lower stories is carried by steel bracings, and in the middle and higher stories, contribution of shear absorbed by moment-resisting frames has increased considerably as levels of yield and ultimate strength of the structure has generated negative shear in the top two and five stories. This issue has demonstrated high lateral stiffness for structures with shear wall system than that with braced system.

6. CONCLUSIONS Some of the key results obtained from the present analytical work are as follows: • In the studied structures, the capacity curves have larger values of lateral strength in the uniform nonlinear static procedure than that in the triangular nonlinear static procedure. However, the peak value is in the MPA. The difference can show the effect of load pattern and importance of considering the higher mode shapes in pushover analysis. • The mean value of m and Rm factors for special steel moment-resisting frame accompanied with special RC shear wall system (model A) is 3.82, whereas the value of mentioned factors is 3.58 for special steel moment-resisting frame accompanied with concentrically steel braced frames (X-braces) system (model B). • The mean value of the over-strength factor, RS, for model A and model B are 1.65 and 1.44, respectively. • The mean value of the response modification factor, R, for model A and model B in allowable stress design method are evaluated as 13.78 and 11.74, respectively. • The mean value of the increasing coefficient of linear to nonlinear displacement, Cd, for model A and model B are evaluated as 6.29 and 5.15, respectively. • The ductility and response modification factors are larger for model A than model B. Therefore, it seems that the use of special steel moment-resisting frame accompanied with special RC shear wall system is more effective than the use of special steel moment-resisting frame accompanied with concentrically steel braced frames (X-brace) system. • In regard to the results, it seems that the Cd factor for the mentioned structural systems is less than the values that are in Standard No. 2800 (2007). The Cd factor is suggested as 0.7 times of the response modification factor, R, in this code. REFERENCES ACI Committee 318. 2008. Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary. American Concrete Institute: Farmington Hills, Michigan. AISC. 2005. Specification for Structural Steel Buildings. American Institute of Steel Construction: Chicago. Applied Technology Council, (ATC-40). 1996. Seismic Evaluation and Retrofit of Concrete Buildings. ATC: Redwood City, USA. Asgarian B, Shokrgozar HR. 2009. BRBF response modification factor. Journal of Constructional Steel Research 65: 290–298. BHRC (Building and Housing Research Center). 2007. Iranian Code of Practice for Seismic Resistant Design of Buildings Standard No. 2800–07. BHRC: Tehran. Chopra AK, Goel RK. 2003. A modal pushover analysis procedure for estimating seismic demands for buildings. Earthquake Engineering and Structural Dynamics 31: 561–582. Comité Europeen de Normalization. 2005. Eurocode 8—Design of Structures for Earthquake Resistance, Part 3: Assessment and Retrofitting of Buildings, EN 1998-3. CEN: Brussels, Belgium. Computers and Structures Inc. 2006a. Perform Components and Elements for PERFORM-3D and PERFORM-COLLAPSE. CSI: Berkeley, CA. Computers and Structures Inc. 2006b. PERFORM-3D, nonlinear analysis and performance assessment for 3D structures, components and elements, version4. CSI: Berkeley, CA. Decanini LD, Liberatore L, Mollaioli F. 2002. Response of bare and infilled RC frames under the effect of horizontal and vertical seismic excitation. In 12th European Conference on Earthquake Engineering. Federal Emergency Management Agency (FEMA). 2000. Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Report No. FEMA 356, Washington, USA. Ferracuti B, Pinho R, Savoia M, Francia, R. 2009. Verification of displacement-based adaptive pushover through multi-ground motion incremental dynamic analyses. Engineering Structures 31: 1789–1799.

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Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal

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Struct. Design Tall Spec. Build. (2011) DOI: 10.1002/tal