American Journal of Scientific Research ISSN 1450-223X Issue 53 (2012), pp. 24-34 © EuroJournals Publishing, Inc. 2012 http://www.eurojournals.com/ajsr.htm

Study the Effect of using Different Kind of Bracing

System in Tall Steel Structures

Behruz Bagheri Azar Department of Civil Engineering, Shomal, Branch

Shomal University, Iran E-mail: B.bagheriazar@yahoo.com

Tel: +989144065831

Mohammad Reza Bagerzadeh Karimi Department of Civil Engineering, Maraghe, Branch

Islamic Azad University, Iran, Member of the Tabriz Elite House E-mail: MRBKarimi@gmail.com

Tel: +989141060397; Fax: +984115570509

Abstract

Tall building structures should be able to tolerate different types of forces such as lateral forces like wind or earthquakes so bracing methods are normally used for steel structures. In this study, steel structures with 20, 30 and 40 floors using cross bracing method with different length and configurations were studied by ABAQUS software in order to find the best suited configuration of bracing. For this purpose various forms of bracing system with equal amount of steel consumption were studied under earthquake loads both in static and dynamic analysis and best array and also type in mega bracing of such structures are then reviewed and selected. Keywords: Mega-brace, tall steel structures, shear-lag, ABAQUS

1. Introduction With increasing of experiences from the events of the last earthquakes and reviewing the behavior of the structures, more and more innovative topics in new buildings has been considered. This paper investigates the application of seismic systems using braces as one of the most effective methods in steel structures. The most important issues in the study of this kind of systems are to determine the appropriate arrangement of bracing. In this study, also the concept of mega bracing and their properties as a new approach of bracing method is investigated. Lateral resistance in braced frames is provided by diagonal members which forms the vertical truss structure together with the main beams. Columns in this structure are basic members. Since the shear forces are supported by horizontal components of tensile or compressive axial forces, bracing systems are very efficient. The desired behavior of bracing system in generation of lateral stiffness with minimum amount of materials, reveal it as an economic solution for a variety of buildings with arbitrary height. Another advantage of diagonal bracings is that the main beams have minimum participation in resisting of lateral loads and therefore of deck systems in different stories can be designed in a repetitive manner that is more desirable in economical point of

Study the Effect of using Different Kind of Bracing System in Tall Steel Structures 25

view. The essential issue of these systems in non-uniform distribution of forces and decreasing total resistant moment of structure lead to reduced economic efficiency.

The major weakness of this phenomenon is called shear lag that causes perpendicular axial load distribution to the columns which is different from the ideal uniform distribution for lateral forces. The main origin of this phenomenon is in the behavior of shear deformations in peripheral beams of the structure and also doesn’t remain plane after bending in this system which increase tension in the corner columns and decrease in tension in the middle columns [1].

Recently, new type of bracing systems called mega bracings has been introduced as shown in figure 1. According to the geometrical shape of these bracings, it is expected that they present different seismic behavior in stiffness, efficiency and ductility compared to current bracing systems. Therefore, detailed study of seismic behavior in these structures is quite considerable.

Adding these bracings to the structural system is associated with increasing lateral stiffness and decreasing shear lag. Bracings in these structures cover several stories and spans as a single bracing. Hence, several structural arrangements of a dedicated bracing type are possible for any structure. Therefore, several structural arrangements for the braces a particular category (such as X) is probable [2]. Therefore, we will investigate the behavior of these types of structures versus alternate with current type of bracings, in medium and high height and the results will be presented.

Figure 1: John Hancock tower

First, the effects of adding mega bracing systems on the structures are carried out by considering three structures with 20, 30 and 40 stories that have 30X30 plan and height of 60, 90 and 120m, respectively. Main parameters of interests in the study of bracings effects are storey drift and capacity diagram of structure. Each of the above mentioned parameters for braced structures is calculated by different types of bracings, and will be refereed later in the parts. 2. Modeling Assumptions All of studied samples are residential with each storey of up to3m height. The plan of structure in two directions consists of six spans with equal length of 5m in both sides. The mentioned plan and different types of bracings are shown in figure 3. It should be noted that limiting the number of bracings arrays, is due to restrictions in fabrication and erection of the bracings members and also their connection so that can support columns in the successive floors.

26 Behruz Bagheri Azar and Mohammad Reza Bagerzadeh Karimi

Figure 2: Structural plan

Figure 3: Different kind of bracing system

Case (4) Case (1) Case (2) Case (3)

Structure is located in an area with high risk of earthquake. The type of local soil is II and

structure importance factor is 1. Since the height of all structures over 50m, nonlinear dynamic analysis is used for analyzing the structures [3]. Deck system is joist block and has sufficient rigidity for distributing lateral forces between vertical elements. The beams types are I and both of bracings and columns are box sections. The steel yield and ultimate stresses are Fy=2400 kg/cm², Fu=3600 kg/cm², respectively and also the compressive strength of concrete is fc=240 kg/cm². 3. Numerical Modeling Computer modeling is performed using ABAQUS version 6.9.3.which is a collection of effective engineering simulation programs that is based on a finite element method. It can solve a widespread range of problems from simple linear to complicated nonlinear analysis. On nonlinear analysis ABAQUS software automatically selects the appropriate force-displacement graphs and set these parameters continuously during the analysis in order to obtain the results accuracy [4]. 3.1. Materials Properties

Due to the plastic and elastic of materials, it is essential to consider plastic and elastic behavior of them. Therefore, the stress-strain relationship of material derived from direct tensile test will be defined. The diagram of stress-strain is shown (fig. 4):

Study the Effect of using Different Kind of Bracing System in Tall Steel Structures 27

Figure 4: Stress-Strain diagram

3.2. Features of Elements Modeled in ABAQUS

Wire elements are used to model the frames and bracings. Beams and columns are modeled by beam elements using B31 that is two nodal element and also bracings modeled by truss elements using T2D2. Connections of the beams to columns are completely clamped and bracings connection to frame is completely pinned. Columns bases connected to the foundation by clamped form. 3.3. Nonlinear Dynamical Analysis

The response of structure in the nonlinear dynamic analysis is calculated by considering the nonlinear behavior of materials and geometric nonlinearity. In this method, stiffness matrix and damping can be updated from one step to another one. However, they are constant during each step and numerical methods are used to calculate the response of structure under earthquake excitation for each step [5]. 4. Comparison on Various Arrays of Bracing In this part, the effects of adding different kinds of bracings are investigated on lateral drift of components. As already mentioned, differences between mega and current bracings in distribution of axial forces was turned mega bracings to an ideal choice. Hence, the displacement of each structure in four various arrays of bracings are shown in the subsequent figures.

As shown in figure 4, results show that using of mega bracings reduce significantly displacements and the reduction depends on selected bracing model. Because of their stiffness, third and forth kinds of bracings are caused a maximum reduction in lateral displacement. Clearly, it is seen that the drift of 23cm on the 30th storey in the first array reduced to 14cm in the third. The results of displacements in various arrays for 30 storey structure are given in table1. The Most Important Reasons for using Mega Bracings are

• The maximum efficiency in structural systems is achieved in the bending mode and it can be provided by mega systems.

• Bracing members are caused more balanced distribution of columns load under gravity and lateral loads.

• Due to shear lag reduction in mega systems, columns distances can be increased.

28 Behruz Bagheri Azar and Mohammad Reza Bagerzadeh Karimi

Figure 5: Displacements

20 floors 30 floors 40 floors Table 1: Displacements for 30-floor building

Floors Case 1 Case 2 Case 3 Case 4 30 22.91786 16.25286 13.5781 12.0878 29 22.00318 15.66318 12.9687 11.5622 28 21.073 15.02178 12.5834 10.9372 27 20.12618 14.3766 12.2734 10.5797 26 19.1645 13.70946 11.8391 10.1837 25 18.18903 13.03386 11.1247 9.872 24 17.20191 12.34026 10.3846 9.5608 23 16.20606 11.6397 9.8978 9.2187 22 15.20563 10.93098 9.5 8.7437 21 14.21805 10.24548 9.0551 8.1383 20 13.24071 9.54582 8.3474 7.3955 19 12.30736 8.9193 7.6524 6.6834 18 11.3788 8.2647 7.1855 6.0037 17 10.45684 7.6137 6.8041 5.5463 16 9.546576 6.97296 6.3427 5.1591 15 8.663408 6.3498 5.7018 4.8507 14 7.799116 5.74314 5.0414 4.5598 13 6.957236 5.14554 4.6097 4.2493 12 6.142344 4.56948 4.2657 3.8823 11 5.358496 4.00764 3.8646 3.3968 10 4.611984 3.46824 3.308 2.8463 9 3.924544 2.98458 2.7777 2.282 8 3.272776 2.51784 2.4144 1.7813 7 2.660528 2.07312 2.1251 1.4417 6 2.093676 1.66092 1.8082 1.179 5 1.57768 1.27644 1.4078 0.9464 4 1.118416 0.93192 0.987 0.7266 3 0.722072 0.6216 0.6776 0.5121 2 0.395772 0.35568 0.422 0.3024 1 0.145704 0.12252 0.1732 0.1051

Study the Effect of using Different Kind of Bracing System in Tall Steel Structures 29

5. The Effect of Different Cases of Braces on Shear-Lag Regards to the differences between the structures with and without braces, axial force distribution in the central columns is different. The difference in the distribution of forces due to the flexibility of the circumferential beams and all the columns do not corporate in absorbing the energy. Because of the importance of shear deformation, it will not remain plane after bending. Distribution of forces perfectly matches the ideal distribution will not be based on common strength materials Formulas (fig 6).

One way to reduce the effects is decreasing the distance between the columns and increasing the stiffness of surrounding beams in the structures without bracing system which limit the dimension of windows in buildings. The most effective method to solve the problem is just to add bracing system to the structures.

In this paper, shear-lag on the flange of the columns which is perpendicular to the lateral forces was studied. To calculate the shear-lag effects in the structure, the proportion of the highest to the lowest of axial forces which was approached by analyzing the structures under lateral forces was studied (Fig 7).

Figure 6: Axial stress distribution in the columns of frames under lateral load

Figure 7: Diagrams of shear-lag

20 floors 30 floors 40 floors

30 Behruz Bagheri Azar and Mohammad Reza Bagerzadeh Karimi

As it is shown in figure 7 in all the structures studied, case 2 and 3 have the most effective on decreasing the shear-lag at the lowest floors. As it is clear by diagram, case 4 shows good behavior at the lowest floors but this trend did not continue to decrease the shear lag at the upper floors and also greatly weakened. In case 1, it shows that this trend continue to decrease the shear-lag. Regards to the Behavior mode of frames and braces, absorbing the forces in mega braces is larger than the common braces at the lowest floors of the building but it’s vice versa at the upper floors. So the braces systems which have the most stiffness absorb maximum forces compare to the other cases of bracing system, and the more reduction of the force in the frame cause to more reduces the amount of shear-lag but also it is vice versa at the upper floors.

It is necessary to note that Interaction of frame and braces are not the only factor in increasing the shear-lag at the upper floors of the building but the effect of higher modes is also effective in the behavior of the structure. The results of shear-lag for different kind of cases for 30-floor building are illustrated in table 2. Table 2: Shear-Lag for 30-floor building

Case 4 Case 3 Case 2 Case 1 Floors 1.87 1.65 3.27 4.67 1 1.65 1.65 3.18 4.36 2 2.01 2.13 1.48 4.14 3 2.24 2.45 1.36 3.79 4 2.13 2.67 1.37 3.68 5 1.05 2.77 1.81 3.54 6 0.96 2.76 1.72 3.32 7 0.86 2.65 1.75 2.98 8 1.20 2.02 1.30 2.57 9 2.20 1.78 0.96 2.36 10 2.60 1.56 0.80 2.25 11 2.90 1.40 1.02 2.00 12 3.20 1.46 1.32 1.88 13 3.50 1.75 1.22 1.75 14 3.70 1.67 1.42 1.70 15 3.80 1.77 1.56 1.75 16 3.89 1.87 1.66 1.87 17 4.01 1.77 1.76 1.77 18 4.10 1.67 1.87 1.63 19 4.20 1.65 1.96 1.56 20 4.32 1.76 2.12 1.55 21 4.20 1.88 2.20 1.81 22 4.00 1.99 2.30 1.93 23 3.90 2.12 2.50 1.99 24 3.70 2.20 2.70 2.03 25 3.60 2.00 3.00 2.14 26 3.50 1.97 2.90 2.18 27 3.40 1.90 2.80 2.45 28 3.50 2.00 2.60 2.55 29 4.00 2.20 2.70 2.87 30

6. Study Elastic Strain Energy Considering that much of the damage caused by earthquake especially under the large earthquake occurs in the reciprocating cycle of non-elastic. Parameters, the most associated with the cyclical behavior of structures and results earthquake damage, are structural energy. In other words, Energy absorption capacity of the structure should be more than the energy is required on structures during an earthquake event [6].

Study the Effect of using Different Kind of Bracing System in Tall Steel Structures 31

I E DE E E= + (1) In which:

IE : Energy applied

EE : Stored elastic energy

DE : Wasted energy The equation 1 can also be written as follows:

( ) ( )I k s f hE E E E E= + + + (2) Where:

kE : Kinetic energy of the structure

sE : Elastic strain energy

fE : Viscous damping energy

hE : Hysteresis energy (Residual energy)

IE and E DE E+ show the needs and Inventories, respectively. At the first step, effective choice of structure design and estimates of IE is for severe earthquakes. According to this, design should retain the behavior of the structure around the safety range. The ability of the structure in order to dissipate the energy under the elastic limit of earthquake through damping and elastic deformation and for the Earthquake near collapse through the damping and deformation of plasticity (plastic) should be investigated. The most important part is how to distribute dissipation energy in the entire structural system. In recent years, increasing the amount of DE with active and inactive damping system has been significantly possible. Although technical and economical satisfy the equation of inventories with increased inventories by increasing EE is considered [7]. In this study, to better understand the different cases of bracing system in terms of strain energy, the total amount of energy analyzed for the entire of the structure and bracing system, the results are illustrated in figure (8) to (10). Also the results of different cases of bracing are shown in table 3. Table 3: Maximum energy absorbed by the entire structural system and bracing systems

Floors Entire structural system Bracing system

Case 1 20 2.14E+06 3.44E+05 30 5.37E+06 5.80E+05 40 1.03E+07 7.47E+05

Case 2 20 1.39E+06 3.86E+05 30 3.31E+06 7.18E+05 40 6.25E+06 9.72E+05

Case 3 20 7.21E+05 4.87E+05 30 1.59E+06 9.81E+05 40 2.79E+06 1.44E+06

Case 4 20 6.08E+05 4.02E+05 30 1.37E+06 8.19E+05 40 2.47E+06 1.16E+06

32 Behruz Bagheri Azar and Mohammad Reza Bagerzadeh Karimi

Figure 8: Energy absorbed by the entire structural system and bracing system in 20-floor buildings

Figure 9: Energy absorbed by the entire structural system and bracing system in 30-floor buildings

Study the Effect of using Different Kind of Bracing System in Tall Steel Structures 33

Figure 10: Energy absorbed by the entire structural system and bracing system in 40-floor buildings

Regards to the illustrations, the rate of Participation of bracing system for energy absorption in the entire structural system, cases 3 and 4 compare to cases 1 and 2 were significantly increased. The difference in energy absorption is due to the specific form of mega bracing system which all columns are in contact unlike common bracing system which is continually in contact with several columns. Table 4: Percentage of energy absorbed by bracing system

Floors Case 1 Case 2 Case 3 Case 4 20 16% 28% 67% 66% 30 11% 22% 62% 60% 40 7.30% 16% 52% 50%

With increasing height of the building percent of participation in the energy absorption of the

bracing system reduces. Case (3 and 4) in terms of energy absorption, have close behavior and also by increasing the height of the building differences are not significant. 7. Conclusions

1. Using mega braces instead of common braces cause to decrease lateral displacement and shear lag which improve structural behavior and increase efficiency of the buildings.

2. If purpose of using braces in order to decrease displacement and shear lag, using the cases 2 and 3 will be the most effective in reducing these parameters.

3. Regards to the mega braces system which are also form as an architectural, so the arrangement of bracing system in the buildings is not only based on structural criteria.

4. With the results of cases 2, 3 and 4 can be seen that the results are very close. To better understand the differences in their functional cases should consider the higher elevations.

34 Behruz Bagheri Azar and Mohammad Reza Bagerzadeh Karimi

5. At all using mega bracing system due to decrease the cross section and the length of braces and also reduce the number of connection plates (between brace and column) And the increased energy absorption compared to other cases of bracing system, The structure is more economically justifiable.

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