Evaluation of Response Modification Factor for
Shear wall-Flat plate Structural Systems
by
Md. Nazmul Alam
MASTER OF ENGINEERING IN CIVIL AND STRUCTURAL ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
March, 2018
Evaluation of Response Modification Factor for
Shear wall-Flat plate Structural Systems
by
Md. Nazmul Alam
Submitted to the Department of Civil Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka
in partial fulfilment of the requirements for the degree of
MASTER OF ENGINEERING IN CIVIL AND STRUCTURAL ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY
March, 2018
iii
DEDICATION
This Thesis is Dedicated to My Parents
iv
DECLARATION
It is hereby declared that, except where specific references are made, the work embodied
in this project is the result of investigation carried out by the author under the supervision
of Dr. Raquib Ahsan, Professor, Department of Civil Engineering, BUET.
Neither the thesis nor a part of it is concurrently submitted elsewhere for the award of any
degree or diploma.
(Md. Nazmul Alam)
v
ACKNOWLEDGEMENTS
First of all the author would like to give thanks to almighty Allah who is very kind to
allow completing this thesis effectively.
The author expresses his profound gratitude and heartiest thanks to his thesis supervisor
Professor Dr. Raquib Ahsan, Department of Civil Engineering, Bangladesh University
of Engineering and Technology (BUET) for his constant guidance, supervision, keen
interest as well as resource management in making this project a success. His helpful
guidance has benefited the author greatly.
The author is grateful to the members of thesis defence committee Dr. Ahsanul Kabir,
Dr. Tahsin Reza Hossain and Dr. Mohammad Al Amin Siddique for their advice and
help in reviewing this thesis.
The author expresses his deepest gratitude to Dr. Iftekhar Anam, Professor, Department
of Civil Engineering, University of Asia Pacific (UAP), for his neverending support
over the years. The author is very thankful to the associates of Engineering & Research
Associates Limited (ERA) for their cooperation and spending their valuable time in
aiding the author in his research.
The author is very grateful to his family members and friends for their unconditional
love, encouragement, blessings and cooperation.
vi
ABSTRACT
Flat Plate (FP) structures are not suitable for use in zones of high seismicity due to their
subpar performance in lateral loads. However architectural and functional benefits from
adopting this system have contributed to the popularity of flat plates in our country.
Recently shear walls are bring used alongside columns in flat plate structures to make
structures stiffer and more resistant to seismic loading.
Shear Wall – Flat Plate (SW-FP) structural systems are still undefined in building codes
since their seismic behavior is little understood. The principle aim of this research is to
study the nonlinear behavior of SW-FP systems under design basis earthquakes (DBE)
in moderate seismic zones and figuring out the response modification factor for SW-
FP structures.
To understand the nonlinear behavior of structures, nonlinear static or pushover
analyses were performed for SW-FP systems. Performance of the buildings, e.g.
maximum displacement, base shear capacity, hinge formation were measured
according to ASCE 41 ‘Displacement Coefficient Method’ and FEMA 440 EL
‘Capacity Spectrum Method’.
Response Modification Factor defines the level of inelasticity expected in structural
systems during an earthquake event. It is used to reduce the design forces in earthquake
resistant design and accounts for damping, energy dissipation capacity and over
strength of the structure.
The value of response modification factor for SW-FP systems could not be found in
many of the widely adopted building codes. Upon performing extensive analyses,
response modification factor for SW-FP systems and FP systems have been suggested
in the ranges of 6 – 7 and 4 – 5 respectively. The value suggested can be used in design
and further researches should be carried out to adopt that value in building codes.
vii
TABLE OF CONTENTS
DEDICATION ...................................................................................................................... iii
DECLARATION .................................................................................................................. iv
ACKNOWLEDGEMENTS ................................................................................................... v
ABSTRACT .......................................................................................................................... vi
TABLE OF CONTENTS ..................................................................................................... vii
LIST OF FIGURES ............................................................................................................... x
LIST OF TABLES .............................................................................................................. xiii
CHAPTER 1 INTRODUCTION ........................................................................................... 1
1.1 General.......................................................................................................... 1
1.2 Background of the Study .............................................................................. 1
1.3 Objectives of the Research ........................................................................... 2
1.4 Methodology ................................................................................................. 2
1.5 Scope of the Work ........................................................................................ 2
1.6 Organization of the Thesis ............................................................................ 2
CHAPTER 2 LITERATURE REVIEW ................................................................................ 4
2.1 Introduction .................................................................................................. 4
2.2 Nonlinear Static or Pushover Analysis (NLSA) Procedure .......................... 4
2.2.1 Capacity spectrum method (CSM) ............................................................... 5
2.2.2 Displacement coefficient method (DCM) .................................................... 6
2.2.3 Nonlinear static analysis (NLSA) procedures adopted by ASCE 41-13 ...... 8
2.3 Response Modification Factor (R) ............................................................. 11
2.3.1 Definition of R factor and its components .................................................. 12
2.3.2 Background of response modification factor .............................................. 15
2.3.3 Response modification factor in Bangladesh National Building Code ...... 18
2.4 Shear Wall-Flat Plate Structural System .................................................... 22
2.4.1 Shear wall structures ................................................................................... 23
2.4.2 Previous study on shear wall structures ...................................................... 23
2.4.3 Flat plate structures ..................................................................................... 29
2.4.4 Previous study on flat plate structures ........................................................ 29
viii
2.4.5 Previous study on shear wall-flat plate structural systems ......................... 34
2.5 Conclusion Drawn from the Literature Review ......................................... 35
CHAPTER 3 NUMERICAL MODELING ......................................................................... 36
3.1 Introduction ................................................................................................ 36
3.2 Linear Static Analysis (LSA) ..................................................................... 36
3.2.1 Design considerations ................................................................................. 36
3.2.2 Design outputs ............................................................................................ 40
3.3 Nonlinear Static or Pushover Analysis (NLSA) ......................................... 40
3.3.1 Load and deformation Criteria ................................................................... 44
3.3.2 Modeling Criteria and hinge properties ...................................................... 45
3.3.3 Effective stiffness for crack section model ................................................. 47
CHAPTER 4 RESULTS ...................................................................................................... 48
4.1 Introduction ................................................................................................ 48
4.2 Structural Performance from Linear Static Analysis .................................. 48
4.3 Structural Performance from Nonlinear Linear Static Analysis ................. 50
4.3.1 Capacity curve (base shear vs top deflection) ............................................ 50
4.3.2 Plastic hinge state at performance point ..................................................... 53
4.3.3 Summary of base shear and maximum top displacement ........................... 61
4.3.4 Base shear and top deflection ..................................................................... 62
4.4 Evaluation of Response Modification Factor (R value) ............................. 67
4.4.1 Reduction factor (R) .................................................................................. 67
4.5 Effect of Mesh Sensitivity in Evaluating R ................................................ 71
CHAPTER 5 CONCLUSIONS AND SUGGESTIONS ..................................................... 72
5.1 Introduction ................................................................................................ 72
5.2 Findings ...................................................................................................... 72
5.3 Suggestions ................................................................................................. 73
REFERENCES ..................................................................................................................... 74
APPENDIX A ...................................................................................................................... 80
DESIGN OUTPUT FROM LINEAR STATIC ANALYSIS .............................................. 80
Annexure A1: Model-1 Design Outputs. ..................................................................... 80
APPENDIX B ...................................................................................................................... 86
MODELING PARAMETERS FOR NON-LINEAR STATIC ANALYSIS ....................... 86
ix
Annexure B1: Models Layouts Used in NLSA ........................................................... 86
Annexure B2: Effective Beam Width (Equivalent to FP) Details of Model 1, 2 and 3
95
Annexure B3: Modeling Parameters and Acceptance Criteria for NLSA ................... 96
APPENDIX C .................................................................................................................... 106
base shear and maximum top displacement ....................................................................... 106
Annexure C1: Summary of Base Shear and Maximum Top Displacement .............. 106
x
LIST OF FIGURES
Figure 2.1: Determination of performance point according to capacity spectrum method. ...... 5
Figure 2.2: Determination of performance point by displacement coefficient method ............. 7
Figure 2.3: Force-deformation relation for plastic hinge ........................................................... 9
Figure 2.4: Idealized force-deformation curve ........................................................................ 11
Figure 2.5: Force displacement response of elastic and inelastic systems .............................. 12
Figure 2.6: Relationship between force reduction factor (R), structural overstrength (0), and
ductility reduction factor (Rµ) .................................................................................................. 14
Figure 2.7: Use of R factors to reduce elastic spectral demands to the design force level (ATC
19). ........................................................................................................................................... 18
Figure 3.1: Typical floor layout of SW-FP structure ............................................................... 37
Figure 3.2: Model 2 flat plate extent, shear wall and column layout ....................................... 42
Figure 3.3: Model 3 flat plate extent, shear wall and column layout ....................................... 43
Figure 3.4: BNBC 1993 response spectrum curve .................................................................. 44
Figure 3.5: Load-deformation relationship .............................................................................. 44
Figure 3.6: Modeling of slab-column connection .................................................................... 46
Figure 3.7: Plastic hinge rotation in shear wall where flexure dominates inelastic response
(Figure 10-4: ASCE 41-13) ..................................................................................................... 46
Figure 3.8: Story drift in shear wall where shear dominates inelastic response (Figure 10-5:
ASCE 41-13) ............................................................................................................................ 47
Figure 4.1: Maximum story displacement ............................................................................... 48
Figure 4.2: Story drift .............................................................................................................. 48
Figure 4.3: Story shear ............................................................................................................. 49
Figure 4.4: Story stiffness ........................................................................................................ 49
Figure 4.5: Capacity curve for M-1, M-2 and M-3 varying story height ................................. 51
Figure 4.6: Capacity curve for M-1, M-2 and M-3 varying story height ................................. 51
Figure 4.7: Capacity curve for M-1, M-2 and M-3 varying story height ................................. 52
Figure 4.8: Capacity curve for M-1, M-2 and M-3 varying story height ................................. 52
Figure 4.9: plastic hinges formed at performance point for model M-1.1.1 ............................ 55
Figure 4.10: plastic hinges formed at performance point for model M-1.1.1 (elevation 3) in x-
direction ................................................................................................................................... 55
xi
Figure 4.11: plastic hinges formed at performance point for model M-1.1.1 (3D view) in y-
direction ................................................................................................................................... 56
Figure 4.14: plastic hinges formed at performance point for model M-2.1.1 (elevation C) in x-
direction ................................................................................................................................... 57
Figure 4.15: plastic hinges formed at performance point for model M-2.1.1 (3D view) in y-
direction ................................................................................................................................... 58
Figure 4.16: plastic hinges formed at performance point for model M-2.1.1 (elevation C) in y-
direction ................................................................................................................................... 58
Figure 4.17: plastic hinges formed at performance point for model M-3.1.1 (3D view) in x-
direction ................................................................................................................................... 59
Figure 4.18: plastic hinges formed at performance point for model M-3.1.1 (elevation C) in x-
direction ................................................................................................................................... 59
Figure 4.19: plastic hinges formed at performance point for model M-3.1.1 (3D view) in y-
direction ................................................................................................................................... 60
Figure 4.20: plastic hinges formed at performance point for model M-3.1.1 (elevation C) in y-
direction ................................................................................................................................... 60
Figure 4.21: Base shear capacity (x-direction) chart ............................................................... 63
Figure 4.22: Base shear capacity (y-direction) chart ............................................................... 63
Figure 4.23: Top deflection (x-direction) chart (f'c= 3 ksi, fy= 60 ksi) ................................... 64
Figure 4.24: Top deflection (y-direction) chart (f'c= 3 ksi, fy= 60 ksi) ................................... 64
Figure 4.25: Base shear capacity (x-direction) chart ............................................................... 65
Figure 4.26: Base shear capacity (y-direction) chart ............................................................... 65
Figure 4.27: Top deflection (y-direction) chart ....................................................................... 66
Figure 4.28: Top deflection (y-direction) chart ....................................................................... 66
Figure 4.29: Strength reduction factor chart (x-direction) ....................................................... 67
Figure 4.30: Strength reduction factor chart (y-direction) ....................................................... 68
Figure 4.31: Overstrength factor chart (x-direction) ................................................................ 68
Figure 4.32: Overstrength factor chart (y-direction) ................................................................ 69
Figure 4.33: Response modification factor chart (x-direction) ................................................ 69
Figure 4.34: Response modification factor chart (y-direction) ................................................ 70
Figure A-3.1: Grid, shear wall and column layout .................................................................. 80
Figure A-3.2: Grade beam layout ............................................................................................ 81
Figure A-3.3: Floor beam and flat plate layout (F1-F5) .......................................................... 82
Figure A-3.4: Floor beam and flat plate layout (F6-Roof) ...................................................... 83
xii
Figure B-3.1: Model 1 flat plate extent, shear wall and column layout ................................... 86
Figure B-3.2: Model 1 effective beam width (eqt to flat plate) layout (F1-F5) ....................... 87
Figure B-3.3: Model 1 effective beam width (eqt to flat plate) layout (F6-Roof) ................... 88
Figure B-3.4: Model 2 flat plate extent, shear wall and column layout ................................... 89
Figure B-3.5: Model 2 effective beam width (eqt to flat plate) layout (F1-F5) ....................... 90
Figure B-3.6: Model 2 effective beam width (eqt to flat plate) layout (F6-Roof) ................... 91
Figure B-3.7: Model 3 flat plate extent, shear wall and column layout ................................... 92
Figure B-3.8: Model 3 effective beam width (eqt to flat plate) layout (F1-F5) ....................... 93
Figure B-3.9: Model 3 effective beam width (eqt to flat plate) layout (F6-Roof) ................... 94
xiii
LIST OF TABLES
Table 2.1: Determination of performance point by ATC 40 and FEMA 440 CSM .................. 5
Table 2.2: Determination of performance point by FEMA356 and FEMA440 DCM .............. 7
Table 2.3: Values of modification factor C0 (Table 7.5: ASCE 41-13) ................................... 10
Table 2.4: Response modification factor as per BNBC 2015 .................................................. 19
Table 2.5: Response modification factor as per BNBC 1993 .................................................. 20
Table 3.1: Model types and their ID ........................................................................................ 41
Table 3.2: Effective stiffness values as per ASCE 41-13 (Table 10.5) ................................... 47
Table 4.1: Summary table of plastic hinge states at performance point .................................. 53
Table 4.2: Displacement at performance point ........................................................................ 61
Table 4.3: Statistical analysis of response modification factor ................................................ 70
Table 4.4: Value of R considering mesh sensitivity (M-1.2.1) ................................................ 71
Table A-3.1: Column details .................................................................................................... 84
Table A-3.2: Shear wall details ................................................................................................ 84
Table A-3.3: Beam details ....................................................................................................... 84
Table A-3.4: Slab details.......................................................................................................... 85
Table B-3.1: Model 1 to model 3 effective beam width (eqt to flat plate) details ................... 95
Table B-3.2: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—reinforced concrete beams .................................................................................. 96
Table B-3.3: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—reinforced concrete columns .............................................................................. 97
Table B-3.4: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—two-way slabs and slab–column connections ..................................................... 99
Table B-3.5: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure ................... 100
Table B-3.6: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure ................... 101
Table B-3.7: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure ................... 102
Table B-3.8: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure ................... 103
xiv
Table B-3.9: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure ................... 104
Table B-3.10: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure ................... 105
Table C-4.1: Summary of base shear and maximum top displacement ................................. 106
Table C-4.2: Summary of base shear and maximum top displacement ................................. 108
CHAPTER 1
INTRODUCTION
1.1 General
Flat plate structures are getting popular in our country nowadays due to architectural
and functional requirements. Since there are no beams in the structure, story heights
can be reduced. Flat plate structures are also easy to construct because of simpler
formworks, which often prove to be cost effective. However flat plates are weaker in
lateral load and the chances of progressive collapse in a seismic event in more likely in
such structures. To impart lateral stability and enhance the seismic performance of flat
plates, shear wall are being incorporated in this system. This system is relatively
unknown and therefore requires extensive numerical and experimental analysis before
being adopted in building codes as an efficient and reliable structural system.
1.2 Background of the Study
In the equivalent linear static method, as the common method proposed in most codes
for seismic analysis of regular structures, the lateral seismic loads are reduced by
response modification factor to be indirectly taken into account for nonlinear behavior
of structures. Since response modification factor was initially introduced in the ATC 3-
06 report, much research has been carried out, and an evaluation equation for response
modification factor was proposed in ATC-19, based on these research results. The
factors of the equation can be used in quantifying the seismic performance of structures.
The shear wall-flat plate structure is an undefined seismic resistance system in the
design code. If it is demonstrated that the seismic performance of a flat plate structure
is similar to that of the seismic force–resisting systems defined in the design code, the
seismic performance factors (response modification factor, R; system over strength
factor, Ω0; Strength Reduction Factor, R) are applicable to design shear wall-flat plate
structures.
Federal Emergency Management Agency (FEMA) has recent publications to quantify
seismic response parameters and to improve non-linear static seismic design of
structures.
2
1.3 Objectives of the Research
The main objectives of this study are:
a. To determine lateral load and deformation resisting capacity of shear wall-flat plate
system by conducting nonlinear analysis as suggested in ASCE 41-13.
b. To compare lateral load capacity of such system with that obtained by linear static
analysis.
1.4 Methodology
a. Develop a finite element model using ETABS for flat plate-shear wall structural
system as per modeling criteria specified in ASCE 41-13.
b. Input non-linear hinge parameters as per ASCE 41-13 and apply loads as per BNBC
1993/2015.
c. Perform nonlinear static or pushover analysis (NLSA).
d. Observe plastic hinge formation, location of the hinges and study nonlinear
behavior and performance of the structure.
e. Evaluate response modification factor (R).
1.5 Scope of the Work
In this thesis nonlinear performance of shear wall flat plate (SW - FP) structural system
has been assessed. Different parameters like – story height (10ft, 12ft and 15ft), number
of story (7, 10 and 13), building configuration (96×174, 73.5×174 and 96×126) and
material strength (fc= 3 ksi and fy= 60 ksi; fc= 4 ksi and fy= 72 ksi)) have been also
varied in the analysis. Total 54 models have been used varying parameters. Seismic
performances of these structures analyzed here will aid researchers in establishing a
response modification factor (R) for shear wall-flat plate structural system.
1.6 Organization of the Thesis
The thesis paper is organized into total five chapters. Apart from chapter one, the
following chapters are organized as follows:
Chapter 2: A literature review is summarized the background study on nonlinear static
analysis procedure, response modification factor and performance under seismic loads
3
of shear wall structures, flat plate structures and shear wall - flat plate structural
systems.
Chapter 3: This chapter presents the numerical modeling of numerous building
structures namely shear wall-flat plate structural system (SW-FP). Basic design
consideration for linear static analysis and modeling criteria, hinge properties and
loading criteria for non-linear static analysis/pushover analysis have been discuss in
this chapter.
Chapter 4: This chapter presents structural performance from linear static analysis
(LSA) and nonlinear static analysis (NLSA). Result output, structural performance of
linear static model, non-linear behaviour of SW-FP structural system models are
summarized and compare with respect to different parameters are shown in this chapter.
Chapter 5: This chapter summarizes the research and lists out the conclusions based
on the outcome of the numerical results and recommend scopes for future studies.
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
A background study on nonlinear static analysis procedure, response modification
factor and performance under seismic load of shear wall structures, flat plate structures
and shear wall - flat plate structural systems have been summarized in this chapter.
2.2 Nonlinear Static or Pushover Analysis (NLSA) Procedure
The use of the nonlinear static or pushover analysis came in to practice in 1970s but
the potential of the pushover analysis has been recognized for last 10-15 years.
Although time history analysis (THA) is the most accurate analysis to evaluate seismic
demand, the application of NLSA is generally considered to be more appropriate for
seismic design due to its simplicity and ease of use. This method is based on assumption
that the response of the multi-degree of freedom (MDOF) structure can be related to
the response of an equivalent single degree of freedom (SDOF). This is the reason why
the NLSA is known as the most used tool in the engineering practice for assessment of
seismic behavior of structures, and currently has resulted in guidelines such as ATC-
40, FEMA-356, and FEMA-440 and standards such as ASCE 41-13.
NLSA is conducted by applying the gravity loads followed by lateral load which is
gradually increased along a direction under consideration. The investigated building is
pushed according to predefined lateral load pattern. A plot of the total base shear versus
top displacement in a structure is obtained by this analysis that would indicate any
premature failure or weakness. The analysis is carried out up to failure, thus it enables
determination of collapse load and ductility capacity. On a building frame, and plastic
rotation is monitored, and lateral inelastic forces versus displacement response for the
complete structure is analytically computed. This type of analysis enables weakness in
the structure to be identified.
5
2.2.1 Capacity spectrum method (CSM)
ATC 40 is published in 1996 by Sigmud Freeman and by Applied Technology Council
afterwards. In ATC 40, performance based analysis by capacity spectrum method is
improved. Also, it is stated that horizontal displacement demands and load carrying
capacities are related each other. This method is enhanced in FEMA 440 which is
published in 2005. Calculation of performance point is given in Figure 2.1 and Table
2.1.
Table 2.1: Determination of performance point by ATC 40 and FEMA 440 CSM
ATC 40-CSM FEMA 440-CSM
1. Any point Vi, t on the multiple degree of freedom capacity curve is converted to
corresponding point Sai, Sdi on the equilibrium single degree of freedom capacity
spectrum using the modal mass coefficient and participation factors equations.
2. A point on capacity spectrum curve is estimated as performance point and
spectrum curve is idealized with two linear lines.
3. Equivalent viscous damping is
obtained as:
0 = 63.7(aydpi - dyapi)/(apidpi)
Existing structures which don’t have
enough ductility, cannot make perfect
Values of post-elastic stiffness α and
ductility μ is calculated as follows:
= (api-ay)/(dpi-dy)/(ay/dy) and =
dpi/dy
Spectral Displacement (Sd)
Spec
tral A
ccel
erat
ion
(Sa)
Capacity Spectrum
Spectrum 5% Damped Standard Elastic Demand
T0
Te
Reduced Demand Spectrum
Performance Point
Figure 2.1: Determination of performance point according to capacity spectrum method.
6
hysteresis loops all the time. Effective
viscous damping can be calculated by
using damping modification factor. is
defined by: eff = 0 + 5
4. Spectral reduction factors are given by
SRA = 3.21 0.68 ln(eff)/2.12
SRV = 2.31 0.41 ln(eff)/1.65
Corresponding effective damping, βeff
and corresponding effective period, Teff
are calculated according to the
coefficients of FEMA 440.
5. When the displacement at the
intersection of the demand spectrum
and the capacity spectrum, di, is within
5 percent (0.95dpi ≤ di ≤1.05dpi) of the
displacement of the trial performance
point, api, dpi, dpi becomes the
performance point. If the intersection
of the demand spectrum and the
capacity spectrum is not within the
acceptable tolerance, then a new api,
dpi point is selected and the process is
repeated.
Spectral Reduction for Effective
Damping is calculated
B = 4/5.6 ln(eff)%; (Sa) = (Sa)%5
/B(eff)
The use of the effective period and
damping equations generate a maximum
displacement di that coincides with the
intersection of the radial effective period
line and the ADRS demand for the
effective damping. Max acceleration ai is
determined on the capacity curve
corresponding to the maximum
displacement, di. If it is within acceptable
tolerance, the performance point
corresponds to ai and di. If it is not within
acceptable tolerance, then a new api, dpi
point is selected and the process is
repeated.
2.2.2 Displacement coefficient method (DCM)
Displacement Coefficient Method which is defined in FEMA-356 base on capacity
curve that is obtained from static pushover analysis. In this method, the biggest
displacement demand is determined with specific coefficients. This method is enhanced
in FEMA 440 which is published in 2005. Target displacement is symbolized with t.
Calculation of performance point is given in Figure 2.2 and Table 2.2.
7
Table 2.2: Determination of performance point by FEMA356 and FEMA440 DCM
Coefficient FEMA356-DCM FEMA440-DCM
C0 The first modal participation factor at the level of the displacement
control node;
The modal participation factor at the level of the control node
calculated using a shape vector corresponding to the deflected shape
of the structure at the target displacement.
It is explained according to framing system and story number at the
table 3.2 of FEMA 356
C1 C1 =1.0 for Te T0
C1 = 1 + (T0 1)T0/Te/R0 for Te T0
C1 = 1 + (R 1)/ (aTe2)
for T<0.2 sec
C1= 1.0 for T>1.0 sec
C2 Values of C2 for different framing systems
and Structural Performance Levels shall
be obtained from Table 3-3 of FEMA 356
C2= 1 + 1/800(R 1)/T2
for T<0.2 sec C2= 1.0
for T >0.7 sec
Bas
e Sh
ear
0.6Vy
Ki Vy
Ke
Ke
y t Roof Displacement
Te = Ti (Ki/Ke) Where, Te = Effective fundamental period Ti = Elastic fundamental period Ki = Elastic lateral stiffness Ke = Effective lateral stiffness
Figure 2.2: Determination of performance point by displacement coefficient method
8
C3 C3 =1.0 for 0
C3 =1.0 abs()(R0 1)3/2/Te for 0
C3 coefficient is not taken
into consideration
2.2.3 Nonlinear static analysis (NLSA) procedures adopted by ASCE 41-13
A. Lateral load pattern
There are three lateral load pattern proposed in FEMA-356 also adopted by ASCE 41-
13, namely (a) inverted triangular distribution, (b) uniform distribution, (c) distribution
of forces proportional to fundamental mode (mode 1). Ghaffarzadeh et al. studied
response seismic demand of RC frames using NLSA procedure. The results show that
push (a) pattern and push (c) pattern yielded similar results and reasonably accurate
estimates of the maximum displacement. Although, slightly overestimate in the upper
stories, while push (b) pattern overestimate demands at the lower stories. Moreover, the
applicability lateral load pattern on evaluation of seismic deformation demands using
NLSA procedure were investigated by Kunnath and Kalkan. It was found that in all
cases, push (a) pattern provided closest results to the mean time history analysis, and
other two load patterns tend to overestimate demands at the lower stories.
B. Structural performance level
The seismic performance of a building structure is measured by the stage of damage
under certain seismic hazard in which is quantified by roof displacement and
deformation of the structural members. Figure 2.3 shows force-deformation relation for
plastic hinge in pushover analysis. This guidelines and standards previously mentioned
define force-deformation criteria for potential locations of plastic hinge. There are five
points labelled A, B, C, D, and E are used to define the force-deformation behavior of
the plastic hinge, and three points labelled IO (immediate occupancy), LS (life safety),
and CP (collapse prevention) are used to define acceptance criteria for the hinge. There
are six levels of structural performance in ASCE 41-13, i.e., Immediate occupancy (S-
1), Damage control range (S-2), Life safety (S-3), Limited safety range (S-4), Collapse
prevention (S-5), and Not considered (S-6). Two levels of seismic hazard are commonly
defined for buildings, namely (a) design basic earthquake (DBE): an earthquake with a
10% probability in 50 years of being exceeded. This is an earthquake with a 500 years
reoccurrence period, and (b) maximum considered earthquake (MCE): an earthquake
9
with a 2% probability in 50 years of being exceeded. This is an earthquake with a 2500
years reoccurrence period.
C. Procedures to determine target displacement
The displacement coefficient method documented in FEMA-440 and modified to
consider effects of strength and stiffness degradation on seismic response in FEMA
440a and adopted in the ASCE-41-13 standard. This method is accomplished by
modifying the elastic response of equivalent SDOF system with coefficient C0, C1 and
C2 is expressed as:
t = C0C1C2Sa (Te2/42) g
Where Sa is response spectrum acceleration at the effective fundamental period and
damping ratio of the building, g is acceleration due to gravity, Te is the effective
fundamental period computed from Te = Ti (Ki/Ke) in which Ki and Ke are the elastic
and effective stiffness of the building respectively in the direction under consideration
obtained by idealizing the pushover curve as a bilinear relationship.
C0 is modification factor to relate spectral displacement of an equivalent SDOF system
to the roof displacement of the building MDOF system obtained from table 2.3.
C1 is modification factor to relate expected maximum inelastic displacement to
displacement calculated for linear elastic response computed from
C1 = 1.0 Te 1.0 sec
Deformation
Force
A
B C
D E
IO CP LS
Figure 2.3: Force-deformation relation for plastic hinge
10
1 + (R 1)/(aTe2) 0.2 sec Te 1.0 sec
1 + 1/800(R 1)/Te2 Te 0.2 sec
Table 2.3: Values of modification factor C0 (Table 7.5: ASCE 41-13)
Number of
stories
Shear buildingsa Other buildings
Triangular
load pattern
Uniform
load pattern
Any
load pattern
1 1.0 1.0 1.0
2 1.2 1.15 1.2
3 1.2 1.2 1.3
5 1.3 1.2 1.5
10+ 1.3 1.2 1.5
Note: Linear interpolation shall be used to calculate intermediate values. a Buildings in which, for all stories, story drift decreases with increasing height.
where a is equal to 130 for soil site class A and B, 90 for soil site class C, and 60 for
soil site classes. D, E, and F, and R is the ratio of elastic and yield strengths is given
as follows: R = SaCm/(Vy/W) in which Vy is the yield strength estimated from pushover
curve, W is the effective seismic weight, and Cm is the effective modal mass factor at
the fundamental mode of the building.
C2 is modification factor to represent the effect of pinched hysteretic shape, stiffness
degradation, and strength deterioration on maximum displacement response computed
from
C2 = 1.0 Te 0.7 sec
1 + 1/800(R 1)/Te2 Te 0.7 sec
To avoid dynamic instability, ASCE 41-13 limit the R value as RRmax = d/y +
abs(e)-h/4; h = 1.0 + 0.15 ln(Te) in which d is the deformation corresponding to peak
strength, y is the yield deformation, and e is the effective negative post yield slope
given by e = p- + (2 p-) where 2 is the negative post yield slope ratio and p-
is the negative slope ratio caused by p- effects defined in Figure 2.4, and λ is the
11
near-field effect factor given as 0.8 for S1 0.6 and 0.2 for S1 0.6 [S1 is defined as the
1 second spectral acceleration for the maximum considered earthquake].
2.3 Response Modification Factor (R)
Design requirements for lateral loads, such as winds or earthquakes, are inherently
different from those for gravity (dead and live) loads. Due to frequency of loading
scenario, design for wind loads is a primary requirement. But in areas of high
seismicity, structures are also designed to withstand seismic lateral actions. Since the
seismic design deals with events with lower probability of occurrence, it may therefore
be highly uneconomical to design structures to withstand earthquakes for the
performance levels used for wind design. For example, building structures would
typically be designed for lateral wind loads in the range of 1% to 3% of their weight.
Earthquake loads may reach 30%-40% of the weight of the structure, applied
horizontally. If concepts of elastic design normally employed for primary loads are used
for earthquake loads, the result will be in the form of extremely heavy and expensive
structures. Therefore, seismic design uses the concepts of controlled damage and
collapse prevention.
Displacement
Base shear Vd
p Ke
d
Vy
0.6Vy e Ke
2 Ke
1 Ke
Ke y
Figure 2.4: Idealized force-deformation curve
(Figure 7.3: ASCE 41-13)
12
In earthquake engineering, the aim is to have a control on the type, location and extent
of the damage along with detailing process. This is illustrated in Figure 2.5, where the
elastic and inelastic responses are depicted, and the concept of equal energy (discussed
further in subsequent sections) is employed to reduce the design force from Ve to Vd
(denoting elastic and design force levels).
2.3.1 Definition of R factor and its components
As already discussed, R factors are essential seismic design tools, which defines the
level of inelasticity expected in structural systems during an earthquake event. The
commentary to the NEHRP provisions defines R factor as “…factor intended to account
for both damping and ductility inherent in structural systems at the displacements great
enough to approach the maximum displacement of the systems.” This definition
provides some insight into the understanding of the seismic response of buildings and
the expected behavior of a code-compliant building in the design earthquake. R factor
reflects the capability of structure to dissipate energy through inelastic behavior. R
factor is used to reduce the design forces in earthquake resistant design and accounts
for damping, energy dissipation capacity and for over-strength of the structure.
Linear elastic response
Idealized yield roof displacement
Nonlinear response
Design level
Roof displacement () max
Ve
Vy
Vd
w y
Bas
e sh
ear (
V)
Figure 2.5: Force displacement response of elastic and inelastic systems
13
Conventional seismic design procedures adopt force-based design criteria as opposed
to displacement-based. The basic concept of the latter is to design the structure for a
target displacement rather than a strength level. Hence, the deformation, which is the
major cause of damage and collapse of structures subjected to earthquakes, can be
controlled during the design. Nevertheless, the traditional concept of reducing the
seismic forces using a single reduction factor, to arrive at the design force level, is still
widely used. This is because of the satisfactory performance of buildings designed to
modern codes in full-scale tests and during recent earthquakes.
In order to justify this reduction, seismic codes rely on reserve strength and ductility,
which improves the capability of the structure to absorb and dissipate energy. Hence,
the role of the force reduction factor and the parameters influencing its evaluation and
control are essential elements of seismic design according to codes. The values assigned
to the response modification factor (R) of the US codes (FEMA, UBC) are intended to
account for both reserve strength and ductility (ATC). Some literature also mentions
redundancy in the structure as a separate parameter. But in this study, redundancy is
considered as a parameter contributing to overall strength, contrary to the proposal of
ATC-19, splitting R into three factors: strength, ductility and redundancy.
The philosophy of earthquake resistant design is that a structure should resist
earthquake ground motion without collapse, but with some damage. Consistent with
this philosophy, the structure is designed for much less base shear forces than would be
required if the building is to remain elastic during severe shaking at a site. Such large
reductions are mainly due to two factors: (1) the ductility reduction factor (Rµ ), which
reduces the elastic demand force to the level of the maximum yield strength of the
structure, and (2) the overstrength factor, (0), which accounts for the over strength
introduced in code-designed structures. Thus, the response reduction factor (R) is
simply 0 times Rµ. See Figure 2.6.
14
A. Ductility reduction factor (Rµ)
The ductility reduction factor (Rµ) is a factor which reduces the elastic force demand to
the level of idealized yield strength of the structure and, hence, it may be represented
as the following equation: Rµ = Ve / Vy where Ve is the max base shear coefficient if the
structure remains elastic. The ductility reduction factor (Rµ) takes advantage of the
energy dissipating capacity of properly designed and well-detailed structures and,
hence, primarily depends on the global ductility demand, µ, of the structure (µ is the
ratio between the maximum roof displacement and yield roof displacement . Newmark
and Hall made the first attempt to relate Rµ with µ for a single degree of freedom
(SDOF) system with elastic perfectly plastic (EPP) resistance curve. They concluded
that for a structure of a natural period less than 0.2 second (short period structures), the
ductility does not help in reducing the response of the structure. Hence, for such
structures, no ductility reduction factor should be used. For moderate period structures,
corresponding to the acceleration region of elastic response spectrum T = 0.2 to 0.5 sec
Elastic strength
Actual strength
Design strength
Top displacement
Idealized envelope
Actual capacity envelope
y u
Vy
Vd
0.75Vy
Ve
R =
R×
R =
Ve/V
y
=
Vy/V
d
Bas
e sh
ear
(V)
Figure 2.6: Relationship between force reduction factor (R), structural overstrength (0), and ductility reduction factor (Rµ)
15
the energy that can be stored by the elastic system at maximum displacement is the
same as that stored by an inelastic system. For relatively long-period structures of the
elastic response spectrum, Newmark and Hall concluded that inertia force obtained
from an elastic system and the reduced inertia force obtained from an inelastic system
cause the same maximum displacement. This gives the value of ductility reduction
factor in a mathematical representation as: Rµ = µ B. Structural overstrength (0)
Structural over strength plays an important role in collapse prevention of the buildings.
The overstrength factor (0) may be defined as the ratio of actual to the design lateral
strength: 0 = Vy / Vd where Vy is the base shear coefficient corresponding to the actual
yielding of the structure; Vd is equivalent to the code prescribed unfactored design base
shear coefficient.
The inertia force due to earthquake motion, at which the first significant yield in a
reinforced concrete structure starts, may be much higher than the prescribed unfactored
base shear force because of many factors such as (1) the load factor applied to the code
prescribed design seismic force; (2) the lower gravity load applied at the time of the
seismic event than the factored gravity loads used in design; (3) the strength reduction
factors on material properties used in design; (4) a higher actual strength of materials
than the specified strength; (5) a greater member sizes than required from strength
considerations; (6) more reinforcement than required for the strength; and (7) special
ductility requirements, such as the strong column-weak beam provision. Even
following the first significant yield in the structure, after which the stiffness of the
structure decreases, the structure can take further loads. This is the structural over
strength which results from internal forces distribution, higher material strength, strain
hardening, member oversize, reinforcement detailing, effect of nonstructural elements,
strain rate effects.
2.3.2 Background of response modification factor
The seismic design of buildings in the United States is based on proportioning members
of the seismic framing system for actions determined from a linear analysis using
prescribed lateral forces. Lateral force values are prescribed at either the allowable
16
(working) stress or the strength level. The Uniform Building Code 91 prescribes forces
at the allowable stress level and the NEHRP Recommended Provisions for the
development of seismic regulations for new buildings, hereafter denoted as the NEHRP
Provisions prescribes forces at the strength level. The seismic force values used in the
design of buildings are calculated by dividing forces that would be associated with
elastic response by a response modification factor, often symbolized as R.
In 1957, a committee of the Structural Engineers Association of California (SEAOC)
began development of a seismic code for California. This effort resulted in the SEAOC
Recommended Lateral Force Requirements (also known as the SEAOC Blue Book)
being published in 1959. Commen-tary to the requirements was first issued in 1960.
These recommendations represented the profession's state-of-the-art knowledge in the
field of earthquake engineering; the seismic design requirements in the 1959 Blue Book
were significantly different from previous seismic codes in the United States. For the
first time the calculation of the minimum design base shear explicitly considered the
structural system type. The equation given for base shear was V = KCW where K was
a horizontal force factor (the predecessor of R and Rw); C was a function of the
fundamental period of the building; and W was the total dead load. The K factor was
assigned values of 1.33 for a bearing wall building, 0.80 for dual systems, 0.67 for
moment resisting frames, and 1.00 for framing systems not previously classified.
The seismic provisions in the 1961 UBC were adopted from the 1959 Bluebook.
Seismic zonation was considered through the use of a Z factor. The minimum design
base shear in the 1961 UBC was calculated as: V = ZKCW
Response modification factors were first proposed by the Applied Technology Council
(ATC) in the ATC-3-06 report published in 1978. The NEHRP Provisions, first
published in 1985, are based on the seismic design provisions set forth in ATC-3-06.
Similar factors, modified to reflect the allowable stress design approach, were adopted
in the Uniform Building Code (UBC) a decade later in 1988.
R factors were intended to reflect reductions in design force values that were justified
on the basis of risk assessment, economics, and nonlinear behavior.
17
The intent was to develop R factors that could be used to reduce expected ground
motions presented in the form of elastic response spectra to lower design levels by
bringing modern structural dynamics into the design process. Figure 2.7 illustrates the
use of R factors to reduce elastic spectral demands to design force levels. R is the
denominator of the base shear equation. The end result was that R factors were inversely
proportional to the K factors used in previous codes. The base shear equation for
structures for which the period of vibration of the building T was not calculated took
form: V = 2.5 AaW/R where V is the seismic base shear force, Aa is the effective peak
acceleration of the design ground motion (expressed as a fraction of g), R is the response
modification factor and W the total reactive weight The factor of 2.5 is a dynamic
amplification factor that represents the tendency for a building to amplify accelerations
applied at the base.
In the figure: 2.7, each point on the elastic response spectrum for a rock site (top curve)
is divided by R to produce the design spectrum (bottom curve) for a given structure
type, in this case a special moment resisting space frame, where R= 8.
Values for structural response modification factors for allowable stress design (Rw)
were determined by the Seismology Committee of the Structural Engineers Association
of California (SEAOC) and published in the 1988 Blue Book. SEAOC elected to
introduce Rw, rather than R, to ease the eventual transition from allowable-stress design
to strength design.
18
Similar to R, Rw is inversely proportional to K. The 1988 Blue Book and 1994 UBC use
an alternative equation for calculating VD namely VD = ZICW/Rw where Z and I are the
seismic zone and importance factors, respectively. The factor C has a maximum value
of 2.75 and is defined as: C = 1.25 S/T0.67 where S is a site coefficient and T is the
fundamental period of vibration.
2.3.3 Response modification factor in Bangladesh National Building Code
Response modification factor (R value) for various structural systems as per BNBC
1993 and BNBC 2015 are tabulated in this section as follows:
ATC 3-06 elastic response spectrum for a rock site and 5% damping
Design spectrum for a special moment resisting space frame (R = 8)
Nor
mal
ized
spec
tral a
ccel
erat
ion
(g)
Period (seconds)
1
0
Figure 2.7: Use of R factors to reduce elastic spectral demands to the design force level (ATC 19).
19
Table 2.4: Response modification factor as per BNBC 2015
Seismic Force–Resisting System
Response
Reduction
Factor, R
A. BEARING WALL SYSTEMS (no frame)
1. Special reinforced concrete shear walls 5
2. Ordinary reinforced concrete shear walls 4
3. Ordinary reinforced masonry shear walls 2
4. Ordinary plain masonry shear walls 1.5
B. BUILDING FRAME SYSTEMS (with bracing or shear wall)
1. Steel eccentrically braced frames, moment resisting connections
at columns away from links 8
2. Steel eccentrically braced frames, non-moment-resisting,
connections at columns away from links 7
3. Special steel concentrically braced frames 6
4. Ordinary steel concentrically braced frames 3.25
5. Special reinforced concrete shear walls 6
6. Ordinary reinforced concrete shear walls 5
7. Ordinary reinforced masonry shear walls 2
8. Ordinary plain masonry shear walls 1.5
C. MOMENT RESISTING FRAME SYSTEMS (no shear wall)
1. Special steel moment frames 8
2. Intermediate steel moment frames 4.5
3. Ordinary steel moment frames 3.5
4. Special reinforced concrete moment frames 8
5. Intermediate reinforced concrete moment frames 5
6. Ordinary reinforced concrete moment frames 3
D. DUAL SYSTEMS: SPECIAL MOMENT FRAMES
CAPABLE OF RESISTING AT LEAST 25% OF
PRESCRIBED SEISMIC FORCES (with bracing or shear wall)
20
1. Steel eccentrically braced frames 8
2. Special steel concentrically braced frames 7
3. Special reinforced concrete shear walls 7
4. Ordinary reinforced concrete shear walls 6
E. DUAL SYSTEMS: INTERMEDIATE MOMENT FRAMES
CAPABLE OF RESISTING AT LEAST 25% OF
PRESCRIBED SEISMIC FORCES (with bracing or shear wall)
1. Special steel concentrically braced frames 6
2. Special reinforced concrete shear walls 6.5
3. Ordinary reinforced masonry shear walls 3
4. Ordinary reinforced concrete shear walls 5.5
F. DUAL SHEAR WALL-FRAME SYSTEM: ORDINARY
REINFORCED CONCRETE MOMENT FRAMES AND
ORDINARY REINFORCED CONCRETE SHEAR WALLS
4.5
G. STEEL SYSTEMS NOT SPECIFICALLY DETAILED FOR
SEISMIC RESISTANCE 3
Table 2.5: Response modification factor as per BNBC 1993
Seismic Force–Resisting System
Response
Reduction
Factor, R
A. BEARING WALL SYSTEM
1. Light framed walls with shear panels
a. Plywood walls for structures, 3 storeys or less 8
b. All other light framed walls 6
2. Shear walls
a. Concrete 6
b. Masonry 6
3. Light steel framed bearing walls with tension only bracing 4
21
4. Braced frames where bracing carries gravity loads
a. Steel 6
b. Concrete 4
c. Heavy timber 4
B. BUILDING FRAME SYSTEM
1. Steel eccentric braced frame (EBF) 10
2. Light framed walls with shear panels
a. Plywood walls for structures 3-storeys or less 9
b. All other light framed walls 7
3. Shear walls
a. Concrete 8
b. Masonry 8
4. Concentric braced frames (CBF)
a. Steel 8
b. Concrete 8
c. Heavy timber 8
C. MOMENT RESISTING FRAME SYSTEM
1. Special moment resisting frames (SMRF)
a. Steel 12
b. Concrete 12
2. Intermediate moment resisting frames (IMRF), concrete 8
3. Ordinary moment resisting frames (OMRF)
a. Steel 6
b. Concrete 5
D. DUAL SYSTEM
1. Shear walls
a. Concrete with steel or concrete SMRF 12
b. Concrete with steel OMRF 6
c. Concrete with concrete IMRF 9
d. Masonry with steel or concrete SMRF 8
22
e. Masonry with steel OMRF 6
f. Masonry with concrete IMRF 7
2. Steel EBF
a. With steel SMRF 12
b. With steel OMRF 6
3. Concentric braced frame (CBF)
a. Steel with steel SMRF 10
b. Steel with steel OMRF 6
c. Concrete with concrete SMRF 9
d. Concrete with concrete IMRF 6
E. SPECIAL STRUCTURAL SYSTEMS -
2.4 Shear Wall-Flat Plate Structural System
Reinforced concrete flat plate is a type of structural system containing slabs with
uniform thickness supported directly on columns without using beams. Shear walls are
vertical elements of the horizontal force resisting system. Flat-slab building structures
exhibit significant higher flexibility compared with traditional frame structures, and
shear walls (SWs) are vital to limit deformation demands under earthquake excitations.
Flat-slab building structure is widely used due to the many advantages it possesses over
conventional moment-resisting frames. It provides lower building heights, unobstructed
space, architectural flexibility, easier formwork, and shorter construction time.
However, it suffers low transverse stiffness due to lack of deep beams and/or shear
walls (SWs). This may lead to potential damage even when subjected to earthquakes
with moderate intensity. The brittle punching failure due to transfer of shear forces and
unbalanced moments between slabs and columns may cause serious problems. Flat-slab
systems are also susceptible to significant reduction in stiffness resulting from the
cracking that occurs from construction loads, service gravity and lateral loads.
Therefore, it is recommended that in regions with high seismic hazard, flat-slab
construction should only be used as the vertical load-carrying system in structures
braced with frames or SWs responsible for the lateral capacity of the structure.
23
2.4.1 Shear wall structures
Shear walls are vertical elements of the horizontal force resisting system. In structural
engineering, a shear wall is a structural system composed of braced panels (also known
as shear panels) to counter the effects of lateral load acting on a structure. Wind and
seismic loads are the most common loads that shear walls are designed to carry.
According to BNBC, Shear wall is a wall designed to resist lateral forces parallel to the
plane of the wall (sometimes referred to as a vertical diaphragm or a structural wall).
According to ACI 318 (chapter-2 & 21), structural walls are defines as being walls
proportioned to resist combinations of shears, moments and axial forces induced by
earthquake motions. Reinforced concrete structural walls are categorized as ordinary
reinforced concrete structural walls and special reinforced concrete structural walls.
The American Society of Civil Engineer’s Minimum Design Loads for Buildings and
Other Structures defines "bearing wall system" as follows:
Bearing wall system: A structural system with bearing walls providing support for all
or major portions of the vertical loads. Shear walls or braced frames provide seismic-
force resistance.
Frame structural system: Building frame system: A structural system with an essentially
complete space frame providing support for vertical loads. Seismic-force resistance is
provided by shear walls or braced frames.
2.4.2 Previous study on shear wall structures
The amount of literature related to nonlinear modeling and performance of shear wall
structures are quite large. Relevant recent studies are summarized below:
Kayal (1986) studied on nonlinear interaction of RC frame‐wall structures. The
nonlinear interaction phenomenon in reinforced concrete frame‐wall systems in the
presence of combined vertical and lateral loading is studied for a range of values of the
four parameters, such as the ratio of beam and column stiffness, the ratio of column and
shear wall stiffness, the slenderness ratio of columns, and the proportion of lateral to
24
vertical load (load ratio). The method used for this study is based on finite element
techniques and takes into account both material and geometric nonlinearities. The
method uses the nonlinear stress‐strain curve of the constitutive materials and does not
use bilinear or trilinear idealizations. The conclusions which have emerged from this
study are as follows: (1) Nonlinear behavior is significantly pronounced in the frame‐
wall systems with stiff walls when under a large load ratio; (2) the bracing effect of the
shear wall is more effective for the case of frames having slender columns and flexible
beams when under a large ratio of lateral to vertical load; (3) nonlinear idealization of
the flexural characteristics of shear walls is important when the shear walls are
connected to stiff frames; and (4) stiff walls undergo more reduction in their stiffness
at failure than flexible walls.
Colotti (1993) studied on shear behavior of RC structural walls. A shear panel model
capable of simulating the nonlinear behavior of reinforced concrete (RC) panels under
membrane‐type loading is developed. The shear panel model is then incorporated into
a macroscopic wall‐member model and implemented in a finite element program to
analyze RC structural walls. The generic wall member is idealized as a group of uniaxial
elements connected in parallel and a horizontal spring. The mechanical properties of
each constituent element of the wall‐member model are based only on the actual
behavior of the materials, without making any additional empirical assumptions. To
check the reliability and the effectiveness of the wall‐member model so derived, a
numerical investigation was carried out by referring to the measured behavior of RC
structural walls subjected to monotonic loading. The comparison between numerical
and experimental results shows that the proposed wall‐member model is capable of
predicting, with acceptable accuracy, the measured flexural and shear responses of
structural walls as well as the flexural and shear displacement components. The wall‐
member model, in its relative simplicity, can be efficiently incorporated into a practical
nonlinear analysis of RC multistory frame‐wall structural systems under monotonic
loading. The possibility of extending the model to the case of cyclic loading is not
investigated in this study.
Rana et al. (2004) studied on pushover analysis of a 19 story concrete shear wall
building located in San Francisco with a gross area of 430,000 square feet. Lateral
25
system of the building consists of concrete shear walls. The building is designed
conforming to UBC 1997 and pushover analysis was performed to verify code's
underlying intent of life safety performance under design earthquake.
Kelly (2004) studied on nonlinear analysis of reinforced concrete shear wall structure.
This paper describes the development of an analysis model which includes nonlinear
effects for both shear and flexure. Equivalent flexural models do not include shear
deformation and are only suited for symmetric, straight walls. The formulation is based
on a "macro" modelling approach and an analysis methodology is developed using
engineering mechanics and experimental results and implemented in an existing
nonlinear analysis computer program. This shows that the model can capture the
general characteristics of hysteretic response and the maximum strength of the wall. An
example shear wall building is evaluated using both the nonlinear static and the
nonlinear dynamic procedures. The procedure is shown to be a practical method for
implementing performance based design procedures for shear wall buildings.
Mullapudi et al. (2001) studied on evaluation of behavior of reinforced concrete shear
walls through Finite Element Analysis. Shear walls are typically modeled with two-
dimensional continuum elements. Such models can accurately describe the local
behavior of the wall element. Continuum models are computationally very expensive,
which limits their applicability to conduct parameter studies. Fiber beam elements, on
the other hand, have proven to be able to model the behavior of slender walls rather
well, and are computationally very efficient. With the inclusion of shear deformations
and concrete constitutive models under a biaxial state of stress, fiber models can also
accurately simulate the behavior of walls for which shear plays an important role. This
paper presents a model for wall-type reinforced concrete structures based on fiber beam
analysis under cyclic loading conditions. The concrete constitutive law is based on the
recently developed softened membrane model. The finite element model was validated
through a correlation study with two experimentally tested reinforced concrete walls.
The model was subsequently used to conduct a series of numerical studies to evaluate
the effect of several parameters affecting the nonlinear behavior of the wall. These
parameters include the slenderness ratio, the transverse reinforcement ratio, and the
axial force. These studies resulted in several conclusions regarding the global and local
behavior of the wall system.
26
Jiang et al. (2012) studied on analytical modeling of medium-rise RC shear walls where
nonlinear shear deformations play a significant role in the wall response under lateral
loads. The analytical models use a fiber element developed based on a micro plane
approach to account for combined axial, flexural, and shear effects in the nonlinear
range. Low-rise shear-critical walls that fail in shear dominated failure modes are not
within the scope of the paper. The verification of the analytical models is achieved
based on comparisons of estimated global (for example, load versus deflection) and
local (for example, reinforcement steel strains and limit states) behaviors with
experimental measurements of RC wall specimens under reversed-cyclic lateral
loading.
Bohl et al. (2011) studied on plastic hinge lengths in high-rise RC shear walls. It is
commonly assumed that the maximum inelastic curvature in a wall is uniform over a
plastic hinge length (height) lp equal to between 0.5 and 1.0 times the wall length lw
(horizontal dimension). Experimental and analytical results indicate that inelastic
curvatures actually vary linearly in walls; however, the concept of maximum inelastic
curvature over lp can still be used to estimate the flexural displacements of isolated
walls. Based on the results of nonlinear finite element analyses using a model validated
by test results, an expression is proposed for lp as a function of wall length, moment-
shear ratio, and axial compression. A procedure to account for the influence of applied
shear stress on lp is also presented. In high-rise buildings, walls are interconnected by
numerous floor slabs, resulting in a complex interaction between walls with different
lw. Longer walls generally have larger shear deformations near the base because their
higher relative flexural stiffness and flexural strength attracts a larger portion of the
total shear force. More slender walls correspondingly have larger flexural deformations
near the base to maintain compatibility of total deformations at the floor levels. An
expression is presented for estimating maximum curvatures in systems of walls with
different lp where the actual linear variation of inelastic curvatures must be accounted
for.
Rahman et al. (2004) studied on nonlinear static pushover analysis of an eight Story RC
frame-shear wall building in Saudi Arabia. The seismic displacement response of the
RC frame-shear wall building is obtained using the 3D pushover analysis using
27
SAP2000 incorporating inelastic material behavior for concrete and steel. Moment
curvature and P-M interactions of frame members were obtained by cross sectional
fiber analysis using XTRACT. The shear wall was modelled using mid-pier approach.
The damage modes includes a sequence of yielding and failure of members and
structural levels were obtained for the target displacement expected under design
earthquake and retrofitting strategies to strengthen the building were evaluated.
Pushover analysis of the Madinah Municipality building showed the building is
deficient to resist seismic loading. Formation of hinges clearly shows that the members
of the building are designed purely for gravity loads as with a small increment of
displacement, most of the members start yielding. Pushover curves show non-ductile
behavior of the building, because almost all the seismic load is carried by the shear
walls and at very small displacement, hinges start forming in shear walls. This indicates
that strengthening of the shear walls in the building is required. The performance points
of the building in positive and negative x-directions are 0.094m and 0.097m based on
actual response spectra available for the Madinah area. The ductility ratio in the positive
x-direction is 14% higher than the negative x-direction due to the different arrangement
of shear walls.
Birely et al. (2014) studied on evaluation of ASCE 41 modeling parameters for slender
reinforced concrete structural walls. ASCE/SEI 41-06 provides guidelines for
evaluating the seismic adequacy of existing buildings. For nonlinear dynamic analysis
of a building, ASCE 41 provides modeling parameters to define the backbone curve for
the response of structural components. Seismic adequacy is then determined by
comparing simulated response to predetermined acceptance criteria. In the reinforced
concrete (RC) community, there is interest in evaluating the modeling parameters and
acceptance criteria for RC components, and if deemed necessary, developing updated
values that reflect the current state of understanding of the seismic performance of RC
components. Slender structural walls, relatively limited tests have been conducted such
that sufficient variation in critical design and loading characteristics including shape,
aspect ratio (elevation and cross- sectional), confinement, and axial load are not
represented by experimental data to justify use of an experimental database to develop
acceptance criteria. Evaluation of this limited set of experimental data indicates current
ASCE 41 modeling parameters and acceptance criteria for flexure-controlled walls is
inappropriate, generally resulting in over prediction of wall deformation capacity at
28
high axial load ratios and under prediction at low axial load ratios and low shear
demands. Although suitable for evaluation of criteria, the data set is not sufficiently
varied such that revised provisions can be developed. To overcome the lack of sufficient
experimental data, a parameter study was conducted to provide data to support
development of updated acceptance criteria. The parameter study was conducted using
a modeling approach validated to provide accurate simulation of flexural failures in
slender reinforced concrete walls. Simulation results were used to develop preliminary
recommendations for revised modeling parameters for slender RC walls. An evaluation
of these simulation results and preliminary recommendations for revised flexure-
controlled RC wall modeling parameters are presented in this paper.
Kammar et al. (2015) studied on nonlinear static analysis of asymmetric building with
and without shear Wall. In this case nonlinear static Pushover analysis method is used.
The main objective of the paper is to study the performance level and behavior of
structure in presence of shear wall for plan irregular building with re-entrant corners.
The parameters considered in this paper are base shear, displacement and performance
levels of the structure. The seismic codes for irregularities are as per the clauses defined
in IS-1893:2002 and pushover analysis procedure is followed as per the prescriptions
in ATC-40.The hinge properties are applied by default method as per provisions in
FEMA 356. The model is analyzed using SAP2000 software.
Rao et al. (2014) studied on nonlinear behavior of shear walls of medium aspect ratio
under Monotonic and Cyclic Loading. Structures designed according to performance-
based seismic design (PBSD) are required to satisfy the target performance. PBSD
requires extensive research for capacity evaluation and development of reliable
nonlinear models. Shear walls are the ideal choice to resist lateral loads in multistoried
RC buildings. They provide large strength and stiffness to buildings in the direction of
their orientation (in-plan), which significantly reduces lateral sway of the building.
Experimental studies on nonlinear behavior of shear walls of medium aspect ratios are
limited. Nonlinear performance of medium aspect ratio shear wall specimens are
studied on three identical shear wall specimens through application of monotonic and
cyclic loading. In order to study the effect of axial load on the flexural behavior and
ductility of shear wall, a parametric study is conducted using a layer-based approach,
which is used to generate the analytical pushover curve for the shear wall and validated
29
with the experimentally evaluated pushover curve of the tested shear wall. A
comparison is made between monotonic and cyclic load behavior. Stiffness and
strength degradation and pinching parameters are evaluated from cyclic tests. Plastic
rotation limits and ductility capacities under monotonic and cyclic loading conditions
are compared with recommended values.
ACI Committee 374 provides information regarding nonlinear modeling of components
in special moment frame and structural wall systems resisting earthquake loads. The
reported modeling parameters provide a modeling option for licensed design
professionals (LDPs) performing nonlinear analysis for performance-based seismic
design of reinforced concrete building structures designed and detailed in accordance
with ACI 318.
2.4.3 Flat plate structures
The slab beam columns system behaves integrally as a three dimensional system, with
the involvement of all the floors of the building, to resist not only gravity loads, but
also lateral loads. However a rigorous three dimensional analysis of the structure is
complex. Unlike the planer frames, in which beam moments are transferred directly to
columns, slab moments are transferred indirectly, due to flexibility of the slab.
2.4.4 Previous study on flat plate structures
Early Patents were issued for RC Slabs as early as 1854 based on the concept of the
concrete forming an arch with reinforcement acting as the tie, and in 1867 based on the
reinforcement acting as a catenary with the concrete used as a filler. The first patent for
a recognizable RC Slab was given to Turner (1903). He described a “mush-room” slab
supported directly by columns with flared tops and reinforced both parallel to the
column lines and along the diagonals. So successful he was that others copied the idea,
and by 1913 over 1000 “flat” slabs had been built. Each builder had to develop his own
design procedures and then verify the design by conducting a performance load test or
by posting a performance bond.
McMillan (1910) compared the quantity of reinforcement required by six design
methods for a 20ft X 20ft interior panel carrying 200 psf live load, and found that they
30
varied by a factor of 4. Nichols (1914) established a simple criterion for the minimum
total moment that must exist across the critical sections of a panel to satisfy equilibrium.
His paper was not well received because he indicated total moments considerably
greater than those used many of the “successful” slab designers. Other designer turned
to classical plate theory as a basis of analysis, since the governing differential equation
for elastic plate bending had been formulated by Lagrange (1811).Solutions of this
equation for rectangular panels bounded by combinations of simply supported and fixed
edges had been developed. However, because these solutions were based on non-
deflecting panel boundaries, the slab bending moments obtained are valid only when
stiff beams are present on all four sides of each panel.
The first slab “code provisions” appeared in 1921 and were two parts. The first part was
placed in the body of the code and presented design coefficients for the slab obtained
from solutions based on classical theory and were applicable only for “two-way” slabs
with stiff beams between all columns. The second part was placed in an appendix to the
code and covered “flat” slabs. It was long recognized that neither procedure was
satisfactory. To resolve these problems a comprehensive study was initiated in the late
1950s primarily at the University of Illinois. As a result Direct Design Method (DDM)
and Equivalent Frame Method (EFM) were developed. These procedures were
incorporated in the code.
Based on the study conducted by Hwang and Moehle, the model proposed by banchik
is good enough to model structure two dimensionally. However, this model cannot give
a comprehensive understanding of behavior of structure. Behavior of structure such as:
plate deformation, internal force distribution, influence of structure and loading
configuration can be observed only by using three dimension analysis. Moreover, by
using nonlinear procedure in three-dimension analysis, inelastic behavior of structure
can be examined. In order to simplify the analysis, including in nonlinear procedure,
the grid model is proposed. In grid model, the slab is replaced by arrangement of
equivalent beam with certain width.
Extensive research has been carried out to find out the behavior of slab-column
connection. The failure mode depends upon the type and extent of loading. Punching
shear strength of slab-column connection is of importance which very much depends
31
on the gravity shear ratio. The mechanism of transfer of moments from slab to column
is very complex when subjected to lateral loading and unbalanced moments. These
unbalanced moments produce additional shear and torsion at the connections and then
get transferred into the column which results in excessive cracking of slab leading to
further reduction in the stiffness of the slab.
Omar et al. (2002) studied on a Numerical model of flat-plate to column connection
behavior. The behavior of laterally loaded flat-plate structures is strongly influenced by
the nonlinear deformations at the plate-to-column connections. In this paper, a simple
procedure is described for predicting the nonlinear moment-rotation behavior of flat-
plate-to-column connections. That behavior is expressed by standardized moment-
rotation functions. These functions were derived using a modified Rambert-Osgood
function and all available experimental data. The influence of the most significant
connection parameters such as the steel ratio, concrete strength, gravity loading, etc.,
on the connection behavior is incorporated into the functions. A physical model of the
column region is described which facilitates the incorporation of the functions into a
structural analysis computer program. The accuracy of the functions has been
demonstrated for several plate-column connections. The computer analysis program is
also described and an example is considered to compare results obtained from the
program with those published in the literature.
Erberik et al. (2014) studied on Seismic vulnerability of flat-slab structures. The
vulnerability study generally focuses on the generic types of construction due to the
enormous size of the problem. Hence simplified structural models with random
properties to account for the uncertainties in the structural parameters are employed for
all representative building types. The study has three main objectives. The first
objective is to investigate the fragility of flat-slab reinforced concrete systems.
Developing the fragility information of flat-slab construction will be a novel
achievement since the issue has not been the concern of any research in the literature.
The second objective is to assess HAZUS as an open-source, nationally accepted
earthquake loss estimation software environment. It is important to understand the
potentials and the limitations of the methodology, the relationship between the hazard,
damage and the loss modules, and the plausibility of the results before using it for the
purposes of hazard mitigation, preparedness or recovery. The last objective is to
32
implement the fragility information obtained for the flat-slab structural system into
HAZUS. The methodology involves many built-in specific building types, but does not
include flat-slab structures. Hence it will be extra achievement to develop HAZUS
compatible fragility curves to be used within the methodology.
Kim et al. (2008) studied on Seismic performance evaluation of non-seismic designed
flat-plate structures. In this study the seismic performance of flat plate system structures
designed without considering seismic load was investigated. Both the capacity
spectrum method provided in ATC-40 in 1996 and nonlinear dynamic analyses were
carried out to obtain maximum inter story drifts for earthquake loads. Also, a seismic
performance evaluation procedure presented in FEMA-355F in 2000 was applied to
evaluate the seismic safety of the model structures. The analysis results showed that the
maximum inter story drifts of the non-seismic designed flat-plate structures computed
by the capacity spectrum method and the nonlinear dynamic analysis were smaller than
the limit state for the collapse prevention performance level. However, the results of
the FEMA procedure showed that the model structures did not have enough strength to
ensure seismic safety.
Wang et al. (2008) studied on Finite-element analysis of reinforced concrete flat plate
structures by layered shell element. A finite-element model for nonlinear analysis of
reinforced concrete flat plate structures is presented. A flexible layering scheme
incorporating the transverse shear deformation is formulated in shell element
environment. Each node of the layered shell element can be specified as either a normal
node or a node with shear correction. A three-dimensional hypo-elastic material model
is implemented to model reinforced concrete. The cracking effects of tension softening,
aggregate interlock, tension stiffening, and compression softening in multidirectional
cracked reinforced concrete are incorporated explicitly and efficiently. A flat plate, a
flat slab with drop panel, and a large size flat plate with irregular column layout have
been analyzed. The influence of the distribution of transverse shear strain on the
punching shear failure mode has been identified in the numerical studies. The proposed
finite-element model has been proved to be capable of simulating the localized
punching shear behavior of slab–column connections and to be suitable for global
analysis of structural performance of flat plate structures.
33
Kang et al. (2009) studied on Nonlinear Modeling of Flat-Plate Systems. Analytical
and experimental studies were undertaken to assess and improve modeling techniques
for capturing the nonlinear behavior of flat-plate systems using results from shake table
tests of two, approximately one-third scale, two-story reinforced concrete and
posttensioned concrete slab–column frames. The modeling approach selected accounts
for slab flexural yielding, slab flexural yielding due to unbalanced moment transfer,
and loss of slab-to-column moment transfer capacity due to punching shear failure. For
punching shear failure, a limit state model based on gravity shear ratio and lateral inter
story drift was implemented into a computational platform (Open Sees). Comparisons
of measured and predicted responses indicate that the proposed model was capable of
reproducing the experimental results well for an isolated connection test, as well as the
two shake table test specimens.
Tian et al. (2009) studied on Nonlinear modeling of Slab-Column connections under
cyclic loading. Based on a beam analogy concept, a two-dimensional (2D) nonlinear
model for interior slab-column connections was developed for use in pushover analyses
of flat-plate structures. The slab lateral resistance from flexure and shear acting on the
connection was modeled by an equivalent beam element and the resistance from torsion
by a rotational spring element. The parameters defining connection lateral stiffness
were calibrated from the tests presented in this study and were validated using
experimental data reported in other studies.
Song et al. (2012) studied on Seismic Performance of Flat Plate System with Shear
Reinforcements. In this study, the results of experimental study about three isolated
interior flat slab-column connections were applied to input data of slab-column
connections for non-linear pushover analysis to investigate the system level seismic
capacity for 45 shear-reinforced flat plate systems. And the over strength factor and a
response modification factor are used as major parameters to define the seismic
capacity of the system, both of which are design factors of the seismic resistance system
in the IBC 2012 as an index. Analysis results showed that the flat plate system
reinforced with shear band showed the efficiency of an RC intermediate moment
resistance frame except for the 5-story case. Also in this study, the effective response
modification factor was evaluated for flat plate structures without walls. Through a
34
comparative analysis of the results, we defined the seismic force-resisting system
applicable to flat plate systems.
2.4.5 Previous study on shear wall-flat plate structural systems
Pawah et al. (2008) studied on Analytical approach to study effect of Shear Wall on flat
slab & two way slab. Slab directly supported on column is termed as flat slab. The
present objective of this work is to compare behavior of flat slab with traditional two
way slab along with effect of shear walls on their performance. The parametric studies
comprise of maximum lateral displacement, story drift and axial forces generated in the
column. For these case studies we have created models for two way slabs with shear
wall and flat slab with shear wall, for each plan size of 16 24 m and 15 25 m,
analyzed with Staad Pro. 2006 for seismic zones III, IV and V with varying height 21m,
27 m , 33 m and 39 m. This investigation also told us about seismic behavior of heavy
slab without end restrained. For stabilization of variable parameter shear wall are
provided at corner from bottom to top for calculation. Results is comprises of study of
36 models, for each plan size, 18 models are analyzed for varying seismic zone.
Goud (2016) studied on Analysis and design of flat slab with and without Shear Wall
of Multi-Storied building frames. Conventional R.C.C structure i.e flat slab, shear wall,
column for different heights are modelled and analyzed for the different combinations
of static loading with varying thicknesses of shear wall with varying height of
multistoried building .The comparison is made between the conventional R.C.C flat
slab structure of 10,20and 30 stories without shear wall . The comparison made between
the conventional R.C.C flat slab structure of 10,20 and 30 stories with varying
thicknesses of shear wall in multi - storied buildings have been provided at some
particular locations .The main objective of analysis is to study the structural behavior
of shear wall – flat slab interaction. The main objective of the analysis is to study the
behavior against different forces acting on components of a multistoried building and
to study the effect of part shear walls on the performance of these two types of buildings
under seismic forces. The analysis is carried out using STAAD Pro2007 software. The
present work also provides a good source of information on various parameters like
lateral displacement, plate stresses and story drift.
35
Melek et al. (2012) studied on effects of modeling of RC flat slabs on nonlinear
response of high rise building systems. This paper discussed in terms of three lateral-
load-resisting systems: (i) concrete core shear walls only, (ii) core shear walls with flat
slab elements; and (iii) core shear walls with damped outrigger systems. The lateral
drifts, story level accelerations and behavior of the flat plates are investigated.
2.5 Conclusion Drawn from the Literature Review
It can be seen that flat plate shear wall systems are still quite rare, as such their behavior
is least understood among different structural forms. Although studies have been
conducted in the past on this system, more rigorous analysis and full-scale testing is
required to develop design guidelines for reinforced concrete flat plate shear wall
system.
CHAPTER 3
NUMERICAL MODELING
3.1 Introduction
Highlight of the numerical modeling of shear wall-flat plate structural system (SW-FP)
has been presented in this chapter. A readymade garments (RMG) factory building
situated at Narayanganj, Bangladesh has been used in this research. Firstly structural
design of this building has been performed using linear static analysis (LSA) as per
BNBC 1993. Using LSA design data, nonlinear static or pushover analysis (NLSA) has
been performed for numerous configurations of the shear wall-flat plate structural
systems. Basic design consideration for LSA and modeling criteria, hinge properties
and loading criteria for nonlinear static or pushover analysis (NLSA) has been
discussed in this chapter.
3.2 Linear Static Analysis (LSA)
Basic design considerations (material properties, loading, boundary conditions etc.) and
design outputs of linear static analysis have been discussed in this section.
3.2.1 Design considerations
Structural analysis and design have been performed according to Bangladesh National
Building Code (BNBC) 1993. Other Codes, Standards, Specifications have been
utilized as required in structural design.
A. Structural geometry considerations
Initially, shape, size, story height and number of story of the building have been
considered as per design requirement and checked as per BNBC 1993 weather it is
regular or irregular structure. Typical Column location, beam location, shear wall
location and slab extents are shown in the following layout (figure 3.1). It is a 10 (ten)
storied building with story height of 10 ft and floor area per floor is (174ft×96ft)
16704ft2.
37
Figure 3.1: Typical floor layout of SW-FP structure
38
B. Material specifications
The grade of steel and concrete strength considered is as follows:
Grade of concrete cylinder strength
For column & beam : 3000 psi
For slab & others : 3000 psi
For Footings : 3000 psi
Grade of Steel (all members) : 60000 psi
C. Loading criteria
The building has been analyzed for possible load actions such as Gravity and Lateral
Loads.
Gravity Loads, such as dead and live loads applied at the floors or roofs of the building
according to the provision of Chapter 2, Part 6 of BNBC 1993 are as follows:
Dead Loads
Self-Weight of Concrete = 150 pcf
Self-Weight of Brick = 120 pcf
Floor finish (FF) on floors = 25 psf
Floor finish (FF) on Roof = 40 psf
Floor finish (FF60) on Stair = 60 psf
Random Partition Wall (RPW) on floors = 25 psf
Fixed Partition Wall (FPW) on floor beams = 900 plf
Parapet Wall (PW) on roof beams = 120 plf
Live Loads
Floor Live Load (LL63) = 63 psf
Roof Live Load (LL42) = 42 psf
Stair Case Live Load (LL100) = 100 psf
39
Lateral Loads, such as Wind Load and Seismic Load applied at the building in
accordance with the provision of Chapter 2, Part 6 of BNBC 1993 is as follows:
Wind Load consideration parameters
Basic Wind Speed, Vb : 195 km/h(Narayanganj, Bangladesh)
Structural Importance Coefficient (CI) : 1.0
Exposure Category : A
Overall Pressure Coefficient, Cp : 1.4(X-direction)
1.59 (Y- direction)
Seismic Load consideration parameters
Seismic Zone (Z) : Zone II (Narayanganj, Bangladesh)
: 0.15 [Table 6.2.22]
Response Modification Coefficient (R) : 8 [Table 6.2.24]
Structural Importance Factor (I) : 1.0 [Table 6.2.23]
Site Coefficient (S) : 1.5 [Table 6.2.25]
Numerical coefficient (Ct) : 0.03 (for ‘h’ in ‘ft’)
Fundamental period of vibration, (T) : 1.09 sec
D. Boundary conditions (support conditions)
To simulate structural behavior, Column base supports have been considered as fixed
supports in 3D model of super structure
E. Design method and load combinations
Ultimate Strength Design (USD) method and various loads have been applied to the
structures in combination with factors listed below in reviewing the quantity of
reinforcement of all structural members.
40
Factored load combinations for RCC design
U = 1.4D
U = 1.4D + 1.7L
U = 0.9D ± 1.3Wx/y
U = 0.9D ± 1.43EQ x/y
U = 1.05D ± 1.275Wx/y
U = 1.05D ± 1.4 EQ x/y
U = 1.05D +1.275L ± 1.275Wx/y
U = 1.05D + 1.275L ± 1.4E EQ x/y
Load combinations for foundation stability as considered according to BNBC are
U = D + L
U = D +L ± Wx/y
U = D +L ± EQ x/y
F. Selection of analysis type
Structural analysis has been performed in a single step using the equivalent linear static
analysis method and Finite Element method.
3.2.2 Design outputs
Structural analysis and design of SW-FP system have been performed using LSA
procedure and USD method as per BNBC 93. Superstructure comprises of 43 columns,
4 shear walls, 30 edge beams and flat plate system at each story level with 63 grade
beams at ground floor level.
Size, location, orientation and reinforcement details of each structural members of
each story levels are summarized in Appendix-A.
3.3 Nonlinear Static or Pushover Analysis (NLSA)
Nonlinear static analysis (NLSA) has been performed for SW-FP structural system
varying parameters like shape of the building, material strength, Story height and
number of story to evaluate and compare performance and calculate response
41
modification factor (R). Models that have been analyzed are listed in Table 3.1. Typical
layouts for Model 1, Model 2 and Model 3 are shown in Appendix B.
Table 3.1: Model types and their ID
SW -FP
structural
system
(Shape)
Story
Height
(in feet)
Model ID
No of story
7 7 10 10
fc= 3 ksi
fy= 60 ksi
fc= 4 ksi
fy= 72 ksi
fc= 3 ksi
fy= 60 ksi
fc= 4 ksi
fy= 72 ksi
Model-1
96×174
(B×L)
10 M-1.1.1 M-1.1.4 M-1.2.1 M-1.2.4
12 M-1.1.2 M-1.1.5 M-1.2.2 M-1.2.5
15 M-1.1.3 M-1.1.6 M-1.2.3 M-1.2.6
Model-2
73.5×174
(B×L)
10 M-2.1.1 M-2.1.4 M-2.2.1 M-2.2.4
12 M-2.1.2 M-2.1.5 M-2.2.2 M-2.2.5
15 M-2.1.3 M-2.1.6 M-2.2.3 M-2.2.6
Model-3
96×126
(B×L)
10 M-3.1.1 M-3.1.4 M-3.2.1 M-3.2.4
12 M-3.1.2 M-3.1.5 M-3.2.2 M-3.2.5
15 M-3.1.3 M-3.1.6 M-3.2.3 M-3.2.6
At first, Model-1 is analyzed and designed using LSA procedure and then configuration
is changed reducing number of bays in y-direction (Model-2) and in x-direction
(Model-3). After that, number of story, story height and material properties have been
varied to generate many other models to perform parametric study using NLSA
procedure. Figure-3.2 and Figure-3.3 represent typical layout of model-2 and Model-3
respectively.
42
Figure 3.2: Model 2 flat plate extent, shear wall and column layout
43
Figure 3.3: Model 3 flat plate extent, shear wall and column layout
44
3.3.1 Load and deformation Criteria
For earthquake load consideration, BNBC 1993 response spectrum curve has been used
(figure 3.4) for the nonlinear static analysis (NLSA).
There are three lateral load patterns proposed in FEMA-356 also adopted by ASCE 41-
13, namely (a) inverted triangular distribution, (b) uniform distribution, (c) distribution
of forces proportional to fundamental mode (mode 1). Third one has been utilized in
this research. The generalized load-deformation relation is shown in Figure 3.5.
Figure 3.4: BNBC 1993 response spectrum curve
Figure 3.5: Load-deformation relationship (Figure 10-1.a: ASCE 41-13)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 1.0 2.0 3.0 4.0 5.0
C
Period T (sec)
45
3.3.2 Modeling Criteria and hinge properties
Modeling criteria of structural members of SW-FP structural systems considered in this
research are discussed in this section:
A. Beam-column moment frame:
Beam-column frame elements are considered as line elements with properties
concentrated at component centerlines in analytical model. The beam–column joint is
considered monolithic rigid joint. Beams and columns are modeled using concentrated
plastic hinge models. Nonlinear modeling parameters and acceptance criteria for
beams, columns, and beam–column joints are provided in Appendix B respectively.
B. Slab–column moment frames
Effective beam width model is considered where columns and slabs are represented by
line elements rigidly interconnected at the slab–column connection and the slab width
included in the model is adjusted to account for flexibility of the slab–column
connection. Slab element width is reduced to adjust the elastic stiffness to more closely
match measured values. Column behavior and slab–column moment and shear transfer
are modeled separately. Effective beam width layout and details are summarized in
Appendix B.
The beam–column joint is considered monolithic and slab beams and columns are
modeled using concentrated plastic hinge models. Nonlinear modeling parameters and
acceptance criteria for slab columns connections are provided in Appendix B.
46
C. Reinforced concrete shear walls, wall segments and coupling beams
In analytical model, Reinforced Concrete Shear Walls are considered as shell elements
which represent the stiffness, strength, and deformation capacity of the shear wall.
Shear walls are modeled using distributed fiber hinges. Modeling Parameters and
Numerical Acceptance Criteria for RC shear wall and associated are provided in
Appendix B.
Elastic column
Elastic slab beam
Slab-beam plastic hinge
Plastic hinge for slab beams or for torsional elements
Torsional connection element Column plastic hinge
Elastic relation for slab beam or column
Joint region
M
Slab beam and column only connected by rigid-plastic torsional connection elements
M
lp
Figure 3.6: Modeling of slab-column connection (Figure C10-2: ASCE 41-13)
Figure 3.7: Plastic hinge rotation in shear wall where flexure dominates inelastic response (Figure 10-4: ASCE 41-13)
47
3.3.3 Effective stiffness for crack section model
Beam, column and shear wall sections are considered as cracked sections in nonlinear
static procedure as per ASCE 41-13. Effective stiffness for cracked sections are
summarized in Table 3.2.
Table 3.2: Effective stiffness values as per ASCE 41-13 (Table 10.5)
Components Flexural Rigidity Shear Rigidity
Beams 0.3 EcIg 0.4 EcAg
Columns 0.7 EcIg 0.4 EcAg
Flat slabs 0.33 EcIg 0.4 EcAg
Walls 0.5 EcAg 0.4 EcAw
L
Figure 3.8: Story drift in shear wall where shear dominates inelastic response (Figure 10-5: ASCE 41-13)
CHAPTER 4
RESULTS
4.1 Introduction
This chapter represents structural performance from linear static analysis (LSA) and
nonlinear static analysis (NLSA). Results from LSA for Model-1 have been
summarized. Nonlinear behavior of Model-1 to Model-3 are discussed and compared
including parametric study like story height, material property and number of story.
4.2 Structural Performance from Linear Static Analysis
Linear static analysis and design have been done only for the model M-1.2.1 using
BNBC 1993 and discussed in chapter 3. The parameters building dimension: 174' by
96'; number of story: 10; story height: 10'; material strength: f'c = 3 ksi and fy = 60 ksi
are considered in linear static analysis and design.
Maximum story displacement, story drift, story shear and story stiffness from linear
static analysis for Model-2 have been summarized in this section.
It is apparent from the Story Height vs. Lateral Displacement plot (figure: 4.1) that the
lateral displacement at the top is higher for earthquake forces compared to wind. For
Figure 4.1: Maximum story displacement Figure 4.2: Story drift
020406080
100120140
0 1 2 3 4
Elev
atio
n (f
t)
Lateral Dispacement (in)
Max Story Displacement
EQX EQYWX WY
020406080
100120140
0 0.0015 0.003 0.0045
Elev
atio
n (f
t)
Story Drift
Story Drift
EQX EQYWX WY
49
earthquake forces displacement along the x–direction is larger than that of the y–
direction, understandably because of the orientation of the shear walls along the y–
direction imparting much more stiffness along that direction. On the other hand for
wind forces displacement along the y–direction is higher due to the much larger
exposed area in that direction. According to BNBC 1993 the allowable displacement is
≤ 0.03 h / R ≤ 0.004 h for time period T ≥ 0.7 seconds. So for the building, = 0.03
(110/8) × 12 = 4.95 inches. The maximum displacement observed is 3.78 inches, which
is well below the allowable limit.
Story drifts (figure: 4.2) are also smaller for wind loading on the structure, since the
magnitude of wind loads are smaller compared to earthquake loads. The presence of
shear walls along the y–direction limits the story drift in the y–direction. Since change
in displacement between two successive stories are larger in the lower floors compared
to the upper floors, story drift gradually decreases along the height of a building. The
allowable limit for story drift according to BNBC 1993 has been calculated to be 0.045,
which is much higher than the observed maximum value of 0.0039.
0
20
40
60
80
100
120
140
0 500 1000 1500
Elev
atio
n (f
t)
Story Shear (kips)
Story Shear
EQX EQYWX WY
0
20
40
60
80
100
120
140
0 20000 40000 60000 80000
Elev
atio
n (f
t)
Story Stiffness (kips/in)
Story Stiffness
EQX EQY
WX WY
Figure 4.3: Story shear Figure 4.4: Story stiffness
50
Story shear (figure: 4.3) due to seismic loads is higher than story shear due to wind
loads. Since seismic base shear isn’t directional, story shears along the x and y–
directions are same for this building. On the other hand, the exposed area of the building
is larger along the y–direction. As such, the story shear due to wind is higher in the y–
direction.
It can also be seen from the graphs (figure: 4.4) that the story stiffness remains the same
along a direction for both earthquake and wind loading. Since the structural
arrangement is same for all lateral loads, i.e. to deflect the structures the same amount
both loads encounter the same moment of inertia, the stiffness stays the same.
4.3 Structural Performance from Nonlinear Linear Static Analysis
Structural performance from nonlinear static or pushover analysis (NLSA) for Model-
1, Model-2 and Model-3 are summarized in this section.
4.3.1 Capacity curve (base shear vs top deflection)
As story heights are increased, the decrease in base shear capacity is significant (figure:
4.5 to figure: 4.8). This can be attributed to the decrease in stiffness due to the increased
column and shear wall height. The decrease in stiffness can be as large as fifty percent
as heights are increased by one hundred and fifty percent. As material strength is
increased the capacity has been observed to increase.
The base shear capacity along the y-direction (figure: 4.7 and figure: 4.8) has been
found to double as the structures are stiffer in the y-direction due to because of the
orientation of the shear walls along the y–direction imparting much more stiffness along
that direction.
51
Figure 4.6: Capacity curve for M-1, M-2 and M-3 varying story height (x-direction)
0
500
1000
1500
2000
2500
3000
3500
0 5 10 15 20 25 30 35
Bas
e Sh
ear
(kip
)
Monitored top Displacement (inch)
M 1.1.1
M 1.1.2
M 1.1.3
M 1.2.1
M 1.2.2
M 1.2.3
M 2.1.1
M 2.1.2
M 2.1.3
M 2.2.1
M 2.2.2
M 2.2.3
M 3.1.1
M 3.1.2
M 3.1.3
M 3.2.1
M 3.2.2
M 3.2.3
0
500
1000
1500
2000
2500
3000
3500
4000
0 10 20 30 40
Bas
e Fo
rce
(kip
)
Monitored Displacement (inch)
M 1.1.4M 1.1.5M 1.1.6M 1.2.4M 1.2.5M 1.2.6M 2.1.4M 2.1.5M 2.1.6M 2.2.4M 2.2.5M 2.2.6M 3.1.4M 3.1.5M 3.1.6M 3.2.4M 3.2.5M 3.2.6
Figure 4.5: Capacity curve for M-1, M-2 and M-3 varying story height (x-direction)
52
Figure 4.8: Capacity curve for M-1, M-2 and M-3 varying story height (y-direction)
0
1000
2000
3000
4000
5000
6000
7000
0 5 10 15 20
Bas
e Fo
rce
(kip
)
Monitored Displacement (inch)
M 1.1.1M 1.1.2M 1.1.3M 1.2.1M 1.2.2M 1.2.3M 2.1.1M 2.1.2M 2.1.3M 2.2.1M 2.2.2M 2.2.3M 3.1.1M 3.1.2M 3.1.3M 3.2.1M 3.2.2M 3.2.3
0
1000
2000
3000
4000
5000
6000
7000
8000
0 5 10 15 20
Bas
e Fo
rce
(kip
)
Monitored Displacement (inch)
M 1.1.4M 1.1.5M 1.1.6M 1.2.4M 1.2.5M 1.2.6M 2.1.4M 2.1.5M 2.1.6M 2.2.4M 2.2.5M 2.2.6M 3.1.4M 3.1.5M 3.1.6M 3.2.4M 3.2.5M 3.2.6
Figure 4.7: Capacity curve for M-1, M-2 and M-3 varying story height (y-direction)
53
4.3.2 Plastic hinge state at performance point
The following list (table: 4.1) presents the states of plastic hinges formed at
performance point/target point for 23 of the 36 models under review. Some of the
models (13 out of 36) under review did not exhibit performance point.
From table 4.1 it can be seen that all 7-story models exhibit performance point,
regardless of the story height. For 10-story models, performance point can only be seen
when story height is limited 10 ft. Along the Y-direction 10-story models exhibit
performance point only for Model 3, where the plan aspect ratio is closer to one.
It is apparent from the table that as story heights are increased the number of plastic
hinges with high magnitude of rotational angle increases. For example, the 7-story
model with story height of 10 ft. has no hinges in the LS-CP region, whereas the 7-story
model with story height of 15 ft. has 4 hinges in the LS-CP region along the X-direction.
Presence of shear walls along the Y-direction makes the structures stiffer along that
direction. As a result all hinges in the Y-direction stays within the acceptable IO-LS
limit. However, along the X-direction the 17 of the 23 models form hinges that go
beyond the acceptable limit. Number of plastic hinges at various levels are more in
number in slender structures compared to others. Another noteworthy finding is that,
increasing material strength leads to a reduction in the number of hinges formed.
Table 4.1: Summary table of plastic hinge states at performance point
Model ID
Story Height Dir. Top
Disp. () Base Force
(kips) A-IO IO-LS LS-CP >CP Total Hinges
M 1.1.1 10 X 9.89 3153 1873 281 0 0 2156 Y 3.72 4604 2037 119 0 0 2156
M 1.1.2 12 X 13.61 2609 1854 301 0 0 2156 Y 4.46 3596 2033 123 0 0 2156
M 1.1.3 15 X 19.41 1979 1789 361 4 0 2156 Y 6.48 2930 2014 142 0 0 2156
M 1.2.1 10 X 17.39 2727 2441 489 7 5 2942 Y
M 2.1.1 10 X 9.80 2576 1573 167 0 0 1740 Y 3.26 3911 1716 24 0 0 1740
M 2.1.2 12 X 12.48 2133 1558 180 0 0 1740
54
Model ID
Story Height Dir. Top
Disp. () Base Force
(kips) A-IO IO-LS LS-CP >CP Total Hinges
Y 3.77 2945 1718 22 0 0 1740
M 2.1.3 15 X 18.78 1638 1507 231 1 0 1740 Y 5.26 2316 1689 51 0 0 1740
M 2.2.1 10 X 16.01 2278 2052 314 2 0 2370 Y
M 3.1.1 10 X 10.48 2301 1488 218 0 0 1708 Y 3.41 4169 1669 39 0 0 1708
M 3.1.2 12 X 13.49 1892 1484 223 0 0 1708 Y 4.24 3324 1634 74 0 0 1708
M 3.1.3 15 X 20.16 1402 1431 261 14 2 1708 Y 5.49 2481 1640 68 0 0 1708
M 3.2.1 10 X 17.71 1979 1949 360 11 6 2326 Y 6.00 3345 2170 156 0 0 2326
M 1.1.4 10 X 9.78 3334 1888 267 0 1 2156 Y 3.69 4847 2037 119 0 0 2156
M 1.1.5 12 X 13.66 2832 1862 292 0 2 2156 Y 4.49 3807 2026 130 0 0 2156
M 1.1.6 15 X 19.63 2177 1833 321 0 2 2156 Y 6.27 2997 2029 127 0 0 2156
M 1.2.4 10 X 17.27 3095 2508 432 0 2 2942 Y
M 2.1.4 10 X 9.49 2735 1580 159 0 1 1740 Y 3.05 3891 1720 20 0 0 1740
M 2.1.5 12 X 12.65 2329 1560 178 0 2 1740 Y 3.76 3081 1718 22 0 0 1740
M 2.1.6 15 X 18.43 1814 1538 199 0 1 1740 Y
M 3.1.4 10 X 10.00 2411 1505 201 0 1 1708 Y 3.14 4100 1678 30 0 0 1708
M 3.1.5 12 X 13.48 2023 1491 215 0 1 1708 Y 3.67 3128 1663 45 0 0 1708
M 3.1.6 15 X 20.41 1551 1455 251 1 1 1708 Y 5.31 2531 1651 57 0 0 1708
M 3.2.4 10 X 17.99 2246 1979 345 0 2 2326 Y 6.04 3540 2170 156 0 0 2326
55
The following figures (figure 4.9-4.20) presents the states of plastic hinges formed at
maximum base shear capacity for model M-1.1.1, mod el M-2.1.1 and model M-3.1.1
under pushover cases in both x and y-directions.
IO-LS
LS-CP
>CP
Figure 4.9: plastic hinges formed at performance point for model M-1.1.1
(3D view) in x-direction
Figure 4.10: plastic hinges formed at performance point for model M-1.1.1
(elevation 3) in x-direction
56
Figure 4.12: plastic hinges formed at performance point for model M-1.1.1
(elevation C) in y-direction
Figure 4.11: plastic hinges formed at performance point for model M-1.1.1 (3D
view) in y-direction
IO-LS
LS-CP
>CP
57
Figure 4.13: plastic hinges formed at performance point for model M-2.1.1 (3D
view) in x-direction
Figure 4.14: plastic hinges formed at performance point for model M-2.1.1
(elevation C) in x-direction
IO-LS
LS-CP
>CP
58
Figure 4.16: plastic hinges formed at performance point for model M-2.1.1
(elevation C) in y-direction
Figure 4.15: plastic hinges formed at performance point for model M-2.1.1 (3D
view) in y-direction
IO-LS
LS-CP
>CP
59
IO-LS
LS-CP
>CP
Figure 4.18: plastic hinges formed at performance point for model M-3.1.1
(elevation C) in x-direction
Figure 4.17: plastic hinges formed at performance point for model M-3.1.1 (3D
view) in x-direction
60
IO-LS
LS-CP
>CP
Figure 4.19: plastic hinges formed at performance point for model M-3.1.1 (3D
view) in y-direction
Figure 4.20: plastic hinges formed at performance point for model M-3.1.1
(elevation C) in y-direction
61
4.3.3 Summary of base shear and maximum top displacement
Base shear and corresponding maximum top displacements have been calculated using
displacement coefficient method (ASCE 41-13) and capacity spectrum method (FEMA
440EL) for all 36 models. Summaries of Target displacements (ASCE 41-13) and
performance point (FEMA 440 EL) have been shown in appendix C.
All the models (23 models) that have been shown performance point are satisfy the
global acceptability limits according to ATC-40 seismic evaluation guidelines. The
displacement at performance point for the three primary types of buildings have been
shown in table 4.2 below.
Table 4.2: Displacement at performance point
Model ID
Performance Point Displacement in x-
direction (inch)
Performance Point Displacement in y-
direction (inch)
Global Acceptability Limits Roof Drift (inch)
ASCE 41 FEMA 440EL ASCE 41 FEMA 440EL LS
M 1.1.1 9.97 9.78 3.64 4.97 19.2 M 1.1.2 13.37 13.34 4.50 6.71 23.04 M 1.1.3 19.52 20.19 6.53 9.79 28.8 M 1.1.4 9.99 10.31 3.56 5.23 19.2 M 1.1.5 13.39 14.33 4.45 7.06 23.04 M 1.1.6 19.56 21.1 6.44 10.35 28.8 M 1.2.1 17.28 16.75 26.4 M 1.2.4 17.37 17.89 26.4 M 2.1.1 9.46 9.35 3.13 4.64 19.2 M 2.1.2 12.7 12.48 3.96 6.25 23.04 M 2.1.3 18.34 18.49 28.8 M 2.1.4 9.48 9.79 3.06 4.88 19.2 M 2.1.5 12.73 13.25 3.82 6.54 23.04 M 2.1.6 18.49 19.58 28.8 M 2.2.1 16.11 15.86 26.4 M 3.1.1 10.15 10.13 3.10 4.50 19.2 M 3.1.2 13.66 13.67 4.03 6.04 23.04 M 3.1.3 20.18 22.03 5.41 8.91 28.8 M 3.1.4 10.16 10.7 3.03 4.72 19.2 M 3.1.5 13.68 14.46 3.97 6.24 23.04 M 3.1.6 20.22 23.14 5.41 9.19 28.8 M 3.2.1 17.71 17.69 6.03 9.53 26.4 M 3.2.4 17.81 18.55 5.89 9.18 26.4
62
4.3.4 Base shear and top deflection
It can be seen that (figure: 4.21 to figure: 4.22) base shear capacity reduces in both
directions as number of stories are increased. Similarly increasing story heights also
reduces the base shear capacity as longer columns lessen the stiffness of the structures.
Top deflection increases with total height of structure - longer the structure, larger the
top deflection (figure: 4.23 to figure: 4.24).
Base shear capacity and top deflection follows the same trend for all the three models.
Model 1 has the highest base shear capacity since it is stiffer than the other two models.
Models 2 and 3 are less stiff. Stiffness of a structure is related to the number and
configuration of the columns in it. In model 2 and 3, spans in one or both directions
has been reduced, which lead to the decrease in number of columns, resulting in lesser
stiffness.
The shear walls have been placed along the y-direction, as such the base shear capacity
is much higher in y-direction for all three models. Higher stiffness due to the presence
of shear walls along y-direction also reduces the top deflection significantly, when
compared to that of the x-direction.
Material strength has a significant impact on base shear capacity. As concrete
compressive strength is increased to 4000 psi from 3000 psi, and yield strength of steel
is increased to 72500 psi from 60000 psi, the base shear capacity has been observed to
increase by as much as 20 percent (figure: 4.25 to figure: 4.26). Although a decrease in
top deflection has also been observed when material strength is increased, the change
is insignificant (figure: 4.27 to figure: 4.28).
63
Figure 4.21: Base shear capacity (x-direction) chart
(f'c= 3 ksi, fy= 60 ksi)
Figure 4.22: Base shear capacity (y-direction) chart
(f'c= 3 ksi, fy= 60 ksi)
0
500
1000
1500
2000
2500
3000
3500
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 1
.2.1
M 2
.1.1
M 2
.1.2
M 2
.1.3
M 2
.2.1
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.2.1
Bas
e Sh
ear C
apac
ity (k
ip)
Model ID
ASCE 41-13 NSP (BNBC 1993 Spectrum)
FEMA 440 EL (BNBC 1993 Spectrum)
0
1000
2000
3000
4000
5000
6000
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 2
.1.1
M 2
.1.2
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.2.1
Bas
e Sh
ear C
apac
ity (k
ip)
Model ID
ASCE 41-13 NSP (BNBC 1993 Spectrum)
FEMA 440 EL (BNBC 1993 Spectrum)
64
0
5
10
15
20
25
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 1
.2.1
M 2
.1.1
M 2
.1.2
M 2
.1.3
M 2
.2.1
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.2.1
Top
Def
lect
ion
(inch
)
Model ID
ASCE 41-13 NSP (BNBC 1993 Spectrum)FEMA 440 EL (BNBC 1993 Spectrum)
Figure 4.23: Top deflection (x-direction) chart (f'c= 3 ksi, fy= 60 ksi)
Figure 4.24: Top deflection (y-direction) chart (f'c= 3 ksi, fy= 60 ksi)
0
2
4
6
8
10
12
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 2
.1.1
M 2
.1.2
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.2.1
Top
Def
lect
ion
(inch
)
Model ID
ASCE 41-13 NSP (BNBC 1993 Spectrum)FEMA 440 EL (BNBC 1993 Spectrum)
65
Figure 4.25: Base shear capacity (x-direction) chart
(f'c= 4 ksi, fy= 72.5 ksi)
Figure 4.26: Base shear capacity (y-direction) chart
(f'c= 4 ksi, fy= 72.5 ksi)
0
500
1000
1500
2000
2500
3000
3500
4000
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 1
.2.4
M 2
.1.4
M 2
.1.5
M 2
.1.6
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.4
Bas
e Sh
ear C
apac
ity (k
ip)
Model ID
ASCE 41-13 NSP (BNBC 1993 Spectrum)
FEMA 440 EL (BNBC 1993 Spectrum)
0
1000
2000
3000
4000
5000
6000
7000
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 2
.1.4
M 2
.1.5
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.4
Bas
e Sh
ear C
apac
ity (k
ips)
Model ID
ASCE 41-13 NSP (BNBC 1993 Spectrum)FEMA 440 EL (BNBC 1993 Spectrum)
66
0
5
10
15
20
25
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 1
.2.4
M 2
.1.4
M 2
.1.5
M 2
.1.6
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.4
Top
Def
lect
ion
(inch
)
Model ID
ASCE 41-13 NSP (BNBC 1993 Spectrum)FEMA 440 EL (BNBC 1993 Spectrum)
0
2
4
6
8
10
12
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 2
.1.4
M 2
.1.5
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.4
Top
Def
lect
ion
(inch
)
Model ID
ASCE 41-13 NSP (BNBC 1993 Spectrum)FEMA 440 EL (BNBC 1993 Spectrum)
Figure 4.27: Top deflection (y-direction) chart
(f'c= 4 ksi, fy= 72.5 ksi)
Figure 4.28: Top deflection (y-direction) chart
(f'c= 4 ksi, fy= 72.5 ksi)
67
Base shear capacity calculated from Displacement Coefficient Method (ASCE 41-13)
and Capacity Spectrum Method (FEMA 440 EL) are almost same along the x-direction.
However the values differ by much – as high as 25 percent, when measured along the
y-direction.
4.4 Evaluation of Response Modification Factor (R value)
This section represents results of seismic performance factors like strength reduction
factor, overstrength factor and response modification factor calculated by using
displacement coefficient method (DCM) as per ASCE 41. BNBC 1993 demand
spectrum has been utilized to calculate those results.
4.4.1 Reduction factor (R)
Strength reduction factor has been calculated by using displacement coefficient method
(DCM) as per ASCE 41(Equation 7-31: R = strength = SaCm/ (Vy/W). The values of
strength reduction factor is much higher in the y-direction compared to the x-direction.
As material strength is increased the value of strength reduction factor increases (figure:
4.29 and figure: 4.30), though not significantly, in both directions.
Figure 4.29: Strength reduction factor chart (x-direction)
0
1
2
3
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 1
.2.1
M 1
.2.4
M 2
.1.1
M 2
.1.2
M 2
.1.3
M 2
.1.4
M 2
.1.5
M 2
.1.6
M 2
.2.1
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.1
M 3
.2.4
Stre
ngth
Red
uctio
n Fa
ctor
Model ID
BNBC 1993 (x-direction)
68
4.4.2 Overstrength factor (o)
The overstrength factor is the ratio of base shear at yielding of the structure (Vy) to
unfactored design base shear (Vd). Vd is value of the base shear at which the first hinge
forms within the elastic limit.
Figure 4.30: Strength reduction factor chart (y-direction)
Figure 4.31: Overstrength factor chart (x-direction)
0
1
2
3
4
5
6
7
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 2
.1.1
M 2
.1.2
M 2
.1.4
M 2
.1.5
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.1
M 3
.2.4Stre
ngth
Red
uctio
n Fa
ctor
Model ID
BNBC 1993 (y-direction)
0
1
2
3
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 1
.2.1
M 1
.2.4
M 2
.1.1
M 2
.1.2
M 2
.1.3
M 2
.1.4
M 2
.1.5
M 2
.1.6
M 2
.2.1
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.1
M 3
.2.4
Ove
rstre
ngth
Fac
tor
Model ID
BNBC 1993 (x-direction)
69
The value of overstrength factor (figure: 4.31 to figure: 4.32) is higher in the x-direction
compared to the y-direction. As material strength is increased value of this factor
decreases. Similarly as structures get stiffer the value of overstrength factor decreases
along both the directions.
4.4.3 Response modification factor (R)
Value of response modification factor has been calculated using the Displacement
Coefficient Method (ASCE 41-13). It can be seen that response modification factor
(figure: 4.33 to figure: 4.34) increases with decrease in stiffness of the structures.
Figure 4.32: Overstrength factor chart (y-direction)
Figure 4.33: Response modification factor chart (x-direction)
0
1
2
3
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 2
.1.1
M 2
.1.2
M 2
.1.4
M 2
.1.5
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.1
M 3
.2.4
Ove
rstre
ngth
Fac
tor
Model ID
BNBC 1993 (y-direction)
0
1
2
3
4
5
6
7
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 1
.2.1
M 1
.2.4
M 2
.1.1
M 2
.1.2
M 2
.1.3
M 2
.1.4
M 2
.1.5
M 2
.1.6
M 2
.2.1
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.1
M 3
.2.4
Res
pons
e M
odifi
catio
n Fa
ctor
Model ID
BNBC 1993 (x-direction)
70
As material strength is increased the seismic modification factor decreases. On the other
hand the value of this factor has been found to be higher in the y-direction.
As stated in the objectives the seismic modification factor for shear wall flat plate
structural system has been figured out here, upon conducting extensive statistical
analysis. R–value for twenty three structures have been considered in figuring out the
average (AVG), no matter how scattered they are. To minimize the effect of the
scattered values, standard deviation (SD) of the data has been figured out.
Table 4.3: Statistical analysis of response modification factor
Earthquake Direction
Number of Data
AVG R-value
SD
X (FP) 23 5.2 0.8
Y (SW-FP) 18 6.8 1.8
From statistical analysis (table 4.3), it can be seen that value of seismic modification
factors are almost same when material strength is changed. No pattern emerges as to
the value of R across the two directions.
Figure 4.34: Response modification factor chart (y-direction)
0
2
4
6
8
10
12
M 1
.1.1
M 1
.1.2
M 1
.1.3
M 1
.1.4
M 1
.1.5
M 1
.1.6
M 2
.1.1
M 2
.1.2
M 2
.1.4
M 2
.1.5
M 3
.1.1
M 3
.1.2
M 3
.1.3
M 3
.1.4
M 3
.1.5
M 3
.1.6
M 3
.2.1
M 3
.2.4
Res
pons
e M
odifi
catio
n Fa
ctor
Model ID
BNBC 1993 (y-direction)
71
Since the average value of R is close to 5 in x-direction and close to 6.5 in y-direction,
the base model (M-1.2.1) has once again been analyzed and designed considering R to
be 5. Afterwards nonlinear static analysis was performed on the same model and the
value of R was found be 5.6 in the x-direction (FP) and 8.9 in the y-direction (SW-FP).
It is apparent that when a higher value of R is used in design, a lower value appears
from nonlinear analysis and vice versa. Further application of this trial and error
procedure might lead to that unique value of R, which would remain unchanged after
nonlinear analysis from the value assumed during initial design.
4.5 Effect of Mesh Sensitivity in Evaluating R
In the analyses shear walls were split into four meshes of around five-and-a-half feet in
the horizontal direction. For further refinement of the results eight and sixteen meshes
along the horizontal direction was done for the base model (M-1.2.1) with R equals 5.
The accuracy in predicting the R value improves significantly when finer meshes are
employed. The table 4.4 shows the effect of mesh sensitivity in evaluating R – value.
Table 4.4: Value of R considering mesh sensitivity (M-1.2.1)
X - direction Y - Direction Mesh Type R R R R
4 - Mesh 2.55 2.21 5.6 4.66 1.92 8.9 8 - Mesh 2.62 2.22 5.8 4.79 1.65 7.9 16 - Mesh 2.52 2.39 6.0 4.59 1.49 6.8
It can be seen from the table that, value of R does not vary that much along the X-
direction as it does along the Y-direction. It is known that using finer meshing leads to
higher lateral deflection along, which is observed when mesh size changes from ‘4-
Mesh’ to ‘8-Mesh’. However, when an even finer ’16-Mesh’ is adopted, lateral
deflection decreases, reasons for which can be the ‘shear locking’ effect.
CHAPTER 5
CONCLUSIONS AND SUGGESTIONS
5.1 Introduction
In this study the performance of flat plate shear wall structural system has been
analyzed. Upon performing linear static analysis, numerical modelling of the structures
have been conducted using ETABS and nonlinear behaviors have been assessed. In
modelling the ten-story RMG building, the effect of soft stories have been ignored, a
thorough approach should include soft stories. This building had no vertical or plan
irregularities. A side–by–side comparison of the same structure with irregularities
would have been extremely insightful.
Using only three models for figuring out the value of seismic modification factor is
insufficient. Further analysis in necessary changing the building configuration and
placing shear walls along both the directions.
When nonlinear static or pushover analyses (NLSA) were performed the joints of the
building were assumed to be rigid, as such no hinges formed at the joints. The joints in
that case have to be detailed not permitting the formation of hinges. The foundations of
the building were modelled as fixed supports, which is not the true representation of
the actual conditions.
Although nonlinear static or pushover analysis (NLSA) generates very reliable results,
there can exist structural deficiencies that can only be figured when nonlinear time
history analysis (NLTHA) is performed. The above stated limitations, although not
highly significant, will produce a more refined result, as is required for development of
design guidelines.
5.2 Findings
Following conclusions were drawn based on the study:
A. Increasing story heights and number of stories lead to poor seismic performance, as
number of hinges in the LS-CP range and beyond CP range increases. Of the 36
73
models under review, 13 do not exhibit performance point, which shows why use
of flat plates are restricted in moderate and high seismic zones.
B. Since shear walls are placed along the Y-direction response modification factor
along that direction (SW-FP system) can be taken in the range of 6.0 – 7.0. On the
other hand in the X-direction the structure has no shear walls (FP system), so the
response modification factor along that direction can be taken in the range of 4.0 –
5.0.
C. Structures are stiffer along the direction of the shear walls, as such have a larger
base shear capacity and smaller deflections in that direction.
5.3 Suggestions
A. Performance of flat plate shear wall structural systems should be assessed placing
shear walls along both directions.
B. The building under consideration had no vertical or plan irregularities. How such
irregularities may affect the seismic performance of buildings need to be studied
C. In order to get more reliable results and finding out latent structural deficiencies
Non Linear Time History Analysis (NLTHA) should be performed.
D. Modelling should take into account the effect of soft stories.
E. The effect of foundation flexibility or soil structure interaction should be
considered.
F. Since the performance of flat plate shear wall is among the least understood
structural systems, full scale testing needs to be conducted.
G. Since the nonlinear seismic performance of the structures have been assessed, the
structures needed to be designed for earthquake loads only. However, the structures
have been designed following the 26 load combinations prescribed in BNBC 1993,
13 of which includes wind loading. As a result, it is possible for the design of any
number of models to have been governed by wind loading. For an accurate
assessment of nonlinear seismic performance of the models, the structures have to
be designed for seismic load combinations only.
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APPENDIX A
DESIGN OUTPUT FROM LINEAR STATIC ANALYSIS
Annexure A1: Model-1 Design Outputs.
Figure A-3.1: Grid, shear wall and column layout
81
Figure A-3.2: Grade beam layout
82
Figure A-3.3: Floor beam and flat plate layout (F1-F5)
83
Figure A-3.4: Floor beam and flat plate layout (F6-Roof)
84
Table A-3.1: Column details
Column
ID
Below Ground level Level-1 Level-2 & Level-3 Level-4 to UP
Column
Size
Reinforc
ement
Column
Size
Reinforce
ment
Column
Size
Reinforce
ment
Column
Size
Reinforc
ement
C1A 23"×23" 18-20mm 20"×20" 18-20mm 20"×20" 16-20mm 20"×20" 12-20mm
C1B 23"×23'' 22-20mm 20"×20" 22-20mm 20"×20" 16-20mm 20"×20" 12-20mm
C2 23''×33" 20-20mm 20"×30" 20-20mm 20"×30" 20-20mm 20"×30" 14-20mm
C3A 23"×39" 24-20mm 20"×36" 24-20mm 20"×36" 18-20mm 20"×36" 16-20mm
C3B 23"×39" 28-20mm 20"×36" 28-20mm 20"×36" 18-20mm 20"×36" 16-20mm
C3C 23"×39" 20-25mm 20"×36" 20-25mm 20"×36" 14-25mm 20"×36" 10-25mm
C3D 23"×39" 24-25mm 20"×36" 24-25mm 20"×36" 18-25mm 20"×36" 12-25mm
C4A 23"×48" 26-25mm 20"×45" 26-25mm 20"×45" 18-25mm 20"×45" 12-25mm
C4B 23"×48" 30-25mm 20"×45" 30-25mm 20"×45" 20-25mm 20"×45" 12-25mm
Table A-3.2: Shear wall details
SW ID
Section Reinforcement
Width
(in)
Thickness
(in) GF-4F 5F-Roof
SW1 270 10 16 mm @ 4 in c/c 16 mm @ 8 in c/c
SW2 270 10 16 mm @ 4 in c/c 16 mm @ 8 in c/c
SW3 270 10 16 mm @ 4 in c/c 16 mm @ 8 in c/c
SW4 270 10 16 mm @ 4 in c/c 16 mm @ 8 in c/c
Table A-3.3: Beam details
Story: 1F to 5F
Frame
Property
Top
Cover
Bottom
Cover
Top Area
I-end
Top Area
J-end
Bottom Area
I-end
Bottom Area
J-end
in in in² in² in² in²
FB1.12×27 4 4 12-20 mm 12-20 mm 8-20 mm 8-20 mm
85
FB2.12×27 4 4 12-20 mm 12-20 mm 8-20 mm 4-20 mm
FB3.12×27 4 4 8-20 mm 12-20 mm 4-20 mm 8-20 mm
FB4.12×27 4 4 8-20 mm 8-20 mm 4-20 mm 4-20 mm
FB5.12×24 4 4 5-20 mm 5-20 mm 5-20 mm 5-20 mm
FB6.12×24 2.5 2.5 2-20 mm 2-20 mm 2-20 mm 2-20 mm
Story: GF
Frame
Property
Top
Cover
Bottom
Cover
Top Area
I-end
Top Area
J-end
Bottom Area
I-end
Bottom Area
J-end
in in in² in² in² in²
GB1.12×20 4 4 5-16 mm 5-16 mm 3-16 mm 3-16 mm
GB2.12×20 4 4 3-16 mm 3-16 mm 3-16 mm 3-16 mm
GB3.12×30 4 4 2-16 mm 2-16 mm 2-16 mm 2-16 mm
GB4.12×20 4 4 5-16 mm 5-16 mm 5-16 mm 5-16 mm
Story: 6F to Roof
Frame
Property
Top
Cover
Bottom
Cover
Top Area
I-end
Top Area
J-end
Bottom Area
I-end
Bottom Area
J-end
in in in² in² in² in²
FB7.12×27 4 4 10-20 mm 10-20 mm 7-20 mm 7-20 mm
FB8.12×27 4 4 10-20 mm 9-20 mm 7-20 mm 4-20 mm
FB9.12×27 4 4 9-20 mm 10-20 mm 4-20 mm 7-20 mm
FB10.12×27 4 4 7-20 mm 7-20 mm 6-20 mm 6-20 mm
FB11.12×24 2.5 2.5 3-20 mm 3-20 mm 3-20 mm 3-20 mm
FB12.12×24 2.5 2.5 2-20 mm 2-20 mm 2-20 mm 2-20 mm
Table A-3.4: Slab details
Slab
Thickness
(inch)
Top Reinforcement
at both Direction
Bottom Reinforcement
at both Direction
Column Strip Middle Strip Column Strip Middle Strip
10 16mm @ 5 in c/c 12mm @ 5 in c/c 10mm @ 5 in c/c 10mm @ 5 in c/c
APPENDIX B
MODELING PARAMETERS FOR NON-LINEAR STATIC ANALYSIS
Annexure B1: Models Layouts Used in NLSA
Model 1 design details have been discussed in Appendix A. Model 2 and Model 3
column and flat plate dimensions and reinforcement details are similar to Model 1,
building shapes are different. Model 1 to Model 3 Effective beam width (Equivalent to
flat plate) is discussed in this section and other relevant information is discussed in
appendix A. Figure B-3.1: Model 1 flat plate extent, shear wall and column layout
87
Figure B-3.2: Model 1 effective beam width (eqt to flat plate) layout (F1-F5)
88
Figure B-3.3: Model 1 effective beam width (eqt to flat plate) layout (F6-Roof)
89
Figure B-3.4: Model 2 flat plate extent, shear wall and column layout
90
Figure B-3.5: Model 2 effective beam width (eqt to flat plate) layout (F1-F5)
91
Figure B-3.6: Model 2 effective beam width (eqt to flat plate) layout (F6-Roof)
92
Figure B-3.7: Model 3 flat plate extent, shear wall and column layout
93
Figure B-3.8: Model 3 effective beam width (eqt to flat plate) layout (F1-F5)
94
Figure B-3.9: Model 3 effective beam width (eqt to flat plate) layout (F6-Roof)
95
Annexure B2: Effective Beam Width (Equivalent to FP) Details of Model 1, 2 and 3
Table B-3.1: Model 1 to model 3 effective beam width (eqt to flat plate) details
Story: 1F to Roof
Frame
Property
Top Area
I-end
Top Area
J-end
Bottom
Area I-end
Bottom
Area J-end
EQ.B80×10 16 mm @
5 in c/c"
16 mm @
5 in c/c"
12 mm @
5 in c/c
12 mm @
5 in c/c
96
Annexure B3: Modeling Parameters and Acceptance Criteria for NLSA
Table B-3.2: Modeling parameters and numerical acceptance criteria for
nonlinear procedures—reinforced concrete beams
Conditions
Modeling Parametersa Acceptance Criteriaa
Plastic
Rotation Angle
(Radians)
Residual
Strength
Ratio
Plastic Rotations Angle
(Radians)
Performance Level
a b c IO LS CP
Condition i. Beams controlled by flexureb
(ρ-
ρ')/ρbal
Transverse
Reinforcementc V/(bwd√fc′)d
≤ 0.0 C ≤ 3 (0.25) 0.025 0.050 0.20 0.010 0.025 0.050
≤ 0.0 C ≥ 6 (0.5) 0.020 0.040 0.20 0.005 0.020 0.040
≥ 0.5 C ≤ 3 (0.25) 0.020 0.030 0.20 0.005 0.020 0.030
≥ 0.5 C ≥ 6 (0.5) 0.015 0.020 0.20 0.005 0.015 0.020
≤ 0.0 NC ≤ 3 (0.25) 0.020 0.030 0.20 0.005 0.020 0.030
≤ 0.0 NC ≥ 6 (0.5) 0.010 0.015 0.20 0.002 0.010 0.015
≥ 0.5 NC ≤ 3 (0.25) 0.010 0.015 0.20 0.005 0.010 0.015
≥ 0.5 NC ≥ 6 (0.5) 0.005 0.010 0.20 0.002 0.005 0.010
Condition ii. Beams controlled by shearb
Stirrup spacing ≤ d /2 0.003 0.020 0.20 0.0015 0.010 0.020
Stirrup spacing ≥ d /2 0.003 0.010 0.20 0.0015 0.005 0.010
Condition iii. Beams controlled by inadequate development or splicing along the spanb
Stirrup spacing ≤ d /2 0.003 0.020 0.00 0.0015 0.010 0.020
Stirrup spacing ≥ d /2 0.003 0.010 0.00 0.0015 0.005 0.010
Condition iv. Beams controlled by inadequate embedment into beam–column jointb
0.015 0.030 0.20 0.010 0.0200 0.030
NOTE: fc′ in lb/in.2 (MPa) units. aValues between those listed in the table should be determined by linear interpolation. bWhere more than one of conditions i, ii, iii, and iv occur for a given component, use the
minimum appropriate numerical value from the table.
97
c“C” and “NC” are abbreviations for conforming and nonconforming transverse
reinforcement, respectively. Transverse reinforcement is conforming if, within the flexural
plastic hinge region, hoops are spaced at ≤ d/3, and if, for components of moderate and high
ductility demand, the strength provided by the hoops (Vs) is at least 3/4 of the design shear.
Otherwise, the transverse reinforcement is considered nonconforming. dV is the design shear force from NSP or NDP.
Table B-3.3: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—reinforced concrete columns
Conditions
Modeling Parametersa Acceptance Criteriaa
Plastic Rotation
Angle (Radians)
Residual
Strength
Ratio
Plastic Rotations Angle
(Radians)
Performance Level
a b c IO LS CP
Condition ib
P/(Agf'c)c ρ=(Av/bws)
≤ 0.1 ≥ 0.006 0.035 0.060 0.20 0.005 0.045 0.060
≥ 0.6 ≥ 0.006 0.010 0.100 0.00 0.003 0.009 0.010
≤ 0.1 = 0.002 0.027 0.034 0.20 0.005 0.027 0.034
≥ 0.6 = 0.002 0.005 0.005 0.00 0.002 0.004 0.005
Condition iib
P/(Agf'c)c ρ=(Av/bws) V/(bwd√fc′)d
≤ 0.1 ≥ 0.006 ≤ 3 (0.25) 0.032 0.060 0.20 0.005 0.045 0.060
≤ 0.1 ≥ 0.006 ≥ 6 (0.5) 0.025 0.060 0.20 0.005 0.045 0.060
≥ 0.6 ≥ 0.006 ≤ 3 (0.25) 0.010 0.010 0.00 0.003 0.009 0.010
≥ 0.6 ≥ 0.006 ≥ 6 (0.5) 0.008 0.008 0.00 0.003 0.007 0.008
≤ 0.1 ≤ 0.0005 ≤ 3 (0.25) 0.012 0.012 0.20 0.005 0.010 0.012
≤ 0.1 ≤ 0.0005 ≥ 6 (0.5) 0.006 0.006 0.20 0.004 0.005 0.006
≥ 0.6 ≤ 0.0005 ≤ 3 (0.25) 0.004 0.004 0.00 0.002 0.003 0.004
≥ 0.6 ≤ 0.0005 ≥ 6 (0.5) 0.000 0.000 0.00 0.000 0.000 0.000
Condition iiib
P/(Agf'c)c ρ=(Av/bws)
≤ 0.1 ≥ 0.006 0.000 0.060 0.00 0.000 0.045 0.060
≥ 0.6 ≥ 0.006 0.000 0.008 0.00 0.000 0.007 0.008
98
≤ 0.1 ≤ 0.0005 0.000 0.006 0.00 0.000 0.005 0.006
≥ 0.6 ≤ 0.0005 0.000 0.000 0.00 0.000 0.000 0.000
Condition iv. Columns controlled by inadequate development or splicing along the clear heightb
P/(Agf'c)c ρ=(Av/bws)
≤ 0.1 ≥ 0.006 0.000 0.060 0.40 0.000 0.005 0.060
≥ 0.6 ≥ 0.006 0.000 0.008 0.40 0.000 0.007 0.008
≤ 0.1 ≤ 0.0005 0.000 0.006 0.20 0.000 0.005 0.006
≥ 0.6 ≤ 0.0005 0.000 0.000 0.00 0.000 0.000 0.000
NOTE: fc′ in lb/in.2 (MPa) units. aValues between those listed in the table should be determined by linear interpolation. bRefer to Section 10.4.2.2.2 of ASCE 41-13 for definition of conditions i, ii, and iii. Columns
are considered to be controlled by inadequate development or splices where the calculated
steel stress at the splice exceeds the steel stress specified by Eq.( 10-2) of ASCE 41-13.
Where more than one of conditions i, ii, iii, and iv occurs for a given component, use the
minimum appropriate numerical value from the table. cWhere P > 0.7Ag f'c, the plastic rotation angles should be taken as zero for all performance
levels unless the column has transverse reinforcement consisting of hoops with 135-degree
hooks spaced at ≤ d/3 and the strength provided by the hoops (Vs) is at least 3/4 of the design
shear. Axial load P should be based
on the maximum expected axial loads caused by gravity and earthquake loads. dV is the design shear force from NSP or NDP.
99
Table B-3.4: Modeling parameters and numerical acceptance criteria for
nonlinear procedures—two-way slabs and slab–column connections
Conditions
Modeling Parametersa Acceptance Criteriaa
Plastic Rotation
Angle (Radians)
Residual
Strength
Ratio
Plastic Rotations Angle
(Radians)
Performance Level
Secondary
a b c IO LS CP
Condition i. Reinforced concrete slab–column connectionsb
(Vg/Vo)c Continuity
Reinforcementd
0.0 Yes 0.035 0.050 0.20 0.01 0.035 0.050
0.2 Yes 0.030 0.040 0.20 0.01 0.030 0.040
0.4 Yes 0.020 0.030 0.20 0.00 0.020 0.030
≥ 0.6 Yes 0.000 0.020 0.00 0.00 0.000 0.020
0.0 No 0.025 0.025 0.00 0.01 0.020 0.025
0.2 No 0.020 0.020 0.00 0.01 0.015 0.020
0.4 No 0.010 0.010 0.00 0.00 0.008 0.010
0.6 No 0.000 0.000 0.00 0.00 0.000 0.000
≥ 0.6 No 0.000 0.000 0.00 __e __e __e
Condition ii. Posttensioned slab–column connectionsb
(Vg/Vo)c Continuity
Reinforcementd
0.0 Yes 0.035 0.050 0.40 0.01 0.035 0.050
0.6 Yes 0.005 0.030 0.20 0.00 0.025 0.030
≥ 0.6 Yes 0.000 0.020 0.20 0.00 0.015 0.020
0.0 No 0.025 0.025 0.00 0.01 0.020 0.025
0.6 No 0.000 0.000 0.00 0.00 0.000 0.000
≥ 0.6 No 0.000 0.000 0.00 __e __e __e
Condition iii. Slabs controlled by inadequate development or splicing along the spanb
0.000 0.020 0.00 0.00 0.010 0.020
Condition iv. Slabs controlled by inadequate embedment into slab–column jointb
0.015 0.030 0.20 0.01 0.020 0.030
aValues between those listed in the table should be determined by linear interpolation.
100
bWhere more than one of conditions i, ii, iii, and iv occur for a given component, use the
minimum appropriate numerical value from the table. cVg is the gravity shear acting on the slab critical section as defined by ACI 318, and Vo is
the direct punching shear strength as defined by ACI 318. d“Yes” should be used where the area of effectively continuous main bottom bars passing
through the column cage in each direction is greater than or equal to 0.5 Vg /( ϕfy). Where
the slab is posttensioned, “Yes” should be used where at least one of the posttensioning
tendons in each direction passes through the column cage. Otherwise, “No” should be
used. eAction should be treated as force controlled.Action should be treated as force controlled.
Table B-3.5: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure
(Model 1: f'c=3ksi, fy=60ksi)
Conditions
Plastic Hinge
Rotation
(Radians)
Residual
Strength
Ratio
Acceptable Plastic
Hinge Rotationa
(Radians)
Performance Level
a b c IO LS CP
Condition i. Shear walls and wall segments
STORY
((As-
As')fy+P)/
twlwf'c
V/
twlwf'c
Confined
Boundaryb
Base -
Level 2 0.25 < 4 NO 0.002 0.005 0.250 0.001 0.003 0.005
ROOF-
Level 7 0.10 < 4 NO 0.006 0.015 0.600 0.002 0.008 0.015
Level 3 0.22 < 4 NO 0.003 0.007 0.318 0.001 0.004 0.007
Level 4 0.19 < 4 NO 0.004 0.009 0.393 0.001 0.005 0.009
Level 5 0.16 < 4 NO 0.004 0.011 0.467 0.002 0.006 0.011
Level 6 0.12 < 4 NO 0.005 0.013 0.542 0.002 0.007 0.013
101
aValues between those listed in the table should be determined by linear interpolation. bA boundary element shall be considered confined where transverse reinforcement exceeds
75% of the requirements given in ACI 318 and spacing of transverse reinforcement does not
exceed 8 db. It shall be permitted to take modeling parameters and acceptance criteria as
80% of confined values where boundary elements have at least 50% of the requirements
given in ACI 318 and spacing of transverse reinforcement does not exceed 8 db. Otherwise,
boundary elements shall be considered not confined.
Table B-3.6: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure
(Model 2: f'c=3ksi, fy=60ksi)
Conditions
Plastic Hinge
Rotation
(Radians)
Residual
Strength
Ratio
Acceptable Plastic
Hinge Rotationa
(Radians)
Performance Level
a b c IO LS CP
Condition i. Shear walls and wall segments
STORY
((As-
As')fy+P)/
twlwf'c
V/
twlwf'c
Confined
Boundaryb
Base -
Level 2 0.25 < 4 NO 0.002 0.005 0.250 0.001 0.003 0.005
ROOF-
Level 10 0.10 < 4 NO 0.006 0.015 0.600 0.002 0.008 0.015
Level 3 0.25 < 4 NO 0.002 0.005 0.254 0.001 0.003 0.005
Level 4 0.23 < 4 NO 0.003 0.007 0.303 0.001 0.004 0.007
Level 5 0.21 < 4 NO 0.003 0.008 0.354 0.001 0.004 0.008
Level 6 0.18 < 4 NO 0.004 0.009 0.406 0.001 0.005 0.009
Level 7 0.16 < 4 NO 0.004 0.011 0.458 0.002 0.006 0.011
Level 8 0.14 < 4 NO 0.005 0.012 0.512 0.002 0.007 0.012
Level 9 0.13 < 4 NO 0.005 0.013 0.542 0.002 0.007 0.013
102
Table B-3.7: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure
(Model 3: f'c=3ksi, fy=60ksi)
Conditions
Plastic Hinge
Rotation
(Radians)
Residual
Strength
Ratio
Acceptable Plastic
Hinge Rotationa
(Radians)
Performance Level
a b c IO LS CP
Condition i. Shear walls and wall segments
STORY
((As-
As')fy+P)/
twlwf'c
V/
twlwf'c
Confined
Boundaryb
Base -
Level 2 0.25 < 4 NO 0.002 0.005 0.250 0.001 0.003 0.005
ROOF-
Level 9 0.10 < 4 NO 0.006 0.015 0.600 0.002 0.008 0.015
Level 3 0.25 < 4 NO 0.002 0.005 0.255 0.001 0.003 0.005
Level 4 0.23 < 4 NO 0.003 0.007 0.305 0.001 0.004 0.007
Level 5 0.21 < 4 NO 0.003 0.008 0.355 0.001 0.005 0.008
Level 6 0.18 < 4 NO 0.004 0.009 0.407 0.001 0.005 0.009
Level 7 0.16 < 4 NO 0.004 0.011 0.459 0.002 0.006 0.011
Level 8 0.14 < 4 NO 0.005 0.013 0.513 0.002 0.007 0.013
aValues between those listed in the table should be determined by linear interpolation. bA boundary element shall be considered confined where transverse reinforcement exceeds
75% of the requirements given in ACI 318 and spacing of transverse reinforcement does not
exceed 8 db. It shall be permitted to take modeling parameters and acceptance criteria as
80% of confined values where boundary elements have at least 50% of the requirements
given in ACI 318 and spacing of transverse reinforcement does not exceed 8 db. Otherwise,
boundary elements shall be considered not confined.
103
aValues between those listed in the table should be determined by linear interpolation. bA boundary element shall be considered confined where transverse reinforcement exceeds 75% of
the requirements given in ACI 318 and spacing of transverse reinforcement does not exceed 8 db. It
shall be permitted to take modeling parameters and acceptance criteria as 80% of confined values
where boundary elements have at least 50% of the requirements given in ACI 318 and spacing of
transverse reinforcement does not exceed 8 db. Otherwise, boundary elements shall be considered
not confined.
Table B-3.8: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure
(Model 1: f'c=4ksi, fy=72ksi)
Conditions
Plastic Hinge
Rotation
(Radians)
Residual
Strength
Ratio
Acceptable Plastic
Hinge Rotationa
(Radians)
Performance Level
a b c IO LS CP
Condition i. Shear walls and wall segments
STORY
((As-
As')fy+P)/
twlwf'c
V/
twlwf'c
Confined
Boundaryb
Base -
Level 2 0.25 < 4 NO 0.002 0.005 0.250 0.001 0.003 0.005
ROOF-
Level 7 0.10 < 4 NO 0.006 0.015 0.600 0.002 0.008 0.015
Level 3 0.17 < 4 NO 0.004 0.011 0.447 0.002 0.006 0.011
Level 4 0.14 < 4 NO 0.005 0.012 0.503 0.002 0.007 0.012
Level 5 0.12 < 4 NO 0.006 0.014 0.559 0.002 0.007 0.014
Level 6 0.09 < 4 NO 0.006 0.015 0.615 0.002 0.008 0.015
aValues between those listed in the table should be determined by linear interpolation. bA boundary element shall be considered confined where transverse reinforcement exceeds
75% of the requirements given in ACI 318 and spacing of transverse reinforcement does not
exceed 8 db. It shall be permitted to take modeling parameters and acceptance criteria as
104
80% of confined values where boundary elements have at least 50% of the requirements
given in ACI 318 and spacing of transverse reinforcement does not exceed 8 db. Otherwise,
boundary elements shall be considered not confined.
Table B-3.9: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure
(Model 2: f'c=4ksi, fy=72ksi)
Conditions
Plastic Hinge
Rotation
(Radians)
Residual
Strength
Ratio
Acceptable Plastic
Hinge Rotationa
(Radians)
Performance Level
a b c IO LS CP
Condition i. Shear walls and wall segments
STORY
((As-
As')fy+P)/
twlwf'c
V/
twlwf'c
Confined
Boundaryb
Base -
Level 2 0.25 < 4 NO 0.002 0.005 0.250 0.001 0.003 0.005
ROOF-
Level 10 0.10 < 4 NO 0.006 0.015 0.600 0.002 0.008 0.015
Level 3 0.19 < 4 NO 0.004 0.009 0.399 0.001 0.005 0.009
Level 4 0.17 < 4 NO 0.004 0.010 0.436 0.002 0.006 0.010
Level 5 0.15 < 4 NO 0.005 0.011 0.474 0.002 0.006 0.011
Level 6 0.14 < 4 NO 0.005 0.013 0.513 0.002 0.007 0.013
Level 7 0.12 < 4 NO 0.005 0.014 0.552 0.002 0.007 0.014
Level 8 0.10 < 4 NO 0.006 0.015 0.592 0.002 0.008 0.015
Level 9 0.09 < 4 NO 0.006 0.015 0.614 0.002 0.008 0.015
aValues between those listed in the table should be determined by linear interpolation. bA boundary element shall be considered confined where transverse reinforcement exceeds
75% of the requirements given in ACI 318 and spacing of transverse reinforcement does not
exceed 8 db. It shall be permitted to take modeling parameters and acceptance criteria as
80% of confined values where boundary elements have at least 50% of the requirements
105
given in ACI 318 and spacing of transverse reinforcement does not exceed 8 db. Otherwise,
boundary elements shall be considered not confined.
Table B-3.10: Modeling parameters and numerical acceptance criteria for nonlinear
procedures—RC shear walls and associated components controlled by flexure
(Model 3: f'c=4ksi, fy=72ksi)
Conditions
Plastic Hinge
Rotation
(Radians)
Residual
Strength
Ratio
Acceptable Plastic
Hinge Rotationa
(Radians)
Performance Level
a b c IO LS CP
Condition i. Shear walls and wall segments
STORY
((As-
As')fy+P)
/ twlwf'c
V/
twlwf'c
Confined
Boundaryb
Base -
Level 2 0.25 < 4 NO 0.002 0.005 0.250 0.001 0.003 0.005
ROOF-
Level 9 0.10 < 4 NO 0.006 0.015 0.600 0.002 0.008 0.015
Level 3 0.19 < 4 NO 0.004 0.009 0.400 0.001 0.005 0.009
Level 4 0.17 < 4 NO 0.004 0.010 0.437 0.002 0.006 0.010
Level 5 0.15 < 4 NO 0.005 0.011 0.475 0.002 0.006 0.011
Level 6 0.14 < 4 NO 0.005 0.013 0.514 0.002 0.007 0.013
Level 7 0.12 < 4 NO 0.005 0.014 0.553 0.002 0.007 0.014
Level 8 0.10 < 4 NO 0.006 0.015 0.593 0.002 0.008 0.015
aValues between those listed in the table should be determined by linear interpolation. bA boundary element shall be considered confined where transverse reinforcement exceeds
75% of the requirements given in ACI 318 and spacing of transverse reinforcement does not
exceed 8 db. It shall be permitted to take modeling parameters and acceptance criteria as
80% of confined values where boundary elements have at least 50% of the requirements
given in ACI 318 and spacing of transverse reinforcement does not exceed 8 db. Otherwise,
boundary elements shall be considered not confined.
APPENDIX C BASE SHEAR AND MAXIMUM TOP DISPLACEMENT
Annexure C1: Summary of Base Shear and Maximum Top Displacement
Base shear and corresponding maximum top displacements have been calculated using
displacement coefficient method (ASCE 41-13) and capacity spectrum method (FEMA
440EL). The column on the extreme right of each table shows acceleration in terms of
g value up to which buildings can perform as per capacity spectrum method.
Table C-4.1: Summary of base shear and maximum top displacement
(as per BNBC 1993 demand spectrum)
Model
ID
No. of
Story
Story
Height
h (ft)
EQ
Direction
f'c=3ksi, fy=60ksi
ASCE 41-13 NSP FEMA 440 EL
Base
Shear
V
(kips)
Top
Deflection
δ (in)
Base
Shear
V
(kips)
Top
Deflection
δ (in)
M 1.1.1
7
10 X 3160 9.97 3142 9.78
Y 4536 3.64 5386 4.97
M 1.1.2 12 X 2597 13.37 2596 13.34
Y 3616 4.50 4548 6.71
M 1.1.3 15 X 1980 19.52 1981 20.19
Y 2945 6.53 3694 9.79
M 1.2.1
10
10 X 2726 17.28 2723 16.75
Y 3947 7.29
M 1.2.2 12 X 2000 23.93
Y 3353 10.25
M 1.2.3 15 X 1255 44.04
Y 2571 14.04
107
Model
ID
No. of
Story
Story
Height
h (ft)
EQ
Direction
f'c=3ksi, fy=60ksi
ASCE 41-13 NSP FEMA 440 EL
Base
Shear
V
(kips)
Top
Deflection
δ (in)
Base
Shear
V
(kips)
Top
Deflection
δ (in)
M 2.1.1
7
10 X 2541 9.46 2529 9.35
Y 3789 3.13 4903 4.64
M 2.1.2 12 X 2144 12.70 2133 12.48
Y 3061 3.96 4134 6.25
M 2.1.3 15 X 1632 18.34 1634 18.49
Y 2320 5.27
M 2.2.1
10
10 X 2280 16.11 2274 15.86
Y 3608 6.82
M 2.2.2 12 X 1726 22.15
Y 2451 7.09
M 2.2.3 15 X 1117 39.63
Y 2133 17.32
M 3.1.1
7
10 X 2278 10.15 2277 10.13
Y 3875 3.10 4968 4.50
M 3.1.2 12 X 1898 13.66 1898 13.67
Y 3205 4.03 4171 6.04
M 3.1.3 15 X 1402 20.18 1392 22.03
Y 2456 5.41 3422 8.91
M 3.2.1
10
10 X 1979 17.71 1979 17.69
Y 3357 6.03 4289 9.53
M 3.2.2 12 X 1414 25.37
Y 2743 7.83
M 3.2.3 15 X 842 46.17
Y 2374 13.10
108
Table C-4.2: Summary of base shear and maximum top displacement
(as per BNBC 1993 demand spectrum)
Model
ID
No. of
Story
Story
Height
h (ft)
EQ
Direction
f'c=4ksi, fy=72ksi
ASCE 41-13 NSP FEMA 440 EL
Base
Shear
V
(kips)
Top
Deflection
δ (in)
Base
Shear
V
(kips)
Top
Deflectionδ
(in)
M 1.1.4
7
10 X 3383 9.99 3453 10.31
Y 4720 3.56 6078 5.23
M 1.1.5 12 X 2796 13.39 2908 14.33
Y 3785 4.45 5132 7.06
M 1.1.6 15 X 2173 19.56 2248 21.10
Y 3054 6.44 4187 10.35
M 1.2.4
10
10 X 3100 17.37 3125 17.89
Y 4142 7.13
M 1.2.5 12 X 2398 24.22
Y 3529 9.99
M 1.2.6 15 X 1485 44.62
Y 2683 13.62
M 2.1.4
7
10 X 2735 9.48 2786 9.79
Y 3910 3.06 5502 4.88
M 2.1.5 12 X 2338 12.73 2389 13.25
Y 3118 3.82 4622 6.54
M 2.1.6 15 X 1817 18.49 1866 19.58
Y 2405 5.21
M 2.2.4
10
10 X 2585 16.29
Y 3761 6.66
M 2.2.5 12 X 2049 22.19
Y 2556 7.06
M 2.2.6 15 X 1357 40.67
Y 2252 17.16
109
Model
ID
No. of
Story
Story
Height
h (ft)
EQ
Direction
f'c=4ksi, fy=72ksi
ASCE 41-13 NSP FEMA 440 EL
Base
Shear
V
(kips)
Top
Deflection
δ (in)
Base
Shear
V
(kips)
Top
Deflectionδ
(in)
M 3.1.4
7
10 X 2436 10.16 2515 10.70
Y 3989 3.03 5529 4.72
M 3.1.5 12 X 2041 13.68 2105 14.46
Y 3326 3.97 4596 6.24
M 3.1.6 15 X 1544 20.22 1619 23.14
Y 2568 5.41 3765 9.19
M 3.2.4
10
10 X 2238 17.81 2264 18.55
Y 3475 5.89 4672 9.18
M 3.2.5 12 X 1704 25.26
Y 2829 7.69
M 3.2.6 15 X 1024 47.29
Y 2481 12.86