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CHAPTER 1
Introduction
1.1 General:
Steel Concentrically Braced Frame (CBF) is commonly used
structural system
(Figure 1.1), developed for resisting forces and deformations
induced by severe
earthquake ground motions and wind loads. This system offers
significant energy
dissipation, ductility, moderate initial stiffness, which render
it an efficient lateral load
resisting system. Concentrically braced frames are defined as
those where the centre lines
of all intersecting members meet at a point as shown in Fig.1.1.
This traditional form of
bracing is widely used for all kinds of construction such as
towers, bridges, and buildings,
creating stiffness with great economy of materials in two
dimensional space frames.
1.1.1 Advantages of using Steel Concentrically Braced Frame
(CBF)
Following are advantages of using CBF as a lateral load
resisting system in
comparison with traditional lateral load resisting systems:
1. Due to light weight of CBF, it reduces the seismic loads
which are directly
proportional to the mass of the structure.
2. From architectural point of view, CBF increases versatility
and space savings
because of the smaller cross section as compared to reinforced
concrete section.
3. By using hot rolled Steel section, high quality control is
achieved and speed of
construction is faster as compared to reinforced concrete
structure.
4. Lateral loading on a building is reversible, braces thus will
be subjected in turn to
both tension and compression, and consequently, they are usually
designed for the
more stringent case of compression.
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1.1.2 Limitations of Steel Concentrically Braced Frame Systems
(CBF)
Following are limitations associated with CBF as a lateral load
resisting system:
1. CBF systems are usually more flexible in comparison to
traditional lateral load
resisting systems.
2. As compared to other reinforced concrete structure, CBF
increases its vulnerability
to fire hazards.
3. The inability to provide reversible inelastic deformation is
the principal
disadvantage of CBF.
4. Ordinary concentrically braced frames are not allowed in
Seismic zones IV and V
and for buildings with an importance factor greater than unity
(I > 1.0) in zone III.
5. K bracing is not permitted in earthquake zones by the code.
The inelastic
deformation and buckling of K bracing members may produce
lateral deflection of
the connected columns, causing collapse.
1.1.3 Design provisions:
Current code-based seismic design provisions, IS 1893 Part1:
Criteria for Earthquake
Resistant Design of Structures, Part 1: General Provisions and
Buildings (Fifth Revision
2002) & AISC Seismic Provision for Structural Steel
Buildings, (ASCE7 2005) adopts
elastic force/strength-based approach and implicitly accounts
for inelastic behavior of
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3
structural system through a response reduction factor R.
Generally for ductile design, the
code-based provision adopted value of R for Steel CBF is between
3-4.
1.1.4. The performance-based seismic design (PBSD):
The performance-based seismic design (PBSD) method is a more
general, reliable
and efficient method which explicitly considers the inelastic
behavior of a lateral load
resisting system. The Performance Based Plastic Design (PBPD), a
displacement-based
approach of PBSD. It is based on a target displacement ductility
ratio and pre-selected
yield mechanism and it uses plastic analysis and design
provisions. This approach was
proposed by Chao and Goel (2006).
1.2 Objectives:
Limitations of code-based design method
1. No consideration of inelastic response:
The current seismic design codes for lateral load resisting
systems are still not
based on proper inelastic design methodology. As a result, the
significant inelastic
displacement capacity of these systems cannot be fully explored.
Elastic design
methodology applied on Steel CBF does not recognize the
redistribution of moments in
the inelastic range.
2. Unpredictable failure:
The design procedures do not always lead to the intended failure
mode and the
expected ductility under severe ground motions
3. Insufficient energy dissipation capacity:
The energy dissipation capacity of structure designed by current
seismic code
procedure can be less than that required for preventing collapse
under severe ground
motion.
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Performance Based Plastic Design (PBPD) is an emerging seismic
design method for
next generation. It is of upmost importance to evaluate or to
check the advantage of PBPD
over traditional code based method through a design case study.
Hence following
objectives are considered for this study:
1. Design a four storey Steel CBF for high seismicity by using
force/strength based
approach of current Indian design standard IS: 1893-2002 (BIS:
2002).
2. Obtaining similar design by using displacement base approach
of recent PBPD
method proposed by Chao and Goel (2001).
3. Comparing design as well as their seismic performance through
nonlinear static
push over analysis (NSPA).
1.3 Scope of the project:
A four storey Steel CBF under high seismic condition is
considered for seismic
design. Due to lack of high capacity/strength of Indian standard
hot rolled Steel
sections (SP:6(1)-1964), American Institute of Steel
Construction standard
sections (AISC 2005b) with high strength Steel (fy=345Mpa) have
been use for
this study.
1.4 Outline of the Project:
The project outline is shown on the next page in the form of
flowchart
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Chapter 1 deals with Introduction, advantages of Steel CBF,
limitations of code based
design provisions for Steel CBF, objectives, scope of project
and outline of report.
Chapter 2 deals with literature review of force/strength based
and displacement-based
approach of seismic design for Steel CBF.
Chapter 3 deals with design of a four storey Steel CBF for high
seismicity by using
force/strength based approach of current Indian design standard
IS: 1893-2002 (BIS:
2002).
Comparison of strength based & displacement
based seismic design of steel concentrically braced
frames
Chapter 1: Introduction
Chapter 2: Literature Review
Chapter 3: Strength Based Design
Chapter 4: Displacement Based
Design
Chapter 5: Comparison between
strength and displacement based
design
Chapter 6 : Findings of study &
Conclusions
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Chapter 4 deals with design of a four storey Steel CBF for high
seismicity by using
displacement base approach of recent PBPD method proposed by
Chao and Goel
(2001).
Chapter 5 deals with comparing with design as well as their
seismic performance
through nonlinear static push over analysis (NSPA).
Chapter 6 deals with findings of study, conclusions, thrust
areas and recommendations
derived from this study.
(a)
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(b)
Figure 1.1: Steel CBF used as a structural system
Concentric Braced Frame
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CHAPTER 2
A Review of Seismic Design of Steel Concentrically Braced
Frames
And Related Research
2.1 Introduction
The design procedures for regular structures specified in the
current seismic codes,
such as IS 1893 PART 1 :2000, are mainly based on elastic
analyses under seismic
horizontal forces (Equivalent Lateral Force Procedure), without
attempting to predict the
inelastic response. These procedures offer considerable
simplification and do not require
the designer to use the understanding of structural dynamics.
The structures designed by
these procedures may possess sufficient strength and stiffness
to satisfy the requirements
of serviceability limit state. However, the design procedures do
not always lead to the
intended failure mode and the expected ductility under severe
ground motions. The
energy dissipation capacity of the structure designed by these
procedures can be less than
that required to prevent collapse under severe ground motions.
Therefore, alternative
design procedure based on inelastic structural analysis and the
plastic design should be
adopted for the ultimate limit state.
This chapter begins with reviewing and discussing the current
seismic design
codes and provisions for steel concentrically braced frames.
After that, related past studies
that addressed the problems of current code procedures or
proposed new design methods
based on inelastic analysis and plastic design concepts are also
reviewed and discussed.
2.2 EQUIVALENT LATERAL BASE SHEAR FORCE PROCEDURE
The characteristics parameters like intensity, duration etc. of
seismic ground
vibrations depend upon the magnitude of the earthquake ,its
depth of focus , distance from
the epicenter, properties of soil of medium through which the
seismic waves travel and
the soil strata where the structure stands. The random
earthquake motions can be resolved
in any directions. Vertical acceleration is considered in large
span structures.
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The response of a structure to ground vibrations depends on the
nature of
foundation soil, form, material, size and mode of constructions
of structures and the
duration and characteristics of ground motion.
2.2.1 Assumptions
The following are the assumptions in the earthquake resistant
design of structures:
1. Impulsive ground motions of earthquake are complex, irregular
in character,
changing in period and time and of short durations, they,
therefore, may not cause
resonance as visualized under steady state sinusoidal
excitations, except in tall
structures founded on deep soft soils.
2. Wind, maximum flood or maximum sea waves will not occur
simultaneously with
the earthquake.
3. For static analysis, elastic modulus of materials shall be
taken unless otherwise
mentioned.
2.2.2 DESIGN LATERAL FORCES
Design Horizontal seismic coefficient
The design horizontal seismic coefficients Ah (cl.6.4.2 of IS
1893 (Part 1): 2000) for
structure is determined from
Ah = .. (2.1)
Where;
Z = the zone factor as given Table 2 of IS 1893 (Part 1):2002,
based on classifying the
country in four seismic zones,
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I= Importance factor, depending upon functional use of the
structures as given in Table 6
of IS 1893 (part 1) :2002,
R= Response reductions factor, depending on the perceived
seismic damage, performance
of the structures, characterized by ductile or brittle
deformations, as given in Table 7 of IS
1893 (Part 1):2002.However, the value of (I/R) shall not be
greater than 1.0, and
S/g= Average response acceleration coefficient for rock or soil
sites as given Fig.2 and
Table 3 of IS 1893 (part 1) :2002.
It is further stipulated in cl.6.4.2 of IS 1893 (part 1) :2002,
that for any structure with
undamped natural period of vibrations of the structure (in
seconds) T 0.1 second, the
value of Ah will not be taken less than Z/2 whatever be the
value of I/R.
2.2.3 DESIGN SEISMIC BASE SHEAR
The total design lateral force or design seismic base shear VB
along any principal
direction (cl.7.5.3 of IS 1893 (part 1):2002) shall be
determined from the following
equations:
VB = Ah W (2.2)
Where;
W is the seismic weight of the building as given in cl.7.4.2 of
IS 1893 (Part 1):2002.
2.2.3.1 Distribution of design force
The design base shear VB shall be distributed along the height
of the building as per the
following equation (cl.7.7 of IS 1893 (Part 1):2002)
Qi = (2.3)
Where;
Qi = design lateral force at floor i,
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Wi = Seismic weight of floor i,
Hi = Height of floor I measured from base, and
n = Number of storeys in the building at which the masses are
located
2.3 REVIEW OF RELATED RESEARCH ON CONCENTRICALLY BRACED
FRAMES
The design of concentrically bracings may be found in Becker
(1995), Becker and
Ishler (1996), Bruneau et al. (1997), Bozorgnia and Bertero
(2004), and Williams (2004).
Thus, many studies have been carried out to investigate and
revise the design procedures
currently used in seismic codes or to develop new design
procedures for the
concentrically braced frames.
Concentrically Braced Frames (CBFs) are very efficient steel
structures that are
commonly used to resist forces due to wind or earthquakes
because they provide complete
truss action.
Based on research performed during last the last twenty years or
so (for example,
Goel, 1992a), current seismic codes such as (ANSI, 2005a) now
include provisions to
design ductile concentrically braced frames called Special
Concentrically Braced Frames
(SCBFs). Since the seismic forces are assumed to be entirely
resisted by means of truss
action , the columns are designed based on axial load demand
only, and simple shear
connections are used to join the beams and columns (Tremblay and
Robert,2000; Mac
Rae et al., 2004; ANSI, 2005c). It has been estimated that CBFs
comprise about 40
percent of the newly built commercial constructions in the last
decade in California
(Uriz,2005).This is attributed to the simpler design and high
efficiency of CBFs compared
to other systems such as moment frames, especially after the
1994 Northridge earthquake.
Mac Rae has proposed the Steel concentrically braced frames are
generally
designed to resist lateral force by means of truss action.
Design considerations for
columns in these frames are therefore governed by the column
axial force while column
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bending moment demands are generally ignored. However, if the
columns cannot carry
moments, then dynamic inelastic time-historey analyses show that
a soft-storey
mechanism is likely to occur causing large concentrated
deformations in only one storey.
Such large concentrations of damage are not generally seen in
real frames since columns
are generally continuous and they possess some flexural
stiffness and strength. This paper
develops relationships for column stiffness and drift
concentration within a frame based
on pushover and dynamic analyses. It is shown that continuous
seismic and gravity
columns in a structure significantly decrease the possibility of
large drift concentrations.
An assessment method and example to determine the required
column stiffness necessary
to limit the concentration of storey drift is provided.
R.G. Redwood, V.S. Channagiri studied that new provisions of the
CSA standard
for steel structures (CAN/CSA-S16.1-M89) dealing with detailing
of concentrically
braced frames for seismic design are described and related to
requirements of the National
Building Code of Canada. The basis of the new requirements is
outlined, and an example
eight-storey frame is used to outline a methodology for the
design process for a ductile
braced frame and to illustrate the impact of the provisions.
Tremblay, R. And N.Robert.2000 suggested that Single-storey
buildings typically
incorporate a steel roof deck diaphragm that is relied on to
transfer lateral loads to the
vertical bracing bents. Modern building codes allow engineers to
use reduced seismic
loads in design provided that the seismic load resisting system
(SLRS) of the structure is
adequately designed and detailed to withstand strong ground
shaking through ductile
response. This approach has been adopted by the North American
model codes which
typically include special provisions to achieve satisfactory
inelastic seismic performance.
The vertical braces of steel buildings are usually selected as
the energy dissipating fuse
element, while the diaphragm and other elements in the SLRS
should be designed to have
a capacity that exceeds the nominal resistance of the braces.
Steel bracing members
designed for compression inherently possess significant reserve
strength when loaded in
tension, which means that large brace tension loads must be
considered in the design of
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the surrounding protected structural components. Capacity design
seismic provisions have
led to the need for much thicker roof deck panels and more
closely spaced diaphragm
connection patterns compared with past practice. This paper
provides a description of the
current US seismic design approach and an example as it is
applied to a single-storey
building and its diaphragm. An overview of the related aspects
of an on-going research
project on the flexibility and ductility of the roof diaphragm
in low-rise steel buildings is
also included.
Shaback, B and T.Brown.2003 deduced that the hysteretic behavior
of nine square
hollow structural steel (HSS) sections with gusset plate end
connections subject to
inelastic cyclic loading has been examined by an experimental
investigation.
2.3.1NHRP Seismic Design Salient Feature On CBFs
The configuration of braces also affects system performance.
Multiple
configurations of bracing are used, and these configurations are
identified in Figure 2.1.
Braces buckle in compression and yield in tension. The initial
compressive buckling
capacity is smaller than the tensile yield force, and for
subsequent buckling cycles, the
buckling capacity is further reduced by the prior inelastic
excursion. Therefore, bracing
systems must be balanced so that the lateral resistance in
tension and compression is
similar in both directions. This means that diagonal bracing
(Figure 2.1) must be used in
matched tensile and compressive pairs. As a result, diagonal
Fig: 2.1 Various Braced Frames Systems
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bracing (Figure 2.1) must be used in opposing pairs to achieve
this required balance.
Other bracing configurations, such as the X-brace, multi-storey
X-brace and chevron
brace directly achieve this balance. X-bracing is most commonly
used with light bracing
on shorter structures. Research shows that the buckling capacity
of X-bracing is best
estimated by using one half the brace length when the braces
intersect and connect at mid
section (Palmer 2012). However, the inelastic deformation
capacity of the X-braced
system is somewhat reduced from that achievable with many other
braced frame systems
because the inelastic deformation is concentrated in one-half
the brace length because the
other half of the brace cannot fully develop its capacity as the
more damaged half
deteriorates. The compressive buckling resistance of most other
brace configurations is
best estimated by considering true end-to-end length of the
brace with an effective length
factor, K, of 1.0 (i.e., neglecting rotation stiffness of the
brace-to-gusset connection.)
Concentration of inelastic deformation in a limited number of
stories occurs with
braced frames. Experiments suggest that multi-storey X-bracing
offers a slight advantage
in that it provides a somewhat more robust path for transferring
storey shear to adjacent
stories even after brace buckling and fracture because the
remaining tension brace may
directly transfer its force to the next storey. Chevron or
inverted-chevron bracing
(inverted V- or V-bracing) has intersecting brace connections at
mid span of the beam
(Figure 2.1). Large unbalanced forces and bending moments on the
beam occur because
the buckling load is smaller than the tensile yield resistance
and decreases with increasing
damage. The bending moment increases as the compressive
resistance deteriorates and
AISC 341 requires that the beam be designed for these bending
moments. Research shows
that the beam deformation associated with the unbalanced forces
in chevron bracing
increases the axial compressive deformation of the brace and
reduces the inelastic
deformation capacity prior to brace fracture (Okazaki et al.
2012). However, flexural
yielding of the beam increases the damping of dynamic
response.
Other bracing configurations are possible, and some are
expressly prohibited in
AISC 341. K-braces intersect at mid-height of the column. They
have the same
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unbalanced force problem as noted with chevron bracing, but
bending moments and
inelastic deformation will occur in the column and may fail,
triggering collapse. As a
result, K-bracing is not permitted for the SCBF system. In
addition, tension-only bracing
has had relatively poor performance during past earthquakes
because the lack of
compressive brace resistance leads to inelastic behavior with
slack braces that have no
stiffness until the slack is taken up. The slack braces may lead
to progressively increasing
drift and impact loading on the brace, and early brace fracture
may occur. Consequently,
tension-only bracing is also prohibited for the SCBF system.
2.4 Performance Based Plastic Design (PBPD) Method
In order to achieve more predictable structural performance
under strong
earthquake ground motions, knowledge of the ultimate structural
behavior such as
nonlinear relationship between force and deformation and the
yield mechanism of the
structure are essential. Consequently, design factor such as
determination of appropriate
design lateral forces and member strength hierarchy, selection
of desirable yield
mechanism, and structure strength & drift for a given hazard
levels should become part of
the design process from the beginning .
The PBPD method uses pre-selected target drift and yield
mechanisms as key
performance limit states. These two limit states are directly
related to the degree and
distribution of structural damage, respectively. The design base
shear for a specified
hazard level is calculated by equating the work needed to push
the structure
monotonically up to the target drift to the energy required by
an equivalent elastic -
Plastic Single Degree of Freedom (EP-SDOF) system to achieve the
same state (Fig
2.2). Also, a new distribution of lateral design forces is used
(Chao et al, 2007), which is
based on relative distribution of maximum storey shears
consistent with inelastic dynamic
response result. Plastic design is then performed to detail the
frame members and
connections in order to achieve the intended yield mechanism
& behavior.
.
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Fig. 2.2: PBPD Design Lateral Force
In this design approach the designer selects the target
displacements & yield
mechanism & determines the design forces and members sizes
for a given a earthquake.
There is no need factor such as R, I & Cd as are required in
the current design course and
over which debate already exists. The PBPD design procedures is
not to different from
what is done in current practices, yet it can be readily
incorporated within the context of
border Performance Bases Earthquake Engineering (PBEE) frame
work. It does differ
from the way PBEE is practiced currently which usually starts
with an initial design
according to conventional elastic design procedures using
applicable design codes,
allowed by a cumbersome and time consuming iterative assessment
process by using
inelastic static or dynamic analyses until the desired
performance objectives are met. The
iteration are carried out in a purely trail & error manner.
No guidance is provided to the
designer as to how to achieve the desired goals such as
controlling drifts or the
distributions and extent of inelastic deformation. In contrast,
the PBPD method is a direct
design method, which required no evaluation after the initial
design because the nonlinear
behavior and key performance criteria are built into the design
process from the start. The
design procedure is easy to follow it can be easily programmed
as well. Al though not
necessary, structures designed by PBPD could be evaluated by
other evaluation methods
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if desired. In cases where significant structural irregularities
are present, the method will
provide a good initial design, which may require some refinement
through nonlinear static
or dynamic analysis.
PBPD application to concentrically braced frames with degrading
hysteretic
behavior due to brace buckling is currently being developed. The
results thus far have
been most encouraging
Fig. 2.3: Typical Hysteretic responses for CBF
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CHAPTER 3
Design of a Four Storey Steel CBF for High Seismicity by using
Force/Strength
Based
Approach of Current Indian Design Standard IS: 1893-2002 (BIS,
2002)
3.1 Introduction
Seismic designs of structure are based on force/strength based
approach used
today and the IS: 1893 (Part I), 2002 code is based on this
approach. Seismic designs of
most of the structure are on the basis of lateral force assumed
to be equivalent to the
actual loading. It is based on providing the structure with a
minimum lateral strength to
resist seismic loads, assuming that the structure will behave
adequately in the non-linear
range. The base shear which is the total horizontal force on the
structure is calculated on
the basis of structure mass and fundamental period of vibration
and corresponding mode
shape. The base shear is distributed along the height of
structure in terms of lateral forces
according to code formula. Only some simple constructional
detail rules are to be satisfied
as material ductility, member slenderness, etc. This method is
usually conservative for
low to medium height buildings with a regular conformation.
Steel CBF is designed as per the IS 800:2007 along with IS 1893
(Part 1):2002 for
site and geometric configurations. In this chapter we formulate
the problem and design it
as per the strength based method and obtain the section. For
analysis we use ABAQUS
finite element software.
3.2 Case Study
A design case study of 4-storey frames in a study building
located in high seismic
zone (Zone V as per IS: 1893-Part-I 2000) for soft soil
condition with Maximum
Considered Earthquake (MCE) is considered for the following
geometric configurations.
The plan and elevation of this CBF is shown in Figure 3.1.
-
Figure 3.1: Plan and elevation of four
Given Data:
Elastic response spectra
Damping factor
Site condition
Material property
Selected study frame for code
19
Figure 3.1: Plan and elevation of four-storey CBF study
building
Elastic response spectra : IS: 1893 (Part 1) 2002.
Damping factor : 5%
: Soft soil
Material property : Fe 345 steel with elastic perfectly
plastic
stress strain relationship
Selected study frame for code-based and displacement-based
seismic design
storey CBF study building
IS: 1893 (Part 1) 2002.
Fe 345 steel with elastic perfectly plastic
stress strain relationship
based seismic design
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20
Hot rolled steel section : From AISC standard. (AISC, 2005b)
Table 3.1 Floor wise seismic weight for study building
Floor Level i Floor Height (m) Seismic Weight (kN)
4th
4.0 5000
3rd
4.0 5000
2nd
4.0 5000
1st 4.0 5000
Design:
Design of steel concentrically braced frame along X-X
direction,
There are two set of steel CBF in X-X direction as lateral load
resisting systems for
earthquake in X-direction.
Thus, seismic weight is distributed equally on each set and
floor wise seismic weight
on each set of steel CBF is as per Table 3.2
-
Total seismic weight, W = 2
Fundamental time period
Total height of building = 16 m
Calculation of Design base shear,
Zone factor Z, is not considered for
Importance factor,
Response reduction factor,
Spectral acceleration,
Figure 3.2: Calculation of
Therefore,
21
Total seismic weight, W = 20000 kN
Fundamental time period for Steel CBF and for soft soil
condition is,
Total height of building = 16 m
s
Calculation of Design base shear,
Ah =
is not considered for Maximum Considered Earthquake (MCE
Importance factor,
ion factor,
Spectral acceleration,
= 2.50
Figure 3.2: Calculation of Sa/g from elastic response spectra of
IS: 1893
condition is,
Maximum Considered Earthquake (MCE ),
from elastic response spectra of IS: 1893-PartI-2002
-
Design base shear,
Table 3.2 Storey
Floor Level
4th
3rd
2nd
1st
3.3 Design of frame components
Code based design method is an iterative procedure which do not
provide design
equation for individual components of Steel CBF. Initial section
for column and beam of
CBF are selected from AISC stee
sections, CBF is modeled using B31 (3 dimensional beam element)
in ABAQUS 6.9
(ABAQUS, 2009) which is general purpose Finite Element Software.
The design is
optimized by elastic analysis of this fram
in Table 3.2), such that demand to capacity ratio is near to
unity.
22
Table 3.2 Storey-wise Lateral Distribution of Design Base
Shear
(kN) (m)
5000 16 1280000 0.534
5000 12 720000 0.30
5000 8 320000 0.133
5000 4 80000 0.033
=2400000 =1.0
3.3 Design of frame components
Code based design method is an iterative procedure which do not
provide design
equation for individual components of Steel CBF. Initial section
for column and beam of
CBF are selected from AISC steel sections by trial and error
method. With these initial
sections, CBF is modeled using B31 (3 dimensional beam element)
in ABAQUS 6.9
(ABAQUS, 2009) which is general purpose Finite Element Software.
The design is
optimized by elastic analysis of this frame under equivalent
static lateral load (as obtained
in Table 3.2), such that demand to capacity ratio is near to
unity.
(cl. 9.3.1.1, IS 800:2007)
gn Base Shear
(kN)
6675
3750
1662.5
412.5
=12500
Code based design method is an iterative procedure which do not
provide design
equation for individual components of Steel CBF. Initial section
for column and beam of
l sections by trial and error method. With these initial
sections, CBF is modeled using B31 (3 dimensional beam element)
in ABAQUS 6.9
(ABAQUS, 2009) which is general purpose Finite Element Software.
The design is
e under equivalent static lateral load (as obtained
(cl. 9.3.1.1, IS 800:2007)
-
Fig: 3.2 Details of beam, column and brace analyzed by code
Table 3.3: Cross Sections of Beam, Column & Brace
23
Fig: 3.2 Details of beam, column and brace analyzed by code
Table 3.3: Cross Sections of Beam, Column & Brace
Fig: 3.2 Details of beam, column and brace analyzed by
code-based method.
Table 3.3: Cross Sections of Beam, Column & Brace
W36X441
(BEAM)
W36X800
(COLUMN)
HSS 16X16X0.625
(RECTANGULAR
BRACE)
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24
Table 3.4: Sectional Properties of Beam, Column & Brace
AISC
SECTION
Ax
(in2)
D
(in)
Bf
(in)
Tf
(in)
Tw
(in)
Iz
(in4)
Ix
(in4)
Iy
(in4)
Zx
(in3)
Zy
(in3)
W36X441 130 38.90 17 2.44 1.36 32100 194 1990 1990 368
W36X800 236 42.60 18 4.29 2.38 64700 1060 4200 3650 743
HSS
16X16X0.625
35 16 - 0.58 - 1370 2170 1370 200 200
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CHAPTER 4
Design of a four storey Steel CBF for high seismicity by using
displacement based
approach of PBPD method
4.1 Introduction
It is desirable to design structures so that they behave in a
predictable manner.
This can be achieved by allowing for the formation of a
preselected desirable yield
mechanism so that the structure has adequate strength and
ductility during design level
ground motions. The preselected yield mechanism can be defined
as a strong column
weak beam mechanism to prevent formation of collapse mechanisms
with poor energy
dissipation capacity for the structure. However, elastic design
procedures used in current
seismic code cannot guarantee to design the structure with a
desirable mechanism and to
predict the predominantly inelastic nature of the structure
response during severe
earthquakes. Therefore, use of plastic theory in seismic design
procedure, especially in
performance-based design, is necessary to avoid undesired
collapse mechanisms.
Many experimental and analytical studies have been carried out
in the past to
investigate the validity of the distribution of lateral forces
prescribed by various seismic
design codes, particularly the IS 1893-Part1 Criteria for
Earthquake Resistant Design of
Structures, Part 1: General Provisions and Buildings (BIS,2002).
For simplicity of the
design procedure, a linear distribution of the equivalent
lateral forces has been generally
used in code. However, many studies have shown that this
distribution may not be valid in
the inelastic state and may underestimate the storey shears.
Since the performance-based plastic design procedure is
primarily based on
inelastic state is used.
-
Fig 4.1: Target Yield Mechanism of CBF with Chevron Bracing
A design case study of 4
condition and maximum selected earthquake is considered.
4.2 Case Study
For target ductility ratio,
Using elastic response spectra in IS: 1893 (Part 1) 2002.
Damping factor = 5%
Site condition = Soft soil
Material property Fe 3
Hot rolled steel section used from AISC standard.
Fundamental Time Period:
Equivalent fundamental time period of inelastic structure
26
Fig 4.1: Target Yield Mechanism of CBF with Chevron Bracing
A design case study of 4-storey frames as same as in chapter 3,
under the soft so
condition and maximum selected earthquake is considered.
For target ductility ratio, t = 4.0
Using elastic response spectra in IS: 1893 (Part 1) 2002.
= 5%
Site condition = Soft soil
Fe 345 steel with elastic perfectly plastic stress strain
relationship
Hot rolled steel section used from AISC standard.
Fundamental Time Period:
Equivalent fundamental time period of inelastic structure ,
Fig 4.1: Target Yield Mechanism of CBF with Chevron Bracing
frames as same as in chapter 3, under the soft soil
45 steel with elastic perfectly plastic stress strain
relationship
-
Where,
= Fundamental time period of linear elastic structure = 0.1 X No
of storey = 0.4 sec
t = Displacement ductility ratio
= Strain hardening ratio = 0
The average response acceleration coefficient
Ductility reduction factor
Ductility reduction factor
Energy modification factor
Yield drift and Plastic drift
27
Fundamental time period of linear elastic structure = 0.1 X No
of storey = 0.4 sec
= Displacement ductility ratio
= Strain hardening ratio = 0
The average response acceleration coefficient Sa/g for and
Sa/g = 1.25
Ductility reduction factor , Energy modification factor
Ductility reduction factor ,
Energy modification factor ,
2 1 0.44
Plastic drift
Fundamental time period of linear elastic structure = 0.1 X No
of storey = 0.4 sec
= 5%
-
For steel moment resisting frames, the yield drift
Assume, = 0.09% = 0.0
Evaluation of Seismic Lateral Force Distr
Table 4.1 Evaluation of Seismic Lateral Force Distribution
Floor Level
4th
3rd
2nd
1st
28
For steel moment resisting frames, the yield drift assumed to be
between
% = 0.009
4 1 $%0.009 $% 0.027 Evaluation of Seismic Lateral Force
Distribution
Table 4.1 Evaluation of Seismic Lateral Force Distribution
(KN)
5000 16 1280000 0.534
5000 12 720000 0.30
5000 8 320000 0.133
5000 4 80000 0.033
=2400000 =1.0
assumed to be between 0.6% to 1%
Table 4.1 Evaluation of Seismic Lateral Force Distribution
8.544
3.600
1.064
0.132
=13.34
-
Calculation of yield base shear
Shear Proportioning Factor
A PBPD method based on inelastic state uses a new term named
shear
proportioning factor derived from the concept of the relative
distributions is defi
Where, i is the static storey
Vn is the static
distribution shape of the first mode of vibration
Assuming an inve
to derive the static storey
Where, is the lateral force distribution factor,
Where,
wi is the weight of the structure at level
hi is the height of beam level
29
Calculation of yield base shear Vby
=
Shear Proportioning Factor
A PBPD method based on inelastic state uses a new term named
shear
proportioning factor derived from the concept of the relative
distributions is defi
storey shears at level i,
is the static storey shears at the top level computed from the
linear lateral force
distribution shape of the first mode of vibration and the
exponent b
Assuming an inverted triangular force distribution along the
height of the structure
storey shears, the lateral force at level i can be expressed
as:
is the lateral force distribution factor, is the total base
shea
the weight of the structure at level i
the height of beam level i from the ground,
A PBPD method based on inelastic state uses a new term named
shear
proportioning factor derived from the concept of the relative
distributions is defined as:
shears at the top level computed from the linear lateral
force
b is a numerical factor.
rted triangular force distribution along the height of the
structure
can be expressed as:
is the total base shear.
-
VB is the design base shear.
The equation of Vi and
The shear proportioning factor
based plastic design procedure. The factor is directly related
to the
and stiffness along the height of the structure. It also
represents the variation of
drifts along the height. Therefore, the factor can be
distribution based on inelastic state and to design beams of the
structure.
Using the shear proportioning factor, the lateral forces,
the top level n can be written as
Where and i+1 are the shear proportioning factors at level
30
is the design base shear.
Vn put in equation of i
The shear proportioning factor i, plays an important role in
based plastic design procedure. The factor is directly related
to the
and stiffness along the height of the structure. It also
represents the variation of
drifts along the height. Therefore, the factor can be used to
derive a lateral force
distribution based on inelastic state and to design beams of the
structure.
Using the shear proportioning factor, the lateral forces,fi and
fn, applied at level
can be written as
are the shear proportioning factors at level i and
, plays an important role in the performance-
based plastic design procedure. The factor is directly related
to the storey lateral strength
and stiffness along the height of the structure. It also
represents the variation of storey
used to derive a lateral force
distribution based on inelastic state and to design beams of the
structure.
, applied at level i and at
and i+1, respectively.
-
Evaluation of Storey-
Table 4.2 Evaluation of Storey
Floor
Level
(m)
(kN)
4th
16 0.53 4140
3rd
12 0.30 2330.4
2nd
8 0.13 1
1st 4 0.03 256.344
Design of Bracing Memb
It is based on following 3 criterias:
Strength Criterion
Fracture Criterion
Compactness Criterion
Strength Criterion:
The braces are designed based on their ultimate state, i.e.,
tension yielding and
post-buckling, to resist total design storey she
columns. Thus,31
-wise Lateral Force Distribution
Table 4.2 Evaluation of Storey-wise Lateral Force
Distribution
(kN)
(kN)
=
4140 4140 1.0 16.00
2330.4 6470.4 1.5628 6.7536
1033.14 7503.54 1.8124 1.9968
256.344 7768 1.8763 0.2556
=6.25 =25.006
Design of Bracing Members:
It is based on following 3 criterias:
Strength Criterion
Fracture Criterion
Compactness Criterion
The braces are designed based on their ultimate state, i.e.,
tension yielding and
buckling, to resist total design storey shear, neglecting
contribution from
columns. Thus,
wise Lateral Force Distribution
66240
27964.8
8265.12
1025.376
=25.006 =103495.
3
The braces are designed based on their ultimate state, i.e.,
tension yielding and
ar, neglecting contribution from
-
32
()*+,-.*-/,)1 (3. 0.535,)1 cos(:) Table 4.3: Required Brace
Strength
Floor Level Vi
(kN)
Vi (for 1 CBF )
(kN)
)1cos (kN)
4 41 4140 1035 1385 2 41 6470.4 1617.5 2164.15 2 41 7503.54
1875.75 2510 1 41 7768
2598.30 2598.30
Designing the braces for the maximum storey shear, i.e., 2598.30
kN, we get the
section HSS 12 X 12 X 0.25 having strength of 2675 kN, thus
satisfying the
strength criterion.
Design of Beams:
The post-buckling strength of a brace is taken as 0.5 Pcr for
in-plane buckling.
Beams intersected by the braces should be designed assuming that
no gravity loads are
resisted by the braces. Those beams should also be designed to
support vertical and
horizontal unbalanced loads resulting from the force difference
in the tension and
compression braces. The design of beams should follow the
beam-column design
requirements due to presence of high axial forces. The
unbalanced loads resulting from
the braces are as follows:
= ( .3. 0.535,) cos => ? .3. 0.535,@ sin
Where,
-
33
Fh is the horizontal unbalanced force
Fv is the vertical unbalanced force
Ry is the ratio of the expected yield strength to the specified
minimum yield
strength, taken equal to 1
Py is the nominal yield strength = FyAg , and
Pcr is the nominal compressive strength = Fcr Ag
Table 4.4: Design Parameters for Beams of 4-storey CBF
Floor
Level
RyPy
(kN)
0.5 Pcr
(kN)
Fh
(kN)
Fv
(kN)
Pu
(kN)
Mu
(kNm)
4th 2403.96 270.445 2017.67 1400 3000 9600
The section corresponding to the moment of 9600 kNm is
W36X395.
Table 4.5: Sectional Properties of Beam, Column & Brace
AISC
SECTION
Ax
(in2)
D
(in)
Bf
(in)
Tf
(in)
Tw
(in)
Iz
(in4)
Ix
(in4)
Iy
(in4)
Zx
(in3)
Zy
(in3)
W36X395 116 38.40 16.8 2.20 1.22 28500 142 1750 1710 325
W36X441 130 38.90 17 2.44 1.36 32100 194 1990 1990 368
HSS
12X12X0.25
10.80 12 - 0.23 - 248 384 248 47.6 47.6
-
Table 4.6: Cross Sections of Beam, Column & Brace
34
Table 4.6: Cross Sections of Beam, Column & Brace
Table 4.6: Cross Sections of Beam, Column & Brace
W36X441
(COLUMN)
W36X395
(BEAM)
HSS
12X12X0.25
(RECTANGUL
AR BRACE)
-
35
CHAPTER 5
Comparison of Code-Based and PBPD Designs
5.1 General
This Chapter deals with comparison of Code-Based and PBPD
designs so as to
arrive at more realistic and reasonable design.
The code-based and PBPD designs are compared on the basis of
1) Lighter design.
2) Achieving the assumed fundamental time period in design
procedure.
3) Performance in nonlinear static pushover analysis (NSPA).
Following analysis techniques are used for comparison
purpose
1) Eigen value analysis:
This analysis evaluate fundamental mode of vibration which is an
important dynamic
characteristic of structural system as the base shear demands is
entirely dependent on the
fundamental time period.
2) Nonlinear static pushover analysis (NSPA):
Pushover analysis is an approximate analysis method in which the
structure is subjected to
monotonically increasing lateral forces with an invariant
height-wise distribution until a
structural system undergoes inelastic state. Figure 5.1 shows a
typical pushover plot of a
structural system with base shear as ordinate and roof
displacement as abscissa.
The various steps involved in carrying out the Nonlinear Static
Pushover analysis are as
follows.
1) Determine the gravity loading and the vertical distribution
of the lateral loads.
2) Determine the desired building performance level.
-
36
3) Calculate the status of the structures based on its
performance level.
4) Compute the maximum target Displacement, t.
Figure 5.1: Typical pushover curve
5.2 Modeling of steel CBF in ABAQUS 6.9
Both steel CBF design are modeled using B31 element in general
purpose FE software
ABAQUS 6.9 (Abaqus, 2009). Typical model of code-based CBF is
shown in Figure 5.2.
This figure also shows the boundary conditions of steel CBF.
-
Figure 5.2: Typical model of code
5.3 Eigen value analysis
Eigen value analysis has been conducted on both designs by
Frequency step with
Lanczos eigen solver of ABAQUS 6.9 (Aba
between assumed and obtained fundamental time period of both
design. Figure 5.3 present
a typical fundamental mode of code
Table 5.1: Comparison between assumed and obtained fundame
Design
Code-based design
PBPD
37
Figure 5.2: Typical model of code-based CBF in ABAQUS 6.9
5.3 Eigen value analysis
Eigen value analysis has been conducted on both designs by
Frequency step with
Lanczos eigen solver of ABAQUS 6.9 (Abaqus, 2009).Table 5.1
shows the comparison
between assumed and obtained fundamental time period of both
design. Figure 5.3 present
a typical fundamental mode of code-based design of four-storey
CBF.
Table 5.1: Comparison between assumed and obtained fundamental
time period of both
design
T1 (assumed)
(s)
based design 0.68
0.80
based CBF in ABAQUS 6.9
Eigen value analysis has been conducted on both designs by
Frequency step with
qus, 2009).Table 5.1 shows the comparison
between assumed and obtained fundamental time period of both
design. Figure 5.3 present
storey CBF.
ntal time period of both
T1 (obtained)
(s)
0.62
1.05
-
Figure 5.3: Typical fundamental mode of code
5.4 Nonlinear static pushover
NSPA is used to evaluate the expected performance of a
structural system by estimating
its strength and deformation demands in design earthquakes. This
evaluation is based on
an assessment of important performance parameters, including
global drift, inter
drift, and inelastic element deformations. The IS: 1893
recommended lateral force d
model of design is subjected to the unidirectional monotonic
push till the respective target
displacement so as to induce significant inelastic deformations
in the system. Thereof
displacement versus base shear plot is bilinearized by equating
the areas under the actual
pushover curve and the approximate one and yield point
for each design.
38
Figure 5.3: Typical fundamental mode of code-based design of
four
Nonlinear static pushover analysis (NSPA):
used to evaluate the expected performance of a structural system
by estimating
its strength and deformation demands in design earthquakes. This
evaluation is based on
an assessment of important performance parameters, including
global drift, inter
rift, and inelastic element deformations. The IS: 1893-Part
I
recommended lateral force distribution is used for NSPA of both
design model. Each
model of design is subjected to the unidirectional monotonic
push till the respective target
isplacement so as to induce significant inelastic deformations
in the system. Thereof
displacement versus base shear plot is bilinearized by equating
the areas under the actual
pushover curve and the approximate one and yield point and yield
base shear is
based design of four-storey CBF
used to evaluate the expected performance of a structural system
by estimating
its strength and deformation demands in design earthquakes. This
evaluation is based on
an assessment of important performance parameters, including
global drift, inter-storey
Part I-2002 (BIS, 2002)
both design model. Each
model of design is subjected to the unidirectional monotonic
push till the respective target
isplacement so as to induce significant inelastic deformations
in the system. Thereof
displacement versus base shear plot is bilinearized by equating
the areas under the actual
yield base shear is obtained
-
39
Figure 5.4 shows the unidirectional monotonic pushover load on
finite element model of
code-based steel CBF
Figure 5.4: Typical pushover load on code-based design of
four-storey CBF
Figure 5.5 shows typical deformed shape of code-based design of
four-storey CBF obtained
from NSPA. From this deformed shape a soft-storey formation is
observed at second
storey indicating that code-based design fails at higher lateral
load.
Monotonic uni-directional pushover load
till plastic collapse mechanism
-
Figure 5.4: Typical deformed shape of
Figure 5.5 shows typical base shear versus roof displacement
plot for code
four-storey CBF obtained from NSPA.
40
Figure 5.4: Typical deformed shape of code-based design of
four
obtained from NSPA
typical base shear versus roof displacement plot for code
storey CBF obtained from NSPA.
based design of four-storey CBF
typical base shear versus roof displacement plot for code-based
design of
-
41
Figure 5.5: Typical base shear versus roof displacement plot for
code-based design of
four-storey CBF obtained from NSPA.
Table 5.2 shows the comparison between design and obtained yield
base shear for both
designs from NSPA. From this table it is observed that
code-based design is too
conservative as compare to PBPD design. The justification for
the same is that PBPD
provides plastic design equations for individual component of
steel CBF whereas in code-
based design the elements need to be optimized by an iterative
procedure such that
capacity is more than demand.
Table 5.2: Comparison between design and obtained yield base
shear for both designs
from NSPA.
Design Vby (Design)
(kN)
Vby (From NSPA)
(kN)
Code-based design 12500 13750
PBPD 7768 7684
-
42
CHAPTER 6
Concluding Summary and Scope for Future Work
6.1 Summary
Aim of this study is to compare the traditional code-based and
recent performance-based plastic
design method for steel CBF. This comparison is based on lighter
section for components of CBF
(light weight design), performance in nonlinear static pushover
analysis (NSPA). Following points
from design and analysis can be summarized for the
comparison
1. Code-based design is more conservative and heavy weight
design as it follows strength-
based approach
2. In displacement-based approach significant inelastic
deformation capacity of system is
fully utilized hence PBPD design result in light weight
system
3. When fundamental time periods of both design as assumed in
respective seismic force
calculations are compared with those obtained from eigen value
analysis it is observed
that PBPD design is more accurate with less difference in
assumed and obtained value.
4. Nonlinear static pushover analysis of these design shows that
code-based design is more
prone to have soft-storey which is undesirable collapse
mechanism where as PBPD design
achieves a pre-selected yield mechanism and hence effective in
utilizing significant
inelastic deformation capacity. Hence it is suggested that
existing design standard should
follow the displacement-based approach rather than elastic
force/strength-based approach.
6.2 Scope for future work
This study is only limited to low rise CBF system. Following can
be considered as scope for
future work
1. Design comparison for medium to high rise CBF.
2. Comparison of seismic performance of design can be evaluated
by using nonlinear
dynamic analysis
-
43
References:
1) N. Subramanian (2008), Design of steel structures, OXFORD
UNIVERSITY
PRESS Publication.
2) BIS, IS 1893 (Part 1): (2002), Criteria for Earthquake
Resistant Design of structures
Part 1 General Provisions and Buildings, Bureau of Indian
Standards, Fifth Revision.
3) BIS, IS 800:2007, General Construction in Steel Code of
practice,Bureau of Indian
Standards, Fifth Revision.
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PLASTIC
DESIGN EARTHQUAKE RESISTANT STEEL STRUCTURES,
INTERNATIONAL CODE OF COUNCIL Publication.
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STEEL
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