ABSTRACT intensities of stress, transverse reinforcement is

ABSTRACT

It
is the factor by which the actual base shear forces, that would be generated if
the structure were to remain elastic during its response to the Design Basis
Earthquake (DBE) shaking, shall be reduced to obtain the design lateral force
(IS 1893 Part 1, 2002).This factor permits a designer to use a linear elastic
force-based design while accounting for non-linear behaviour and deformation
limits. Response reduction factor of 3 is used for OMRF and 5 for SMRF during
the building design. This paper present on overview of literature related to
the response reduction factor for RC – Structure . The review includes various
method for calculation of response reduction factor which is proposed by
different author.

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1. INTRODUCTION

1.1

Various models for the stress-strain relation of concrete have been
suggested in the past. Thoughthe performance of concrete up to the peak
concrete strength is well established, the post-peak part and the behaviour of
high-strength concrete have not been explored.

A proper stress-strain relation for confined concrete is required.
Confinement in concrete is attained by the suitable provision of transverse
reinforcement. At small intensities of stress, transverse reinforcement is
barely stressed; the concrete behaves much like unconfined concrete. At
stresses near to the uniaxial strength of concrete interior fracturing leads
the concrete to expand and bear out versus the transverse reinforcement which
causes a confining action in the concrete. This occurrence of confining
concrete by appropriate arrangement of transverse reinforcement grounds a
significant hike in the strength and ductility of concrete. The improvement of
strength and ductility by confining the concrete is a significant feature that
needs to be reflected in the design of structural concrete elements
particularly in areas susceptible to seismic activity. Again, several models
are available for the stress-strain relation of confined concrete. In this
study different models are taken into account and studied. IS code provides a
stress-strain relation which does not consider any effect of confinement. Other
models that were developed which evaluated the stress strain relation
considering the confinement effect were Kent and Park model (1971), Modified
Kent and Park model (Scott 1982), Mander’s model (Mander 1988a, 1988b), Razvi
Model (Saatcioglu and Razvi 1992) etc. Detailed explanations of each model are
given in Chapter 3. In this project Modified Kent and Park model is used, as this model
shows the highest percentage increase in column capacity and ductility and is
more close to Indian conditions.

 

Special And Ordnary Moment Resisting Frames (SMRF And OMRF)

According to Indian standards moment resisting frames are classified as
Ordinary Moment Resisting Frames (OMRF) and Special Moment Resisting Frames
(SMRF) with response reduction factors 3 and 5 respectively. Another main
difference is the provision of ductile detailing according to IS 13920 as
explained in Section 1.1 for the SMRF structures. The differences between these
two are given in Table 1.1. Different international codes classify buildings in
different ways which are elaborated in Section 2.2.

 

 

Table 1.1 Differences between SMRF and OMRF

 

SMRF

OMRF

It is a
moment-resisting frame specially detailed to provide ductile behaviour and
comply with the requirements given in IS 13920.

It is a
moment-resisting not meeting special detailing requirement for ductile
behavior.

Used under
moderate-high earthquakes

Used in low
earthquakes

R = 5

R = 3

Low design base
shear.

High design base
shear.

It is safe to design
a structure with ductile detailing.

It is not safe to
design a structure without ductile detailing.

 

Moment-resisting
frames are commonly used in urban areas worldwide as the dominant mode of
building construction. However, documented poor performance of ordinary moment
frames in past earthquakes warned the international community that this
structural system required special design and detailing in order to warrant a
ductile behaviour when subjected to the action of strong earthquake. When large
earthquake occurs, SMRF is expected to have superior ductility and provide
superior energy dissipation capacity. Current design provisions assigned the
highest R factor to SMRF. The elastic forces are reduced by a response
reduction factor to calculate the seismic design base shear. The building shall
be detailed as Special Moment Resisting Frames (SMRF) if the value of R assumed
is 5. Once the design is being done, it is required to ensure that the designed
building exhibit the adequate behaviour factors or response reduction factors.
Present study is an attempt to evaluate the response reduction factors of SMRF
and OMRF frames and to check the adequacy of R factors used by IS code.

1.2
Definition of Response Reduction Factor

Response
reduction is used to scale down the elastic response of the structure 8. The
structure is allowed to be damaged in case of severe shaking. Hence, structure
is designed for seismic force much less than what is expected under strong
shaking if the structure were to remain linearly elastic.

It
is simply represents the ratio of the maximum lateral force, Ve, which would
develop in a structure, responding entirely linear elastic under the specified
ground motion, to the lateral force, Vd, which has been designed to withstand.
Response reduction factor R, is expressed by the equation:

R
= Ve/ Vd (1)

The
factor R is an empirical response reduction factor intended to account for
damping, overstrength, and the ductility inherent in the structural system at
displacements great enough to surpass initial yield and approach the ultimate
load displacement of the structural system 1. The concept of a response
reduction factor was based on the premise that well-detailed seismic framing
systems could sustain large inelastic deformations without collapse(ductile
behavior) and develop lateral strength in excess of their design strength(often
termed reserve strength)2. R factor is first introduced in 19783, used to
reduce the elastic shear force (Ve) obtained by elastic analysis using a 5%
damped acceleration response spectrum for the purpose of calculating a design
base shear(Vd). Major static analysis routines are Equivalent Lateral Force
Method and Response Spectrum Method; in both procedures R factors are utilized
to calculate the design base shear.

Now,
the IS code provides the realistic force for elastic structure and divides
those forces by (2R) 16.

Force
reduction factor (2R) =Elastic Strength Demand / Design Strength = Rµ ?

Figure
3.1. Concept of response reduction factor

Response
Reduction Factor Formulation

In
the mid-1980s, Berkeley 1 described R as the product of three factors that
accounted for reserve strength, ductility, and added viscous damping.

Rs
stands for overstrength and calculated to be equal to the maximum base shear
force at the yield level (Vy) divided by the design base shear force (Vd).


stands for ductility factor and calculated as the base shear (Ve) for elastic
response divided by the yield base shear (Vy). The damping factor was set equal
to 1.0.ATC 19 27 splitting R into three component factors.

Where R? is replaced by RR(redundancy
factor). Differences in the values of the behavior factors specified in various
codes for the same types of structure.

 

2. LITERATURE REVIEW

2.1 SMRF & OMRF

IS
1893 (Part 1), 2002.Criteria for earthquake resistant design of structures Part
1 General provisions and buildings, Bureau of Indian Standards (BIS) classifies
RC frame buildings into two classes, Ordinary Moment Resisting Frames (OMRF)
and Special Moment Resisting Frames (SMRF) with response reduction factors 3
and 5 respectively. Response Reduction Factor (R) is the factor by which the
actual base shears that would be generated if the structure were to remain
elastic during its response to the Design Basis Earthquake (DBE) shaking, shall
be reduced to obtain the design lateral force. 

ACI
318: Building code requirements for reinforced concrete and commentary,
published by American Concrete Institute. ASCE 7 classifies RC frame buildings
into three ductility classes: Ordinary Moment Resisting Frame (OMRF),
Intermediate Moment Resisting Frames (IMRF) and Special Moment Resisting Frames
(SMRF) and corresponding reduction factors are 3, 5 and 8, respectively.

Han
and Jee (2005) investigated the seismic behavior of columns in Ordinary Moment
Resisting Frames (OMRF) and Intermediate Moment Resisting Frames (IMRF). In
their study two three-story OMRF and IMRF were designed as per the minimum
design and reinforcement detailing requirements suggested by ACI 318-02. The
IMRF interior column specimens exhibited superior drift capacities compared to
the OMRF column specimens. According to the test results, the drift capacities
greater than 3.0% and 4.5%, respectively.

Khose
et al. (2012) performed an overview of ductile detailing requirements for RC
frame buildings in different seismic design codes. The results obtained were as
shown in Table 2.1. 

?             Provision is not available

?             Provision is available

 

 
Ductile Detailing Criteria

ASCE 7

Euro-code 8

IS 1893

OMRF

IMRF

SMRF

DCL

DCM

DCH

OMRF

SMRF

 
Capacity Design

 
Strong column Weak beam

?

?

?

?

?

?

?

?

 
Capacity shear for column

?

?

?

?

?

?

?

?

 
Capacity shear for beam

?

?

?

?

?

?

?

?

 
Special Confinement Reinforcement

 
Column

?

?

?

?

?

?

?

?

 
Beam

?

?

?

?

?

?

?

?

 
Special Anchorage Reinforcement

 
Interior joint

?

?

?

?

?

?

?

?

 
Exterior joint

?

?

?

?

?

?

?

?

Joint shear design

?

?

?

?

?

?

?

?

Euro-code
8: Design of structures for earthquake resistance – Part 1: General rules, seismic
actions and rules for buildings, European Committee for Standardization, aims
to ensure the protection of life during a major earthquake simultaneously with
the restriction of damages during more frequent earthquakes. Euro-code 8 (EN
1998-1) classifies the building ductility as Ductility Class low (DCL) that
does not require delayed ductility and the resistance to seismic loading is
achieved through the capacity of the structure and reduction factor q = 1.5,
Ductility Class Medium (DCM) that allows high levels of ductility and there are
responsive design demands with reduction factor 1.5 4.

Sadjadi
et al. (2006), conducted an analytical study for assessing the seismic
performance of RC frames using non-linear time history analysis and push-over
analysis. A typical 5-story frame was designed as ductile, nominally ductile
and GLD structures. Most of the RC frame structures built before 1970 and
located in areas prone to seismic actions were designed only for gravity loads
without taking into account the lateral loads. These structures were referred
to as Gravity Load Designed (GLD) frames. The lack of seismic considerations in
GLD structures resulted in non-ductile behavior in which the lateral load
resistance of these buildings may be insufficient for even moderate
earthquakes. It was concluded that both the ductile and the nominally ductile
frames behaved very well under the considered earthquake, while the seismic
performance of the GLD structure was not satisfactory. After the damaged GLD
frame was retrofitted the seismic performance was improved.

 

2.2 Ductility

V.
Gioncu (2000) performed the review for ductility related to seismic response of
framed structures. The required ductility was determined at the level of full
structure behaviour, while the available ductility was obtained as local
behaviour of node (joint panel, connections or member ends). The checking for
ductility of columns is generally a difficult operation. For SMRF structures,
the column sections are enlarged to achieve a global mechanism. This
over-strength of the column may reduce the available ductility of columns. At
the middle frame height a drastic reduction of available ductility was
observed.  Since the required ductility
is maximum at this height, the collapse of the building may occur due to lack
of sufficient ductility. This was commonly observed during the Kobe earthquake,
where many building were damaged on the storeys situated at the middle height
of structure. It was observed that the factors regarding seismic actions, such
as velocity and cycling loading, reduce the available ductility.

 Moehle et al. (2008), conducted study on the
principles of seismic design of reinforced concrete Special Moment Framesas per
ACI 318. The proportioning and detailing requirements for special moment frames
were provided to ensure that inelastic response is ductile. The major
principles were to achieve a strong-column/weak-beam design that distributes
the inelastic response over several storeys, to prevent shear failure and to
provide details that enable ductile flexural response in yielding regions. When
a building sways during an earthquake, the distribution of damage over height
depends on the distribution of lateral drift. If the building has weak columns,
drift tends to concentrate in one or a few stories (Fig: 2.1 a), and may exceed
the drift capacity of the columns. On the other hand, if columns provide a
stiff and strong spine over the building height, drift will be more uniformly
distributed (Fig: 2.1 c), and localized damage will be reduced. It is important
to recognize that the columns in a given story support the weight of the entire
building above those columns, whereas the beams only support the gravity loads
of the floor of which they form a part; therefore, failure of a column is of
greater consequence than failure of abeam. Recognizing this behavior, building
codes specify that columns be stronger than the beams that frame into them.
Studies (Kuntz and Browning, 2003) have shown that the full structural
mechanism of Fig: 2.1 can only be achieved if the column-to-beam strength ratio
is relatively large (on the order of four). As this is impractical in most
cases, a lower strength ratio of 1.2 is adopted by ACI 318. Thus, some column
yielding associated with an intermediate mechanism (Fig: 2.1 b) is to be
expected, and columns must be detailed accordingly.

2.3 RESPONSE REDUCTION
FACTOR

Mondal
et al. (2013) conducted a study to find R for reinforced concrete regular frame
assemblies designed and detailed as per Indian standards IS 456, IS 1893 and
IS13920. Most seismic design codes today comprise the nonlinear response of a
structure obliquely through a ‘response reduction/modification factor’ (R).
This factor permits a designer to use a linear elastic force-based design while
accounting for nonlinear behaviour and deformation limits. This research was
aimed on the estimation of the actual values of this factor for RC moment frame
buildings designed and detailed as per Indian standards for seismic and RC
designs and for ductile detailing, and comparing these values with the value
given in the design code. Values of R were found for four designs at the two
performance levels. The results showed that the Indian standard suggests a
higher value of R, which is potentially hazardous. Since Indian standard IS
1893 does not provide any clear definition of limit state, the Structural
Stability performance level of ATC-40 was used here, both at the structure
level and at the member levels. In addition to this, actual member plastic
rotation capacities, were also calculated. Priestley recommended an ultimate
concrete compression strain for unconfined concrete = 0.005. The ultimate
compressive strain of concrete confined by transverse reinforcements as defined
in ATC-40 was taken in this work to obtain the moment characteristics of
plastic hinge segments. In order to prevent the buckling of longitudinal
reinforcement bars in between two successive transverse reinforcement hoops,
the limiting value of ultimate strain was limited to 0.02. Suitable modelling
of the preliminary stiffness of RC beams and columns is one of the important
aspects in the performance evaluation of reinforced concrete frames. Two
performance limits (PL1 and PL2) were considered for the estimation of R for
the study frames. The first one resembled to the Structural Stability limit
state defined in ATC-40. This limit state is well-defined both at the storey
level and at the member level. The second limit state was based on plastic
hinge rotation capacities that were found for each individual member depending
on its cross-section geometry. The global performance limit for PL1 was
demarcated by a maximum inter-storey drift ratio of 0.33Vi/Pi. The R values
attained were ranging from 4.23 to 4.96 for the four frames that were
considered, and were all lesser than specified value of R (= 5.0) for SMRF
frames in the IS 1893. The taller frames exhibited lower R values. Component
wise, the shorter frames (two-storey and four-storey) had more over-strength
and Rs, but slightly less ductility and R? compared to the taller frames.
According to Performance Limit 1 (ATC-40 limits on inter-storey drift ratio and
member rotation capacity), it was found that the Indian standard overestimates
the R factor, which leads to the potentially dangerous underestimation of the
design base shear. Based on Performance Limit 2 the IS 1893 recommendation was
found to be on the conservative side.

Krawinkler
et al. (1998) studied the advantages  and
disadvantages of Pushover analysis and suggested that element behaviour cannot
be  assessed in  the 
state of  currently  employed 
global  system  quality 
factors  such as  the  R
and  Rw factors  used 
in  existing  US 
seismic  codes. They also
recommended that pushover analysis will deliver insight into structural aspects
that control performance during severe earthquakes. For  structures that  vibrate 
chiefly  in  the 
fundamental  mode,  the 
pushover  analysis  will 
very  probably  provide 
good  estimations  of global, 
as  well  as 
local  inelastic,  deformation 
demands. This  analysis  will 
also  expose  design 
weaknesses  that  may remain 
hidden  in  an 
elastic  analysis.  Such 
weaknesses include  story
mechanisms,  excessive deformation
demands, strength  irregularities  and 
overloads  on  potentially 
brittle elements  such  as 
columns  and  connections.

Asgarian
and Shokrgozar (2008) evaluated over-strength, ductility and response
modification factor of Buckling Restrained Braced frames. Seismic codes
consider a decrease in design loads, taking benefit of the fact that the
structures possess substantial reserve strength (over-strength) and capacity to
disperse energy (ductility). The over-strength and the ductility are
incorporated in structural design through a force reduction or a response
modification factor. This factor represents ratio of maximum seismic force on a
structure through specified ground motion if it was to remain elastic to the
design seismic force. Thus, seismic forces are reduced by the factor R to
obtain design forces. The basic fault in code actions is that they use linear
methods not considering nonlinear behaviour. The structure can engross quiet a
lot of earthquake energy and repels when it enters the inelastic zone of
deformation. Over-strength in structures is connected to the fact that the
maximum lateral strength of a structure usually beats its design strength. It
was perceived that the response modification factor drops as the height of
building increases. This result was outward in all type of bracing outline.

3. CONCLUSION

This
paper dealt with the numerous numbers of papers and journals that has been
found helpful for carrying out the work. An extensive literature review is done
and the inference is noted down. It is well established from various studies
that ductile detailing is necessary to resist earthquakes. SMRF buildings
exhibit higher ductility and resistance to seismic loading through proper
confinement of transverse reinforcement compared to OMRF buildings. A detailed
review of the above models in addition to IS 456 model is done in this study.
In-order to study the ductility, response reduction factors are to be
calculated which can be obtained using non-linear static pushover analysis. For
obtaining a much reliable pushover curve of frames, a stress-strain confinement
model which actually distinguishes the behaviour of confined and unconfined
concrete has to be used.