chapter 3 modeling of the existing rcc structures...
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CHAPTER 3
MODELING OF THE EXISTING RCC STRUCTURES
3.1 INTRODUCTION
In Coimbatore city many existing buildings which had been built
prior to 2002 are seismically deficient due to the fact that the seismic design
code IS 1893: 2002 (Part-I) requirements have been upgraded. Furthermore,
some of the Coimbatore buildings built over the past few years even after
2002 are seismically deficient because of lack of awareness of the builders
regarding the seismic behavior of structures. Most of the existing buildings in
this city are designed for gravity loads only. A large number of existing
buildings in Coimbatore need seismic evaluation due to various reasons such
as noncompliance with the codal requirements, updating of code, poor design
and construction practice and change in the use of the building. However, the
existing deficient structures in Coimbatore falling in Zone-III can be
upgraded to improve and sustain the expected performance level. Before
rehabilitation work, it is necessary to understand the capacity of the existing
building and to check if it meets the intended performance level.
The Nonlinear Finite Element Analysis software SAP2000
version 11 is utilized to create a three dimensional model and static pushover
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analysis was studied. The software is able to predict the geometric nonlinear
behavior of space frames under static or dynamic loadings, taking into
account both geometric nonlinearity and material inelasticity. The software
accepts static loads (either forces or displacements) as well as dynamic
(accelerations) actions and has the ability to perform eigen values, nonlinear
static pushover and nonlinear dynamic analyses.
3.2 RESEARCH METHODOLOGY
The research work had been carried out in three phases. In the First
phase of the study is the creation and analysis of the model has to evaluate the
performance of a typical selected deficient existing building having different
types of lateral load resisting systems such as R.C. frame and Infilled frame
behavior with respect to seismic vulnerability. For this evaluation, a pushover
analysis had been performed. The analysis result showed the performance
levels, behavior of the components and failure mechanism of the building.
It also provided the sequence of hinge formation. Based on the analysis
the elements which needed retrofitting were identified. The process of the
Phase –I is shown in Figure 3.1.
The Second phase of the study involved the seismic strengthening
of the existing bare frame structure based on the SAP 2000 analysis results.
For strengthening of the existing building Glass Fiber Reinforced Polymer
Composite (GFRP) was used extensively to address the strength requirements
related to flexure and shear in the structural system. This phase highlighted
the behavior and performance of composite beams by the moment – rotation
relation and the ductility of the tested beams. The test result showed that the
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beams strengthened with GFRP wrapped exhibited better performance. The
process of the Phase –II is shown in Figure 3.2.
The Third phase of the study involved the analysis of bare frame
with strengthened beams. After seismic strengthening of the existing hostel
building, its behavior during the earthquake was studied based on the
wrapped GFRP beams. The improved performance of the existing RCC
structure was studied in detail with reference to pushover curves, hinges
formation, moment-rotation, capacity spectrum and performance level of the
building by using SAP 2000.
Finally the GFRP composite retrofitting techniques are
suggested so that the strength and performance level of the structure could be
enhanced during the earthquake. The process of the Phase –III is shown in
Figure 3.3.
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Figure 3.1 Analysis of the Existing RCC Building
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Figure 3.2 Investigation of Seismic Strengthening of the Existing RCC
Bare Frame Building
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Figure 3.3 Analysis of Bare Frame with Strengthened Beams
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3.3 EVALUATION OF SEISMIC PERFORMANCE
To select an appropriate retrofitting method, an accurate evaluation
of the seismic performance and the condition of an existing structure is
necessary. Based on this evaluation, engineers can choose the most effective
retrofit technique among the various intervention techniques and optimize the
improvement in seismic performance for an existing structure. Seismic
deficiencies should first be identified through a seismic evaluation of the
structure. The selection of an appropriate intervention technique based on the
structural type and its deficiencies is the most important step in retrofitting.
Seismic evaluation consists of gathering as-built information and obtaining
the results of a structural analysis based on collected data. The Prestandard
and Commentary for the Seismic Rehabilitation of Buildings – FEMA 356
(2000) provides guidance for evaluating the seismic performance of existing
structures and determining the necessary retrofitting methods to achieve the
performance objectives ASCE (2000).
3.3.1 As-Built Information
Generally, in order to obtain a reliable result from a structural
analysis of an existing structure, sufficient as-built information is required.
As-built information refers to the configuration of the structural system, as
well as the type, detailing, material strength and condition of the structural
elements. Data are available from detailed drawings, construction documents,
and previously conducted seismic evaluations of the building. The reason is
for gathering this information, so that engineers can arrive at accurate results
from their analyses and compare those results with current requirements in
order to determine the deficiencies of a building. To obtain realistic as built
information, FEMA 356 (2000) suggests that a minimum of one site visit
should be made to observe exposed conditions of building configuration,
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building components, site and foundation conditions and adjacent structures.
This information is to be used to verify that as-built information obtained
from other sources is representative of the existing conditions.
3.3.2 Evaluation Procedures
Based on as-built information, an evaluation of the seismic
performance of an existing structure can be conducted. FEMA 356 (2000)
outlines four different procedures for analysis of the seismic evaluation of a
structure: the linear static procedure, the linear dynamic procedure, the
nonlinear static procedure (push-over analysis) and the nonlinear dynamic
procedure. Using one of these procedures, the seismic performance of a
structure can be evaluated and the deficiencies or vulnerable elements can be
found. Therefore, the results of these analyses provide key information for
selecting proper retrofitting techniques.
3.3.2.1 Linear Procedures
The linear analysis procedures provided in FEMA 356 (2000)
consist of linear static and linear dynamic analysis. When the linear static or
dynamic procedures are used for seismic evaluation, the design seismic
forces, the distribution of applied loads over the height of the buildings and
the corresponding displacements are determined using a linearly elastic
analysis. It is difficult to obtain accurate results for structures that undergo
nonlinear response through linear procedures. Therefore, linear procedures
may not be used for irregular structures, according to the FEMA 356 (2000)
guidelines.
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3.3.2.2 Nonlinear Procedures
Nonlinear procedures consist of nonlinear static and nonlinear
dynamic analysis. A nonlinear static analysis, also known as a push-over
analysis, consists of laterally pushing the structure in one direction with a
certain lateral force or displacement distribution until either a specified drift is
attained or a numerical instability has occurred (signaling a collapse).
Because linear procedures have limitations and nonlinear dynamic procedures
are complicated, nonlinear static analysis is commonly used by structural
design engineers. The nonlinear dynamic procedure (dynamic time-history
analysis) provides a more accurate estimate of the dynamic response of the
structure. However, because the results computed by the nonlinear dynamic
procedure can be highly sensitive to characteristics of individual ground
motions, the analysis should be carried out with more than one ground motion
record. This is also true for the linear dynamic analysis. FEMA 356 (2000)
provides guidelines regarding the required number of ground motions that
should be used for dynamic analysis.
3.3.3 Rapid Visual Screening, Data Collection and Preliminary
Evaluation
The Rapid visual screening involved a quick assessment of a
building based on visual inspection alone. It is a kind of guideline to the
inspectors to identify and to have inventory of the vulnerable buildings.
In order to facilitate seismic evaluation, it is necessary to collect
relevant data of a building as much as possible through drawings, enquiry,
design calculation, soil report, inspection reports of previous investigation,
previous repair work, any complaints by the occupants etc.
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The purpose of preliminary evaluation is to identify the areas of
seismic deficiencies in an engineered building before detailed evolutions are
undertaken. The code compliance for seismic design and detail evaluation
need to be studied thoroughly.
3.3.4 Overview of the Existing Structures
Coimbatore is a fast growing city in India which is located in
seismic Zone-III. Many of the reinforced concrete frame buildings in
Coimbatore were designed and built prior to the year 2002. The Indian
seismic code IS 1893 was revised in 2002. Hence, buildings built prior to
2002 do not comply with the codal requirement. Diptesh Das and Murty
(2004) states that, most of the buildings with infilled walls have not
considered infills in their design. This chapter aims to evaluate the
performance of a typical selected building having different types of lateral
load resisting systems such as R.C. frame and infilled frame behavior with
respect to seismic vulnerability. In order to evaluate the Seismic behavior of
existing building with rigid floor diaphragms an existing hostel building was
selected in Coimbatore zone. For this evaluation, a Pushover analysis had
been performed. The analysis showed the behavior levels of various
components of building for different specified performance objective as per
ATC 40 (1996). Based on this evaluation, it is concluded that the building
needed retrofitting to enhance its performance to the required level.
The objective of the present analysis is to choose a typical building
in the Coimbatore (Zone III) region for evaluating the performance of the
building and identify the type of deficiency.
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The above objective was achieved by following steps
1. Chosen a typical existing building designed prior to 2002
whose structural data was available.
2. Making a three dimensional model of the building using the
available data but ignoring partitions.
3. Making a three dimensional model of the building
considering effect of partitions as infills.
4. Conducted a pushover analysis of the models referred in steps
2 and 3.
5. Identified the hinge formation, base shear capacity and
performance with respect to immediate occupancy, life safety
and collapse prevention as per ATC 40 (1996) for the models
in steps 2 and 3.
3.4 DESCRIPTION OF THE FRAMED STRUCTURES
The present study was to evaluate the behavior of G+2 reinforced
concrete bare frame and infill frame building subjected to zone III level
earthquake forces. The three dimensional reinforced concrete structures were
analyzed by nonlinear static analysis (Pushover Analysis) using SAP2000
software. The analysis results showed the performance levels, behavior of the
components and failure mechanism of the building. It also showed the
sequence of hinge formation. Based on the analysis, the elements which need
retrofitting were identified.
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The three dimensional frame of the selected building having
different types of lateral load resisting systems such as R.C. bare frame and
Infilled frame were considered in this study. Figure 3.4 shows the plan of the
building representing the X and Y direction used for analysis. Figure 3.5
shows a three dimensional line sketch of the frame in the X, Y and Z
direction. Figure 3.6 shows a typical longitudinal bare frame (in the X
direction in XZ plane). Figure 3.7 shows a configuration model of braces
representing infills. Figure 3.8 shows an elevation of the existing study hostel
building. The building exists in Coimbatore and is a typical example of many
such buildings in this region. It was built with M15 grade of concrete and
Fe415 grade of steel, Figure 3.9 shows the elevation of buildings similar to
the one examined in this region.
Figure 3.4 Plan of the Existing Hostel Building
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Figure 3.5 Three Dimensional View of the Bare Frame
Figure 3.6 Bare Frame
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Figure 3.7 Three Dimensional view of the representing Infills Frame
with Braces
Figure 3.8 Elevation of the Existing Study Hostel Building
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Figure 3.9 Examples of Existing Buildings
IS 456:2000 demands M20 to be the concrete grade for structural
applications. However, many buildings in Coimbatore region were built with
only M15 grade concrete. In order to check the vulnerability of such
buildings, the strength of concrete and grade of steel based on test results was
used in the pushover analysis.
For the selected building the strength of concrete was assessed as
16.5 N/mm2 using rebound hammer test and strength of steel was assessed as
Fe420 based on tensile strength test .These values were used in the pushover
analysis.
The chosen G+ 2 existing study hostel building has total height of
the building is 8.79 m. The building is 25.41 m in length and 11.95 m in
width. Typical floor to floor height is 2.93 m and slab thickness is 140 mm.
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The dimensions of the beams and columns of the R.C. frames are shown in
Table 3.1.
Table 3.1 Dimension of the Beams and Columns (As per Structural
Designer Drawing)
S.NoStructural member
NotationsSizes (mm)
Length of the
member (mm)
Area of the steel (mm2 )
Percentage of the steel
(%)
1 Beam B1 273x412 3500 653 0.58
2 Beam B1a 273x312 2450 854 1.00
3 Beam B2 280x600 4750 1859 1.10
4 Beam B2a 280x701 4550 1859 0.94
5 Beam B3 280x600 4750 2173 0.08
6 Beam B4 200x500 3630 1206 1.20
7 Interior column
C1 400x2282930
1030 1.12
8 Exterior column
C2 460x2282930
1319 1.25
3.4.1 Analysis of Bare Frame
In Coimbatore region, most of the existing buildings designed and
constructed with masonry infill as a non-structural element and the analysis as
well as design were carried out by considering the mass but neglecting the
strength and stiffness contribution of infill. Thus, the structure was modeled
as bare frame and usually considered fixed at base. This is the commonly
accepted model for structural analysis and design for the buildings. The only
contribution of masonry infill is adding to the mass of the building acting as a
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non-structural element. Consequently, analysis of the structure is based on the
bare frame. Since infills are not considered for load resistance, their
contributions to the lateral stiffness and strength may invalidate the analysis
and the proportioning of structural members for seismic resistance on the
basis of its results. However, this method is still being widely used by
designers even in the earthquake prone areas and has considered for
comparison in the present study.
With reference to, Mohamed Nour El-Din Abd-Alla (2007) beam
and column members had been defined as frame elements with the
appropriate dimensions and reinforcements. Slabs were defined as an area
element having the properties of shell elements with required thickness. Slabs
had been modeled as rigid diaphragms based on Sundar and Elangovan
(2000). Soil structure interaction was not considered and columns were
restrained with respect to all six degrees of freedom at the base. The building
was constructed in the medium soil site conditions on a firm ground with
underlying soil that has a value of bearing capacity which is equal to
200 kN/m2. In SAP2000 the behavior of the concrete is considered as non-
linear.
3.4.1.1 Assigning Loads
After having modeled the structural components, all possible load
cases are considered and they are listed below:
3.4.1.1.1 Gravity Loads
With reference to, Ishan Jyoti Sharma (2005) gravity loads on the
structure include the self weight of beams, columns and slabs other permanent
members. The self weight of beams, columns (Frame members) and slabs
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(Area section) were automatically considered by the program itself. Infill
weight has been calculated and added.
3.4.1.1.2 Seismic Weight of the Building
With a reference to Pankaj Agarwal and Manish Shrikhande
(2008), the Seismic Weight of the whole building was the sum of the seismic
weights of all the floors. The seismic weight of each floor was its full dead
load plus appropriate amount of imposed load. While computing the seismic
weight of each floor, the weight of columns in any storey was equally
distributed to the floors above and below the storey.
The live load was considered for seismic weight calculation as per
Table – 8, IS 1893 (Part-1) 2002. Percentage of Imposed load to be
considered in Seismic weight calculation, since the live load class is up to 3
kN/m2, 25% of the imposed load was considered on floor. The imposed load
on roof was taken as zero.
3.4.1.1.3 Base Shear Calculations
The live load was assigned as uniform area loads on the slab
elements as per IS 1893 (part-1) 2002. Live load on floor = 2.0 kN/m2. In this
case 25% of the imposed load was considered on floor as seismic weight. The
live load on roof was taken as zero.
The design seismic base shear (Vb) was calculated using procedure
given in IS 1893(part 1)-2002 as follows.
Vb = Ah W (3.1)
Where Ah is the design horizontal seismic coefficient and is given by
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Ah = ZI {Sa/g} / 2R (3.2)
Where Z - Zone factor given in table 2 of IS 1893-2002
I - Importance factor given in table 6 of IS 1893-2002 (Part-I)
R - Response reduction factor given in table 7 of IS 1893-2002
Sa/g - Average response acceleration coefficient.
Calculation
The approximate fundamental natural period of vibration (Ta), in
seconds, of a moment-resisting frame building without brick infill panels was
estimated by the empirical expression:
Ta = 0.075h0.75 (IS 1893-2002, Part-I) (3.3)
Where h = height of the building in m
= 0.075(8.79)0.75= 0.382 sec
From the response spectrum graph (Figure -2 of IS 1893-2002),
Average response acceleration coefficient (Sa/g) is found to be 2.5
Ah = 0.16x1{2.5}/ (2 x 3) = 0.067
Here
Z = 0.16- considering zone factor -III
I = 1.0 considering residential building.
R = 3.0 considering ordinary moment resisting frame (OMRF)
S a /g = 2.5
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Table 3.2 Seismic weight of the building for Bare Frame (W)
Floor No
Floor height from ground level (m)
Seismic weight ( kN)
1 2.93 4463.474
2 5.86 4463.474
3 8.79 1039.470
Total seismic weight of the building (W) 9966.418
The design base shear is calculated using =Vb =Ah W
W = Total seismic weight of the building, Refer Table 3.2.
Hence, Vb = 0.067 x 9966.418 = 667 kN
In the proposed model the reduction of the design base shear is
allowed based on the remaining useful life of the building reported by
Durgesh C. Rai (2005). The modification factor for the reduction of base
shear is given as follows,
0.5
rem
des
TU 0.7T
(3.4)
Here,
Trem- remaining useful life of the building, 38 years
Tdes- design useful life of the building, 50 years
Modification factor U= 0.871
The reduced base shear = 667x0.871= 580 kN.
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3.4.2 Analysis of Infill Frame
One of the main reasons in using masonry infill is being
economical and ease of construction, because it uses locally available
material and labor skill. Moreover, it has a better acoustics and heat insulation
and waterproofing properties, resulting in greater comfort for the occupants.
In Coimbatore many of the existing buildings were with masonry
infills as nonstructural element. The analyses as well as design of the frames
in these existing building were carried out by considering the mass but
neglecting the strength and stiffness contribution of the infill. Therefore, the
entire lateral load is assumed to be resisted by the frame only. One of the
disadvantages of neglecting the effect of infill is that, the building can
have both horizontal as well as vertical irregularities due to uncertain
positioning of infill and openings in them. Also, the infill walls are sometimes
rearranged to suit the changing functional needs of the occupants. The
changes are carried out without considering their effects on the overall
structural behavior.
The conventional finite element modeling of RC structures without
considering the effect of infill in the analytical model renders the structures
more flexible than they actually are. For this reason building codes imposes
an upper limit to the natural period of a structure by way of empirical
relations. Binay Charan Shrestha (2008) states that, since the infills are not
considered in conventional modeling in seismic design, their contributions to
the lateral stiffness and strength may invalidate the analysis and proportioning
of structural members for seismic resistance on the basis of its results. In
reality, the additional stiffness contributed by these secondary components
increases the overall stiffness of the buildings, which eventually leads to
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shorter time periods, as they are observed during earthquakes; and hence
attracts larger seismic force to the structure.
Since early 50’s there have been numerous experimental as well as
analytical researches to understand the influence of infill on the lateral
strength and stiffness of the framed structures. Past earthquakes have shown
that buildings with regular masonry infill have a better response than with the
irregular ones. Also, masonry infills have a very high initial stiffness and low
deformability (Moghaddam and Dowling 1987) thus, making infill wall a
constituent part of a structural system. This changes the lateral load transfer
mechanism of the framed structure form predominant frame action to
predominant truss action (Murthy and Jain 2000), which is responsible for
reduction in bending moments and increase in axial forces in the frame
members. The presence of infill also increases damping of the structures due
to the propagation of cracks with increasing lateral drift. However, behavior
of masonry infill is difficult to predict because of significant variations in
material properties and failure modes that are brittle in nature. If not
judiciously placed, during seismic excitation, the infills also have some
adverse effects. One of the major ill effects is the soft storey effect. This is
due to absence of infill wall in a particular storey. The absence of infill in
some portion of a building plan will induce torsional moment. Also, the
partially infilled wall, if not properly placed may induce short column effect
thus creating localized stress concentration.
In Coimbatore, during the past days the designers used to ignore
the stiffness and strength of infill in the design process and treated the infill as
non-structural elements. This is mainly due to lack of awareness generally
accepted seismic design methodology in the present Indian Code that
incorporates structural effects of infill. Hence, there is a clear need to develop
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a design methodology for seismic design of masonry infill Reinforced
Concrete structure.
Alternatively, a macro-model replacing the entire infill panel as a
single equivalent-strut has become the most popular approach for analyzing
infilled frame systems as shown in Figure 3.10 and it was proposed by Pauley
and Priestley (1992) and Holmes (1961). In this method, the brick infill was
idealized as a pin jointed diagonal strut and the RC beams and columns were
modeled as three-dimensional beam elements having six degree of freedoms
at each node. The idealization was based on the assumption that there was no
bond between frame and infill. The brick masonry infill was modeled as a
diagonal strut member whose thickness was same as that of the masonry and
the length was equal to the diagonal length between compression corners of
the frame. The effective width of the diagonal strut depends on various
factors like; contact length, aspect ratio of the infill and the relative stiffness
of frame and the infill. The brick-infill wall was simulated by the
compression-strut model suggested by the FEMA 356 (2000). In FEMA 356
(2000), the strut model is suggested based on the seismic behavior of RC
frames with brick infill.
Figure 3.10 Idealization of Brick Infill Panel as Equivalent Diagonal Strut
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3.4.2.1 Calculation of Strut Area
The strut area is given by the following expressions,
Ae= wet (3.5)
we = 0.175( h)-0.4 w’ (3.6)
i4
c c
E tsin 24E I hi
Where, Ei - The modulus of elasticity of the infill material, N/mm2
Ei - 550fm -As recommended by FEMA 356 (2000)
fm - Compressive strength of hand molded burnt clay brick
Ef - The modulus of elasticity of the frame material, N/mm2
Ic - The moment of inertia of column section, mm4
t - The thickness of infill, mm
we - Equivalent strut width
h - The centre line height of the frame
hi - The height of infill
w' - The diagonal length of infill panel
- The slope of infill diagonal to the horizontal.
The brick masonry infill thickness is 230 mm and 115 mm for outer
and inner walls respectively. Based on the above equation (3.5) the strut areas
are calculated as 454 mm x 230 mm (Exterior wall) and 367 mm x 115 mm
(Interior wall).
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3.4.2.2 Base Shear Calculations
The approximate fundamental natural period of vibration (Ta), in
seconds, of a moment-resisting frame building with brick infill panels may be
estimated by the empirical expression: Ta = 0.009h/ d with infill stiffness
considered given in IS 1893 (part-1) 2002, where h - is the height of the
building in m, d - is the base dimensions of the building in the direction of the
vibration in m.
Ta = 0.009h/ d = 0.009x8.79 25.41 = 0.398 sec in X- direction (3.7)
Ta = 0.009h/ d = 0.009x8.79 11.95 = 0.273 sec in Y- direction (3.8)
The spectral acceleration coefficient (Sa/g) values are calculated as follows.
For medium soil sites,
(3.9)
From the response spectrum graph (Figure -2) IS 1893-2002,
Average response acceleration coefficient (Sa/g) is found to be 2.5
The design horizontal seismic coefficient (Ah) = 0.16x1{2.5}/ (2 x 3) = 0.067
Ah= 0.16x1{2.5}/ (2 x 3) = 0.067
Here
Z = 0.16- considering zone factor -III
I = 1.0 considering residential building.
R = 3.0 considering ordinary moment resisting frame (OMRF)
S a /g = 2.5
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Table 3.3 Seismic weight of the building for Infill Frame (W)
Floor No
Floor height from ground level (m)
Seismic weight (kN)
1 2.93 4463.474
2 5.86 4463.474
3 8.79 1039.470
Total seismic weight of the building (W) 9966.418
The design base shear is calculated using =Vb =Ah W (3.10)
Hence, Vb = 0.067 x 9966.418= 667 kN
The reduction base shear = 667x0.871= 580 kN.
Though Fundamental natural period of vibration (Ta), is different
for frame with and without infill, since Sa/g is 2.5, there is no difference in
base shear (Vb) in both cases.
3.5 PUSHOVER ANALYSIS
Nonlinear static analysis or pushover analysis has been developed
over the past twenty years and has become the preferred analysis for
design and seismic performance evaluation purposes since the procedure is
relatively simple and considers post elastic behavior. However, the procedure
involves certain approximations and simplifications that some amount of
variation is always expected to exist in seismic demand prediction of
pushover analysis.
The non-linear static procedure or simply push over analysis is a
simple option for estimating the strength capacity in the post-elastic range.
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This procedure involves applying a predefined lateral load pattern which is
distributed along the building height. The lateral forces are then
monotonically increased in constant proportion with a displacement control
mode of the building until a certain level of deformation is reached. The
applied base shear and the associated lateral displacement at each load
increment are plotted. Based on the capacity curve, a target displacement
which is an estimate of the displacement that the design earthquake will
produce on the building is determined. The extent of damage experienced by
the building at this target displacement is considered as representative of the
damage experienced by the building when subjected to design level ground
shaking.
The most frequently used terms in pushover analysis as given in
ATC-40 (1996) are:
3.5.1 Demand
It is a representation of the earthquake ground motion or shaking
that the building is subjected to. In nonlinear static analysis procedures,
demand is represented by an estimation of the displacements or deformations
that the structure is expected to undergo. This is in contrast to conventional,
linear elastic analysis procedures in which demand is represented by
prescribed lateral forces applied to the structure.
3.5.2 The Capacity Spectrum and Demand Spectrum
The Capacity Spectrum Method (CSM) is a method which allows
for a graphical comparison between the structure capacity and the earthquake
demand. The lateral resisting capacity of the structure is represented by a
force-displacement curve obtained from the pushover analysis. The demand
of the earthquake is represented by its response spectrum curve.
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Simultaneously, the acceleration and displacement spectral values are
calculated from the corresponding response spectrum for a certain damping
(say 5% initially), are plotted as the ordinate and abscissa respectively. The
presentation of the two curves in one graph is termed as the Acceleration
versus Displacement Response Spectrum (ADRS) format as shown in
Figure 3.11. With increasing nonlinear deformation of the components, the
equivalent damping and the natural period increase. The spectral values of the
acceleration and displacement can be modified from the 5 percent damping
curve by multiplying a factor corresponding to the effective damping
(Table 3, IS 1893:2002). Thus, the instantaneous spectral acceleration and
displacement point (demand point) shifts to a different response spectrum for
higher damping. The locus of the demand points in the ADRS plot is referred
to as demand spectrum.
Figure 3.11 Demand and Capacity Spectra Mehar Prasad (2008)
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3.5.3 Displacement-Based Analysis
It refers to analysis procedures, such as the nonlinear static analysis
procedures, whose basis lies in estimating the realistic, and generally
inelastic, lateral displacements or deformations expected due to actual
earthquake ground motion. Component forces are then determined based on
the deformations.
3.5.4 Elastic Response Spectrum
It is the 5% damped response spectrum for the (each) seismic
hazard level of interest, representing the maximum response of the structure,
in terms of spectral acceleration Sa, at any time during an earthquake as a
function of period of vibration T.
3.5.5 Performance Level and Performance Point
A limiting damage state or condition described by the physical
damage within the building, the threat to life safety of the building’s
occupants due to the damage, and the post earthquake serviceability of the
building. A building performance level is that combination of a structural
performance level and a nonstructural performance level.
The performance point is the point where the capacity spectrum
crosses the demand spectrum, as shown in Figure 3.11. If the performance
point exists and the damage state at this point is acceptable, then the building
is considered to be adequate for the design of earthquake forces. To have
desired performance, every structure has to be designed for this level of
forces.
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3.5.6 Yield Point
The point along the capacity spectrum where the ultimate capacity
is reached and the initial linear elastic force-deformation relationship ends
and effective stiffness begins to decrease.
3.5.7 Building Performance Levels
A performance level describes a limiting damage condition which
may be considered satisfactory for a given building and a given ground
motion. The limiting condition is described by the physical damage within the
building, the threat to life safety of the building’s occupants created by the
damage, and the post-earthquake serviceability of the building.
3.5.7.1 Immediate Occupancy
The earthquake damage state in which only very limited structural
damage has occurred, the basic vertical and lateral forces resisting the
systems of the building retain nearly all of their pre-earthquake characteristics
and capacities. The risk of life threatening injury from structural failure is
negligible.
3.5.7.2 Life Safety
The post-earthquake damage state in which significant damage to
the structure might have occurred but in which some margin against either
total or partial collapse remains. Major structural components have not
become dislodged and fallen, threatening life safety either within or outside
the building. While injuries during the earthquake may occur, the risk of life
threatening injury from structural damage is very low. It should be expected
that extensive structural repairs will likely be necessary prior to reoccupation
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of the building, although the damage may not always be economically
repairable.
3.5.7.3 Collapse Prevention Level
This building performance level consists of the structural collapse
prevention level with no consideration of nonstructural vulnerabilities, except
that parapets and heavy appendages are rehabilitated.
3.5.7.3.1 Primary Elements and Secondary Elements
These are the primary elements that are required to resist lateral
loads after several cycles of inelastic response to the earthquake ground
motion.
The secondary elements may be required to support vertical gravity
loads and may resist some lateral loads.
3.5.8 Nonlinear Plastic Hinge Properties
This requires the development of the force - deformation curve for
the critical sections of beams, columns and brick masonry by using the
guidelines FEMA 356 (2000). The force deformation curves in flexure are
obtained from the reinforcement details and assigned for all the beams and
columns. The Nonlinear properties of beams and columns have been
evaluated using the section designer and have been assigned to the computer
model in SAP2000. The flexural default hinges (M3) and shear hinges (V2)
were assigned to the beams at two ends. The interacting (P-M2-M3) hinges
assigned for all the columns at upper and lower ends. The axial hinges (P)
were assigned to the brick masonry strut element.
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Figure 3.12 the plot of the lateral force on a structure against the
lateral deformation of the roof of the structure. This is often referred to as the
‘push over’ curve. Performance point and location of hinges in various stages
can be obtained from pushover curve as shown in the Figure 3.12. Five points
labeled A, B, C, D and E are used to define the force deflection behavior of
the hinge. The points labeled A to B – Elastic state, B to IO- below immediate
occupancy, IO to LS – between immediate occupancy and life safety, LS to
CP- between life safety to collapse prevention, CP to C – between collapse
prevention and ultimate capacity, C to D- between ultimate capacity and
residual strength, D to E- between residual strength and collapse and greater
than E – collapse.
Figure 3.12 Different Stages of Plastic Hinge ATC 40 (1996)
3.5.9 Pushover Cases
The pushover hinges were assigned for beams and columns and the
lateral forces were applied at each floor level. Pushover analysis was
performed separately for the two orthogonal directions in order to study the
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performance of the buildings in these two directions independently. Therefore
there are three cases for the evaluation of the buildings.
Three pushover cases for the evaluation of buildings are follows.
Gravity push, which is used to apply gravity load,
(D.L. + 0.25 LL)
Push 1- is the lateral push in the X direction, starting at the
end of gravity push
Push2- is the lateral push in the Y direction starting at the end
of gravity push
In general, the gravity load push is force controlled while lateral
push is deformation controlled. The displacements are monitored at the roof
level. The pushover analysis is performed in the frame considering the
P- effect. The pushover analysis involves the application of monotonically
increasing lateral deformation and monitoring the inelastic behavior of the
structure. The relationship of base shear and roof displacement (capacity
curve) and 5 % damped elastic design response spectrum (demand curve) of
the two models were established. The capacity and demand curves were
converted into a spectral displacement and the spectral acceleration format to
obtain the performance point. The performance point is the intersection point
of the capacity and demand curves.
The output of the capacity curve gives the co-ordinates of each step
of the pushover curve and summarizes the number of hinges in each state.
The coordinates of capacity curve and demand curve were transformed into
spectral acceleration versus spectral displacement coordinates. The curves
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plotted in this format are called as capacity spectrum and demand spectrum
respectively. The number of hinges formed in the beams and columns at the
performance point and their performance levels are used to study the local
vulnerability of the structure and global behavior of the building.
3.5.10 Pushover Analysis in SAP2000
1. The basic computer model (without the pushover data) in the usual
manner was created. The graphical interface of SAP2000 makes
this a quick and easy task.
Figure 3.13 Modeling of the Frame
2. The properties and acceptance criteria for the pushover hinges were
defined.
3. The program includes several built-in default hinge properties that
are based on average values from ATC-40 (1996) for concrete
members and average values from FEMA-273 (1997) for steel
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members. These built in properties were used for preliminary
analyses but user-defined properties were used for final analyses.
Figure 3.14 Default Hinge Properties of the Frame
4. The pushover hinges on the model were located by selecting the
frame members and assigning them one or more hinge properties at
hinge locations.
5. The pushover load cases were defined in SAP2000, where more
than one pushover load case could be run in the same analysis. Also
a pushover load case could be started from the final conditions of
another pushover load case that was previously run in the same
analysis. Typically the first pushover load case is used to apply
gravity load and then subsequent lateral pushover load cases are
specified to start from the final conditions of the gravity pushover.
Pushover load cases can be force controlled, that is, pushed to a
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certain defined force level, or they can be displacement controlled,
that is, pushed to a specified displacement.
Typically a gravity load pushover is force controlled and
lateral pushovers are displacement controlled. SAP2000
allows the distribution of lateral force used in the pushover to
be based on a uniform acceleration in a specified direction, a
specified mode shape, or a user-defined static load case.
6. Initially the basic static analysis was made to run in SAP 2000 and
then the static nonlinear pushover analysis.
Figure 3.15 Analysis Cases of the Frame
7. The pushover curve was displayed in the system as shown in
Figure 3.16. A table which gives the coordination of each step of
the pushover curve and summarizes the number of hinges in each
state as defined in Figure 3.9 (for example, between IO and LS or
between D and E).
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Figure 3.16 Pushover Curve of the Frame
8. Next the capacity spectrum curve was displayed. The performance
point for a given set of values is defined by the intersection of the
capacity curve (green) and the single demand spectrum curve (red).
Figure 3.17 Capacity Spectrum of the Frame
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9. The pushover displaced shape and sequence of hinge formation were reviewed on a step-by-step basis. Hinges appear when they yield and they are color coded based on their state.
Figure 3.18 Sequence of Hinge Formation of the Frame
10. Output for the pushover analysis can be printed in a tabular form for the entire model or for selected elements of the model. The types of output available in this form include joint displacements at each step of the pushover, frame member forces at each step of the pushover and the hinge force, displacement and state at each step of the pushover.
Figure 3.19 Output of the Pushover Analysis
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3.5.11 Use of Pushover Analysis
Pushover analysis is the preferred method for seismic performance
evaluation of structures by the major rehabilitation guidelines and codes
because it is conceptually and computationally simple. Pushover analysis
allows tracing the sequence of yielding and failure on member and structural
level as well as the progress of overall capacity curve of the structure.
The expectation from pushover analysis is to estimate critical
response parameters imposed on structural system and its components as
close as possible to those predicted by nonlinear dynamic analysis. Pushover
analysis provides information on many response characteristics that cannot be
obtained from an elastic static or elastic dynamic analysis. The following are
the response characteristics of the pushover analysis:
The realistic force demands on potentially brittle elements,
such as axial force demands on columns, force demands on
brace connections, moment demands on beam to column
connections, shear force demands in deep reinforced concrete
spandrel beams, shear force demands in unreinforced
masonry wall piers, etc.
Estimation of the deformations demands for elements that
have to form inelastically in order to dissipate the energy
imparted to the structure.
Consequences of the strength detoriation of the individual
elements on the behavior of the structural system.
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Identification of the critical regions in which the deformation
demands are expected to be high and that have to become the
focus through detailing.
Identification of the strength discontinuities in plan elevation
that will lead to changes in the dynamic characteristics in
elastic range.
Estimates of the interstory drifts that account for strength or
stiffness discontinuities and that may be used to control the
damages and to evaluate P-Delta effects.
Verification of the completeness and adequacy of load path,
considering all the elements of the structural system, all the
connections, the stiff nonstructural elements of significant
strength, and the foundation system.
3.6 CONCLUSIONS
In this chapter, Seismic evaluation procedure, modeling of the
existing RCC building with and without infill, pushover analysis, hinge
properties, procedure of pushover analysis using SAP2000 and use of
pushover analysis were discussed and presented.