PERFORMANCE POINT EVALUATION OF MASONRY INFILL
RC SOFT STOREY BUILDINGS UNDER SEISMIC LOAD USING
PUSHOVER ANALYSIS
Submitted by
Md. Faysal Student No: 0604038
Submitted to the
DEPARTMENT OF CIVIL ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
In partial fulfillment of requirements for the degree of
BACHELOR OF SCIENCE IN CIVIL ENGINEERING
MARCH, 2012
ii
ABSTRACT
Due to rapid urbanization to provide sufficient car parking space, open ground story
has become a typical feature in the modern multi-storied building. This causes vertical
stiffness irregularity and develops soft story mechanism. Soft story mechanism is a
potential mode of failure of reinforced concrete structures as experienced during past
earthquake. Although some of the national codes do have certain design guide to
avoid soft story problem, the Bangladesh National Building Code (BNBC, 1993) does
not have any such provision.
This thesis has been conducted to investigate the performance of soft story structures.
For this purpose, a total of five structures range from six to twelve stories have been
considered to evaluate the performance of soft story building under seismic loading.
The performances of the structures have been evaluated using the nonlinear static
pushover analysis as per the procedure of ATC-40, 1996.
From nonlinear inelastic performance based analysis the actual behavior of the
structure during earthquake can be found. There are mainly two guidelines of this
analysis FEMA-356 and ATC-40, 1996. These analysis procedures have been
discussed in this thesis.
It has been observed that performances of these structures under seismic loading are
highly unsatisfactory. The value of base shear obtained by using Pushover analysis is
higher than any other methods like equivalent static force method or response
spectrum method. The value of displacement and inter-story drift are very high in soft
ground story. Stiffness of open ground story is significantly less than the above. The
capacity curve of soft story structure never meets seismic demand. It is seen that the
value of base shear increase with the increase in height. Investigation of buildings
with soft story shows that soft story mechanism reduces the performance of the
structure and makes them vulnerable type of construction in earthquake prone areas.
So it is vital for the engineers to provide adequate safety measures to achieve
acceptable performance in open ground story structure under seismic action. It is high
time to include provisions for soft story structure in Bangladesh National Building
Code.
iii
DECLARATION
It is hereby declared that this thesis work carried out by author and any part of it or
the thesis has not been submitted elsewhere for any other purpose.
March, 2012.
MD. FAYSAL
iv
ACKNOWLEDGEMENT
Foremost, the author would like to express his sincere gratitude to his supervisor Dr.
Khan Mahmud Amanat, Professor of Department of Civil Engineering, BUET for his
encouragement, indispensible guidance and support from the initial to final stage of
this thesis.
The author pays his deepest homage to his parents, sister and friends for their constant
inspiration.
Above all the author thanks the Almighty for all his blessings.
v
TABLE OF CONTENETS
Page No.
ABSTRACT ii
ACKNOWLEDGEMENT iii
LIST OF TABLES viii- ix
LIST OF FIGURES x-xiii
CHAPTER-1 INTRODUCTION
1.1 GENERAL 1
1.2 OBJECTIVE AND SCOPE OF THE STUDY 2
1.3 METHODOLOGY 3
1.4 ORGANIZATION OF THE THESIS 4
CHAPTER-2 LITERATURE REVIEW
2.1 INTRODUCTION 5
2.2 THE SOFT GROUND STORY CONFIGURATION
2.2.1 Definition of Soft Story 6
2.2.2 Behavior of RC Frame under Lateral Load 7
2.3 BEHAVIOR OF SOFT GROUND STORY STRUCTURE 10
2.4 BUILDING DESIGN STRATEGIES IN BUILDING CODE 13
2.4.1 Indian Seismic Code, Is-1893 (2002) 14
2.5 COMPUTATIONAL MODELING AND ANALYSIS OF INFILL
FRAME 15
2.5.1 Equivalent Diagonal Strut Method 15
2.6 PAST RESEARCH ON SOFT STORY BUILDING 17
2.7 REMARKS 19
CHAPTER-3 CONCEPT OF PERFORMANCE BASED DESIGN
3.1 INTRODUCTION 20
vi
3.2 MODELING OF INFILL WALLS 20
3.2.1 Equivalent Strut Method 21
3.2.2 Equivalent Strut Width 22
3.2.1.2 Eccentricity of Equivalent Strut 23
3.2.1.3 Existing infill damage 23
3.2.3 Infill Properties 24
3.2.4 Determination of fm and Em 24
3.2.5 Calculation of Equivalent Strut Width 27
3.3 NON-LINEAR STATIC PROCEDURE
3.3.1 Reduced Demand Spectra 27
3.3.2 Development of Elastic Site Response Spectra 28
3.3.3 Seismic Zone 29
3.3.4 Seismic Source Type 30
3.3.5 Near Source Factor 30
3.3.6 Seismic Coefficients 31
3.3.7 Establishing Demand Spectra 32
3.4 CAPACITY CURVE 36
3.4.1 Capacity Spectrum Method 38
3.5 PERFORMANCE POINT 39
3.5.1 Non linear Static Procedure for Capacity evaluation
Of Structures 40
3.5.2 Structural Performance Levels and Ranges 41
3.5.3 Immediate Occupancy Structural Performance Level (S-1) 42
3.5.4 Damage Control Structural Performance Range (S-2) 43
3.5.5 Life Safety Structural Performance Level (S-3) 43
3.5.6 Limited Safety Structural Performance Range (S-4) 43
vii
3.5.7 Collapse Prevention Structural Performance Level (S-5) 43
3.6 TARGET BUILDING PERFORMANCE LEVELS 44
3.7 RESPONSE LIMITS 44
3.8 ACCEPTABILITY LIMIT 44
3.9 ELEMENT HINGE PROPERTY 46
3.9.1 Concrete Axial Hinge 47
3.9.2 Concrete Moment Hinge and Concrete P-M-M Hinge 48
3.9.3 Concrete Shear Hinge 49
3.10 CONCRETE FRAME ACCEPTABILITY LIMITS 50
3.10.1 Hinge Properties for Modeling 51
3.11 PERFORMANCE CRITERIA FOR THE STRUCTURE 51
3.11.1 Drift 51
3.11.2 Story Displacement 51
CHAPTER-4 PERFOMANCE EVALUATION OF SOFT GROUND STORY
STRUCTURE
4.1 INTRODUCTION 52
4.2 LOADING CONDITION 52
4.3 MATERIAL PROPERTIES 52
4.4 MODEL GEOMETRY 53
4.5 ASSUMPTIONS FOR PUSH OVER ANALYSIS 53
4.6 SOFTWARE USED IN THE ANALYSIS 54
4.7 DESCRIPTION OF THE STRUCTURES CONSIDERED FOR ANALYSIS 55 4.8 PERFORMANCE EVALUATION OF THE STRUCTURES 56
4.8.1 Performance Evaluation of the Structure 1 56 4.8.2 Performance Evaluation of the Structure 2 63
4.8.3 Performance Evaluation of the Structure 3 69
4.8.4 Performance Evaluation of the Structure 4 74
viii
4.8.5 Performance Evaluation of the Structure 5 79 4.9 REMARKS 82
CHAPTER-5 CONCLUSION AND RECOMMENDATIONS
5.1 GENERAL 83
5.2 FINDINGS OF THE STUDY 83
5.3 RECOMMENDATIONS FOR FUTURE STUDY 84
REFERENCES 85-86
APPENDIX 87-93
LIST OF TABLES
Table 3.1: In-plane damage reduction factor 24
ix
Table 3.2: Specified Compressive Strength of Masonry f’m (psi), based on
specifying the compressive strength of masonry units. (ACI 530, 192/
ASCE 6-92/ TMS 602-92) 25
Table 3.4: Sample Calculation of equivalent strut width 27
Table 3.5: Minimum Allowable SRA and SRv values 29
Table 3.6: Seismic Zone Factor, Z 30
Table 3.7: Seismic source type as per ATC- 40, 1996 30
Table 3.8: Seismic Source Factor 31
Table 3.9: Seismic coefficient, CA 31
Table 3.10: Seismic coefficient CV (ATC-40, 1996) 32
Table 3.11: Response quantities for 5% elastic demand 35
Table 3.12: Allowable maximum story drift ratio (ATC-40) 51
Table 4.1: Description of the Structure Considered for Analysis 55
Table 4.2: Effective damping and spectral reduction factor for structure 1 56
Table 4.3: Effective damping and spectral reduction factor for structure 1 57
Table 4.4: Effective damping and spectral reduction factor for structure 1 58
Table 4.5: Base Shear Comparison among different methods for structure 1 59
Table 4.6: Base shear at performance point and number and number of hinges
developed up to performance point 60
Table 4.7: Effective damping and spectral reduction factor for structure 2 63
Table 4.8: Effective damping and spectral reduction factor for structure 2 64
Table 4.9: Effective damping and spectral reduction factor for structure 2 64
Table 4.10: Base Shear Comparison among different methods 65
Table 4.11: Base shear at performance point and number and number of
hinges developed up to performance point 66
x
Table 4.12: Effective damping and spectral reduction factor for structure 3 69
Table 4.13 Effective damping and spectral reduction factor for structure 3 69
Table 4.14 Effective damping and spectral reduction factor for structure 3 70
Table 4.15: Base Shear Comparison among different methods 71
Table 4.16: Base shear at performance point and number and number of hinges
developed up to performance point 72
Table 4.17: Effective damping and spectral reduction factor for structure 4 74
Table 4.18: Effective damping and spectral reduction factor for structure 4 75
Table 4.19: Effective damping and spectral reduction factor for structure 4 76
Table 4.20: Base Shear Comparison among different methods 77
Table 4.21: Base shear at performance point and number and number
of hinges developed up to performance point 77
Table 4.22: Effective damping and spectral reduction factor for structure 5 both in
long (X) and short (Y) direction 80
Table 4.23: Base shear at performance point and number and number of hinges 80
LIST OF FIGURES
Figure: 2.1 Building with soft story 5
Figure: 2.2 Soft story failure mechanisms 6
xi
Figure: 2.3 Change in lateral load transfer mechanism due to masonry in-fills 8
(Murty and Jain 2000)
Figure: 2.4.1 Interactive behavior of Frame and Infill 8
Figure: 2.4.2 Analogous Bare Frame 8
Figure: 2.5 Modes of infill failure 9
Figure: 2.6 Modes of frame failure 10
Figure: 2.8 Lateral behavior of soft story structure 11
Fig. 2.9 Effects of masonry in-fills on the first mode shape of a typical RC frame
building (a) Displacement Profile; (b) Fully in-fill frame; (c) Open ground story
frame; (Adopted from Kaushik et. Al, 2006) 12
Figure: 2.10 Effects of earthquake on buildings having soft story 13
Figure: 2.11 Material modeling of masonry infill as diagonal strut 16
Figure: 2.12.1 Masonry in-filled frame Sub-assembly in masonry infill panel
frame 16
Figure: 2.12.2 Masonry infill panel in frame structure 16
Figure 3.1: Specimen Deformation Shape 21
Figure 3.2: Strut Geometry 22
Figure 3.3: 5% Damped Elastic Response Spectrum 34
Figure 3.4: 5% Damped elastic response spectrum in ADRS format 35
Figure 3.5: Typical Capacity Curve 36
Figure: 3.6 Capacity Curve 38
Figure 3.7: Determination of performance point 40
Figure 3.8: Force deformation action and acceptance criteria 45
Figure 3.9: Concrete axial hinge properties (FEMA-356, 2000) 48
Figure 3.10: Concrete moment and P-M-M hinge property 49
xii
Figure 3.11: Concrete Shear Hinge Property 50
Figure 3.12: Generalized Load-Deformation Relationship for Components 50
Figure 4.1: Plan View Type- A & B 55
Figure 4.2: Comparison of capacity spectrum of structure 1 for different
infill condition 57
Figure 4.3: Comparison of capacity spectrum of structure 1 for different infill
condition 57
Figure 4.4: Comparison of capacity spectrum of structure 1 for different
infill condition 58
Figure 4.5: Comparison of story shear observed from different method 59
Figure 4.6: Comparison of displacement (mm) in X direction 60
Figure 4.7.1: Comparison of maximum total drift ratio in X direction of structure 1 60
Figure 4.7.2: Comparison of maximum total drift ratio in X direction of structure 1 61
Figure 4.7.3: Comparison of maximum total drift ratio in X direction of structure 1 61
Figure 4.8: Deformation pattern of structure 1 at performance point 62
Figure 4.9: Comparison of capacity spectrum of structure 2 for different infill
condition 63
Figure 4.11: Comparison of capacity spectrum of structure 2 for different
infill condition 64
Figure 4.12: Comparison of story shear observed from different method 65
Figure 4.13: Comparison of displacement (mm) in X direction 66
Figure 4.14.1: Comparison of maximum total drift ratio in X direction of
structure 2 67
Figure 4.14.2: Comparison of maximum total drift ratio in X direction of
xiii
structure 2 67
Figure 4.14.3: Comparison of maximum total drift ratio in X direction of
structure 2 68
Figure 4.15: Comparison of capacity spectrum of structure 3 for different
infill condition 69
Figure 4.16: Comparison of capacity spectrum of structure 3 for different
infill condition 69
Figure 4.17: Comparison of capacity spectrum of structure 3 for different
infill condition 70
Figure 4.18: Comparison of story shear observed from different method 71
Figure 4.19: Comparison of displacement (mm) in X direction 72
Figure 4.20.1: Comparison of maximum total drift ratio in X direction of
structure 3 72
Figure 4.20.2: Comparison of maximum total drift ratio in X direction of
structure 3 72
Figure 4.20.3: Comparison of maximum total drift ratio in X direction of
structure 3 73
Figure 4.21: Comparison of capacity spectrum of structure 4 for
different infill condition 74
Figure 4.22: Comparison of capacity spectrum of structure 4 for
different infill condition 75
Figure 4.23: Comparison of capacity spectrum of structure 4 for
different infill condition 75
xiv
Figure 4.24: Comparison of story shear observed from different method 76
Figure 4.25: Comparison of displacement (mm) in X direction 77
Figure 4.26.1: Comparison of maximum total drift ratio in X direction of
structure 4 78
Figure 4.26.2: Comparison of maximum total drift ratio in X direction of
structure 4 78
Figure 4.26.3: Comparison of maximum total drift ratio in X direction of
structure 4 79
Figure 4.26: Comparison of capacity spectrum of structure 5 for 60% infill
condition in both long and short direction 80
Figure 4.27: Comparison of displacement (mm) in both long and short direction 80
Figure 4.28: Comparison of maximum total drift ratio in both long and short
direction of structure 5 81
1
CHAPTER 1
INTRODUCTION
1.1 GENERAL
Earthquake Engineering has come a long way since its birth and still a rapid growing
subject. Numerous researches are going on this topic especially concerned with the
design of the building structures. A structure designed to higher standards to sustain
under relative frequent earthquake and being safe under destructive earthquake may
prove to be costly but preferred by owners of the buildings now-a-days.
Rapid pace of urbanization especially in big cities like Dhaka, Chittagong etc. creates
a great demand on human shelter. As a result, a lot of multistoried buildings are found
to have open ground story (soft story) in the ground floor to provide place for car
parking. It is common to have brick infill wall panels on the upper stories. This
irregularity of vertical stiffness leads to development of soft story mechanism. In
order to satisfy architectural demand, sometimes soft stories are seen in other stories.
Presence of soft story in a building makes it vulnerable especially in the earthquake
prone areas like Dhaka city situated in moderate earthquake zone. The performances
of open ground story buildings have consistently performed poorly during
earthquakes across the world. During earthquakes of Turkey 1999, Bhuj (India) 2001
etc. had collapsed due to the presence of soft story. Bangladesh has faced a number of
minor earthquakes recent years and there is a strong possibility of major earthquake.
Most of the buildings constructed without seismic resistance a moderate earthquake
may prove to be fatal for the population.
Proper seismic design can minimize the risk of fatal casualties. Seismic design has
been made mandatory in BNBC (2006). BNBC specified methods like equivalent
static force method and dynamic response spectrum method. But the seismic force
distribution depends on the distribution of story stiffness rather than its natural period.
Because of more flexibility at open ground story results in extreme deflection of story,
which in turn, leads to concentration of forces at the connections of story above
accompanied by large plastic deformations. In this process plastic hinges are formed
2
at the ends of columns of the soft story which results in an unavoidable collapse of the
total story. Therefore, the building with soft story requires special design
consideration. To understand the effect of earthquake on building structures properly
especially consist of soft story performance based analysis or Pushover analysis is
now considered most effective. In order to meet specific performance objectives
under the action of the frequent or rarer seismic events that it may experience in its
lifetime. A soft story is considered deficient to keep vertical stability under seismic
loading and to fulfill the target performance objectives. Presence of masonry infill on
upper floors making them stiffer causes rigid body movement under seismic vibration.
By implementing the diagonal strut as a replacement of brick panels the actual effect
on the building is analyzed using Pushover Method.
1.2 OBJECTIVE AND SCOPE OF THE STUDY The objectives of the present study are summarized as follows:
To develop a 3D finite element model of building with infill on upper floors
and soft ground floor.
Modeling of infill as diagonal struts and applied in different percentage
randomly on frame system.
Comparison of base shear values by the three methods for certain structural
variables.
To analyze the variation in base shear for same percentage of randomly
applied infill in different methods.
To establish the pushover curve (capacity curve) of simple structures having
soft ground story and bare frame.
To evaluate adequacy and performance of conventionally designed typical
bare frame model and soft story structure under maximum expected
earthquake
To demonstrate the effect of the soft ground story through lateral displacement
on the profile of building and base shear force.
To compare among the alternative measures to determine which measure is
suitable for the particular structure to the service requirements of the ground
story.
To investigate the failure pattern of buildings at performance point.
3
Pushover curve will present the lateral displacement as a function of the force
applied to the structure.
The capacity spectrum will be plotted that reduces the elastic spectrum to
intersect the capacity curve in spectral co-ordinates to find the performance
point.
The inter-story drift will be plotted to analyze the changes in the slope of
consecutive story at performance point.
The story displacement curve will be plotted to investigate the maximum
displacement.
1.3 METHODOLOGY Reinforced concrete moment resisting frame with open ground story and unreinforced
brick infill walls in the upper stories will be modeled using ETABS 9.7 software
package for this study. Nonlinear static pushover analysis will be performed as per as
described in ATC-40.
The investigation is based on the following assumptions:
The infill wall will be modeled as shell element as per available literature
(Stafford and Smith).
Failure of infill wall will be ignored in the study.
All dead load, live load and earthquake will be applied as described in BNBC
1993. Wind load will be applied as described in UBC 94 as it is slightly varies
from the BNBC (1993) code.
Dead load of partition wall will be applied on the beam and diagonal strut will
be considered only as active member having zero weight.
For nonlinear analysis hinge property is chosen from the provided
experimental data.
Hinges are assigned to each element to allow progressive damage of the
element to reach plastic deformation stage.
Structural behavior type is assumed to be C considering them as existing
structure.
Earthquake load will be applied incrementally in order to monitor the
formation of plastic hinges, stiffness degradation and plastic rotation.
4
1.4 ORGANIZATION OF THE THESIS The research work conducted for the achievement of the stated objective is presented
in several chapters organized in a way so that the steps involved in the study may
properly delineate the methodology. This document is organized in five chapters. A
brief description of the contents of each chapter follows:
Chapter 1 gives a statement of the basic idea of the objectives, methodology, scope
and a brief description on the organization of the thesis work being done under the
research.
Chapter 2 provides available earthquake load analysis methods, their guideline in
different codes.
Chapter 3 describes seismic analysis and design methodologies, provision for
earthquake load in building codes, various parameters of nonlinear push over analysis,
performance evaluation procedure etc. are reviewed.
Chapter 4 represents performances evaluation of different structures with variable
infill condition. Compare the value of base shear using different analysis method.
Chapter 5 depicts findings of the study, limitation of present study and
recommendations for future study.
.
5
CHAPTER 2
LITERATURE REVIEW
2.1 INTRODUCTION
Bangladesh is a developing country with a huge population. It is now facing a rapid
growth of urbanization. To improve the economic condition, this country also needs
infrastructure support. As a result a lot of buildings are built as residences or for other
purposes. The selection of the appropriate configuration of the structural system is the
key to build a safe, comfortable structure. Bangladesh is situated in active earthquake
zone. So, the threat of earthquake is inevitable although a little importance is given in
seismic design. Only few of the recent design codes underline the problem. Hence, the
problem has not been taken into sufficient consideration in the current professional
practice. To provide space for car parking most of the structures now miss the infill at
ground floor. These types of structures are known as soft story structure. These
structures are more susceptible to earthquake having irregularities in stiffness. These
irregularities occur due to random distribution of infill on the upper floors with open
ground floor. Many soft story buildings have performed poorly in the past earthquake
Figure: 2.1 Building with soft story
6
A number of cases of soft story failure have also been reported in Algeria earthquake
in 1980, San Salvador earthquake in 1986, North Ridge earthquake in 1994, Bhuj
earthquake in 2001, Bingol earthquake in 2003.This type of failure results from the
combination of several other unfavorable reasons, such as torsions, excessive mass on
upper floors, P-Δ effects and lack of ductility in the bottom story. So the soft story
structures deserve a special consideration in analysis and design. Soft story
phenomenon occurs due to inadequate bracing of structure at ground floor which is
less resistant to lateral forces of earthquake. The specific floor suffers the drift more
Fig: 2.2 Soft story failure mechanisms.
than the upper stories. Being less resistant it becomes the weakest point of the
structure and cause of the collapse of whole structure during even moderate
earthquake.
In this chapter the literature regarding structural configuration, treatment of soft story
in building codes, behavior of soft story buildings, different methods used for
evaluating the performance level of existed building and design criteria are reviewed.
2.2 THE SOFT GROUND STORY CONFIGURATION
This configuration allows a lot of space for car parking (fig 2.2). The soft story
structures are very vulnerable from a seismic point of view. As the large rotation
ductility requests concentrated alt the extreme sections of the columns of the ground
story, while the above stories behave like a quasi-rigid body. The definition of soft
story is provided by various codes. In the following section, the behavior of soft story
will be discussed.
7
2.2.1 DEFINITION OF SOFT STORY
The definition of soft story varies in different building codes. The definitions of soft
story as given by various codes are discussed below.
Uniform Building Code, 1991
A soft story is one in which the lateral stiffness is less than 70 percent of that in the
story above or less than 80 percent of the average stiffness of the three story above.
ASCE 7- Minimum Design Loads for Building and Other Structures, 2002
Soft story:
Soft story is one in which lateral stiffness is less than 70 percent of that in the story
above or less than 80 percent of the average stiffness of the three stories above.
Extreme Soft Story:
An extreme soft story is one in which the lateral stiffness is less than 60 percent of
that in the story above or less than 70 percent of the average stiffness of the three
stories above.
Bangladesh national building code (BNBC), 1993
Soft story is one in which the lateral stiffness is less than 70 percent of that in the
story above or less than 80 percent of the average stiffness of the three story above.
2.2.2 BEHAVIOR OF RC FRAME UNDER LATERAL LOAD
Basically infill is provided as partition wall, sound barrier, heat reduction etc.
According to research works of Mehrabi et al. 1996 that careful use of infill can
significantly increase the stiffness of the structure. It helps in resisting the earthquake
motion. So it is necessary to provide infill carefully to minimize the torsion and soft
story effect. But due to lack of knowledge of participation of infill during earthquake
resistance its effect remains neglected. The presence of in-filled walls on the upper
stories of a multi storied buildings make them mush stiffer than the soft ground story.
During earthquake shaking the whole upper part moves together as one system and
soft ground story takes most of the displacement.
8
Experiments like (Moghaddam and Dowling in 1987, Smith and Coul in 1991, Murty
and Jain in 2000) are done to initiate an approach to use infill to resist the lateral load
of earthquake. The present of infill in RC frames change the load transfer mechanism
from predominant frame action to predominant truss action (Fig. 2.3).
Fig. 2.3 Change in lateral load transfer mechanism due to masonry in-fills (Murty and Jain 2000)
Containing the brittle masonry ductile frame stiffens significantly because of in-plane
rigidity of the masonry wall. With its in-plane shear resistance and partly by its
behavior as diagonal bracing strut it braces the frame (Fig.2.4.1).
(1) (2)
Fig. 2.4 (1) Interactive behavior of Frame (2) Analogous braced frame.
and infill.
9
Double curvature bending of the columns and girders occur under horizontal loading.
The translation of the upper part of the column in each story and the shortening of the
leading diagonal of the frame cause the column to lean against the wall as well as to
compress the wall along its diagonal. It is roughly analogous to diagonal bracing
frame (Fig. 2.4.2)
The types of potential modes of failure of wall due to its interaction with the frame
are:
1. Shear failure stepping down through the joints of the masonry.
2. Shear stress concentration in the bed joints.
3. Diagonal cracking of the wall through the masonry along a line, lines or
parallel to the leading diagonal.
4. Tensile stress perpendicular to the leading diagonal.
5. Due to corner compressive stress infill at the end of the diagonal crushed.
The perpendicular tensile stresses are caused by the divergence of the compressive
stress trajectories on the opposite sides of the leading diagonal as they approach the
mid region of the infill. The shear failure of wall steps down through the joints of
masonry and participated by the horizontal shear stresses in the bed joints. The
diagonal cracking of the wall is through the masonry along a line or line parallel to the
Fig. 2.5 Modes of infill failure
10
loading diagonal and caused by tensile stresses perpendicular to the loading diagonal.
The perpendicular tensile stresses caused by the divergence of the compressive stress
trajectories on opposite sides of the loading diagonal as they approach the middle
region of the infill. The diagonal cracking is initiated and spreads from the middle of
the infill while the tensile stresses are at maximum tending to stop near the
compression corners, where the tension is suppressed.
Fig. 2.6 Modes of frame failure
The nature of the forces in the frame can be understood by referring to the analogous
braced frame shown in (Fig. 2.5). The windward column or the column facing the
seismic load first is in tension and the leeward column or the other side of the
building facing seismic load last is in compression. Since the infill bears on the frame
not as exactly a concentrated force at the corners, but over the short lengths of the
beam and column adjacent to each compression corner, the frame members are
subjected also to transverse shear and a small amount of bending. Consequently the
frame members or their connections are liable to fail by axial force or shear and
especially by tension at the base of the windward column (Fig. 2.6).
2.3 BEHAVIOR OF SOFT GROUND STORY STRUCTURE Soft story mechanism yields a poor frame system as there is a sudden drop in stiffness
and strength in ground floor (2.7). Bare frame is only considered during design
practice. Soft story structure shows large displacement in open story than fully infill
11
frame structure (Fig. 2.8) as most of the stress concentrated on the ground floor (Fig.
2.9).
Fig. 2.7 (1) actual building (2) Considered in design during practice.
Fig. 2.8 Lateral behavior of soft story structure
The building having soft ground story oscillates like simple pendulum during
earthquake and column of the open ground story are severely stressed (Fig. 2.9). It is
required that the column must have sufficient stiffness and also adequate ductility.
Otherwise, it will be damaged and may cause subsequent collapse of the whole
structure.
Ductility
Ductility demands refers to the extent of deformation (rotation or displacement)
beyond the elastic limit, expressed numerically as the ratio of the maximum
deformation to yield deformation at initial yield (ATC-40).
12
Thus,
µu = µm / µy Eqn. - 2.1
Here, µm = Maximum deformation prior to failure and µy = Deformation at yield
Fig. 2.9 Effects of masonry in-fills on the first mode shape of a typical RC frame
building (a) Displacement Profile; (b) Fully in-fill frame; (c) Open ground story
frame; (Adopted from Kaushik et. Al, 2006)
Ductility capacity of a structure is the ability of the structure to deform beyond the
elastic limit. Ductility demand refers to the requirements on the design of the system
should be such that exceed the ductility demand. Allowable ductility is based on the
allowable deformation that depends on the structural characteristics and materials
used. Ductility demand varies for a multi storied building varies over its height and
differs from the allowable ductility used in defining the design spectrum and
computing the story yield strength.
Effects of earthquake in soft story buildings are as follows –
13
Fig. 2.10 Effects of earthquake on buildings having soft story
The seismic force distribution and energy dissipation is dependent on the distribution
of the stiffness and mass of the structure along its height. The upper stories being very
stiff undergoes less inter-floor lateral drift while the soft ground floor being less stiff
undergoes very high lateral drift and the soft story columns dissipate most of the
seismic energy in the process of plastic hinges. Thus the possibility and risk of
collapse is very high in case of soft story under lateral loads. The feature of soft story
mechanism is not considered in the present method of analysis for earthquake load. In
static method we only consider the first mode of vibration (that’s suitable for regular
bare frames) while the behavior of infill and irregular frames are far more
complicated and uncertain. That’s why the dynamic analysis is helpful to account for
the other modes of vibration and consider the irregularity of stiffness features in
building frame caused by random distribution of infill on upper floors. If we can
consider the true dynamic features of the frame system then the design will be safer
and adequate.
2.4 BUILDING DESIGN STRATEGIES IN BUILDING CODE Most of the building codes have not yet given emphasis on designing soft story
buildings though these are more vulnerable to earthquake. Building codes such as
14
BNBC (1993), UBC (1997), ASCE (2002), ACI (2005), NZS (4203) ETC. define
analysis procedure based on structural height for irregular structure including soft
story irregularity. Due to damage of various soft story buildings in Bhuj earthquake,
2002 Indian Seismic Code IS: 1893-2002 Part-1 has included special design features
for soft story buildings. In most cases the codes state that the regular geometry
structures with properly located masonry walls perform better than irregular
geometric structures with improper masonry infill structures. As per as codes state for
low rise buildings static method and for high rise building dynamic method of
analysis are performed. Generally the natural period for in-fill RC frames are lower
than the bare RC frames. For that reason forces consider more in infill frames than in
bare frames. As per as few codes such as IS-1893 (2002), NBC-105 (1995), NSR-98
(1998) Egyptian code (1988), Venezuelan code (1988), Algerian code (1988), ESCP-
1 (1983); the empirical relationship for the time period is given by the following
equation:
Ta = d
h09.0
Eqn. – 2.2
Where, h is the height of building in meter and d is the base dimension of building in
meter at the plinth level along the considered direction of the lateral force.
French code (AFPS-90, 1990) recommends the following equation for masonry infill
buildings;
T = 0.06hd
hdh
2 Eqn. – 2.3
2.4.1 Indian Seismic Code, IS-1893 (2002)
As stated earlier, Indian code has featured some modification for soft story.
In case buildings with a flexible story, such as the ground story consisting of open
spaces for parking, that is Stilt Building. Special arrangement needs to be made to
increase lateral strength and stiffness of the soft story.
Dynamic analysis of building is carried out including the strength and stiffness effects
of infill and inelastic deformations in the members, particularly, those in the soft
story.
15
(a) The columns and beams of the soft story are to be designed for 2.5 times the
story shears and moments calculated under seismic loads specified in the other
relative clauses; or,
(b) Besides the columns designed and detailed for the calculated story shears and
moments, shear walls placed symmetrically in both directions of the building as far
away from the center of the building as feasible; to be designed extensively for 1.5
times the lateral story shear force calculated as before.
2.5 COMPUTATIONAL MODELING AND ANALYSIS OF
INFILL FRAME There are various types of modeling approach were attempted before for featuring
infill characteristics in RC frame. Holmes (1961) replaced the infill by an equivalent
pin-jointed diagonal strut. Smith (1962) conducted a series of tests on laterally loaded
square mild steel frame models infill with micro-concrete. From the model
deformation results he concluded that the wall could be replaced by an equivalent
diagonal strut connecting the loaded corners. As the elastic methods were not able to
fully feature the actual characteristics of infill frames, attention was paid to the
theories of plasticity. Wood (1958) extended the limit analysis of plasticity with the
assumption of perfect plasticity. Recently a method was developed by Saneinejad.
(1995) that allows for interface shear forces and both the elastic and plastic behavior
of material. Variations in geometrical and mechanical characteristics are used to
determine the stiffness of structural system. The analysis is carried out utilizing the
boundary element method (BEM) for the infill and dividing the frame into finite
elements, so as to transform the mutual interactions of the two subsystems into
stresses distributed along the boundary for the infill and into nodal actions for the
frame. In this analysis equivalent diagonal strut method is used which is described
below.
2.5.1 Equivalent Diagonal Strut Method
Strength predictions of infill frames are a complex, statically indeterminate problem.
The strength of a composite infill frame system is a combination of frame system and
infill. Polyakov (1960), Stafford Smith (1962, 1966, 1969), Mainstone (1971),
Klingner and Sereto (1976, 1978) Liaw and Lee (1977) are only a few of them who
has formed the basis to understand the in-plane behavior of infill frame. During
16
testing of the specimens, diagonal cracks developed in the center of the panel and
gaps formed between the frame and the infill in the non loaded diagonal corners of
the specimen, while full contact was observed in the two diagonal corners. This
behavior leads to a simplification in the in-filled frame analysis by replacing the
masonry infill by an equivalent compressive masonry strut of same mechanical
properties as the infill and the both ends must be pinned to the corner of the frame.
As per as research on modeling of infill panel as an equivalent diagonal strut method
was applied by Holmes (1961). He assumed that the infill wall acts as diagonal
compression strut as shown in (fig-2.5.a) of the same thickness and elastic modulus as
the infill with a width equal to one-third the diagonal length. He also concluded that
at the infill failure, the lateral deflection of the in-filled frame is small compared to
the deflection of the corresponding bare frame.
Saneinejad and Hobbs (1995) developed a method based on the equivalent diagonal
strut approach for the analysis and design of steel or concrete frames with concrete or
masonry infill walls subjected to in-plane forces.
Fig. 2.11 Material modeling of masonry infill as diagonal strut
Fig. 2.12.1 Masonry in-filled frame Sub-assembly in masonry infill panel frame
Fig. 2.12.2 Masonry infill panel in frame structure
17
The analytical assumptions are the contribution of the masonry infill panel (Fig.
2.12.1) to the response of the in-filled frame can be modeled by replacing the panel
by a system of two diagonal masonry compression struts (Fig: 2.12.2). However, the
combinations of both diagonal struts provide a lateral resisting mechanism for the
opposite lateral directions of loading.
2.6 PAST RESEARCH ON SOFT STORY BUILDING
Amanat and Hoque (2006) studied the fundamental periods of vibration of a series of
regular RC framed buildings using 3-D FE modeling and modal eigenvalue analysis
including the effects of infill. The time period determined from eigenvalue analysis
was remarkably close to those predicted by the code formulas. It’s also observed that
the randomness of infill application does not cause much variation of the period if the
total amount of infill panel is same. Based on the findings of the study some practical
guidelines were suggested for determining the fundamental period of RC frames
using rational approaches like modal analysis.
Costa Rican code (1986) requires that all structural resisting system must be
continuous from the foundation to the top of the building and stiffness of a story must
not be less than 50% of that of the story below.
Arlekar, Jain and Murty (1997) highlighted the importance of explicitly recognizing
the presence of the open ground story in the analysis of the building. The error
involved in modeling such buildings as complete bare frames, neglecting the presence
of in-fills in the upper story, is brought out through the study of an example building
with different analytical models.
Fardis and Panagiotakos (1997) studied through numerical analyses the effects of
masonry in-fills on the global seismic response of reinforced concrete structures.
Response spectra of elastic SDOF frames with nonlinear in-fills show that, despite
their apparent stiffening effect on the system, in-fills reduce spectral displacements
and forces mainly through their high damping in the first large post-cracking
excursion.
Mezzi (2004) illustrated soft story to be very dangerous from seismic viewpoint as the
lateral response of these buildings is characterized by a large rotation ductility
demand concentrated at the extreme sections of the columns of the ground floors,
while the superstructure behaves like a quasi-rigid body. A solution was proposed for
the preservation of a particular architectonic double soft story configuration.
18
Huang (2005) studied the structural behaviors of low-to-midrise concrete buildings of
various configurations with emphases on dynamic properties, internal energy, and the
magnitude and distribution of seismic load. Several idealized models were made to
represent different structural configurations including pure frame, frames with fully
or partially infilled panels, and frames with a soft story at the bottom level, and
Comparison was made on the fundamental periods, base shear, and strain energy
absorbed by the bottom level between these structures.
M. Helen Santhi, G. M. Samuel Knight (2005) studied two single-bay, three-story
space frames, one with brick masonry infill in the second and third floors representing
a soft-story frame and the other without infill were designed and their 1:3 scale
models were constructed according to non-seismic detailing and the similitude law.
Rodsin (2005) evaluated the potential seismic performance of building with soft story
in an area of low to moderate seismicity regions (such as Australia) by a
displacement-based method involving a push-over analysis.
Nagae (2006) studied six storied reinforced concrete building and focused on seismic
response of the soft ground floor based on the results on dynamic response analysis.
Jahid Hasnain (2009) studied this phenomenon of soft story building. He determined
the effect of randomly distributed in-fills on seismic base shear for RC buildings with
soft ground floor. In spite of providing an extensive analysis, his study is also limited
due to the following issues:
Random application of infill.
Constant beam and column size.
Application of earthquake load only along X direction.
Application of partition wall load as a constant.
Equal distribution of total number of infill along the span and bay.
Rumia Tasmim (2010) has done an extensive study of the above mentioned issues and
successfully overcome the limitations. The following modifications have been
proposed with randomly applied infill:
Variation of beam and column size with varying span or bay length. A
minimum dimension is also used.
Application of earthquake load along X and Z directions.
Variation of partition wall load along with varying percentage of infill.
19
Distribution of total number of infill as a ratio of span and bay along
the span and bay.
Mokhlesur Rahman studied the soft story phenomenon using Push over analysis. But
the study was limited to six story buildings.
In our research we provide random infill on the panel of soft story to study the
difference in performance level with increasing height and variable stiffness. It is also
one of the objectives to find the modification factor of base shear comparing among
Static Force Method, Response Spectrum Method and Pushover Analysis Method.
Data of modification factor for base shear between Static Force Method and Response
Spectrum Method is obtained from the previous research work of Ms. Rumia Tasmim.
2.7 REMARKS Like most other building codes discussed in this chapter Bangladesh National
Building Code (1993) is no different, having no provisions for building with soft
story. Irregular structures including soft story are required dynamic analysis to
understand its actual behavior. The Indian Seismic Code IS: 1893 (2002) Part-1 has
also included design provisions for soft story buildings. It is high time to incorporate
these provisions in BNBC also. In the upcoming chapters performances of soft story
building will be studied applying non-linear static analysis method or Pushover
analysis.
20
CHAPTER 3
CONCEPT OF PERFORMANCE BASED DESIGN 3.1 INTRODUCTION The most common case of soft story, especially in residential building, is the
presence of bare ground story while the upper stories are filled with masonry panel.
Although there are few other reasons of soft story formation the study here is limited
to the formation of soft story due to the existence of masonry infill. The building will
become more vulnerable to earthquake because of the presence of soft story. The
traditional approach to seismic design of a building is a force based design. The
design lateral forces on the building are determined using the response spectrum. In
this approach, there is no measure of the deformation capability of a member or of the
building. During earthquake, it is expected that the members of the building will go
beyond elastic condition which is not possible to analyze using force based design or
response spectrum method. So a performance based analysis is required to get a result
from nonlinear lateral load versus deformation analysis. It gives more choices of
performance of the building as compared to the limit states of collapse and
serviceability in a design on limit state method. In this chapter, the modeling of infill
frame by equivalent strut method and some other features of infill modeling will be
discussed. In the later portion pushover analysis procedure and performance criteria
will be discussed. In the final portion modeling parameter for hinges and site response
spectra for Dhaka zone is established.
3.2 MODELING OF INFILL WALLS
The infill walls used in the structures for partitions and other purposes can be
represented in many ways. Here in this study equivalent strut method will be used for
the simplicity.
21
3.2.1 Equivalent Strut Method
Strength predictions of in filled frames are a complex and statically indeterminate
problem. The strength of a composite in filled frame system is not only the
summation of the infill properties plus those of the frame. To better understand and
estimate the composite behavior of masonry in filled frames both analytically and
experimentally lot of efforts have been made by Polyakov (1960), Stafford-Smith
(1962, 1966, 1969), Mainstone (1971) are the few to be named. During the
experiment, as observed by Polyakov, the masonry infill can be replaced by
equivalent diagonal masonry strut because cracks developed in the center of the panel
diagonally.
Their experiments of in filled frames under lateral loads resulted in specimen
deformation shapes similar to one illustrated in figure 3.1 below-
Figure 3.1: Specimen Deformation Shape
The equivalent compressive masonry strut of width a, same thickness of masonry and
same modulus of elasticity. It is also assumed to be pinned at both ends of the
confining frame.
22
3.2.2 Equivalent Strut Width
The evaluation of the equivalent width a, varies from one reference to other. Stafford-
Smith and Carter (1969), Mainstone (1971) and others derived complex expressions
to estimate the equivalent strut width a by considering the parameters like the length
between the column/ beam and the infill as well the relative stiffness of the infill to
the frame.
Expressions used in this chapter have been adopted from Mainstone (1971) and
Stafford-Smith and Carter (1969) for their consistently accurate predictions of in
filled frame in-plane behavior when compared with experimental results of others.
a
d
h
th et a
l
Figure 3.2: Strut Geometry
The equivalent strut width a, depends on the relative flexural stiffness of the infill to
that of the columns of the confining frame. The relative infill to frame stiffness shall
be evaluated using eqn. 3.1-
λ1H = H ((Em t sin 2θ)/ (4 Ec I col hm)) 0.25 Eq. - 3.1
Where, t is the thickness of the masonry wall.
Using the expression, Mainstone (1971) considers the relative infill to frame
flexibility in the evaluation of the equivalent strut width of the panel as shown in
eqn.3.2-
a = 0.175 D (λ1H)-0.4 Eq. - 3.2
23
If there are openings present, existing infill damage or FRP overlay, however, the
equivalent width must be modified using-
amod= a (R1) (R2) ζi Eq.- 3.3
Here,
(R1)= reduction factor in plane evaluation due to presence of openings
(R2)= reduction factor for in plane evaluation due to existing infill damage
ζi = Strength increase factor due to presence of FRP overlay
Although the expression for equivalent strut width given above was derived to
represent the elastic stiffness of an infill panel, this document will extend its use to
determine the ultimate capacity of in filled structures. The strut will be assigned
strength parameters consistent with the properties of the infill if represents. A non
linear static method commonly referred to as a pushover analysis, will be used to
determine the capacity of the in filled structure.
3.2.1.2 Eccentricity of Equivalent Strut The equivalent masonry placed as shown in figure (3.2). 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 l column from the face of the beam.
The distance is defined in equation below.
l column = a/(cosθ column) Eq.- 3.4 tanθ column = (hm - a/ cosθ column ) / l Eq.- 3.5 3.2.1.3 Existing infill damage
As the elastic limit is exceeded, the behavior of masonry infill deteriorates. So it is
important to determine exceeded limit. Existing panel damage must be classified as –
no damage, moderate damage or severe damage. If in doubt to determine the
magnitude of existing panel damage assume severe damage for a conservative
estimate. A reduction factor for existing panel damage (R2 ) must be obtained from
Table (3.1). If the slenderness ratio (hm/t) of the panel is greater than 21, (R2) is not
defined and repair is required. For panels with no existing panel damage, the
reduction factor must be taken as 1.
24
Table 3.1: In-plane damage reduction factor
Type of Damage Type of Damage
hm/t Moderate Severe
<21 0.7 0.4
>21 Repair is required. Repair is required.
3.2.3 Infill Properties
The infill masonry panel will be presented as strut member. The equivalent strut width
shall be determined according to Coul & Smith described earlier. For the modeling of
infill the following properties must be determined.
Modulus of elasticity of concrete Ec value for column and beam materials.
Sectional propertied (i.e. Depth, Width, Moment of Inertia, Center of Gravity)
of the column and beam.
Equivalent width of the masonry infill strut “a”.
fm compressive strength of the masonry assembled units.
Em modulus of elasticity of the masonry unit.
3.2.4 Determination of fm and Em
In this study masonry bricks are considered as infill material. In Bangladesh although
a variety of bricks are used as a building material but most common of them is solid
clay bricks. So, NW type brick, according to ASTM C62, 1994 is considered in this
study. Table 3.2: Specified Compressive Strength of Masonry f’m (psi), based on
specifying the compressive strength of masonry units. (ACI 530, 192/ ASCE 6-92/
TMS 602-92)
25
Compressive Strength of Masonry Units
(psi)
Specified Compressive Strength of Masonry, f'm
Type M or S Mortar (psi)
Type N mortar (psi)
14000 or more 5300 4400 12000 4700 3800 10000 4000 3300
8000 3350 2700 6000 2700 2200 4000 2000 1600
Compressive Strength of Concrete Units
(psi)
Specified Compressive Strength of Masonry, f'm
Type M or S Mortar (psi)
Type N mortar (psi)
4800 or more 3000 2800 3750 2500 2350 2800 2000 1850 1900 1500 1350
NOTE:
1. Compressive strength of solid clay masonry units is based on gross area. Compressive strength of hollow clay masonry units is based on minimum net area. Value may be interpolated.
2. Assumed assemblage. The specified compressive strength of masonry fm is based on gross area strength when using solid units or solid grouted masonry and net area strength when using ungrouted hollow units.
3. Type M, N or S mortar are according to ASTM C270 definition.
From the table for strength of clay masonry unit 4000 psi is chosen and for that fm
1600 psi for N mortar.
Em is the ratio of the stress to the strain of a material or combinations of materials as
in the case for grouted masonry.
To find out the value of Em considering the ACI/ ASCE/ TMS masonry code the
modulus of elasticity is given in the following table-
26
Compressive strength of clay Masonry (psi)
Specific Compressive Strength of
Clay Masonry Assemblage
fm( psi)
Modulus of
Elasticity (psi)
Modular Ratio, n
Modulus of
Rigidity, G = 0.40 Em (psi)
14000 or more 4400 3000000 9.7 1200000
12000 3800 2850000 10.2 1140000
10000 3300 2475000 11.7 990000
8000 2700 2025000 14.3 810000
6000 2200 1650000 17.6 660000
4000 1600 1200000 24.2 480000
Type M or S Mortar
Compressive strength of clay Masonry (psi)
Specific Compressive Strength of
Clay Masonry Assemblage
fm( psi)
Modulus of
Elasticity (psi)
Modular Ratio, n
Modulus of
Rigidity, G = 0.40 Em (psi)
14000 or more 5300 3000000 9.7 1200000
12000 4700 3000000 9.7 1200000
10000 4000 3000000 9.7 1200000
8000 3350 2512500 11.5 1005000
6000 2700 2025000 14.3 810000
4000 2000 1500000 19.3 600000
According to the table, for Em= 1270 ksi
27
3.2.5 Calculation of Equivalent Strut Width
In the following table calculation of some sample strut is shown. In the study due to
various change in geometry several equivalent strut is used. Detail sample calculation
of Equivalent strut width is given below-
Table 3.4: Sample Calculation of equivalent strut width
Column Dimension Beam Dimension θcolumn Strut
Width, a B L B H
mm mm mm mm radian inch
457 457 305 508 0.42 27
508 508 305 508 0.42 27
558 558 305 558 0.46 28
609 609 305 609 0.46 28
Eccentricity is assumed d distance below the column as per advice.
3.3 NON-LINEAR STATIC PROCEDURE
Various analysis methods- both elastic and inelastic are available for the analysis of
concrete building. Elastic analysis method available includes code static lateral force
procedure, code dynamic lateral force procedure and elastic procedures using demand
capacity ratios. The most basic inelastic analysis method is the complete non linear
time history analysis, which at this time is considered overly complex and impractical
for general use. Available simplified nonlinear method referred to as nonlinear static
analysis procedure; include the capacity spectrum method (CSM) that uses the
intersection of capacity (pushover) curve and a reduced response spectrum to estimate
maximum displacement. Simplified nonlinear static analysis procedure using
pushover method such as the capacity spectrum method and the displacement
coefficient method requires determination of three primary elements: capacity,
demand (displacement) and performance. Each of these elements is briefly discussed
below
28
Capacity
The overall capacity of a structure depends on the strength and deformation capacities
of the individual components of the structure. In order to determine capacities beyond
the elastic limits, some form of nonlinear analysis such as Pushover Analysis is
required. This procedure uses a series of elastic analysis, superimposed to
approximate a force-displacement capacity diagram of the structure. The
mathematical model of the structure is modified to account for reduced resistance of
yielding components. A force distribution is again applied until the additional
components yields through forming plastic hinges. This process is continued until the
structure becomes unstable or until the predetermined limit is reached. The push over
capacity curve approximates how the structure behaves after exceeding elastic limit.
Demand (Displacement)
Ground motion during an earthquake produce complex horizontal displacement
patterns in structures that may vary with time. Tracking this motion at every time-step
to determine structural design requirements is judged impractical. Traditional linear
analysis methods use lateral forces to represent a design condition. For nonlinear
methods it is easier and more direct to use a set of lateral displacement demand is an
estimate of the maximum expected response of the building during the ground
motion. The displacement demand is established by use of the conventional response
spectra by covering it onto Spectral Acceleration vs. Spectral Displacement.
Performance
Once a capacity curve and demand displacement is defined, a performance check can
be done. A performance check verifies that structural and nonstructural components
are not damaged beyond the acceptable limits of the performance objective for the
forces and displacement imposed by the displacement demand.
3.3.1 Reduced Demand Spectra
The capacity of a particular building and the demand imposed upon it by a given
earthquake motion are not independent. One source of this mutual dependence is
evident from the capacity curve itself. As the demand increases the structure
29
eventually yields and stiffness decreases. Conversion of the capacity curve to spectral
ordinates (ADRS) makes this concept easier to visualize. Since the seismic
acceleration depends on period, demand also changes as the structure yields. Another
source of mutual dependence between capacity and demand is effective damping. As
a building yield in response to seismic demand it dissipates energy with hysteretic
damping. Building that have large, stable hysteresis loops during cyclic yielding
dissipate more energy than those with pinched loops caused by degradation of
strength and stiffness.
Since the energy dissipated need not be stored in the structure, the effective damping
diminishes displacement demand. The reduced displacement demand is shown in
figure above. The equation for the reduced factor SRA and SRv are given by-
SRA = (3.21- 0.681ln βeff) / 2.12 ≥ value in Table Eq.- 3.6
SRv = (2.31-0.41ln βeff)/ 1.65 ≤ value in Table Eq.- 3.7
Table (3.5): Minimum Allowable SRA and SRv values
Structural Behavior Type SRA SRv
Type A 0.33 0.5
Type B 0.44 0.56
Type C 0.56 0.67
Values for SRA and SRv shall not be less than those shown in this table.
Type A, B and C is taken as defined in ATC 40.
3.3.2 Development of Elastic Site Response Spectra
Elastic response spectra for a site are based on estimate of Seismic Co-efficient, CA
which represents the effective peak acceleration (EPA) of the ground and Cv which
represents 5% damped response of a 1- second system. These coefficients for a
particular zone are dependent on the seismicity of the area, the proximity of the site to
active seismic sources and site soil profile characteristics.
3.3.3 Seismic Zone
Bangladesh is divided into three seismic zones as per BNBC (1993). The table below
shows the values of zone coefficients of Bangladesh.
30
Table 3.6: Seismic Zone Factor, Z
Zone 1 2 3
Z 0.075 0.15 0.25
3.3.4 Seismic Source Type
As per ATC- 40 (1996), three types of seismic source may be defined as a shown in
Table below.
Table 3.7: Seismic source type as per ATC- 40, 1996
Seismic Source
Seismic Source Description Maximum Moment
Slip Rate, SR (mm/ yr)
A Faults which are capable of producing large magnitude events.
M> 7 SR> 5
B All faults other than types A and C N/A N/A
C Faults that are not capable of producing large magnitude events and which have a high rate
M< 6.5 SR< 2
3.3.5 Near Source Factor
Currently data pertaining to the active faults close to Dhaka city is not available. It is
not possible to estimate the seismic source distance from a specific site being
considered in this thesis. But it may be safe to assume that all the sources are located
at distance more than 15 km and the Table(3.8) (ATC- 40, 1996) may be used to
consider the Near Source effects for the present study. The near source factor may be
used on the linear interpolation of values for distance other than those shown in the
table. The closest distance of the seismic source shall be taken as the minimum
distance between the site and the area described by the vertical projection of source on
the surface. The surface projecting need not include portions of the source a depth of
10 km or greater. The largest value of the near source factor considering all sources
shall be used in design.
31
Table 3.8: Seismic Source Factor
Seismic Source Type
Closed Distance to Known Seismic Source
< 2km 5km 10km > 15 km
NA Nv NA Nv NA Nv NA Nv
A 1.5 2 1.2 1.6 1 1.2 1 1 B 1.3 1.6 1 1.2 1 1 1 1
C 1 1 1 1 1 1 1 1
3.3.6 Seismic Coefficients
For each earthquake hazard level, the structure is assigned a seismic coefficient CA in
accordance with Table (3.9) (ATC- 40, 1996) and a seismic coefficient Cv in
accordance with Table (3.10) (ATC- 40, 1996). Seismic coefficient CA represents the
effective peak acceleration (EPA) of the ground. A factor of about 2.5 times of CA
represents the average value of peak response of a 5% damped short period system in
acceleration domain. The seismic coefficient Cv represents 5% damped response of 1
sec system. Cv divided by period (T) defines acceleration response in the velocity
domain. These coefficients are dependent on soil profile type and the product of
earthquake zoning coefficient- Z, severity of earthquake- E and near source factor
(ZEN).The soil profile types are taken from the classification of (ATC- 40, 1996).
The soil profile type SE is applicable for Dhaka City. This type includes any soil
profile with more than 10 feet or soft clay defined as a soil with PI > 20, WMC > 40
and Su< 500 psf. Table 3.9: Seismic coefficient, CA
Soil profile type Shaking Intensity, ZEN
ZEN 0.075 0.15 0.2 0.3 SB 0.08 0.15 0.2 0.3 Sc 0.09 0.18 0.24 0.33 SD 0.12 0.22 0.28 0.36 SE 0.19 0.3 0.34 0.36
SF Site Specific Geotechnical Investigation required to determine
CA
32
The value of E used to determine the product, ZEN, should be taken to be equal to 0.5 for the serviceability Earthquake, 1.0 for the design earthquake and 1.25 for serviceability earthquake.
Seismic coefficient CA should be determined by liner interpolation for values of the product ZEN other than those shown in the table.
Table 3.10: Seismic coefficient CV (ATC-40, 1996)
Soil profile type
Shaking Intensity, ZEN
ZEN 0.075 0.15 0.2 0.3
SB 0.08 0.15 0.2 0.3
Sc 0.13 0.25 0.32 0.45 SD 0.18 0.32 0.4 0.54 SE 0.26 0.5 0.64 0.84 SF Site Specific Geotechnical Investigation required to determine CA
The value of E used to determine the product, ZEN, should be taken to be equal to 0.5 for the serviceability Earthquake, 1.0 for the design earthquake and 1.25 for serviceability earthquake.
Seismic coefficient CA should be determined by liner interpolation for values of the product ZEN other than those shown in the table.
According to (ATC-40, 1996), Soil profile types for Dhaka city is SE because it
includes any soil profile with more than 10 feet or soft clay defined as a soil with
PI>20, WMC> 40 and Su < 500 psf.
3.3.7 Establishing Demand Spectra
The purpose of subsequent analysis to be made in this thesis, it is necessary to
establish an earthquake demand spectra against which building performance will be
evaluated. The following controlling parameters are considered:
Location of the site : Dhaka City
Soil profile at the site : Soil type SE as per (ATC-40), soft soil with shear wave
velocity Vs< 600 fps, N< 50 and Su < 100 psf
Earthquake source type: A – considering the events similar to the great Indian
Earthquake in Assam in 12 June, 1897
Near Source Factor : > 15 km
33
Calculation of CA
Seismic Zone Factor, Z 0.15 as per BNBC
Earthquake Hazard Level, E 1 Design Earthquake
Near Source Factor, N 1 > 15 km, Table
Shaking Intensity, ZEN 0.15
For soil type, SE 0.3 From Table
Elastic response spectra, for each earthquake hazard level of interest at a site, isbased
on the site seismic coefficients CA and CV calculated above. The coefficient CA
represents the effective peak acceleration (EPA) of the ground. A factor of about 2.5
times CA represents the average value of peak response of a 5% damped short period
system in the acceleration domain. The seismic coefficient CV represents 5% damped
response of a 1 second system and when divided by period defines acceleration
response in velocity domain.
Calculation of CV
Seismic Zone Factor, Z 0.15 as per BNBC
Earthquake Hazard
Level, E 1 Design Earthquake
Near Source Factor, N 1 > 15 km, Table
Shaking Intensity, ZEN 0.15
For soil type, SE 0.5 From Table
The following establishes 5% damped elastic response spectra as shown in figure 3.3.
Effective peak ground acceleration (EPA) = 0.3g
Average value of peak response = 0.75g
Seismic coefficient, CV = 0.5g
Ts = 0.667 sec Ts =Cv / 2.5 CA
34
Ta = 0.133 sec Ta = 0.2Ts
For seismic performance evaluation purpose, this newly constructed site specific 5%
elastic response spectra need to be converted in to ADRS format using relation-
Sd = (T2/ 4π2) Sa g Eqn. – 3.8
Figure 3.3: 5% Damped Elastic Response Spectrum
Calculated spectral acceleration, spectral displacement with respect to the period is
shown in Table 3.11. These values are used to construct the 5% Elastic response
spectrum in Sa vs. Period format (figure: 3.3) and in ADRS format (figure: 3.4).
35
Figure 3.4: 5% Damped elastic response spectrum in ADRS format
Table 3.11: Response quantities for 5% elastic demand
T (sec) Sa, g Sd, cm
0 0.3 0
0.13 0.75 0
0.667 0.75 82.99705
0.8 0.625 99.49694
1 0.5 124.3712
1.2 0.416667 149.2454
1.4 0.357143 174.1196
1.6 0.3125 198.9939
1.8 0.277778 223.8681
2 0.25 248.7423
2.2 0.227273 273.6166
2.4 0.208333 298.4908
2.6 0.192308 323.365
2.8 0.178571 348.2393
3 0.166667 373.1135
3.2 0.1563 397.9877
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd
36
3.4 CAPACITY CURVE
The nonlinear pushover analysis requires development of the capacity curve. The
capacity curve is derived from a nonlinear analysis for the structure. In the process of
performing this incremental nonlinear static analysis, a capacity curve is developed
for the building. The capacity curve is simply the plot of the total lateral seismic
demand “V”, on the structure, at various increment of loading, against the lateral
deflection of the building at the roof level, under that applied lateral force. If a
building had infinite linear capacity, this capacity curve would be a straight line with
a slope equal to the global stiffness of the structure. Since real building do not have
the infinite linear capacities, the capacity curve typically consists of a series of
straight line segments with decreasing slope, representing the progressive degradation
in structural stiffness that occurs as the building is subjected to increased lateral
displacement, yielding and damage. The slope of a straight line drawn from the origin
of the plot for this curve to a point on the curve at any lateral displacement “d”
represent the secant or “effective” stiffness of the structure when pushed laterally to
that displacement. A typical capacity curve of a hypothetical structure is shown-
Figure 3.5: Typical Capacity Curve.
The discreet points indicated occurrence of important events in the lateral response
history of the structure. Such an event may be the initiation of yield in a particulars
structural element or a particular type of damage, such as spalling of cover concrete
on a column or shear failure of a spandrel element. Each point is determined by a
37
different analysis sequence. Then by evaluating the cumulative effects of damage
sustained at each of the individual events and the overall behavior of the structure is
increasing lateral displacement, it is possible to determine and indicate on the capacity
curve those total structural lateral displacements that represent limits on the various
structural performance levels, as has been done in Fig.3.5 . The Immediate Occupancy
(IO), the Life Safety level (LS) and the Structural Stability level (SS) are three
performance levels.
The point on the capacity curve at which the first element exceeds the permissible
deformation level for a structural performances level does not necessarily represent
that the structural performance level. Most structures contain many elements and have
considered redundancy. Consequently, the onset of unacceptable damage to a small
percentage of these elements may not represent an unacceptable condition with regard
to the overall performance of the building. When determining the points along the
capacity curve for the structure at which the various structural performance level may
said to be reached, the engineer must view the performance of a building as whole and
consider the importance of damage predicted for the various elements on the overall
behavior of the building.
The methodology described in ATC- 40 (1996), incorporates the concept of
“Primary” and “Secondary” elements to assist the engineers in making these
decisions. Primary elements are those that are required as part of the lateral force
resisting system for the structure. All the other elements are designated as secondary
elements. For a given performance level, secondary elements are generally permitted
to sustain more damage than primary elements since degradation of secondary
elements does not have a significant effect on the lateral load resisting capability of
building. If in the development of the capacity curve it is determined that a few
element fail to meet the acceptance criteria for a given performance level at an
increment of lateral loading and displacement, the engineer has the ability to liberal
acceptance criteria for these few elements. Care is exercised not to designate an
excessive number of elements that are effective in resisting lateral force as secondary.
38
3.4.1 Capacity Spectrum Method
The capacity spectrum method, a nonlinear static procedure, provides a graphical
representation of global force-displacement capacity curve of the structure and
compares it to the response spectra representations of the earthquake demand. This
method is a very useful tool in the evaluation and retrofit design of existing concrete
buildings. Capacity spectrum is the simple representation of the capacity curve in
ADRS domain. A capacity curve is the representation of Base shear to roof
displacement. In order to develop the capacity spectrum from a capacity curve it is
necessary to do a point by point conversion to first mode spectral co ordinates. Figure
3.6 shows a typical spectrum converted from capacity curve of a hypothetical
structure. It is seen that in the capacity spectrum that up to some displacement
corresponding to 1st point while the structure is in elastic deformation. The structure
deflects more to 2nd point. It goes to inelastic deformation. When Sa vs. Sd capacity
Figure: 3.6 Capacity Curve
curve is plotted, radial lines drawn from the origin of the plot through the curve at
various spectral displacements has a slope where ω is the radial frequency of the
effective first mode response of the structure if pushed by an earthquake to that
spectral displacement. Using the relationship T= 2π/ ω, it is possible to calculate, for
each of this radial lines, the effective period of the structure if it is pushed to a given
spectral displacements.
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150 200
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
39
3.5 PERFORMANCE POINT
The capacity spectrum method initially characterizes seismic demand using an elastic
response spectrum. This spectrum is plotted in spectral ordinates (ADRS) format
showing the spectral acceleration as a function of spectral displacement. This format
allows the demand spectra to be “overlaid” on the capacity spectrum for the building.
The intersection of the demand and capacity spectra, if located in the linear range of
the capacity, would define the actual displacement for the structure; however this is
not normally the case as most analysis includes some inelastic behavior. To find the
point where demand and capacity are equal, a point on the capacity spectrum need to
be selected as an initial estimate. Using the spectral acceleration and displacement
defined by this point, reduction factors may be calculated to apply to the 5% elastic
spectrum to account for the hysteretic energy dissipation or effective damping,
associated with the specific point. If the reduced demand spectrum intersects the
capacity spectrum at or near the initial assumed point, then it is the solution for the
unique point where capacity equals demand. If the intersection is not reasonably close
to the initial point, then a new point somewhere between may be assumed and repeat
the process until a solution is reached. This is the performance point where the
capacity of the structure matches the demand or the specific earthquake.
Once the performance point has been determined, the acceptability of a rehabilitation
design to meet the project performance objectives can be judged by evaluating where
the performance points falls on the capacity curve. For the structure and earthquake
represented by the overlay indicated in Figure 3.7, indicating that for this earthquake
this structure would have less damage than permitted for the Life Safety level and
more than would be permitted for the Immediate Occupancy level.
40
Figure 3.7: Determination of performance point
With this information, the performance objective and/ or the effectiveness of the
particular rehabilitation strategy to achieve the project performance objectives can be
judged.
3.5.1 Non linear Static Procedure for Capacity evaluation of Structures
Instead of comparing forces, nonlinear static procedures use displacements to
compare seismic demand to the capacity of a structure. This approach included
consideration of the ductility of the structure on an element by element basis. The
inelastic capacity of a building is then a measure of its ability to dissipate earthquake
energy. The current trend in seismic analysis is toward these simplified inelastic
procedures.
The recommended central methodology is on the formulation of inelastic capacity
curve for the structure. This curve is a plot of the horizontal movement of a structure
as it is pushed to one side. Initially the plot is a straight line as the structure moves
linearly. As the parts of the structure yield the plot begins to curve as the structure
softens. This curve is generated by building a model of the entire structure from
nonlinear representation of all of its elements and components. Most often this is
accomplished with a computer and structural analysis software. The specific forces
and displacement characteristics are specified for each piece of the structure resisting
the earthquake demand. These pieces are assembled geometrically to represent the
Performance Point
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
41
complete lateral load resisting system. The resulting model is subjected to increasing
increment of load in a pattern determined by its dynamic properties. The
corresponding displacements define the inelastic capacity curve of the building. The
generation of capacity curve defines the capacity of the building uniquely and
independently of any specific demand. When an earthquake displaces the building
laterally, its response is represented by a point on this curve. A point on the curve
defines a specific damage state of the building. The deformation of its entire
components can be related to the global displacement of the structure.
Building capacity and demand requires from earthquake are mutually dependent
which is depicted by capacity curve. As the demand increases the structure eventually
yields and stiffness decreases. Its period lengthens. Since the seismic accelerations
depend on period, demand also changes as the structure yields. Another source of
mutual dependence between capacity and demand is effective damping. As building
yields in response to seismic demand, it dissipates energy with yielding dissipate
more energy than those with pinched loops caused by degradation of strength and
stiffness. Since the energy that is dissipated need not be stored in the structure, the
damping has the effect of diminishing displacement demand.
3.5.2 Structural Performance Levels and Ranges
The performance of a building under any particular event is dependent on a wide
range of parameters. These parameters are defined (ATC-40, 1996; FEMA 356, 2000)
qualitatively in terms of the safety afforded by the building to the occupants during
and after the event; the cost and feasibility of restoring the building to pre- earthquake
condition; the length of time the building is removed from service to effect repairs;
and economic, architectural or historic impacts on the larger community. These
performance characteristics are directly related to the extent of damage that would be
sustained by the building.
The Federal Emergency Management Agency in its report ‘pre-standard and
Commentary for the Seismic Rehabilitation of Buildings, (FEMA-356, 2000) defines
the structural performance levels and two intermediate structural performance ranges.
42
The discrete Structural Performance Levels are –
Immediate Occupancy (S-1)
Life Safety (S-3)
Collapse Prevention (S-5) and
Not Considered (S-6)
The Intermediate Structural Performance Ranges are-
Damage Control Range (S-2) and
Limited Safety Range (S-4)
The definition of these performance ranges are given by FEMA (FEMA-356, 2000)
Acceptance criteria for performance within the Damage Control Structural
Performance Range may be obtained by interpolating the acceptance criteria provided
for the Immediate Occupancy and Life Safety Levels. The performance levels and
ranges. As per FEMA (FEMA-356, 2000), are described in the sections that follow.
3.5.3 Immediate Occupancy Structural Performance Level (S-1)
Structural Performance Level S-1- Immediate occupancy, may be defined as the post-
earthquake damage state of a structure and remains safe to occupy the pre-earthquake
design strength and stiffness of the structure and is in compliance with the acceptance
criteria specified in this standard for this Structural Performance Levels defined at
FEMA-356, 2000.
Immediate Occupancy also means the post-earthquake damage state in which only
very limited structural damage has occurred. The basic vertical and lateral force
resisting system of the building retain nearly all of their pre-earthquake strength and
stiffness. The risk of life threatening injury as a result of structural damage is very low
although some minor damage repair may be required prior to re-occupancy.
3.5.4 Damage Control Structural Performance Range (S-2)
Structural Performance Range S-2, Damage Control, may be defined as the
continuous range of damage states between the Life Safety Structural Performance
43
Level (S-3) and Immediate Occupancy Structural Performance Level (S-1) defined in
Table A1 to Table A3.
Design for the Damage Control Structural Performance Range may be desirable to
minimize repair time and operation interruption, as a partial means of protecting
valuable equipment and contents, or to preserve important historic features when the
cost of design for immediate occupancy is excessive.
3.5.5 Life Safety Structural Performance Level (S-3)
Structural Performance Level S-3, Life Safety, shall be defined as the post-earthquake
damage state that includes damage to structural components but retains a margin
against onset of partial or total collapse in compliance with the acceptance criteria
specified in FEMA for this Structural Performance Level defined at Tables A1 to A3
in FEMA-356, 2000.
Structural Performance Level S-3, Life Safety, means the post-earthquake damage
state in which significant damage to the structure has occurred but some margin
against either partial or total structural collapse remains. Some structural elements and
components are severely damaged but this has not resulted in large falling debris
hazards, either within or outside the building. Injuries mat occur during the
earthquake; however the overall risk of life threatening injury as a result of structural
damage is expected to be low. It should be possible to repair the structure; however,
for economic reasons this may not be practical. While the damaged structure is not an
imminent collapse risk, it would be prudent to implement structural repairs or install
temporary bracing prior to re-occupancy.
3.5.6 Limited Safety Structural Performance Range (S-4)
Structural Performance Range S-4, Limited Safety, may be defined as the continuous
range of damage states between the Life Safety Structural Performance at Tables A1
to A3 in FEMA-356, 2000.
3.5.7 Collapse Prevention Structural Performance Level (S-5)
Structural Performance Level S-5, Collapse Prevention, may be defined as the post-
earthquake damage state that includes damage to structural components such that the
44
structure continues to support gravity loads but retains no margin against collapse in
compliance with the acceptance criteria specified in FEMA for this Structural
Performance Level defined at Tables A1 to A3 in FEMA-356, 2000.
Structural Performance Level S-5, Collapse Prevention, means the post-earthquake
damage state in which the building is on the verge of partial or total collapse.
Substantial damage to the structure has occurred, potentially including significant
degradation in the stiffness and strength of the lateral-force resisting system, large
permanent lateral deformation of the structure and- to more limited extent-
degradation in vertical- load-carrying capacity. However, all significant components
of the gravity load resisting system must continue to carry their gravity load demands.
The fall of structural debris increases the risk significantly. The structure may not be
technically practical to repair and is not safe for re-occupancy, as aftershock activity
could induce collapse.
3.6 TARGET BUILDING PERFORMANCE LEVELS
Building performance is a combination of both structural and nonstructural
components. Tables A1 to A3 in FEMA-356, 2000 describe the approximate limiting
levels defined for a target seismic demand. These tables represent the physical states
of mathematical calculation of different performance levels.
3.7 RESPONSE LIMITS
To determine whether a building meets a specified performance objective, response
quantities from a nonlinear analysis are compared with limits given for appropriate
performance levels (ATC-40, 1996 and FEMA, 2000). The response limits fall into
two categories (i) Global Building Acceptability Limits and (ii) Element and
Component Acceptability Limits.
3.8 ACCEPTABILITY LIMIT
A given component may have a combination of both force and deformation controlled
actions. Each element must be checked to determine whether its individual
components satisfy acceptability requirements under performance point forces and
deformations. Together with the global requirements, acceptability limits for
45
individual components are the main criteria for assessing the calculated are the main
criteria for assessing the calculated building response.
Figure 3.8: Force deformation action and acceptance criteria
The figure 3.8 shows a generalized load-deformation relation appropriate for most
concrete component. The relation is described by linear response from A (unloaded
component) to an effective yield point B, linear response at reduced stiffness from B
to C, sudden reduction in lateral load resistance to D, response at reduced resistance to
E and final loss of resistance thereafter. The following main points relate to the
depicted load-deformation relation:
Point A corresponds to the unloaded condition. The analysis must recognize
that gravity loads may induce initial forces and deformations that should be
accounted for in the model. Therefore, lateral loading may commence at a
point other than the origin of the load-deformation relation.
Point B has resistance equal to the nominal yield strength. The slope from B to
C, ignoring the effects of gravity loads acting through lateral displacements, is
usually taken as between 5% and 10% of the initial slope. This strain
hardening may have an important effect on the redistribution of internal forces
among adjacent components.
The abscissa at C corresponding to the deformation at which significant
strength degradation begins.
The drop in resistance from C to D represents initial failure of the component.
A
B
C
DE
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25 30 35
Late
ral L
oad
Lateral Deformation
46
The residual resistance from D to E may be non-zero in some cases and may
be effectively zero in others. Where specific information is not available, the
residual resistance usually may be assumed to be equal to 20% of the nominal
strength.
Point E is a point defining the maximum deformation capacity. Deformation
beyond that limit is not permitted because gravity load can no longer be
sustained.
3.9 ELEMENT HINGE PROPERTY
It is known that reinforced concrete does not respond elastically to load level about
half the ultimate value. When an element is stressed beyond elastic limit, due to
inelastic deformation of the materials, the element will continue to deform
disproportionate to its load, this process is called formation of plastic hinge. Hinge
properties of RC members under different loading conditions are likely to be
different. These are discussed in the next sections.
Figure 3.8: Force deformation action and acceptance criteria
The figure 3.8 shows a generalized load-deformation relation appropriate for most
concrete component. The relation is described by linear response from A (unloaded
component) to an effective yield point B, linear response at reduced stiffness from B
to C, sudden reduction in lateral load resistance to D, response at reduced resistance to
E and final loss of resistance thereafter. The following main points relate to the
depicted load-deformation relation:
A
B
C
DE
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25 30 35
Late
ral L
oad
Lateral Deformation
47
Point A corresponds to the unloaded condition. The analysis must recognize
that gravity loads may induce initial forces and deformations that should be
accounted for in the model. Therefore, lateral loading may commence at a
point other than the origin of the load-deformation relation.
Point B has resistance equal to the nominal yield strength. The slope from B to
C, ignoring the effects of gravity loads acting through lateral displacements, is
usually taken as between 5% and 10% of the initial slope. This strain
hardening may have an important effect on the redistribution of internal forces
among adjacent components.
The abscissa at C corresponding to the deformation at which significant
strength degradation begins.
The drop in resistance from C to D represents initial failure of the component.
The residual resistance from D to E may be non-zero in some cases and may
be effectively zero in others. Where specific information is not available, the
residual resistance usually may be assumed to be equal to 20% of the nominal
strength.
Point E is a point defining the maximum deformation capacity. Deformation
beyond that limit is not permitted because gravity load can no longer be
sustained.
3.9 ELEMENT HINGE PROPERTY
It is known that reinforced concrete does not respond elastically to load level about
half the ultimate value. When an element is stressed beyond elastic limit, due to
inelastic deformation of the materials, the element will continue to deform
disproportionate to its load, this process is called formation of plastic hinge. Hinge
properties of RC members under different loading conditions are likely to be
different. These are discussed in the next sections.
3.9.1Concrete Axial Hinge
Concrete axial hinge is formed when the axial load carrying capacity of a section
exceeds its elastic limit. The elastic limit for axial capacity is different for tension and
compression. The limits are explained in figure 3.9.
48
Figure 3.9: Concrete axial hinge properties (FEMA-356, 2000)
Axial hinge features used in analysis are explained below:
Py= Asfy
Pc=0.85 Ac f’c
Slope between points B and C is taken as 10% total strain hardening for steel
Hinge length assumption for Δy is based on the full length.
Point B, C, D and E based on FEMA 273 Table 5.8, Braces in Tension
Point B’= Pc
Point E’ taken as 9Δy
3.9.2 Concrete moment hinge and concrete P-M-M hinge
Concrete moment hinge is formed when the flexural moment carrying capacity of a
section exceeds its elastic limit. The limit of flexural moment capacity and bi-axial
moment with axial load are explained in Fig. 3.10.
0
B
C
D E
0Δy
0
Fy
0
Fbuckling
<-- ----- Compression Tension ------>
49
Figure 3.10: Concrete moment and P-M-M hinge property
P-M-M hinge features used in analysis are explained below-
Slope between points B and C is taken as 10% total strain hardening for steel
Θy = 0, since it is not needed.
Points C, D and E based on ATC-40, table 9.6. The four conforming
transverse reinforcing rows of the table are averaged.
My based on reinforcement provided, otherwise based on minimum allowable
reinforcement.
P-M-M curve is for M3 and is taken to be the same as the Moment curve in
conjunction with the definition of Axial-Moment interaction curves.
3.9.3 Concrete Shear Hinge
Concrete shear hinge is formed when the shear carrying capacity of a section exceeds
it elastic limit. The elastic limit for shear carrying capacity for coupling beams
controlled by the flexure and controlled by shear is explained in Fig. 3.11(ATC-40,
1996).
0
B
C
D E
0θy
0
My
<-- ----- Compression Tension ------>
50
Figure 3.11: Concrete Shear Hinge Property
Shear hinge feature used in analysis:
Slope between points B and C is taken as 10% total strain hardening for steel
Vy= 2 As√fc’ + fyAsd
Points C, D and E based on ATC-40 Table 9.12, Item 2, average of the two
rows labeled “Conventional longitudinal reinforcement” and “Conforming
transverse reinforcement”
3.10 CONCRETE FRAME ACCEPTABILITY LIMITS
To determine the performance of a structure, response quantities from a nonlinear
static analysis are compared with limits for appropriate performance levels. Fig. 3.12
illustrates a generalized load-deformation relation applied in the structural component
a
b
L ate ra l D efo rm ation
Late
ral L
oad
A
B
C
D E
T Y P E - A
c
d
L ate ra l D efo rm ation
Late
ral L
oad
A
B
C
D E
T Y P E - B
F igu re 3 .12 : G enera lized load -d efo rm ation re lation fo r com ponen ts
under the present study. Curve Type A in the Fig. 3.12 has been used when the
deformation is a flexural plastic hinge. Curve type B in the Fig. 3.12 has been used
0
B
C
D E
0Δy
0
Vy
0
Vbuckling
<-- ----- Compression Tension ------>
51
when the deformation is inter-story drift, shear angle, sliding shear displacement or
beam column joint rotation.
3.10.1 Hinge Properties for Modeling
Depending upon the longitudinal reinforcement, transverse reinforcement etc.
different hinge properties may be modeled based on the modeling parameters defined
through Tables 9-6, 9-7 and 9-12 in ATC- 40. Different points A, B, C etc. are
defined in Fig. 3.4 of this chapter. For the purpose of the thesis, the ETABS’s built in
default hinge properties of concrete have been assumed. These built-in default hinge
properties are generally based on Tables 9.6, 9.7 and 9.12 in ATC-40.
3.11 PERFORMANCE CRITERIA FOR THE STRUCTURE
3.11.1 Drift
Inter-story drift ratio is defined as the ration of the inter-story drift of the story to
height of that story
Maximum drift ratio is defined as the inter-story drift ratio at the performance point
displacement.
Accepted maximum story drift ratios for different structural performance condition
are given in the table below-
Table 3.12: Allowable maximum story drift ratio (ATC-40)
Structural performance condition Maximum story drift ratio
Immediate Occupancy (IO) 0.01
Life Safety (LS) 0.02
3.11.2 Story Displacement
Story displacement at the performance point is also observed. In case of the structure
not having a performance point, Story displacement at the last step is considered since
the last step is the failure step.
52
CHAPTER 4
PERFORMANCE EVALUATION OF SOFT GROUND
STORY STRUCTURE
4.1 INTRODUCTION The procedure of the non-linear pushover analysis, nonlinear hinge property,
acceptance criteria and equivalent strut modeling for the in-filled panel have been
described in the previous chapter. In this chapter some three dimensional soft story
structure and bare frame of same configuration will be modeled and designed
following the conventional design procedure provided by finite element software
ETABS. Then the effect of infill on the frame which is designed as bare frame will be
investigated. Performance evaluation will be done by push over analysis and results of
story will be compared with conventional bare frame.
4.2 LOADING CONDITION Self weight is calculated automatically by the program. In addition to self weight
1.437×10-3 N/mm2 of floor finish and 2.395×10-3 N/mm2 of live load is applied.
Partition wall load of 0.42 kip per ft is provided uniformly on the beam.
Wind Load is automatically calculated by analysis software as per UBC 94 code.
Wind speed of 130 mph is considered for Dhaka city and exposure A is considered.
Earthquake Load automatically calculated by program as per UBC 94. As per
modification factor R= 8 has been considered. Other co- efficient used is –
Seismic zone condition, Z= 0.15 for Zone 2
Structural Importance Co- efficient, I = 1.00
Site Co- efficient, S = 1.5
4.3 MATERIAL PROPERTIES Concrete properties
Modulus of elasticity 20000 N/mm2
Poisson’s ratio 0.13
53
Density 2.4×10-9 Ton/mm3
Unit weight 2.36×10-5 N/mm3
Concrete Strength 27.6 MPa
Infill properties
Density 1.92×10-9 Ton/mm3
Thickness 130mm
Modulus of Elasticity 8273.3 N/mm2
4.4 MODEL GEOMETRY
Buildings are designed as bare frame and effect of infill is investigated on a
frame that is designed as bare frame. As partition load is provided on the beam
the weight of diagonal strut is neglected.
Equivalent struts are pin connected with the column as masonry cannot take
moment.
Struts are capable of taking both tension and compression.
All supports are considered as fixed support.
All structure are assumed to have strong column-weak beam by ensuring that
flexure strength of column shall satisfy the relation ∑ Mc ≥ 1.2 ∑Mg.
Where,
∑ Mc= sum of moments at the center of the joint, corresponding to the design
flexural strength of the columns framing into joint.
∑Mg= sum of moments at the center of the joint corresponding to the design
flexural strength of the girder framing into joint.
4.5 ASSUMPTIONS FOR PUSH OVER ANALYSIS
The following assumptions relate to the pushover analysis of the structure
Moment (M3) and Shear (V2) hinges are considered at the ends of beam
members and moment (M2, M3) and axial (P) is considered at the ends of
column members. Here 2 and 3 specify the axis or directions of the loads. For
column members axis 2 is perpendicular to the line object. The direction of the
54
positive local 2 axis onto the global X-axis is in the same direction as the
positive global X axis. Axis 3 is perpendicular to the line object. The direction
of the positive local 3 axis is determined from applying the right-hand rule
using the direction of the 1 and 2 axis where 1 is along the line object. For
beam members, axis 2 is perpendicular to the line object. The positive local 2
axis points in the same direction as the global Z-axis, upward. Axis 3 is
perpendicular to the line object and is horizontal. The direction of the positive
local 3 axis is determined from applying the right hand rule using the direction
of the 1 and 2 axes where 1 is along the line object (ETABS Manual).
Push over Analysis has been done using the load pattern of equivalent static
load as calculated as per provision of BNBC, 1993.
Gravity load has been considered as the previous pushover cases for each
analysis.
Unload entire structure is selected for distribution of loads when local hinges
fail. When a hinge reaches a negative sloped portion of the stress- strain curve,
the program continues to try to increase the applied load. If the results in
increased strain (decreased stress) the analysis proceeds. If the strain tries to
reverse, the program instead reverses the load on the whole structure until the
hinge is fully unloaded to the next segment on stress- strain curve. At this
point the program reverts to increasing the load on the structure. Other parts of
the may now pick up the load that was removed from the unloading hinge.
Geometric non- linearity (p-Δ effect) is considered with full dead load and 2%
live load.
Horizontal displacement of top most corner node has been selected for
performance monitoring of the roof displacement.
4.6 SOFTWARE USED IN THE ANALYSIS
ETABS Nonlinear version 9.7, extended 3D analysis software for building systems,
product of Computers and Structures, Inc, Berkeley, California, USA is used for
modeling and performance evaluation of the structures.
55
4.7 DESCRIPTION OF THE STRUCTURES CONSIDERED FOR ANALYSIS Table 4.1: Description of the Structure Considered for Analysis Structure
No. Plan Type
No. of
Story
No. of Bays and Span in
Direction X
No. of Bays and Span in
Direction Y
Interior Column
Size (mm)
Exterior Column
Size (mm)
Size of Beam (mm)
1 A 6 4 @ 6m 4 @ 6m 457x457 457x457 305x508 2 A 8 4 @ 6m 4 @ 6m 508x508 508x508 305x508 3 A 10 4 @ 6m 4 @ 6m 558x558 558x558 305x558 4 A 12 4 @ 6m 4 @ 6m 609x609 558x558 305x609
5 B 10 4 @ 6m 3 @ 6m 558x558 558x558 305x558
4 @ 6m
4 @ 6m
PLAN- A
4 @ 6m
3 @ 6m
PLAN- B
Figure 4.1: Plan View Type- A & B
4.8 PERFORMANCE EVALUATION OF THE STRUCTURES
The performances of the structures under seismic condition are evaluated for the bare
frame and soft story condition using push over analysis. Their performances are then
compared.
56
Notifications:
RSD= Reduced Seismic Demand
CC= Capacity Curve
EDRS= Earthquake Demand Reduced Spectrum (ADRS format)
After analysis in case where structure collapses before reaching performance
point, the value of βeff is taken from the step where base shear reaches its
maximum i.e. from the collapse state.
In case of soft story structure, if fails to meet performance point, base shear
and hinge status are considered from collapse state for comparison.
4.8.1 Performance Evaluation of the Structure 1
Table 4.2: Effective damping and spectral reduction factor for structure 1
Frame Type Bare Frame Soft Story (40%
infill)
Effective Damping, βeff 10.40% 10.80%
Spectral Reduction Factor, SRA 0.762 0.749
Spectral Reduction Factor, SRv 0.818 0.809 Seismic State Co-efficient, CA 0.3 Seismic State Co-efficient, CV 0.5
Figure 4.2: Comparison of capacity spectrum of structure 1 for different infill
condition
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd mm
CC 40% infill
EDRS 40% infill
EDRS Bare Frame
CC Bare Frame
57
Table 4.3: Effective damping and spectral reduction factor for structure 1
Frame Type Bare Frame Soft Story (60%
infill)
Effective Damping, βeff 10.40% 10.90% Spectral Reduction Factor, SRA 0.762 0.747 Spectral Reduction Factor, SRv 0.818 0.808 Seismic State Co-efficient, CA 0.3 Seismic State Co-efficient, CV 0.5
Figure 4.3: Comparison of capacity spectrum of structure 1 for different infill condition
Table 4.4: Effective damping and spectral reduction factor for structure 1
Frame Type Bare Frame Soft Story
(80% infill)
Effective Damping, βeff 10.40% 11.30%
Spectral Reduction Factor, SRA 0.762 0.735
Spectral Reduction Factor, SRv 0.818 0.795
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement. Sd (mm)
CC 60% infill
EDRS 60% infill
CC 60% infill
EDRS Bare Frame
58
Figure 4.4: Comparison of capacity spectrum of structure 1 for different infill
condition
Structure 1 is a six storied structure. Detailed configuration is given in section 4.7
under this chapter. The capacity spectrum of the structure is shown in figure 4.2 to 4.4
and table 4.2 to 4.4. From evaluation, it has been found that capacity of bare frame
meets demand but structure has to deform a considerable amount to meet the demand
curve. As a result some of its elements are stressed above their elastic limit and
elements become nonlinear. Fig. 4.2 to 4.4 describes the fact more clearly. It has also
been observed in case of soft storied structure with the increase in infill the value of
βeff increases but capacity spectrum never meets the demand curve. Columns of the
ground floor collapse before reaching the demand result the failure of the structure.
Table 4.5: Base Shear Comparison among different methods for structure 1
Base Shear (KN) Bare Frame 40% infill 60% infill 80% infill
ESFM Method 2104 2104 2104 2104
RSM Method 3299 3760 4234
Push Over Method 3797 5570 5789 5958
Table above shows, the more the presence of infill above the ground story the more is
the value of base shear because story above are stiffer than the ground floor.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement. Sd mm
CC 80% infill
EDRS 80% infill
CC Bare Frame
EDRS Bare Frame
59
Figure 4.5: Comparison of story shear observed from different method
From table 4.6, it is found that for bare frame structure develops limited number of
hinges beyond life safety performance level at performance point. The base shear
developed at performance point is less than that of the soft story structure because of
no active member in form of diagonal strut.
Table 4.6: Base shear at performance point and number and number of hinges
developed up to performance point
In-fill Condition of Frame
Base Shear (KN)
Status of Hinge Formation at Different Performance Stages
A-B B-IO IO-LS LS-CP CP-C C-D
D-E
>E Total
Bare Frame
3797 1020 205 68 175 0
2 0 1470
Soft story (40% infill)
5570 1049 300 35 85 0 0 1 0 1470
Soft story (60% infill)
5788 1072 292 21 81 0 0 4 0 1470
Soft story (80% infill)
5958 1105 261 19 79 0 2 4 0 1470
0
1000
2000
3000
4000
5000
6000
7000
Base
She
ar, K
N
No infill 40% 60% 80%
ESFM
RSM Method
Push Over Method
60
The following figure 4.6 shows the displacement of structure 1 at different percentage
of infill present. The deformation of soft story is not uniform and also maximum.
Figure 4.6: Comparison of displacement (mm) in X direction
The following figure 4.7 shows the drift at different story level of structure 1 having
different infill percentage.
Figure 4.7.1: Comparison of maximum total drift ratio in X direction of structure 1
0
1
2
3
4
5
6
7
0 50 100 150 200 250 300
No
of s
tory
Displacement (mm)
60% infill
80% infill
40% infill
Bare Frame
0
1
2
3
4
5
6
7
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift in X
40% infill
Bare Frame
IO
LS
61
Figure 4.7.2: Comparison of maximum total drift ratio in X direction of structure 1
Figure 4.7.3: Comparison of maximum total drift ratio in X direction of structure 1
Figure 4.7 shows that the drift of the soft ground story is above the level of immediate
occupancy and also non uniform along both directions. Difference of performance
level in bare and soft story is due to stiffness irregularity.
0
1
2
3
4
5
6
7
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift , X
60% infill
Bare Frame
IO
LS
0
1
2
3
4
5
6
7
0 0.005 0.01 0.015 0.02 0.025
No
of S
tory
Drift in X
80% infill
bare frame
IO
LS
62
a) Exterior Frame (Bare) b) Interior Frame (Bare)
c) Exterior Frame (Bare) d) Interior Frame (Bare)
Figure 4.8: Deformation pattern of structure 1 at performance point
4.8.2 Performance Evaluation of the Structure 2 Table 4.7: Effective damping and spectral reduction factor for structure 2
Frame Type Bare Frame Soft Story (40% infill)
Effective Damping, βeff 11.50% 11.90% Spectral Reduction Factor, SRA 0.727 0.718 Spectral Reduction Factor, SRv 0.791 0.785 Seismic State Co-efficient, CA 0.3 Seismic State Co-efficient, CV 0.5
63
Figure 4.9: Comparison of capacity spectrum of structure 2 for different infill condition
Table 4.8: Effective damping and spectral reduction factor for structure 2
Frame Type Bare Frame Soft Story
(60% infill)
Effective Damping, βeff 11.50% 12.20%
Spectral Reduction Factor, SRA 0.727 0.71
Spectral Reduction Factor, SRv 0.791 0.746
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
Figure 4.10: Comparison of capacity spectrum of structure 2 for different infill condition
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
SS 40% infill
EDRS SS 40% infill
EDRS Bare Frame
CC Bare Frame
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
CC SS 60% infill
EDRS 60% infill
EDRS Bare Frame
CC Bare Frame
64
Table 4.9: Effective damping and spectral reduction factor for structure 2
Frame Type Bare Frame Soft Story (80%
infill)
Effective Damping, βeff 11.50% 12.20%
Spectral Reduction Factor, SRA 0.727 0.71
Spectral Reduction Factor, SRv 0.791 0.746
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
Figure 4.11: Comparison of capacity spectrum of structure 2 for different infill
condition
Structure 2 is an eight storied structure. Detailed configuration is given in section 4.7
under this chapter. The capacity spectrum of the structure is shown in figure 4.9 to
4.11 and table 4.7 to 4.9. From evaluation, it has been found that capacity of bare
frame meets demand but structure has to deform a considerable amount to meet the
demand curve. As a result some of its elements are stressed above their elastic limit
and elements become nonlinear. Fig. 4.9 to 4.11 describes the fact more clearly. It has
also been observed in case of soft storied structure with the increase in infill the value
of βeff increases but capacity spectrum never meets the demand curve. Columns of the
ground floor collapse before reaching the demand result the failure of the structure.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
SS 80% infill
EDRS 80% infill
EDRS Bare Frame
CC Bare Frame
65
Table 4.10: Base Shear Comparison among different methods
Base Shear (KN) Bare Frame 40% infill 60% infill 80% infill
ESFM Method 1823 1823 1823 1823
RSM Method 4494 5021 5566
Push Over Method 5570 7420 7816 8136
Table above shows, the more the presence of infill above the ground story the more is the value of base shear because story above are stiffer than the ground floor.
Figure 4.12: Comparison of story shear observed from different method
From table 4.11, it is found that for bare frame structure develops limited number of
hinges beyond life safety performance level at performance point. The base shear
developed at performance point is less than that of the soft story structure because of
no active member in form of diagonal strut.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Base
She
ar (K
N)
NO infill 40% 60% 80%
ESFM
RSM
Push over
66
Table 4.11: Base shear at performance point and number and number of hinges
developed up to performance point
Infill Condition of Frame
Base Shear (KN)
Status of Hinge Formation at Different Performance Stages
A-B B-IO
IO-LS LS-CP CP-C C-D
D-E
>E Total
Bare Frame
5570 1491 94 54 246 0 0 5 0 1890
Soft Story (40% infill)
7420 1544 216 33 96 0 1 0 0 1890
Soft Story (60% infill)
7816 1548 234 18 88 0 0 2 0 1890
Soft Story (80% infill)
8136 1578 207 22 79 0 2 2 0 1890
The following figure 4.13 shows the displacement of structure 2 at different
percentage of infill present. The deformation of soft story is not uniform and also
maximum.
Figure 4.13: Comparison of displacement (mm) in X direction
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200 250 300 350 400
No.
of S
tore
y
Displacement (mm)
SS 40% infill
SS 80% infill
SS 60% infill
Bare Frame
67
The following figure 4.14.1 - 3 shows the drift at different story level of structure 2
having different infill percentage.
Figure 4.14.1: Comparison of maximum total drift ratio in X direction of structure 2
Figure 4.14.2: Comparison of maximum total drift ratio in X direction of structure 2
0
1
2
3
4
5
6
7
8
9
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift in X direction
SS 40% infill
Bare Frame
IO
LS
0
1
2
3
4
5
6
7
8
9
0 0.005 0.01 0.015 0.02 0.025
No.
Sto
ry
Drift in X
SS 60% infill
Bare Frame
IO
LS
68
Figure 4.14.3: Comparison of maximum total drift ratio in X direction of structure 2
Figure 4.14.1- 3, shows that the drift of the soft ground story is above the level of
immediate occupancy and also non uniform along both directions. Difference of
performance level in bare and soft story is due to stiffness irregularity.
4.8.3 Performance Evaluation of the Structure 3
Table 4.12: Effective damping and spectral reduction factor for structure 3
Frame Type Bare Frame Soft Story (40% infill)
Effective Damping, βeff 11.20% 11.60%
Spectral Reduction Factor, SRA 0.738 0.727
Spectral Reduction Factor, SRv 0.799 0.791
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
0
1
2
3
4
5
6
7
8
9
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift in X
SS 80% infill
Bare Frame
IO
LS
Linear (LS)
69
Figure 4.15: Comparison of capacity spectrum of structure 3 for different infill
condition
Table 4.13 Effective damping and spectral reduction factor for structure 3
Frame Type Bare Frame Soft Story (40% infill)
Effective Damping, βeff 11.20% 11.60%
Spectral Reduction Factor, SRA 0.738 0.727
Spectral Reduction Factor, SRv 0.799 0.791
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
Figure 4.16: Comparison of capacity spectrum of structure 3 for different infill
condition
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
elar
atio
n, S
a (g
)
Spectral Displacement, Sd mm
CC SS 40% infill
EDRS 40% infill
EDRS Bare Frame
CC Bare Frame
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
elar
atio
n, S
a (m
m)
Spectral Displacement, mm
CC SS 60% infill
EDRS 60% infill
CC Bare Frame
EDRS Bare Frame
70
Table 4.14 Effective damping and spectral reduction factor for structure 3
Frame Type Bare Frame Soft Story (80% infill)
Effective Damping, βeff 11.20% 11.7
Spectral Reduction Factor, SRA 0.738 0.724
Spectral Reduction Factor, SRv 0.799 0.788
Seismic State Co-efficient, CA 0.3 Seismic State Co-efficient, CV 0.5
Figure 4.17: Comparison of capacity spectrum of structure 3 for different infill condition
Structure 3 is a ten storied structure. Detailed configuration is given in section 4.7
under this chapter. The capacity spectrum of the structure is shown in figure 4.15 to
4.17 and table 4.12 to 4.14. From evaluation, it has been found that capacity of bare
frame meets demand but structure has to deform a considerable amount to meet the
demand curve. As a result some of its elements are stressed above their elastic limit
and elements become nonlinear. Fig. 4.15 to 4.17 describes the fact more clearly. It
has also been observed in case of soft storied structure with the increase in infill the
value of βeff increases but capacity spectrum never meets the demand curve. Columns
of the ground floor collapse before reaching the demand result the failure of the
structure.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
elar
atio
n, S
a
Spectral Displacement, Sd
SS CC 80% infill
EDRS 80% infill
EDRS Bare Frame
CC Bare Frame
71
Table 4.15: Base Shear Comparison among different methods
Base Shear (KN) Bare Frame 40% infill 60% infill 80% infill
ESFM Method 2104 2104 2104 2104
RSM Method
3299 3760 4234
Push Over 5033 7828 9402 9543
Table above shows, the more the presence of infill above the ground story the more is
the value of base shear because story above are stiffer than the ground floor.
Figure 4.18: Comparison of story shear observed from different method
From table 4.17, it is found that for bare frame structure develops limited number of
hinges beyond life safety performance level at performance point. The base shear
developed at performance point is less than that of the soft story structure because of
no active member in form of diagonal strut.
Table 4.16: Base shear at performance point and number and number of hinges
developed up to performance point
In-fill Condition of
Frame
Base Shear (KN)
Status of Hinge Formation at Different Performance Stages
A-B B-IO IO-LS LS-CP CP-C C-D
D-E
>E Total
Bare Frame 5033 1815 138 117 230 0 5 5 0 2310
Soft Story (40% infill) 7828 1829 213 136 128 0 1 3 0 2310
Soft Story (60% infill)
9402 1892 299 24 93 0 0 2 0 2310
Soft Story (80% infill) 9543 1949 254 18 87 0 1 1 0 2310
0
2000
4000
6000
8000
10000
12000
Base
She
ar (K
N)
NO infill, 40%, 60%, 80%
ESFM
RSM
Push over
72
The following figure 4.19 shows the displacement of structure 3 at different
percentage of infill present. The deformation of soft story is not uniform and also
maximum
Figure 4.19: Comparison of displacement (mm) in X direction
The following figure 4.20.1 - 3 shows the drift at different story level of structure 3
having different infill percentage.
Figure 4.20.1: Comparison of maximum total drift ratio in X direction of structure 3
0
2
4
6
8
10
12
0 50 100 150 200 250 300 350
No
of S
tory
Displacement, mm
60% infill
Bare Frame
40% infill
80% infill
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02 0.025
No
of S
tory
Drift in X
40% infill
Bare Frame
IO
LS
73
Figure 4.20.2: Comparison of maximum total drift ratio in X direction of structure 3
Figure 4.20.3: Comparison of maximum total drift ratio in X direction of structure 3
Figure 4.20.1- 3, shows that the drift of the soft ground story is above the level of
immediate occupancy and also non uniform along both directions. Difference of
performance level in bare and soft story is due to stiffness irregularity.
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02 0.025
No
of S
tory
Drift in X
60% infill
Bare Frame
IO
LS
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02 0.025
No
of S
tory
Drift in X
Bare Frame
80% infill
IO
LS
74
4.8.4 Performance Evaluation of the Structure 4
Table 4.17: Effective damping and spectral reduction factor for structure 4
Frame Type Bare Frame Soft Story (40%
infill)
Effective Damping, βeff 11.60% 11.1%
Spectral Reduction Factor, SRA 0.727 0.741
Spectral Reduction Factor, SRv 0.791 0.802
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
Figure 4.21: Comparison of capacity spectrum of structure 4 for different infill
condition
Table 4.18: Effective damping and spectral reduction factor for structure 4
Frame Type Bare Frame Soft Story (60%
infill)
Effective Damping, βeff 11.60% 11.2%
Spectral Reduction Factor, SRA 0.727 0.738
Spectral Reduction Factor, SRv 0.791 0.799
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
CC 40% infill
EDRS Bare Frame
CC Bare Frame
EDRS SS 40% infill
75
Figure 4.22: Comparison of capacity spectrum of structure 4 for different infill
condition
Table 4.19: Effective damping and spectral reduction factor for structure 4
Frame Type Bare Frame Soft Story (80%
infill)
Effective Damping, βeff 11.60% 10.8%
Spectral Reduction Factor, SRA 0.727 0.75
Spectral Reduction Factor, SRv 0.791 0.808
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
Figure 4.23: Comparison of capacity spectrum of structure 4 for different infill
condition
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
eler
atio
n, S
a (g
)
Spectral Displacement, Sd (mm)
Series1
EDRS 60% infill
EDRS Bare Frame
CC Bare Frame
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400
Spec
tral
Acc
eler
atio
n, S
a m
m
Spectral Displacement, Sd mm
EDRS 80% infill
CC SS 80% infill
CC Bare Frame
EDRS Bare Frame
76
Structure 4 is a twelve storied structure. Detailed configuration is given in section 4.7
under this chapter. The capacity spectrum of the structure is shown in figure 4.21 to
4.23 and table 4.17 to 4.19. From evaluation, it has been found that capacity of bare
frame meets demand but structure has to deform a considerable amount to meet the
demand curve. As a result some of its elements are stressed above their elastic limit
and elements become nonlinear. Fig. 4.21 to 4.23 describes the fact more clearly. It
has also been observed in case of soft storied structure with the increase in infill the
value of βeff increases but capacity spectrum never meets the demand curve. Columns
of the ground floor collapse before reaching the demand result the failure of the
structure. It is also observed that hinges formed for soft story is more and some of
them reach damage state. As a result the structure fails ultimately. The structure also
fails before developing base shear.
Table 4.20: Base Shear Comparison among different methods
Base Shear (KN) Bare Frame 40% infill 60% infill 80% infill
ESFM Method 2255 2255 2255 2255
RSM Method
4494 5021 5566
Push Over Method (KN) 4745 9111 9381 9572
Table above shows, the more the presence of infill above the ground story the more is
the value of base shear because story above are stiffer than the ground floor.
Figure 4.24: Comparison of story shear observed from different method
From table 4.22, it is found that for bare frame structure develops limited number of
hinges beyond life safety performance level at performance point. The base shear
developed at performance point is less than that of the soft story structure because of
no active member in form of diagonal strut.
0
2000
4000
6000
8000
10000
12000
Base
She
ar (K
N)
NO infill, 40%, 60%, 80%
ESFM
RSM
Push over
77
Table 4.21: Base shear at performance point and number and number of hinges
developed up to performance point
In-fill Condition of Frame
Base Shear (KN)
Status of Hinge Formation at Different Performance Stages
A-B B-IO
IO-LS
LS-CP
CP-C
C-D
D-E
>E Total
Bare Frame 4915 2200 125 124 276 0 2 3 0 2730 Soft Story
(40% infill) 9111 2231 324 70 96 0 1 8 0 2730
Soft Story (60% infill)
9381 2248 329 48 103 0 0 2 0 2730
Soft Story (80% infill)
9572 2274 345 16 86 0 3 6 0 2730
The following figure 4.25 shows the displacement of structure 4 at different
percentage of infill present. The deformation of soft story is not uniform and also
maximum.
Figure 4.25: Comparison of displacement (mm) in X direction
The following figure 4.26.1 - 3 shows the drift at different story level of structure 4
having different infill percentage.
0
2
4
6
8
10
12
14
0 100 200 300 400 500
No
of S
tory
Displacement (mm)
Bare Frame
SS 80% infill
SS 60% infill
SS 40% infill
78
Figure 4.26.1: Comparison of maximum total drift ratio in X direction of structure 4
Figure 4.26.2: Comparison of maximum total drift ratio in X direction of structure 4
0
2
4
6
8
10
12
14
0 0.005 0.01 0.015 0.02 0.025
No
of S
tory
Drift in X
40% infill
Bare Frame
IO
LS
0
2
4
6
8
10
12
14
0 0.005 0.01 0.015 0.02 0.025
No
of S
tory
Drift in X
SS 60% infill Drift
Bare Frame Drift
IO
LS
79
Figure 4.26.3: Comparison of maximum total drift ratio in X direction of structure 4
4.8.5 Performance Evaluation of the Structure 5
All of the structures investigated above are square in shape. To see the effect of soft
story on building of rectangular shape next investigation has been done. Usually most
of buildings consist of 40% to 60% infill so this investigation has been done on a ten
storied soft story structure containing 60% infill.
Table 4.22: Effective damping and spectral reduction factor for structure 5 in long (X)
and short (Y) direction
Frame Type Bare Frame Soft Story (80%
infill)
Effective Damping, βeff 15.20% 18.10%
Spectral Reduction Factor, SRA 0.64 0.584
Spectral Reduction Factor, SRv 0.723 0.68
Seismic State Co-efficient, CA 0.3
Seismic State Co-efficient, CV 0.5
0
2
4
6
8
10
12
14
0 0.005 0.01 0.015 0.02 0.025
No.
of S
tory
Drift in X
Bare Frame
SS 80% infill
IO
LS
80
Figure 4.26: Comparison of capacity spectrum of structure 5 for 60% infill condition
in both long and short direction
From figure 4.26 it is found that capacity curve does not meet demand curve in long
direction but it meets demand curve in short direction. The reason must be the lack of
stiffness in short direction as number of brick infill panel is less.
Table 4.23: Base shear at performance point and number and number of hinges
From the table 4.24, it is observed that number of hinges developed at performance
point have reached in damage state. Hinges form in damage state more in short
direction.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 100 200 300 400
Spec
tral
acel
erat
ion,
Sa
(g)
Spectral Displacement, Sd (mm)
CC 60% infill (long)
CC 60% infill (Short)
EDRS 60% infill (long)
EDRS 60% infill (short)
In-fill Condition of Frame
Base Shear (KN)
Status of Hinge Formation at Different Performance Stages
A-B B-IO IO-LS LS-CP CP-C C-D
D-E >E Total
Soft Ground Story in
X
7720 1571 143 35 53 0 0 2 0 1804
Soft Ground Story in
Y
7656 1651 60 43 46 0 1 3 0 1804
81
Figure 4.27: Comparison of displacement (mm) in both long and short direction
From the figure above, it is seen that drift of soft story is slightly more in short
direction than in long direction.
Figure 4.28: Comparison of maximum total drift ratio in both long and short direction of structure 5
The value of drift in short direction is slightly more than in long direction although capacity curve in short direction meet the demand curve.
0
2
4
6
8
10
12
0 20 40 60 80 100 120
No
of s
tory
Displacement (mm)
Displacement (long)
Displacement (short)
0
2
4
6
8
10
12
0 0.005 0.01 0.015 0.02
No.
of S
tory
Drift
Drift (long)
Drift (Short)
82
4.9 REMARKS
The results obtained from the evaluations of the structures are presented in previous
sections. The observation results are as follows-
The value of base shear obtain from pushover method is much more than the
value obtained from equivalent static force method or response spectrum
method.
Open ground story buildings are extremely vulnerable to earthquake loading.
In case of seismic loading the capacity curve does not meet the demand curve.
Some structural members face displacement of higher value.
The number of hinges form is more and some of them reach at damage state.
As a result structure suffer collapse before reaching their require demand.
Inter-story drift are very high in soft ground story.
The amount of displacement is very high in soft story. The demand of ductility
is also very high. Stiffness of the above stories is much higher than ground
story.
So it must be a vital concern for the design engineer to provide adequate measures
to achieve acceptable performance in open ground story structure which can be
done by adding strength, stiffness, ductility or any combination of these or
alternatively the demand from the earthquake load can be reduced by adding
damping.
83
CHAPTER 5
CONCLUSION AND RECOMMENDATIONS
5.1 GENERAL
Open ground story has now become a common feature in the modern day multi-
storied apartment buildings to fulfill the demand of parking spaces. As a result
vertical stiffness irregularity develops the soft story mechanism. It is most common
failure mode of RC structures during earthquake. This thesis has been conducted to
find out the actual behavior of the soft story under the seismic activity and to compare
the value of base shear found from different analysis techniques. For this reason a
total of five structures range from six to twelve stories has been used to perform the
pushover analysis. The performances of the structures have been evaluated as per the
procedure of ATC-40, 1996 and FEMA 356, 2002.
5.2 FINDINGS OF THE STUDY The findings of the study can be summarized as follows-
The values of base shear found from different analysis method are compared.
Base shear value found from push over method is very much higher than
equivalent static force method or response spectrum method.
The value of base shear increases with the increase in story height and
percentage of infill.
The seismic performances of buildings having soft ground stories are very
poor during earthquake shaking. In most of the cases structure collapses due
to failure of ground story columns before reaching performance point.
The performance of soft ground story signifies that these are the most
vulnerable type of structure in the event of earthquake. So alternative
measures must be taken to prevent the damage of the structures.
The top and bottom parts of the column are most susceptible point because
strut action of infill imposes a concentrated load at these joints. So special
seismic detailing as recommended in the seismic code should be adopted.
84
The value of inter story drift, displacement and ductility demand are very high
in soft story.
The lateral stiffness of soft story is very less than that of the stories above.
Although the seismic performance of bare frame buildings are better than soft
story structure but these type structures are not present.
The capacity curve of bare frame structure meets the demand curve but it has
to displace a lot more than their elastic limit.
The displacement and inter story drift of bare frame are uniform throughout
the structure because no change in stiffness throughout the story.
5.3 RECOMMENDATIONS FOR FUTURE STUDY
This research has been carried out over reinforced concrete structure of regular
geometry. Number of bays and span remain same from six to twelve stories. The
condition of soft story was considered only at the bottom story. No remedial measures
have been discussed. Considering the limitations, the following recommendations for
future study may be suggested:
The thesis is concentrated only on the reinforced concrete structure. Further
analysis can be done on steel structure.
Effect of the presence of soft story on different level of structure can be
investigated.
Studies can be performed on existing old reinforced concrete structure to
improve their performance against earthquake by adding shear wall, bracing
etc.
Base isolation is an effective technique to reduce earthquake demand. Further
studies can be performed to see the effect of it at the performance point.
The research can be extended considered structures higher than twelve stories
for finding out the appropriate remedial measures for taller structures.
Retrofit design of existing structure can be investigated.
Finding out remedial measures and verification of the selected measures can
be done to extend the study.
85
REFERENCES
ACI Committee 318, (2002) Building Code Requirement for Structural Concrete,
American Concrete Institute, Detroit.
ATC (1996) Seismic Evaluation and and Retrofit of Concrete Building (Volume 1).
Report (ATC-40), Applied Technology Council, California, USA.
BNBC (1993) Bangladesh National Building Code, Housing and Building Research
Institute, Mirpur, Dhaka, Bangladesh.
IS-1893 (2002) Bureau of Indian Standards, Indian Standard Criteria for Earthquake
Resistant Design of Structures-Part-1: General Provisions and Buildings (Fifth
revision), New Delhi, India
Chopra, A.K (2003) Dyanmics of structure- Theory and application of Earthquake
Engineering, Second Edition, Prentice-Hall of India, New Delhi, India.
Computer and Structures Inc. ETABS Nonlinear Version 9.7, California, USA.
FEMA 356, 273. (2002) Pre-standard and Commentary for the Seismic Rehabilitation
of Buildings, Federal Emergency Management Agency, Washington D.C., USA.
Stafford-Smith, B., “ Lateral Stiffness of In-filled Frames” Journal of the structural
Division, ASCE, vol. 92, December 1962.
Stafford-Smith, B., “ Behavior of square In-filled Frames” Journal of the structural
Division, ASCE, vol. 92, December 1966.
Stafford-Smith, B. and C.Carter, “A Method of Analysis for Infill Frames.”
Proceedings of the institution of Civil Engineers, vol. 44, 1969.
86
Amanat, K. M. and Hoque, E. (2006) “A Rationale for Determining the natural
period of RC Building FramesHaving Infill” Engineering Structures, Vol.28, pp. 495-
502.
Rahman, “S.M. Enhancement of Seismic Performance of Soft Ground Story RCC
Structures.” .” B.Sc Engg. Thesis, Department of Civil Engineering, Bangladesh
University of Engineering and Technology.
Shahrin R. (2009) “Seismic Performance Evaluation of RC Buildings by Pushover
Analysis.” B.Sc Engg. Thesis, Department of Civil Engineering, Bangladesh
University of Engineering and Technology.
Tasmim R. (2011), “Effect on Base Shear Under Seismic Load for Masonry Infilled
RC Soft Story Buildings.” .” B.Sc Engg. Thesis, Department of Civil Engineering,
Bangladesh University of Engineering and Technology.
87
APPENDIX
88
89
90
91
92
Manual Calculation
Calculation of Equivalent Strut Width:
Sample calculations of equivalent strut width are shown below-
A frame having 3m vertical height from floor to floor, beam thickness of 508 mm or
20inch is considered. In horizontal direction the center to center distance is 6m and
the column size is 457mm x 457 mm or 18” x 18” in cross section.
Icol= (18x 18^3)/ 12 = 8748 inch^4
H= 120 inch
hm= Clear height from floor top to beam bottom
= 120-20 = 100 inch
Ec = 2900 ksi
Em= 1260ksi
l = 20*12- 20 = 220 inch
t = thickness of the infill wall = 5 inch
D = √ (H^2 + l^2) = 241.66 inch
Tanθ = (100/220) => θ = 24.44 deg.
λ1H = H ((Em t sin 2θ)/ (4 Ec I col hm)) 0.25
λ1H = 3.144
a = 0.175 D (λ1H)-0.4 => a = 26.44 inch
tanθ column = (hm - a/ cosθ column ) / l => θcol = 18.2deg
l column = a/(cosθ column) => l column = 27.8inch A typical calculation of reduced demand spectrum (ADRS format) is done below-
93
Calculation is done for 12 storied structure (Plan A) with 60% infill. βeff = 11.2% (from ETABS)
SRA = (3.21- 0.681ln βeff) / 2.12 = 0.738
SRv = (2.31-0.41ln βeff)/ 1.65 = 0.799
As shown in table 4.18.
CA= SRA* 0.7/2.5 = 0.207
Cv = SRv * 0.5/0.3 = 0.344
Peak, SA= 2.5 CA = 0.525 (g)
Ts = Cv/ (2.5 CA) = 0.665 sec.
Ta= 0.2 Ts = 0.133 sec.
At T = 1 sec , Spectral Acceleration, Sa (g)= Cv/ T = 0.344 (g)s
Spectral Displacement, Sd = T^2* Sa * 9810 /(4* 3.14 ^2) = 85.48 mm