review on research work on various irregularities

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JOURNAL OF STRUCTURAL ENGINEERING 393

Vol. 39, No. 4, OCTOBER - NOVEMBER 2012

Journal of Structural Engineering

Vol. 39, No. 5, December 2012 - January 2013 pp. 393-418 No. 39-51

Review of different Structural irregularities in buildings

S.Varadharajan*, V.K. Sehgal**, and B.Saini*

Email:

* Civil Engineering Department, National Institute of Technology Kurukshetra, Haryana - 136 119, INDIA.

Received: 28 April 2011; Accepted: 09 September 2011

The present study summarizes the research works done in the past regarding different types of structural irregularities

i.e. Plan and vertical irregularities. Criteria and limits specified for these irregularities as defined by different codes

of practice (IS1893:2002, EC8:2004 etc.) have been discussed briefly. It was observed that the limits of both Plan andvertical irregularities prescribed by these codes were comparable. Different types of modeling approaches used have

also been discussed briefly. The review of previous research works regarding different types of plan irregularities

justified the preference of multistorey building models over single storey building models and concept of balanced

CV (Center of strength) – CR (Center of rigidity) location was found to be useful in controlling the seismic response

parameters. Regarding the vertical irregularities it was found that strength irregularity had the maximum impact and

mass irregularity had the minimum impact on seismic response. Regarding the analysis method MPA (Modal pushover

analysis) method even after much improvement was found to be less accurate as compared to dynamic analysis.

KEYWORDS: Plan irregularity; vertical irregularity; structural irregularities in buildings.

When a building is subjected to seismic excitation,

horizontal inertia forces are generated in the building.

The resultant of these forces is assumed to act through

the center of mass (C.M) of the structure. The vertical

members in the structure resist these forces and the

total resultant of these systems of forces act through

a point called as center of stiffness (C.S). When

the center of mass and center of stiffness does not

coincide, eccentricities are developed in the buildings

which further generate torsion. When the buildingsare subjected to lateral loads, then phenomenon of

torsional coupling occurs due to interaction between

lateral loads and resistant forces. Torsional coupling

generates greater damage in the buildings. Eccentricity

may occur due to presence of structural irregularities.

These irregularities may be broadly classified as Plan

(Horizontal) and Vertical irregularity as shown in

Fig.1.

Mass

Vertical

Irregularity

HorizontalIrregularity

Irregularity

Stiffness Strength Setback Asymmetrical plan shapes

Re-Entrantcorners

Diaphragmdiscontinuity

Irregular distribution of Mass,Strength, Stiffness along plan

Fig. 1 Classification of irregularities

A structure can be classified as irregular if the

structure exceeds the limits as prescribed by different

seismic design codes. The irregularity limits for both

horizontal and vertical irregularities as have been

discussed briefly in Table 1 and Table 2.


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The Horizontal and vertical irregularity limits as per

IBC 2003, Turkish code 2007 and ASCE 7 – 05 are

shown in Table 2.

Figure 2 Shows the pictorial representation of

different irregularity limits as per IS 1893:200219.

TABLE 1

IRREGULARITY LIMITS PRESCRIBED BY IS 1893:2002, EC8:2004, UBC 97, NBCC 2005

Type of Irregularity IS 1893:2002] [14] EC8 2004 [26] UBC 97 [81] NBCC 2005 [57]

Horizontal

a) Re-entrant corners R i ≤ 15% (Fig.2) R i ≤ 5% R i ≤ 15% -

b) Torsional irregularity dmax ≤ 1.2 davg r x > 3.33 eox

r y > 3.33 eoy

r x and r y > ls,

dmax ≤ 1.2 davg dmax ≤ 1.7 davg

c) Diaphragm

Discontinuity

Od > 50% r x2 > ls2 + eox2 Od > 50% -

Sd > 50% r y2 > ls

2 + eoy2 Sd > 50%

Vertical

a) Mass Mi < 2 Ma Should not reduce abruptly Mi < 1.5 Ma Mi < 1.5 Ma

b) Stiffness Si < 0.7Si+1 Or Si <

0.8 (Si+1 + Si+2 + Si+3)

(Fig.2b)

Si < 0.7Si+1 Or Si < 0.8

(Si+1 + Si+2 + Si+3)

Si < 0.7Si+1 Or Si < 0.8

(Si+1 + Si+2 + Si+3)

Si < 0.7Si+1 Or Si < 0.8

(Si+1 + Si+2 + Si+3)

c) Soft Storey Si < 0.7S

i+1 or S

i < 0.8

(Si+1 + Si+2 + Si+3)

- Si < 0.7S

i+1 Or S

i < 0.8

(Si+1 + Si+2 + Si+3)

Si < S

i+1

d) Weak Storey Si < 0.8Si+1 - Si < 0.8Si+1 -

e) Setback irregularity SBi < 1.5 SBa (Fig 2c) Rd < 0.3Tw < 0.1 Tw at any

level

SBi < 1.3 SBa SBi < 1.3 SBa

TABLE 2

IRREGULARITY LIMITS PRESCRIBED BY IBC 2003, TEC 2007 AND ASCE – 7.05

Type of Irregularity IBC 2003 [37] TEC 2007 [71] ASCE – 7.05 [5]

Horizontal

a) Re-entrant corners - Ri ≤ 20% Ri ≤15%

b) Torsional irregularity - dmax ≤ 1.2 davg dmax ≤ 1.2 davg

dmax ≤ 1.4 davg

c) Diaphragm Discontinuity - Oa > 33% Oa > 50% S > 50%

Vertical

a) Mass Mi < 1.5 Ma - Mi < 1.5 Ma

b) Stiffness Si < 0.7Si+1 Or

Si < 0.8 (Si+1 + Si+2 + Si+3)

- Si < 0.7Si+1 Or

Si < 0.8 (Si+1 + Si+2 + Si+3)

c) Soft Storey Si < 0.7Si+1 Or

Si < 0.8 (Si+1 + Si+2 + Si+3)

[ ηki = (Δi / hi) avr /

(Δi+1 / hi +1) avr > 2.0 or

Si < 0.7Si+1 Or

Si < 0.8 (Si+1 + Si+2 + Si+3)

d) Weak Storey Si < S

i+1[ ηci = (Ae)

i / < 0.80] S

i < 0.6S

i+1 Or

Si < 0.7 (Si+1 + Si+2 + Si+3)

e) Setback irregularity SBi < 1.3 SBa - SBi < 1.3 SBa


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Heavy Mass

(a)

(b)

(c)

(d)

d1

L L

AA

A/L >0.25

A/L >0.15 - 0.20 A/L >0.15 - 0.20

A/L >0.15 - 0.20

A/L >0.15

A/L >0.10

A

LA A

d2 d3

(i) (ii)

LA

A

A

L

Fig. 2 a) Re-entrant corner irregularity b) Irregular stiffness

distributions c) Irregular mass distributions d) Vertical

Setback irregularity.

Models Used for Analytical Study

The models used by authors can be broadly categorized

by two systems of classifications. As per first system of

classification these models can be broadly categorized

into three types namely Shear beam (SB), plastic hinge

(PH) and 3D frame models. In thefirst model the building

system is assumed to consist of a rigid rectangular deck

of mass m supported by lateral load resisting elements

represented by a shear beam. This type of building model

is used to represent single and multistorey building

systems with lesser degree of freedom. But use of thismodel to represent multistorey systems is questionable

due to variety of reasons as discussed in Table 17.This

model is used by a large number of researchers due

to its simplicity and easy representation. Since the

shear beam model (SB) is not suitable for representing

multistorey building systems these models does not

represent the actual building systems. So predictions

given by these models are less accurate. In the second

type of models the plastic hinges are modeled at end of

beams and columns to evaluate the nonlinear response

of building systems. Some researchers have adopted

this type of model as given in Table 17. These models

are closer to reality as compared to first type of models but still do not represent the actual building systems.

The application of first two models is more frequent in

case of 2D plane frames than 3D building frames due

to complex geometry of 3D building frames. The third

type of models can be termed as 3D frame models and

these models have been developed by recent researchers.

These models are quite complex and involve large

number of degree of freedom systems and are prepared

with the help of complex software programs. These

models are very close to the actual building systems and

yield accurate results.

The second system of classification of building

systems is based on the force – displacement hysteretic

relationship of resisting elements of buildings. The

resisting elements can have different type of force-

deformation represented by models namely

a. Elasto – plastic and bilinear hysteric model

b. Clough’s model

c. Takeda’s model

These models have been pictorially described in

Fig.3.

a. Elasto- plastic and bilinear hysteric models

The elasto-plastic hysteretic model has been used by

many researchers due to it’s simplicity. The maximum

displacement of a building system with elasto-plastic

force deformation relationship was found same as for

elastic force – deformation relationship for building

systems with initial time period greater than 0.5 s. To

account for the strain hardening effect a positive slope

was assigned to post yield stiffness and this model was

called as bilinear model. The main disadvantage of this

model is that with increase in displacement amplitude

reversal this model does not represent the stiffnessdegradation appropriately. So, this model is not suited

for non-linear analysis of RC structures.

b. Clough’s model of stiffness degradation

A qualitative model incorporating the stiffness

degradation in conventional elasto – plastic model


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was developed by Clough and this model was called

clough’s stiffness degrading models. In this model the

main response point during the loading cycle shifted

towards the maximum response point but the slope

during unloading remained same as the initial elastic

slope. By virtue of this modification, the Clough’s

model was able to represent the flexural behavior ofreinforced concrete. From the analysis of series of

SDOF system using this model Clough arrived at the

following conclusion

a. For building systems with higher initial time

period both clough’s and elasto-plastic model

yielded same results in terms of ductility demand

b. The clough’s model yielded larger ductility

demand as compared to elasto-plastic model for

short period structures.

c. Response waveforms of both models were

different.

The main advantage of this model is that it is simple

and can be used for non-linear analysis using strain

hardening characteristics.

d. Takeda’s hysteretic model

A more refined and complex model for representing the

stiffness degradation was prepared by Takeda in 1970

based on his experimental observations. The proposed

model includes the stiffness changes due to flexural

cracking, yielding and strain hardening. In Takeda’s

model the stiffness during unloading cycle was reduced

as the fraction of the previous maximum deformation.

Takeda also prepared set of guidelines for the load

reversals within the outermost hysteresis loop which

were major improvement over Clough’s model. The

main disadvantage of this model was that extensive

damage caused by shear and bond deterioration was

not considered in this model.

REVIEW OF RESEARCH WORKS

REGARDING PLAN IRREGULARITIES

Assessment of the performance of building structures

during past earthquakes suggests that plan irregularitiesare one of the important causes of damage during

occurrence of an earthquake. Plan irregularity may

occur due to irregular distribution of mass, stiffness

and strength along the plan. In past years lot of research

effort has been done to study the behavior of plan

asymmetric buildings during seismic excitation74-77.

F

F

F

Force

Force

F

No yield

Previous yield

Force

Force

d

(a) (b)

(c)

(d)

d

d

ki

kiki

ki

ki

kiki

kiki

rki

rki

rki

rki

rki

ku

kuki

d y d md

Displacement

No yield in compression

Previous yield in Tension

Displacement

Displacement

Fig. 3 a) Elasto-plastic model b) Bi-linear hysteresis models

c) Clough’s degrading stiffness model d) Takeda’s

hysteresis model

In Fig. 3 Ki, rKi and Ku are intial, modified and

unloading stiffness

Single Storey Building Models

Earlier studies investigated the torsional effects on plan

irregular building systems with single storey building

models. One of the main reasons for adopting singlestorey models was their simplicity. These models

were used to determine the influence of torsion on

seismic response parameters and these results were

used to formulate design methodologies for plan

irregular building systems. However in recent years

multistorey building models are used to determine the


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realistic inelastic torsional response of plan irregular

building systems. But due to complexities, the use of

multistorey building models is limited and it is one of

the major reasons that single storey building models

are still preferred by many researchers46-48. Previous

researchers on plan irregularities using single storey

models mainly focused on variation of positions ofC.M (Center of mass) or C.S (Center of stiffness) with

respect to each other to create eccentricity. The Main

aim of these researches was to determine the torsional

response of building systems due to eccentricity. To

create eccentricity some researchers varied position

of C.S or C.R keeping position of C.M. constant,

the eccentricity generated in this case was called as

stiffness eccentricity (es)76, 77. Some researchers varied

position of C.M. keeping position of C.S as constant,

the eccentricity generated in this case was called

as mass eccentricity(em)46. Differing from earlier

approaches some researchers created differences in

strengths of resisting elements to vary position of center

of strength (C.V) with respect to C.M the eccentricity

generated was known as strength eccentricity (ev)10,66.

The definitions of eccentricity have been described

pictorially in Fig. 4.

C.M

e.m

C.S

(a)

(c)

C.M

e.m

C.S

C.V C.M

Fig. 4 Definitions of different types of eccentricity a) Mass

eccentricity, b) Stiffness eccentricity, c) Strength

eccentricity

Research works on plan irregular building systems

started in early 1980’s with Tso and Sadek (1985)determined the variation in ductility demand by

performing inelastic seismic response of simple one

storey mass eccentric model with stiffness degradation

using Clough’s stiffness degradation model and bi-

linear hysteric model. Results of analytical study

showed that the time period had predominant effect

on the ductility demand after the elastic range. The

comparison of results of showed a 20 % difference in

the results obtained.

Irregular distributions of strength and stiffness are one

of the major causes of failures during the earthquakes.

Both of these irregularities are interdependent and

to study the effect of these irregularities on seismicresponse, the researchers like Tso and Bozorgnia

(1986) determined the inelastic seismic response of

plan asymmetric building models (as described in

Table 3) with strength and stiffness eccentricity using

curves proposed by Dempsey and Tso. Results of

analytical study showed the effectiveness of the curves

proposed by Tso and Dempsey except for torsionally

stiff structures with low yield strength.

Sadek and Tso (1989) performed inelastic analysis

of mono-symmetric building systems with strength

eccentricity as described in Table 3. The center ofstrength was defined in terms of yield strength of

resisting elements. From analytical studies it was

found that the code defined eccentricities based on

stiffness criteria were useful in predicting the elastic

seismic response. However in inelastic range parameter

of strength eccentricity was found to be useful in

determining seismic response.

TABLE 3

DESCRIPTIONS OF DIFFERENT MODELS ADOPTED

S.No Model Name Description

1 M Mass eccentric model with all

three resistant elements having

equal yield deformation

2 S1 Stiffness eccentric Model with

identical yield strength.

3 S2 Stiffness eccentric Model with

identical yield deformation.

Pekau and Guimond (1990) checked the adequacy

of accidental eccentricity to account for the torsion

induced due to the variation of strength and stiffness

of the resisting elements which was achieved using

elasto-plastic force-deformation relationship. Resultsof analytical study showed occurrence of torsional

amplification due to strength and stiffness variation.

Finally the code prescribed provision of 5% for

accidental eccentricity was found to inadequate.

Duan and Chandler (1991) based on their analytical

studies on plan irregular building systems the change


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in design eccentricity in Mexico code 87 was

recommended as 1.5es + b and 0.5es - 0.1b. as compared

to the earlier value of es – 0.1b and es – 0.05b.

Chandler and Hutchinson (1992) determined the

effects of torsional coupling on one storey stiffness

eccentric building systems and from analytical

studies the strong dependence of torsional couplingeffects on natural time period of the structure was

found. The authors also evaluated the effectiveness of

torsional design provisions as prescribed by different

codes of practice (ATC 3-06, NEHRP, NBCC 90, and

EC8:1989). The code evaluation results obtained for

asymmetric building system as per different codes are

shown in Table 4.

Codes namely UBC code, NBCC code and New

Zealand code of practice. The authors carried out Elastic

and inelastic analysis methods on one storey stiffness

eccentric building systems. Results of analytical studyshowed the greater displacement of flexible edge

as compared to stiff edge. The results obtained by

consideration of different codes are given in Table 5.

TABLE 4

CODE EVALUATION RESULTS

S.No Code Results

1 NEHRP [59] Inadequate for building systems with

small and moderate eccentricity.

Satisfactory results for building

systems with large eccentricity.

2 ATC [6] Same as NEHRP.3 NBCC [56] Inadequate for buildings with low

time periods (T 1 Sec. In case of TU systems designed

according to EC 8 -1989 the ductility demand exceeded

by 2.5 % as compared to the TB system.

TABLE 5

RESULTS OBTAINED CONSIDERING DIFFERENT CODES

S.No Code Name Results

1 NZS [58] Conservative Estimate of displacement2 UBC [79] Conservative Estimate of displacement

for DAF/FRF = 1

3 NBCC [56] Conservative Estimate of displacement

for DAF/FRF = 0.6-1.0

Ferhi and Truman (1996) determined seismic

response of building systems with presence of stiffness

and strength eccentricity. Both elastic and inelastic

seismic behavior were studied. From analytical study

of the building systems it was found that the seismic

response showed greater dependence on stiffness

eccentricity and in the inelastic range influence

of strength eccentricity on seismic response is

predominant.

Duan and Chandler (1997) developed an optimized

procedure for determining the seismic response of

torsion balanced and unbalanced structures. The

parameters like eccentricity (e), normalized stiffness

radius of gyration ( P k ), force reduction factor (R) and

uncoupled lateral period (T y) were included in the

proposed optimized procedure. The authors proposed

design eccentricity expression and over strength

factor expressions and compared it with code defined

expressions. The codes used in the study were UBC –9480, EC8-9325 and NBCC-9557 .The analytical study

was conducted both on Torsionally balanced (TB)

and torsionally unbalanced (TU) models. Results of

analytical study showed that the over strength factor

proposed by authors was found to be substantially

lower as compared to UBC-94 and NBCC-95 but higher


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than EC8 for entire range of P k . However the results

of proposed procedure are comparable to code defined

procedures for torsionally unbalanced structures (TU).

The parameters e, pk , R, T y considered in the design

procedure were found to influence the seismic response.

Finally the procedure was found to be applicable to

single storey and multistorey torsionally unbalancedstructures.

De-La-Colina (1999) studied the effects of torsion

on simple torsionally unbalanced building systems

considering the earthquake components in two

perpendicular directions. The effects of following

parameters were studied a) seismic force reduction

factor b) design eccentricity c) natural time period. The

structural model used for the analytical study is shown

in Fig 5.

n b

E4

E6

E1

E2 E5

E3

C.M C.R

Fig. 5 Structural model considered by De-La colina

Based on the results of analytical study it was

conclude that, with increase in the force reductionfactor, the ductility demand reduces forflexible element.

Regarding the effect of initial lateral time period it was

found that for torsionally unbalanced stiff elements the

ductility demand increased with time period and vice

versa for torsionally unbalanced flexible elements and

increase in value of stiffness eccentricities reduced the

normalized ductility demand. Based on these results it

was concluded that strength eccentricity had greater

effect on seismic response as compared to stiffness

eccentricity.

Ghersi and Rossi (2001) determined the influence

of bidirectional seismic excitation on seismic responseof stiffness eccentric one storey building systems using

elastic and inelastic analysis. The seismic response of

the inelastic analysis was compared with the results

of elastic analysis. Results of analysis showed that

the consideration of effects of bidirectional seismic

excitation results in minor variation in seismic response.

Elastic analysis using unidirectional seismic excitation

was found to overestimate the seismic response.

De Stefano and pintuchhi (2002) considered the

phenomenon of inelastic interaction between axial

force and horizontal forces in modeling of plan irregular

stiffness asymmetric building systems. Based on results

of analytical study it was concluded that considerationof interaction phenomenon between axial force and

horizontal force resulted in reduction of floor rotation

by 20%.

Dutta and Das (2002) studied the seismic response

of a single storey plan asymmetric structures subjected

to bidirectional seismic excitation. For analytical study

the authors proposed two hysteric models as represented

in Fig 6 (a, b). These hysteric models account for

strength and stiffness deterioration of RC structural

elements subjected to cyclic loading. From results of

analytical study it was found that local deformationdemands both at stiff and flexible edge showed

variation when strength deterioration was considered.

The consideration of unidirectional seismic excitation

results in lower values of deformation demands at both

flexible and stiff edge. These results were found similar

to Tso and Myslimaj (2002).

Unloading branch with initial

stiffness k

Deteriorated loading

branch

(a)

Displacement

α- Rate of strength deterioration

β = 1-3 α

λ = 1-2 α

η = 1- α

Target points of loading

branch

F o r c e

F β

F λ

F η

Fk

Unloading branch with initial

stiffness k Displacement

α- Rate of strength deterioration

β = 1-3 α

λ = 1-2 α

η = 1- α

F o r c e

β

FF λ

F η

k

k (1-3δ)

k (1-2δ)

k (1-δ)

(b)

Fig. 6 (a, b): Second Hysteretic model proposed by Dutta and Das

(2002)

Tso and Myslimaj (2003) proposed a new approach

called yield distribution based approach for strength

and stiffness distribution. For analytical study the

authors modeled a single storey structure with a rigid

rectangular deck supported by two resisting elements


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in X and five resisting elements in Y direction. The

resisting elements were modeled using elasto-plastic,

the bilinear and Clough’s hysteresis models for force

– deformation relationship. The authors proposed

a design parameter β on which location of center of

mass (C.M), rigidity (C.R), strength (C.V) and yield

displacement (C.V) depend. Table 6 shows different position of centers for different values ofβ. The models

were subjected to dynamic analysis to determine the

balanced CV-CR location. From results of analytical

study it was found that the structure satisfied balanced

CV-CR location and had low torsional response when

value of β lies between zero and unity.

Fujii et al. (2004) suggested a simplified non-linear

analysis procedure for plan asymmetric structures with

stiffness eccentricity modeled as SDOF and MDOF

system. Results of analytical study showed that the

torsionally stiff building systems experienced greater

oscillations in first mode as compared to the torsionally

flexible building systems. On comparison of responses

of MDOF and SDOF models for TS and TF building

systems it was found that SDOF models were found to

be applicable to torsionally stiff building systems only.

Finally the proposed analysis procedure was found to

ef ficient in determining the seismic response of TS

building systems.

TABLE 6

DIFFERENT POSITION OF CENTERS OF MASS,

STIFFNESS, STRENGTH AND DISPLACEMENT FOR

DIFFERENT VALUES OF Β.S.NO β Positions of C.M, C.V, C.D

1 1 Position of CV coincides with CD, strength

distribution takes same shape as yield

displacement

2 0-1 Value of ev decreases position of CV starts

shifting from CD towards CM.

3 0 Position of CV coincides with CM and

position of CR is shifted towards left of

C.M at a distance equal to ed.

4 0, the displacement demand on stiff edges is greater

as compared to the flexible edges. In case of far fault

motions when β < 0, the displacement demands are

greater on flexible edges as compared to stiff edges.

Jarernprasert et al. (2008) determined the inelastic

torsional response of single storey plan asymmetric

systems with stiffness eccentricity designed in

accordance with IBC 2006 and Mexico city building

code 2004. For analysis of this building model modal

analysis procedure was adopted. The affect of seismic

excitation on following parameters was studied, a)

ratio of uncoupled torsional to transitional frequencies,

b) design target ductility, c) elastic natural time period

and normalized static eccentricity. The authors also

proposed new reduction and amplification factor for

these parameters (a,b,c). From results of analytical

study it was found that these parameters (a,b,c) had

large influence on the inelastic behavior of the building

system. Regarding the comparison of codes it was

found that IBC 200638 code overestimate the design

forces at both flexible and stiff edge of building system

whereas the Mexico city building code overestimates

design forces atfl

exible side. The use of reduction andamplification parameters leads to the ductility demands

closer to target ductility demands but the displacements

computed are nearly four times to that of equivalent

symmetric structure.

Ladinovic (2008) represented inelastic seismic

response of plan asymmetric structures with stiffness


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and structural eccentricity in form of base shear torque

surface (BST). The factors influencing BST surface

were strength eccentricity, lateral capacity, torsional

capacity and distribution of strength along plan.

Aziminezad and Moghadam (2010) determined the

effects of strength distribution and configuration of

strength, rigidity and mass on seismic response of onestorey plan asymmetric building system subjected to

near field and far field ground motions. Eight models

with different values of yield displacement, strength

and stiffness eccentricity were considered as shown in

Fig.7 and Table 7.

Cm Cv

Cr

Model 1

Cm

Cv

d

Cr

Model 2

Cm

Cv

d

Cr

Model 3

Cm

Cv

d

Cr

Model 4

CmCv

d

Cr

Model 5

CmCv

d

Cr

Model 6

CmCv

d

Cr

Model 7

CmCv

d

Cr

Model 8

Fig. 7 Models considered by Aziminejad and Moghadam [10]

TABLE 7

DIFFERENT POSITION OF CENTERS OF MASS, STIFFNESS,

STRENGTH AND DISPLACEMENT FOR DIFFERENT

VALUES OF Β.

S.No Model Number Model Name ev/ed

1 1 Symmetric 0

2 2 Stiffness Symmetric 1

3 3 Balance 0.75

4 4 Balance 0.5

5 5 Balance 0.25

6 6 Strength Symmetric 0

7 7 - -0.33

8 8 - -1

The models were analyzed by dynamic nonlinear

analysis and from results of analytical study it was

found that for torsionally flexible building systems, the

strength distribution and configuration of centers had

minor effect both for near field and far field excitations.But seismic response of torsionally stiff building

systems was largely influenced by strength distribution

and configuration of centers. Regarding the modal

periods it was found that modal periods along X-axis

had the maximum value as compared to other two

modal periods and ratio of lateral to torsional frequency

was found to be greater in y direction. Further it was

concluded that the torsionally stiff building systems

with balanced CV-CR location perform better than

other building models both in case of near and far field

excitation.

Luchinni et al. (2011) determined the nonlinear

seismic response of single storey building models witheccentricities in both directions with BST procedure

and verified the BST approach using IDA analysis. For

analytical study four types of building models namely

S1, S2, R1, and R2 were modeled. The S1 model was a

one way asymmetric system with es = 0.1b.The model

S2 was a two way asymmetric system with es = 0.05b

in both directions. The model R1 contained uniform

strength distribution in x-direction only whereas model

R2 contained uniform strength distributions in both

directions. The results of analytical study showed that

BST surface is ef fi

cient in predicting the location ofcenter of rigidity. The seismic response predicted by

BST is comparable with that of IDA analysis. Table

8 shows Summary of research work regarding single

storey Plan irregular building models.

In Table 8 es, em and ev are stiffness, mass and

strength eccentricities and b is the Longer plan width.

Multistorey Plan Asymmetric Structures

In previous analytical studies on plan irregular

structures the single storey models were widely used

due to their simplicity and their ability to clearly depictthe effect of different seismic response parameters.

Most of the design criteria were formulated on basis

of results obtained in single storey models. But several

researchers66 proved that single storey models give

inaccurate prediction of torsional response. The

development of powerful software tools has made

modeling and analysis of multi-storey building models

much simpler and moreover the multi-storey building

models give realistic prediction of torsional response.

Although studies on plan irregular building models

started in 1990’s, Fajfar et al. (2002) was one of the

major researcher in this field who proposed a newmethod which was an extension of N2 method. The

proposed method was applicable to the realistic 3D

building models. For analytical study a eight storey

R.C. building with structural walls modeled. The mass

eccentricity was introduced in the building model by

displacing center of mass in both horizontal directions


10/26



by 5% and 15%. The results of proposed procedure were

compared with that of non-linear dynamic analysis.

From comparison of results the ability of proposed

method to predict the seismic response of torsionally

stiff structure was justified. However, the method did

not include the effects of lateral torsional coupling andwas found to be under-conservative as compared to the

N2 method.

De-la-Colina (2003) made assessments of several

code specified procedures regarding analysis procedures

for multistorey building systems with mass and stiffness

irregularity subjected to bidirectional seismic excitation

(EI Centro earthquake). Analytical studies were carried

out on several 5 storey buildings having mass and

stiffness eccentricity. Shear beam models were used by

researchers to represent resisting elements. Based on

the code defined procedures the authors had found out

the optimal values of storey eccentricity.Chopra and Goel (2004) proposed a new method

based on extension of their earlier method (Chopra

and Goel 2002). In the proposed method the torsional

amplification of the structure was accounted for by

application of the lateral forces in combination with the

torsional moments at each floor of the structure. The

TABLE 8

SUMMARY OF RESEARCH WORK REGARDING SINGLE STOREY PLAN IRREGULAR BUILDING MODELS

S.No Researcher Year Type and extent of eccentricity Main conclusion

1 Tso Sadek 1985 es = 0 - 0.25b Clough’s and bilinear hysteric model, a 20 % difference

in results of both models was observed.

2 Sadek Tso 1989 es and ep = 0 -0.2b Code defined eccentricities were valid for elastic range

only. For the inelastic range Strength eccentricity is

more effective.

3 Duan Chandler 1991 ea= 0 - 0.1b

es= 0.1b- 0.3b

The recommended change in design eccentricity

in Mexico code 87 as 1.5es + b and 0.5es - 0.1b. as

compared to the earlier value of 1es – 0.1b and 1ess

– 0.05b.

4 Chandler Hutchinson 1992 es = 0.05b-0.2b Different codes of practice yielded different results.

5 Chandler et al. 1995 ea = 0.05b The codified value of accidental eccentricity of 0.05 b

was most consistent.

6 De-La colina 1999 es = 0 - 0.20b R =1,3,6 For torsionally unbalanced stiff elements the ductility

demand increases with time period and vice versa for

torsionally unbalanced flexible elements

7 Dutta Das 2002 es = 0.05b - 0.2b Strength and stiffness irregularities areinterdependent.

8 Fujii et al. 2004 es= 0.682b, 0.5b Drift demand due to stiffness degradation

underestimated by SDOF model.

9 Shakib and Ghasemi 2007 es = 0.09b -0.01b

ev = 0.03b - 0.06b

For β > 0 - displacement demand on stiff edges is

greater as compared to the flexible edges. For β < 0,

the displacement demands are greater on flexible dges

as compared to stiff edges.

10 Ladinovic 2008 em-0.1b -0.5b

es = ev -0.12b

Distribution of strength. Stiffness eccentricity along

plan does not affect the shape of the BST surface.

11 Aziminejad Moghadam 2010 es = 0.025b - 0.10b,

ev = 0 – 0.2b

Torsionally flexible building systems are least affected

by strength distribution and location of centers both in

case of near and far field excitations. Torsionally stiff

building systems with balanced CV-CR location show better seismic performance both in case of near and far

field excitations.

12 Luchinni et al. 2011 es = 0 – 0.3 b The seismic response predicted by BST is comparable

eith that of IDA analysis.


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lateral forces and torsional moments were obtained

from the modal analysis of the structure. A comparison

between the results of the proposed method and non-

linear dynamic analysis were made for building

systems with different uncoupled lateral to torsional

vibration periods. From the results of analytical study

the accuracy of proposed procedure for symmetricstructures was verified. However the accuracy of

proposed procedure decreases with the increase in

magnitude of torsional coupling which is due to the use

of CQC modal combination rule.

Correlating with his earlier studies29 Fajfar et al.

(2005) again proposed a new method based on N2

method. In the proposed method, combination of

modal responses obtained from pushover analysis of

3D structures were made with the results obtained from

linear dynamic analysis. In the proposed procedure

the displacements and deformation distributionsalong height were controlled by N2 method and the

magnitude of torsional amplification is defined by the

linear dynamic analysis.

Stathopoulos and Anagnostopoulos (2005) were

one of the few researchers who had made attempt to

evaluate torsional response of realistic 3D structures

by nonlinear analysis (Both as per EC8 and UBC 97).

The authors conducted analytical studies on realistic 3

storey and 5 storey RC framed buildings (with flexible

and stiff edges) subjected to bidirectional excitations.

From the results obtained (Multistorey structures) it

was found that the inelastic displacement was found to

be greater at flexible side as compared to the stiff side,

however the results obtained in case of single storey

structures were contradictory to the results obtained in

case of multistorey structures with mass irregularity

under the action of bidirectional seismic excitation.

Furthermore the authors found that the torsionally stiff

building systems undergo less plastic deformation as

compared to the torsionally flexible building systems.

These findings contradict the results obtained from

single storey models.

Penelis and kappos (2005) proposed a methodto determine the inelastic torsional response of plan

asymmetric single storey and multistorey structures.

The models used for analytical studies were single

degree of freedom (SDOF) systems and incorporated

the effects of torsional and transitional modes. In the

proposed method the spectral load vectors were obtained

from the elastic spectral analysis and these vectors

were applied on the structure to carryout 3D pushover

analysis. The results of the proposed procedure were

compared with that of non-linear dynamic analysis.

From the results it was found that the inelastic seismic

response obtained by both methods vary by 10% in

case of single storey structures and by 20 % in case ofmultistorey structures.

Marusic and Fajfar (2005) determined the elastic and

inelastic seismic response of five storey steel framed

structure with mass eccentricity. The eccentricities

were taken as 5%, 10% and 15% of plan dimensions.

For Analytical study the author modeled three types of

building models as described in Table 9.

TABLE 9

DESCRIPTION OF MODELS USED BY MARUSIC AND

FAJFAR (2005)

Model Name Description

S Torsionally stiff building model with moment

resistant beam column connections (All beam-

column connections).

F1 Building Model with torasional stiffness equal

to Model S with moment resisrtant beam

column connections (Corner beams only)

F2 Building Model with torasional stiffness less

than Model S and F1.

For the building model the first storey height was

kept as 4m and other storey heights were kept as

3.5m. The multistorey structure was subjected to the

bidirectional seismic excitation. The results obtained atflexible edges were almost comparable with Perus and

fajfar (2005). However, the results of both papers did

not correlate in case of stiff edges of torsionally stiff

and flexible building systems.

Stefano et al. (2006) determined the difference

between the inelastic seismic response of single

storey and multistorey plan asymmetric structures.

For analytical study a single storey and a six storey

steel frame with mass applied at 0.15 b (b is the width

of longer plan) of the geometric structure, thus mass

eccentricity was created in the building model. Theeffect of over-strength of resisting elements was also

evaluated. Analytical studies showed the influence

of over-strength on ductility demand of the building

systems and this influence showed variation for single

and multistorey building systems. Finally it was found

that seismic response obtained from single storey


12/26



models was different from those obtained from multi-

storey models. From results of analytical study it was

found that for e/r ≤ 0.5 and μ ≤ 0.4, number of resistant

planes in direction of seismic response had no influence

on seismic response and the lateral displacements

decrease with increase in ductility demand. Finally the

Parameters like degree of torsional coupling, uncoupledlateral time period and eccentricity had larger influence

on seismic response.

Ghersi et al. (2007) determined the effectiveness

of modal analysis procedure in evaluating the inelastic

seismic response of multistorey plan asymmetric

structure. A six storey steel framed building and

asymmetry was induced by variation of applying load

at 0.15L away from geometric center inducing mass

eccentricity. Results of modal analysis was compared

with that of static analysis and by chandler procedure

to check the proposed procedure. The proposed methodleads to good seismic performance of buildings as

compared to other methods of analysis. However the

strength distribution along plan given by the proposed

method is comparable with method suggested by Ghersi

and Rossi but it is simpler in application as compared

to the latter method.

TABLE 10

DIFFERENT MODEL CONFIGURATIONS PROPOSED

S.No Model Name Ratio of Stiffness to

Yield displacement

eccentricity (ev/ed)1 Symmetric 0

2 Stiffness Symmetric 1

3 Balance (0.75Cv – Cr) 0.75

4 Balance (0.5Cv – Cr) 0.5

5 Balance (0.25Cv – Cr) 0.25

6 Strength Symmetric 0

7 De-Stefano (0.25Cm-Cr) -0.33

8 De-Stefano (0.5Cm-Cr) -1

Aziminejad and Moghadam (2009) determined

seismic performance of eight 5 storey plan asymmetric(Stiffness and strength) building systems with different

strength distributions. The eight different building

systems in location of position of center of rigidity

and strength (Table 10). These building models

were analyzed for nonlinear dynamic response using

OPENSEES software. From results of analytical study

it was concluded that building systems with strength

eccentricity equal to one fourth of distance between

positions of strength and stiffness performed better on

rotation and drift criteria.

Stahopoulos and Anangnopoulos (2010) evaluated

the effectiveness of accidental eccentricity provisions.

For analytical study the authors created four types of building models. The first and second models were one

storey shear beam with stiffness eccentricity and one

storey frame models with mass eccentricity respectively.

The third model was three storey frame type building

and fourth one was five storey frame type of models,

both these models had combination of mass and stiffness

asymmetry along plan. The shear beam models were

modeled considering a bilinear force-displacement

behavior and magnitude of strain hardening was taken

equal to 0.05. For idealization of frame members,

plastic hinge model was used and Takeda’s moment-rotation relationships were used in creating the plastic

hinge model. The one storey and three storey building

models were subjected to the accidental eccentricities

from 0 to 0.05L, whereas the five storey building model

was subjected to an additional eccentricity of 1.0L in

addition to earlier mentioned eccentricities.. Results of

analytical study suggest that in case of one storey shear

beam models, the consideration of accidental design

eccentricity (ADE) results in reduction of ductility

demands of edge elements in case of building systems

with larger time period(Ty). For Ty > 0.5s the ductility

demand reduces by 10 % for ADE = 0.05L and by 10-20% for ADE = 0.10L.

Anangnopoulos et al.(2010) determined inelastic

torsional response of single storey and multi-storey

building models with mass and stiffness eccentricity.

The building models were designed in accordance with

EC8 and IBC code provisions. The inelasticity in the

building models were introduced by assuming Takeda’s

moment-rotation relationship and strain hardening ratio

was taken as 0.05. The inelastic plastic hinge models

were further subdivided into three categories namely

SIMP1, SIMP2 and SIMP3 as described in detail inTable 10. The building models were analyzed using time

history analysis using ANSR software programs. From

results of analytical study it was found that for models

SIMP1 and SIMP2 the flexible edges of building were

found to be the critical elements which correlates with

results obtained for single storey models by previous


13/26



researchers. The seismic response of SIMP3 model

was found to be strongly dependent on seismic loading

and in this case critical elements were stiff edges which

contradicts with results obtained for single storey

models. Table 11 shows Summary of research works

regarding Multi storey plan asymmetric structures.

REVIEW OF RESEARCH WORKS

REGARDING VERTICAL IRREGULARITIES

Irregularities of mass, stiffness, strength and geometry

along building height may be termed as vertical

irregularity. These irregularities may be present

singly or in combination. Different types of vertical

irregularities have different effects on seismic response.

So, the effect of these irregularities should be considered

and incorporated in current seismic design codes. The

research works concerned with vertical irregularities

started in early 1970s with Chopra (1973) who studied

the seismic response of series of eight storey shear buildings subjected to the earthquake motion data. The

main objective of the author was to determine the effect

of yielding of first storey on upper stories. From results

of analytical study it was found that an ideal plastic

mechanism and a low yield force are required in the

first storey for safety of higher floors of the structure.

TABLE 11

SUMMARY OF RESEARCH WORKS REGARDING MULTI STOREY PLAN ASYMMETRIC STRUCTURES

S.No Researcher Year N Type and extent of

eccentricity

Main conclusion

1 Stahthopoulos

Anagnopoulos

2003 3 5 em= 0.1b - 0.3b

es = 0 - 0.3L

ea = 0 - 0.05b

The Building Systems with biaxial eccentricity

showed the increased ductility demand.

The displacements at flexible edge was found

to be greater for SB models as compared to PH

models. SB models were found inef ficient in

assessment of codal provisions.

2 Chopra Goel 2004 9 em = 4.57m Accuracy of proposed procedure decreased with

the increase in magnitude of torsional coupling.

3 Fernandez et al. 2005 5 es = 0.25r - 0.75r For e/r ≤ 0.5 and μ (Ductility coef ficient) ≤ 0.4,

number of resistant planes in direction of seismic

response have no influence on seismic response.

4 Stefano et al. 2006 6 em = 0.15b Overstrength factor influences the seismic

response.5 Ghersi et al. 2007 6 em = 0.05b - 0.30b The proposed method leads to good seismic

performance of buildings as compared to other

methods of analysis.

7 Luchinni et al. 2009 2 es = 0, 0.5b The deformation demand in the Irregular

buildings was found to be non-linear.

8 A z i a e n m i z a d

Moghadam

2010 5 es = 0 - 0.14b est =0

- 0.25b

In building systems with strength eccentricity

equal to one fourth of the distance between

positions of strength and stiffness performed

better on rotation and drift criteria.

9 S t ah t h o p o u l o s

Anagnopoulos

2010 1 3 5 em = 0 – 0.3b es=0.1b

- 0.7b ea = 0 - 0.10b

Consideration of accidental design eccentricity

(ADE) results in reduction of ductility demands

of edge elements in case of building systems with

larger time period (Ty). For Ty > 0.5s the ductilitydemand reduces by 10 % for A = 0.05L and by 10-

20% for A= 0.10L.

10 Anangnopoulos

et al.

2010 3 5 em es= 0-0.30 b ea =

0.05b

For models SIMP1 and SIMP2 the flexible edges

were the critical elements. In SIMP3 models the

stiff edges were critical elements.

N – Represents number of stories


14/26



The irregularities of mass, stiffness and strength are

represented by parameters of mass ratio (Mr ), stiffness

ratio (Sr ), Strength ratio (STr ) which may be defined as

the ratio of mass, stiffness and strength of storey under

consideration to the adjacent storey.

Humar and Wright (1977) studied the seismic

response of multistorey steel building frames with andwithout setback irregularity using one ground motion

data. Based on analytical study it was concluded that,

in case of building frames with setbacks, the storey drift

was found to be greater at upper portion of setback and

smaller in the base portion. Also, the drift of building

frames with setbacks was found to be lesser as compared

to the building frames without setback irregularity.

Aranda (1984) extended the approach of earlier

researchers36.The author determined and compared the

seismic response of structure with and without setback

irregularity founded on soft soil. From the results ofanalytical studies it was confirmed that the ductility

demand and its increase in upper portion of setback was

higher as compared to the base portion and structures

with setbacks experienced higher ductility demand as

compared to their regular counterparts.

Fernandez (1983) determined the elastic and inelastic

seismic response of multistorey building frames with

irregular distribution of mass and stiffness. Reduction

in storey stiffness resulted in increased storey drift and

structures with constant variation of mass and stiffness

in vertical direction showed better seismic performance

as compared to the structures with abrupt variations.

Presence of shear walls leads to variation in stiffness

and researchers like Moelhe (1984) determined the

seismic response of R.C structures with irregularities.

For analytical study, nine storey building frames with 3

bays and structural walls were modelled. The irregularity

in building models was created by discontinuation of

structural walls at different storey heights. Based on the

analytical results it was found that the seismic response

not only depended on extent of structural irregularities

but also on the location of irregularities. Experimental

studies are necessary to verify the accuracy of analyticalresults and researchers like Moehle and Alarcon (1986)

performed experimental tests on two small prototype

R.C. building frames subjected to the ground motion

data. The tests were performed using shake table. The

two building models used for the study were named

as ‘FFW’ and ‘FSW’. The ‘FFW’ model had two

frames of nine storey having 3 bays each and the third

frame was also of 9 storey but had prismatic wall, this

model represented the building systems without any

irregularity. The Vertical irregularities were introduced

in the building models by discontinuation of shear wall

at first storey and this building models were designated

as ‘FSW’ Rest of the features in both ‘FFW’ and‘FSW’ were same. The displacements of top floor were

computed for all these building models using elastic and

inelastic dynamic analysis. From the analytical study it

was concluded that in case of ‘FSW’ductility demand

increased abruptly at the vicinity of discontinuity

of shear wall and this increase was found to be 4 to

5 times higher as compared to the ‘FFW’ models.

Further the inelastic dynamic analysis was found to

be more ef ficient as compared to the elastic analysis in

determining the effect of structural discontinuities.

Barialoa (1988) determined the effects of strengthand stiffness variation on nonlinear seismic response

of multistorey building frames. For analytical study 8

storey building with 5 bays were modeled. The building

frames were subjected to three different category of

time periods namely low, medium and high. Each

building category was further subdivided into two

more categories based on base shear namely weak and

strong. In the weak building the base shear was 15 %

of total seismic weight whereas in strong building the

bases shear was 30 % of total weight of the structure.

The results of analytical study showed that the time

period of structure increases during seismic excitationand this increase is more pronounced in case for weaker

structures. A linear elastic spectrum can be used to

determine the seismic response if increase in damping

along with increase in damping is considered.

Ruiz and Diederich (1989) conducted analytical

studies on five and twelve storey building models with

strength irregularity. The strength irregularity in the

building model was created by modeling first storey of

the structure as the weak storey in the first case. In the

second case the infill walls in top storey were modeled

as brittle and in the third case the infi

ll walls weremodeled as ductile. From results of analytical study it

was found that the yielding, failure and formation of

plastic hinges in infill walls was greatly influenced by

time period of seismic excitation.

Shahrooz and Moehle (1990) determined the

seismic response of building systems with vertical


15/26



setbacks. The authors conducted both experimental

and analytical tests to improve methodologies for

design of setback buildings. For performing the

experimental study model of a six storey R.C. frame

having 50 % setback at midheight was prepared. From

results of experimental study it was found that there

was no abrupt variation in the displacement along the building height. The interstorey drifts were found to be

largest with increased damage and abrupt reduction in

lateral force at location of setbacks. The distribution of

lateral displacement and force along building height

suggest that the translational seismic response of the

building parallel to direction of setback is influenced

by fundamental mode of vibration. For performing

analytical study six storey building frames with six

different patterns of setbacks were modeled and

designed in accordance with UBC code of practice.

For all of these frames the floor plan dimensions and

mass ratios were varied from 3 to 9 times as suggested

by UBC 1988 code of practice which differentiated

symmetric and setback structures on basis of plan

dimensions and mass ratios. The analyses of these

frames were carried out by modal analysis procedure as

prescribed by UBC 1988 code of practice. From results

of analytical study it was concluded that all these frames

experienced similar magnitude and distribution of

ductility demand. The frames with similar mass ratios

and floor plan dimensions but with different setback

heights experienced different amount of damage which

contradicted the approach of UBC 1988 code. Nasser and Krawlinker (1991) conducted parametric

study on multistorey (3, 5,10,20,30, 40 storey) SDOF

and MDOF systems (with strength irregularity) with

different periods of seismic excitation ranging from

0.217s – 2.051s. The models used are described in

Table 12.

TABLE 12

BUILDING MODELS USED BY NASSER AND

KRAWLINKER (1991)

S.No Model Name No. of Stories Model Description

1 Beam Hinge 3,10,20,30,40 Plastic hinges formin beam only

2 Column Hinge 3,10,20,30,40 Plastic hinges form

in column only

3 Model 3 3,10,20,30,40 Plastic hinges form

in columns of first

storey only

Three types of building systems as described in Table

13 were studied.. In case of SDOF models the strength

demand was represented in terms of strength reduction

factor which represents the reduction in strength of

structural elements. In case of MDOF systems it was

found that strength demand and target ductility ratios

depend on failure mechanisms developed and presenceof weak first storey increased the ductility demand and

overturning moments.

Esteva (1992) evaluated the seismic response of

building frames with soft first storey by using non-

linear analysis. For simplification of analytical study

the shear beam model was used to represent the building

systems. The first main purpose of analytical study was

to observe the bilinear hysteric behavior of the building

systems with and without consideration of P-Delta

effects. The second main purpose of the analytical study

was to determine the affect of influence ratio r (which

was defined as the ratio of average value of lateral shear

safety factor for upper stories to the bottom stories) on

ductility demand. The results of analytical study are

shown in Table 13.

TABLE 13

RESULTS OF ANALYTICAL STUDY OBTAINED BY

ESTEVA (1992)

S.No Time period Influence ratio Ductility Demand

1 Low Increase from

1.0 to 3.0

Increase by 30 %

2 Medium No impact No impact

3 High Increase from

1.0 to 3.0

Increase from 50 %

- 100%

Wood (1992) found that presence of setbacks did

not affect the dynamic seismic response which was

more or less similar for symmetrical structures.

Wong and Tso (1994) used elastic response spectrum

analysis to determine seismic response of structures

with setback irregularity and it was observed that

buildings with setback irregularity had higher modal

masses causing different seismic load distribution as

compared to the static code procedure.

Duan and Chandler (1995) conducted analytical

studies on building systems with setback irregularity

using both static and modal spectral analysis and based

on the results of analytical studies, it was concluded

that both static and modal analysis procedures were

inef ficient in preventing the concentration of damage

in structural members near level of setbacks.


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Vamudson and Nau (1997) evaluated seismic

response of multistorey buildings with vertical

irregularities. For analytical study two dimensional

shear beam building models with five, ten and twenty

stories were prepared. The structural irregularities were

introduced in the building models by varying the mass,

stiffness and strength. From analytical studies it wasfound that introduction of mass and stiffness irregularity

resulted in minor variation in the seismic response. The

storey drifts were increased in range of 20% - 40 %

for 30 % decrease in the stiffness of the first storey,

with constant strength. The strength reduction of 20 %

doubled the ductility demand.

Al-Ali and Krawinkler (1998) evaluated the effect

of mass, stiffness and strength and their combinations

on seismic response of a 10 storey structure. Elastic and

inelastic dynamic analyses were used for the analytical

study. Based on the results of analytical study it wasobserved that, when irregularities were considered

separately; the strength irregularity had the maximum

impact on roof displacement and mass irregularity had

the minimum impact on the roof displacement. When

combination of irregularities was considered, the

combination of stiffness and strength irregularity had

the maximum impact on roof displacement.

Kappos and Scott (1998) made comparison between

static and dynamic methods of analysis for evaluating

the seismic response of R.C frames with setback

irregularity. On comparison between results of both

methods it was concluded that dynamic analysis yielded

results different from that of static analysis. However

in the analytical study the other forms of irregularities

like mass, stiffness and strength irregularity were not

included.

Magliulo et al. (2002) conducted parametric studies

on multistorey RC frames (5, 9 storey) with mass,

stiffness and strength irregularity designed for “low

ductility class” as per EC 8 provisions. The authors

evaluated the seismic response of the irregular frames

and have compared it with the seismic response of

building frames without any irregularity. From theanalytical studies it was found that mass irregularity

does not effect plastic demands. In case of strength

irregularity, irregular distribution of strength in beams

increased the seismic demand. However seismic

demands were not affected due to irregular strength

distribution in columns. Finally the authors concluded

that the parameter of storey strength as prescribed

by EC8 and IBC codes was ineffective in predicting

strength irregularity.

Das and Nau (2003) evaluated the effects of stiffness,

strength and mass irregularity on inelastic seismic

response of large number of multistorey structures. For

analytical study a large number of buildings with three bays in direction of seismic action and with number of

stories ranging from 5-20 were modeled.

TYPE A TYPE B

(a) TYPE A,B,C – Taller first, intermediate and top storey

TYPE C

TYPE t TYPE m

TYPE E1 - E2 TYPE E3 - E6

(b) TYPE t, m, b - Irregular mass distributions

(c) E1-E2 – Open ground floor, E3 – E6 – Partial infill

TYPE b

a) TYPE A,B,C – Taller first, intermediate and top storey b)

TYPE t, m, b - Irregular mass distributions c) E1-E2 – Open

ground floor, E3 – E6 – Partial infill

Fig. 8 Different types of vertically irregular building models, Das

and Nau19

The structural irregularities in these building

models were introduced by variation of mass ratio,

stiffness ratio , storey strength and by considering the

effect of masonry infills. These frames were designed

as special moment resisting frames (S.M.R.F.) basedon strong column – weak beam design philosophy in

accordance with different codes of practice namely

ACI 1999 and UBC 97. The forces on these S.M.R.F

frames were computed using ELF (Equivalent Lateral

force) procedure as prescribed in ACI 99 and UBC 97

code. From results of analytical study it was concluded


17/26



that the seismic response parameters like first mode

shape and fundamental time period as computed by

ELF procedure were similar for symmetrical and

unsymmetrical structure. The storey drift computed for

five storey and ten storey structures with combination

of mass, strength and stiffness irregularities at bottom

storey showed an abrupt increase over code prescribedlimit of 2 %. The ductility demands showed an abrupt

increase near the location of irregularity but this increase

never exceeded the designed ductility capacity of the

members. Finally the mass irregularity had least impact

on the structural damage index and for all the building

models analyzed it was found to be less than 0.40.

Chintanpakdee and Chopra (2004) evaluated

the effects of strength, stiffness and combination of

strength and stiffness irregularity on seismic response

of multistorey frames. For analytical study, different 12

storey frames were modeled based on strong column – weak beam theory. The irregularity in strength and

stiffness were introduced at different locations along

height of the building models. The building models were

analyzed using time history analysis by subjecting the

building model to 20 different ground motion data. From

analytical studies it was concluded that irregularities in

strength and stiffness when present in combination had

the maximum affect on the seismic response. Further

maximum variation in the displacement response along

height was observed when irregularities are present on

the lower stories.

Tremblay and Poncet (2005) evaluated the seismic

response of building frames with vertical mass

irregularity (Fig. 15) designed according to NBCC

provisions by static and dynamic analysis. Based on

the analytical study it was concluded that both static

and dynamic method of analysis (as prescribed by

NBCC provisions) resulted in similar values of storey

drifts and hence they were ineffective in predicting the

effects of mass irregularity.

Fragiadakis et al. (2005) determined the seismic

response of building systems with irregular distribution

of strength and stiffness in vertical direction. Afterconducting the analytical study it was concluded that

seismic performance of the structure depended on type

and location of irregularity and on intensity of seismic

excitation. Modal pushover analysis (MPA) procedure

is an important analytical tool to evaluate the seismic

performance and several researchers like Lignos and

Gantes (2005) investigated the effectiveness of Modal

pushover analysis procedure (MPA) in determination

of multistorey steel braced frame (4, 9 storey) with

stiffness irregularities. Based on the results of analytical

study it was concluded that MPA procedure was

incapable of predicting failure mechanism and collapse

of the structure.Khoure et al. (2005) designed a 9 storey steel framed

structures with setback irregularity as per Israeli steel

code SI 1225(1998).The authors made variation in

height and location of setbacks in building frames.

Results of analytical studies confirmed that higher

torsional response was obtained in tower portion of

setbacks.

Some researchers preferred dynamic analysis over

MPA procedure to evaluate seismic response due to

its accuracy. Fragiadakis et al. (2006) proposed an

IDA (Incremental dynamic analysis) procedure forestimating seismic response of multistorey frame (9

storeys) with stiffness and strength irregularity contrary

to Lignos and Gantes (2005), Alba et al. (2005) who

used MPA procedure to evaluate the seismic response

of building frames with stiffness irregularity. Based

on the analytical results the authors concluded that the

proposed method was effective in predicting effects

of irregularity in building frames. Finally, the authors

concluded that effect of irregularity is influenced

by location and type of irregularity and building

systems subjected to unidirectional seismic excitation

underestimate the seismic demand significantly.

Tremblay and Poncet (2005) conducted extensive

study on multistorey building frames with mass

irregularity as per NBCC code. Ayidin (2007) evaluated

the seismic response of buildings with mass irregularity

by ELF procedure (as prescribed by Turkish code of

practice) and by time history analysis. The researcher

had modeled multistorey structure ranging from 5 to

20 storey height. The mass irregularity is created by

variation in mass of a storey with constant mass at other

stories. Based on the analytical study author concluded

that the mass irregularity effects the shear in the storey below and ELF procedure overestimates the seismic

response of the building systems as compared to the

time history analysis.

Basu and Gopalakrishnan (2007) developed a

simplified method of analysis for determination

of seismic response of structures with horizontal


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setbacks and torsional irregularity. The assessment

of the proposed method was made by applying it

on four building models. In case of building models

with scattered positions of C.M. the proposed method

evaluates seismic response considering average value

of position of C.M. whereas perturbation analysis

considers exact location of positions of C.M. at differentfloor levels to evaluate the seismic response. Results

of analytical study showed that for building systems

with vertically aligned C.M. the frequencies obtained

by proposed procedure and perturbation analysis were

found to be in close agreement, but results of frame

shear forces differed by 7 %.. In case of second example,

the modal response obtained by proposed method and

perturbation analysis was similar, but difference in

frame shear force was found to be 4% for upper stories

and 1 % for base stories. In case of third building

model, the frequencies obtained by proposed procedure

and perturbation analysis were in close agreement, but

difference of results in case of frame shear forces were

10 % at ground storey level and 4% at first storey level.

In case of fourth example the difference of results in

estimation of frame shear forces were as high as 50 %,

so it was concluded that the proposed position is not

applicable to the building models where the prescribed

limit of scattering of C.M. is exceeded.

Karavallis et.al. (2008) performed extensive

parametric study on steel frames with different types of

setback irregularity designed as per European seismic

and structural codes. From analysis the databank ofdifferent output parameters like no. of stories, beam

to column strength ratio, geometrical irregularity etc.

which influence the deformation demands was created.

Based on the deformation demands four performance

levels were identified and these are a) occurrence of

first plastic hinge b) Maximum interstorey drift ratio

(IDRmax) equal to 1.8 % ; c) IDRmax equal to 3.2%

d)IDRmax equal to 4.0%. The results for different

types of setback structure were expressed in terms of

these performance levels . From analytical study it was

concluded that interstorey drift (IDR) ratio increased

with increase in storey height and tower portion

of setback experienced maximum deformation as

compared to the base portion.

Athanassiadou (2008) made the assessment of seismic

capacity of the RC structures irregular in elevation. The

author modeled three multistorey frames, out of these

three frames two ten storey plane frames were modeled

with two and four large setbacks in their upper floors

and the third frame was regular in elevation. These

three frames were subjected to 30 different ground

motions d and designed by the researchers as DCH and

DCM frames (Designed for high ductility and medium

ductility) as per Euro code 8.Then non linear dynamicanalysis of the frames was carried out by subjecting the

frame to the ground motion data of the earthquake and

parameters of rotation, base shear and interstorey drift

were evaluated. Based on the analytical study it was

found that the performance of both DCM and DCH

frames were found to be satisfactory as per guidelines

of Euro code 8.

Karavallis et al. (2008) evaluated the seismic

response of family of 135 plane steel moment resisting

frames with vertical mass irregularities and created

databank of analytical results. Furthermore the authorsused regression analysis technique to derive simple

formulae to evaluate seismic response parameters

using the analysis databank. Results of analytical

studies suggested that the mass ratio had no influence

on deformation demand. The results obtained from

proposed formulae were found to be comparable with

results of dynamic analysis.

Sadasiva et al. (2008) evaluated the effect of location

of vertical mass irregularity on seismic response of the

structure. A 9 storey regular and irregular (with vertical

irregularity) frame was analyzed and designed as per

New Zealand code of practice in two ways, firstly it was

designed to have maximum interstorey drift at all levels

(represented as CDCSIR) . Secondly, it was designed

to have a constant stiffness (represented by CS) at all

levels. To make clear distinction between regular and

irregular structure, a special notation form was used

by the authors of form NS-M-L-(A), where N-no.of

stories, S-Shear beam, M- Type of model [i.e. S(Shear

beam) or SFB (Shear Flexure beam), (A) – Mass ratio].

The deformation is represented in form of graphs. For

making the study Los Angeles earthquake records had

been used and authors carried out inelastic time historyanalysis of the structure using Ruamoko software. Based

on this analysis it was concluded that in case of both

CS and CISDR model the interstorey drift produced is

maximum when mass irregularity is present at topmost

storey and irregularity increases the interstorey drift of

the structure. However this magnitude varies for both


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CS and CISDR type of models .

Sarkar et al. (2010) developed a new parameter

called as regularity index (defined as the ratio of 1st

mode participation factor of the stepped building frame

to the regular frame) to express the extent of irregularity

and the authors developed an empirical formula to

calculate the fundamental time period of buildingframes with vertical setbacks. By use of this formula

the fundamental time period was represented as the

function of regularity index. To validate the approach,

modal analysis of 78 different building frames with

different types of setback irregularity were conducted

and it was found that the empirical formula yielded

accurate results even for 3D building models. Table

14 shows the summary of research works regarding

vertical irregularity.

In Table Mr, Sr and STr are mass, stiffness and

strength ratios.

COMPARISON OF MODELS USED BY

DIFFERENT RESEARCHERS

Classification 1: Table 15 shows First system of

classification of models used by different researchers

M 1 - Elasto-plastic hysteric model

M 2 - Bi-linear hysteric model

M 3 - Clough’s hysteric model

M 4 - Takeda’s hysteric model

TABLE 14

SUMMARY OF RESEARCH WORKS REGARDING VERTICAL IRREGULARITY

S.No Name of Researcher Year Key Parameters N Main conclusion

1 Ruiz and Diedrich 1989 Sr – 4,0.9

Sr - 0.65-2.0

1.0-2.0

5 The behavior of infill wall is greatly influenced by

time period of seismic excitation.

2 Shahrooz and Moelhe 1990 50 % setback

Mr –300 % to 900%

6 High rotational ductility in vicinity of irregularity

3 Vamudsson and Nau 1997 Mr - 0.1,0.5,1.5,2,5

Sr - 0.5- 0.9

STr - 0.5-0.9

5,

10,

20

ELF predicts accurate response upto Mr =5.

Storey stiffness reduction by 30 % increases

storey drift by 20 – 40% and reduction of storey

strength by 20 % doubles the ductility demand.

4 Ali Ali and Krawlinker 1997 Mr - 0.25,0.5,2,4Sr - 0.1,0.25,0.5, 2,4,10

STr -0.5

10 Mass irregularity had the least impact whereasstrength irregularity had the maximum impact.

5 Das Nau 2003 Mr - 2.5-5.0

Sr - 0.09 -1.6

- 0.09 - 1.7

- 0.08 - 1.81

STr - 0.27-1.05

5

10

20

Ductility demands increased in vicinity of

irregularity but never exceeded design ductility

demand.

6 Chintanpakdee Chopra 2004 Sr –0.25,0.5, 2.0,5.0

STr -0.25,0.5, 2.0,5.0

12 Irregularities in upper stories had least influence

on displacement demand as compared to

irregularities in lower stories.

7 Fragiadakis 2006 Sr - 0.5,2.0

STr - 0.5,2.0

9 Seismic response depends on type of structural

irregularity.

8 Ayidin 2007 Mr 0.1,0.5,1,1.5,2,5 5 10 20 ELF procedure overestimates seismic response.

Mass irregularity affects shear.

9 Karavallis et al 2008 Mr = 2,4,6 3 9 15 Mass ratio has no influence on drift, rotation and

ductility demands.

10 Sadasiva et.al. 2008 Mr = 2.5,5 9 Effects of irregularity depends on Structural

model, Location and type of irregularity.


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TABLE 15

FIRST SYSTEM OF CLASSIFICATION OF MODELS USED

BY DIFFERENT RESEARCHERS

M Reference

no.

Advantages Disadvantages

1 23, 34, 35,

74, 77, 82

Simple Less accurate for building

systems with T>0.5s.

2 13, 22, 39,

67, 68, 74

Includes strain

hardening effect.

Does not account for

stiffness change due to

increase in displacement

amplitude reversal.

3 20, 21, 74,

77, 82

Used for nonlinear

analysis includes

strain hardening

effect.

Larger ductility demand

as compared to elasto –

plastic elements.

Comparable values with

model 1 for high period

structures.

4 19, 33, 68 Includes effects of

flexural, cracking

and strain

hardening.

Excessive damage caused

by shear and bond not

considered.

Classification 2: Table 16 shows Second system of


SS - Single-storey models

MS – Multi-storey models

TABLE 16

SECOND SYSTEM OF CLASSIFICATION OF MODELS

USED BY DIFFERENT RESEARCHERS

S.

No

M Reference

no.

Advantages Disadvantages

1 SS 1, 13, 15,

18, 20, 21,

22, 23, 34,

35, 39, 46,

48, 67, 68,

69, 74, 75,

76, 77

Simple Easy

idealization and

formulation.

Does not represent

the actual

structure.

Does not involve

building systems

with large degree

of freedom.

2 MS 1, 2, 3, 4,

8, 9, 10, 11,

12, 16, 18,

19, 28, 29,

30, 31, 32,

36, 40, 41,

42, 43, 47,

48, 50, 52,53, 62, 63,

64, 67, 68,

69, 72, 82,

83, 84.

R e p r e s e n t s

actual structure.

Seismic response

obtained much

closer to reality.

Can involve large

no. of degree of

freedom.

More complex and

dif ficult to model

as compared to

SB models.

Need of

s o p h i s t i c a t e d

softwares.

Classification 3: Table 17 shows third system of


TABLE 17

SECOND SYSTEM OF CLASSIFICATION OF MODELS USED BY DIFFERENT RESEARCHERS

S.No M Reference no. Advantages Disadvantages

1 SB 3, 9, 13, 15, 18, 20, 21, 22,39, 46, 63, 66, 67, 68, 69,

73, 74, 75, 76, 77

Simple

Easy idealization and formulation.

Does not represent the actual structure. Does notinvolve building systems with large degree of

freedom.

Not suitable to represent multistorey building

systems as simplified S-B models are not designed

for gravity loads. So relation between strength and

stiffness for these models is different from that

of actual strength – stiffness relation of framed

structures.

Strength of resisting elements can be adjusted

without changing the stiffness. However it has

been already proved by researchers that both these

parameters are interdependent.

2 PH 3, 9, 21, 67, 68, 69 Non – linear analysis. Inelastic seismicresponse prediction. Plastic hinges

formed at ends of beams and columns.

More complex and dif fi

cult to model as comparedto SB models. Seismic response depends on

location of plastic hinge. Plastic hinge assumed to

occur at ends of beams and columns only.

3 3D 4, 8, 11, 12, 17, 19, 27, 28,

30, 36, 40, 41, 42, 43, 47,

52, 53, 60, 62, 64, 65, 66,

68, 70, 72, 82, 83, 84

Closer to actual buildings. Complex and dif ficult formulations.


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SB - Shear Beam

PH - Plastic hinge

3D - 3D frame models

Some authors also have used two or more than two

models so same reference number in some cases appears

against two model names in classification 1, 2 and 3.

DISCUSSIONS AND CONCLUSIONS

The presence of structural irregularity changes the

seismic response and the change in the seismic

response depends upon type of struc

review on research work on various irregularities

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