Effect of Seismic Zone and Story Height on Response Reduction Factor for SMRF Designed According to...

SPECIAL ISSUE MANUSCRIPT

Effect of Seismic Zone and Story Height on Response ReductionFactor 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

� 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 �Non-linear static pushover analysis � Overstrength factor �

Response reduction factor � Steel moment resisting frame �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

[email protected]

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

http://orcid.org/0000-0003-2291-4033

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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

Rð1Þ

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 � Rl � 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


123

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


123

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


123

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 � W ð5Þ

Ah ¼ Z

2:

I

R:Sa

gð6Þ

T ¼ 0:09hffiffiffi

dp 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


123

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:h

2i

Pnj¼1 Wj � 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


123

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

dp 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


123

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 � D2Þh

� 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� Structure weight ðWÞ � C:G

ð14Þ

Overturning Moment ¼ ðF1� 3:6Þ þ ðF2� 7:2Þ þ ðF3� 10:8Þ

ð15Þ

Fig. 6 Variation of first mode

periods of example building


123

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� Structure weight ðWÞ � l ð16ÞSliding 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


123

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.


5-story building


7-story building


123

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


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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




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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. 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


123

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.



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



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


123

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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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


123

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