Journal Article

1. SPECIAL ISSUE MANUSCRIPT
Effect of Seismic Zone and Story Height on Response Reduction
Factor for SMRF Designed According to IS 1893(Part-1):2002
P. Pravin Venkat Rao1 • L. M. Gupta2
Received: 10 May 2015 / Accepted: 17 October 2016
Ó The Institution of Engineers (India) 2016
Abstract Indian seismic code design procedure, which
permit the estimation of inelastic deformation capacity of
lateral force resisting systems, has been questioned since
no coherence exists for determining the values of response
reduction factor tabulated in code. Indian code at present
does not give any deterministic values of ductility reduc-
tion factor and overstrength factor to be used in the design,
because of the inadequacy of research results currently
available. Hence, this study focuses on the variation of
overstrength and ductility factors in steel moment resisting
frame with different seismic zones and number of story. A
total of 12 steel moment resisting frames were analyzed
and designed. Response reduction factor has been deter-
mined by performing the non-linear static pushover anal-
ysis. The result shows that overstrength and ductility
factors varies with number of story and seismic zones. It is
also observed that for different seismic zones and story,
ductility reduction factor is found to be different from
overall structural ductility. It is observed that three build-
ings of different heights had an average overstrength of
63% higher in Zone-II as compared to Zone-V. These
observations are extremely significant for building seismic
provision codes, that at present not taking into considera-
tion the variation of response reduction factor.
Keywords Ductility reduction factor Á
Non-linear static pushover analysis Á Overstrength factor Á
Response reduction factor Á Steel moment resisting frame Á
Structural ductility
Introduction
The philosophy of earthquake resistant design is that a
structure should resist earthquake ground motion without
any collapse, although it may undergo some structural as
well as non-structural damage. So to be consistent with this
philosophy, seismic design provisions have been developed
with the intent of ensuring life safety where high seismic
risk exists. When designing structures for earthquakes,
inelastic deformations are allowed to take place in some
critically stressed elements. This is because, it is not
practical or economical for a structure to respond elasti-
cally, when subjected to the level of Design Basis Earth-
quake (DBE). It is the intent of modern design codes that
many types of seismic force resisting systems are assumed
to behave in a ductile manner and undergo large inelastic
cycles of deformation when subjected to a major earth-
quake [1].
Larger earthquakes have much lower frequency of
occurrence compared to smaller earthquakes. Therefore, a
structure during its lifetime has a very low probability of
experiencing ground motion from a large earthquake, but
when a structure is subjected to inertia forces caused by a
severe earthquake; it will not collapse, but it is subjected to
heavy structural damage, if capable of responding in the
elastic range [2]. A structure to become earthquake proof,
immensely expensive designs and materials are required.
Generally, structure may have a design life of 50–
100 years. In such a case, it may be uneconomical to
design a building, so that it remains undamaged during a
larger earthquake that may takes place say once in
& P. Pravin Venkat Rao
ppkvr49@gmail.com
1
Department of Earthquake Engineering, Indian Institute of
Technology, Roorkee, India
2
Applied Mechanics Department, Visvesvaraya National
Institute of Technology, Nagpur, India
123
J. Inst. Eng. India Ser. A
DOI 10.1007/s40030-016-0183-x

2. 500 years. Hence, the structure is designed for much lower
base shear forces compared to actual seismic load coming
on to the structure. This allows the introduction of strength
reduction factors to lower down the elastic strength
capacity and to increase the inelastic drift demand.
Therefore, Indian seismic code [3] divides the seismic
response by the response reduction factor (R) to get a lower
elastic design force or design base shear. Design base shear
(Fd) is determined using Eq. 1,
Fd ¼
Felastic
R
ð1Þ
Response reduction factor of 5 is currently recommended
for special moment resisting steel frames [3]. As per Uni-
form Building Code (UBC), such reductions are mainly
because of two factors:
(a) Ductility reduction factor (Rl)
(b) Overstrength factor (X)
As a result of ductility, the structure has a capacity to
dissipate hysteretic energy. Because of this energy dissi-
pation capacity, ductility reduction factor is introduced that
reduces the elastic demand force to the level of the
maximum yield strength of the structure, whereas over-
strength factor accounts for the overstrength introduced in
code designed structures.
Response Reduction Factor (R)
Response reduction factor has emerged as a single most
important number that reflects the capability of structure to
dissipate energy through inelastic behaviour. It is used to
reduce the design forces in earthquake resistant design and
accounts for overstrength, redundancy, energy absorption
capacity, ductility capacity, dissipation as well as structural
capacity to redistribute forces from inelastic highly stressed
regions to other low stressed locations in the structure.
Response reduction factors are important in the specifica-
tion of design seismic loading. This factor is unique for
different kind of structures and the materials used.
Response reduction factor was proposed based on the fact
that well detailed framing systems could sustain large
inelastic deformation without collapse (ductile behaviour)
and develop lateral strength in excess of their design
strength (often termed as reserve strength or overstrength).
Response reduction factors tabulated in the current
seismic codes are primarily based on observation of the
performance of different structural systems in past strong
earthquakes and the detailing procedure used for the design
[4]. In present study, response reduction factor has been
determined using Eq. 2.
R ¼ X Á Rl Á Rsm ð2Þ
where Rsm is the material overstrength factor, which is
product of two factors i.e. R1 and R2. R1 factor is used to
account for the difference between actual and nominal
static yield strength of material respectively. For structural
steel, the value of R1 may be taken as 1.05. R2 factor is
used to consider the increase in yield stress, as a result of
strain rate effect during an earthquake excitation. For the
strain rate effect, a value of 1.1 or a 10% increase could be
used. Therefore, Rsm of 1.155 is taken into consideration
for finding out the response reduction factor [5].
Overstrength (X) and Ductility Reduction Factor
(Rl)
During earthquakes, it is closely observed that the building
structures could take the forces considerably larger than
that they were designed for. This is explained by the
presence of such structures with significant reserve strength
not accounted for in design [6]. Overstrength helps the
structures not only to stand safely against severe tremors
but reduces the elastic strength demand as well [7]. This
objective is performed using force reduction factor by
several codes of practice. Figure 1 represents the base
shear coefficient versus roof displacement relationship of a
structure, which can be developed by a non-linear static
pushover analysis. The overstrength factor and ductility
reduction factor from Fig. 1 is defined as follows:
X ¼
Cy
Cw
ð3Þ
Fig. 1 Global structural response
J. Inst. Eng. India Ser. A
123

3. Rl ¼
Ceu
Cy
ð4Þ
where Cy is the base shear coefficient corresponding to bi-
linearized yield roof displacement, Cw is the base shear
coefficient corresponding to code prescribed design base
shear, and Ceu is the maximum base shear coefficient that
develops in the structure, if it were to remain in the elastic
range. From the analysis results, overstrength and ductility
reduction factor of the Steel Moment Resisting Frame
(SMRF) are determined using Eqs. 3 and 4 respectively.
These equations were based on the use of nominal material
properties applied.
Previous Work
Many researchers have attempted to identify the factors
that may have contributed to the observed overstrength.
The possible sources of overstrength are: (1) actual
strength of the material used in construction is higher than
the strength used in calculating the capacity in design; (2)
effect of using discrete member sizes, for example: selec-
tion of members from a discrete list of available sections;
(3) effect of non-structural elements, such as infill walls;
(4) effect of structural elements that are not included in the
prediction of lateral load capacity, for example: contribu-
tion of reinforced concrete slabs; (5) effect of minimum
requirements on member sections in order to meet the
stability and serviceability limits; (6) architectural consid-
erations that dictate provision of extra or larger structural
members, for example: shear walls; (7) use of single degree
of freedom spectra alone with assumed load distribution;
and (8) redistribution of internal forces in the inelastic
range [7]. The researchers have [7] obtained the over-
strength factor ranging from 1.5 to 3.5 for different types of
ten-story braced frame.
Some of the investigators have [8] pointed out that the
survival of code designed structures in the event of sig-
nificantly higher seismic shaking is possible only because
of implicitly assumed overstrength. Osteraas and Krawin-
kler [9] studied structural overstrength of steel framing
systems: distributed moment frames, perimeter moment
frames, and concentric braced frames designed in compli-
ance with the Uniform Building Code working stress
design provisions. They reported overstrength factors
ranging from 1.8 to 6.5 for the three framing systems. Also,
they have found that the perimeter moment resisting frames
have a smaller structural overstrength than moment
resisting space frames, because the gravity loads do not
Fig. 2 Building plan
configuration
J. Inst. Eng. India Ser. A
123

4. substantially influence the design of perimeter moment
resisting frames.
It is difficult to quantify the overstrength due to most of
the above factors mentioned by Humar and Rahgozar [7].
However, the overstrength attributable to redistribution of
internal forces in the inelastic range, arising from simpli-
fication in design procedure, is dependable and can be
estimated reliably. After getting the first significant yield in
a structure, stiffness of the structure decreases, but the
structure is capable of taking further loads. This is because
of the structural overstrength which results from: (1)
internal force distribution; (2) higher material strength; (3)
strain hardening; (4) member oversize; (5) effect of non-
structural elements and structural non-seismic elements;
(6) strain rate effects, etc. [10]. The researchers have [10]
reported overstrength of 2–3 for a one-, three-, and five-bay
steel frame with four, eight, and twelve story located in a
region of high seismic risk; and overstrength of a four-story
steel frame is about 40% higher than that of a twelve-story
steel frame, while the overstrength is not very sensitive to
the number of bays.
The importance of overstrength in the performance of
buildings during a severe earthquake has been discussed by
the earlier investigators [11] who looked at several factors
that contribute to the actual performance of buildings in a
severe ground motion. The researchers have [12] showed
through an experimental study on a 1/4-scale model of a
six-story concrete frame structure that a structure designed
for an unfactored base shear coefficient of 0.092 could
theoretically resist 7.65 times as much. Miranda and
Bertero [13] based on the study of low-rise buildings in
Mexico City, have noted the value of overstrength in the
range of 2–5 which is significantly higher, if slab contri-
bution and masonry distribution are taken into
consideration.
Dynamic analysis results by some of the researchers
[14] on wall, dual wall-frame, and frame systems indi-
cated an overstrength value of 3–5 with frame systems
generally having a higher value of overstrength than wall
systems. The literature [15] showed that the available
overstrength varies widely depending on the type of
structure and characteristics of ground motion. The
researchers have [16] found that when rigid connections
are replaced with semi-rigid connections, the over-
strength factor decreases around 50%, while the ductility
factor increases more than 25%.
Fig. 3 a Elevation of 3-story building, b elevation of 5-story building, c elevation of 7-story building
J. Inst. Eng. India Ser. A
123

5. Analysis of Building Models
For present study, a building plan having centreline
dimension of 26.8 m 9 23.7 m was considered (refer
Fig. 2). Soil conditions were assumed to be a hard soil.
Elevation configuration of buildings consists of three-, five-
, and seven-story with same floor plan arrangement located
in seismic Zones II, III, IV, and V were shown in Fig. 3.
Live load on floor and roof was taken as 2.5 and 1.5 kN/m2
respectively. Dead load on floor, roof, and for water
proofing was taken as 1.0, 1.0, and 1.5 kN/m2
respectively.
Brick wall thicknesses on peripheral and internal beams
were taken as 230 and 115 mm respectively. All storys
have a height of 3.6 m each. The design base shear for each
building was calculated as per Indian seismic code using
Eq. 5.
VB ¼ Ah Á W ð5Þ
Ah ¼
Z
2
:
I
R
:
Sa
g
ð6Þ
T ¼ 0:09
h
ffiffiffi
d
p ð7Þ
where Ah is the horizontal seismic coefficient calculated
using Eq. 6, W is seismic weight of the structure, Z is the
zone factor, Importance factor is denoted by I, R denotes
the response reduction factor and Sa/g is the design spectral
acceleration that depends on the fundamental period of the
structure and soil type. The fundamental time period
(s) was estimated by using Eq. 7. Where h is the building
height and d is the base dimension of the building in
meters, along the considered direction of the lateral force.
To distribute various loads from slab to beams, yield
line pattern of loading was used (see Fig. 4). For seismic
analysis, seismic zone factor of 0.1, 0.16, 0.24, and 0.36
were used for Zone II, III, IV, and V respectively as per
Indian seismic code. Importance factor of 1, and prelimi-
nary response reduction factor of 5 had been used. Steel
moment resisting frames were simulated in SAP 2000
software. A total of 12 different steel frame configurations
was analyzed and designed as per Indian seismic code and
Indian steel code. Dynamic analysis has been carried out
using the response spectrum method. In response spectrum
analysis, user defined spectrum has been generated as
shown in Fig. 5. Beam and column joints of steel frames
are assumed to be rigid. Geometric non-linearity had been
taken into account by considering P-Delta effect.
Rigid diaphragm is provided at all floor levels to have a
continuous load path in the building and also to transfer the
horizontal load to the vertical resisting elements in direct
proportion to their relative rigidities. In analysis, damping
for steel is taken as 2% and multiplication factor for
Fig. 4 Slab load distribution on
peripheral and internal beams
J. Inst. Eng. India Ser. A
123

6. damping was taken as 1.4 in order to reduce response
motion of a structural system as a result of energy loss. The
design lateral forces at each floor level for all the story are
distributed using Eq. 8.
Qi ¼ VB:
Wi:h2
i
Pn
j¼1 Wj Á h2
j
ð8Þ
where Qi is design lateral force at floor i, Wi is seismic
weight of floor i, hi is height of the floor i measured from
base, and n is the number of story in the building.
Design of Building Models
Indian standard steel sections were used for the design of
all structural members of 3-, 5-, and 7-story steel moment
resisting frames located in different seismic zones. The
designs of the steel frames were obtained by an iterative
process. The sections were designed according to IS
800:2007 [17] using limit state. The following load com-
binations were used as per limit state of strength: (1)
1.5(DL ? LL); (2) 1.5(DL ? EQx); (3) 1.5(DL - EQx);
(4) 1.5(DL ? EQy); (5) 1.5(DL - EQy); (6)
1.2(DL ? LL ? EQx); (7) 1.2(DL ? LL - EQx); (8)
1.2(DL ? LL ? EQy); (9) 1.2(DL ? LL-EQy); (10)
0.9DL ? 1.5EQx; (11) 0.9DL - 1.5EQx; (12)
0.9DL ? 1.5EQy; (13) 0.9DL - 1.5EQy; where DL is
dead load, LL is live load, and EQ is earthquake or seismic
load. Section properties of building models were shown in
Table 1. Interaction checks for bending moment, combined
axial force and bending moment, and overall buckling
strength has also been satisfied using Eqs. 9, 10, 11, and 12
respectively for all the steel sections designed as per IS
800:2007 and they are as follows:
My
Mdy
þ
Mz
Mdz
1 ð9Þ
N
Nd
þ
My
Mdy
þ
Mz
Mdz
1 ð10Þ
P
Pdz
þ 0:6Ky
CmyMy
Mdy
þ Kz
CmzMz
Mdz
1 ð11Þ
P
Pdy
þ Ky
CmyMy
Mdy
þ KLT
Mz
Mdz
1 ð12Þ
where My and Mz are factored applied moments about the
minor and major axis of the cross section, N is factored
applied axial force, Nd is design strength in compression,
Mdy and Mdz are bending strength about minor and major
axis of the cross section, Cmy and Cmz are equivalent uni-
form moment factor.
Fundamental Period of Building Models
Table 2 shows the first mode period of vibration of all
buildings designed for the study. It can be seen that period
of vibration of building decreases as the severity of ground
motion increases in different seismic zones; because, in
higher seismic zones, ground acceleration is more and
therefore earthquake force coming on the structure is
Fig. 5 Response spectra for hard
soil for 2% damping
J. Inst. Eng. India Ser. A
123

7. comparatively larger than lower seismic zones. Figure 6
shows that as the number of storys of the building
increases, the differences of the first mode period for each
set of 3-, 5-, and 7-story buildings become larger. In
addition, the periods from the empirical equations as per IS
1893(Part-1):2002 provisions were calculated and shown in
Table 2.
Table 1 Section properties of building models
Story
levels
Zone-II Zone-III Zone-IV Zone-V
Column Beam Column Beam Column Beam Column Beam
Exterior Interior Exterior Interior Exterior Interior Exterior Interior
Three-story design
1 ISWB
450
ISHB
450(1)
ISMB
350
ISHB
450(1)
ISHB
450(2)
ISWB
350
ISHB
450(2)
ISWB
550
ISWB
350
ISWB
550
ISWB
600(1)
ISWB
400
2 ISHB
450(1)
ISWB
450
ISMB
350
ISHB
450(2)
ISHB
450(1)
ISWB
350
ISWB
500
ISHB
450(1)
ISWB
350
ISWB
500
ISHB
450(2)
ISWB
400
3 ISWB
400
ISWB
400
ISMB
300
ISWB
450
ISWB
400
ISMB
300
ISWB
450
ISWB
400
ISMB
300
ISWB
450
ISWB
400
ISMB
350
Five-story design
1 ISWB
550
ISWB
600(1)
ISMB
350
ISWB
550
ISWB
600(1)
ISMB
350
ISWB
600(1)
ISWB
600(2)
ISWB
400
ISWB
600(1)
ISWB
600(2)
ISWB
500
2 ISHB
450(2)
ISWB
600(1)
ISMB
350
ISWB
550
ISWB
600(1)
ISWB
400
ISWB
600(1)
ISWB
600(1)
ISWB
450
ISWB
600(1)
ISWB
600(2)
ISWB
500
3 ISHB
450(1)
ISHB
450(1)
ISMB
350
ISWB
550
ISHB
450(1)
ISWB
400
ISWB
550
ISWB
550
ISWB
400
ISWB
550
ISWB
550
ISWB
450
4 ISWB
400
ISWB
450
ISMB
300
ISHB
450(1)
ISHB
450(1)
ISMB
300
ISHB
450(2)
ISHB
450(2)
ISMB
350
ISHB
450(2)
ISHB
450(2)
ISWB
450
5 ISWB
400
ISWB
350
ISMB
300
ISHB
450(1)
ISWB
400
ISMB
300
ISHB
450(1)
ISWB
400
ISMB
300
ISWB
450
ISWB
400
ISMB
350
Seven-story design
1 ISWB
600(1)
ISWB
600(1)
ISMB
350
ISWB
600(1)
ISWB
600(1)
ISWB
400
ISWB
600(1)
ISWB
600(1)
ISMB
500
ISWB
600(2)
ISWB
600(2)
ISWB
550
2 ISWB
600(1)
ISWB
600(2)
ISWB
400
ISWB
600(1)
ISWB
600(2)
ISWB
400
ISWB
600(1)
ISWB
600(2)
ISWB
500
ISWB
600(2)
ISWB
600(2)
ISMB
600
3 ISWB
550
ISWB
600(1)
ISWB
400
ISWB
600(1)
ISWB
600(1)
ISWB
400
ISWB
600(1)
ISWB
600(1)
ISWB
450
ISWB
600(1)
ISWB
600(2)
ISWB
550
4 ISWB
500
ISWB
550
ISMB
350
ISWB
550
ISWB
550
ISWB
400
ISWB
600(1)
ISWB
600(1)
ISMB
450
ISWB
600(1)
ISWB
600(2)
ISWB
450
5 ISWB
500
ISWB
500
ISMB
350
ISWB
500
ISWB
550
ISWB
400
ISWB
550
ISWB
550
ISMB
450
ISWB
600(1)
ISWB
600(1)
ISMB
450
6 ISWB
450
ISHB
450(1)
ISMB
300
ISHB
450(1)
ISHB
450(2)
ISWB
400
ISHB
450(2)
ISWB
500
ISMB
450
ISWB
500
ISWB
500
ISMB
450
7 ISWB
450
ISWB
450
ISMB
300
ISHB
450(1)
ISWB
450
ISMB
300
ISHB
450(2)
ISHB
450(1)
ISMB
350
ISHB
450(2)
ISHB
450(2)
ISMB
350
Table 2 First mode period (s) of building models
Building height Designed building models
Seismic zones Empirical code equations
Zone-II Zone-III Zone-IV Zone-V 0:09hffiffi
d
p Ta = 0.085h0.75
3 0.917 0.872 0.816 0.722 0.188 0.506
5 1.454 1.308 1.176 1.038 0.313 0.742
7 1.891 1.735 1.514 1.353 0.438 0.956
J. Inst. Eng. India Ser. A
123

8. Stability and Drift Checks
Deflections must be limited during earthquakes for a
number of reasons. Relative horizontal deflections within
the building (e.g. between one story and the next, known as
story drift) must be limited. This is because non-structural
elements such as cladding, partitions and pipework must be
able to accept the deflections imposed on them, during an
earthquake without failure. Failure of external cladding,
blockage of escape routes by fallen partitions and ruptured
firewater pipework all have serious safety implications.
Moreover, some of the columns in a building may only be
designed to resist gravity loads, with the seismic loads
taken by other elements, but if deflections are too great
they will fail through ‘P-delta’ effects however ductile they
are. Overall deflections must also be limited to prevent
impact, both across separation joints within a building and
between buildings.
Drift Check
Drift in any story can be calculated using Eq. 13 (see
Fig. 7). Drift needs to be checked for serviceability
criterion. In the present study, drift is checked for a load
combination of (DL ? LL ? EQx). The story drift with
partial load factor of 1.0 shall not exceed 0.004 times the
story height (i.e. 0.4% of story height) due to the min-
imum specified design lateral force according to IS 1893
(Part-1):2002. Drift check is performed for all the 12
steel moment resisting frames and is found to be safe as
the story drift for all the buildings are less than 0.4% of
story height. Variation of inter-story drift for all build-
ings located at different seismic zones is shown in
Figs. 8, 9, and 10.
Drift ¼
ðD1 À D2Þ
h
 100 ð13Þ
Overturning Check
The stability of a structure as a whole against overturning
shall be ensured so that the stabilizing moment, shall not be
less than the sum of 1.2 times the maximum overturning
moment due to characteristic dead load and live load. In
cases where dead load provides the stabilizing moment,
only 0.9 times the characteristic dead load shall be con-
sidered. The Stabilizing and overturning moment is cal-
culated using Eqs. 14 and 15 respectively. Overturning
check is performed for all the 12 steel buildings and is
found to be safe. Refer Fig. 11 for the nomenclatures given
in Eqs. 14 and 15.
Stabilizing moment ¼ 0:9 Â Structure weight ðWÞ Â C:G
ð14Þ
Overturning Moment ¼ ðF1 Â 3:6Þ þ ðF2 Â 7:2Þ þ ðF3
 10:8Þ
ð15Þ
Fig. 6 Variation of first mode
periods of example building
J. Inst. Eng. India Ser. A
123

9. Sliding Check
The structure shall have a factor against sliding of not less
than 1.4 under the most adverse combination of the applied
characteristic forces. In this case, only 0.9 times the char-
acteristic dead load shall be taken into account. The Sta-
bilizing and sliding force is calculated using Eqs. 16 and 17
respectively.
Stabilizing Force ¼ 0:9 Â Structure weight ðWÞ Â l ð16Þ
Sliding Force ¼ Base shear ð17Þ
where l is the coefficient of friction and the value is taken
as 0.8. The ratio between stabilizing force and sliding force
for all the buildings are found to be more than 1.4, hence it
is safe.
Non-linear Static Analysis
Non-linear static pushover analysis under incremental lat-
eral displacement controlled loading were performed on 3-,
5-, and 7-story steel buildings in all four seismic zones by
Fig. 7 Deformed shape of a building
Fig. 8 Variation of story drift in
3-story building
J. Inst. Eng. India Ser. A
123

10. using SAP 2000 software to evaluate its lateral strength and
post-yield behaviour. The loading applied was monotonic
in nature. Pushover analysis was done only in X-direction.
Plastic hinge properties were assigned to steel beam and
column sections as per FEMA 356 [18]. Force and dis-
placement capacity of the structure along with the
sequential formation of hinges are found under pushover
analysis. The result of non-linear static analysis was rep-
resented in the form of pushover curve, i.e. base force
coefficient versus roof displacement. The seismic base
shear coefficient was calculated from the ratio of lateral
force or base shear to structural seismic weight.
The pushover curve is generally constructed to represent
the first mode response of the structure based on the
assumption that the fundamental mode of vibration is the
predominant response of the structure. The capacity curve
represents the primary data for the evaluation of the
response reduction factor for steel moment resisting
frames, but first of all it must be idealized in order to
extract the relevant information from the plot.
Fig. 9 Variation of story drift in
5-story building
Fig. 10 Variation of story drift in
7-story building
J. Inst. Eng. India Ser. A
123

11. A bi-linear curve is fitted to the capacity curve, such that
the first segment starts from the origin, intersects with the
second segment at the significant yield point and the sec-
ond segment starting from the intersection ends at the
ultimate or maximum displacement point. Bi-linearization
is done by means of equal energy concept in which the area
under the capacity curve and the area under the bi-linear
curve are kept equal. After the bi-linearization of pushover
curve, overstrength factors (X) and ductility reduction
factors (Rl) were found out. Overall ductility demand (l)
was taken as the maximum displacement (Dmax) to the
yield displacement (Dy) of the structure.
Results and Conclusion
The force–displacement relationship for the three-, five-,
and seven-story buildings are shown in Figs. 12, 13, and 14
respectively. These figures show that the three-story
building has a higher base shear coefficient and less roof
displacement than the five -story building, which in turn
has a higher base shear coefficient and less roof displace-
ment than the seven-story building. This is due to the
increasing stiffness and higher moment resisting capacity
of steel sections which were required to support additional
gravity loads in higher buildings.
Figure 15 shows the variation of overstrength with the
number of storey for different seismic zones. It can be seen
that the overstrength of buildings in lower seismic zones is
significantly higher than the overstrength of buildings in
higher seismic zones. For example: the overstrength of a
three-story building in Zone-II is 4.074, while it is 2.730 in
seismic Zone-V. The same is for the case of five-story
building (overstrength factor = 2.960 in Zone-II, and
1.816 in Zone-V), and for the seven-story building (over-
strength factor = 2.685 in Zone-II, and 1.434 in Zone-V).
Thus, the overstrength for different zones may vary due to
the prominence of gravity loads in the design for low
seismic zones. Figure 15 also shows that the three-story
building has a higher overstrength as compared to the five-
story building, which in turn has higher overstrength than
the seven-story building. This is because in low-rise
buildings the gravity loads play a significant role in the
design of members than in high-rise buildings located in
the same seismic zone.
For example: In 3-story building frame, the maximum
bending moment for a first floor beam due to DL and LL is
72.65 and 34.05 kN m respectively, whereas EQ load in
Zone-II and Zone-V is found to be 24.86 and 84.87 kN m
respectively. Therefore, according to load combinations,
this gives the values of 1.5(DL ? LL), 1.5(DL ? EQx),
1.2(DL ? LL ? EQx), and 0.9DL ? 1.5EQx in Zone-II as
160.05, 146.26, 157.87, and 102.67 kN m respectively, and
for Zone-V as 160.05, 236.28, 229.88, and 192.69 kN m
respectively. Thus, the same beam is designed for a
moment of 160.05 kN m in Zone-II and 236.28 kN m in
Zone-V. During the actual seismic event, by assuming that
full DL and 25% of LL will act on the structure, the
moment acting on the beam due to gravity load is
81.16 kN m. The remaining moment capacity of the beam
becomes available for resisting the EQ load are
78.89 kN m for Zone-II and 155.12 kN m for Zone-V
respectively. Therefore the effective load factor on earth-
quake load for Zone-II is 3.17 (=78.89/24.86), and for
Zone-V is 1.83 (=155.12/84.87). This simple example of a
particular beam may be true for many members of the
frame.
The overstrength factor (X), ductility reduction factor
(Rl), and overall structural ductility or ductility demand
(l) values are shown in Tables 3, 4, and 5 respectively.
It was found that the ductility demand, as well as the
ductility reduction factors decreases as the number of
Fig. 11 Stabilizing and overturning moment calculation procedure for a building
J. Inst. Eng. India Ser. A
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12. storys increased. Ductility factor ranges from Zone-II to
Zone-V as 2.35–1.39 for three-story building, 2.22–1.18
for five-story building, and 1.66–1.01 for seven-story
building. It was also observed that the ductility factors
vary with seismic zones. This has serious implications
for seismic design codes especially that the ductility
reduction factor decreases slightly with increasing the
risk of the seismic zone. From Fig. 16, it has been
observed that the seismic zoning has an impact on the
Rl for all studied buildings. It is also observed that for
different seismic zones and for different building
heights, ductility reduction factor is found to be different
from overall structural ductility.
It is obvious that overstrength against lateral load is
significantly affected by the gravity loads used in the
design. Hence, it results in the overstrength being much
higher for low seismic zones, for low rise buildings, and for
higher design live load. From the results it is seen that the
significance of seismic zone on overstrength is very much
dependent. The average overstrength factor of steel frames
Fig. 12 Force-displacement
relationship for 3-story building
Fig. 13 Force-displacement
relationship for 5-story building
J. Inst. Eng. India Ser. A
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13. in Zone-II and Zone-V is 3.24 and 1.99, respectively.
Overstrength factor for three-story building is higher than
seven-story building by 52% in Zone-II and 90% in Zone-
V. These results conclude that overstrength factors
decreases with increase in story height and with increase in
ground motion intensity.
Fig. 14 Force-displacement
relationship for 7-story building
Fig. 15 Variation of overstrength
factor
Table 3 Overstrength, ductility reduction factor and overall ductility demand of 3-story building
Seismic zone Ceu Cy Cw Dmax, mm Dy, mm X Rl l
Zone-II 0.336 0.143 0.035 159.875 49.600 4.074 2.356 3.223
Zone-III 0.455 0.224 0.056 178.903 61.200 3.993 2.035 2.923
Zone-IV 0.462 0.276 0.084 195.053 76.000 3.286 1.674 2.566
Zone-V 0.480 0.344 0.126 222.118 78.750 2.730 1.395 2.821
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14. The response reduction factor (R) for 3-, 5-, and 7-story
buildings with different seismic zones are presented in
Table 6. Figure 17 shows that the seismic zones and
number of story have a strong influence on response
reduction factor. From Table 7, it is seen that design base
shear force is less for buildings located in the lower seismic
zones. This effect is presented by calculating VB, firstly by
considering R = 5 and secondly, by considering R = 1.
Table 4 Overstrength, ductility reduction factor and overall ductility demand of 5-story building
Seismic zone Ceu Cy Cw Dmax, mm Dy, mm X Rl l
Zone-II 0.230 0.104 0.035 183.181 100.640 2.960 2.224 1.820
Zone-III 0.243 0.140 0.056 187.619 101.840 2.500 1.736 1.842
Zone-IV 0.254 0.181 0.084 222.972 112.500 2.150 1.406 1.982
Zone-V 0.272 0.229 0.126 264.401 116.600 1.816 1.189 2.268
Table 5 Overstrength, ductility reduction factor and overall ductility demand of 7-story building
Seismic zone Ceu Cy Cw Dmax, mm Dy, mm X Rl l
Zone-II 0.143 0.086 0.032 220.000 136.400 2.685 1.667 1.613
Zone-III 0.155 0.099 0.051 249.088 152.000 1.936 1.566 1.639
Zone-IV 0.159 0.115 0.077 293.695 159.300 1.499 1.383 1.844
Zone-V 0.167 0.165 0.115 360.779 182.500 1.434 1.012 1.977
Fig. 16 Variation of ductility
reduction factor
Table 6 Response reduction factors for 3, 5, and 7 story buildings
Building models’ Three-story Five-story Seven-story
Seismic zone X Rl Rsm R X Rl Rsm R X Rl Rsm R
Zone-II 4.074 2.356 1.155 11.088 2.960 2.224 1.155 7.603 2.685 1.667 1.155 5.169
Zone-III 3.993 2.035 1.155 9.384 2.500 1.736 1.155 5.012 1.936 1.566 1.155 3.501
Zone-IV 3.286 1.674 1.155 6.353 2.150 1.406 1.155 3.493 1.499 1.383 1.155 2.395
Zone-V 2.730 1.395 1.155 4.400 1.816 1.189 1.155 2.493 1.434 1.012 1.155 1.677
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15. Table 7 shows that the R influences the value of bases
shear. The base shear (VB) is increased enormously in
higher seismic zones, mainly for higher buildings and
reduced in lower seismic zones as shown in Fig. 18.
Table 8 shows a comparison of elastic base shear forces
using code based equation and analysis results. From
Fig. 19, it can be seen that base shear force calculated from
the code based equation is not matching with elastic base
shear from the analysis. Because, empirical equation
suggested by the code to find base shear is to give the
preliminary idea; hence, to know the actual elastic beha-
viour of the structure, linear analysis was carried out and
the elastic base shear was found out from the push-over
curve.
It has been observed that most analytical and experi-
mental research in earthquake engineering is focused on
high risk seismic zones. While drafting the design codes,
discussion is normally focused on the seismic coefficient
Table 7 Comparison of base shear force
Building models Three-story Five-story Seven-story
Seismic zone Base shear (VB), kN
R = 5 R = 1 R = 5 R = 1 R = 5 R = 1
Zone-II 673.95 3370.92 1186.85 5934.27 1559.68 7798.87
Zone-III 1082.00 5411.53 1908.82 9546.30 2503.44 12,547.39
Zone-IV 1627.18 8128.93 2874.23 14,400.50 3789.30 18,951.01
Zone-V 2454.19 12,274.91 4344.77 21,729.94 5728.81 28,648.17
Table 8 Comparison of elastic base shear force using R = 1
Building models Three-story Five-story Seven-story
Seismic zone Elastic base shear (VB), kN
Formula Analysis Formula Analysis Formula Analysis
Zone-II 3370.92 6595.39 5934.27 8103.93 7798.87 7208.74
Zone-III 5411.53 9082.11 9546.30 8612.07 12,547.39 7840.76
Zone-IV 8128.93 9278.14 14,400.50 9038.42 18,951.01 8093.82
Zone-V 12,274.91 9801.27 21,729.94 9730.49 28,648.17 8549.14
Fig. 17 Variation of response
reduction factor
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16. for higher zones, whereas the coefficient for lower seismic
zones is simply given in proportion to the expected ground
motion intensity in different zones. Thus, the variation in
overstrength and ductility factor for different zones is never
been considered, even implicitly. This results in seismic
design provisions for lower seismic zones being much
more conservative compared to higher seismic zones.
Similarly, the earthquake design for low-rise buildings is
more conservative than it is for high-rise buildings.
This present study clearly shows that the overstrength in
steel moment frame buildings could have a very large
variation. Therefore, significant research efforts are
required with the ultimate aim to account for overstrength
in an explicit manner through the evaluation of seismic
design force on such buildings and other type of structures.
The values shown in this study; however, are only repre-
sentative of the pattern. Actual values will vary with dif-
ferent building systems and configurations.
Acknowledgements This paper is a revised and expanded version of
the article entitled ‘‘Effect of Seismic Zone and Story Height on
Response Reduction Factor for SMRF Designed According to IS
1893(Part-1):2002’’ held at Indian Institute of Technology Delhi,
New Delhi, India, during December 22–24, 2014. The authors are also
thankful to CSIR-Structural Engineering Research Centre, Chennai,
India for giving permission to publish this article.
Fig. 18 Effect of response
reduction factor on base shear
Fig. 19 Variation of elastic base
shear force through code based
equation and elastic analysis
J. Inst. Eng. India Ser. A
123

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