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Eccentric braced frames: A new approach in steel and concrete
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Eccentric braced frames: A new approach in steel and concrete

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Content Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ECCENTRIC BRACED FRAMES:
A NEW APPROACH IN STEEL AND CONCRETE
by
Bharath Gowda
A Thesis Presented to the
FACULTY OF THE SCHOOL OF ARCHITECTURE
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment o f the
Requirements for the Degree
MASTER OF BUILDING SCIENCE
May 1998
Copyright 1998 Bharath Gowda
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UMI N um ber: 1 3 9 1 0 8 6
UMI Microform 1391086
Copyright 1998, by UMI Company. A H rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
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UNIVERSITY OF SOUTHERN CALIFORNIA
SCHOOL OF ARCHITECTURE
UNIVERSITY PARK
LOS ANGELES, CA 90089-0291
This thesis, written G y
B H A R A T H AJ 6 0 \ aS P A ___________
under the direction o fh \ s Thesis Committee,
and approved G y ad its m em G ers, G a s Seen presented
to and accepted G y the (D ean o f The ScG o oC o f
Architecture in partiaCfuCfidment o f the requirements
fo r the degree o f
I
(Dean
(D ate l 3
THESIS COMMITTEE
Chair
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CONTENTS ii
Abstract iii
Acknowledgment iv
Introduction v
CHAPTER-1
EARTHQUAKES
1.1 INTRODUCTION 1
1.2 COMPARISON OF DESIGN CODES 3
1.3 SUMMARY OF RESULTS 8
CHAPTER-2
DAMAGE CONTROL DESIGN FOR SEISMIC LOADING
2.1 INTRODUCTION 11
2.2 ELASTIC AND PLASTIC RESPONSE OF STRUCTURES 12
2.3 STRENGTH VERSES STIFFNESS DESIGN OF STRUCTURES 14
2.4 DAMAGE CONTROL DESIGN PROCEDURE 17
2.4.1 STIFF STRUCTURE VERSUS FLEXIBLE STRUCTURE 19
2.4.2 APPLICATION TO STEEL BUILDINGS 20
2.4.3 APPLICATION TO CONCRETE BUILDINGS 21
CHAPTER-3
VARIABLE ECCENTRIC BRACED FRAME (V.E.B.F.)
3.1 CURRENT DESIGN PRACTICE 23
3.2 INTODUCTION TO ECCENTRIC BRACED FRAME 24
3.3 ECCENTRICITY CONFIGURATION AND FRAME BEHAVIOUR 25
3.3.1 STIFFNESS 25
3.3.2 TIME PERIOD 26
3.4 EARTHQUAKE LOADING AND ECCENTRIC BRACED FRAME 30
3.5 CONTROL OF BUCKLING 31
3.6 DESIGN EXAMPLE PROCEDURE AND RESULTS 32
3.7 CONCLUSIONS 40
CHAPTER-4
ECCENTRIC CONCRETE INFILL FRAME (E.C.I.F.)
4.1 INTRODUCTION TO INFILL FRAME 42
4.2 ADVANTAGES OF INFILL FRAME 43
4.3 STRUCTURAL IMPLICATION OF INFILLS 44
4.4 INTRODUCTION TO ECCENTRIC INFILL FRAME 46
4.5 COMPARISON WITH STEEL ECCENTRIC FRAME 48
4.6 ECCENTRIC CONFIGERATION AND FRAME BEHAVIOUR 49
(STIFFNESS. TIME PERIOD)
4.7 FULL DESIGN EXAMPLE PROCEDURE AND RESULTS 52
4.8 CONCLUSIONS 61
List of figures 63
Glossary 64
Bibliography 67
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Acknowledgment
My whole purpose of coming to University of Southern California was to pursue
my research in Structural Design. I am grateful to the University, Prof. Marc
Schiler, and Prof. Goetz Schierle, for giving me this opportunity.
My sincere thanks to my academic advisors. Prof. Goetz G.Schierle, Prof.
Dimitry Vergun, Prof. Marc Schiler, Prof. Pierre Koenig for their valuable
contribution and support throughout the whole research.
My special thanks to Prof. Goetz G. Schirle, Prof. Dimitry Vergun for the
knowledge and the experience that they shared with me for shaping my future as
an Architectural Engineer.
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ABSTRACT
The current practice of seismic design in different parts of the world and the
performance of buildings in an earthquake have revealed the inherent limitations
of earthquake resistant design.
Two structural systems proposed in this thesis address these limitations in a new
way :
a) Concrete Eccentric Braced Frame. Here the sudden brittle failure of a concrete
infill frame is avoided and made ductile by introducing a fuse in the form of link
beam (eccentricity). However the damage (inelasticity) is confined and restricted
to infill (masonry) only. These infills can be replaced after the earthquake. And it
is also shown that staggering the infill wall controls the pattern of damage.
b) Variable Eccentric Braced Frame. This is essentially an eccentric braced frame
but damages (inelastic behavior) in an earthquake is restricted to bracing as
against the conventional eccentric frame where the damages occur at the link
beam. These braces can be replaced after the earthquake. Variation of eccentricity
is used to control the pattern of failure.
Key Words
1) Eccentric braced frame
2) Seismic design.
3) Concrete infill frame
4) Variable eccentric frame.
5) Concrete infill eccentric frame
6) Staggered infill wall
7) Damage Control Design
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INTRODUCTION
Each earthquake answers many old questions, and simultaneously raises new ones.
Economic earthquake resistant design research is still an open-ended topic and will
continue to be so, for the next few decades.
Damage control design is not necessarily about smart materials it is about the smart
usage of conventional building materials. It is expression of understanding the unique
behavior of materials and natural forces on the built form and the channelizing of these
unique properties towards a solution.
The idea of Damage Control Design idea is based on current practice of seismic
design in different parts of the world and the performance of buildings in an earthquake
which revealed the inherited limitations of earthquake resistant design. Damage
Controlled design is not an absolute solution but an attempt to address these limitations in
a more conceptual way with possible new solutions (Concrete Eccentric Infill Frame)
improving old solutions (Variable Eccentric Braced Frame).
Damage control design is a step towards an economic earthquake resistant design
which could be made part of common design practice. If it could be tested with full rigor,
which includes physical model testing.
Finally a reminder which Prof. Dimitry Vergun.S.E. would always tell me
"Earthquake is a better judge than any critic, theory or any computer simulation”
Damage Control Design is a door to the abyssmal world of building science. It is still
in its infancy. There is much to be explored and, much to be understood and we look with
a great sense of optimism at our world as we stand in the threshold of new century.
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Chapter-1
EARTHQUAKES
"Disasters may indeed be messengers in that they force us to think about our priorities. They drive us
back to "GOD”, they remind us o f mistakes and failures, they call forth reserves o f energy and
commitment, which might otherwise, remained untapped. Disasters also remind us o f the fragility o f life
and our human achievements”
Archbishop of York in
The Times.
1.1 INTRODUCTION TO EARTHQUAKES
Man may have reached the outer space but he still has not understood the inner
core of the earth, because of his inability to predict or avoid a natural disaster like
earthquakes. They are the most destructive of the forces that nature reveals on the
planet.
The earthquake as such is not a problem. The catastrophe caused by the
collapse of the structures which kills people is the problem. They not only cause loss
of life and property but also leave a long lasting impression on the community by
shaking up the morale of the people.
The 1994 Northridge (U.S.A) earthquake, the 1995 Kobe (Japan) earthquake
and the Khilari(India) earthquake, have only proved the above conclusion.
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Figure 1.1. Northridge Earthquake failure. (Source: www.)
Earthquakes in the past have shown and proved that most structures designed
according to the code have a great deal of difficulty in obtaining economic earthquake
resistant structures. Damage is imminent to structure. The 1994 Northridge earthquake
and the 1995 Kobe earthquake have only reinforced the above statement. Many
engineered buildings, which were designed according to codes, have collapsed. One of
such an example is noted here. A commercial building was designed according to
uniform building code using Static Analysis.
However in the response spectra constructed for the Northridge earthquake and
the building site and the peak acceleration was found it was noticed that the the forces
for this peak acceleration was 3 times greater than the forces computed by Equivalent
Static Method prescribed by the code.
The Japanese engineers were quick to comment on the above discrepancy and
ridiculed the U.S engineers for designing weak buildings, without accounting for the
actual earthquake forces in the code.
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The Japanese had a strong reason for their comment, as they designed buildings in
Japan for the actual forces of the earthquake.
1.2 COMPARISON OF DESIGN CODES
To illustrate this, a building design example is considered in Japan, the United
States and India. The building is a rectangle in plan having dimensions of 40ft by 60ft
and is 3 storey high. The building structural framing consist of 4 moment resistant steel
frames of 3 bays each, spaced at 20ft on center as shown in figure 1.2. The building is on
a medium soil.
I 1 I I
I . : f . I
t: r i t
Figure 1.2. Building framing plan
The building is designed according to Equivalent Static Analysis for these three locations
in Japan, U.S.A, and India. And as per the respective codes of these countries and for the
worst condition of earthquake in these locations. The study is basically the comparison of
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the base shear, and the shear force under a structure caused by an earthquake. The mass
of the structure tends to resist the movement, caused by the earthquake and this causes a
shear force between the ground and the mass. This shear force is called Base Shear.
UBC static approach(U.S.A.)
Basic design equation:
V=(ZIC/Rw)W
Z : seismic zone factor
Z correlates with the effective peak acceleration in g
Zone Z
1 .075
2a .15
2b .20
3 .30
4 .40
I: importance factor
C: ground motion amplification
Rw: Inelasticity & Ductility modification
For steel/concrete special moment resistant frame Rw is 12
Minimum value of C/Rw is .075
T: fundamental time period in seconds
T=Ct (h3/4)
H: height of building
Ct for steel moment resistant frame is .035
Ct H H3/4 T
0.035 36 14.6969 0.51439
4
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OL25S/T2/3 Cmax =2.75
S: soil factor depends on the soil condition
1.25 S T T2/3 C
1.25 1.5 0.51439 0.64199 2.92059
2.92>2.75 so C=2.75
Base shear coefficient
Z I C Rw ZIC/Rw
0.4 1 2.75 12 0.09167
Design of building in Japan
In accordance with Building standard law enforcement order.
V=(ZxRtxAixCo)W
Z=1.0
T=H (.02+. 01 y)
=11.4(.02+. 01)
=. 36sec
y=l for steel construction
Rt=l
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i-o-a(*rs--n
t-O.2 C - i —
0.6
o.«
S U i S ” " 1* T" * 3
Soil Profile Typ* 2
(lediua)
T»« I
0.0
Figure 1.3. Japan Code. Rt values. (Source: Japanese Building Code)
Ai: horizontal shear distribution factor
Ai=l+((1/Vai)- ai) 2T/1+3T
ai = Wi/Wo
LEVEL Wi Wo ai Vai T
1/Vai T Ai
120 120 0.33333 0.57735 0.36 1.398717 0.346154 1.484171
2
120 240 0.666667 0.816497 0.36 0.558078 0.346154 1.193181
1 120 360 1 1 0.36 0 0.346154 1
Co=.2 min to 1 max
Z Rt Ai Cmin Ci
1 1 1.48417 0.2 0.29683
1 1 1.193181 0.2 0.238636
1 I 1 0.2 0.2
Z Rt Ai Cmax Ci
1 1 1.484171 1 1.484171
1 1 1.193181 1 1.193181
1 1 1 1 1
Base shear coefficient 0.2 to 1.0
6
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Design of building in India
In accordance with is 1983-1975
V= axpxCxIxW
a: Seismic zone factor
(3 : Soil factor depends on the soil condition and is taken as I for medium soil.
C: flexibility factor given by the graph below.
I: importance factor
T: estimated natural fundamental time period
T=0.1xN
N: number of storeys
U
w
u .
g
u
\
\
\
•
\
V .
V
ot o» 1 .1 l« |.0 t.«
kaivw ai Pcm oo m second
i t
Flexibility coefficient
Figure 1.4. C value. ( Source: Indian Code)
T=. 1X3=. 3 sec
For T=. 3 C is 1
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Base shear coefficient = ax(3xCxI
COUNTRIES BASE SHEAR COEFFICIENT
U.S.A .09
JAPAN .2 to 1
INDIA .08
U n ifo rm B u ild in g C o d e
, /?„ = 4 to 12
N atu ral vibration* p e rio d 7^,, sec
Figure 1.5. Base shear coefficient versus natural time period. (Source: Anil K. Chopra, 1996. p. 241)
1.3 SUMMARY OF RESULTS
As per the Equivalent Static Analysis the minimum typical base shear values in
Japan are twice that of the U.S. The maximum is 5times that of U.S.. Even then many
engineered buildings failed in Kobe, Japan, in the 6.7 magnitude earthquake.
Inspite of the higher standards in Japan there was large-scale damage in the 1995
Kobe earthquake (figure 1.7)
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B A SE SHEAR I N POUNDS
BOTTOM FLOOR BASE SHEAR COMPARISON
160000
140000
120000
100000
80000
60000
40000
20000
INDIAN- MAX U.S.A.-MAX JAPAN-MIN
COUNTRIES
JAPAN-MAX
Figure 1.6. Base shear comparison o f different countries
I
Figure 1.7. Kobe earthquake, japan, 1995. (source:\vww.EQE.com)
The current design philosophy in Japan is to keep seismic stresses within the
elastic (non-damaging) range for a moderate earthquake. The building is expected to have
little or no damage. This makes buildings in Japan stronger than similar buildings in the
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United States. This again may be counter-productive as the building gets stronger and it
attracts more earthquake force; and if the stiffness in not evenly distributed throughout
the building, it might lead to failure at one level of the building rather that the collaps of
the whole building.
The United States design philosophy is based on the following(figure 1.5):
1) To resist earthquake of minor intensity without causing damage, the structures should
resist the frequent but minor shocks within its elastic range of stresses.
2) To resist moderate earthquake with minor structural and non-structural damage.
3) To resist major catastrophic earthquake without collapse.
The lower base shear value specified by the U.S.A standards is because it depends
upon the ductility and over strength o f the framing system to handle the actual earthquake
forces instead of requiring the system to remain essentially elastic (Rw=1.0). although
damage is considered acceptable for moderate-sized earthquakes.
The Indian code is essentially based on the Uniform Building Code with little
difference from the US standards. It may be interpreted as a simplified version of the UBC,
where base shear values correspond with the UBC values as seen in the graph page.
Based on the above broad statements, it is possible to device a number of
methodologies that may render these codes more specific in space and time. It is in this
light that Damage Controlled Design finds significance.
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Chapter-2
DAMAGE CONTROLLED DESIGN*
2.1 INTRODUCTION
Damage Controlled Design is based on the facts that total earthquake resistant
design is a matter limited by economics. Damage is bound to happen and we can only
partially control the extent of damage to the structure.
The challenge to the engineer is to design the structure so that the damage is
controlled to an acceptable degree, and that the damage is repaired economically. This
demonstrated through the following case study by making the structure ductile.
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2.2 EFFECT OF ELASTIC AND PLASTIC RESPONSE OF STRUCTURES
The response of a different system which includes
a) Elastic system
b) System with 10% damping
c) Inelastic or Plastic system.
d) System with pA effect.
e) System with pA and 10% damping.
soar s y s t e m l e g e n d b * *
Undvnpad —
Oanv*d(tO%) M —
0 0 a t 0 2 0 3 04 o s 0 6 0 7 0 0 09 <0
Figure 2.1. Response of a single degree of freedom system to an impulse. (Source: Robert Enelekirk, 1996,
p. 103)
’ Concept first introduced in Japan, see “ First World Conference on Structural Controls”
12
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The response is represented by the time versus deformation graph 1 and acceleration
versus deformation graph 2 in figure 2.1
As seen from the figure (2.1), the response of an inelastic system is much lower
than that of a plastic system. The reason for the lower response of the inelastic system is
because the input earthquake energy in an inelastic system by an earthquake is dissipated
by both viscous damping and yielding.
So the energy equation for an inelastic system is:
Et = kE+Ed+Ey
Et = Total energy imparted to the structure.
kE = Kinetic energy of motion relative to the base.
Ed = Energy dissipated by damping.
Ey = Energy dissipated by yield.
If much of the energy is dissipated through yielding of the structure, then the
kinetic energy imparted to the structure is reduced. The structure needs to be designed for
a smaller earthquake force. However, yielding that dissipates energy causes damage to
the structure, and leaves in it a permanently deformed condition at the end of the
earthquake.
The design of the structure is such that the energy could be dissipated through
special devices which can be easily replaced after an earthquake. This forms the basics,
for Damage Control Design.
Further, the effect of having two kinds of behavior (elastic and inelastic) in the
same building does not affect the overall behavior because peak deformation of an
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elastoplastic system and corresponding elastic system is same for a particular excitation
as shown in the figure (2.1).
Figure 2.2. Elastic and inelastic response o f a single degree o f freedom system. ( Source: Robert Englekirk,
1996, p. 123)
The response of a system represented by the force versus deformation curve is a
linear relationship for an elastic system. It is linear up to the yield point and becomes
non-linear after yield in a plastic system. However the displacement in both the systems
is same.
23 STRENGTH VERSUS STIFFNESS DESIGN OF STRUCTURES *
Recent advances in material science and engineering have resulted in significant
increase in the strength of building materials such as steel and concrete. Although the
strength of material has essentially doubled, its elastic modulus is constant.
Since the modulus of elasticity ‘E’ is constant, stiffness rather than strength is
likely to govern the design of structures of high strength material.
* Jerome J.C, Burtos. S.A.K
Dfaptacmnent A
14
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To illustrate the dominance of stiffness over strength as the strength of steel used in the
structure increases, a lO ft high W14 section column as shown in the figure(2.3) below is
considered. The lateral load applied is a concentrated load P applied at the tip of the
column and the column support at the base is fixed.
So the column is modeled as a bending cantilever.
Figure 2.3. Column W14 section.
The maximum bending moment M in the column due to applied concentrated load
P occurs at the base and is equal to P*h, where ‘IT is height of the column, the
maximum stress is
f =M/S
S = 2I/d S is the section modulus
15
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I is moment of inertia of the section about bending axis, d is the depth of the section
Fa = allowable stress P*h*d/2I
The moment of inertia required to satisfy Fa allowable stress requirement is given by
I stress = P*h*d/2Fy
The maximum deflection ‘A7 is at the tip of the column and is equal to
A = P hA 3/ 3 E I
where E is modulus of elasticity of the column material
A is limited to allowable deflection in design
The moment of inertia required to satisfy A allowable deflection requirement is given by
Stiffness = P h3 / 3 EA
The ratio of Istiffness to I stress is given by
I stiffness P hA 3 2 Fy h h FY
--------------- =   = .67 ........................
I stress P*h*d 3 E D d E
h= 10* 12 = 144 inches
d = 14 inches
D = .005 h (allowable UBC limit)
Fy = 24 ksi for 36 grade steel
E = 29000 ksi
Figure 2.4 shows the variation of Moment of Inertia required for stiffness / Moment of
Inertia required for stress with height/Deflection for two kinds of steel
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COMPARISON OF HIGH STRENGTH (Fy50) AND LOW STRENGTH (Fy 36)
STEEL
C O
C O
U l
ce
► -
55
co
c u
z
0 6
0 6
0 4
75 100 t25 50 150 175 225 250 200
Figure 2.4. Ratio of Moment o f Inertia required for stiffness to Moment o f Inartia required for Stress versus
deflection.
The value of h/D at which a transition from stress to deflection control occurs for
the W14 column is when I stiffness/I stress < 1 i.e. 140 for 50ksi steel and is 220 for 36
ksi steel. Since the maximum allowable h/D according to UBC is 200, hence stiffness
essentially controls the design for the full range of allowable deflection.
2.4 DAMAGE CONTROL DESIGN PROCEDURES
First the design loading criteria is established and the building is designed for
deflection. The ideal design would be a uniform distribution of deformation throughout
the structure, which is established, by optimal stiffness distribution, as the distribution of
deformation in a structure is governed by distribution of stiffness.
The requirement of maximum response of the structure to the earthquake is also
met by passive energy dissipation and absorption
17
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The design essentially consists of distributing
1) Energy storing elements (stiffness)
2) Energy dissipating elements (damping)
3) Energy absorption elements (yielding)
Structures designed by conventional methods stay within the elastic range up to
the service limit, and when the serviceability limit is exceeded, mainly the beams of the
structure are allowed to plastically deform. (This is based on the philosophy of the strong
column weak beam concept).
But in damage control design which is based on the concept of performance based
design i.e. the rationale of one design requirement corresponds to one design parameter.
The performance level anticipated is damage limited to only certain members.
The parameters for our design were
a) Gravity loads
b) Seismic loads
Gravity loads are vertical loads and are taken by a vertical system basically beams
and columns.
Lateral loads are seismic loads and are predominantly taken by a horizontal system
such as a lateral bracing/infill (partially taken by columns).
Vertical systems (columns and beams) are kept within the elastic range and allow the
plastic deformation and energy absorption to the lateral system (braces, infill) only.
Thus the design requirements are:
a) Vertical system (Elastic through out time history of earthquake)
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b) Horizontal system (Initially elastic becomes plastic during earthquake as a result of
absorbing energy during this process)
2.4.1 STIFF STRUCTURE VERSUS FLEXIBLE STRUCTURE COMPARISON
Structure type ADVANTAGES DISADVANTAGES
FLEXIBLE
STRUCTURE
1) Specially suited for sites with a
short earthquake time period and
for building with long period
2) Ductility easily achieved
3) Analysis is directly applicable
since the behavior could be
predicted
1) High response on site with a
long earthquake time period
sites
2) Deflection easily controlled
3) Analysis may be invalidated
due to the presence of non-
structural elements
4) Non-structural elements
difficult to detail
STIFF
STRUCTURE
1) Suitable for long earthquake
time period sites
2) Easier to strengthen by adding
stiffness
3) Deflection easy to control.
4) Non-structural elements easy to
detail
1) High response on short
earthquake time period sites
2) Appropriate ductility not
easy to achieve
3) Analysis non-authentic
because of the non­
predictability ofbehavior
As seen from the above, both flexible structure and stiff structure have both
advantages and disadvantages to be adopted as structural systems in Damage Controlled
Design.
Thus a stiffer structure is preferred to a flexible one as seen from the above table.
Design forces are smaller for large period buildings, however due to the large deflection
in the flexible building, it will lead to many undesirable effects.
The significance of stiffness in design indicated through these two examples, the
one above and the previously considered example (see page 15)
19
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Thus the Damage Control Design of a building should be a stiff structure with out
sacrificing on their economy.
A stiff structure does not exploit its ductility completely under small and
moderate earthquakes but under severe shaking the structure undergoes a certain amount
of stiffness degradation. This lesser stiff structure as compared to before degradation,
now uses the ductility potential and dissipates the input seismic energy through the
inelastic deformation.
2.4.2 APPLICATION TO STEEL BUILDINGS
In the context of steel building the structural system adopted would be a brace
frame, with high strength steel used for the main columns and beams, and low strength
steel used for the bracing.
By the use of two kinds of steel the stress-strain is relationship is as shown in the
figure 2.5.
At level A both steels have the same stress and strain levels; at level B also both
steels have the same stress and strain level but the low strength steel yields; at level C
both have same stress level but different strain level so the low strength steel goes into
the plastic range whereas the high strength steel is still in the elastic range.
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120
A 5 1 4
F
100 -
Defined F when a dear
plastic plateau is not in existence
80 -
Tensile
strength
A441
60 -
A36
F
40 -
F
Well defined plastic plateaus
20 -
0.2% Strain off-set line
0.20 0.24 0 16 0.12 0.08 0.04
(not to scale)
Figure 2.5. Tensile stress-strain curves for three ASTM-designation stress.(Source: Charles G. Salmon &
John E. Johnson, 1996, p. 200)
2.4.3 APPLICATION TO CONCRETE BUILDINGS
The structural system adopted would be a dual system of moment frame and shear
wall. Where in concrete is used for the moment frame and infill masonry wall steel is
used for the shear wall.
Due to the use of concrete and masonry the stress strain relationship is as shown
in the figure 2.6
2 1
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8
6
4
Critical stress
2
'Failure
First visible crack-'*
0
0 0.003 0.004 0.001 0.002 0.005
Figure 2.6. Stress strain curve for different concrete and masonry. (Source: Ferguson, Breen, Jirsa,
1988, p.33)
At level A both steels have the same stress and strain levels; at level B also both
concrete and masonry have the same stress and strain level but the masonry yields; at
level C both have the same stress level but different strain level so the low masonry goes
into the plastic range whereas the concrete is still in the elastic range.
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22
CHAPTER-3
Analysis and design of steel-frame buildings
3.1 CURRENT DESIGN PRACTICE
Moment frames are vierendeel frames that cantilever out of the foundation. As
such, they derive their strength from the flexural strength of their beams and the
axial/flexural strength of their columns. Displacement is usually a major consideration in
the design of moment frames.
Since the modulus of elasticity ‘E’ for both steels is same, designing frames to
resist lateral load using high strength steel is governed by stiffness rather than strength.
Buildings traditionally have been braced by a dual bracing system, which
combine an axial and a flexural bracing system. The stiffer component of a dual system is
provided by a X brace. This dual system is stiff but also brittle because much of the load
path is in compression. (Using a concentric braced frame would be a solution for stiffness
23
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design but the ductility requirement for a seismic design rules out concentric braced
frame).
An eccentric braced frame has inherent stiffness compared to a moment frame
and is ductile compared to a concentric braced frame. This addresses the desire for a
laterally stiff framing system with significant energy dissipating capability to
accommodate a large seismic force.
3.2 INTODUCTION TO ECCENTRIC BRACED FRAME
The figure 3.1 shows the typical behavior of an eccentric braced frame in an
earthquake.
The link beam not only acts as a fuse but also the length of the link beam has a
major influence on the stiffness character of the frame. It is it’s this character, which we
are concerned with here, which can be used to get the different stiffness.
M M T M W
I -----
r~
(b)
m w w /w vvrw
Figure 3.1. Failure mechanisms for a frame in two opposite directions leading to identical conclusions. (
Popov and Manhaim, 1981b, p, 87)
24
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3.3 STUDY OF DIFFERENT ECCENTRICITY CONFIGURATION ON THE
FRAME BEHAVIOR
3.3.1 STIFFNESS
A study of a one story, one bay (30 ft) frame is considered, and the frame
configuration is as shown in figure 3.2. The frame with out the brace is a moment frame
and the frame fully braced is a concentric braced frame. The frame with brace in-between
column and beam as shown in figure 3.3 is an eccentric frame.
Figures .2 Eccentric frame
The stiffness of a system is given by L/AE Cos.0 where
L: length of frame
A: Area of cross section of the brace
E: Modulus of elasticity
25
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0 : Angle between the brace and the horizontal
Among all these systems the moment frame is the least stiff as Cos0 =0 0 =90 and the
concentric braced frame has the maximum stiffness as 0 is minimum, where as the
eccentric braced frame stiffness is in-between the two and it can have any value between
the two depending on the angle 0 .
Stiffness is also function of the cross sectional area and the length of the brace.
This is explained in figure 3.3
140
120
100
80
60
40
20
0
S3
CO CM
CM
IT)
CM
lin k length
.Sarea
.Secce
. S both
Figure 3.3. Frame stiffness for different link length/cross section area o f the brace.
3.3.2. TIME PERIOD
Stiffness affects the fundamental time period, which determines the dynamic
character of a frame.
The study of a 10 story, 3 bay (30 ft) frame is considered, and the frame
configuration is as shown in figure3.4. The frame with out the brace is a moment frame
26
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and the frame fully braced is a concentric braced frame. The frame with brace in-between
column and beam shown in figure 3.4 is an eccentric frame.
a) Moment frame
Figure 3.4.
b) Braced frame.
Figure 3.5. Eccentric braced frame.
27
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As the link length becomes shorter, the frame becomes stiffen approaching the stiffness
of a concentric braced frame. As the link becomes longer, the frame becomes more
flexible approaching the stiffness of a moment frame. The frame with a long period is
flexible and the frame with shorter period is stiffen Which can be inferred from the graph
figures.6.
a
z
o
o
U i
w
z
UJ
s
p
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0. 1
0
MF 10% 2Q 30 40 50 60 70 80 9 0 RF
.Seriesl
RATIO OF LINK/BEAM
Figure 3.6. Time period of a 10 storey steel frame for different eccentricity.
As seen from the above study, a wide range of stiffness variation can be achieved
in an eccentric braced frame by configuring the braces. This is achieved by a multiple
eccentric braced frame with each bracing element eccentricity fine-tuned at every floor to
get the desired stiffness.
Since the modulus of elasticity *E’ for both steels is the same, designing frames to
resist lateral load using high strength steel is governed by stiffness rather than strength.
Buildings traditionally have been braced by a dual bracing system, which combines axial
and flexural bracing system. The stiffer component of a dual system is provided by a X-
brace. This dual system is stiff but also brittle because much of the load path is in
28
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compression (using a concentric braced frame would be a solution for strength design but
the ductility requirement for a seismic design rules out concentric braced frame).
This makes an eccentric braced frame ideal to design in seismic regions
using high strength steel.
3.4 EARTHQUAKE LOADING AND ECCENTRIC BRACED FRAME
The shear distribution along the height of the building due to seismic loading is
the inverse of the force distribution and is minimum at the top and maximum at the base,
I t w S H j m «r * 5 * ~ M ? ■ *
Figure 3.7 Shear distribution along the height of a 10-storey building.
The stress level within the structure due to seismic loading is a function of
deformation. The variation of deformation along the height of the structure is controlled
by the distribution of stiffness within the structure. The ideal state is to have a uniform
29
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variation of deformation throughout the structure. In other words, the objective here is to
have a uniform bending deformation profile over the entire height of the structure, so that
the earthquake energy is evenly distributed throughout the frame.
Also the frame is design such that all the members of the frame develop a
unistress level due to the varying shear distribution.
In order to develop unistress and uniform stiffness level in all the floors in the
frame, due to the varying shear distribution, in the damaged controlled hybrid frame the
structural system stiffness is varied by tuning the eccentricity in each floor to get the
optimal stiffness.
This optimal stiff frame develops a condition for unistress level due to seismic
loading as explained above.
The figure 3.8 shows a typical frame configuration for Damage Controlled
Design.
3.8. Damage control frame configuration.
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3.5 CONTROL OF BUCKLING
In the above frame configuration, the bracing elements will be in tension when
loaded in one direction, but will be in compression for loading in opposite direction..
Compression failure is basically buckling of the brace.
Earthquake loading is bi-directional and energy absorption is basically by tension
yield of the brace. So the problem of failure in compression is addressed by detailing the
brace as shown in figure3.8.
y M
V
V
/
/
/
s
Figure 3.8. Brace encasing detail.
\ S
Figure 3.9 Adopted in an eccentric frame
The braces are encased in a steel pipe with lightweight concrete poured in-
between. It is also detailed such that the pipe and concrete provide only lateral support
and does not increase the stiffness of the brace.
31
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3.6 DESIGN CRITERIA FOR 10-STORY OFFICE BUILDING ADOPTING
DAMAGE CONTROL DESIGN APPORACH
The example building is an office building, 150ft by 90ft rectangular in plan with
6 nos. 3 bay frames spaced at 30ft on center.
The building will be designed in accordance with the 1994 edition of the Uniform
Building Code. The building is located in seismic zone No.4.
The framing system is as shown in the figure 3.10, it has the VEBF's only in the
middle bay in the shorter direction on the column line 1 and 6. Typical storey height is
15ft. Floor and roof are 3 inches metal deck with 3-1 Minch lightweight (1 lOpcf) concrete
fill.
I I
Figure 3.10. Building framing plan
32
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Material Specifications are:
Steel columns, beams: ASTM A50 GradeSO Fy=50ksi
Steel braces : ASTM A36 Fy = 36 ksi
LOADS
Roof Loading:
Roofing and insulation 7.0 psf
Metal deck 3.0
Concrete slab 44.0
Ceiling and Mechanical 5.0
Steel framing and fireproofing 8.0
Dead load 67.0 psf
Live load (reducible) 20.0
Total Load 87.0 psf
Floor Loading:
Metal deck 3.0 psf
Concrete slab 44.0
Ceiling and Mechanical 5.0
Partition 20.0
(The partition load could be reduced to 10 psf for lateral analysis)
Steel framing,
which includes beam girders, columns, and spray-on fire proofing 13.0
Dead Load
Live Load (reducible)
Total Load
Curtain wall:
Average weight
85.0 psf
50.0 psf
135.0 psf
15.0 psf
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UBC static approach
Basic design equation:
V=(ZIC/Rw)W
Z : seismic zone factor
Z correlates with the effective peak acceleration in g
Z=4
I: importance factor
C: ground motion amplification
Rw: Inelasticity & Ductility modification
For steel/concrete eccentric braced frame Rw is 12
Minimum value of C/Rw is .075
T: fundamental time period in seconds
T=Ct(h3/4)
Ct for steel moment resistant frame is .02
H Ct T
150 42.86160 0.02 0.857232
C=1.25S/T2/3 Cmax =2.75
S: soil factor depends on the soil condition
1.25 S T C
1.25 1.5 0.857232 .9023 2.077793
C=2.07
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Base shear coefficient
Z
I c Rw ZIC/Rw
0.4 1 2.077 10 0.08317
Length Width Area Unit load Total roof
load
No. of
floors
Total dead
load
150 90 13500 0.067 904.5 1 904.5
Length Width Area Unit load Total roof
load
No. of
floors
Total dead
load
150 90 13500 0.112 1512 9 13605
Base shear v= (13605+904.5)*0.08= 1160 kips
Distributing the base shear to each level of the building
The total base shear is distributed over the height of the structure in accordance with the
following formulas
V= Ft +£Fi
Ft=0.07 V Ft concentrated force at top in addition to the force due to v Ft=81.2
Fx=((V-ft) *w*h)/ IW *h
Level F loor weight(w) Floor height(h) w*h V-Ft Fx
Roof 904.5 150 135675 1160 136.11+82.2
9 1512 135 204120 1160 204.78
8 1512 120 181440 1160 182.02
7 1512 105 158760 1160 159.27
6 1512 90 136080 1160 136.52
5 1512 75 113400 1160 113.77
4 1512 60 90720 1160 91.01
3 1512 45 68040 1160 68.26
2 1512 30 45360 1160 45.51
1 1512 15 22680 1160 22.75
Z W *h =1156275
The 1992 uniform building code (UBC) triangular load (1/2 total building load)
applied to VEBF is representative of the first mode of response using a structure factor
35
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Rw=10 (eccentric braced frame), and a trial computer run by software stadd3/multiffame
is made with w!4 sections for columns and wl8 section for beams
Smaller sections for bracing are used for the initial run and the frame time period
and the drifts were identified. Now the influences of each of the brace on the storey drift
were isolated and quantified and the stress levels in these bracing are also noted.
The time period was identified to be .8sec(UBC value .84sec) The eccentricity is
tuned to have a uniform bending profile which helps develop unistress level in the frame,
the members (the columns, beams and bracing) are sized for these forces and the
allowable drift criteria of UBC which is .05% of height in our case 9 inches
POST YIELD BEHAVIOUR OF THE FRAME (plastic deformation only in brace)
Sequential yield analysis
The static loading is increased by a ratio 5% until the first bracing component
yields (all the bracing components should yield simultaneously because of the uniform,
stress in bracing). However marginal variation in the eccentricity/ cross section area of
the brace in each floor is made so that the top floor brace yields first and then follows to
other lower floors ending with the last bottom floor brace yield. Since bracing is welded
the plastic capacity of the each brace is the combination of the axial tension and the
moment in the brace, then the first bracing yield, which is in the top story by the
formation of the plastic hinge. Each of the plastic hinge is replaced in the brace by an
analytical hinge. The procedure is repeated as each hinge is formed in the next lower
story braces and this is repeated till all the 10 braces were replaced by an analytical
hinge.
36
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When all the braces have yielded (failed) the frame is reduced to a flexible
moment resistant frame; this flexible moment frame attracts less earthquake force
compared to an earlier stiff eccentric frame, because of the lengthening of the time period
of the frame from 0.854 sec to 1.3 sec. Further lengthening is due to the secondary
p-delta effect and in addition to this yielding; the bracing absorbs energy and
reduces the total energy input to the frame as shown in the figure 3.11
Figure 3.11 Stress in members o f VEBF
FORCE REDUCTION CALCULATION
INITIAL FRAME BASESHEAR
V= 1578kips
POST YIELD FRAME
BASESHEAR = ZI(C/Rw)(W)
37
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C=1.25 S /TA 2/3
S = site factor 1.5 for medium soil
Rw= structure factor 12 moment frame
T=1.3 sec
C= 1.25*1.5/ 1.3A .666
W = total weight 19737 kips
C=1.875/.879=1.43
V =( 0.4) (1)(1.43/12)*W
V = 933kips
There is a 40.83% reduction in the base shear and the damaged frame has to
resist a base shear of only 933 kips but the damage frame could resist a base shear of
1837 kips before the first beam yielded (failed). The drift associated with this base shear
was 11.38 inches which is 30% greater than that of the allowable drift criteria of the
UBC, but it could resist the 933 kip base shear with 5% excessive drift
INELASTIC DEFORMATION: Due to plastic or inelastic deformation as in this case.
The yielding of some components of the structure absorbs some of the earthquake energy,
so the forces in the yielded structure are less compared to the initial elastic structure.
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FORCE REDUCTION DUE TO ENERGY ABSORPTION
Total kinetic energy of the building is given by V z M VA 2
Where M is the mass of the frame = weight / acceleration due to gravity = W/g
W = 14512 kips g = 386 in/secA 2
W/g = 14512/386 = 37.59
V is the velocity of the frame for the maximum acceleration in this case is 85 % g and its
value is taken from spectral curve, which is 4 in/sec
1/2 MVA 2 = 1/2 * 37.59 * 16
= 300.72 kip/in
Energy absorbed by a brace is a function of strain in the brace. The strain in the
brace associated with maximum inter story drift of 1.2 inches is .2%
Energy absorption for .2% strain is .24*40 = 9.6 kip/in per brace (.24inches elongation in
brace, 40 ksi stress in brace at yield)
Total number of brace is 20 10 on each frame 9.6*20 = 192 per cycle
Reduced kinetic energy is 192
Kinetic energy after yield is given by
Initial kinetic energy - reduced kinetic energy = 300.72 - 192=108.72
Velocity for the new kinetic energy is E = 1/2 M V A 2
E = kinetic energy after yield
M= 37.59 kip-secA 2/in
V = (108.72*2/2.332)Al/2 = 2.40 in/sec
For V= 2.40 and time period of 1.3 seconds acceleration is 6% g
Base shear for 6%g acceleration is 834 kips. Reduced base shear is 1160-834 = 326 kip
39
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3.7CONCLUSIONS
1) Damage control design is an economic solution to earthquake resistant design.
2) Damage in structures due to earthquakes can be restricted to only certain elements,
using both material and effective structural systems. As shown it is only the bracing,
which fails, due to the use of low strength steel. The link length and the cross section area
of the brace determine the pattern of the brace failure.
3) The variation of deformation along the height of the structure is controlled by the
distribution of stiffness within the structure. The ideal state is to have a uniform variation
of deformation throughout the structure. Tuning of eccentricity can achieve the uniform
bending profile along the height of structure for lateral earthquake loading. As the link
length becomes shorter, the frame becomes stiffer, approaching the stiffness of a
concentric braced frame. As the link becomes longer, the frame becomes more flexible
approaching the stiffness of a moment frame. This helps in uniform distribution of
earthquake forces, which is uneven over the height of the building.
4) The Damage Controlled Design is a stiff structure for mild earthquakes and wind, but
in a major earthquake this structure is reduced to a flexible structure due to stiffness
degradation caused by failure of the braces.
5) The uniform bending profile along the height of structure achieved by tuning of
eccentricity also makes the stiffness degradation consistent over the entire height of the
structure in a major earthquake.
6) There is a 40.83% reduction in the base shear and the damaged frame has to resist a
base shear of only 933 kips but the damage frame could resist a base shear of 1837 kips
before the first beam yielded (failed) but the drift associated with this base shear was 8.38
40
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inches which is 30% greater than that of the allowable drift criteria of the UBC, but it
could resist the 933 kip base shear with 5% excessive drift.
Related conclusions-
Since the cost of manufacturing of both high strength steel and low strength steel are the
same, and the manufacturers are inclined to producing high strength steel in the future
therefore, with the use o f high strength steel in the building industry as shown by the
results in chapter -2, the design of structures is going to be governed by stiffness rather
than strength. Thus engineers should not totally discard the old Allowable Stress Design
(ASD) method for Load and Resistant Factor Design (LRFD), since we know that design
of structures for stiffness requires the ASD method
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41
CHAPTER-4
DESIGN OF CONCRETE ECCENTRIC INFILL FRAMES
(CEIF)
4.1 INTRODUCTION TO INFILL FRAMES
Reinforced concrete is one of the principals building materials used in
engineering structures in many countries around the world. The economy, efficiency,
durability, and mouldability of reinforced concrete make it an attractive material for a
wide range of structural applications.
In a typical RCC shear wall dual system frame, the frame resists the vertical
forces whereas the lateral forces were predominantly resisted by the shear wall, which is
built of concrete and partially resisted by the frame.
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In damage controlled design all the vertical forces are resisted by the frame and
all the lateral forces are resisted by the shear wall built of dual material masonry and
concrete, which is called as an infill frame.
11
1 (nql to Ha**)
n « s .22 la rx iw
Figure 4.1. Infill panels interaction. (Source: Dowrick, 1975. p.45)
In a concrete frame structure if the opening is built of masonry brick as in figure 4.1 it is
called an infill frame. The presence of the infill serves both architectural and structural
purposes.
4.2 ADVANTAGES OF INFILL FRAME
Even with the introduction of exotic new building materials and techniques, 70%
of the world’ s buildings are constructed of masonry. One of the most versatile and varied
classes of materials available, masonry continues to offer the following eight benefits,
43
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which together, make masonry an almost unbeatable choice for a wide range of building
construction:
1: Worldwide availability
2: Beauty
3: Versatility
4: Fire resistance
5: Thermal insulation
6: Sound resistance
7: Wind and earthquake resistance (reinforced masonry)
8: Affordability
4.3 STRUCTURAL IMPLICATION OF INFILLS
The presence of in-fill in the frame alters the overall behavior, especially when
the structure is subjected to lateral loads.
Generally, designers neglect these infill walls as a non-structural element. This is
because of lack of understanding of the structural behavior of Masonry.
The structural function depends very much on type of in-fill and also its
interaction with the frame. These infills are vertical members and are helpful in resisting
the lateral forces.
But, resistance to lateral forces by the infill much depends on its interaction with
the frame.
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Flexible/separate infill panel-
In case of flexible infill panel the deformation of the frame is maximum as the
infill does not assist the structure in the over all behavior. The in fills are non structural
and the frame would behave like a moment resistant frame which basically resist the
lateral forces by its rigid connection between the column and beam. Hence the beam and
column of the frame deform maximum.
Strong infill panel-
In case of strong infill panel and good structural interaction between the infill and
the frame, the presence of the infill increases the stiffness and hence reduces the
deformation, and the horizontal forces are resisted by the infill. Further, infills have
considerable mass, which increases the overall energy absorption capacity of the building
in the post yield period.
Infill frame is an equivalent of concentric braced frame in a steel building, where
the infill performs the same function as the brace as shown in figure 4.2
Inunction between a frame and infill matanry ■
Figure 4.2. Interaction between a frame and infill masonry.(Source: Dowrick. 1975, p.5l)
45
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The main disadvantage to the use of concentric braced structural system in a seismic area
is its brittle or nonductile mode of failure.
How do we make the frame ductile?
4.4 INTRODUCTION TO CONCRETE ECCENTRIC INFILL FRAME (CEIF)
An eccentric braced frame has inherent stiffness compared to a moment frame
and is ductile compared to a concentric braced frame. This addresses the desire for a
laterally stiff framing system with significant energy dissipating capability to
accommodate a large seismic force.
As in the case of eccentric braced frame in steel frames, even in concrete in fill frames
eccentricity can be created by leaving a gap in the panel of the wall as shown in the
figure 4.3. The behavior of masonry for lateral loading is similar to a brace in a steel
building as previously shown in figure 4.2
a) Eccentric brace frame in steel b) Concrete eccentric infill frame.
Figure 4.3
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4.5 COMPARISON WITH STEEL FRAME
For this a simple example is a 3 storeys, one bay frame on a medium soil (soil
factor -1. 5), importance factor (I) is considered as a conceptual frame configuration and
is shown in figure 4.4. The 1992 uniform building code (U.B.C) triangular load applied is
representative of the first mode of response using a structure factor Rw=10 (eccentric
braced frame).
The Shear distribution along the height of the building due to seismic loading is
the inverse of the force distribution and is minimum at the top and maximum at the base
as seen in figure 4.4. The stress level within the structure due to seismic loading is a
function of deformation. The variation of deformation along the height of the structure is
controlled by the distribution of stiffness within the structure. The ideal state to have a
unistress level is to have a uniform variation of deformation through out the structure i.e.
the objective here is to have a uniform bending deformation profile over the entire height
of the structure.
This is achieved by staggering the in fill wall as shown in the figure 4.4 this also
addresses the issue of synergy which could be termed as Form follows the Force.
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47
fa'll
me
M l JlftrlM feM T felliL* fctftt p r f+m fttfi
i * m m n m
a) Shear distribution^ Schierle, 1994) b ) Eccentric frame with staggered infill
Figure 4.4
This frame is analyzed using a finite element analysis program (COSMOS)
The frame is modeled using 2d area mesh and the size of the mesh is kept as
1 ft x I ft. Supports at the base fixed. Figure 4.6 shows the computer run results, which
does not have any difference from the ideal steel frame behavior figure 4.5.
b)
jm 'M jm w J*
Figure 4.5. Steel eccentric frame behavior
48
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■
Figure 4.6. Concrete eccentric infill frame behavior, modelled using Cosmos.
The link beam not only acts as a fuse but also the length of the link beam has a major
influence on the stiffness character of the frame. It is this character which we are
concerned here with because it can be used to get the different stiffness.
4.6 STUDY OF DIFFERENT ECCENTRICITY CONFIGURATIONS ON THE
CEIF (STIFFNESS, TIME PERIOD)
Stiffness/ time period of CEIF is a function of the cross sectional area and the length of
the masonry wall.
As a study a 10 story, 3 bay (30 ft) frame is considered, and the frame configuration is as
shown below. The frame without the brace is a moment frame and the frame fully braced
is a concentric braced frame. The frame with partial infill in-between column and beam
as shown below in figure4.7 is an eccentric frame.
49
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a) Moment frame.
Figure 4.7
b)Moment frame with shear wall/brace frame.
Figure 4.8. Concrete eccentric infill frame.
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As in the case of eccentric braced frame in steel frames, even in concrete in fill frames
lateral stiffness is primarily a function of the ratio of the link length.
As the link length becomes shorter, the frame becomes stiffer, approaching the
stiffness of a concentric braced frame. As the link becomes longer, the frame becomes
more flexible approaching the stiffness of a moment frame.
This is explained in the graph figure 4.9. The time period of moment frame is 1.2
seconds,
Where as the time period of the braced frame is .6 seconds again this is basically a
function of the amount of shear masonry wall present.
Technically, flexibility and stiffness determine the dynamic characteristics of the
frame. The frame with a with longer time period is flexible and the frame with a shorter
time period is stiffer.
DYNAM IC BEHAVIOUR OF CEIF
2
1 8
1 6
^ 4
5 12
3
a
U l
K
IL.
u3
Z
P
0 8
0 6
0 4
02
0
M F 60% 70% 50% 20% BF
FRAME TYPE
— TIM E P E R IO D “ • “ F R E Q U E N C Y
Figure 4.9. Frequency and time period o f ten stories eccentric infill frame for different eccentricity.
51
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4.7 DESIGN EXAMPLE FOR 10-STORY OFFICE BUILDING ADOPTING
DAMAGE CONTROL DESIGN APPORACH
The example building is an office building, 150ft by 90ft rectangular in plan with
6Nos, 3bay frames spaced at 30ft on center.
The building will be designed in accordance with the 1994 edition of the Uniform
Building Code. The building is located in seismic zone No.4.
•G'-O 3 0 '
/ / / /
*
iC -0 i C '- O " 30 - 0
/
i \
\ i
\ I
\ i
Figure 4. 10. Building framing plan
52
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The framing system is as show in figure 4.10. It has the CEIF's only in the
middle bay of the shorter direction on column line 1 and 6. Typical storey height is 15 ft.
Floor and roof are 3 inches metal deck with 3-1/4 inches lightweight (1 lOpcf) concrete
slab.
Material Specifications are:
Columns, beams: concrete fc =6ksi
Infill panel: reinforced masonary fc= 1.5 ksi
LOADS
Roof Loading:
Roofing and insulation 7.0 psf
Concrete floor/beams 100.0 psf
Ceiling and Mechanical 5.0
Dead load 112.0 psf
Live load (reducible) 20.0
Total Load 132.0 psf
Floor Loading:
Concrete floor/beams 100.0 psf
Ceiling and Mechanical 5.0
Partition 20.0
(The partition load could be reduced to 10 psf for lateral analysis)
Dead Load
Live Load (reducible)
Total Load
150.0 psf
Curtain wall:
53
125.0 psf
50.0 psf
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Average weight 15.0 psf
UBC static approach
Basic design equation:
V=(ZIC/Rw)W
Z : seismic zone factor
Z correlates with the effective peak acceleration in g
Z=.4
I: importance factor 1=1
C : ground motion amplification
Rw: Inelasticity & Ductility modification
For steel/concrete eccentric braced frame frame Rw is 10
Minimum value of C/Rw is .075
T: fundamental time period in seconds
T=Ct(h3/4)
H: height
Ct for steel moment resistant frame is .02
H H3/4 Ct T
150 42.86160 0.02 0.857232
C=1.25S/T2/3 Cmax =2.75
S: soil factor depends on the soil condition
1.25 S T T2/3 C
1.25 1.5 0.857232 0.9023997 2.077793
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C=2.07
Base shear coefficient
z I c Rw ZIC/Rw
0.4 1 2.077 10 0.08317
Length Width Area Unit load Total roof
load
No. of
floors
Total dead
load
150 90 13500 0.112 1512 1 1512
Length Width Area Unit load Total roof
load
No. of
floors
Total dead
load
150 90 13500 0.150 2025 9 18225
Base shear v= (18225+1512)*0.08= 1578 kips
Distributing the base shear to each level of the building
The total base shear is distributed over the height of the structure in accordance with the
following formulas
V= Ft +!Fi
Ft=0.07 V Ft concentrated force at top in addition to the force due to v Ft=l 10.46
Fx=((V-ft) *w*h)/ XW*h
Level Floor weight(w)
Floor height(h) w*h V-Ft Fx
Roof 1512 150 226800 1578 228.93+110
9 2025 135 273375 1578 275.94
8 2025 120 243000 1578 245.2
7 2025 105 212625 1578 214.62
6 2025 90 182250 1578 183.96
D 2025 75 151875 1578 153.30
4 2025 60 121500 1578 122.64
3 2025 45 91125 1578 91.98
2
2025 30 60750 1578 61.32
1 2025 15 30375 1578 30.66
IW*h= 1593675
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The 1992 uniform building code (U.B.C) triangular load (1/5 of the building load)
applied is representative of the first mode of response using a structure factor Rw=10
(eccentric braced frame).
A trial computer run by using software cosmos is made with 24x18 inches
concrete sections for columns 24x18 inches section for beams and 9" thick brick wall
half of the center bay for the initial run the frame time period and the drift are identified.
Now the influences of each of the infills on the story drift is isolated and quantified and
the stress level in this frame is also noted.The time period was identified to be
.7sec.(UBC value .83sec)
Figure 4.11. Concrete eccentric infill frame configuration.
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The infill panel is staggered to have a uniform bending profile which helps develop
unistress level in the frame, as well as members (columns, beams and infills) are sized for
these forces and the allowable drift criteria of UBC which is .05% of the height
POST YIELD BEHAVIOR OF THE CEIF (plastic deformation only in infill)
Sequential yield analysis
The static loading is increased by a ratio 5% until the first infill panel yields (all
the infill should yield simultaneously because of the uniform stress in frame). However
marginal variation in the eccentricity of the infill in each floor is made so that the top
floor infill pane! yields first and then follows to other lower floors ending with the last
bottom floor panel yield. Figure4.12
Figure 4.12. CEIF. first panel yield.
57
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The first panels, which is in the top storey yields by the formation of the plastic hinge.
Each of the plastic hinge is replaced in the panel by an analytical hinge (the panel is
removed).The procedure is repeated as each hinge formed in the next lower story panel
and this is repeated until all ten panels are replaced by an analytical hinge.
Figure 4.13. CEIF. after all the panel yield.
When all the infill panels have yielded (figure 4.13) the frame is reduced to a
flexible moment resistant frame. This flexible moment frame attracts less earthquake
force compared to an earlier stiff eccentric frame, because of the lengthening of the time
period of the frame from 0.84 sec to 1.1 sec. Further, lengthening is due to the secondary
58
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p-delta effect and in addition to this yielding, the infill absorbs energy and reduces the
total energy input to the frame.
FORCE REDUCTION CALCULATION
INITIAL FRAME BASESHEAR
V=1578
POST YIELD FRAME
BASESHEAR = ZI(C/Rw)(W)
C=1.25 S /TA 2/3
S = site factor 1.5 for medium soil
Rw- structure factor 12 eccentric braced frame
T=l.l sec
C= 1.25* 1.5/ .84779A .666
W = total weight 18225 kips
C=1.875/.879=2.09
V =( 0.4) (1)(2.09/12)*W
V= 1069.7 kips
There is a 36.66% reduction in the base shear and the damaged frame has to resist a base
shear of only 1069 kips. However the damage frame could resist a base shear of 2600
kips before the first beam yielded (failed). The drift associated with this base shear was
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11.2 inches which is 24% greater than that of the allowable drift criteria of the UBC. it
could resist the 1069.7 kip base shear with 4% excessive drift.
INELASTIC DEFORMATION: Due to plastic or inelastic deformation as in
this case. The yielding of infill masonry in the structure absorbs some of the earthquake
energy, so the forces in the yielded structure are less compared to the initial elastic
structure
Figure 4.12. CEIF. Before the first beam yield
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60
4.8 CONCLUSIONS
1) Damage control design is especially significant in concrete infill structures because of
the worldwide availability and acceptability of concrete/ masonry as a building material.
2) Infill masonry provides lateral stiffness and increases the load carrying capacity of
reinforced concrete structure.
3) The stiffness of the infill frame is higher than that of a concrete ffame.The larger
stiffness of the infill frame attracts larger earthquake loads. Therefore larger earthquake
loads should be accounted for in the design (Rw should be chosen between 8-10).
4) In an infill frame subjected to major ground shaking, the failure occurring in masonry
by crushing of brick, which leads to nonductile failure, is dangerous.
5) The behavior of infill frame is better than the conventional concrete frame in all
aspects expect ductility which is the main issue in earthquake resistant design.
6) Ductility of the infill frame can be improved by adopting the proposed CEIF.
7) In CEIF failure is made ductile by introducing a fuse in the form of link beams.
8) Damage in structure due to earthquake can be restricted to only certain elements by
both uses of material and effective structural systems. In the case of CEIF, masonry takes
up all the earthquake energy and goes into plastic range, while the concrete frame is
elastic throughout the earthquake.
9) Staggering the infill panels can easily achieve the uniform bending profile along the
height of the structure for lateral earthquake loading. This helps in the uniform
distribution of earthquake force, as earthquake forces are uneven over the height of the
building.
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10) The Damage Controlled design is a stiff structure for mild earthquakes and wind, but
in a major earthquake the structure becomes a flexible structure due to stiffness
degradation caused by failure of the infill walls.
11) The uniform bending profile, along the height of structure, achieved by staggering the
infill panels makes the stiffness degradation in a major earthquake consistent over the
entire height of the structure.
12) There is a 36.66% reduction in the base shear and the damaged frame has to resist a
base shear of only 1069 kips but the damage frame could resist a base shear of 2600 kips
before the first beam yielded (failed) but the drift associated with this base shear was 11.7
inches which is 30% greater than that of the allowable drift criteria of the UBC, it could
resist the 1069.7 kip base shear with 5% excessive drift
13)Base shear reduction due to yielding is 300-500% dependent on the No of cycles the
structure is subjected in an earthquake.
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62
LIST OF FIGURES
1.1 Northridge Earthquake Failure 2
1.2 Plan of Building 3
1.3 Japan code Rt values 6
1.4 C values 7
1.5 Base Shear Coefficient 8
1.6 Base Shear Comparison 9
1.7 Kobe Earthquake 9
2.1 Response of single degree of freedom system 12
2.2 Elastic and inelastic response 14
2.3 W14 Column 15
2.4 Ratio of Moment Of Inertia required for stiffness to Moment of Inertia 17
required for stress versus deflection
2.5 Tensile stress-strain curve for three ASTM-designation steel 21
2.6 Stress-strain curve for different grade concrete and masonry 22
3.1 Failure mechanisms for frame in two opposite directions leading to 24
identical conclusion
3.2 Example Frame 25
3.3 Frame stiffness for different link length/cross section area of the brace 26
3.4 a)Moment frame b) Braced frame 27
3.5 Eccentric Braced Frame 27
3.6 Time period of a 10 storey steel frame for different eccentricity 28
3.7 Shear distribution along the height of a 10 storey building 29
3.8 Damage control frame configuration 30
3.8 Brace encasing detail 31
3.9 Adopted in an eccentric frame 31
3.10 Building framing plan 32
3.11 Stress in members of VEBF 37
4.1 Infill panel interaction 43
4.2 Interaction between a frame and infill masonry 45
4.3 a) eccentric braced frame in steel b) Concrete eccentric infill frame 46
4.4 a) Shear distribution b) Eccentric frame with staggered infill 48
4.5 Steel eccentric frame behavior 48
4.6 Concrete Eccentric infill Frame behavior 49
4.7 a) Moment frame b) Moment frame with shear wall 50
4.8 Concrete eccentric infill frame 50
4.9 Frequency and time period of a 10 storey infill frame for different 51
eccentricity
4.10 Building framing plan 52
4.11 Concrete eccentric infill frame configuration 56
4.12 CEIF first panel yield 57
4.13 CEIF after all panel yield. 58
4.14 CEIF before the first beam yield 60
63
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GLOSSARY
Modulus of elasticity: Modulus of elasticity or Young’s modulus is the ratio of the stress
to the corresponding strain.
Moment of Inertia: The moment of inertia is the measure of the distribution of the mass
of an object relative to a given axis. The moment of inertia is also known as the second
moment of an area and expressed mathematically: Ixx = Sum of [A*y2] Where: Ixx =
the moment of inertia around the x axis, A = the area of the plane of the object y = the
distance between the centroid of the object and the x axis.
Centroid: The centroid or center of mass of an object is a point through which the
resultant of the force of gravitation act. The centroid is also its balance point.
Period of vibration: The time it trikes for an object in vibration to complete one
oscillation cycle. It is usually measured in seconds per cycle.
Richter Magnitude: The Richter magnitude scale was developed in 1935 by Charles F.
Richter as a mathematical device to compare the size of earthquakes. It is a quantitative
measure of the amount of energy released by of an earthquake. It is independent of the
place of observation.
Base Shear: When the ground under a structure moves in an earthquake, the mass of the
structure tends to resist the movement, due to which a shear force is developed between
the ground and the mass. This shear force is also called as Base Shear.
Epicenter: The geographical point on the surface of the earth vertically above the focus
that is the origin of the earthquake.
64
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P-Wave & S Wave: These are seismic waves generated during an earthquake. Primary
waves or P waves cause oscillation motion along the direction in which they travel. S
Waves or shear waves cause oscillatory motion at a right angle to the direction of travel.
Moment Diagram: A diagram that represents graphically the moment at every point
along the length of a member.
Section modulus: The physical property of a section, mathematically given by S=I/c
where 'I' is the moment of inertia of the cross-section about the neutral axis and 'c' is the
distance from the neutral axis to the outermost fibers.
Stiffness: It is the intrinsic property of the material or a system to resist deformation. It is
measured by the ratio of the applied force to the corresponding displacement.
Statically indeterminate: A member or structure that cannot be analyzed solely by the
equations of statics. It contains unknowns in excess of the number of equilibrium
equations available.
Euler formula: This is a formula developed by Leonhard Euler to determine the ultimate
load carrying capacity of long columns. Given by Pu= n2 EI/(kL) 2, Where Pu =ultimate
load,7t is a constant, E = Modulus of elasticity, 1= Least moment of Inertia, L= length of
column, k= constant which depends on the boundary condition of the column.
Kern: It is a zone within the cross section of the column where the vertical load could be
applied, without producing any tensile stress at the comers or at any part of the column
section.
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Ductility: The ability of a material to deform beyond the elastic limit is referred to as its
ductility. It is measured by the ratio of deformation at failure to the deformation at yield.
Moment resistant frame: They are a type of structural system in which the lateral load
resistance is derived from the bending stiffness of the rigid connection between columns
and beams.
Braced frames: Essentially a vertical truss system of the concentric or eccentric type that
is provided to resist lateral forces. The lateral load resistance is predominantly provided
by diagonal bracing elements.
Shear Wall: Structural walls in a building that behaves like a cantilever vertical beam to
resist lateral forces. Shear walls may be part of the peripheral wall or interior wall or can
be incorporated into the stair well or the elevator shaft.
P-A effect: The secondary effects on shear, axial force and moment of frame members
induced by the vertical forces on the lateral displaced building frame.
Damping: The property of the structure to absorb vibration energy.
Critical Damping: The minimum amount of viscous damping for which the system will
not vibrate.
Response Spectra: It is the plot of the maximum response (maximum displacement,
velocity, and acceleration) or any other quantity of interest versus the natural frequency
or period of a system subjected to an earthquake excitation.
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REFERENCES
Anil K.C. (1996) Dynamics of Structures; Theory and Applications to Earthquake
Engineering, Prentice Hall, NJ
AISC, Manual of Steel Construction. Allowable Stress Design, 1991, AISC, Chicago
A m brose J, Dimitry V, (1985) Seism ic Design o f Buildings, John W iley & Sons.
Astley R.J,(1992) Finite Elements in Solids and Structures an Introduction, Chapman and
Hall.
Bungale S.T(1988) Structural Analysis and Design of Tall Buildings. McGraw-Hill, NY
Beadle L S,(1983) Developments in tall buildings, Hutchinson Ross Publisher.
Baker N. C, Goodno B J.( 1994) Proceeding Structures Congress XII, American Society
of Civil Engineers.
Charles G. S., John E. J(1996) Steel Structures Design and Behavior, Harper Collins
publishers Inc.
Dowrick,(1988) Earthquake Resistant Design, John Wiley & Sons.
Englekirk R E.,(1994) Steel Structures Controlling Behavior Through Design, John
Wiley & Sons.
Farzad N (1989) The Seismic Design Hand Book,Von Nostrand Reinhold.
First World Conference on Structural Controls, August 3, 1994 Proceedings, Los
Angeles, CA.
Ferguson P.M., Breen J.E , Jirs J 0 ,( 1988) R einforced Concrete Fundam entals, John W iley &
Sons.
Green N.B,(1978) Earthquake Resistant Design and Construction, Von Nostrand
Reinhold.
Housner G.W, Masri S.F.( October 1990) Proceeding of the U.S National work shop on
Structural Control Research,
Jeroma J. C ,Burtos. S. A. K (1996) Introduction to Motion Based Design-Computational
Mechanics Publication Southampton U.K. & Boston U.S.A.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M acgregor J.G.( 1992). R einforced concrete M echanics and Design, Prentice Hall Inc.
Meyer C.(1996) Design of Concrete Structures, Prentice Hall Inc.
PC A, Notes on ACI 318-89. Building Code Requirements for Reinforced Concrete, with
Design Applications, 1990, PC A
Popov E.P.(1968) Introduction to Solid Mechanics, Prentice Hall Inc.
Paz M.(1990) Structural Dynamics Theory and Computation,Von Nostrand Reinhold.
Schinderdes R.R.( 1980) Walter L Dickey, Reinforced Masonry Design, Prentice Hall
Inc.
Schierle,G. G.(1994) Computer Aided Seismic Design Journal of Architecture and
Planning Research (Seidel A. D.), Loake Science Publication.
SMIP96(1996)Seminar on Seismological and Engineering Implications Strong-Motion
Data, Proceedings, May 14, Sacramento, CA
W right J K (Editor)(1985) E arthquake Effects on Reinforced C oncrete Structures U S-Japan
Research A m erican C oncrete Institute.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
68
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lIV M GE.Inc
1653 East Main Street
Rochester, NY 14609 USA
Phone: 716/482-0300
Fax: 716/288-5989
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Asset Metadata
Creator Gowda, Bharath Narasimhe (author) 
Core Title Eccentric braced frames: A new approach in steel and concrete 
School School of Architecture 
Degree Master of Building Science / Master in Biomedical Sciences 
Degree Program Building Science 
Publisher University of Southern California (original), University of Southern California. Libraries (digital) 
Tag Architecture,engineering, civil,OAI-PMH Harvest 
Language English
Contributor Digitized by ProQuest (provenance) 
Advisor Schierle, G. Goetz (committee chair), Koenig, Pierre (committee member), Schiler, Marc E. (committee member) 
Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-23138
Unique identifier UC11342270 
Identifier 1391086.pdf (filename),usctheses-c16-23138 (legacy record id) 
Legacy Identifier 1391086.pdf 
Dmrecord 23138 
Document Type Thesis 
Rights Gowda, Bharath Narasimhe 
Type texts
Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection) 
Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au... 
Repository Name University of Southern California Digital Library
Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA
Tags
engineering, civil