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Comparative Study on Different Types of Bracing Systems in Steel Structures

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 World Academy of Science, Engineering and Technology 73 2011

Comparative Study on Different Types of

Bracing Systems in Steel Structures
Shahrzad Eghtesadi, Danesh Nourzadeh, Khosrow Bargi

 were located in an identical typical seismic zone and were

Abstract²Choosing an appropriate lateral force resisting system analyzed by static equivalent method. After all, they were
has a significant effect on performance of the structure in steel compared in different aspects and interesting conclusions
frames. So this paper is aimed at investigating and comparing various were obtained, that could be hints to the designers.
types of bracing systems. For this reason, four types of bracing
systems including X-bracing, Diagonal bracing, Inverted chevron
CBF and Inverted chevron EBF, in four different height levels, are II. MODELING BASICS
modeled and analyzed. These models are compared in different In this study, three types of steel concentric braced frames
aspects, such as economical viewpoint with evaluating the weight of and one eccentric braced frame (in which the geometric length
the structure, the maximum top story displacement under seismic of link beams, indicated by e, is assumed to be 1/8 L, L being
loading and the energy absorption. Results show that although
diagonal bracing systems increase the energy absorption capacity of
the length of the braced span), with height of 3, 6, 9 and 12
the structure, but because of its less rigidity it leads to increasing the stories, have been selected. All frames are four-bay wide with
buildings weight. So in order to optimize the amount of steel two end bays braced, as shown in Fig. 1. To avoid modeling
consumption and obtain the light weight structure, best solution is to of dual systems and the effect of moment frames, simple
apply the Inverted chevron CBF bracing systems in steel frames. connections have been considered between beams and
columns in all these models and the structures are assumed to
Keywords²Concentric brace frames, eccentric brace frames, be located in the seismic areas in which earthquakes of
seismic design, steel structures.
moderate intensity are expected, with a peak ground
acceleration of 0.25g. For linear static analysis with
I. INTRODUCTION
considering the P-Delta effect, computer code SAP 2000

S teel structures are obviously one of the most common

choices for residential building constructions in the world.
Among these buildings, different types of braced structures
version 11 was used to predict the frame responses .Frame
members are designed in accordance with AISC-ASD 89 code
[1], to account for the gravity loads and lateral forces of
are probably the most favorite types, due to less skill needed earthquake. During the design procedure, it was tried to
for welding and joints, and possibility to use common and optimize the required sections to their minimum possible
lighter section for beams and braces. Braced frames categorize sizes, along with checking the drift limitations to achieve the
into two different types, concentric and eccentric, which have desired strength and stiffness. For this purpose plate girder I-
specific characteristics and design requirements. shaped sections are assigned to beams and columns and
In this research, different types of bracings including X, double angel sections are used for bracing members.
inverted Chevron and diagonal concentric and eccentric two- All beam and column sections are checked and resized if
dimensional braced frames are analyzed using a commercial necessary to meet the requirements defined by AISC code [2]
software and the differences and the advantages of each type on plate girder design, with the following equations:
is tried to be evaluated. Although the method for this
investigation does not cover all the aspects of the models and bf k
d 795 C For: 0.35 d k c d 0.763 (1)
structures, this analysis still provides a good comparison 2t f Fy
between all the common bracing types.
The type of loadings are derived from Iranian seismic code, The limitation of width to thickness ratio of the flange in
moreover the sections are the common Euro sections, which plate girder sections, in order to prevent local flange buckling,
were checked and designed by American Institute of Steel is shown in (1)[3].
Construction (AISC) seismic provisions [1,2]. All the frames
h 985×103
d (2)
S. Eghtesadi is a structural engineer in SepahanAndazeh Co., Isfahan, Iran tw Fy (Fy +1160)
(email: sh.eghtesadi@gmail.com).
D. Nourzadeh is graduate student in School of Civil Engineering,
Equation (2) shows the limitation of height to thickness
University of Tehran, Tehran, Iran (+98 913 318 5587; email: ratio of the web in plate girder sections, in order to prevent
nourzadeh@ut.ac.ir). vertical web buckling, without using of stiffeners [4].
K. Bargi is Professor in School of Civil Engineering, University of Tehran,
Maximum amount of height to thickness ratio of web, in
Tehran, Iran (email: kbargi@ut.ac.ir).

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 World Academy of Science, Engineering and Technology 73 2011

order to prevent flexural web buckling, is given in (3). The design criteria for link beams in eccentric braced frame
h 6370 are as following:
d (3)
tw Fb The link beams should meet the requirements of the
where h, bf , tf , tw , kc , Fy and Fb are outside height of compact section with the width to thickness ratio of flange,
cross section of beams and columns, flange width, flange according to the (4):
thickness, web thickness, local buckling coefficient, yield bf 435
d (4)
stress and allowable bending stress respectively. These 2t f Fy
parameters are mentioned for different types of sections in Mp=Z Fy
table I and II. The type of steel used in this study, is assumed (5)
Vp=0.55 Fydtw
to be ST37 with yield stress Fy =240 MPa and maximum
allowable bending stress Fb =144 MPa. Where Z is the plastic modulus, d the depth of web, Vp the
plastic shear and Mp the plastic bending moment of links.
TABLE I
Mp
SPECIFICATIONS OF PLATE GIRDER SECTIONS For e d 1.6 Q=Vp (6)
Plate girder h (m) bf (m) tf (m) tw(m) Vp
type Mp Mp
B180 0.18 0.1 0.008 0.006 For e t 2.6 Q 2 (7)
Vp e
B200 0.2 0.1 0.01 0.006
In above equations, Q is the expected resistance of links.
B240 0.24 0.12 0.012 0.006
In the models used in this research, neither of the link
B300 0.30 0.15 0.015 0.006 beams appears to be of bending types, according to the
C14 0.14 0.14 0.01 0.008 dimensional considerations presented above.
C16 0.16 0.16 0.015 0.008
C20 0.2 0.2 0.015 0.01 III. LOADING
C22 0.22 0.22 0.015 0.008 In the braced frames under study, the story loads were
C24 0.24 0.24 0.02 0.01 determined by using a uniform distribution over the height in
C26 0.26 0.26 0.02 0.01 which the dead load and live load of stories are considered to
C28 0.28 0.28 0.02 0.012 be 6 kN and 2 kN , respectively. Since the loading span in
m2 m2
C30 0.3 0.3 0.02 0.01
the perpendicular direction is 4 meters, vertical dead and live
C32 0.32 0.32 0.02 0.012 loads per unit length of the beams are equal to:
C34 0.34 0.34 0.02 0.012 DL = 24 kN & LL= 8 kN .[5]
m m

Fig .1 Typical geometry of bracing systems in 6 story frame

TABLE II
SPECIFICATIONS OF DOUBLE ANGLE SECTIONS
Double angle type h tf tw
(based on Euro sections) (m) (m) (m) Shear force created in the base of the structures due to
L80 0.08 0.008 0.008
earthquake loads, named base shear, is obtained from (8), in
L100 0.1 0.01 0.01
L120 0.12 0.012 0.012
accordance with equivalent static analysis method [5,6].
L150 0.15 0.015 0.015
V=CW (8)

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 World Academy of Science, Engineering and Technology 73 2011

Where w is the weight of the system which consists of total TABLE VI

FI AND STORY SHEAR
dead load plus 20% of live load, and c is the seismic
coefficient. C factor is dependent on some parameters Model hi wi V Fi Story shear
including the number of story, the period of vibration, the no (m) (kN) (kN) (kN) (kN)
peak ground acceleration (PGA) and the behavior factor (R). 9 1426.8 160 80 80
R factor indicates the ductility capacity of the structure which 3 6 1426.8 160 53.3 133.3
depends on the type of bracing system. Seismic coefficients 3 1426.8 160 26.7 160
are calculated for different models, as shown in Table III.
The base shear v is distributed over the height of the frame TABLE VII
FI AND STORY SHEAR
linearly, with the maximum lateral load on the roof floor and
the minimum lateral load on the first floor, through the Model hi wi V Fi Story shear
formulation below. no (m) (kN) (kN) (kN) (kN)
Wi h i 9 1433 160 80 80
Fi = (V) (9)
¦
n 4 6 1433 160 53.3 133.3
j=1
Wj h j
3 1433 160 26.7 160
In (9) Fi , Wi , hi and n are the lateral force at floor level i ,
weight of floor level i , height of floor level i and number of IV. ANALYSIS AND RESULTS
stories, respectively. Tables IV to VII show the Seismic lateral
force distribution in height (Fi) and story shear, for different As it was mentioned before, dead and live gravitational loads
bracing systems in 3-story frames. are considered to be the same in all cases, therefore the most
important factor which affects the total weight of the
TABLE III structures, is the weight of the frame members which varies in
VALUES OF C FACTOR different types of bracing systems. So in order to investigate
Model Story the influence of the types of bracing systems on the weight of
Bracing system R C
number number the structure, the amount of steel consumption have been
1 3 x 6 0.115 evaluated for all models and results are given in table VIII.
2 3 Inv-chev EBF 7 0.098 Figs. 2 and 3 show the comparison between four different
3 3 Inv-chev CBF 6 0.115
bracing systems based on the weight of steel used per unit
4 3 Diagonal 6 0.115
5 6 x 6 0.115
area of the frame.
6 6 Inv-chev EBF 7 0.098
TABLE VIII
7 6 Inv-chev CBF 6 0.115
WEIGHT OF STEEL USED PER UNIT AREA OF FRAME
8 6 diagonal 6 0.115
steel weight Steel weight per unit area
9 9 x 6 0.115 Model number
(kN) (KN/m2)
10 9 Inv-chev EBF 7 0.098
11 9 Inv-chev CBF 6 0.115 1 49.1 0.30
12 9 diagonal 6 0.115 2 39.2 0.24
13 12 x 6 0.11
14 12 Inv-chev EBF 7 0.095 3 44.48 0.27
15 12 Inv-chev CBF 6 0.11 4 112.6 0.35
16 12 diagonal 6 0.11
5 104.28 0.32
TABLE IV 6 102.6 0.32
FI AND STORY SHEAR
7 204.1 0.42
Model hi wi V Fi Story shear
8 188.8 0.39
no (m) (kN) (kN) (kN) (kN)
1431.5 164.05 82.03 82.03 9 177.4 0.37
9
1 6 1431.5 164.05 54.68 136.71 10 321 0.50
3 1431.5 164.05 27.34 164.05
11 295.5 0.46

TABLE V 12 294 0.45

FI AND STORY SHEAR
13 50.6 0.31
Model hi wi V Fi Story shear
14 119.8 0.37
no (m) (kN) (kN) (kN) (kN)
15 219 0.45
9 1421.6 139.3 69.7 69.7
2 6 1421.6 139.3 46.4 116.1 16 329 0.51
3 1421.6 139.3 23.2 139.3

In the following figures, in order to prevent the complexity of

diagrams some abbreviations are used in the horizontal axis to
illustrate the types of bracing systems, which can be seen in
table IX.

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 World Academy of Science, Engineering and Technology 73 2011

TABLE IX of members, for different bracing systems are shown in Figs. 6

FIGURES¶ GUIDE
and 7. For each parameter, two types of comparison are done,
Bracing system Abbreviation one is based on the number of story and the other one is based
on the type of bracing system.
x-bracing X

Inverted chevron EBF E

Inverted chevron CBF C

Diagonal bracing D

Fig. 4 Maximum roof displacement versus the number of story

Fig. 2 Weight of steel versus the number of story

Fig. 5 Maximum roof displacement versus the type of bracing system

Fig. 3 Weight of steel versus the type of bracing system

In Fig.2 each curve indicates the weight of steel used per unit
area of frame in different stories, for each type of bracing
system. As it was expected, the weight of the structures
increase with the increasing in the height of the structure and Fig. 6 Energy absorption versus the number of story
it is noted that the rate of this increment is almost similar in all
types of bracing systems.
In Fig. 3, by keeping the number of stories constant in each
curve, the weight of steel used per unit area of frame, is
determined for different types of bracing systems.
Figs. 4 and 5 show the maximum roof displacement induced
by the lateral forces, in different bracing systems. The energy
absorption which is obtained from the internal efforts diagram

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 World Academy of Science, Engineering and Technology 73 2011

Fig. 7 Energy absorption versus the type of bracing system

V. CONCLUSION
As it is shown in the figures above, the maximum roof
displacement and consequently the maximum energy
absorption is happened in the diagonal bracing system,
because in this systems there is only one lateral force resisting
member in each span, so the total rigidity of these frames are
less than another systems, in order to compensate for the lack
of stiffness in bracing members, the stronger sections are
required for beams and columns in the braced spans that it
leads to creates a tremendous increment in the weight of the
structure. In contrast, while Inverted chevron CBF system has
the high energy absorption capacity, the amount of steel used
per unit area of the frame and the total weight of the structure
is less than other types of bracing systems. So from this article
it can be concluded that applying the inverted chevron
concentric bracing system may be proper and economical for
the steel braced frames.

REFERENCES

[1] AISC,Manual of Steel Construction,Allowable Stress Design,9th

Edition, American Institute of Steel Construction, Chicago, USA,
1989.
[2] AISC,Manual of Steel Construction,American Institute of Steel
Construction, Chicago, USA, 2005.
[3] E. H. Gaylord, C. N. Gaylord, and J. E. Stallmeyer, Design of Steel
Structures, 3rd ed. McGraw-Hill, New York, 1992.
[4] 67LPRVKHQNR³7KHRU\RI%HQGLQJ7RUVLRQDQG%XFNOLQJRI7KLQ-
Walled Members of Open Cross-Section¶¶ Journal of Franklin
Inst.,Vol.239, No. 3,4 and 5, 1945.
[5] ASCE 7-05, Minimum Design Loads for Buildings and Other
Structures, American Society of Civil Engineers, Virginia, USA,
2005.
[6] Building and Housing Research Center,Iranian Code of Practice for
Seismic Resistant Design of Buildings, 3rd Edition, Standard
No.2800-05

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