the effect of masonry infill on the seismic response of reinforced concrete frames

i

DEDICATION

To

My parents

ii

DECLARATION

It is hereby declared that except for the contents where specific reference have been

made to the work of others, the studies contained in this thesis is the result of

investigation carried out by the author. No part of this thesis has been submitted to any

other university or educational establishment for a degree, diploma or other qualification

(except for publication).

Signature of the candidate

iii

ACKNOWLEDGEMENT

First of all, I would like to remember the supreme, my creator almighty Allah who made

everything possible for me and for his never ending blessings.

I wish to express our deepest gratitude to our esteemed supervisor Dr. Md. Abdur Rouf,

Professor, Department of Civil Engineering, BUET for his careful supervision and guideline

throughout the whole time of working on this thesis.

I would like to thank our dear teacher Md. Ruhul Amin, assistant professor, Department

of Civil Engineering, BUET for his kind support and help. The idea of this thesis came from

his work on a topic similar to my work.

Finally, I would like to express my reverence to all the youtubers and uploaders on the internet providing valuable materials for free which made the learning process so much easier.

iv

ABSTRACT

Reinforced concrete (RC) frames such as bare frames, soft story frames and completely

infilled frames were considered for model in this study. Each frame was further

considered as 6, 9, 12 and 15 story buildings. Soft story and infilled frames were provided

with two types of masonry infill (Em = 1875 and 5625 N/mm2). Frames were subjected to

harmonic ground motions of peak ground acceleration 1, 2 and 3 m/s2. Each acceleration

was of 12 frequency levels starting from .25 to 3 Hz. The duration of the ground motions

was taken as 5s and damping of RC buildings was assumed to be 5%.

The study was nonlinear dynamic analysis of the models using ETABS 2013. Natural

frequency, interstory drift ratio and time passed before collapse were considered to

analyze the response of the RC frames. The UBC limitation on drift ratio for long period

(≥.7s) structures is .02. The structures were assumed to fail at this drift ratio.

After performing time history analysis, behaviors of the structures are compared. It was

found that when subjected to ground motion infilled frames perform best. Strength of

infill has effect on the response of frames under seismic loading and also on the natural

frequencies of the frames. Completely infilled frames with higher strength infill performed

better. Structures with higher number of story were found to sustain seismic loading for

longer duration before failure. The response of soft story and infilled frames (12 and 15

story buildings) were found to be close if weak infills are used. When subjected to ground

motions, frames were vulnerable to frequency level up to 1.5 Hz.

v

Contents

DEDICATION ....................................................................................................................................... i

DECLARATION ................................................................................................................................... ii

ACKNOWLEDGEMENT ...................................................................................................................... iii

ABSTRACT ......................................................................................................................................... iv

INTRODUCTION .................................................................................................................................1

1.1 General ....................................................................................................................................1

1.2 Objectives and scope of study ................................................................................................1

1.3 Methodology of thesis work ...................................................................................................1

1.4 Organization of the thesis .......................................................................................................2

LITERATURE REVIEW .........................................................................................................................3

2.1 Masonry infill in RC building ...................................................................................................3

2.2 Modeling of infill walls in RC buildings ...................................................................................5

2.2.1 Macro-Modeling of infill walls ......................................................................................6

2.2.1.1 Determination of Equivalent Strut Width ..............................................................7

2.2.2 Micro-Modeling of infill walls ................................................................................ 11

2.3 Concept of soft story in buildings ........................................................................................ 12

2.3.1 Definition of soft story in different codes ................................................................. 13

2.4 Interstory drift of frames ..................................................................................................... 14

2.4.1 Code provisions for interstory drift ........................................................................... 14

METHODOLOGY ............................................................................................................................. 16

3.1 Nonlinear dynamic analysis ................................................................................................. 16

3.2 Modal analysis ..................................................................................................................... 16

3.3 Time history analysis ............................................................................................................ 17

3.4 Building configuration .......................................................................................................... 19

3.5 Material properties .............................................................................................................. 22

3.5.1 Concrete and steel ..................................................................................................... 22

3.5.2 Mortar ........................................................................................................................ 22

3.5.3 Masonry ..................................................................................................................... 22

3.6 Properties of equivalent diagonal strut ............................................................................... 24

3.7 Loads on building ................................................................................................................. 25

vi

RESULTS AND DISCUSSIONS ........................................................................................................... 29

4.1 Natural Frequency of models compared with BNBC 1993 and BNBC 2010 ........................ 29

4.2 Comparison of natural frequency due to change in infill .................................................... 30

4.3 Maximum interstory drift ratio at different story levels ..................................................... 32

4.4 Comparison of maximum interstory drift ratio ................................................................... 57

4.4.1 Frames with weaker infill ........................................................................................... 57

4.4.2 Frames with stronger infill ......................................................................................... 61

4.5 Difference in interstory drift ratio due to change in infill .................................................... 65

4.6 Time history of drift ............................................................................................................. 69

4.6.1 Frames with weaker infill ........................................................................................... 69

4.6.2 Frames with stronger infill ......................................................................................... 99

4.7 Comparison of collapse time for different types of frames ............................................... 130

4.7.1 Bare frames .............................................................................................................. 130

4.7.2 Soft story frames ..................................................................................................... 131

4.7.3 Infilled frames .......................................................................................................... 133

CONCLUSIONS AND RECOMMENDATIONS .................................................................................. 135

5.1 Conclusions: ....................................................................................................................... 135

5.1.1 Natural frequency of frames: .................................................................................. 135

5.1.2 Interstory drift ratio of frames: ............................................................................... 135

5.1.3 Time of collapse for different frames: ..................................................................... 136

5.2 Recommendations for future work: .................................................................................. 136

REFERENCES ................................................................................................................................. 137

1

CHAPTER ONE

INTRODUCTION

1.1 General

Walls are created in buildings by infilling parts of the frame with stiff construction such as

bricks or concrete blocks. Unless adequately separated from the frame, the structural

interaction of the frame and infill panels must be allowed for in the design. This interaction

has a considerable effect on the overall seismic response of the structure and on the

response of the individual members.

The behavior of the infilled frame under seismic loading is very complex and complicated.

Since the behavior is nonlinear and closely related to the link between the frame and the

infill, it is very difficult to predict if by analytical methods unless the analytical models are

supported and revised by using the experimental data. Due to the complex behavior of

such composite structures, experimental as well as analytical research is of great

importance to determine the strength, stiffness and dynamic characteristics at each stage

of loading. It is widely recognized that nonlinear time history analysis constitutes the most

accurate way for simulating response of structures subjected to strong levels of seismic

excitation. This method is based on sound underlying principles and features the

capability of reproducing the intrinsic inelastic dynamic behavior of structures.

1.2 Objectives and scope of study This study will examine building structures with reinforced concrete frames having

masonry infill under dynamic base excitations as time history with the following specific

objectives:

To investigate various structural response for which typical frame structure

buildings (with different number of story) is most vulnerable to earthquake

excitation with particular frequency.

To determine and compare the response of different types of frames (bare

frame, soft story frame, infilled frame) under earthquake motion.

To investigate and compare the effects of masonry infill walls on RC frames

subjected harmonic ground motion.

1.3 Methodology of thesis work The proposed methodology consists of following steps:

Three types of buildings will be modeled for frames with full infill, frames without

any infill (bare frame) and frames with infill in upper stories and having a soft story

at the ground floor.

2

Masonry infill with 5 inch wall thickness will be modeled manually by macro-

modeling method using works of previous researchers.

Masonry infill having different properties will be selected for analysis of RC frame.

ETABS 2013 will be used for creating and nonlinear dynamic analysis of the models.

Time history analysis will be performed using Nonlinear Modal (FNA) load case.

Modal cases using Eigen vector will be used. Analysis will be performed for 5%

damping.

Analysis will be done for different earthquake frequencies, peak ground

accelerations and varying number of stories.

1.4 Organization of the thesis

Chapter 1 is a general introduction to the themes that will be dealt; the main topic is

described, the purposes of the work are set and a brief summary of the present job is

presented

Chapter 2 presents the review of previously published literature in the field of infilled

reinforced concrete frame structures. It also reviews the modeling of infill wall and

definition of soft story and interstory drift.

In chapter 3, the features of models used for time history analysis; after a short description

of finite element processes involved i.e. time history analysis, Modal analysis, the element

properties adopted in the model, the material properties assumed, the strut models used

in the analysis is explained.

In chapter 4, the results of analysis are given in detail that includes numerical evaluation

of dynamic response of nonlinear system when subjected to harmonic ground motions of

different amplitude and different frequencies. Behavior of buildings for different type of

infill walls has been observed.

Chapter 5 presents the conclusions of the thesis and the final considerations achieved,

giving some suggestions for further works on this topic.

3

CHAPTER TWO

LITERATURE REVIEW

2.1 Masonry infill in RC building P. G. Asteris and D. M. Cotsovos (2012) used finite element modeling to find out the effect

of infill walls on the structural response of RC frames. The results obtained from static

loading cases was that infill walls act as diagonal compression struts which undertakes

portion of the applied load thus offering relief to certain structural elements of the frame.

This action results in significant redistribution of the internal actions developing within

the structural elements of the frame by essentially redirecting the loads into other regions

of the structure. Although this redistribution of internal actions can result, on one hand,

in an increase of the overall stiffness and load carrying capacity of the frame, on the other

hand, it may cause stress concentrations in other regions of the structure never designed

to undertake the internal actions which develop due to the additional loads transferred

through the diagonal strut.

Observation of dynamic loading cases was that the two story infilled frame can be

essentially described by a one degree of freedom system instead of the two degree of

freedom system describing the response of the bare frame as the introduction of the infill

plane essentially cancels the degree of freedom associated with the displacement of the

floor level of the frame to which infill walls were introduced. More damages were

sustained by the structural elements of the story frame which had no infill wall.

Mohammad H. Jinya, V. R. Patel (2014) prepared sixteen models for static linear analysis

and dynamic analysis (time history). They compared the results of models i.e. without

strut and with strut of infill wall with 15% and 25 central outer opening. From the analysis

it was concluded that diagonal strut will change the seismic performance of RC building.

Axial force in column increased, story displacement and story drift are decreased and base

shear increased with higher stiffness of infill. If in the ground level at least periphery wall

is provided then soft story effect can be minimized. It was also concluded that increase in

the percentage of opening can lead to a decrease in lateral stiffness.

Hossein Mostafaei and Toshimi Kabeyasawa (2004) carried out nonlinear time history

analysis on Bam telephone center to find out effect of infill masonry walls on the seismic

response of reinforced concrete buildings subjected to the 2003 Bam earthquake strong

motion. A nonlinear analysis of the Bam telephone center-reinforced concrete building,

subjected to the horizontal components of the recorded strong motion, was carried out

to obtain an analytical explanation of the almost linear performance of the building during

the earthquake. An approach was developed to employ analytical models for masonry

infill walls with and without openings and applied in the analysis. A significant effect of

infill walls was observed on the structural response of the

building. It could be concluded that the Bam telephone center building without masonry

infill walls would suffer large nonlinear deformations and damage during the earthquake.

The maximum overall story drift ratio of .8% was obtained for the ground floor of the

4

building, which is less than a limit yielding drift ratio of 1%. Therefore, it may be concluded

that the linear responses observed correlate well with the analytical results. Drift ratios

for different damaged infill walls were obtained and compared to the observed responses.

In most cases the comparisons lead to a fairly acceptable agreement. Further studies

might be recommended for the analytical modeling of the infill walls with openings to

obtain a simplified equivalent approach.

C V R MURTY and Sudhir K JAIN (2000) presented some experimental results on cyclic test

of RC frames with masonry infill to evaluate the influence of masonry infill walls on seismic

performance of RC frame buildings. It was seen that the masonry infills contribute

significant lateral stiffness, strength, overall ductility and energy dissipation capacity. With

suitable arrangements to provide reinforcement in the masonry that is well anchored into

the frame columns, it should be possible to also improve the out-of-plane response of

such infills.

Adel Ziada, Mohamed Laid Samai, Abdelhadi Tekkouk (2015) conducted a numerical study

using the software computer package SAP 2000 to investigate the effects of masonry infill

on the seismic performance of RC framed buildings located in a moderate seismic risk area

in Algeria. For this purpose, a number of nonlinear static (pushover) analyses have been

performed on spatial bare structures, fully and partially infilled structures. The infills have

been modeled with two crossed diagonal struts able to represent the contribution under

compression of the panels subjected to dynamic loading along two main directions. The

conclusions from the study was that the distribution of the masonry infill walls throughout

the story has insignificant effect on seismic behavior of reinforced concrete buildings

provided that symmetric plan layout of a building and symmetric arrangement of the infill

walls are satisfied. The behavior of an infilled frame is dependent on the properties of

frame and infill; hence, the response of such frames should be based on overall frame to

infill composite action rather than on isolated bare frame

behavior. The collapse mechanisms of the three models of six stories clearly show that

the presence of the infills affect in negative way the ductility of the whole structure. The

presence of the infills reduces considerably the displacements at all stories compared with

the bare structure (246%). The fundamental period of infilled structures is in a good

agreement with the estimated value provided by RPA99 and EC8 (T=0.050H0.75).

Ahmed Sayed Ahmed Tawfik Essa, Mohamed Ragai Kotp Badr, Ashraf Hasan El-Zanaty

(2014) performed an experimental study for behavior and ductility of high strength

reinforced concrete frames with infill wall under the effect of cyclic loading. The

experimental program was conducted on four specimens (frames). The parameters are

studied change panel of frame from non-infill to infill, change thickness of infill wall and

change type of bricks. The dimension of frames is selected to represent half scale frames

and tested under cyclic loading. From the representation and the analysis of the obtained

results, the main conclusions are pointed out; the lateral load resistance for infilled frames

with infill wall (red bricks) thickness 12, 6 cm and cement bricks 12 cm, respectively was

greater than the bare frame by about 184%, 61% and 99%, respectively. The ductility

5

factor for infilled frames was less than the bare frame by about 57%, 51% and 46%,

respectively.

2.2 Modeling of infill walls in RC buildings P.G. Asteris (2008) in his paper Finite Element Micro-Modeling of infilled frames

presented a comprehensive review of modeling techniques of infill walls. The discussion

below is given from this paper.

To understand the approach and capabilities of each model it is convenient to classify the

models by macro- and micro- models. This classification is based on their complexity, the

details by which they model an infill wall, and the information they provide to the analyst

about the behavior of structure.

A basic characteristic of a macro- (or simplified) model is that they try to encompass the

overall (global) behavior of a structural element without modeling all the possible modes

of local failure. Micro- (or fundamental) models, on the other hand, model the behavior

of a structural element with great detail trying to encompass all the possible modes of

failure. The following sections constitute a brief review of the most representative macro-

and micro-models.

Fig: Masonry infill panels in framed structure

6

Fig: Change in the lateral load transfer mechanism owing to inclusion of masonry infill

walls

2.2.1 Macro-Modeling of infill walls Since the first attempts to model the response of the composite infilled frames structures,

experimental and conceptual observations have indicated that a diagonal strut with

appropriate geometrical and mechanical characteristics could possibly provide a solution

to the problem. In 1958, Polyakov (Polyakov 1960) suggested the possibility of considering

the effect of the infilling in each panel as equivalent to diagonal bracing and this

suggestion was later taken up by Holmes (Holmes 1961) who replaced the infill by an

equivalent pin-jointed diagonal strut made of the same material and having the same

thickness as the infill panel and a width equal to one third of the infill diagonal length

(Figure 1). The ‘one-third’ rule was suggested as being applicable irrespective of the

relative stiffnesses of the frame and the infill.

Stafford Smith (Smith 1966) and Stafford Smith and Carter (Smith and Carter 1969) related

the width of the equivalent diagonal strut to the infill/frame contact lengths using an

analytical equation which has been adapted from the equation of the length of contact of

a free beam on an elastic foundation subjected to a concentrated load (Hetenyi 1946).

Based on the frame/infill contact length, alternative proposals for the evaluation of the

equivalent strut width have been given by Mainstone (Mainstone 1971) and Kadir (Kadir

1974). Stafford Smith and Carter (Smith and Carter 1969), and Mainstone (Mainstone

1971) used the equivalent strut approach to simulate infill wall in steel frames and study

the behavior of infilled structures subjected to monotonic loading. They also developed

equations by which the properties of these struts, such as initial stiffness and ultimate

strength, were calculated. This approach proved to be the most popular over the years

because of the ease with which it can be applied.

In the last two decades it became clear that one single strut element is unable to model

the complex behavior of the infilled frames. As reported by many researchers (Reflak and

Faijfar 1991; Saneinejad and Hobbs 1995; Buonopane and White 1999), the bending

moments and shearing forces in the frame members cannot be replicated using a single

7

diagonal strut connecting the two loaded corners. More complex macro-models were

then proposed, but they were still usually based on a number of diagonal struts.

Chrysostomou (Chrysostomou 1991) had the objective of simulating the response of

infilled frames under earthquake loading by taking into account stiffness and strength

degradation of the infills. They proposed to model each infill panel by six compression-

only inclined struts. Three parallel struts are used in each diagonal direction and the

offdiagonal ones are positioned at critical locations along the frame members. At any

point during the analysis of the non-linear response only three of the six struts are active,

and the struts are switched to the opposite direction whenever their compressive force

reduces to zero. The advantage of this strut configuration over the single diagonal strut is

that it allows the modeling of the interaction between the infill and the surrounding

frame.

2.2.1.1 Determination of Equivalent Strut Width

Fig: Placement of Equivalent diagonal strut

K. H. Abdelkareem, F. K. Abdel Sayed, M. H. Ahmed, N. AL-Mekhlafy (2013) presented a

detail review of various researches to find out the width of the equivalent diagonal strut

(w) using a number of expressions.

Holmes (1961) states that the width of equivalent strut to be one third of the diagonal

length of infill, which resulted in the infill strength being independent of frame stiffness

� = �

�� Where �� = diagonal length of infill

Later Stafford Smith and Carter (1969) proposed a theoretical relation for the width

of the diagonal strut based on the relative stiffness of infill and frame.

8

� = .58(�

�)�.��(�� ).��(�

�� ).��

�� = ∜(��

��)

t = thickness of the infill

�� = height the infill

�� = modulus of the infill

= the angle between diagonal of the infill and the horizontal

�� = modulus of elasticity of the column,

�� = the moment of inertia of the columns,

H = total frame height

�� is a dimensionless parameter (which takes into account the effect of relative stiffness

of the masonry panel to the frame).

Mainstone (1971) gave equivalent diagonal strut concept by performing tests on

model frames with brick infills. His approach estimates the infill contribution both to the

stiffness of the frame and to its ultimate strength.

� = .16��(�� )�.�

Mainstone and Weeks and Mainstone (1974), also based on experimental and

analytical data, proposed an empirical equation for the calculation of the equivalent strut

width:

� = .175��(��)�.�

Bazan and Meli (1980), on the basis of parametric finite-element studies for onebay,

one-story, infilled frames, produced an empirical expression to calculate the

equivalent width w for infilled frame:

� = (.35 + .22�)ℎ

� = ��

��

� is a dimensionless parameter

Ac is the gross area of the column

��= (�� t) is the area of the infill panel in the horizontal plane and

9

�� is the shear modulus of the infill

Liauw and Kwan (1984) proposed the following equations based on experimental and

analytical data

� = .��

√(�� )

Paulay and Preistley (1992) pointed out that a high value of w will result in a stiffer

structure, and therefore potentially higher seismic response. They suggested a

conservative value useful for design proposal, given by:

� = .25��

Durrani and Luo (1994) analyzed the lateral load response of reinforced concrete infilled

frames based on Mainstone’s equations. They proposed an equation for effective width

of the diagonal strut, w, as

� = �√(� � + ��)sin2�

� = .32√sin2�(��

��)�.�

� = 6(1 +��

п��)

L is the length of the frame c/c

FEMA (1998) proposed that the equivalent strut is represented by the actual infill

thickness that is in contact with the frame (tinf) and the diagonal length (dinf) and an

equivalent width, W, is given by:

� = .175��(��)�.�

Hendry (1998) has also presented equivalent strut width that would represent the

masonry that actually contributes in resisting the lateral force in the composite structure:

� = .5√(�� + ��

�)

�� = п

�(

��

��)

��

�� = п(��

��)

��

10

�� , �� are contact length between wall and column and beam respectively at the time

of initial failure of wall

�� is the moment of inertia of the beam

�� is the length of the infill (clear distance between columns)

Al-Chaar 2002 proposed that the equivalent masonry strut is to be connected to the frame

members as depicted in Figure 5. The infill forces are assumed to be mainly resisted by

the columns, and the struts are placed accordingly. The strut should be pin-connected to

the column at a distance lcolumn from the face of the beam. This distance is defined by the

following equations

�� = �

��

tan�� = ��

�

��

��

Where the strut width (w) is calculated by using Mainstone and Weeks Equation without

any reduction factors:

� = .175��(��)�.�

Papia et al. 2008 developed an empirical equation for the effective width of the diagonal

strut as

� = �

�

�

�∗��

� = .249 − .016�� + .567υ��

� = .146 + .0073�� + .126υ��

�∗ = ��

��(

��

�� +

��

��)

Z = 1 if ��

��= 1

Z = 1.125 if ��

��≥ 1.5

Where

Z is an empirical constant

λ* = stiffness parameter

υinf = poison ratio for the infill

Ec = Young’s modulus of the frame

11

Ac = cross sectional area of the column and

Ab = cross sectional area of the beam

2.2.2 Micro-Modeling of infill walls All models described in this section are based on the Finite Element Method, using three

different kinds of elements to represent the behavior of infilled frames subjected to lateral

loading. According to these models the frame is constituted by plane or beam element,

the infill by plane elements, and the interface behavior by interface elements or by one

dimensional joint elements.

Mallick and Severn (Mallick and Severn 1967), and Mallick and Garg (Mallick and Garg

1971) suggested the first finite element approach to analyze infilled frames, addressing

the problem of an appropriate representation of the interface conditions between frame

and infill. The infill panels were simulated by means of linear elastic rectangular finite

elements, with two degrees of freedom at each four nodes, and the frame was simulated

by beam element ignoring axial deformation. This was a consequence of the assumption

that the interaction forces between the frame and the infill along their interface consisted

only of normal forces. In this model, the slip between the frame and the infill was also

taken in account, considering frictional shear forces in the contact regions. Several single

story rectangular infilled frames under static loading were analyzed and the results were

in a good agreement with experimental results if the height to span ratio was not greater

than two.

Liauw and Kwan (Liauw and Kwan 1984) used three different types of elements to study

the behavior of infilled frames subjected to monotonic loading. The infill-frame interface

was modeled by simple bar type elements capable of simulating both separation and slip.

The infill panel was modeled by triangular plane stress elements. In tension, the material

was idealized as a linear elastic brittle material. Before cracking, the material was assumed

to be isotropic and after cracking was assumed to become anisotropic due to the presence

of the crack. It was assumed that for an open crack the Young’s modulus perpendicular to

the crack and the shear modulus parallel to the crack were zero. When the crack was

closed, the Young’s modulus was restored, and the shear force is assumed to be taken

over by friction. In compression, the panel was assumed to exhibit extensive nonlinearity

in the stress-strain relationship. Although the material was subjected to bi-axial stress, it

was assumed that the panel was under uniaxial stress based on experimental results,

which show that one of the principal stresses is much smaller than the other. Using an

iterative procedure with incremental displacement, several four-story one-bay model

frames infilled with micro-concrete were analyzed. Close agreement between

experimental and analytical results has been observed.

Dhanasekar and Page (Dhanasekar and Page 1986), using one-dimensional joint elements

to model the mortar joint between the infill and the frame, have shown that the behavior

of the composite frame not only depends on the relative stiffness of the frame and the

infill and the frame geometry, but is also critically influenced by the strength properties

12

of the masonry (in particular, the magnitude of the shear and tensile bond strengths

relative to the compressive strength).

A simpler and much quicker finite element technique (Axley and Bertero 1979) consist in

reducing by condensation, the stiffness of the infill to the boundary degrees of freedom.

It is assumed that the frame constrains the form (but not the degree) of deformation on

the infill. Separate stiffnesses are formed. A constraint relation is assumed between the

12 frame degrees of freedom (DOF) and the boundary degrees of freedom. Thus, a

congruent transformation of the separate systems to a composite approximate frame-

infill system (with only 12 DOF) is possible.

2.3 Concept of soft story in buildings L. Teresa Guevara-Perez (2012) analyzed the architectural reasons why ‘soft story’ and

‘weak story’ configurations are present in contemporary cities and explains in conceptual

terms their detrimental effects on building seismic response. The soft story irregularity,

refers to the existence of a building floor that presents a significantly lower stiffness than

the others, hence it is also called: flexible story. It is commonly generate unconscientiously

due to the elimination or reduction in number of rigid non-structural walls in one of the

floors of a building, or for not considering on the structural design and analysis, the

restriction to free deformation that enforces on the rest of the floors, the attachment of

rigid elements to structural components that were not originally taken into consideration.

Because of the effects produced by nonstructural components on the seismic

performance of the building, the term non-intentionally nonstructural has been assigned

to these components since the end of the 1980’s (Guevara, 1989). Table 12.3-2 in the

ASCE/SEI 7-10 document, (p. 83) defines soft story as irregularity type 1. If the soft story

effect is not foreseen on the structural design, irreversible damage will generally be

present on both the structural and nonstructural components of that floor. This may cause

the local collapse and in some cases even the total collapse of the building.

Concerning soft story, the National Information Service for Earthquake Engineering (2000)

states:

In shaking a building, an earthquake ground motion will search for every structural

weakness. This weaknesses are usually created by sharp changes in stiffness, strength

and/or ductility, and the effects of these weaknesses are accentuated by poor distribution

of reactive masses. Severe structural damage suffered by several modern building during

recent earthquakes illustrates the importance of avoiding sudden changes in lateral

stiffness and strength. A typical example of the detrimental effects that these

discontinuities can induce is seen in the case of buildings with a “soft story”. Inspections

of earthquake damage as well as the results of analytical studies have shown that

structural systems with a soft story can lead to serious problems during earthquake

ground shaking. [Numerous examples] illustrate such damage and therefore emphasize

the need for avoiding soft story by an even distribution of flexibility, strength and mass.

13

2.3.1 Definition of soft story in different codes

1. ASCE 07 – Minimum Design Loads for Buildings and other Structures, USA

(2002): soft story is one in which the lateral stiffness is less than 70% of that in

the story above or less than 80% of the average stiffness of the three story

above. An extreme soft story is one in which lateral stiffness is less than 60%

of that in the story above or less than 70% of the average stiffness of the three

story above. For example, building on stilts will fall under this category.

2. Specifications for Structures to be built in Disaster Area, Turkey (1998): the

case where stiffness irregularity factor in each of the two orthogonal

earthquake directions is greater than 1.5 is considered as soft story.

Stiffness irregularity factor is defined as ratio of the average story drift at any

story to average story drift at the story immediate above.

Ƞki = (∆i) / (∆i+1)

Story drift ∆I of any column or structural wall shall be determined by

∆i = di – di-1

Where di and di-1 represents the displacement obtained from the analysis at

the end of any column or structural wall at stories i and i-1.

3. Indonesian Earthquake Design Code, Indonesia (1983): the ratio of floor mass

to the stiffness of a particular story shall not differ by more than 50% of the

average for the structure.

4. Criteria for Earthquake Design of Structures, India (IS 1893:2002): soft story

when stiffness

�� < .7�� Or

�� < .8{(�� )

�}

5. General Structural Design and Design Loading for Buildings, New Zealand (NZS

4203:1992): a story where the ratio of the interstory deflection divided by the

product of the story shear and story height exceeds 1.4 times the

corresponding ratio for the story immediately above this level.

6. Bangladesh National Building Code, Bangladesh (BNBC 1993): soft story is one

in which the lateral stiffness is less than 70% of that in the story above or less

than 80% of the average stiffness of the three story above.

14

2.4 Interstory drift of frames Gary R. Searer and Sigmund A. Freeman (2004) presented a brief history of design drift

requirements, technical background for the requirements, and the reasoning behind the

changes, starting with the 1961 Uniform Building Code (UBC) through present day.

Emphasis was given to the discussion of minimum base shears for calculation of drift for

long-period structures.

Lateral deflection is the predicted movement of a structure under lateral loads; and story

drift is defined as the difference in lateral deflection between two adjacent stories. During

an earthquake, large lateral forces can be imposed on structures; both the 1997 UBC (the

basis of the 2001 California Building Code) and ASCE 7-02 (which is based on NEHRP)

require that the designer assess the effects of this deformation on both structural and

nonstructural elements. Lateral deflection and drift have three primary effects on a

structure; the movement can affect the structural elements (such as beams and columns);

the movements can affect non-structural elements (such as the windows and cladding);

and the movements can affect adjacent structures. Without proper consideration during

the design process, large deflections and drifts can have adverse effects on structural

elements, nonstructural elements, and adjacent structures.

2.4.1 Code provisions for interstory drift 1. Algeria: RPA (1989)

∆�= �� − �� With �� = 0

�� = lateral displacement

∆≤ .0075�� ℎ��ℎ�

∆ = ��

2. Argentina: INPRES-CIRSOC 103 (1991)

� = Lateral displacement

∆�= �� − �� With δ0 = 0

Limiting values

Group Non-structural elements attached are damaged

Non-structural elements attached are not

damaged

A0 .01 .01

A .011 .015

B .014 .019

3. Australia: AS11704 (1993)

δx – interstory drift = ��

�� – Lateral displacements at level i

= ��(�2п� )2

=(��

�� )(�

2п� )2

15

4. Europe: 1-1(Oct94); 1-2(Oct 94); 1-3(Feb95); part 2(Dec94); part 5(Oct t94); Euro

code 8

For buildings with non-structural elements ��

��≤ .004ℎ

When structural deformation is restricted ��

��≤ .006ℎ

�� = design resistance

5. India and Pakistan: IS1893 (1984) and PKS 395-Rev (1986)

∆max between two floors ≤.004hi

For height ≤ 40m (India)

6. Iran: ICRD (1988)

Lateral drift ∆ ≤ .005hi

Both lateral forces and torsional moments are coupled

7. Israel: IC-413 (1994)

For T ≤.7s ∆i lim = min ( ��

��,

��

�� )

T > .7s ∆i lim = min ( .��

��,

��

�� )

8. Japan: BLEO (1981)

∆ ≤ ��

�� or ∆ =

��

�� for non-structural elements for building not exceeding 60m height

∆ ≤ ��

�� for steel building ≤ 31m

9. Mexico: UNAM (1983) M III (1988)

∆ ≤ .006ℎ� (main structural elements)

∆ ≤ .012 (for partition)

10. USA: UBC-91 (1991) and SEAOC (1990)

For T <.7s ∆ ≤ .005hi

T ≥ .7s ∆ ≤ .004hi

In UBC 1997 it is stated that Story drifts shall be computed using the Maximum Inelastic

Response Displacement, ∆M. and calculated story drift using M shall not exceed 0.025

times the story height for structures having a fundamental period of less than 0.7 second.

For structures having a fundamental period of 0.7 second or greater, the calculated story

drift shall not exceed 0.020 times the story height with provision for exceptions.

16

CHAPTER THREE

METHODOLOGY

3.1 Nonlinear dynamic analysis Nonlinear dynamic analysis utilizes the combination of ground motion records with a

detailed structural model, therefore is capable of producing results with relatively low

uncertainty. In nonlinear dynamic analyses, the detailed structural model subjected to a

ground-motion record produces estimates of component deformations for each degree

of freedom in the model and the modal responses are combined using schemes such as

the square-root-sum-of-squares.

In non-linear dynamic analysis, the non-linear properties of the structure are considered as part of a time-domain analysis. This approach is the most rigorous, and is required by some building codes for buildings of unusual configuration or of special importance. However, the calculated response can be very sensitive to the characteristics of the individual ground motion used as seismic input; therefore, several analyses are required using different ground motion records to achieve a reliable estimation of the probabilistic distribution of structural response. Since the properties of the seismic response depend on the intensity, or severity, of the seismic shaking, a comprehensive assessment calls for numerous nonlinear dynamic analyses at various levels of intensity to represent different possible earthquake scenarios. This has led to the emergence of methods like the Incremental Dynamic Analysis.

3.2 Modal analysis A modal analysis calculates the frequency modes or natural frequencies of a given system,

but not necessarily its full-time history response to a given input. The natural frequency

of a system is dependent only on the stiffness of the structure and the mass which

participates with the structure (including self-weight). It is not dependent on the load

function.

It is useful to know the modal frequencies of a structure as it allows you to ensure that the frequency of any applied periodic loading will not coincide with a modal frequency and hence cause resonance, which leads to large oscillations.

The method is:

1. Find the natural modes (the shape adopted by a structure) and natural frequencies

2. Calculate the response of each mode 3. Optionally superpose the response of each mode to find the full modal response

to a given loading

17

Modal analysis, or the mode-superposition method, is a linear dynamic response procedure which evaluates and superimposes free-vibration mode shapes to characterize displacement patterns. Mode shapes describe the configurations into which a structure will naturally displace. Typically, lateral displacement patterns are of primary concern. Mode shapes of low-order mathematical expression tend to provide the greatest contribution to structural response. As orders increase, mode shapes contribute less, and are predicted less reliably. It is reasonable to truncate analysis when the number of mode shapes is sufficient.

A structure with N degrees of freedom will have N corresponding mode shapes. Each mode shape is an independent and normalized displacement pattern which may be amplified and superimposed to create a resultant displacement pattern, as shown in Figure below

Fig: resultant displacements and modal components

3.3 Time history analysis Time-history analysis provides for linear or nonlinear evaluation of dynamic structural

response under loading which may vary according to the specified time function. Dynamic

equilibrium equations, given by K u (t) + C d/dt u (t) + M d2/dt u (t) = r (t), are solved using

either modal or direct-integration methods. Initial conditions may be set by continuing

the structural state from the end of the previous analysis.

A full time history will give the response of a structure over time during and after the application of a load. To find the full time history of a structure's response, one must solve the structure's equation of motion.

18

Example

A simple single degree of freedom (a mass, M, on a spring of stiffness, k for example) has the following equation of motion:

Where is the acceleration (the double derivative of the displacement) and x is the displacement.

If the loading F (t) is a Heaviside step function (the sudden application of a constant load), the solution to the equation of motion is:

Where

and the fundamental natural frequency

.

The static deflection of a single degree of freedom system is:

so one can write, by combining the above formulae:

This gives the (theoretical) time history of the structure due to a load F (t), where the false assumption is made that there is no damping.

19

Although this is too simplistic to apply to a real structure, the Heaviside Step Function is a reasonable model for the application of many real loads, such as the sudden addition of a piece of furniture, or the removal of a prop to a newly cast concrete floor. However, in reality loads are never applied instantaneously - they build up over a period of time (this may be very short indeed). This time is called the rise time.

As the number of degrees of freedom of a structure increases it very quickly becomes too difficult to calculate the time history manually - real structures are analyzed using nonlinear finite element software.

Damping

Any real structure will dissipate energy (mainly through friction). This can be modelled by modifying the Dynamic Amplification Factor (DAF)

Where

3.4 Building configuration

Simple beam-column frames are analyzed. There are three types of frames.

Bare frame: no equivalent struts are provided at any story level of this type of

frame

Soft story frame: frames; at bottom story of which no equivalent struts are

provided, falls into this category

Infilled frame: equivalent struts are provided at all story levels of this type of

frame

Each type of frames are considered for total four story levels, namely, 6, 9, 12, 15 story

Details of the frames are given below

Story Column

(inch X inch) Beam

(inch X inch)

Column to column spacing

(ft)

Story height (ft)

Support condition at ground

level

6 9

12 15

12*12 15*15 18*18 21*21

12*20 20 10 fixed

20

Fig: 9 story building bare frame

Fig: 9 story building soft story frame

21

Fig: 9 story building infilled frame

Fig: extruded view of 6 story infilled frame

22

3.5 Material properties

3.5.1 Concrete and steel

Concrete

Weight = 150 lb/ft3

Modulus of elasticity Ec = 3600 ksi

Steel

Minimum yield stress Fy = 50 ksi

Minimum tensile strength Fu = 65ksi

Modulus of elasticity Es = 29000ksi

3.5.2 Mortar Specified compressive strength of Masonry ��

�

From BNBC 1993 part 6 chapter 4 section 4.3.2

Grade of Mortar

Mix proportion by volume Minimum compressive

strength at 28 days N/mm2

Cement Sand

M1

M2

M3

M4

M5

M6

1

3 4 5 6 7 8

10 7.5 5 3 2 1

In this case mortar compressive strength value 2.5 and 7.5 N/mm2 is used

3.5.3 Masonry Weight of masonry work

From BNBC 1993 part 6 chapter 2 table 6.2.2

Weight of brick masonry work excluding plaster

burnt clay, per 100 mm thickness 1.910 kN/m2

Modulus of elasticity for masonry

From BNBC 1993 1993 part 6 chapter 4 section 4.3.8

�� = 750�� ≤ 15000 N/mm2

23

Used value:

1. 750*2.5 = 1875 N/mm2

2. 750*7.5 = 5625 N/mm2

Allowable compressive stress, axial in masonry

From BNBC 1993 part 6 chapter 4 section 4.3.5

�� = ��

�

��1 − (

��

��)��

There is also relationship found experimentally between compressive strength of mortar

and masonry for a given strength brick units. This relationship is illustrated below:

Fig: Relationship between brick crushing strength and brickwork strength for various

mortar strength. Based on test results. (Design of masonry structures, A.W.Hendry,

B.P.Sinha, S.R.Davies)

Axial compressive strength in masonry unit

Using a brick compressive strength of 30 N/mm2

Compressive strength of Mortar N/mm2

BNBC 1993 N/mm2

From Chart N/mm2

2.5 7.5

.446 1.338

9 13

Values of axial compressive strength obtained using formula provided in BNBC 1993 are

used

24

3.6 Properties of equivalent diagonal strut

The relative infill-to-frame stiffness was calculated using the equation given by Stafford,

Smith and Carter (1969)

�� = ∜(��

��)

t = thickness of the infill

�� = height the infill

�� = modulus of the infill

= the angle between diagonal of the infill and the horizontal

�� = modulus of elasticity of the column,

�� = the moment of inertia of the columns,

H = total frame height

Using this expression the width of strut is determined using the expression given by

Mainstone (1971) which considers the relative infill-to-frame flexibility

� = .175��(��)�.�

For each type of frame (varying column size) and two modulus of elasticity of masonry Em

width of equivalent struts were calculated as given below:

Story Colum size

(inch X inch)

Width of strut (mm)

Em = 1875 N/mm2 Em = 5625 N/mm2

6 9

12 15

12*12 15*15 18*18 21*21

769.204 841.018 904.645 962.181

689.102 753.364 810.514 862.076

Compression limit of struts:

Axial strength is calculated using the formula given in BNBC 1993 for masonry work for

two types of mortar strength fm as given below:

Story Compression limit

(kN)

fm = .446 N/mm2 fm = 1.338 N/mm2

6 9

12 15

43.564 47.637

51.2339 54.5022

117.096 128.016 137.727 147.489

25

Tension limit of struts:

Tensile strength of the struts is taken as zero.

Release:

At two end of the struts releases are provided for moment about major axis (M3 release)

Weight of struts:

Struts are modeled as weightless members; their weights are considered in partition wall

load.

3.7 Loads on building

Self-weight of slab = �.�

��150 psf = 68.75

Partition wall = 80 psf

Floor finish = 30 psf

Seismic mass = 178.75 psf (excluding live load)

Seismic mass lumped at floor level (for an interior frame)

= 178.75 psf x (20 ft x 60 ft)

= 214500 lb

Uniformly distributed load at each story level = 52.173 kN/m (3.575 kip/ft)

Uniformly distributed load at roof level = 29.188 kN/m (2 kip/ft)

5% damping (typical for building) is used

Ground motion applied:

Frequencies considered: .25, .5, .75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75, 3 Hz

Peak Ground acceleration (PGA) considered: 1, 2, 3 m/s2

Earthquake strong motion duration: 5s

For PGA 1 m/s2 earthquake input signals are shown below:

26

Fig: Earthquake ground motion with frequency = .25Hz



Fig: Earthquake ground motion with frequency = 1Hz

27

Fig: Earthquake ground motion with frequency = 1.25Hz




28





29

CHAPTER FOUR

RESULTS AND DISCUSSIONS

4.1 Natural Frequency of models compared with BNBC 1993 and BNBC 2010

Natural frequency of the models are found out using modal analysis in ETABS 2013.

Infilled frames are found to have the natural frequencies closest to the values of

frequencies found using formula provided in BNBC 1993 and 2010.

Fig: Natural frequency vs. number of story for frames with infill Em = 1875 N/mm2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

5 6 7 8 9 10 11 12 13 14 15 16

nat

ura

l fre

qu

ency

story no

bare frame

soft storey

infilled

BNBC1993

BNBC2010

30

Fig: Natural frequency vs. number of story for frames with infill Em = 5625 N/mm2

4.2 Comparison of natural frequency due to change in infill

Fig: natural frequency for different story frames with compared with BNBC

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

5 6 7 8 9 10 11 12 13 14 15 16

nat

ura

l fre

qu

ency

story no

bare frame

soft storey

infilled

BNBC1993

BNBC2010

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

6 9 12 15

nat

ura

l fre

qu

ency

(H

z)

story no

soft story frame

infill moe 1875 N/mm^2 infill moe 5625 N/mm^2 BNBC 1993 BNBC2010

31

Fig: natural frequency for different story frames with compared with BNBC

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

6 9 12 15

infilled frame

infill moe 1875 N/mm^2 infill moe 5625 N/mm^2 BNBC 1993 BNBC2010

32

4.3 Maximum interstory drift ratio at different story levels

Interstory drift ratios at every story is found after time history analysis. Then maximum

interstory drift ratio at each story level in the 5 second time history is also found out for

every ground motion. Story levels are then plotted against this ratios.

It can be observed that at higher frequency level the shapes of the curves become highly

irregular. But at lower frequency levels (up to 1Hz) the drift ratio at one story are smaller

than the drift ratio at the underlying stories.

For soft story frames, the soft story effect can be easily observed in the graphs.

In the following graphs drift ratios are shown for peak ground acceleration (PGA) 1 m/s2

only. The drift ratios corresponding to PGA 2 and 3 1 m/s2 can be found by simply

multiplying these drift ratios by 2 and 3 respectively.

Six story buildings:

Fig: maximum interstory drift ratio at different levels; for frames with infill Em = 1875

N/mm2 (left) and 5625 N/mm2 (right) at Freq.25Hz PGA 1m/s2

0

1

2

3

4

5

6

7

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio

bare frame soft story frame

infilled frame

0

1

2

3

4

5

6

7

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

33





0

1

2

3

4

5

6

7

0 0.01 0.02 0.03 0.04 0.05

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.01 0.02 0.03 0.04 0.05

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.01 0.02 0.03 0.04 0.05

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.01 0.02 0.03 0.04

sto

ry le

vel

drift ratio


infilled frame

34


N/mm2 (left) and 5625 N/mm2 (right) at Freq1Hz PGA 1m/s2


N/mm2 (left) and 5625 N/mm2 (right) at Freq1.25Hz PGA 1m/s2

0

1

2

3

4

5

6

7

0 0.01 0.02 0.03

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.01 0.02 0.03 0.04 0.05

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.005 0.01 0.015 0.02

sto

ry le

vel

drift ratio


infilled frame

35





0

1

2

3

4

5

6

7

0 0.005 0.01

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.002 0.004 0.006 0.008

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.002 0.004 0.006 0.008

sto

ry le

vel

drift ratio


infilled frame

36





0

1

2

3

4

5

6

7

0 0.002 0.004 0.006

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

37





0

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.002 0.004 0.006

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

38



Nine story buildings:

Fig: maximum interstory drift ratio at different levels; for frames with infill moe 1875


0

1

2

3

4

5

6

7

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

0 0.001 0.002 0.003

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.005 0.01 0.015 0.02

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.005 0.01 0.015 0.02

sto

ry le

vel

drift ratio


infilled frame

39



Fig: maximum interstory drift ratio at different levels; for frames with infill moe 1875


0

1

2

3

4

5

6

7

8

9

10

0 0.01 0.02 0.03 0.04

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.01 0.02 0.03 0.04

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.01 0.02 0.03 0.04

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.01 0.02 0.03

sto

ry le

vel

drift ratio


infilled frame

40





0

1

2

3

4

5

6

7

8

9

10

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.01 0.02 0.03

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.002 0.004 0.006 0.008

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

41





0

1

2

3

4

5

6

7

8

9

10

0 0.002 0.004 0.006 0.008

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.002 0.004 0.006 0.008

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infillde frame

42





0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

43





0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

44



Twelve story buildings:



0

1

2

3

4

5

6

7

8

9

10

0 0.0005 0.001 0.0015 0.002

sto

ry le

vel

drift ratio


infilled frame

0

1

2

3

4

5

6

7

8

9

10

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

0 0.005 0.01 0.015 0.02 0.025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.005 0.01 0.015 0.02 0.025

sto

ry le

vel

drift ratio


infilled frame

45





0

2

4

6

8

10

12

0 0.005 0.01 0.015 0.02 0.025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.005 0.01 0.015 0.02 0.025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.01 0.02 0.03

sto

ry le

vel

drift ratio


infilled frame

46





0

2

4

6

8

10

12

14

0 0.002 0.004 0.006 0.008

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.005 0.01

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.002 0.004 0.006 0.008 0.01

sto

ry le

vel

drift ratio


infilled frame

47





0

2

4

6

8

10

12

14

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.002 0.004 0.006

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

48





0

2

4

6

8

10

12

14

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

49





0

2

4

6

8

10

12

14

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

50



Fifteen story buildings:



0

2

4

6

8

10

12

14

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

0 0.001 0.002 0.003

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.01 0.02 0.03

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.01 0.02 0.03

sto

ry le

vel

drift ratio


infilled frame

51





0

2

4

6

8

10

12

14

16

0 0.005 0.01 0.015 0.02 0.025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.005 0.01 0.015 0.02

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.002 0.004 0.006 0.008

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

52





0

2

4

6

8

10

12

14

16

0 0.002 0.004 0.006 0.008 0.01

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.005 0.01 0.015

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

53





0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

54





0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003 0.004

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003 0.004 0.005

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003

sto

ry le

vel

drift ratio


infilled frame

55





0

2

4

6

8

10

12

14

16

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.001 0.002 0.003

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.0005 0.001 0.0015 0.002 0.0025

sto

ry le

vel

drift ratio


infilled frame

56



0

2

4

6

8

10

12

14

16

0 0.0005 0.001 0.0015

sto

ry le

vel

drift ratio


infilled frame

0

2

4

6

8

10

12

14

16

0 0.0005 0.001 0.0015

sto

ry le

vel

drift ratio


infilled frame

57

4.4 Comparison of maximum interstory drift ratio Maximum interstory drift ratio of a frame (considering all story levels) are taken from

graphs of section 4.3 and plotted against frequency and frequency ratio.

4.4.1 Frames with weaker infill

(Modulus of elasticity of infill Em = 1875 N/mm2)


Fig: drift ratio vs. frequency for PGA 1 m/s2 (six story building)

Fig: drift ratio vs. frequency ratio for PGA 1 m/s2 (six story building)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 0.5 1 1.5 2 2.5 3 3.5

Max

imu

m D

rift

Rat

io

Input Frequency (Hz)

Bare Frame

soft story frame

Infilled Frame

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 1 2 3 4 5 6

Max

imu

m D

rift

Rat

io

Frequency Ratio

Bare Frame

Soft Story Frame

Infilled Frame

58


Fig: drift ratio vs. frequency for PGA 1 m/s2 (nine story building)

Fig: drift ratio vs. frequency ratio for PGA 1 m/s2 (nine story building)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 0.5 1 1.5 2 2.5 3 3.5

Max

imu

m D

rift

rat

io


Bare Frame

Soft Story Frame

Infilled Frame

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 1 2 3 4 5 6 7

Max

imu

m D

rift

Rat

io

Frequency Ratio

Bare Frame

Soft Story Frame

Infilled Frame

59


Fig: drift ratio vs. frequency for PGA 1 m/s2 (twelve story building)

Fig: drift ratio vs. frequency ratio for PGA 1 m/s2 (twelve story building)

0

0.005

0.01

0.015

0.02

0.025

0 0.5 1 1.5 2 2.5 3 3.5

Max

imu

m D

rift

Rat

io


Bare Frame

Soft Story Frame

Infilled Frame

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5 6 7 8 9

Max

imu

m D

rift

Rat

io

Frequency Ratio

Bare Frame

Soft Story Frame

Infilled Frame

60


Fig: drift ratio vs. frequency for PGA 1 m/s2 (fifteen story building)

Fig: drift ratio vs. frequency ratio for PGA 1 m/s2 (fifteen story building)

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.5 1 1.5 2 2.5 3 3.5

Max

imu

m D

rift

Rat

io


Bare Frame

Soft Story Frame

Infilled Frame

0

0.005

0.01

0.015

0.02

0.025

0.03

0 1 2 3 4 5 6 7 8 9 10

Max

imu

m D

rift

Rat

io

Frequency Ratio

Bare Frame

Soft story Frame

Infilled Frame

61

4.4.2 Frames with stronger infill (Modulus of elasticity of infill Em = 5625 N/mm2)


Fig: drift ratio vs. frequency for PGA 1 m/s2 (six story building)

Fig: drift ratio vs. frequency ratio for PGA 1 m/s2 (six story building)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 0.5 1 1.5 2 2.5 3 3.5

Max

imu

m D

rift

Rat

io


Bare Frame

soft story frame

Infilled Frame

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 1 2 3 4 5 6

Max

imu

m D

rift

Rat

io

Frequency Ratio

Bare Frame

Soft Story Frame

Infilled Frame

62


Fig: drift ratio vs. frequency for PGA 1 m/s2 (nine story building)

Fig: drift ratio vs. frequency ratio for PGA 1 m/s2 (nine story building)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 0.5 1 1.5 2 2.5 3 3.5

Max

imu

m D

rift

rat

io


Bare Frame

Soft Story Frame

Infilled Frame

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 1 2 3 4 5 6 7

Max

imu

m D

rift

Rat

io

Frequency Ratio

Bare Frame

Soft Story Frame

Infilled Frame

63


Fig: drift ratio vs. frequency for PGA 1 m/s2 (twelve story building)

Fig: drift ratio vs. frequency ratio for PGA 1 m/s2 (twelve story building)

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.5 1 1.5 2 2.5 3 3.5

Max

imu

m D

rift

Rat

io


Bare Frame

Soft Story Frame

Infilled Frame

0

0.005

0.01

0.015

0.02

0.025

0.03

0 1 2 3 4 5 6 7 8 9

Max

imu

m D

rift

Rat

io

Frequency Ratio

Bare Frame

Soft Story Frame

Infilled Frame

64


Fig: drift ratio vs. frequency for PGA 1 m/s2 (fifteen story building)

Fig: drift ratio vs. frequency ratio for PGA 1 m/s2 (fifteen story building)

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.5 1 1.5 2 2.5 3 3.5

Max

imu

m D

rift

Rat

io


Bare Frame

Soft Story Frame

Infilled Frame

0

0.005

0.01

0.015

0.02

0.025

0.03

0 1 2 3 4 5 6 7 8 9 10

Max

imu

m D

rift

Rat

io

Frequency Ratio

Bare Frame

Soft story Frame

Infilled Frame

65

4.5 Difference in interstory drift ratio due to change in infill Maximum interstory drift ratios during the earthquake motion (5 second) are plotted for

soft story and infilled frames. It can be observed that after frequency level 1.5 Hz drift

ratio decrease rapidly for frames with both weaker and stronger infill.


Fig: maximum interstory drift ratio vs. input frequency for frames with difference infill

properties (Em = 1875 and 5625 N/mm2); six story buildings


properties (Em = 1875 and 5625 N/mm2); six story buildings

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

dri

ft r

atio

Input frequency (Hz)

soft story frame

infill moe 1875 N/mm^2 infill moe 5625 N/mm^2

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

dri

ft r

atio


infilled frame


66



properties (Em = 1875 and 5625 N/mm2); nine story buildings


properties (Em = 1875 and 5625 N/mm2); nine story buildings

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

dri

ft r

atio


soft story frame


0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

dri

ft r

atio


infilled frame


67



properties (Em = 1875 and 5625 N/mm2); twelve story buildings


properties (Em = 1875 and 5625 N/mm2); twelve story buildings

0

0.005

0.01

0.015

0.02

0.025

0.03

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

dri

ft r

atio


soft story frame


0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

dri

ft r

atio


infilled frame


68



properties (Em = 1875 and 5625 N/mm2); fifteen story buildings


properties (Em = 1875 and 5625 N/mm2); fifteen story buildings

0

0.005

0.01

0.015

0.02

0.025

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

dri

ft r

atio


soft story frame


0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3

dri

ft r

atio


infilled frame


69

4.6 Time history of drift Interstory drift ratio vs. time is plotted below usig the data obtained from time history

analysis. The response pattern does not follow any regular shape (as in elastic analysis).

The shapes are same for a frequency level in any peak ground acceleration.

4.6.1 Frames with weaker infill Modulus of elastic of infill Em = 1875 N/mm2

Six story buildings bare frames:

Fig: drift ratio vs. time for 6 story building bare frame at frequency .5 Hz PGA 1 m/s2

Fig: drift ratio vs. time for 6 story building bare frame at frequency 1.5 Hz PGA 2 m/s2

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4 5

story 1 story 2 story 3 story 4 story 5 story 6

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 1 2 3 4 5

Dri

ft r

atio

Time (S)

Story 1 Story 2 Story 3 Story 4 Story 5 Story 6

70




-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


-0.12

-0.09

-0.06

-0.03

0

0.03

0.06

0.09

0 1 2 3 4 5


-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


71




-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


-0.16

-0.12

-0.08

-0.04

0

0.04

0.08

0.12

0.16

0 1 2 3 4 5


-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5


72

Fig: drift ratio vs. time for 6 story building bare frame at frequency 1 Hz PGA 3 m/s2



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5


-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5


73


Six story buildings soft story frames:

Fig: drift ratio vs. time for 6 story building soft story frame at frequency .5 Hz PGA 1 m/s2

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5


-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 1 2 3 4 5


74

Fig: drift ratio vs. time for 6 story building soft story frame at frequency .75 Hz PGA 1

m/s2

Fig: drift ratio vs. time for 6 story building soft story frame at frequency 1 Hz PGA m/s2

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5


75



m/s2

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5


76

Fig: drift ratio vs. time for 6 story building soft story frame at frequency 1 Hz PGA 2 m/s2

Fig: drift ratio vs. time for 6 story building soft story frame at frequency 1.25 Hz PGA 2

m/s2

-0.12

-0.09

-0.06

-0.03

0

0.03

0.06

0.09

0.12

0 1 2 3 4 5


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


77


m/s2


m/s2

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


78



m/s2

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4 5


-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4 5


79



m/s2

-0.16

-0.12

-0.08

-0.04

0

0.04

0.08

0.12

0.16

0 1 2 3 4 5


-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5


80


m/s2


m/s2

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


81

Six story buildings infilled frames:

Fig: drift ratio vs. time for 6 story building infilled frame at frequency 1 Hz PGA 2 m/s2

Fig: drift ratio vs. time for 6 story building infilled frame at frequency 1.25 Hz PGA 2 m/s2


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


82


Nine story building bare frames:


-0.045

-0.03

-0.015

0

0.015

0.03

0.045

0 1 2 3 4 5


-0.04

-0.02

0

0.02

0.04

0 1 2 3 4 5

story 1 story 2 story 3 story 4 story 5

story 6 story 7 story 8 story 9

83



-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5



84



-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5



-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5



85



-0.12

-0.09

-0.06

-0.03

0

0.03

0.06

0.09

0.12

0 1 2 3 4 5



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



86



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5



87

Nine story buildings soft story frames:


m/s2


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



88


m/s2


-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5



-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5



89


m/s2


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4 5



90


m/s2


-0.12

-0.09

-0.06

-0.03

0

0.03

0.06

0.09

0.12

0 1 2 3 4 5



-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



91

Nine story buildings infilled frames:

Fig: drift ratio vs. time for 9 story building infilled frame at frequency .75 Hz PGA 2 m/s2


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5



92


Fifteen story buildings bare frames:


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5

story 3 story 4 story 5 story 6 story 7 story 8 story 9

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5




93



-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5




-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5




94



-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4 5




-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0 1 2 3 4 5




95


Fifteen story buildings soft story frames:


m/s2

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5




-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5




96


m/s2


m/s2

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4 5




-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5




97


m/s2

Fifteen story buildings infilled frames:

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5




-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5




98




-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5




-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5




99

4.6.2 Frames with stronger infill Modulus of elasticity Em = 5625 N/mm2

Six story building bare frame:



-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4 5


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


100




-0.12

-0.09

-0.06

-0.03

0

0.03

0.06

0.09

0 1 2 3 4 5


-0.045

-0.03

-0.015

0

0.015

0.03

0.045

0 1 2 3 4 5


-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


101




-0.16

-0.12

-0.08

-0.04

0

0.04

0.08

0.12

0.16

0 1 2 3 4 5


-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


102



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


103

Six story buildings soft story frames:


m/s2


-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4 5


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


104



m/s2

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4 5


105



m/s2

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


106


m/s2


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5


-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0 1 2 3 4 5


107


m/s2



m/s2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 1 2 3 4 5


-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4 5


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5


108


m/s2

Six story building infilled frame:


-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5


-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5


109

Nine story buildings bare frames:



-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



110




-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5



-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5



111



-0.12

-0.09

-0.06

-0.03

0

0.03

0.06

0.09

0.12

0 1 2 3 4 5



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



112


Nine story buildings soft story frames:


m/s2

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



113



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5



114


m/s2


-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5



-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5



115



m/s2

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5



116



m/s2

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5



-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



117

Nine story building infilled frame:


m/s2

Twelve story building bare frame:


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



118



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4 5



119



-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5



-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5



120



-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



121


Twelve story buildings soft story frames:


m/s2

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



122


m/s2


m/s2

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5



123


m/s2

Fig: drift ratio vs. time for 12 story building soft story frame at frequency 1 Hz PGA 3

m/s2

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 1 2 3 4 5



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



124

Twelve story buildings infilled frames:


m/s2

Fifteen story buildings bare frames:


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5



-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5




125



-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 1 2 3 4 5




-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5




126



-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4 5




-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0 1 2 3 4 5




127


Fifteen story buildings soft story frames:


m/s2

-0.045

-0.03

-0.015

0

0.015

0.03

0.045

0 1 2 3 4 5




-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5




128


m/s2


m/s2

-0.045

-0.03

-0.015

0

0.015

0.03

0.045

0 1 2 3 4 5




-0.045

-0.03

-0.015

0

0.015

0.03

0.045

0 1 2 3 4 5




129

Fifteen story buildings infilled frames:



-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5




-0.045

-0.03

-0.015

0

0.015

0.03

0.045

0 1 2 3 4 5




130

4.7 Comparison of collapse time for different types of frames UBC limitation on maximum drift ratio is .02 for long period (≥ .7s) structures. From time

history of drift ratio graph (preceding sections; 4.6.1 and 4.6.2) the time taken to reach

this limitation is found out. This times are plotted against input frequency for all peak

ground accelerations levels. All buildings did not reach the drift ratio limitation of .02.

4.7.1 Bare frames

Fig: Collapse time vs. frequency for bare frame at PGA 1 m/s2


0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

tim

e (s

)


6 story 9 story 12 story 15 story

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2

tim

e (s

)



131


4.7.2 Soft story frames

Fig: Collapse time vs. frequency for soft story frame at PGA 1 m/s2

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2

tim

e (s

)



0

1

2

3

4

5

6

0 0.5 1 1.5 2

Tim

e (s

)

frequency (Hz)

6story infill moe 1875 N/mm^2 6story infill moe 5625 N/mm^2




132



0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2

Tim

e (s

)

frequency (Hz)





0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2

Tim

e (s

)

frequency (Hz)





133

4.7.3 Infilled frames

Fig: Collapse time vs. frequency for infilled frame at PGA 1 m/s2


2.3

2.35

2.4

2.45

2.5

2.55

2.6

2.65

2.7

0 0.5 1 1.5 2

Tim

e (s

)

frequency (Hz)





0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2

Tim

e (s

)

frequency (Hz)





134


0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2

Tim

e (s

)

frequency (Hz)





135

CHAPTER FIVE

CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusions:

5.1.1 Natural frequency of frames:

1. The natural frequency found by the formula provided in BNBC 1993 and

2010 is almost the same for 6 and 9 story buildings but there is small

difference for 12 and 15 story buildings.

2. In case of bare frames, natural frequency obtained by modal analysis are

much less than those obtained by formula provided in BNBC 1993 and

2010. The natural frequency decreases gradually as height of frame

increases.

3. For frames with weaker infill (Em = 1875 N/mm2) the natural frequencies

are closer to values obtained from formula provided in BNBC 1993 and

2010. But the difference is prominent. As the height increases, the natural

frequencies for both soft story and infilled frame are very close.

4. For frames with stronger infill (Em = 5625 N/mm2), natural frequencies

obtained for infilled frame is almost the same as values found from the

formula provided in BNBC 1993 and 2010. In case of soft story frame, as

height increases, the values approaches rapidly to the natural frequencies

obtained from BNBC 1993 and 2010.

5.1.2 Interstory drift ratio of frames:

1. In all cases infilled frames achieves the least interstory drift ratio.

2. For all frames, the UBC specified limitation on interstory drift ratio is

obtained at frequency level 1.5 Hz or lesser. One six story building bare

frame reached this value on frequency level 1.75 Hz on PGA 1m/s2.

3. For all frames maximum drift ratio is obtained at frequency ratio 1 as

expected.

4. For infilled frames buildings up to 12 story with weaker infill and at

frequency level .25, .5, .75 Hz the maximum interstory drift ratio is always

greater than buildings with stronger infill.

5. For 15 story buildings with weaker infill (both soft story and infilled frame)

maximum drift ratios are very close but in cases with stronger infill soft

story frames were subjected to greater interstory drift ratio.

6. Maximum interstory drift ratio of bare frame is always greater than soft

story and infilled frame with respect to frequency ratio.

136

7. From the drift ratio vs. time and story no vs. drift ratio graphs the soft story

effect can be easily observed. The drift ratio at level 1 is much larger than

drift ratios at other levels. But in case of 15 story buildings with weaker

infills the difference in drift ratio between level 1 and other levels is not

prominent.

5.1.3 Time of collapse for different frames:

1. The time of collapse increases with story height for a frame with certain

type of infill for a given frequency in case of all peak ground acceleration

level.

2. Frames with weaker infill collapses faster than frames with stronger infill.

3. Maximum time of collapse for a bare frame, soft story frame and infilled

frame is 3.155s for a 12 story building, 4.81s for a 15 story building and

4.04s for a 15 story building respectively.

4. Minimum time of collapse for a bare frame, soft story frame and infilled

frame is .49s for a 6 story building, .34s for a soft story building and 1.235s

for a 6 story building respectively.

5.2 Recommendations for future work:

1. Only plane frame is considered in this study. A more rigorous three-dimensional

study considering out-of-plane strength and stiffness of masonry can be carried

out.

2. This study was carried out for harmonic loads only. Arrangements should be made

to input more general and realistic time series or amplitude spectra of seismic

behavior.

3. Only three types of frames are studied. As soft story can occur in any floor, other

frames having different infill orientation in the upper story can be investigated.

4. Column base is assumed to be fixed at bottom. In reality it is surrounded by soil,

so, more work can be done considering soil-foundation-structure interaction.

5. Presence of openings within the infill due to doors and windows can be

incorporated.

137

REFERENCES

Adel Ziada, Mohamed Laid Samai, Abdelhadi Tekkouk The Effect of Masonry Infill Walls on the Seismic Response of Reinforced Concrete Frames ISBN 978-93-84422-22-6 Proceedings of 2015 International Conference on Innovations in Civil and Structural Engineering (ICICSE'15) Istanbul (Turkey), June 3-4, 2015 pp. 264-271 C V R MURTY and Sudhir K JAIN beneficial influence of masonry infill walls on seismic performance of RC frame buildings Gary R. Searer and Sigmund A. Freeman Design Drift Requirements for Long-Period Structures 13th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 3292 Hossain Mohammad Muyeed-Ul-Azam and Khan Mahmud Amanat Effect of Infill as a Structural Component on the Column Design of Multi-Storied Building Hossein Mostafaei and Toshimi Kabeyasawa Effect of Infill Masonry Walls on the Seismic Response of Reinforced Concrete Buildings Subjected to the Bam Earthquake Strong Motion: A Case Study of Bam Telephone Center Bull. Earthq. Res. Inst. Univ. Tokyo vol. 79 (2004) pp.133-156 L. Teresa Guevara-Perez “Soft Story” and “Weak Story” in Earthquake Resistant Design: A Multidisciplinary Approach 15WCEE lisboa 2012 M.Y.H. Bangash Earthquake resistant buildings, springer Mohammad H. Jinya1, V. R. Patel Analysis of RC Frame with and without Masonry Infill Wall With Different Stiffness With Outer Central Opening IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 N. AL-Mekhlafy et al., Equivalent strut width for modeling R.C. infilled frames, pp. 851 – 866 P.G. Asteris and D.M. Cotsovos Numerical Investigation of the Effect of Infill Walls on the Structural Response of RC Frames The Open Construction and Building Technology Journal, 2012, 6, (Suppl 1-M11) 164-181 P.G. Asteris Finite Element Micro-Modeling of Infilled Frames electronic journal of structural engineering (8) 2008 Sinan Akkar; Ufuk Yazgan; and Polat Gülkan Drift Estimates in Frame Buildings Subjected to Near-Fault Ground Motions 1014 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / JULY 2005

the effect of masonry infill on the seismic response of reinforced concrete frames

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