Evaluation of Response Modification Factor for Shear wall ...

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 4.9: 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


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


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







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


procedures—reinforced concrete columns .............................................................................. 97


procedures—two-way slabs and slab–column connections ..................................................... 99


procedures—RC shear walls and associated components controlled by flexure ................... 100







xiv





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




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




E. DUAL SYSTEMS: INTERMEDIATE MOMENT FRAMES

CAPABLE OF RESISTING AT LEAST 25% OF

PRESCRIBED SEISMIC FORCES (with bracing or shear wall)


2. Special reinforced concrete shear walls 6.5


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

https://en.wikipedia.org/wiki/Structural_engineering

https://en.wikipedia.org/wiki/Structural_engineering

https://en.wikipedia.org/wiki/Structural_system

https://en.wikipedia.org/wiki/Braced_frame

https://en.wikipedia.org/wiki/Lateral_load

https://en.wikipedia.org/wiki/Wind

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

)



0

1000

2000

3000

4000

5000

6000

7000

8000

0 5 10 15 20

Bas

e Fo

rce

(kip

)



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


(elevation 3) in x-direction

56


(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


view) in x-direction


(elevation C) in x-direction

IO-LS

LS-CP

>CP

58





IO-LS

LS-CP

>CP

59

IO-LS

LS-CP

>CP


(elevation C) in x-direction


view) in x-direction

60

IO-LS

LS-CP

>CP





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



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


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



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


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


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


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


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


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


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


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.

REFERENCES

ACI 318 (2008): “Building Code Requirements for Structural Concrete and

Commentary”, American Concrete Institute, Michigan.

ACI 374.3R (2016): “Guide to nonlinear modeling parameters for earthquake-

resistant Structures”, American Concrete Institute, Michigan.

ASCE/SEI 7 (2010): “Minimum Design Loads for Buildings and Other Structures”,

American Society of Civil Engineers, Virginia.

ASCE/SEI 41 (2013): “Seismic Evaluation and Retrofit of Existing Buildings”,

American Society of Civil Engineers, Virginia.

Altug E. and Elnashai A. S. (2003), “Seismic vulnerability of flat-slab structures”,

University of Illinois at Urbana-Champaign, Tech. Rep. DS-9 Project.

ATC 3-06 (1978): “Tentative Provisions for the Development of Seismic Regulations

for Buildings”, Applied Technology Council, California.

ATC-19 (1995): “Structural response modification factor”, Applied Technology

Council, California.

ATC 40 (1996): “Seismic Evaluation & Retrofit of Concrete Buildings”, Applied

Technology Council, California.

Birely A. C., Lowes L. N. and Lehman D. E. (2014), “Evaluation of ASCE 41

modeling parameters for slender reinforced concrete structural walls”, ASCE Special

Publication, volume 297, pp. 201-226.

BNBC (1993): “Bangladesh National Building Code”, Housing and building

Research Institute, Dhaka.

75

BNBC (2015): “Bangladesh National Building Code”, Housing and building

Research Institute, Dhaka (To be published).

Bohl A. and Adebar P. (2011), “Plastic hinge lengths in high-rise concrete shear

walls”, ACI Structural Journal, Vol. 108, pp. 148-157.

Colotti V. (1993), “Shear behavior of RC structural walls”, ASCE Journal of

Structural Engineering, Vol.119, pp. 728-746.

Erberik M. A. and Elnashai A. S. (2004), “Vulnerability analysis of flat slab

structures”, in 13th World conference on earthquake engineering, Vol. 5, pp. 3102.

FEMA 273 (1997): “NEHRP Guidelines for the Seismic Rehabilitation of Buildings”,

Federal Emergency Management Agency, Washington, D.C.

FEMA 274 (1997): “NEHRP Commentary on the Guidelines for the Seismic

Rehabilitation of Buildings”, Federal Emergency Management Agency, Washington,

D.C.

FEMA 302a (1997): “NEHRP Recommended Provisions for Seismic Regulations for

New Buildings and Other Structures”, Building Seismic Safety Council, Washington,

D.C.

FEMA 303a (1997): “NEHRP Recommended Provisions for Seismic Regulations for


D.C.

FEMA 356 (2000): “Prestandard and Commentary for the Seismic Rehabilitation of

Buildings”, Federal Emergency Management Agency, Washington, D.C.

FEMA 368 (2000): “NEHRP Recommended Provisions for Seismic Regulations for


D.C.

76

FEMA 369 (2000): “NEHRP Recommended Provisions for Seismic Regulations for


D.C.

FEMA 450-1 (2003): “NEHRP Recommended Provisions for Seismic Regulations

for New Buildings and Other Structures”, Building Seismic Safety Council,

Washington, D.C.

FEMA 450-2 (2004): “NEHRP Recommended Provisions for Seismic Regulations

for New Buildings and Other Structures”, Building Seismic Safety Council,

Washington, D.C.

FEMA 440 (2005): “Improvement of Nonlinear Static Seismic Analysis Procedures”,


FEMA 440A (2009): “Effects of Strength and Stiffness Degradation on Seismic

Response”, Federal Emergency Management Agency, Washington, D.C.

FEMA 695 (2009): “Quantification of Building Seismic Performance Factors”,


FEMA 750 (2009): “NEHRP Recommended Seismic Provisions for Seismic

Regulations for New Buildings and Other Structures”, Building Seismic Safety

Council, Washington, D.C.

FEMA 751 (2009): “NEHRP Recommended Seismic Provisions”, Building Seismic

Safety Council, Washington, D.C.

FEMA 795 (2011): “Quantification of Building Seismic Performance Factors”,


Gagan K. R. R. and Nethravathi S. M. (2015), “Pushover analysis of framed structure

with flat plate and flat slab for different structural systems” in International Journal

of Innovative Research and Creative Technology, Vol. 2, pp. 54-59.

77

Gasparini D.A. (2002),” Contribution of C.A.P. turner to development of RC flat

slabs 1905-1909”, ASCE Journal of Structural Engineering, Vol.128, pp. 728-746.

Gasparini D. A. (2005), “Discussion of Contributions of C. A. P. Turner to

Development of Reinforced Concrete Flat Slabs 1905–1909” ASCE Journal of

Structural Engineering, Vol. 131, pp. 524-525.

Goel R. K. (2008), “Evaluation of current nonlinear static procedures for reinforced

concrete buildings”, The 14th World Conference on Earthquake Engineering, Beijing,

China.

Goud V. (2016), “Analysis and design of flat slab with and without shear wall of

multi-storied building frames”, IOSR Journal of Engineering, volume 06, pp. 30-37.

Harras O. A. (2015), “Seismic behaviour and nonlinear modeling of reinforced

concrete flat slab-column connections” M. Sc. Engg. Thesis, University of British

Columbia, Canada.

Jiang H. and Kurama Y. C. (2012), “An analytical investigation on the seismic retrofit

of older medium-rise reinforced concrete shear walls under lateral loads”, Eisevier

Journal of Engineering Structures, Vol. 46, pp. 459-470.

Kammar S. I. and Doshi T. D. (2015), “Nonlinear static analysis of asymmetric

building with and without Shear Wall”, International Research Journal of Engineering

and Technology, volume 02, pp. 1838-1841.

Kang T. H. K., Wallace J. W. and Elwood K. J. (2009), “Nonlinear Modeling of flat-

plate systems”, ASCE Journal of Structural Engineering, Vol. 135, pp. 135-147.

Kayal S. (1986), “Nonlinear interaction of R C frame-wall structures”, Journal of

structural engineering”, ASCE Journal of Structural Engineering, Vol. 112, pp. 245-

258.

https://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9445%282005%29131%3A3%28524%29

78

Kelly T. (2004), “Nonlinear analysis of reinforced concrete shear wall structure”,

Bulletin of the New Zealand society for earthquake engineering, Vol 37, pp. 156-180.

Kim J. and Kim T. (2008), “Seismic performance evaluation of non-seismic designed

flat-plate structures”, ASCE Journal of Performance of Constructed Facilities, Vol.

22, pp. 356-363.

Melek M., Darama H., Gogus A. and Kang T. (2012), “Effects of modeling of RC

flat slabs on nonlinear response of high rise building systems”, The 15th World

Conference on Earthquake Engineering, Lisbon.

Mullapudi R.T., Charkhchi P. and Ayoub A.S., “Evaluation of behavior of reinforced

concrete shear walls through finite element analysis”, ACI Special Publication, Vol.

265, pp. 73-100.

NBCC (2005): “National Building Code of Canada”, Canadian Commission on

Building and Fire Codes, National Research Council of Canada, Canada.

Pawah S., Tiwari V. and Prajapati M. (2008), “Analytical approach to study effect of

shear wall on flat slab and two way slab”, International Journal of Engineering

Technology and Advanced Engineering, volume 4, pp. 244-252.

Rahman M. K., Ajmal M., Baluch M. H. and Celep Z. (2012), “Nonlinear static

pushover analysis of an eight story RC frame-shear wall building in Saudi Arabia”,

The 15th World Conference on Earthquake Engineering, Lisbon.

Rana R., Jin L. and Zekioglu A. (2004), “Pushover analysis of a 19-storied concrete

shear wall building”, in 13th World conference on earthquake engineering, Aug.

2004, P. 133-165.

Rao G. V. R., Gopalakrishnan N., Jaya K. P., Muthumani K., Reddy G. R. and

Parulekar Y. M. (2014), “Studies on nonlinear behavior of shear walls of medium

aspect ratio under monotonic and cyclic loading, ASCE Journal of Performance of

Constructed Facilities”, Vol. 30, pp. 330-346.

79

SEAOC Blue book (2009): Seismic design recommendations, Structural Engineers

Association of Califonia, Califonia.

Song J.W., Song J.G., Lee Y.W. and Kim G.W. (2012), “Seismic performance of flat

plate system with shear reinforcements”, The 15th World Conference on Earthquake

Engineering, Lisbon.

Tian Y., Jirsa J. O. and Bayrak O. (2009), “Nonlinear modeling of slab-column

connections under cyclic loading”, ACI structural journal, Vol. 106, pp. 30-38.

UBC (1961): “Uniform Building Code, edition 1961”, International Conference of

Building Officials, California.

UBC (1988): “Uniform Building Code”, International Conference of Building

Officials, California.







Wang W. and Teng S. (2008), “Finite-element analysis of reinforced concrete flat

plate structures by layered shell element”, ASCE Journal of Structural Engineering,

Vol. 134, pp. 1862-1872.

Zafar A. (2009), “Response modification factor of reinforced concrete moment

resisting frames in developing countries”, M. Sc. Engg. Thesis, Department of Civil

Engineering, University of Illinois at Urbana-Champaign.

https://ascelibrary.org/journal/jsendh

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


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


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


91


92

Figure B-3.7: Model 3 flat plate extent, shear wall and column layout

93


94


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.


procedures—reinforced concrete columns

Conditions


Plastic Rotation

Angle (Radians)

Residual

Strength

Ratio


(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


≤ 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


≤ 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


Plastic Rotation

Angle (Radians)

Residual

Strength

Ratio


(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.


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.




Conditions

Plastic Hinge

Rotation

(Radians)

Residual

Strength

Ratio

Acceptable Plastic

Hinge Rotationa

(Radians)

Performance Level

a b c IO LS CP


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




Conditions

Plastic Hinge

Rotation

(Radians)

Residual

Strength

Ratio

Acceptable Plastic

Hinge Rotationa

(Radians)

Performance Level

a b c IO LS CP


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







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.




Conditions

Plastic Hinge

Rotation

(Radians)

Residual

Strength

Ratio

Acceptable Plastic

Hinge Rotationa

(Radians)

Performance Level

a b c IO LS CP


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




104







Conditions

Plastic Hinge

Rotation

(Radians)

Residual

Strength

Ratio

Acceptable Plastic

Hinge Rotationa

(Radians)

Performance Level

a b c IO LS CP


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





105






Conditions

Plastic Hinge

Rotation

(Radians)

Residual

Strength

Ratio

Acceptable Plastic

Hinge Rotationa

(Radians)

Performance Level

a b c IO LS CP


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







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


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


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


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

Evaluation of Response Modification Factor for Shear wall ...

Documents

Transcript of Evaluation of Response Modification Factor for Shear wall ...