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STUDY ON THE FUNDAMENTAL PERIOD OF VIBRATION FOR
BUILDINGS WITH DIFFERENT CONFIGURATIONS
A Thesis Submitted To
The Graduate School of Natural and Applied Sciences
of
Atilim University
By
Bashar A. Shon
In Partial Fulfilment of The Requirements for The Degree of
Master of Science
In
The Department of Civil Engineering
APRIL 2015
Approval of the Graduate School of Natural and Applied Sciences, Atilim University.
Prof. Dr. İbrahim Akman
Director
I certify that this thesis satisfies all the requirements as a thesis for the degree of Master
of Science.
Assoc. Prof. Dr. Tolga Akış
Department Chair
This is to certify that we have read the thesis “Study on The Fundamental Period of
Vibration for Buildings with Different Configurations” submitted by Bashar A. Shon
and that in our opinion it is fully adequate, in scope and quality, as a thesis for the
degree of Master of Science.
Assist. Prof. Dr. Gökhan Tunç
Supervisor
Examining Committee Members
Assoc. Prof. Dr. Tolga Akış
Assist. Prof. Dr. Gökhan Tunç
Assist. Prof. Dr. Riyad Shihab
I declare and guarantee that all data, knowledge and information in this
document has been obtained, processed and presented in accordance with academic
rules and ethical conduct. Based on these rules and conduct, I have fully cited and
referenced all material and results that are not original to this work.
Name, Last name: Bashar A., Shon
Signature:
ABSTRACT
STUDY ON THE FUNDAMENTAL PERIOD OF VIBRATION FOR
BUILDINGS WITH DIFFERENT CONFIGURATIONS
Bashar A. Shon
M.S., Civil Engineering Department
Supervisor: Assist. Prof. Dr. Gökhan Tunç
April 2015, 140 pages
The determination of the fundamental period of vibration for a building is essential in
the earthquake design field. According to the various building codes, there are
limitations on this topic. In this study, only reinforced concrete buildings with various
floor levels and structural configurations are investigated. As part of this investigation,
a total of 105 models representing unique sets of 21 layouts is constructed using a
commercially available software package, ETABS. In the seismic analysis phase the
response spectrum analyses are conducted according to the Turkish Seismic Code,
2007. Not only the periods, but also the lateral deflections are evaluated in detail by
using the code associated limitations outlined in the 1997 and 2007 Turkish Seismic
Codes and the ASCE 7-10. The intent of this study is to understand the dynamic
behaviors of buildings with different configurations under severe seismic loads. The
framing type, and number of floors and in-plane aspect ratios are studied in this thesis.
For this purpose, five sets of floor levels, 10, 20, 30, 40, and 50 stories are studied.
The results are discussed and their associated effects on the existing period equations
in the Turkish and American codes are studied.
Keywords: Fundamental period, Structural Configurations, Seismic Codes.
iv
ÖZ
FARKLI ÖZELLİKLERE SAHİP BİNALARIN BİRİNCİ DOĞAL TİTREŞİM
PERYODLARININ HESAPLANMASI ÜZERİNE BİR ÇALIŞMA
Bashar A. Shon
Yüksek Lisans (M.S.), İnşaat Mühendisliği Bölümü
Tez Danışmanı: Yrd. Doç. Dr. Gökhan Tunç
Nisan 2015, 140 pages
Deprem mühendisliği tasarımında bir binann birinci doğal titreşim peryodunun
belirlenmesi büyük önem arz eder. Farklı bina yönetmeliklerinde, bu konu hakkında
değişik sınırlamalar olduğu bir gerçektir. Bu çalışmada farklı kat adetlerine ve taşıyıcı
sistem özelliklerine sahip sadece betonarme binalar incelenmiştir. Bu kapsamda 21
ayrı taşıyıcı sisteme sahip binalar toplamda 105 adet modelle ticari bir paket program
olan ETABS kullanılarak oluşturulmuştur. Binaların deprem mühendisliği analiz
aşamasında, 2007 Türkiye Deprem Yönetmeliği’ne göre oluşturulan özel tasarım
spektrumları kullanılmıştır. Sadece peryodlar değil yatay deplasman değerleri de
detaylı bir şekilde incelenmiş ve 1997 ile 2007 Türkiye Deprem Yönetmelikleri’ndeki
sınırlamalar ile ASCE 7-10’da verilen sınır değerler kullanılarak gerekli mukayeseler
yapılmıştır. Bu çalışmanın amacı farklı taşıyıcı sistemlere sahip binaların en gayri
müsait durumdaki deprem kuvvetlerine göre oluşacak dinamik davranışlarının
belirlenmesi olarak özetlenebilir. Taşıyıcı sistem türü, kat adetleri ve plandaki boyutsal
oranlar bu tezin kapsamı içerisine dahil edilmiştir. Bu amaç doğrultusunda, toplam 5
farklı kat özelliğine sahip sırası ile 10, 20, 30, 40 ve 50 katlı binalar modellenmiştir.
Paramterik çalışmaya bağlı analiz sonuçları tartışılmış ve Türkiye ile Amerika’daki
mevcut peryod denklemlerdeki etkileri incelenmiştir.
Anahtar Kelimeler: Doğal Tireşim Peryodu, Taşıyıcı Sistem Konfigürasyonu, Deprem
Yönetmelikleri.
v
DEDICATION
This thesis is dedicated to my family
April, 2015
vi
ACKNOWLEDGEMENTS
I express my sincere appreciation and thanks to my supervisor Assist. Prof. Dr.
Gökhan Tunç. I am very grateful to him since he provided invaluable support,
guidance, insight, and endless patience throughout this research.
I would like to also send my sincere regards and deep appreciation to my
mother who passed only six years ago. I also offer my sincere thanks to my wife for
her continuous encouragement and patience during this period. I am also grateful to
my family members, who have given me constant love and support throughout my
whole life, for helping me become who I am.
I would like to express my special appreciation to the thesis committee
members for providing their valuable comments, suggestions, and corrections. I also
offer my thanks to all other individuals who helped me complete this work.
I would like to take this opportunity and express my deepest gratitudes to my
brother without whom I couldn’t be able to achieve what I have achieved today.
vii
TABLE OF CONTENTS
ABSTRACT………………………………………………………………
iv
ÖZ…………………………………………………………………………
v
DEDICATION…………………………………………………………
vi
ACKNOWLEDGEMENTS……………………………………………
vii
TABLE OF CONTENTS………………………………………………
viii
LIST OF FIGURES……………………………………………………
xii
LIST OF TABLES………………………………………………………
xvii
LIST OF ABBREVIATIONS…………………………………………
xix
LIST OF SYMBOLS……………………………………………………
xx
CHAPTER 1
INTRODUCTION
1.1
Introduction……………………………………………………….
1
1.2
Background….…………………………………………………....
3
1.2.1 The Uniform Building Code, UBC…....................................
4
1.2.2 Turkish Seismic Code, TSC…..............................................
6
1.2.3 The American Society of Civil Engineers, ASCE….............
7
1.2.4 The National Building Code of Canada, NBCC…................
7
1.3
Problem Statement…………..........................................................
8
1.4
Scope…………...............................................................................
9
1.5
Conclusions….…............................................................................
9
viii
CHAPTER 2
LITERATURE REVIEW
2.1
Introduction….…...………………………….................................
11
2.2
Estimation of Fundamental Period According to Various
Building Codes…………………………………………................
11
2.2.1 ASCE 7-10………………………………….........................
11
2.2.2 TSC 07……………………………………………...............
13
2.2.3 Eurocode 8……………………………………….................
14
2.2.4 National Building Code of Canada, 2005…………..............
15
2.2.5 New Zealand Code, 2004…………………...........................
16
2.3
Mass and Stiffness in Period Calculations…………......................
17
2.4
Literature Review on Determination of Building Periods…..........
17
2.4.1 Simplified Methods………………........................................
17
2.4.1.1 G.W.Housner and A.G.Brady, 1963…......................
18
2.4.1.2 Goel and Chopra, 1997…………..............................
18
2.4.1.3 Rui Pinho and Helen Crowley, 2009….....................
19
2.4.1.4 Oh-Sung Kwon and Eung Soo Kim, 2010….............
20
2.4.1.5 Nilesh V Prajapati1, A.N.Desai, 2012…...................
20
2.4.1.6 Kadir Guler, Ercan Yuksel, and Ali Kocak, 2008.....
21
2.4.1.7 Helen Crowley and RuiPinho, 2006..........................
22
2.4.1.8 R. Ditommaso, M.Vona, M. R. Gallipoli, and
Mucciarelli, 2013......................................................
23
2.4.1.9 Can Balkaya and Erol Kalan, 2003............................
24
2.4.2 Hand Calculation Methods...........................................
25
2.4.2.1 Bryan Stafford Smith and Elizabeth ,1986…...........
25
2.4.2.2 K.A.Zalka, 2001….....................................................
26
ix
CHAPTER 3
PARAMETRIC STUDIES AND COMPARISONS OF RESULTS
3.1
Introduction………..........................................................................
27
3.2
Building Information.......................................................................
29
3.2.1 Layouts Information…...........................................................
29
3.2.2 Dimensions of Elements …....................................................
40
3.2.3 Material Properties……..........................................................
51
3.3
Modeling in ETABS……................................................................
51
3.4
Results………..................................................................................
53
3.4.1 Layouts A1, A2, and A3…….................................................
59
3.4.2 Layouts B1, B2, and B3…………..........................................
63
3.4.3 Layouts C1, C2, and C3………..............................................
67
3.4.4 Layouts D1, D2, and D3….....................................................
71
3.4.5 Layouts E1, E2, and E3…......................................................
74
3.4.5.1 Layout E1....................................................................
74
3.4.5.2 Layouts E2, E3…........................................................
77
3.4.6 Layouts F1, F2, and F3…………….......................................
81
3.4.6.1 Layout F1....................................................................
81
3.4.6.2 Layouts F2, F3............................................................
84
3.4.7 Layouts G1, G2, andG3…………..........................................
88
3.4.7.1 Layout G1…...............................................................
88
3.4.7.2 Layouts G2, G3...........................................................
91
3.4.8 Layouts A, B, C, and D...........................................................
95
3.4.8.1 Layouts A1, B1, C1, and D1…....................................
95
3.4.8.2 Layouts A2, B2, C2, and D2........................................
97
x
3.4.8.3 Layouts A3, B3, C3, and D3........................................
99
….................................................................
101
3.4.10 Lateral Deflections……........................................................
123
3.4.10.1 X Direction….............................................................
123
3.4.10.2 Y Direction……….....................................................
128
3.4.9 Mode Shapes
CHAPTER 4
CONCLUSIONS AND RECOMMENDATIONS
4.1
Introduction……..............................................................................
132
4.2
Conclusions……..............................................................................
132
4.3
Recommendations………................................................................
135
4.4
Suggestions for Future Research…….............................................
137
REFERENCES……………………………………………
xi
138
LIST OF FIGURES
FIGURE 3.1
Layout A1 (48 m by 36 m)……………………………………
30
FIGURE 3.2
Layout A2 (48 m by 24 m)…………………………………....
30
FIGURE 3.3
Layout A3 (48 m by 18 m)………………………………........
31
FIGURE 3.4
Layout B1 (48 m by 36 m) …………………………………...
31
FIGURE 3.5
Layout B2 (48 m by 24 m)……………………………………
32
FIGURE 3.6
Layout B3 (48 m by 18 m)……………………………............
32
FIGURE 3.7
Layout C1 (48 m by 36 m)……………………………............
33
FIGURE 3.8
Layout C2 (48 m by 24 m)…………………………………....
33
FIGURE 3.9
Layout C3 (48 m by 18 m)…………………………………...
34
FIGURE 3.10
Layout D1 (48 m by 36 m)…………………………………....
34
FIGURE 3.11
Layout D2 (48 m by 24 m)……………………………………
35
FIGURE 3.12
Layout D3 (48 m by 18 m)……………………………………
35
FIGURE 3.13
Layout E1 (48 m by 36 m)……………………………………
36
FIGURE 3.14
Layout E2 (48 m by 36 m)……………………………………
36
FIGURE 3.15
Layout E3 (48 m by 36 m)……………………………………
37
FIGURE 3.16
Layout F1 (48 m by 36 m)……………………………………
37
FIGURE 3.17
Layout F2 (48 m by 36 m)……………………………………
38
FIGURE 3.18
Layout F3 (48 m by 36 m)……………………………………
38
FIGURE 3.19
Layout G1 (48 m by 36 m)……………………………………
39
FIGURE 3.20
Layout G2 (48 m by 36 m)……………………………………
39
xii
FIGURE 3.21
Layout G3 (48 m by 36 m)……………………………………
FIGURE 3.22
First period versus number of floors for building layouts A1,
A2, A3 ……………………………………………………….
FIGURE 3.23
72
Second period versus number of floors for building, D1, D2,
D3 ……….................................................................................
FIGURE 3.33
70
First period versus number of floors for building layouts, D1,
D2, D3………………………………………………………
FIGURE 3.32
70
Third period versus number of floors for building layouts,
C1, C2, C3……………………………………………………
FIGURE 3.31
69
Second period versus number of floors for building layouts,
C1, C2, C3……………………………………………………
FIGURE 3.30
66
First period versus number of floors for building layouts, C1,
C2, C3………………………………………………………
FIGURE 3.29
66
Third period versus number of floors for building layouts,
B1, B2, B3……………………………………………………
FIGURE 3.28
65
Second period versus number of floors for building layouts,
B1, B2, B3…………………………………………………….
FIGURE 3.27
62
First period versus number of floors for building layouts, B1,
B2, B3………………………………………………………
FIGURE 3.26
62
Third period versus number of floors for building layouts,
A1, A2, A3……………………………………………………
FIGURE 3.25
61
Second period versus number of floors for building layouts,
A1, A2, A3……………………………………………………
FIGURE 3.24
40
73
Third period versus number of floors for building layouts,D1,
D2, D3.......................................................................................
xiii
73
FIGURE 3.34
First period versus number of floors for building layout E1..... 76
FIGURE 3.35
First period versus number of floors for building layouts, E2,
E3……………………………………………………………..
FIGURE 3.36
Second period versus number of floors for building layouts,
E1, E2, E3……………………………………………………
FIGURE 3.37
79
80
Third period versus number of floors for building layouts, E1,
E2, E3……………………………………………………........
80
FIGURE 3.38
First period versus number of floors for building layout F1….
83
FIGURE 3.39
First period versus number of floors for building layouts, F2,
F3.…………………………………………………………..
FIGURE 3.40
Second period versus number of floors for building layouts,
F1, F2, F3…………………………………………….
FIGURE 3.41
86
87
Third period versus number of floors for building layouts, F1,
F2, F3……………………………………………………........
87
FIGURE 3.42
First period versus number of floors for building layout G1....
90
FIGURE 3.43
First period versus number of floors for building layouts, G2,
G3……………………………………………………………..
FIGURE 3.44
Second period versus number of floors for building layouts,
G1, G2, G3…………………………………………………
FIGURE 3.45
First period versus number of floors for building layouts, A1,
B1, C1, D1…………………………………………………….
FIGURE 3.47
94
Third period versus number of floors for building layouts,
G1, G2, G3…………………………………………………
FIGURE 3.46
93
94
96
First period versus number of floors for building layouts, A2,
B2, C2, D2................................................................................
xiv
98
FIGURE 3.48
First period versus number of floors for building layouts, A3,
B3, C3, D3…………………………………………………….
100
FIGURE 3.49
Mode shapes for layout A1…………………………………...
102
FIGURE 3.50
Mode shapes for layout A2……………………………….......
103
FIGURE 3.51
Mode shapes for layout A3…………………………………...
104
FIGURE 3.52
Mode shapes for layout B1……………………………………
105
FIGURE 3.53
Mode shapes for layout B2 ……………………………...........
106
FIGURE 3.54
Mode shapes for layout B3…………………………………....
107
FIGURE 3.55
Mode shapes for layout C1……………………………………
108
FIGURE 3.56
Mode shapes for layout C2……………………………………
109
FIGURE 3.57
Mode shapes for layout C3……………………………………
110
FIGURE 3.58
Mode shapes for layout D1…………………………………
111
FIGURE 3.59
Mode shapes for layout D2…………………………………
112
FIGURE 3.60
Mode shapes for layout D3…………………………………
113
FIGURE 3.61
Mode shapes for layout E1……………………………………
114
FIGURE 3.62
Mode shapes for layout E2……………………………………
115
FIGURE 3.63
Mode shapes for layout E3……….…………………………
116
FIGURE 3.64
Mode shapes for layout F1……………………………………
117
FIGURE 3.65
Mode shapes for layout F2……………………………………
118
FIGURE 3.66
Mode shapes for layout F3……………………………………
119
FIGURE 3.67
Mode shapes for layout G1…………………………………
120
xv
FIGURE 3.68
Mode shapes for layout G2…………………………………
121
FIGURE 3.69
Mode shapes for layout G3…………………………………
122
FIGURE 3.70
Deflections in the x-direction versus layout numbers due to
seismic load...............................................................................
126
FIGURE 3.71
Layout numbers versus H/∆x....................................................
127
FIGURE 3.72
Deflections in the y-direction versus layout numbers due to
seismic load ………………………………………………......
FIGURE 3.73
Layout numbers versus H/∆Y………………………………...
xvi
130
131
LIST OF TABLES
TABLE 2.1
Ct and x values in ASCE 7-10………………………………..........
12
TABLE 2.2
Values of C, b1, b2, b3, b4, b5, b6, Ϭt, R2 …………………….......
24
TABLE 3.1
Layout details of A1…………………….........................................
41
TABLE 3.2
Layout details of A2……………………………………………….
41
TABLE 3.3
Layout details of A3………………………………………………
42
TABLE 3.4
Layout details of B1……………………………………………….
42
TABLE 3.5
Layout details of B2……………………………………………….
43
TABLE 3.6
Layout details of B3……………………………………………….
43
TABLE 3.7
Layout details of C1……………………………………………....
44
TABLE 3.8
Layout details of C2……………………………………………….
44
TABLE 3.9
Layout details of C3……………………………………………….
45
TABLE 3.10
Layout details of D1……………………………………………….
45
TABLE 3.11
Layout details of D2……………………………………………….
46
TABLE 3.12
Layout details of D3……………………………………………….
46
TABLE 3.13
Layout details of E1……………………………………………….
47
TABLE 3.14
Layout details of E2……………………………………………….
47
TABLE 3.15
Layout details of E3……………………………………………….
48
TABLE 3.16
Layout details of F1………………………………………………..
48
TABLE 3.17
Layout details of F2……………………………………………….
49
xvii
TABLE 3.18
Layout details of F3………………………………………………..
49
TABLE 3.19
Layout details of G1……………………………………………….
50
TABLE 3. 20
Layout details of G2……………………………………………….
50
TABLE 3.21
Layout details of G3……………………………………………….
51
TABLE 3.22.a
The results of the first three periods for layouts A, B, C, D, E
(in seconds)…………………………………………………….......
TABLE 3.22.b
57
The results of the first three periods for layouts F, G
(in seconds)………………………………………………………...
58
TABLE 3.23
Lateral deflections due to seismic loads in x-direction (RX)……...
125
TABLE 3.24
Lateral deflections due to seismic loads in y-direction (RY)……
129
xviii
LIST OF ABBREVIATIONS
ASCE:
The American Society of Civil Engineers.
ATC3-06:
Applied Technology Council.
BF:
Braced Frames.
CBF:
Concentrically Braced Frame.
CEN:
The European Committee For Standardization.
DL:
Damage Levels.
EC8:
Eurocode 8.
EMS 98:
European Macroseismic Scale.
FE:
Finite Element.
MRF:
Moment-Resisting Frames.
NBCC:
National Building Code of Canada.
PGA:
Peak Ground Acceleration.
RC MRF:
Reinforced Concrete Moment-Resisting Frames.
RC:
Reinforced Concrete.
RCC
Reinforced Concrete Cement.
SW:
Shear Walls.
TS:
Turkish Standards.
TSC:
Turkish Seismic Code.
UBC:
The Uniform Building Code.
xix
LIST OF SYMBOLS
𝐀𝟎:
The effective ground acceleration coefficient.
𝐀𝐁:
Area of base of structure, ft 2 .
𝐀𝐜:
The total effective area of the shear walls in the first storey of the
building in m2
𝐀𝐢:
Area of shear wall "i" in ft 2 .
𝐂𝐭 :
Constants related to building period.
𝐃𝐢 :
Length of shear wall "i" in ft.
D:
Length of the lateral load - resisting system.
𝐝𝐟𝐢 :
Deformations calculated under fictitious loads in the ith storey.
d:
Lateral displacement of the top of the building in meters due to the
gravity loads applied in the horizontal direction.
𝐄𝐜 :
Modulus of elastisity of concrete (Chapter 3).
𝐅𝐟𝐢 :
The fictitious load acting on the story in the first natural vibration
period calculation.
𝐠𝐢:
Dead load (Chapter 2).
H:
Building height.
𝐡𝐢 :
Height of shear wall "i" in ft.
𝐡𝐧 :
Height in meters from the base of the structure to the upper most
seismic weight or mass (Chapter 2).
J:
Plan polar moment of inertia.
𝐤𝐭:
0.05 for all other frame structure.
xx
𝐤𝐭:
0.06 for eccentrically braced steel frame.
𝐤𝐭:
0.11 for moment-resisting steel frames.
𝐤𝐭:
0.075 for moment-resisting concrete frame.
k:
Stiffness.
L:
Buildings Length.
m:
Effective seismic mass.
N:
Number of stories above the base (Chapter 2).
n:
Live load participation factor.
𝐪𝐢 :
Live load (Chapter 2).
𝐓𝐚 :
Approximate fundamental period.
T:
Period in seconds.
X:
Number of shear walls in the building effective in resisting lateral
forces in the direction under consideration.
Z:
Local site class.
β:
Ratio of long to short side dimension of a building.
𝛒𝐚ᵴ :
Ratio of short side shear wall area to total floor area.
𝛒𝐚𝗹 :
Ratio of long side shear wall area to total floor area.
𝛒𝐦𝐢𝐧 :
Ratio of minimum shear wall area to total floor area.
Ѵ:
Poisson’s ratio (Chapter 3).
xxi
CHAPTER 1
INTRODUCTION
1.1 Introduction
Natural period of vibration of a building is defined as the time needed to
complete one full cycle. The natural period which will be denoted using T1 in seconds
in this study is the inverse of natural frequency.
The determination of the fundamental period of vibration for building is
essential to earthquake design. The fundamental period represents the global
dynamic characteristics describing the 3D behavior of buildings under seismic loads.
For this reason, it is easily and directly usable to determine the global demands on a
structure due to a given seismic input. Moreover, the estimation of fundamental
period of buildings is important to identify any possible resonance phenomena, and
the probability map of expected resonance phenomena for future earthquakes [1].
The vibration period of reinforced concrete (RC) and steel buildings is
affected by many factors such as structural irregularity, number of stories and bays,
dimensions of structural members, infill panel properties and their positions,
distribution and intensity of gravity loads. For these reasons, a reliable estimation of
the fundamental period of buildings is not easy to determine for both the new and
existing buildings. To address this issue, various earthquake design codes provide
equations in order to estimate the fundamental period for buildings based on their
typological characteristics such as height, framing system and material type [2].
Traditionally, the period expressions provided worldwide by seismic codes
have been obtained by regression analysis of values estimated using both numerical
and empirical approaches. The most common expressions available worldwide have
been obtained on the basis of vibration data recorded during past earthquakes.
Usually, they are height-dependent relationships setting up considering the total
1
height of buildings or their number of stories. The seismic code associated equations
used to compute the fundamental period of a building can be divided into three main
groups based on buildings’ length (L), height (H) in meters and numbers of floors
(N):
1. Equation using building length (L).
2. Nonlinear equations as a power-law function of buildings height.
3. Linear equations.
Furthermore, other studies have been recently carried out on the basis of both
numerical approaches (see item two and three provided above) particularly with
respect to existing buildings [2].
In this study, a total of twenty one layouts are selected as a parametric study,
focusing primarily on the reinforced concrete buildings. The parametric study
includes different building layouts and number of floors. As part of this study, a total
of 105 models representing unique sets of 21 layouts is constructed using a
commercially available software package, ETABS. In the seismic analysis phase, the
response spectrum analyses are conducted according to the Turkish Seismic Code,
2007. Not only the periods, but also the lateral deflections are evaluated in detail by
using the code associated limitations according to the 1997 and 2007 Turkish Seismic
Codes and the ASCE 7-10.
The intent of this study is to understand the dynamic behaviors of buildings
with different configurations under severe seismic loads. Therefore, all buildings are
assumed to be located in the most severe earthquake zone. It is a well known fact that
the first fundamental period is directly affected by not only the framing type but also
the number of floors and the in-plane aspect ratio. Therefore, the later two parameters
are used in the parametric studies by selecting three different aspect ratios and
number of floors. For this purpose, five sets of floor levels, 10, 20, 30, 40, and 50
stories, are studied in evaluating the fundamental period. The results are discussed
and their associated effects on the existing period equations in the Turkish and
American codes are studied.
2
1.2. Background
During the past three decades, probabilistic risk analysis tools have been
applied to asses the performance of new and existing buildings, structural systems,
structural designs and evaluation of buildings with regard to their ability to withstand
the effects of earthquakes.
The fundamental periods of buildings has a remarkable effect on the
magnitude of its response. The ability to predict these characteristics, are essential to
calculate the design base shear and lateral forces. In this section, only generalized
periods equations will be provided. The detailed information will be presented in
Chapter 2. The first semi-empirical formula employed in seismic design codes or
guidance documents was from the ATC3-06 [ATC, 1978], and has the following
form [3]:
T = Ct H 0.75
(1 .1)
where, H is in feet, and Ct is 0.03 for reinforced concrete moment-resisting frames.
H represents the height measured from the base of a building.
The equation (1.1) was theoretically derived using the Rayleigh’s method
based on the assumptions that the equivalent static lateral forces are distributed
linearly over the height of the building, the distribution of stiffness with height
produces a uniform story drift under the linearly distributed lateral forces, the base
shear is proportional to 1/T 3/4 , and finally the deformations are controlled by the
drift limit-state.
The numerical value of the constant Ct in equation (1.1) was obtained from
the measured periods of buildings during the 1971 San Fernando earthquake.
In the European seismic design regulation code, Eurocode 8 [CEN, 2003],
the fundamental period versus height relationship for force-based design of moment
resisting frames is expressed as shown in Eq. (1.2). This equation is very similar to
the Eq. (1.1) given above, the only difference is that the coefficient Ct has been
conveniently adapted from feet to meters (0.073 ≈ 0.075).
3
T = 0.075 H 0.75
(1.2)
Goel and Chopra [1997], who collected the data from eight Californian
earthquakes, starting with the 1971 San Fernando earthquake and ending with the
1994 Northridge event, showed that Eq. (1.1) tends to underestimate the periods of
vibration based on the measurements from a total of 27 reinforced concrete frames,
particularly for buildings with sixteen or more floors. Hence, these researchers
proposed an alternative period versus height formula, with the best-fit minus 1
standard deviation recommended for conservative force-based design, while the bestfit plus 1 standard deviation was recommended for displacement-based assessment
[Chopra and Goel, 2000] [4].
Simplified period versus height equations are also important for the
assessment of analytical loss methodologies.
Up to now, various types of relationships have been proposed to accurately
estimate the fundamental period of buildings. Some of these relationships have
become the cornerstone for different building codes. Bellow, you will find detailed
information about this topic:
1.2.1 The Uniform Building Code, UBC
The Uniform Building Code specifies that the period of a multi-story framed
building can be estimated by dividing the total number of stories by ten, (1982 UBC)
[5]:
T = N/10
(1.3)
where N defines the number of stories.
In the 1988 version of the UBC, one of the following two methods are
recommended to be used in computing the natural period. The first method is called
Method A and, it takes the material of building into account. The period equation
according to this method is:
4
3
T = Ct (hn )4
(1.4)
Where, Ct is equal to 0.020 for dual moment resisting frames and eccentric braced
frames, Ct = 0.1 /√Ac for structures with concrete masonry shear walls, where Ac
D
equal to ∑ Ae[0.2 +(h e )2 ]. Ac depends on the dimensions of shear walls. In the Ac
n
equation, the parameter hn , is the effective height in feet above the base of the
building.
According to the 1988 UBC modified code, the value of Ct was changed to
0.035 for frame concrete structures. For dual systems, the value of Ct are as follows:
Ct = 0.02 when hn ≤ 160 ft.
Ct = 0.03 when hn ≥ 400 ft
and
In the 1997 UBC code, two methods were provided to determine the
fundamental period of structures. These methods are called Method A and Method B
[6]. The period according to these method are described as follows:
1. Method A: For all buildings, the value , T, may be approximated from the
following equation:
T = Ct (hn )3/4
(1.5)
where, Ct is 0.035 (0.0853) for steel moment-resisting frames, 0.030 (0.0731) for
reinforced concrete moment-resisting frames and eccentrically braced frames, and
finally 0.020 (0.0488) for all other buildings. The numbers in parentheses are for
metric units.
Alternatively, the value of, Ct , for structures with concrete or masonry shear
walls may be taken as 0.1/Ac , (in SI units Ct is 0.0743√Ac ), where Ac is in m2 . The
value of Ac is determined from the following equation:
D
Ac = ∑ Ae [0.2 + (h e )2 ]
n
However, the value of, De / hn used in the above equation shall not exceed 0.9.
5
(1.6)
2. Method B: The fundamental period, T, may be calculated using the structural
properties and deformational characteristics of the lateral resisting elements
in a properly substantiated analysis. The value of, T, from Method B shall not
exceed a value 30 percent greater than the value of, T, obtained from Method
A in seismic zone 4, and 40 percent in seismic zones 1, 2 and 3. The
fundamental period, T, may be computed using the following equation:
T = 2ᴨ √(∑ni=1 wi ∆i 2 )/(g ∑ni=1 fi ∆i )
(1.7)
1.2.2 Turkish Seismic Code, TSC
As stated in the introduction, the two TSC codes, 1997 and 2007 will be used
in this study in evaluating the fundamental period for various types of RC buildings.
Below, you will find information about the fundamental period calculation described
in the TSC 97 and the TSC 07.
TSC 97
The 1997 Turkish Seismic Code, TSC, concerning construction in seismic
was modified in 1998 [7]. In the TSC 97, the equation for predicting the fundamental
period of structures was directly referenced to the equations in the 1997 UBC with
some minor modifications. The general form of the period equation in the TSC 97 is
as follows:
T = Ct (hn )3/4
(1.8)
where, T, is the period in seconds, hn is the height of building in meters. The
parameter Ct in this equation is 0.08 (0.0853) for steel frames, 0.07 (0.0731) for
reinforced concrete moment resisting frames and eccentrically braced frames, and
0.05 (0.0488) for all other buildings. The numbers within the parentheses show the
corresponding values given in the UBC 97. By comparing the Ct values from the TSC
97 to UBC 97, it is clear that both codes almost have the same values of Ct .
TSC 07
In the case where equivalent seismic load method is applied , according to the
TSC 2007, the natural period of a building in the direction of the earthquake
6
considered shall not be larger than the value calculated by the following equation
[8]:
∑N mi dfi 2
T= 2ᴨ ( ∑I=1
N
i=1 Ffi dfi
1/2
)
(1.9)
where,
where, mi = (g i + n q i )/g .
g i : dead load .
q i : live load .
n: live load participation factor.
dfi : deformations calculated under fictitious loads in the ith storey .
Ffi : fictitious load acting on the story in the first natural vibration period calculation.
Regardless of the value calculated by this equation, natural period shall not
be taken larger than 0.1 N for buildings that has a number of floors larger than 13
excluding basements.
1.2.3 The American Society of Civil Engineers, ASCE
In both ASCE 7-05 and ASCE 7-10 building codes, the approximate
fundamental period, Ta , is determined in seconds as in the following equation [9]:
T = Ct (hn )𝑥
(1.10)
where, hn is the height of the building from its base. The values of Ct and x are
provided in chapter 2.
1.2.4 The National Building Code of Canada, NBCC
Since the 1970 edition of the National Building Code of Canada, design
seismic loads have been specified as a function of the fundamental lateral period
(NRC/IRC 1970). From 1970 to 1995, the NBCC suggested the following empirical
equations to estimate the fundamental period [10]:
7
1. For most buildings
T= 0.09
h
√D
(1.11)
2. Except for buildings where the lateral loads are resisted by moment resisting
frames, MR:
T = 0.1 N
(1.12)
In the equations (1.11) and (1.12), T, h, and N are the fundamental period (in
seconds), building height (in meters), and number of stories, respectively. The
variable, D represents the length of the lateral load resisting system.
However in the later editions of the NBCC code, the fundamental period
calculations are extended (refined) into different construction types.
The 2005 edition of the NBCC provides the following equations to estimate
the fundamental period of a building [11]:
1. For steel moment-resisting frames (steel MRF)
T = 0.085h3/4
(1.13)
2. For concrete moment-resisting frames (RC MRF)
T = 0.075h3/4
(1.14)
3. For other moment-resisting frames (MRF)
T=0.1 N
(1.15)
T = 0.025h
(1.16)
4. For braced frames, BF
5. For shear walls (SW) and other structures
T = 0.05h3/4
(1.17)
1.3 Problem Statement
The dynamic behavior of a building during an earthquake depends on the
characteristics of the ground shaking and dynamic properties of the building’s
8
system, namely its natural periods, mode shapes, and damping characteristics. Of
these, the fundamental period plays a crucial role in building response. Therefore,
when engineers try to predict the seismic demands on a building, they must first
estimate the building’s fundamental period. All the building codes provides some
sort of empirical equations to estimate the fundamental lateral period of a building.
Due to the complex nature of the parameters involved in the dynamic
analysis of a building, the fundamental period of a building that will be obtained from
its site might be considerably different than its period used in its design. The degree
of uncertainties associated with the fundamental period might, therefore,
significantly influence the accuracy of the design seismic loads. As a result, when
the period from the appropriate empirical equation is used in the building design,
base shear may be considerably overestimated. However, if the maximum period
allowed by the code is used then the base shear may be considerably underestimated.
Since seismic loads depend on the fundamental period, poorly predicting the
fundamental period may lead to a prediction of inaccurate seismic design loads.
Therefore, the need for determining the upper and lower limits for the fundamental
periods of structures become significantly important.
1.4 Scope
As explained before, there are various methods that exist in various seismic
codes in calculating the natural periods of structures. Seismic codes provide
equations to estimate the period as accurately as possible based on simple building
structural characteristics when there is no possibility to determine the period
experimentally. This study’s goal is to evaluate the accuracy of the period equations
provided in the TSC 97, 07 and ASCE 7-10 with respect to the results of finite
element analyses for reinforced concrete buildings with various structural framing
options.
1.5 Conclusions
In this study, only reinforced concrete buildings with various floor levels and
structural configurations are investigated. As part of this investigation, a total of 105
models representing unique sets of 21 layouts is constructed using a commercially
available software package, ETABS. In the seismic analysis phase, the response
9
spectrum analyses are conducted according to the Turkish Seismic Code, 2007. Not
only the periods, but also the lateral deflections are evaluated in detail by using the
code associated limitations according to the 1997 and 2007 Turkish Seismic Codes
and the ASCE 7-10. The intent of this study is to understand the dynamic behaviors
of buildings with different configurations under severe seismic loads and determine
the fundamental period as accurately as possible.
The literature review regarding the period estimation efforts is provided in
Chapter 2. Using the existing code associated equations from the TSC 97 and 07 and
the ASCE 7-10, a parametric study is conducted on a total of 105 models. The results
from the finite element analyses of these models and those produced periods from
the code associated equations are studied in Chapter 3. In this chapter, the lateral
deflections of the models are also investigated to understand the effect of various
lateral resisting systems. In the last chapter, Chapter 4, conclusions and
recommendations along with the findings are provided.
10
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
The estimation of the fundamental period of a building is important to
determining the base shear and the lateral forces. A number of studies have been
performed on the fundamental period of buildings in an attempt to develop an
expression to calculate and define the factors that influence the period. More and more
buildings have been monitored and their seismic response data have been recorded [1].
In this chapter, previous studies are summarized along with the various approaches
that exist in some commonly used building codes.
2.2 Estimation of Fundamental Period According to Various Building Codes
In Chapter 1, a generalized discussion about the fundamental period
calculations are provided. In this chapter, detailed discussion is given. Below list
includes the various approaches outlined in different building codes required to
calculate the fundamental period of a building.
2.2.1 ASCE 7-10
The American Society of Civil Engineers (ASCE) has a special committee that
prepares building codes, and is called ASCE 7-10 committee. In the code prepared by
this committee the fundamental period, Ta , in seconds can be obtained using the
following equation [9, 12]:
Ta = Ct hxn
11
(2.1)
where, hn , is the height of a building. The values of Ct and x in metric system can be
obtained from Table 2.1.
Fundamental periods obtained from a rational analysis can be used according
to the ASCE7-10. However, as described in the code there is an upper limit on a
calculated period. The upper limit is defined as the multiplication of factor Cu and the
period from the Eq. (2.1). This multiplication factor varies from 1.4 to 1.7 depending
on the design spectral response acceleration at 1 second.
Table 2.1 Ct and x values in ASCE 7-10
𝐂𝐭
x
Steel moment resisting frames
0.0724
0.8
Concrete moment resisting frames
0.0466
0.9
Steel eccentrically braced frames
0.0731
0.75
Steel buckling-restrained braced frames
0.0731
0.75
All other structural systems
0.0488
0.75
Structure Type
These factors required to calculate the fundamental period depend on the level
of seismicity. It is worthwhile to note that the fundamental periods obtained from a
rational analysis can be directly used without applying any upper bounds in checking
drift requirements.
Alternatively, it is also permitted to determine the approximate fundamental
period, Ta, in seconds from the following equation for buildings not exceeding 12
stories above their base where the seismic force-resisting system consists of concrete
or steel moment resisting frames and the average story height is at least 10 ft. (3
meters):
Ta = 0.1 N
12
(2.2)
where, N indicates the number of stories above the base [9].
The approximate fundamental period, Ta , in seconds for masonry or concrete
shear wall structures is permitted to be determined according to the Equation (2.3).
Ta =
0.0019
√Cw
hn
(2.3)
where, Cw , is calculated as follows:
Cw =
100
AB
h
∑xi=1 ( n )
h
i
2
Ai
2
h
[𝟏+𝟎.𝟖𝟑 ( i ) ]
(2.4)
Di
The definitions of parameters in this equation are listed below:
AB = area of base of structure, ft 2 .
Ai = web area of shear wall "i" in ft 2 .
Di = length of shear wall "i" in ft.
hi = height of shear wall "I" in ft.
x = number of shear walls in the building effective in resisting lateral forces in the
direction under consideration [9].
2.2.2 TSC 07
The Turkish Earthquake Code (TSC 07) does not offer any empirical equation
and recommends a formulation based on the Rayleigh’s method [1]. As a result, this
method requires the mass and displacements of the building under a fictitious load.
Therefore, designer must carry out a first trial design to determine these parameters.
In the TSC 07, the fundamental period of any type of building might be calculated as
follows:
∑N m d2
1/2
i fi
T1 =2ᴨ ( ∑i=1
N F d )
i=1 fi fi
where,
mi = (g i + n q i )/g .
13
(2.5)
g i : dead load .
q i : live load .
n: live load participation factor.
dfi : deformations calculated under fictitious loads in the ith storey .
Ffi : fictitious load acting on the story in the first natural vibration period calculation.
In this building code, it is stated that for buildings with number of floors larger
than 13, excluding basement(s), the natural period shall not be more than 0.1 N which
is independent from the value calculated according to Equation (2.5) [8].
2.2.3 Eurocode 8
Eurocode 8 has a similar approach in determining the fundamental period when
compared to the one in ASCE7-10. The same empirical equations given in the ASCE
7-10 with slight modifications is also recommended in this building code [13]. It is
stated that for buildings with heights up to 40 meters, the value of the fundamental
period, T1, in seconds can be approximated by using following equation:
T1 = Ct H 3/4
(2.6)
where, Ct , is 0.085 for moment resistant steel frames, 0.075 for eccentrically braced
steel frames, and 0.050 for all other structures. H, in this equation is the height of the
building in meters measured from its foundation or from the top of a rigid basement.
Alternatively, for structures with concrete or masonry shear walls, the value of
Ct in the Equation (2.6) may be taken as,
Ct = 0.075/√Ac
(2.7)
where,
l
2
Ac = ∑ [Ai (0.2 + ( wi
)) ]
H
14
(2.8)
Ac by definition is the total effective area of shear walls in the first storey of a building
in m2 , Ai is the effective cross section area of shear wall "i" in the first storey of the
building in m2 , lwi , is the length of shear wall in the first storey in the direction parallel
to the applied forces, in meters. However, according to this building code the ratio of
lwi
H
shall not exceed 0.9.
Alternatively, the estimation of T1, in seconds, may be calculated by using the
following equation:
T1 = 2√d
(2.9)
where, d is the lateral displacement of the top of the building in meters due to the
gravity loads applied in the horizontal direction [13].
2.2.4 National Building Code of Canada, 2005
The 2005 National Building Code of Canada offers a more simplified
expression in calculating the natural periods of buildings [11]. In this code, the period
calculation is divided into three different groups:
• For concrete moment-resisting frames (RC MRF):
T = 0.075h3/4
(2.10)
• For other moment-resisting frames (MRF):
T = 0.1 N
(2.11)
• For steel moment-resisting frames (steel MRF):
T = 0.085h3/4
15
(2.12)
2.2.5 New Zealand Code, 2004
In New Zealand Code 2004, there are three empirical methods proposed for
calculating the fundamental period of structures [14]. These empirical methods and
their details are given below:
1. Empirical Method A:
For the serviceability limit state:
T = 1.0 k t h0.75
n
(2.13)
For the ultimate limit state:
T = 1.25 k t h0.75
n
(2.14)
where,
k t = 0.075 for moment-resisting concrete frame.
k t = 0.11 for moment-resisting steel frames.
k t = 0.06 for eccentrically braced steel frame.
k t = 0.05 for all other frame structure.
In these two equations, hn , is the height in measured meters from the point where
the base of the structure to the uppermost seismic weight or mass is located [14].
2.
Empirical Method B:
Alternatively, the value, k t , used in clause C4.1.2.1 of the related code, for
structures with concrete shear walls may be taken as:
kt =
0.075
(2.15)
√Ac
where, Ac , is the total effective area of the shear walls in the first storey in m2 , and can
be calculated as follows:
2
l
Ac = ∑ Ai (0.2 + hwi )
n
16
(2.16)
In Equation (2.16), Ai is the effective cross-sectional area of shear walls in the first
storey of the building in m2 , hn , is described in clause C4.1.2.2 of the related code,
and, lwi , is the length of shear walls in the first storey in the direction parallel to the
applied forces, in meters, however, there is an upper limit of 0.9 defined for the ratio
of
lwi
hn
.
3. Empirical Method C
The fundamental period, T1 , may be estimated using the following equation:
T1 = 2 √d
(2.17)
where, d is the lateral elastic displacement of the top of building in meters due to
gravity loads applied in the horizontal direction.
2.3 Mass and Stiffness in Period Calculations
The natural Period, Tn , is a dynamic property of a building directly controlled
by the building’s mass and stiffness which denoted by "m" and "k", respectively. These
three parameters are related to each other by the following equation:
m
Tn = 2π √ k
(2.18)
Buildings that are heavy (with larger mass) and flexible (with smaller stiffness) exhibit
larger natural periods than those are light and stiff [15].
2.4 Literature Review on Determination of Building Periods
Literature reviews conducted in this area can be divided into two categories,
(a) simplified methods, and (b) hand calculations methods [1].
2.4.1 Simplified Methods
Below, a historical development of simplified method is presented along with
a summary of individual research works.
17
2.4.1.1 G.W.Housner and A.G.Brady, 1963
This is one of the early studies conducted in determining building periods.
Simplified equations were derived to determine the fundamental periods of idealized
buildings and they were compared to the measured ones. For shear wall buildings, it
was found that the simple empirical equations did not provide good estimates unless
wall stiffness was involved in the fundamental period calculations. If design of a
building was affected by calculated period, it was recommended that the period would
be computed using Rayleigh method or estimated by a reference to a measured period
of a similar building. The calculated periods of steel frames were formulated using the
following equation:
T=1.08√N − 0.86
(2.19)
where, N indicated the number of stories. The measured periods of steel structures
were estimated as follows:
T=0.5√N − 0.4
(2.20)
They stated that the natural vibration period of the building was an important
indicator for the dynamic behavior of structure. It was observed that when California
Building Code was used, the estimated period of buildings with shear walls was less
accurate than the other structural types. This paper also showed that a precise
estimation of the natural period of a structure was not possible by using simple
empirical expressions [1].
2.4.1.2 Goel and Chopra, 1997
The aim of this paper was to improve the code related equations which were
used to calculate periods of structures by means of recorded motions. This study
involved RC and steel moment-resisting frames. The regression analysis of measured
data was used to develop formulas to estimate fundamental periods of the buildings.
The building database contained a total of 106 Californian buildings including 21 of
them with peak ground acceleration (PGA) higher than 0.15g. It was observed that the
calculated code periods were shorter than the measured periods from the recorded
18
motions. For buildings up to 36 meters high, the code formulas produced
approximately lower-bound values compared to measured period data, on the other
hand, the same formulas resulted in 20% to 30% shorter periods compared to the
measured ones for buildings taller than 36 meters. For many buildings, measured
period values were bigger than 1.4T, where T was described as the fundamental period
obtained from the empirical equation. This implied that the code limits on the period
calculations are too conservative. It was stated that the database must had been
expanded to include the results from the new earthquake data [16].
2.4.1.3 Rui Pinho and Helen Crowley, 2009
This paper evaluated the estimation of natural period for reinforced concrete
buildings with moment resisting frames using various building codes while performing
linear static and dynamic analyses. The effect of the period on structural design was
discussed briefly, and some improvements for period estimating in Eurocode 8 was
achieved. It was observed that there was a big difference between the stiffnesses of
pre-1980 and post-1980 buildings because of the changes in the design philosophy;
where the new buildings were found to be stiffer. Thus, the period equation in
Eurocode 8 resulted reasonable numbers compared to the measured periods for new
buildings erected in Europe.
As stated in Eurocode 8, the code allows to use the lateral force method for
buildings whose response is not broadly affected by contribution of higher mode
vibration. If higher mode contribution becomes effective for a building, a modal
response spectrum analysis should be used to be more realistic results. Recent studies
have shown that these two types of methods differ with calculated design base shear
forces for a given building. This difference mainly rises from calculated the periods
by period-height equation for lateral force method and period of vibration by
eigenvalue analysis. As a result, many codes recognize that simplified period-height
equations looks more realistic if the effects of higher modes are not dominant. Some
codes suggest that if the modal base shear is less than 85% of the lateral force method
base shear, the modal forces should be multiplied by 0.85v/vt where, v is base shear
of lateral force method and vt is the modal base shear. This coefficient will be a
safeguard to avoid lower forces from the analytical models with unrealistically high
periods of vibration [1].
19
2.4.1.4 Oh-Sung Kwon and Eung Soo Kim, 2010
The aim of this paper was to evaluate the results of the period equations from
various seismic codes by applying the equation to 800 existing buildings.
The ASCE 7-05 code was investigated and its evaluation was performed for
RC structures with steel moment resisting frames, shear wall buildings, braced frames,
and other structural types. The database included 34 concentrically braced frames
(CBFs), and 125 steel moment resisting frames and other structural types. The
comparison between the measured periods and the ones from the code defined equation
showed that the steel MRFs estimated lower bound of the measured periods for all
building heights. It was found that the difference was relatively high for low and
medium rise buildings. Moreover, the periods of essential buildings with high
importance factors resulted in 40% shorter periods than those of the non-essential
buildings periods. The code equation for braced frames estimated lower bound periods
for low-to-medium rise buildings. Based on the limited available data for CBFs, the
code defined equation tended to underestimate lower bound for the periods of
buildings taller than 61 meters. It was concluded that the code defined equation offered
a good estimate ofor periods for low to medium rise buildings [1].
2.4.1.5 Nilesh V Prajapati1, A.N.Desai, 2012
The scope of this study was limited to determine the change in natural
frequency with respect to variation in height for Reinforced Cement Concrete (R.C.C.)
building. The height of the R.C.C. building changed from 60 meters to 90 meters, and
the number of floors varied from 20 to 30, keeping the storey height at 3 meters for all
floors. The in-plan dimensions of each floor was assumed to be the same.
The general aim of this work was to prepare various models for R.C.C.
buildings using a commerically available FE software, STADD-Pro. In this study, the
change in natural frequency with respect to number of floors as well as the height of
building was studied. The specific objectives were to prepare various R.C.C. models
to assess the change in natural frequency and to derive the appropriate expression to
calculate the natural period.
As the number of floors increased, the height of the building increased resulting
a decrease in the natural frequency determined as per the equation given in the
20
International Standards 1893:2002 (IS). Therefore, the equation in the code was
revised to account for the combined effects of number of floors and height [17].
2.4.1.6 Kadir Guler, Ercan Yuksel, and Ali Kocak, 2008
The objective of this article was to examine the relationship between the height
and the fundamental period of vibration of RC moment resisting frames using ambient
vibrations and comparing the results with the code-specified period equation in the
TSC 07. The investigation of the effects of infill walls on the period calculation was
also provided in the same article.
The first series of vibration measurements were conducted on a 12 story
reinforced concrete building during three different construction stages to calibrate the
numerical models prepared for the building. On the other hand, similar ambient
vibration tests were conducted on a total of five actual RC buildings applied in the two
principle directions. In each of the tests, the buildings’ story heights were the same as
3 meters. The ambient vibration tests were performed using a highly sensitive
seismometer so the seismometer was located at the geometrical center of the very top
floor assuming that this point coincided with its center of mass.
A fully elastic 3D numerical model comprising frame-type structural elements
representing uncracked stiffness was used for Building No1. The elastic analyses of
numerical models were performed using SAP2000 software. The fundamental period
of the building was evaluated numerically using a fully elastic 3D model with
uncracked stiffness for beams and columns and diagonal struts for infill walls. The
numerical analyses based on those performed on Building No1 was repeated for seven
different cases. The results of the numerical analyses provided a relationship for the
quick estimation of the fundamental period of infilled RC frame-type structures under
ambient vibrations.
Ta = 0.026 H 0.9
(2.21)
In addition to the analyses, five more buildings (Building No’s. 2, 3, 4, 5, and
6) were examined experimentally to evaluate and verify the accuracy of the proposed
equation.
21
The experimentally derived fundamental period of the buildings under
consideration were in good agreement with those determined using the proposed
relationship. The average relative error was approximately in the range of 13%.
Therefore, the proposed relationship was recommended to be used for the estimation
of the elastic fundamental period of mid-rise RC frame-type buildings in Turkey.
Furthermore, the results showed that for moderate intensity earthquakes, the period
can be calculated by increasing the result from the proposed equation by 75% [18].
2.4.1.7 Helen Crowley and Rui Pinho, 2006
The aim of this study was to produce a period versus height equation in order
to determine the fundamental period of vibration for actual reinforced concrete
buildings with moment resisting frames and with infill panels. Such buildings were
considered in this study by modelling representative 2D frames analytically.
The reinforced concrete frames considered in this study corresponded to
existing buildings from five different European countries exposed to earthquake forces
(Greece, Italy, Portugal, Romania, Yugoslavia).
The majority of the existing buildings were designed and built between 1930
and 1980. The study led to a simplified period versus height equation in the assessment
of existing RC buildings taking due account of the presence of infill panels. The
following equation was proposed in this study:
Ty =0.055 H
(2.22)
This equation was compared to the empirical formula in EC8 [CEN, 2003] for
the assessment of reinforced concrete buildings. This study represented a starting point
for revisiting the empirical formulas in EC8 to estimate the period of vibration for the
the existing buildings in Europe. In order to do that, the proposed formula needed to
be verified on the buildings located in other European countries such as Turkey. using
appropriate material properties to model the masonry panels and considering the
proportions of bare, fully infilled and partially infilled frames. Furthermore, the period
estimated obtained from the proposed formula were compared to the results obtained
from detailed analyses of 3D analytical models of infilled reinforced concrete
buildings.
22
The period of vibration which was derived represented the period of the first
mode of vibration for a fixed-base building model. This horizontal translation periods
of the building as it moves as a rigid body on flexible soil were omitted. However, it
was noted that this omission might had an importance on the overall dynamic response
of buildings. As part of future studies, the effect of soil-structure interaction was
recommended in evaluating the period calculations [4].
2.4.1.8 R. Ditommaso, M.Vona, M. R. Gallipoli, and M. Mucciarelli, 2013
The aim of this study was to develop an empirical estimation of the
fundamental period of reinforced concrete buildings with structural and non-structural
damages. A total of 68 buildings with different characteristics, such as age, height and
damage level, was investigated by performing ambient vibration measurements that
provided their fundamental translational periods. Four different damage levels (DL0,
DL1, DL2, DL3) were considered according to the definitions in EMS 98 (European
Macroseismic Scale), trying to regroup the estimated fundamental periods versus
building heights using damage level as a key parameter.
The fundamental period of RC buildings estimated for low level damage was
equal to the previous relationship obtained in Italy and Europe for undamaged
buildings. When damage levels were higher, the fundamental periods increased, but
again result of values were much lower than those provided by the codes. Finally, the
authors suggested a possible update of the code equation for the simplified estimation
of the fundamental period of vibration for existing RC buildings, taking also the
inelastic behavior into account. The two suggested experimental period height
relationships were obtained. The first one for undamaged buildings considering it as a
lower limit in elastic force-based design (DL1 and DL0) is provided in the following
equation:
T = 0.026 H
(2.23)
And the second one related to buildings with DL2 and DL3 is given as follows:
T = 0.028 H
23
(2.24)
The second one represents the higher limit value for the assessment and
retrofitting of existing RC buildings, in particular when the post-elastic behavior of the
structure was taken into account [19].
2.4.1.9 Can Balkaya and Erol Kalan, 2003
In this article it was stated that the concrete structures constructed by using a
special tunnel form technique had been built in countries facing a major seismic risk,
such as Chile, Japan, Italy and Turkey. In spite of their high resistance to earthquake
events, current seismic code provisions included the Uniform Building Code, and the
Turkish Earthquake Code offered limited information for their design criteria.
In this study, the uniformity of equations in those seismic codes related to their
dynamic properties were investigated. It was observed that the empirical equations for
prediction of fundamental periods of this specific type of structures produced
unconservative results. For that reason, a total of 80 different building configurations
were analyzed by using three-dimensional finite element modelling, and a set of new
empirical equations was proposed. The results of the analyses demonstrated that the
proposed equation including new parameters provided accurate results for the broad
range of different architectural configurations, such as roof heights and shear-wall
distributions. The following equations was proposed in this study:
b4
b5 b6
T= C hb1 βb2 ρb3
aᵴ ρa𝗅 ρmin j
(2.25)
where, the parameters, C, b1, b2, b3, b4, b5, b6, ϬT, R2 , are listed in the Table 2.2
Table 2.2 Values of c, b1, b2, b3, b4, b5, b6, Ϭt, R2
Plan
𝐑𝟐
b1
b2
b3
b4
b5
Squ.
0.158
1.400
0.972
0.812
1.165
-0.719 0.130 0.025 0.982
Rect.
0.001
1.455
0.170
-0.485 -0.195 0.170
Type
b6
ϭT
C
0.094 0.025 0.989
In the Equation 2.25, T is the natural period of the building, h is the building height, β
is the ratio of long to short side dimension, ρaᵴ ratio of short side shear wall area to
total floor area, ρa𝗅 , is the ratio of long side shear wall area to total floor area, ρmin is
24
the ratio of minimum shear wall area to total floor area, an finally j is the plan polar
moment of inertia. The parameters defined as C, b1, b2, b3, b4, b5 and b6 are the ones
that to be determined by regression analysis.
This study demonstrated that current earthquake codes overestimated the
results of finite-element analyses for rectangular shaped plans and most of the time
underestimated the periods for square shaped plans. This observation was due to
omittance of torsional disturbance as a parameter in the code defined equations. In
fact, torsion was an exceptionally important criteria appearing in the dynamic mode of
those structures that should have been taken into account in the design phase. The
recommended empirical equations were considered to be appropriate for the estimation
of the period of tunnel form building structures from 2 to 15 storey levels with various
architectural configurations [20].
2.4.2 Hand Calculation Methods
Below, you will find the two hand calculations methods to calculate the
fundamental period of buildings.
2.4.2.1 Bryan Stafford Smith and Elizabeth Crowe, 1986
A hand calculation method in estimating the fundamental periods of building
was developed to use in calculating the minimum base shear for earthquake design.
Structures which were analyzed with this method were regular in plan and had uniform
properties along the height. Also, the structure needed to be loaded symmetrically
without a torsional effects. The method was based on a procedure that regarded
coupled walls, rigid frames, braced frames and wall-frames and braced frames or any
combination of these as a shear-flexure structure in order to determine their static
deflection with coupled wall theory. It was useful to decouple static deflection into
two parts as flexural component and shear plus flexure, so that dynamic behavior of
the structure could be captured by decoupled eigenvalue approach. The results of this
study were summarized for braced frames as follows:

First natural period could be obtained by this method with a 2.9% error.

For all structure types, the estimated second mode of vibration period had a 15%
error [21].
25
2.4.2.2 K.A.Zalka, 2001
This was a hand calculation method provided for the three-dimensional
frequency analysis of buildings such coupled shear walls, shear walls with cores.
Lateral vibration was defined by three deformation types such as full height local
bending, full height global bending and shear deformation of the frameworks. The aim
of the study was to develop a closed from solution to estimate lateral frequencies using
their stiffnesses. The buildings were assumed to have a uniform properties along their
heights, and the coupling of the lateral and pure torsional modes was taken into
account. The accuracy of this method was verified with the results of finite element
solution for 4, 10, 16, 22, 28, 34, 40, 60, 80 storey buildings. The storey height was 3
meters and each span was 6 meters long. For the 144 cases, the average error between
the hand method and finite element solution was found to be around 2% and with a
maximum error of 7%. It had been shown that this closed-from solution could be used
for the calculation of the natural frequencies of multi storey buildings [22].
26
CHAPTER 3
PARAMETRIC STUDIES AND COMPARISONS OF RESULTS
3.1 Introduction
The starting point of this study is to construct finite element modelling of
buildings whose details are provided below using a commercially available software,
ETABS, based on the rules outlined in the Turkish seismic code TSC 07.
For this purpose, a total of twenty one layouts are selected as a parametric
study. The intent of this study is to understand the dynamic behaviors of buildings with
different configurations under severe seismic loads. Therefore, all buildings are
assumed to be located in Bursa, where the seismic zone is zone 1 as stated in the TSC
07. The seismic forces are applied to the buildings using response spectrum method.
The details of this method are provided in the later sections.
The focus in this chapter is on the determination of first three periods
specifically the fundamental period, and on the lateral deflections associated with
seismic forces acting both in the “x” and “y” directions. In order to investigate the
fundamental period and the lateral deflections, the twenty one layouts are modeled
with different aspect ratio and framing types. For this purpose, twenty one layouts are
increased to a total of 105 models.
The letters A through D are used to identify the four different floor layouts.
The dimensions of the floor layouts are studied as a parameter to create different inplan aspect ratios to understand the ratio’s effect on the fundamental periods. For this
purpose, three different aspect ratios are studied in this thesis 1.33, 2.00, and 2.66.
The aspect ratios are designated as numbers starting from one to three next to
the four letters of A through D that are used to identify the different floor layouts. (For
example, A1 indicates the layout A with the aspect ratio of one). Therefore, the four
layouts are increased to a total of twelve layouts.
27
As stated in Chapter 2, the number of floors plays a significant role in
determining the fundamental period. Therefore, it is decided to study this effect as an
additional parameter in evaluating the periods of buildings. This effect is included in
the analyses part by selecting the five floor levels. These floor levels are named as ten
story level, twenty story levels, thirty story level, forty story level, and finally fifty
story level.
Thus, the total of twelve buildings increased to a total of 60 buildings (i.e.
twelve building layouts times the five separate sets of floor levels increased the number
of buildings to sixty).
Furthermore, as the previous research and studies stated in Chapter 2, framing
type is another important key parameter that needs special attention in studying the
fundamental period. To be able to understand the impact of framing type on the period
calculations, three main framing systems are selected randomly. In the first framing
type, the buildings are assumed to have all moment frames with columns only. In the
second type, the columns are all replaced by the shear walls. In the third and final
framing type, the vertical structural members are assumed to be replaced by the
combination of columns and shear walls.
This additional parameter (framing type) increase the total number of building
from 60 models to a grand total of 105. Below list summarizes the details of the models
along with their characteristics:
1. Buildings with different aspect ratios:

Buildings A1, B1, C1, D1 with an aspect ratio of 1.33.

Buildings A2, B2, C2, D2 with an aspect ratio of 2.

Buildings A3, B3, C3, D3 with an aspect ratio of 2.66.
Where the model process start from 10 to 50 story buildings for each layout.
2. Buildings with different layouts configuration:

Buildings E1, F1, G1 with columns only.

Buildings E2, F2, G2 with shear walls only.

Buildings E3, F3, G3 with combination of columns and shear walls.
In summary, a total of 105 models are constructed in ETABS. The results from the
ETABS analyses, focus specifically on the fundamental period and the lateral
28
deflections. The fundamental period values resulting from the ETABS are compared
to the equations provided in the Turkish Seismic Codes dated 1997 and 2007 and the
ASCE 10.
In evaluation process of the fundamental periods, the equations from the three
codes, TSC 07, TSC 97, and ASCE 7-10, are used. Although the TSC 97 is superseded
by new seismic code called TSC 07, the equations outlined in the older code are
decided to be included in this study since they are adopted from the UBC 97 and they
include the effect of different framing types. The intent in this comparison is not to
provide a detailed comparison between the old and new Turkish Seismic Codes.
3.2 Building Information
This section provides the necessary information required to understand the
layouts, dimensions, and the material properties for the 105 building models
constructed in ETABS.
3.2.1 Layouts Information
The main layouts of the buildings not including the five sets of total floor
numbers (i.e., ten story, twenty story, thirty story, forty story, and fifty story) are
provided below (see Figures 3.1 through 3.21). In these floor layouts, the floor
dimensions, the column and wall layouts, and the dimensions of bays are given. In
selecting the layouts, all the buildings are assumed to have no openings since their
presence will not adversely affect the period calculations.
29
Figure 3.1 Layout A1 (48 m by 36 m)
Figure 3.2 Layout A2 (48 m by 24 m)
30
Figure 3.3 Layout A3 (48 m by 18 m)
Figure 3.4 Layout B1 (48 m by 36 m)
31
Figure 3.5 Layout B2 (48 m by 24 m)
Figure 3.6 Layout B3 (48 m by 18 m)
32
Figure 3.7 Layout C1 (48 m by 36 m)
Figure 3.8 Layout C2 (48 m by 24 m)
33
Figure 3.9 Layout C3 (48 m by 18 m)
Figure 3.10 Layout D1 (48 m by 36 m)
34
Figure 3.11 Layout D2 (48 m by 24 m)
Figure 3.12 Layout D3 (48 m by 18 m)
35
Figure 3.13 Layout E1 (48 m by 36 m)
Figure 3.14 Layout E2 (48 m by 36 m)
36
Figure 3.15 Layout E3 (48 m by 36 m)
Figure 3.16 Layout F1 (48 m by 36 m)
37
Figure 3.17 Layout F2 (48 m by 36 m)
Figure 3.18 Layout F3 (48 m by 36 m)
38
Figure 3.19 Layout G1 (48 m by 36 m)
Figure 3.20 Layout G2 (48 m by 36 m)
39
Figure 3.21 Layout G3 (48 m by 36 m)
3.2.2 Dimensions of Elements
The buildings modelled in ETABS are all assumed to have the same floor
height of 3.2 meters. The beams in all the models are assumed to have the same
dimensions of 0.4 m width and 0.75 m height. Tables 3.1 through 3.21 list the details
of each layout for each sets of floor levels (ten, twenty, thirty, forty, and fifty story).
As opposed to the beam dimensions that are kept the same, in these tables, the column
dimensions are changed for every ten story.
For example, in Table 3.1, for the fifty story case, the column dimensions are
increased for the upper ten floors from 0.55 m. by 0.55m. to a 1.2 m. by 1.2 m. for the
lower ten floors. In other words, the column dimensions are increased gradually for
each stack of 10 floors.
Since the main focus of this study is on the fundamental period and on the
lateral deflections, it is assumed that the beam, column, wall and slab dimensions in
these ETABS models all have slightly larger values than their optimum design
dimensions. Therefore, slightly larger dimensions are selected for all structural
members. As explained, the reason behind this decision comes from the fact that the
focus is not on the design optimization but rather on the overall behavior of buildings
under seismic loads.
40
Table 3.1 Layout details of A1
Number of
Stories
10
20
30
40
50
Column
Dimensions
(m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
No. of Bays
(x.dir.) Each
@ 6 m.
8
No. of Bays
(y.dir.) Each
@ 6 m.
6
Slab
Thickness
(m)
0.15
8
6
0.15
8
6
0.15
8
6
0.15
8
6
0.15
No. of Bays
(x.dir.) Each
@ 6 m.
8
No. of Bays
(y.dir.) Each
@ 6 m.
4
Slab
Thickness
(m)
0.15
8
4
0.15
8
4
0.15
8
4
0.15
8
4
0.15
Table 3.2 Layout details of A2
Number of
Stories
10
20
30
40
50
Column
Dimensions
(m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
41
Table 3.3 Layout details of A3
Number of
Stories
10
20
30
40
50
Column
Dimensions
(m)
No. of Bays
(x.dir.) Each
@ 6 m.
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
No. of Bays
(y.dir.) Each
@ 6 m.
Slab
Thickness
(m)
8
3
0.15
8
3
0.15
8
3
0.15
8
3
0.15
8
3
0.15
Table 3.4 Layout details of B1
Number
Shear Wall
of Stories
Thickness (m)
10
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
20
30
40
50
No. of Bays
No. of
(x.dir.) Each
Bays
@ 6 m.
(y.dir.)
8
4
0.2
8
4
0.2
8
4
0.2
8
4
0.2
8
4
0.2
42
Slab Thickness
(m)
Table 3.5 Layout details of B2
Number
Shear Wall
of Stories
Thickness (m)
10
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
20
30
40
50
No. of Bays
No. of
(x.dir.) Each
Bays
@ 6 m.
(y.dir.)
8
2
0.2
8
2
0.2
8
2
0.2
8
2
0.2
8
2
0.2
Slab Thickness
(m)
Table 3.6 Layout details of B3
Number
of Stories
Shear Wall
Thickness (m)
10
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
20
30
40
50
No. of Bays
(x.dir.) Each
@ 6 m.
8
No. of Bays
(y.dir.)
Slab Thickness
(m)
2
0.2
8
2
0.2
8
2
0.2
8
2
0.2
8
2
0.2
43
Table 3.7 Layout details of C1
Number
of Stories
10
20
30
40
50
Shear
Wall
Thickness
(m)
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
No. of Bays
(x.dir.) Each
@ 6 m.
Column
Dimensions
(m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
No. of Bays
(y.dir.) Each
@ 6 m.
Slab
Thick.
(m)
8
6
0.15
8
6
0.15
8
6
0.15
8
6
0.15
8
6
0.15
Table 3.8 Layout details of C2
Number
of Stories
10
20
30
40
50
Shear
Wall
Thickness
(m)
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
Column
Dimensions
(m)
No. of Bays
(x.dir.) Each
@ 6 m.
No. of Bays
(y.dir.) Each
@ 6 m.
Slab
Thick.
(m)
0.55*0.55
0.55*0.55
0.75*0.75
8
4
0.15
8
4
0.15
8
4
0.15
8
4
0.15
8
4
0.15
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
44
Table 3.9 Layout details of C3
Number
of Stories
10
20
30
40
50
Shear
Wall
Thickness
(m)
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
Column
Dimensions
(m)
No. of Bays
(x.dir.) Each
@ 6 m.
No. of Bays
(y.dir.) Each
@ 6 m.
Slab
Thick.
(m)
0.55*0.55
0.55*0.55
0.75*0.75
8
3
0.15
8
3
0.15
8
3
0.15
8
3
0.15
8
3
0.15
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
Table 3.10 Layout details of D1
Number
of Stories
10
20
30
40
50
Shear
Wall
Thickness
(m)
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
Column
Dimensions
(m)
No. of Bays
(x.dir.) Each
@ 6 m.
No. of Bays
(y.dir.) Each
@ 6 m.
Slab
Thick.
(m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
8
6
0.18
8
6
0.18
8
6
0.18
8
6
0.18
8
6
0.18
45
Table 3.11 Layout details of D2
Number
of Stories
10
20
30
40
50
Shear
Wall
Thickness
(m)
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
Column
Dimensions
(m)
No. of Bays
(x.dir.) Each
@ 6 m.
No. of Bays
(y.dir.) Each
@ 6 m.
Slab
Thick.
(m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
8
4
0.18
8
4
0.18
8
4
0.18
8
4
0.18
8
4
0.18
Table 3.12 Layout details of D3
Number
of Stories
10
20
30
40
50
Shear
Wall
Thickness
(m)
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
Column
Dimensions
(m)
No. of Bays
(x.dir.) Each
@ 6 m.
No. of Bays
(y.dir.) Each
@ 6 m.
Slab
Thick.
(m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
8
3
0.18
8
3
0.18
8
3
0.18
8
3
0.18
8
3
0.18
46
Table 3.13 Layout details of E1
Number of
Stories
10
20
30
40
50
Column
Dimensions
(m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
8
Slab
Thickness
(m)
0.15
8
0.15
8
0.15
8
0.15
8
0.15
No. of Bays (x.dir.)
Each @ 6 m.
Table 3.14 Layout details of E2
Number of
Stories
10
20
30
40
50
Shear Wall Thickness No. of Bays (x.dir.)
(m)
Each @ 6 m.
0.25
8
0.25
8
0.30
0.25
0.30
8
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
47
Slab Thickness
(m)
0.2
0.2
0.2
8
0.2
8
0.2
Table 3.15 Layout details of E3
Number
of Stories
Shear Wall
Thickness (m)
10
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
20
30
40
50
Column
Dimensions
(m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
8
Slab
Thick.
(m)
0.15
8
0.15
8
0.15
8
0.15
8
0.15
No. of Bays (x.dir.)
Each @ 6 m.
Table 3.16 Layout details of F1
Number of
Stories
10
20
30
40
50
Column
Dimensions (m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
48
8
Slab
Thick.
(m)
0.15
8
0.15
8
0.15
8
0.15
8
0.15
No. of Bays (x.dir.)
Each @ 6 m.
Table 3.17 Layout details of F2
Number of
Stories
Shear Wall Thickness (m)
10
0.25
0.25
0.30
0.25
0.30
0.35
20
30
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
40
50
8
Slab
Thick.
(m)
0.2
8
0.2
8
0.2
8
0.2
8
0.2
No. of Bays (x.dir.)
Each @ 6 m.
Table 3.18 Layout details of F3
Number
of Stories
Shear Wall
Thickness (m)
10
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
20
30
40
50
Column
Dimensions (m)
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
49
No. of Bays
(x.dir.) Each
@ 6 m.
8
Slab
Thick.
(m)
0.15
8
0.15
8
0.15
8
0.15
8
0.15
Table 3.19 Layout details of G1
Number of
Stories
Column Thickness (m)
No. of Bays (x.dir.)
Each @ 6 m.
10
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
8
Slab
Thick.
(m)
0.15
8
0.15
8
0.15
8
0.15
8
0.15
20
30
40
50
Table 3.20 Layout details of G2
Number of
Stories
10
20
30
40
50
Shear Wall thickness (m)
No. of Bays (x.dir.)
Each @ 6 m.
0.25
0.25
0.30
0.25
0.30
0.35
8
Slab
Thick.
(m)
0.2
8
0.2
8
0.2
8
0.2
8
0.2
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
50
Table 3.21 Layout details of G3
Number of
Stories
Shear Wall
Thickness (m)
10
0.25
0.25
0.30
0.25
0.30
0.35
0.25
0.30
0.35
0.40
0.25
0.30
0.35
0.40
0.50
20
30
40
50
Column
Dimensions (m)
8
Slab
Thick.
(m)
0.15
8
0.15
8
0.15
8
0.15
8
0.15
No. of Bays (x.dir.)
Each @ 6 m.
0.55*0.55
0.55*0.55
0.75*0.75
0.55*0.55
0.75*0.75
0.90*0.90
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
0.55*0.55
0.75*0.75
0.90*0.90
1.05*1.05
1.20*1.20
3.2.3 Material Properties
Concrete class C25 as described in the Turkish Standards 500 (TS 500) is
selected to be the concrete class for all structural members where the modulus of
elasticity is 6,000,000 ton /m2 . The poison’s ratio for concrete as described in the TS
500 is assumed to be 0.2. In the self-weight calculation, the unit weight of the
reinforced concrete is selected to be 2.5 ton /m3 [24]. Since the focus of this study is
not on the design part of structural members, no material properties are assigned to
rebars. Therefore, this designation is not included in the ETABS analyses.
3.3 Modeling in ETABS
In the seismic design of a total of 105 models, a response spectrum method as
outlined in the TSC 07 is used both in the “x” and “y” directions.
The buildings are all assumed to be located in Bursa where the region is under
the most severe earthquake threat. Therefore, the effective ground acceleration
coefficient, A0 , as described in the TSC 07 is selected 0.4.
All the buildings in this study are considered residential and, thus its associated
building importance factor again according to the TSC 07 is selected one (1).
51
In order to eliminate the need for a pile foundation, the tallest building that
have fifty stories are all assumed to be located in a stiff soil where the soil bearing
capacity is not exceeded by the imposed load on it resulting from the dead and live
loads acting on the building. For this purpose a local site class Z2 as described in the
TSC 07 is selected for all building models with ten, twenty, thirty, forty, and fifty
stories. In other words, the local site class Z2 is the site class for all types of buildings.
As for the loads, load cases and load combinations, the equations provided both
in the TS 500 and the TSC 07 are used in the ETABS models. In the dynamic analyses
part, a total of 36 modes are used for all buildings models, since the number of mode
shapes is not the key parameter under consideration.
The focus of this study is on the determination of the fundamental period and
the lateral deflections, no load combination is selected in the ETABS analyses. In other
words, only load cases are considered in evaluating the periods and deflections in this
study. In the seismic analysis, the self-weight of the building is a key component. The
self- weight of the structural members are automatically included by the program and
therefore, they are not calculated as an additional load. The live loads and the super
imposed dead loads, however, are assigned as a pressure load to each floor.
The magnitude of the live loads for all the models are assumed to be 0.35
ton/m2 . In fact, 0.2 ton/m2 as described in the Turkish Standards TS 498 (TS 498 is
the standard for design for buildings) is assumed to be the live load for all floor levels.
But since the locations of partition walls might change, and also to account for the stair
cases that are designated as 0.35 ton/m2 for live loads, the 0.2 ton/m2 value is
increased to 0.35 ton/m2 . For the super imposed dead load, a constant pressure load
value of 0.15 ton/m2 is selected again for all the models. This magnitude is calculated
as an average value resulting from stone work placed on an average of 4 cm thick
mortar [25].
According to the TSC 07, the seismic weight of a building is determined by the
combination of full effect of dead load and partial effect of live loads. The partial effect
of live load is introduced by a factor called live load participation factor. In this study,
this factor is selected as 0.3, which is the value described for the residential buildings.
In ETABS, modeling, there are two options that exist in defining the
diaphragms. These options are rigid and semi-rigid. In this study, rigid diaphragm is
52
selected for all floor diaphragms. Although, in reality, building floors are expected to
have openings in different sizes which would adversely impact the rigid diaphragm
assumption, it is assumed in this study that this assumption would not cause negative
in the period calculations. Therefore, no parametric study concerning diaphragms is
investigated in this thesis. All buildings modeled in ETABS are assumed to have fixed
supports. Therefore, as in the diaphragm case, no parametric study concerning this
parameter is also investigated. It is also important to note that the effect of soilstructure interaction that exist in foundation and building design is also ignored in this
study. In addition to this omittance, the effect of basements floors are also neglected
intentionally in evaluating the fundamental period and the lateral deflections.
Below list summarizes the important assumptions made in the ETABS
analyses:

Rigid diaphragm is assumed.

Automatic mesh is used for all structural elements.

Thin shell element type for slabs is assumed.

Thin shell element type for walls is assumed.

Frame element type for columns are assumed.

Concrete assumed to be uncracked.

Structural design of members are not completed.

Gross moment of inertia is used for all structural members.

Soil-structure interaction is not included.

The effect of basement floors is neglected.
3.4 Results
The results of the parametric study are discussed in this section. First of all, the
first fundamental period is investigated for each model. The mode shapes and other
results are studied in detail to understand the degree of changes in periods from one
model to another one. Then, the first fundamental period is investigated further by
comparing the results from individual FE models to the code associated limitations.
Thus, it is intended to determine how good the code associates equations with respect
to the results from the FE analyses. Finally, the deflected shapes of buildings both in
53
the “x” and “y” directions are studied to understand the impact of various structural
configurations.
Table 3.22.a and 3.22.b have the list of the first three periods for 10, 20, 30, 40,
and fifty stories for the 21 layouts. As it is discussed in the later sections, the dominant
directions of building periods vary from model to model, but each model has at least
one in the “x” direction, one in the “y” direction, and one in the rotational direction.
As listed in Table 3.22.a and 3.22.b, the first periods for the 10 story R.C.
buildings vary from approximately 0.5 to 1.2 seconds. The larger periods indicate the
relatively less lateral stiffnesses resulting from the various structural configurations.
For the 20 story building, the periods vary from 1.1 to 2.5, for the 30 story case from
1.7 to 3.9, for the 40 story from 2.4 to 5.3, and finally for the 50 story case from 3.2 to
6.7. As expected the increase in the number of floors from the 10 story case to the
tallest one, the 50 story case is 5, but the increase in the fundamental period of the 10
story to the 50 story one is approximately 6. So, it can be suggested that there is almost
like a linear relationship between the increase in the period and in the number of floors.
The minimum fundamental periods for all sets of floor levels are obtained for
the layout E3, where the floor layout is cross-shaped layout. In this layout, the in-plan
dimensions in the “x” and “y” directions are 48 meters and 36 meters, respectively. As
illustrated in Figure 3.15, the layout E3 has “L shaped” shear walls located all around
the twelve corners where this choice significantly increased the overall stiffness of the
building both in the “x” and “y” directions. It is, therefore, important to state that shear
walls located around building corners work more effectively than the layouts where
this walls are located within the plan.
As opposed to the one layout that produced the smallest fundamental period,
there are no unique layouts that produce the largest fundamental periods. Therefore,
the largest fundamental periods are obtained from the layout A3 for the 10 story case,
and layout B2 for the 20 story, 30 story, 40 story, and 50 story case. As illustrated the
layout for A3 has an in- plan dimensions of 48 meters to 18 meters. This layout is the
one that lateral resisting system composed of columns only. The layout B2, on other
hand, has an in-plan dimensions of 48 meters to 24 meters, and it as a lateral resisting
system it includes shear walls only. However, the stiffness of the lateral resisting
system is weak in the “x” direction when compared to the one in the “y” direction due
54
to the orientation of the walls (see Figure 3.5). It is due to this shear wall orientation
that there is a significant drop in the second period value compared to the first one.
Due to the fact that each building has a number of natural frequencies, at which
it offers minimum resistance to shaking induced by external effects, the results provide
clear variation between the time periods of vibration for a building depending on the
stiffness characteristics and construction materials including other factors such as
damping affecting the fundamental periods.
In the following sections, detailed comparisons of the FE analyses and the code
associated equations are provided for each layout. The code associated equations
(please refer to Chapter 2 and 3) used in these figures are as follows:
TSC 07
For all building types and layouts:
T1 = 0.1 N (3.1)
TSC 97
Buildings with columns only:
T = 0.07 h0.75
n
(3.2)
T = 0.05 h0.75
n
(3.3)
T = 0.044 h0.9
n
(3.4)
T = 0.055 h0.75
n
(3.5)
For all other buildings types:
ASCE 7-10
Buildings with columns only:
For all other buildings types:
The equation for the fundamental period in the TSC 97 has four separate cases.
These cases namely are (a) buildings where seismic loads are fully resisted by
55
reinforced concrete walls, (b) buildings whose structural systems are composed only
of reinforced concrete frames or structural steel eccentric braced frames, (c) buildings
made only of steel frames, and (d) for all other types of buildings not mentioned in
items a, b, and c.
In constructing the code associated figures resulting from the TSC 97, the
layouts that have shear walls coupled with reinforced concrete beams are considered
to be treated as the case defined in item d. These layouts with this specific lateral
resisting system is assumed to be different than the one in item (a) due to the fact that
the framing system is a special one without any RC beams. This framing is called
tunnel form framing and is different than the ones considered in this study.
56
57
58
3.4.1 Layouts A1, A2, and A3
Figure 3.22 illustrates the change in the first fundamental period for the layouts
A1, A2, and A3 with 10, 20, 30, 40 and 50 stories.
In this figure, the period values from the ASCE 7-10, TSC 97 and the TSC 07
are also included in order to compare the FE analyses results to the code associated
ones. As stated in section 3.1, A3 has a higher in-plan aspect ratio compared to the
ones for A1 and A2. Therefore, the layout, A3 will be used as a reference in comparing
the results of the layouts, A1 and A2. In this layout, it is clear that for a low-rise
buildings the differences in periods among A1, A2 and A3 are considerably small.
However, when the number of floors increases, the differences become more
prominent. Furthermore, the aspect ratio increases, the fundamental period increases.
For a ten story buildings, the smallest value for the period is obtained as 1.134
seconds for the layout A1 (the aspect ratio is 1.33). The largest period is obtained for
the layout A3 (the aspect ratio is 2.67) is 1.159 seconds. Therefore, the ratio of the first
periods of A3 to A1 for a ten story building is 1.02. Although the ratio of the in-plan
aspect ratios between the layouts A1 and A3 is 2, the first periods are almost the same.
This indicates that the in-plan aspect ratio does not play a significant role in
determining the first period for low-rise buildings. It is also important to note that the
1.15 seconds period ratio obtained for a fifty story building does not change
significantly, and remains almost equal to the one for the ten story case. This
observation concludes that for moment-frames, the effect of number of floors on the
fundamental periods is not as significant as the frame types with walls.
The equation from the TSC 97 provides a very conservative result compared
to the ones from the FE analyses. For a ten story building, the TSC 97 underestimates
the first period for A3 by 19%. This estimation becomes more prominent for a fifty
story building since the ratio increases to 41%. This increase in ratio is a result of the
direct impact of the number of floors. The code associated equations causes the period
increase directly proportionally to the number of floors while the FE analyses do not
reflect this much increase on the period. Therefore, it is clear that the TSC 97 produces
more conservative limits specifically for taller buildings in estimating the fundamental
period.
59
The ASCE 7-10 estimates the first fundamental period of layout A3 with ten
story as 0.99 second. Therefore, the code underestimates the first period by 14%. This
underestimation for the first period of layout A3 with fifty story building increases to
20%. As opposed to the trend observed in the TSC 97, the ASCE 7-10 does not cause
a significant change in estimating the first period. Therefore, it can be concluded that
code associated period values demonstrate a fairly good correlation when they are
compared to the FE analyses results. The same conclusion is also valid for the other
two layouts, A1 and A2.
The equations of the TSC 07 are also used for layout A3 to make a comparison
to the FE analysis. The first fundamental period of layout A3 with ten story building
according to the TSC 07 is calculated 1.0 second. The code underestimates the first
period by 13%. This degree of underestimation decreases to 6% for 50 story building.
Therefore, for this layout, it can be concluded that the TSC 07 provides fairly good
results. The same observation is also valid for the layout A2. Although, there are some
differences in period, these are very small and considered negligible. But for the layout
A1, the code does not provide safe results, beyond 20 stories. This phenomenon
indicates that as the aspect ratio with columns only approaches to the unity, the code
begins overestimating the period eventually and results in smaller design forces.
Figures 3.23 and 3.24 provide comparison for the second and third periods. For
the layouts A1, A2 and A3 with 10, 20, 30, 40 and 50 stories the difference in periods
for each sets of floor numbers is not significant, which implies that the aspect ratio has
almost no effect on the second or third periods.
60
61
5
4.5
4
T2, sec
3.5
3
2.5
A1(48*36)
2
A2(48*24)
1.5
A3(48*18)
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.23 Second period versus number of floors for building layouts, A1, A2, A3
4.5
4
3.5
3
T3, sec
2.5
A1(48*36m)
2
A2(48*24m)
A3(48*18m)
1.5
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.24 Third period versus number of floors for building layouts, A1, A2, A3
62
3.4.2 Layouts B1, B2, and B3
Figure 3.25 shows the change in the first fundamental period for layouts B1,
B2, and B3 with 10, 20, 30, 40 and 50 stories.
The differences between each sets of floor numbers (10, 20, 30, 40, and fifty)
in this layout are more significant, as the aspect ratio increases from 1.33 to 2 and then
2.67. The period results from the ASCE 7-10, TSC 97 and the TSC 07 are also included
in this figure in order to compare the FE analyses’ results to the code associated ones.
B2 has an in-plan aspect ratio of 2. In this layout, it is clear that for all floors, the layout
B2 has a period larger than B1 and B3 due to the weaker lateral strength resulting from
the wall configuration.
For a ten story building case, the first period for B2 (the aspect ratio is 2) is
1.134 seconds, while the same period for B3 (the aspect ratio is 2.67) is 0.993 second.
Therefore, the ratio of the first period of B2 to B3 for a ten story building becomes
1.14 while, the same ratio for a fifty story building is 1.10. This slight decrease
indicates that the shear wall configuration for layout B3 is more effective as the
number of floors increases.
For low height buildings (such as 10 story building), all code associated
equations provide close period estimations when they are compared to the FE results.
However, for taller buildings (50 story case), the codes greatly underestimate the
periods. This observation is specifically correct for the TSC 97 and ASCE 7-10. The
TSC 97, underestimates the first fundamental period of B2 with 50 story by 53%. This
in return, causes greatly overestimated design forces.
The ASCE 7-10 again underestimates the first fundamental period for the same
layout (B2) with fifty story case by 63% (the period is 2.47 seconds). However, the
degree of underestimation according to the TSC 07, is not as bad as the ones from the
TSC 97 and ASCE 7-10. The first fundamental period of layout B2 with fifty story
case according to the TSC 07 is 5 seconds (25% underestimation).
Out of three layouts considered in this section, the layout B3 has the largest inplan aspect ratio (it is 2.67). Also, B3, due to the configuration of shear wall layouts
has the smallest fundamental periods for all sets of floors. For example, for a fifty story
case, the smallest period is calculated 6.078 seconds. The best estimated period for this
63
layout is obtained from the equation in the TSC 07 (5 seconds). Even with this best
estimated period, the code underestimated the period by approximately 18%.
Therefore, the period values obtained from the codes overestimates the design
forces for all layouts with all the sets of floor numbers considered (the code associated
forces are larger than the ones from the FE analyses).
Figures 3.26 and 3.27 illustrate the change in the second and third periods for
layouts B1, B2, and B3 with 10, 20, 30, 40 and 50 stories. The differences for the
second and the third periods for each sets of floor cases (10, 20, 30, 40 and 50 story)
are not significant specifically for layouts B1and B2. However, this observation is not
valid for layout B3 when its periods are compared to the second and third periods of
B1 and B2, since B3’s span in the y direction in between the shear walls is decreased
from 7.325 meters for B1 to 3.75 meters. This decrease in the span causes increase the
overall stiffness of layout B3 which results decrease in its second and third periods.
64
65
5
4.5
4
3.5
T2, sec
3
2.5
B1(48*36m)
2
B2(48*24m)
1.5
B3(48*18m)
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.26 Second period versus number of floors for building layouts, B1, B2, B3
5
4.5
4
3.5
T3, sec
3
2.5
B1(48*36m)
2
B2(48*24m)
B3(48*18m)
1.5
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.27 Third period versus number of floors for building layouts, B1, B2, B3
66
3.4.3 Layout C1, C2, and C3
The change in the first fundamental period for layouts C1, C2, and C3 with 10,
20, 30, 40 and 50 stories is plotted in Figure 3.28.
Figure 3.28 includes the periods resulting from the ASCE 7-10, TSC 97 and
the TSC 07, and provides a comparison to the FE analyses’ results. The layout C3 has
a higher in-plan aspect ratio compared to the layouts C1 and C2. For all sets of floors,
the differences in the first periods from the three layouts are considerably small.
However, it is important to note that the largest period for a ten story case is observed
for layout C1 while the smallest one for fifty story case is observed for the same layout.
This reverse change in period is a direct result of in-plan aspect ratio. This ratio, is the
smallest for C1. Therefore, as the number of floors increase, the slenderness effect
become more dominant in increasing the period.
In a ten story case, the first period for C1, which has the smallest aspect ratio
of 1.33 is calculated 0.757 second according to the FE analyses. The same period for
C3, which has the largest aspect ratio of 2.67 is calculated 0.624 second. Hence, as the
aspect ratio increases, the period decreases due to the less prominent effect of
slenderness.
In order understand the effectiveness of the code associated periods, building
layout with largest periods are decided to be investigated. Therefore, for this purpose
layout C3 is selected.
The TSC 97 overestimates the first fundamental period of layout C3 with ten
story case by 8%. This trend get reversed for cases over 10 stories since the code
intentionally underestimates the periods for medium to high rise buildings. Therefore,
it is clear that the TSC 97 provides a conservative approach for buildings.
The ASCE 7-10 estimates the first fundamental period of layout C3 with ten
story as 0.74 second. Therefore, it overestimates the first period by 19% when it is
compared to the FE results. The same code, however, underestimates the first period
of the same layout with fifty story case by 44%. Therefore, it can be concluded that
the code associated periods produce a conservative results for medium to high rise
buildings.
According to the TSC 07, the first fundamental period of layout C3 with ten
story case is 1.0 second, and the code overestimates the first period by 60%. For a 50
67
story building, this code again overestimates the period by approximately 12%. It is,
therefore, important to state that the TSC 07 equation provides unsafe design forces.
Figures 3.29 and 3.30 provide the second and third period comparisons. For
layouts C1, C2 and C3 with 10, 20, 30, 40 and 50 stories, the difference in periods for
each case is not significant, and it can be concluded that the aspect ratio does not have
any significant effect on the second or third periods.
68
69
4.5
4
3.5
T2, sec
3
2.5
2
C1(48*36m)
1.5
C2(48*24m)
C3(48*18m)
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.29 Second period versus number of floors for building layouts, C1, C2, C3
3.5
3
2.5
T3, sec
2
C1(48*36m)
1.5
C2(48*24m)
C3(48*18m)
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.30 Third period versus number of floors for building layouts, C1, C2, C3
70
3.4.4 Layouts D1, D2, and D3
Figure 3.31 shows the change in the first fundamental period for layouts D1,
D2, and D3 with 10, 20, 30, 40 and 50 stories.
As for the other layouts, the periods from the ASCE 7-10, TSC 97 and the TSC
07 are also included in this figure to be able to compare the FE analyses results to the
code associated ones.
When compared to the TSC 07 and ASCE 7-10, the TSC 97, provides the most
conservative result. The layout D3 is selected as a reference layout since it has the
largest fundamental period beyond 30 story case. As illustrated in Figure 3.31, for a
ten story building, the TSC 97 underestimates the first fundamental period for D3 by
5%. The same code underestimates the period for D3 with 50 story by 53%. This
drastic change in period estimation is a result of the safety measures used in the code
associated equations.
The layout D3 is also used to compare to the ASCE 7-10 equations, the first
fundamental period of layout D3 with ten story is 0.74 second, the code overestimates
the first period by 5% when compared to the FE results. The same code underestimates
the first period with fifty story by 47%. This change, again, is a result of safety
measures included in the code derived equations. This code, however, provides safe
results for all layouts with all sets of floor levels. The same conclusion is valid for the
other two layouts, D1 and D2.
The first fundamental period of layout D3 with ten story building according to
TSC 07 is calculated 1.0 second. The TSC 07 code overestimates the first period by
42%. This trend, however, gets reversed when a fifty story building is considered. In
a fifty story building, the code overestimates the first period by 4%. Therefore, for the
layout D3, up to 40 stories, the TSC 07 provides a non-conservative approach by
producing less design forces than those from the FE analyses. The same observation
is also valid for the other two layouts D1 and D2.
Figures 3.32 and 3.33 illustrate the variation in the second and third periods for
the layouts D1, D2 and D3 with 10, 20, 30, 40 and 50 stories. The difference in periods
for each set of floor case is not significant implying that the aspect ratio does not have
any effect on the second period. However, the third period for layout D2 decreases due
to the relative increase in the size of the shear walls located at the center of the building.
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72
4.5
4
3.5
T2, sec
3
2.5
D1(48*36m)
2
D2(48*24m)
D3(48*18m)
1.5
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.32 Second period versus number of floors for building layouts, D1, D2, D3
4
3.5
3
T3, sec
2.5
D1(48*36m)
2
D2(48*24m)
1.5
D3(48*18m)
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.33 Third period versus number of floors for building layouts, D1, D2, D3
73
3.4.5 Layouts E1, E2, and E3
In order to understand the significance of framing type on the fundamental
period, three different framing types are selected in this study. In the first framing type,
the layout E1 is assumed to have all moment frames with columns only. In the second
layout, E2, the columns are all replaced by shear walls. In the third and final layout
type, E3, the vertical structural members are assumed to be replaced by the
combination of columns and shear walls. The first period is calculated by using the
equations outlined in the ASCE 7-10, TSC 97, and TSC 07 codes. The discussion of
the results is provided in the following sections:
3.4.5.1 Layout E1
The change in the first fundamental period for layout E1 (columns only) with
10, 20, 30, 40 and 50 stories is provided along with the code associated limits in Figure
3.34.
When compared to the TSC 07 and ASCE 7-10, the TSC 97 provides the most
conservative results. For a ten story building, the TSC 97 underestimates the first
fundamental period for E1 by 15%. While this percentage increases to 36% for a fifty
story building since the building’s lateral resistance gets decreased as the number of
floors increases while this phenomenon is ignored in the code associated equations due
to the safety measures. Therefore, it can be concluded that the TSC 97 provides a
conservative approach specifically for taller buildings in estimating the fundamental
period.
The ASCE 7-10 underestimates the first fundamental period of layout E1 with
ten story by 10% when compared to the FE results. This difference in percentage
increases to 14% for the same layout with a fifty story building due to the similar
reason stated for the same layout in evaluating the TSC 97 equations. Therefore, the
code associated periods demonstrate a fairly good correlation when compared to the
FE results.
The first fundamental period of layout E1 with ten story building according to
the TSC 07 is calculated 1.0 second. Considering the fact that this period from the FE
analysis is 1.113 seconds, the code underestimates this period by 10%. For the 50 story
building, the same code and the FE analysis produce almost the same results. In general
74
it is safe to say that, for layout E1 the results from the TSC 07’ match reasonably well
with the ones from the FE results.
75
76
3.4.5.2 Layouts E2 and E3
Figure 3.35 illustrates the change in the first fundamental period for layouts E2
and E3 with 10, 20, 30, 40 and 50 stories.
As for the other layouts, the periods from the ASCE 7-10, TSC 97 and the TSC
07 are also included in this figure to be able to compare the results of the FE analyses
to the code associated ones.
According to the results, it is clear that for low rise buildings, the differences
in the first period between E2 and E3 are considerably small. However, as the number
of floors increases, the differences become more prominent.
For a ten story building, the first period for E2 (shear walls only) according to
the FE results is 0.699 seconds, while the same period for E3 (with columns and shear
walls) is 0.52 second. Therefore, the ratio of the first period of E2 to E3 for a ten story
building becomes 1.3. The same ratio, however, increases to 1.5 for a fifty story
building since layout E3 becomes more susceptible to lateral stiffness due to its
increasing slenderness effect.
The period equation from the TSC 97, provides a conservative result compared
to the FE analyses. For a ten story building, the TSC 97 underestimates the first
fundamental period for E2 by 4%. While this differences in period increases to 52%
for a fifty story building. This significant increase in period comparison is due to the
fact that the buildings’ lateral stiffness plays a significant role as the number of floors
increases. The increase in the number of floors causes a slender type of buildings while
this phenomenon is again ignored in the code equations due to the safety reasons
Therefore, it is clear that the TSC 97 provides a conservative approach specifically for
taller buildings in estimating the fundamental period.
The ASCE 7-10 overestimates the first fundamental period of layout E2 with
ten story by 6% compared to the FE results. This trend gets reversed for a fifty story
building, since the same code underestimates the FE results by 48%. This change, is a
result of safety measures included in the code derived equations. Therefore, the code
provides a conservative approach in estimating the fundamental period.
The first fundamental period of layout E2 with ten story building according to
the TSC 07 is calculated 1.0 second. Considering the fact that this period from the FE
analysis is 0.699 seconds, the code overestimates the period by 43%. The code
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therefore, provides unsafe results with all sets of floor levels, the same conclusion is
also valid for layout E3.
Figures 3.36 and 3.37 provide the change in the second and third periods. In
layout E1 (columns only), it is clear that the columns are not providing adequate lateral
stiffness when compared to the two other layouts, E2 and E3. Therefore, the layout E1
has larger second and third periods than those for the other two layouts.
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79
5
4.5
4
3.5
T2, sec
3
E1
2.5
E2
2
E3
1.5
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.36 Second period versus number of floors for building layouts, E1, E2, E3
5
4.5
4
3.5
T3, sec
3
E1
2.5
E2
2
E3
1.5
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.37 Third period versus number of floors for building layouts, E1, E2, E3
80
3.4.6 Layouts F1, F2, and F3
In this parametric study, three main framing systems are selected using a Lshaped layout. In the first framing type, the layout F1 is assumed to have all moment
frames with columns only. In the second type, F2, the columns in layout F1 are all
replaced by shear walls. In the third and final framing type, F3, all the vertical
structural members are assumed to be replaced by the combination of columns and
shear walls. The equations outlined in the TSC 97, TSC 07, and ASCE 7-10 codes are
conducted for each framing type and their effects are discussed in the following results:
3.4.6.1 Layout F1
Figure 3.38 illustrates the variation of the first fundamental period for layout,
F1 with 10, 20, 30, 40, and 50 stories.
In Figure 3.38, the period values obtained from the TSC 97, ASCE 7-10, and
the TSC 07 are included in the same figure in order to compare the FE analyses’ results
to the code associated ones.
The first periods for F1 (the layout with columns only) according to the FE
analyses, are obtained 1.134 seconds and 4.946 seconds for ten and fifty story
buildings respectively.
For the ten story building, the TSC 97 underestimates the first fundamental
period for the layout F1 by 17%. This underestimation becomes more prominent for
the fifty story building since the ratio 17% increases to 36% due to the fact that as the
number of floor increases the lateral stiffness of the overall building decreases.
Therefore, it is clear that the TSC 97 provides a conservative approach specifically for
taller buildings with columns only in estimating the fundamental period.
The ASCE 7-10, similar to the trend for the TSC 97, underestimates the first
fundamental period for the layout F1 with ten story by 11%. This percentage slightly
increases to 14% for the fifty story building. It is safe to say that, the period values
from the ASCE 7-10 provides a good correlation compared to those from the FE
analyses’ results.
The period evaluations provided above for the TSC 97 and ASCE 7-10 will be
discussed for the TSC 07, as well. The first fundamental period for the layout F1 with
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ten story building according to the TSC 07 is calculated 1.0 second. The code
underestimates the first period by 10% when it is compared to the FE analyses. This
percentage for the 50 story building significantly decreases to a point when the code
and the FE results produce almost the same results. Therefore, it can be concluded that
the TSC 07 generates fairly reasonable numbers compared to the analytical studies.
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83
3.4.6.2 Layouts F2 and F3
Figure 3.39 illustrates the variation of the first fundamental period for the
layouts F2, and F3 with 10, 20, 30, 40, and 50 stories.
In Figure 3.39, the period values obtained from the ASCE 7-10, TSC 97 and
the TSC 07 are together to be able to compare the FE analyses’ results to the code
associated ones. Out of two layouts (F2 and F3), the F2 produces the largest periods,
and therefore, will be studied as a reference layout.
Based on the figure, for layout F2, it is clear that for low-rise buildings the
period difference between F2 and F3 is considerably small. However, as the number
of floors increases, the difference becomes more and more prominent.
In a fifty story building case, the first period for F2 (with shear walls only)
according to the FE analyses, is 4.882 seconds, while the same period for F3 is 4.190
seconds. The period for layout F3 is less than the period for layout F2 since the overall
lateral stiffness of F3 is higher than the one for F2 due to the presence of shear walls
located at the corners.
For a ten story building, the TSC 97 estimates the first fundamental period for
F2 almost equal to the one for the FE analysis. However, this trend changes in
evaluating the fifty story building. In a fifty story building case the code
underestimates the period by 54%. Due to the fact that the lateral stiffness in the global
x direction as the number of floors increase becomes more susceptible to deformations.
Therefore, it can be concluded that the TSC 97 provides a conservative approach
specifically for taller buildings in estimating the fundamental period.
The ASCE 7-10, as opposed to the one for the TSC 97, overestimates the first
fundamental period for the same layout with ten story by 8%. However, this trend gets
reversed as the number of floors increases due to the safety measures existing in the
code.
In fact for the fifty story building, the code underestimates the FE results by
49%. Therefore, the periods from the ASCE 7-10 also provide a conservative approach
compared to the results from the FE analyses. This conclusion is also valid for the
layout F3.
84
A comparison similar to the TSC 97 and ASCE 7-10 will also be discussed
here. The first period for the layout F2 with ten story case according to the TSC 07 is
calculated from the FE analysis, 1.0 second. Compared to the period of 0.68 the code
underestimates the first period by 47%. This percentage for the 50 story building,
however, decreases to 3% and there is no specific engineering reason behind this
phenomenon. However, for all levels, code overestimates the fundamental periods for
layout F2. The same conclusion is also valid for layout F3.
The changes in the second and third periods for layouts F1, F2, and F3 are
plotted in Figures 3.40 and 3.41. For the layout F1 (columns only) it is clear that the
columns are not providing adequate stiffness when compared to the layouts for F2 and
F3 with combination of shear walls and column. Therefore, the layout F1 for all sets
of floors produce larger second and third periods than those for the other two layouts.
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86
5
4.5
4
3.5
T2, sec
3
F1
2.5
F2
2
F3
1.5
1
0.5
0
0
10
20
30
40
50
60
No. of fllors
Figure 3.40 Second period versus number of floors for building layouts, F1, F2, F3
4.5
4
3.5
T3, sec
3
2.5
F1
2
F2
F3
1.5
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.41 Third period versus number of floors for building layouts, F1, F2, F3
87
3.4.7 Layouts G1, G2, and G3
As in-depth discussions are provided for the layouts F1, F2, and F3 in the
previous section. As described there, three framing types are also selected for the
layouts G1, G2, and G3. In the first framing type, the layout G1 is assumed to have all
moment frames with columns only. In the second type, the columns are all replaced
by the shear walls. Finally, in the third and last framing type, the vertical structural
members are assumed to be replaced by the combination of the columns and shear
walls. Below, a detailed discussion of the period calculation are provided for the
layouts G1, G2, and G3 including the code associated ones.
3.4.7.1 Layout G1
The change in the first fundamental period for the layout G1 with 10, 20, 30,
40 and 50 stories is plotted in Figure 3.42.
The periods resulting from the ASCE 7-10, TSC 97 and the TSC 07 are also
included in the same figure along with the FE analyses’ results.
The equation in the TSC 97 underestimates the first fundamental period for G1
with ten story case by approximately 17%. This percentage increases to 35% for the
fifty story building case, since the lateral stiffness of the layout as the number of floors
increases, decreases. Therefore, it can be concluded that the TSC 97 provides a
conservative approach specifically for taller buildings.
As it is observed in the TSC 97 code, the ASCE 7-10 also underestimates the
first period for the same layout G1 by 12%. However, in a fifty story building case,
both the code and the FE produces almost the same results. The explanation behind
this behavior can be attributed to the fact that the code provides reasonable periods
specifically for buildings around fifty story. Therefore, the code associated periods
demonstrate fairly good correlation compare to the FE analyses’ results.
The period evaluations provided above for the TSC 97 and ASCE 7-10 is
discussed below for the TSC 07, as well.
The first period of layout G1 with ten story case is calculated 1.0 second
according to the TSC 07. Compared to the first period of 1.127 seconds from the FE
analyses, the code underestimates the first period by 11%. This gap between the code
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and the FE, however, decreases as the number of floors increases. In fact, in a fifty
story building case, the two periods from these two sources become almost the same.
As a result, in this layout, it can be concluded that the TSC 07 provides moderately
good results.
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90
3.4.7.2 Layouts G2 and G3
The change in the first fundamental period for the layouts G2 and G3 with 10,
20, 30, 40 and 50 stories is plotted as illustrated in Figure 3.43.
The periods resulting from the equations in the ASCE 7-10, TSC 97 and the
TSC 07 are also included in the same figure. For low-rise buildings, the difference in
the first period between G2 and G3 is relatively small. However, as the number of
floors increases, this difference becomes more and more prominent. Below you will
find the detailed comparison between the code associated periods and the FE analysis.
The TSC 97 slightly underestimates the first fundamental period for G2 with
ten story building by 1%. This percentage increases to 54% for the fifty story building
case. This increase in percentage indicates that the lateral stiffness becomes less
effective in the global x direction as the number of floors increase. Therefore, it can
be concluded that the TSC 97 provides a conservative approach specifically for taller
buildings resulting an over estimation for the seismic design forces. The same
conclusion is also valid for layout G3.
As opposed to the observation made in the TSC 97 case, the ASCE 7-10
overestimates the first period for layout G2 by 7%. In a fifty story building case, this
trend changes and the code underestimates the FE results by 50%. This significant
increase in percentage as stated for the TSC 97 case indicates that the lateral stiffness
becomes extremely less effective in the global x direction as the number of floors
increase. Therefore, it can be concluded that the code provides a conservative approach
in determining the first period. The same conclusion is also valid for the other layout
G3.
A comparison similar to the TSC 97 and ASCE 7-10 is also discussed here.
The first period of layout G2 with ten story building is calculated 1.0 second according
to the equations in the TSC 07. Compared to the 0.679 second from the FE analyses,
the code overestimates the first period by 47%. This percentage for the 50 story
building case, however, decreases to 2% and as it explained for the layout F2, there is
no specific engineering reason behind this phenomenon. However, this code
overestimates the fundamental periods for layout G2 producing unsafe design forces.
The same conclusion can be drawn for G3 as well.
91
Figures 3.44 and 3.45 represent the second and third periods. As illustrated in
the figure, the layout G1 produces considerably higher periods compared to those for
the layouts G2 and G3. This observation is due to the fact that for the layout
G1(columns only), clearly do not provide adequate stiffness when compared to those
for the layouts G2 and G3.
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93
5
4.5
4
3.5
T2, sec
3
G1
2.5
G2
2
G3
1.5
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.44 Second period versus number of floors for building layouts, G1, G2, G3
4.5
4
T3, sec
3.5
3
2.5
G1
2
G2
1.5
G3
1
0.5
0
0
10
20
30
40
50
60
No. of floors
Figure 3.45 Third period versus number of floors for building layouts, G1, G2, G3
94
3.4.8 Layouts A, B, C, and D
In this section the layouts from A1, B1, C1, D1 and A2, B2, C2, D2 and A3,
B3, C3, D3 are decided to be compared for the first fundamental period in order to
understand the importance of framing type. Below the detail information about the
three comparisons.
3.4.8.1 Layouts A1, B1, C1, and D1
Figure 3.46 shows the fundamental period versus number of the floors for
building A1 (with columns, Figure 3.1), B1 (with shear walls, Figure 3.4), C1 (with
columns and shear walls, Figure 3.7), D1 (with shear walls at the center Figure 3.10).
As illustrated in Figure 3.46, the first fundamental period of layout B1 is much
larger than the period of layouts A1, C1 and D1. The gaps between the periods of B1
and A1, B1and C1, and B1 and D1 are much larger as the number of floors increases.
The larger first period for layout B1 is a direct result of shear wall orientation causing
a lot less stiffness in the x direction.
When layouts A1, C1 and D1 are compared, it is seen that the periods for layout
A1 are larger than those for layouts C1 and D1. The reason for this behavior can be
explained by evaluating the stiffnesses of layouts A, C and D in the x and y directions.
The layout A is the one with all columns and the other two layouts are the ones with
the combinations of columns and shear walls. Since the overall stiffness of layout A is
less than those of layout C and D, the first periods from layout B1 are larger.
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3.4.8.2 Layouts A2, B2, C2, and D2
Figure 3.47 represents the fundamental period versus number of floors for
layouts A2 (with columns, Figure 3.2), B2 (with shear walls, Figure 3.5), C2 (with
columns and shear walls, Figure 3.8), and D2 (with shear walls at the center Figure
3.11). It is important to compare these layouts since they all have the same aspect ratio
of 2. By doing so, it is intended to understand the effect of framing on the overall
behavior of buildings.
In this figure, it is clear that the fundamental period of layout B2 is much larger
than the period of layouts A2, C2 and D2. The differences between the periods of B2
and A2, B2 and C2, and B2 and D2 increase as the number of floors increases. The
largest first period for a fifty story case is obtained for layout B2.
The first period comparison among A2, C2 and D2 demonstrates that the layout
A2 produces larger ones than those for the layouts C2 and D2 for all floor levels. This
again is a result of less lateral stiffness that the layout A2 has compared to the layouts
C2 and D2 since the later layouts have the combination of shear walls and columns.
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3.4.8.3 Layouts A3, B3, C3, and D3
Figure 3.48 illustrates the fundamental period versus the number of the floors
for layouts A3 (with columns, Figure 3.3), B3 (with shear walls, Figure 3.6), C3 (with
columns and shear walls, Figure 3.9), and D3 (with shear walls at the center Figure
3.12). These four layouts all have the same aspect ratio of 2.67.
In this figure, the fundamental period of layout B3 is larger than the periods of
layouts A3, D3 and C3. The differences between the periods of B3 and A3, B3 and
D3, and B3 and C3 are become more moderate when the number of floors increases.
The larger first period for layout B3 is due to the shear wall orientation since it causes
a lot less stiffness in the x direction when it is compared to the other layouts.
Excluding the layout B3, when the other three layouts are compared (A3, C3,
and D3), the periods for layout A3 are larger than those for the layouts D3 and C3.
This phenomenon is a direct result of less lateral stiffness that the layout A3 possess.
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100
3.4.9 Mode Shapes
In this section, the first three mode shapes from each layout will be studied and
discussed. The dominant direction from each mode shape will also be presented to
understand the effect of lateral resisting system. By doing so, translational or rotational
modes will be evaluated. A mode shape of any building is the deformed shape
associated with its natural period. The vibration of a building at its first fundamental
period is called the first mode shape, and is the most important mode shape since the
majority of the buildings mass is used in this case.
The first three modes for a regular building occurs in the translational (x and y
directions) and rotational modes. A regular building can be described in terms of the
orientation of its lateral resisting system. If this system has symmetry either along the
x and/or y directions, then the first dominant mode shape becomes pure translational
not rotational.
In this study, this phenomenon is illustrated in Figures 3.49 through 3.60 for
the layouts A, B, C, and D. However, if the lateral resisting system causes asymmetry,
then not the translational modes but rather the rotational modes become more critical.
Figures 3.61 through 3.69 illustrate such phenomenon for the layouts E, F, and G.
Although, the overall response of a building is the sum of the responses of all
of its modes, in this study only three mode shapes with its associated periods are
considered due to the fact that these first three periods play a major role in determining
the design seismic forces. Figures 3.49 through 3.69 illustrate the first mode shapes
for all the layouts.
101
Non-deformed
Figure 3.49 Mode shapes for layout A1
102
Non-deformed
Figure 3.50 Mode shapes for layout A2
103
Non-deformed
Figure 3.51 Mode shapes for layout A3
104
Non-deformed
Figure 3.52 Mode shapes for layout B1
105
Non-deformed
Figure 3.53 Mode shapes for layout B2
106
Non-deformed
Figure 3.54 Mode shapes for layout B3
107
Non-deformed
Figure 3.55 Mode shapes for layout C1
108
Non-deformed
Figure 3.56 Mode shapes for layout C2
109
Non-deformed
Figure 3.57 Mode shapes for layout C3
110
Non-deformed
Figure 3.58 Mode shapes for layout D1
111
Non-deformed
Figure 3.59 Mode shapes for layout D2
112
Non-deformed
Figure 3.60 Mode shapes for layout D3
113
Non-deformed
(*) Combination of translation and rotation
Figure 3.61 Mode shapes for layout E1
114
Non-deformed
(*) Combination of translation and rotation
Figure 3.62 Mode shapes for layout E2
115
Non-deformed
(*) Combination of translation and rotation
Figure 3.63 Mode shapes for layout E3
116
Non-deformed
(*) Combination of translation and rotation
Figure 3.64 Mode shapes for layout F1
117
Non-deformed
(*) Combination of translation and rotation
Figure 3.65 Mode shapes for layout F2
118
Non-deformed
(*) Combination of translation and rotation
Figure 3.66 Mode shapes for layout F3
119
Non-deformed
(*) Combination of translation and rotation
Figure 3.67 Mode shapes for layout G1
120
Non-deformed
(*) Combination of translation and rotation
Figure 3.68 Mode shapes for layout G2
121
Non-deformed
(*) Combination of translation and rotation
Figure 3.69 Mode shapes for layout G3
122
3.4.10 Lateral Deflections
In evaluating the layouts studied in this thesis, the last parameter to be
discussed is called lateral deflections. It is important to determine the lateral
deflections resulting from the seismic forces. Since the deflections have to meet certain
comfort levels as defined in individual building specifications and provisions. This
parameter clearly defines how good or bad the lateral resisting system is since the
system has to satisfy the maximum allowable deflections.
In this section, the lateral deflections will be investigated for both x and y
directions.
Tables 3.23 and 3.24 list the magnitudes of the lateral deflections at the top
floor due to the seismic loads applied as response spectrum.
The fifty floor case is selected to be the most critical one in evaluating the
significance of the parameter called lateral deflections. Therefore, in these tables, the
lateral deflections at the top floor (at fiftieth floor level) are listed.
Below, you will find a discussion about this topic in evaluating the
effectiveness of each layout.
3.4.10.1 X Direction
Table 3.23 lists the lateral deflections at the fiftieth floor level in both x and y
directions for a total of 21 layouts. The ratios between the total height of the building
versus top deflection is also provided in the same table to evaluate the effectiveness of
each layout. This ratio is selected intentionally since it is commonly used in practice.
The seismic force in this layout is a response spectrum force only in the x
direction. Therefore, the deflection values in the y direction are considerably small
when they are compared to their counterparts in the x direction. However, this
phenomenon is not valid for irregular layouts as in the cases of layouts E, F, and G.
According to the table, the largest lateral deflection in the x direction (in the
direction of seismic load) is obtained for the layout B2. The layout B2 has the smallest
lateral stiffness in the x direction and, this causes maximum deflection.
Similarly, the smallest deflection is obtained for the layout E3. Since this layout
has the largest lateral stiffness in the x direction. The ratio of the largest deflection to
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the smallest deflection is approximately 2.5. This large ratio clearly emphasizes the
significance of the shear walls located all around the corners of the building. It is
therefore, important to note that, if architecturally possible, the shear walls should be
located near the corners of a building. As expected, the layouts with the combination
of columns and shear walls provide more stiffness when they are compared to the
layouts with all columns. For example, the deflection for the layout D3 is 10.3 cm
whereas the deflection for the layout A3 12.2 cm.
In all layouts, the smallest ratio of total height to lateral deflection is obtained
for the layout B2 as 812. This ratio is acceptable assuming the fact the maximum
allowable deflection ratio for tall buildings is around 500.
Figure 3.70 illustrates the top deflection in the x direction due to the seismic
load applied in the same direction.
Figure 3.71 presents the variation of deflection ratio versus layout number. As
stated in the previous paragraphs, the numbers near 500 are all acceptable. However,
it is a common practice to maintain this ratio near 1,000 in designing tall buildings. If
the ratios are larger than 1,000, then it is recommended to decrease the overall stiffness
of the lateral resisting members in the direction of the seismic loading by reducing
their dimensions.
124
Table 3.23 Lateral deflections due to seismic loads in x-direction (RX)
Layout
Numbers
Layout
Type
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
A1
A2
A3
B1
B2
B3
C1
C2
C3
D1
D2
D3
E1
E2
E3
F1
F2
F3
G1
G2
G3
Lateral
Deflection
x-direction(2)
(cm)
12.8
12.5
12.2
18.3
19.7
17.5
11.4
10.9
10.5
11.7
11.0
10.3
12.9
13.4
8.0
16.7
10.1
11.1
13.1
11.3
9.2
Lateral
𝐓𝐨𝐭𝐚𝐥 𝐇𝐞𝐢𝐠𝐡𝐭 (𝟏)
Deflection
y-direction(2) 𝐋𝐚𝐭𝐞𝐫𝐚𝐥 𝐝𝐞𝐟𝐥𝐞𝐜𝐭𝐢𝐨𝐧 𝐱
(cm)
1250
1*10−5
−5
1280
4.6*10
−5
1312
7.2*10
0.03
874
812
9.366*10−8
−6
914
5*10
−9
1404
1.65*10
1468
1*10−6
−5
1524
1.6*10
−8
1368
2.063*10
1455
6.62*10−8
−7
1553
2.582*10
1.6
1240
1194
7*10−6
−10
2000
4.798*10
-0.16
958
1.4
1584
4.3
1441
6.6
1221
9.4
1416
4.5
1739
(1) The total height of the building is 160 meters.
(2) Deflections are at the fiftieth floor level.
125
126
127
3.4.10.2 Y Direction
Table 3.24 lists the lateral deflections at the fiftieth floor level in both x and y
directions for a total of 21 layouts in order to evaluate the effectiveness of each layout,
the ratio between the total height of the building versus top deflection is also provided
in the same table. This ratio is selected intentionally since it is commonly used in
practice.
The seismic forces in this layout is a response spectrum forces that are applied
only in the y direction. Therefore, the deflection values in the x direction are
considerably small when they are compared to their counterparts in the y direction.
However, the same observation is not valid for layouts E, F, and G, since they have
irregular layouts.
According to Table 3.24, the largest lateral deflection in the direction of
seismic load y direction is obtained for the layout A3 since this layout has the smallest
lateral stiffness in the y direction compared to the others.
The smallest deflection is obtained 8.0 cm for the layout E2 due to the fact that
this layout has the largest lateral stiffness in the y direction. The ratio of the largest
deflection to the smallest deflection is calculated approximately 2.125. This large ratio
again emphasizes the significance of the shear walls located all around the corners of
the building for layout E2. As mentioned previously for the deflection in the x
direction, the layouts with the combination of columns and shear walls provide more
stiffness when they are compared to the layouts with all columns.
In all layouts, the smallest ratio of total height to lateral deflection is obtained
for the layout A3 as 941. This ratio is acceptable when evaluated with respect to the
common practice follows in the private industry.
The top deflection in the y direction is illustrated in Figure 3.72 due to the
seismic load applied in the same direction.
Figure 3.73 shows the variation of deflection ratio versus layout numbers. As
stated in the previous paragraphs, the numbers close 500 are all acceptable. However,
it is a common practice to maintain this ratio near 1,000 in designing tall buildings. If
the ratios are larger than 1,000, then the building is stiff and it is recommended to
decrease the overall stiffness of the lateral resisting members in the direction of the
seismic loading by reducing their dimensions.
128
Table 3.24 Lateral deflections due to seismic loads in y-direction (RY)
Layout
Numbers
Layout
Type
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
A1
A2
A3
B1
B2
B3
C1
C2
C3
D1
D2
D3
E1
E2
E3
F1
F2
F3
G1
G2
G3
Lateral
Deflection
x-direction(2)
(cm)
6*10−6
1*10−5
7*10−6
0.7
1.1*10−5
0.03
5.14*10−10
2*10−6
2.392*10−10
1.6*10−5
1.1*10−5
9*10−6
0.5
0.03
3.256*10−10
5.5
5.6
4.3
8*10−6
0.96
0.04
Lateral
Deflection
y-direction(2)
(cm)
13.7
15.2
17.0
12.8
13.9
13.4
12.2
13.1
13.8
10.5
11.3
15.3
15.2
8.0
9.1
12.5
10.2
10.6
14.6
11.0
11.2
(1) The total height of the building is 160 meters.
(2) Deflections are at the fiftieth floor level.
129
𝐓𝐨𝐭𝐚𝐥 𝐇𝐞𝐢𝐠𝐡𝐭 (𝟏)
𝐋𝐚𝐭𝐞𝐫𝐚𝐥 𝐝𝐞𝐟𝐥𝐞𝐜𝐭𝐢𝐨𝐧 𝐲
1168
1053
941
1250
1151
1194
1312
1221
1159
1524
1416
1046
1053
2000
1758
1280
1569
1509
1096
1455
1435
130
131
CHAPTER 4
CONCLUSIONS AND RECOMMENDATIONS
4.1 Introduction
In this study, a total of twenty one layouts are considered in evaluating the
fundamental period of the reinforced concrete buildings with different structural
configurations. A detailed parametric study is conducted for this purpose by taking the
number of floors and in-plan aspect ratio into account. Therefore, the twenty one
unique layout is extended to a total of 105 layout cases that are modeled using a
commercially available software, ETABS. The aim of these parametric studies is to
understand the dynamic behavior of buildings with different configurations. For this
purpose, the first three modes and their associated mode shapes are investigated. The
impact of lateral resisting systems are studied by evaluating the lateral deflections in
the two principal directions. Based on the analyses’ results, the best layout that will
provide the most effective lateral strength is suggested. Also, the existing equations in
the building codes are carefully evaluated by comparing and contrasting them to the
analyses’ results. Based on this evaluation process, some recommendations are
proposed.
4.2 Conclusions
The periods and the lateral deflections from the 105 FE models are evaluated.
According to the results from the FE analyses and the ones derived from the equations
in the Turkish and American building codes, it is confirmed that the period estimations
from the building codes are either conservative or unconservative depending on the
complexity of the layout. Therefore, it is concluded that the code associated equations
depending on the layout might be inadequate. In all layouts, there are differences
between the dynamic analyses’ results and the code estimated periods due to the
132
omittance of torsional disturbance and the effect of various framing types. It is deduced
from the FE results that the effect of various in-plan aspect ratios do not necessarily
have a significant impact on the first three periods and the associated mode shapes. In
other words, the in-plan aspect ratio might not play a significant role on the periods.
However, this conclusion is limited to the approach followed in this study when the
length or the thickness of the shear walls are not subjected to any change even if the
building dimensions are reduced.
It is also concluded that as the aspect ratio increases, the buildings’ periods
increase. Unlike the proportionality that exist between the aspect ratios and the
building periods, the periods increase as the number of floors increase. Compared to
the impact on the building periods due to the decrease in the aspect ratio, the increase
in the number of floors will have more prominent effects.
The results of the dynamic analyses of the buildings with different structural
configurations demonstrate that, for many cases, the TSC 97 equations result in smaller
periods than those obtained from the FE analyses specifically for the high-rise
buildings (i.e., 25, 30, 40 and 50 story). The smaller periods resulting from the code
associated equations produce larger forces than those from the FE analyses. These
larger forces might lead to a case where conservative forces have to be considered in
designing buildings members. Unlike the phenomenon observed for the low-rise
buildings (i.e., 25 story or less), the TSC 97 equations overestimate the computed
periods. This overestimation causes less design forces than those that are anticipated
from the FE analyses.
Unlike the inconsistency that exists in the TSC 97 case, the FE results for the
good portion of the cases verify that the TSC 07 produces less design forces than those
that the buildings are actually subjected to. The FE results show that the buildings
whose shear walls are located around the building corners have larger lateral
stiffnesses than those whose walls are located near the core of the layouts. This
observation is expected, but is important to emphasize that the positive impact of the
walls located around the building corners are quite significant.
The results demonstrate that the layouts with columns only provide less lateral
stiffness when compared to the layouts with shear walls only or the combination of
shear walls and columns.
133
As expected, design wise it is preferred to have translational modes followed
by rotational modes in order to prevent the negative effect of torsion on the overall
design of buildings. This phenomenon is observed for the layouts that have
symmetrical lateral resisting system. Unlike the symmetrical lateral resisting system,
if the layout has asymmetrical lateral resisting system, then the dominant mode shape
becomes rotational not translational.
In the ASCE 7-10 code, the approximate fundamental period alternatively can
be calculated using the 0.1 N equation as stated in item 9.5.5.3.2. The code limits the
use of this equation for the buildings not exceeding 12 stories. This limitation clearly
eliminates the overdesign issue experienced specifically for taller buildings. However,
the same limitation is reversed in the current TSC 07. The item 2.4.7.2 in the TSC 07,
states that the natural period shall not be larger than 0.1 N for buildings with more than
13 floors. This limitation in the TSC 07 code clearly violates the logic behind the
philosophy in the ASCE 7-10. Therefore, as verified in the FE analyses a very
conservative approach is dictated by the TSC 07.
In general the period equations in the TSC 97, 07 and the ASCE 7-10 provide
conservative approach for low to mid rise buildings. The definition for a mid-rise
building is considered to be a building with 20 to 25 floors. For buildings beyond these
floor levels, in this study according to the period calculations, are considered high-rise.
According to the study by Khayyat, Z.K., (2015), the effects of the springs
types supports representing the soil-structure interaction does not have any significant
effect on the fundamental period of the building [26].
Based on the period equations in the building codes studied in this thesis, it is
recognized that the effect of lateral stiffness in plane is ignored. In other words, the
weaker direction in lateral stiffness is not taken into account in estimating the
fundamental period. It is, therefore, important to include this effect into period
calculations.
It is not recommended to design buildings based on their gross moment of
inertias. Therefore, the cracked properties should be used in the analysis and design
phases. The deduction on the moment of inertias can be studied as a future research
topic.
134
There should be two equations in calculating the fundamental periods, one for
the low-to-mid-rise buildings (up to 25 floor levels) and the other one is for the highrise buildings (beyond 25 floor levels).
4.3 Recommendations
The fundamental period of a building is a parameter that describes its dynamic
behavior. This parameter is used to determine the lateral loads resulting from seismic
actions. Therefore, it is rather important to accurately determine the upper limits for
building periods. This limitation varies from building codes to building codes, and is
important to evaluate its accuracy with respect to the FE models. In achieving this
goal, there are some recommendations that need to be taken into account as listed
below:

In designing a building with a layout that has columns only with an in-plan
aspect ratio of 1.33, the ASCE 7-10 produces results that are in good correlation
with the FE analyses results. Therefore, it is recommended to use the ASCE 710 for these types of layouts with an aspect ratio of 1.33. However, the same
code tends to produce more conservative results as the aspect ratio increases.

The three investigated building codes, TSC 97, TSC 07, and ASCE 7-10
provide a conservative design approach when they are used to design the
buildings that have shear walls only. Out of these three building codes, the TSC
07 generates the closest approach since the other two codes overestimate the
design forces. This trend in overestimation of the design forces becomes more
prominent as the aspect ratio increases from 1.33 to 2. Therefore, it is
recommended to use the TSC 07 for the layouts with shear walls only.

According to the FE results, it is observed that the TSC 97 does not accurately
predict the natural periods for the 105 building layouts due to the fact that the
code define period equation does not take the effects of the aspect ratio and
framing type into account. As a result of this omittence, it is recommended to
study the two aforementioned parameters as independent parameters for all
framing types.
135

The TSC 07 produces satisfactory results when compared to the FE results for
buildings low to moderate height (i.e., up to 25 floors). As a result, it is
recommended to use the TSC 07 for buildings low to med-rise.

In designing a building with irregular layout (asymmetrical lateral resisting
system in either of the principal directions), it is recommended to locate the
shear walls around the buildings’ corners since this type of arrangement would
provide better stiffness and would prevent the torsional movement, and the
negative impact of stress concentration.

As expected, the layouts with the combination of columns and shear walls
provide more stiffness when they are compared to the layouts with all columns.
Hence, if additional stiffness or limited deformations are needed, it is better to
have a framing with walls and columns only, specifically in severe seismic
zone area (such as zone 1 in the TSC 07).

The quality of construction varies from region to region in Turkey. It is also
valid to say that depending on the complexity of a project, the quality of works
might vary. In order to reflect this vary idea into the design part, the quality of
construction might be incorporated into the period equation as a new
parameter. The numerical values of the parameter might be selected a 1.00
being the most reliable construction to an arbitrary selected number of 1.2
being the least reliable construction.

Statistical study might be conducted among the professional engineers and the
general contractors estimate the numerical values of the quality of construction.

The effect of varying floor-to-floor height on the period calculation might be
significant one. It is recommended to determine (a) a limitation on this effect
by providing a ratio of the maximum floor height, and (b) number of
occurrences of maximum floor height to the average one.

As discussed in Chapter 3, the in-plane aspect ratio depending on the framing
type might have an adverse effect on the period calculation. Therefore, it is
recommended to include a new parameter to the period equation.

The effects of plan and vertical irregularities on the period calculation should
be studied. A study by Duyar. B. (2015) will investigate this impact for RC.
136
buildings. However, it is recommended to include these effects using additional
parameters in the period calculations [27].
4.4 Suggestions for Future Research
The list given below includes the suggestions for future research:
1. The study in this thesis is limited to the following parameters: (a) the
number of floors, (b) in-plan aspect ratio, and (c) framing type.
However, the impact of the following parameters should also be
considered in determining the fundamental period: (a) effect of
basement floors, (b) soil-structure interaction, (c) different slab types
(waffle slab, two way slab, ribbed slab, composite slab and flat slab),
(d) modulus of elasticity for cracked concrete case, (e) varying floor to
floor height, (f) existence of in-fill walls, (g) different opening sizes and
locations, and (h) plan and vertical irregularities.
2. The effects of buildings with different floor layouts such as trapezoidal,
triangular or elliptical shapes should also be investigated.
3. The material nonlinearity can be considered as an additional parameters
in the FE analyses.
4. Composite structures might be studied as an additional building type
specifically investigating the high-rise buildings.
5. Steel buildings with various lateral resisting systems (such as bracing
types, moment frames, steel shear wall plates) can also be subjected to
future research.
6. As expected, floor layouts might have several openings in varying sizes
and locations. These openings might also affect the behavior of the
diaphragm. These effects can be studied as an additional research topic
in calculating their impact on the periods.
137
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