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STABILITY OF A SIX STOREY STEEL FRAME STRUCTURE
SHAMSHINAR BINTI SALEHUDDIN
A dissertation submitted in partial fulfilment of the
requirements for the award of the degree of
Master of Engineering ( Civil - Structure )
Faculty of Civil Engineering
Universiti Teknologi Malaysia
MAY, 2011
iii
To my beloved husband, family, lecturers and friends
iv
ACKNOWLEDGEMENT
In the process of preparing and completing this report, I was in contact either
directly or indirectly with many people, academicians and wholesaler. They have
contributed towards my understanding and thought.
In particular, I wish to express my greatest appreciation to my supervisor, Assoc.
Prof. Dr. Suhaimi Abu Bakar for his encouragement, guidance, critics, and motivations.
Without his continued support and interest, this report would have been the same as
presented here.
At the same moment, I am grateful to all my family members for their support
and encouragement. My sincere appreciations also to my beloved husband, Mohd Faisal
bin Mohd Azlan and my father in law, Dr. Mohd Azlan bin Yahya who have provided
assistance and useful tips indeed. Finally, special thank dedicated to Universiti Malaysia
Perlis and Ministry of Higher Education for giving opportunity to sponsor my master
and those who directly or indirectly involve in the process of producing this study.
I hope my findings in this study will expand the knowledge in this field and
contribute to all of us in future.
v
ABSTRACT
The world nowadays requires more tall buildings to overcome limited land
space and creating high esthetic value. However, these high rise buildings require high
frame structure stability for safety and design purposes. This research focused on non
linear geometric analysis to be compared to previous studies on linear analysis. The
linear analysis did not consider deformed configuration which can be considered as least
accurate. On top of this, several designers did not incorporate the wind load which could
lead to sway effect to tall buildings. In this study, a six storey 2-D steel frame structure
with twenty four meter height has been selected to be idealized as tall building model.
The model was analyzed by using SAP2000 structural analysis software with the
consideration of geometric non linear effect. At the same time, several factors including
the use of bracing, varying distributed loads on beam’s element and an increased in
column size at bottom part of the building were also applied to study the sway and
stability of the building. In addition, several cases including placing a fully bracing,
bracing at half height of the building and alternate bracing were also studied. This study
showed that a steel frame with the consideration of wind load produce greater sway
value as compared to the steel frame without wind load. The sway prediction by using
linear analysis was found to be less than 4% compared to the sway prediction from non
linear analysis. This indicates that the non linear analysis is vital and significant element
to be adopted for the analysis of tall building. The study also found that the use of
bracing system results in small sway values compared to the frame without bracing
system. As for consideration to costing aspect, the use of alternate bracing provide
better option compared to half bracing in terms of stability of the building. The analysis
results also showed that the adjustment of distributed load at upper part of steel frame
structure able to provide different sway values, creating higher stiffness at lower part of
the building which reduces the sway values and increases the stability of the building.
SAP2000 software is found as reliable tool in evaluating structural analysis especially
when involving non linear analysis.
vi
ABSTRAK
Pada masa sekarang, dunia memerlukan lebih bangunan tinggi untuk mengatasi
masalah kekurangan ruang tanah dan untuk mencipta nilai estetika yang tinggi.
Walaubagaimanapun, bangunan tinggi ini memerlukan lebih kestabilan dalam struktur
kerangka untuk tujuan keselamatan dan rekabentuk. Kajian ini menumpu lebih kepada
analisis geometrik tak linear kerana kajian sebelumnya lebih kepada analisis linear.
Analisis linear tidak mengambil kira perubahan bentuk yang boleh di anggap kurang
tepat. Selain daripada itu, ramai jurutera kadang kala tidak mengendahkan beban angin
yang juga boleh menyumbang kesan huyung kepada bangunan tinggi. Dalam kajian
ini,enam tingkat struktur kerangka keluli 2-D setinggi dua puluh empat meter dipilih
sebagai bahan kajian untuk bangunan tinggi. Model ini telah dianalisis menggunakan
perisian SAP2000 dengan mengambil kira analisis geometrik tak linear. Pada masa yang
sama, beberapa pendekatan dilakukan seperti meletak perembat, mempelbagai beban
teragih seragam di atas rasuk dan menambah saiz tiang di bahagian bawah di aplikasi
untuk mengkaji huyung atau kestabilan bangunan. Tambahan lagi, beberapa kes seperti
meletak keseluruhan kerangka dengan perembat, hanya separuh di bahagian atas dan
berselang seli juga dikaji. Jelas menunjukkan bahawa kerangka keluli dengan beban
angin memberi lebih tinggi nilai huyung dari kerangka keluli tanpa beban angin.
Ramalan huyung menggunakan analisis linear didapati kurang melebihi 4% dari ramalan
huyung oleh analisis tak linear. Ini menunjukkan analisis tak linear adalah keperluan
dan penting digunakan untuk menganalisis bangunan tinggi. Sistem kerangka
berperembat memberi nilai huyung yang lebih kecil berbanding sistem kerangka tanpa
berperembat. Dari aspek kos pembinaan, pilihan antara hanya separuh perembat di
bahagian atas dan berselang seli menunjukkan kerangka berselang seli adalah lebih baik
untuk meningkatkan kestabilan bangunan. Keputusan analisis jelas menunjukkan
ubahsuai beban teragih seragam di atas rasuk di bahagian atas bangunan boleh memberi
nilai huyung yang sedikit. Tambahan lagi, meningkatkan kekukuhan bangunan pada
bahagian bawah juga boleh mengurangkan nilai huyung dan meningkatkan kestabilan
bangunan. Perisian SAP2000 didapati adalah alat yang boleh digunakan untuk
menganalisis struktur terutama yang melibatkan analisis non linear.
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
THESIS TITLE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES xi
LIST OF FIGURES xiii
NOTATIONS xvi
CHAPTER 1 INTRODUCTION 1
1.0 Introduction 1
1.1 Statement of Problems 2
1.2 Objectives of the Research 3
1.3 Scope of the Research 3
1.4 Significance of the Research 4
CHAPTER 2 LITERATURE REVIEW 5
2.0 Introduction 5
2.1 Structural Stability 7
2.2 Linear and Non Linear Analysis 8
viii
2.3 Theoretical Formula of Non Linear Analysis 9
2.4 Linear and Non Linear Analysis of Frame
Structure
12
2.5 Brace System 14
2.6 Wind Loading 15
CHAPTER 3 VERIFICATION OF STRUCTURAL
ANALYSIS SOFTWARE SAP2000
18
3.0 Introduction 18
3.1 Manual Calculation Using Mathcad 20
3.2 Analysis of Frame Structure Using
SAP2000
33
CHAPTER 4 LINEAR AND GEOMETRIC NON
LINEAR ANALYSIS OF STEEL
FRAME STRUCTURE
35
3.0 Introduction 35
4.1 The Distributed Load on Beam 35
4.2 Wind calculation using CP3, Chapter V
( Part 2)
39
4.3 Linear and Geometric Non Linear Analysis
Using SAP2000
44
4.4 Cases to be Analyzed Using SAP2000 48
CHAPTER 5 ANALYSIS RESULTS AND
DISCUSSIONS
56
5.0 Introduction 56
5.1 Results for Linear and Geometric Non
Linear Analysis of Steel Frame
56
ix
5.1.1
Case 1 - Linear and Non Linear Analysis of
Steel Frame without Wind Load
57
5.1.2 Case 2 – Linear and Non Linear Analysis of
Steel Frame with Wind Load Consideration
61
5.1.3 Case 2(a) – Non Linear Analysis of Steel
Frame with Maximum Wind Load
Consideration
64
5.1.4 Case 3 – Linear and Non Linear Analysis of
Steel Frame with Fully Bracing
66
5.1.5 Case 4 – Linear and Non Linear Analysis of
Steel Frame with Bracing Placed at Half
Top Side of Building
69
5.1.6 Case 5 – Linear and Non Linear Analysis of
Steel Frame with Alternate Bracing
72
5.1.7 Case 6 – Linear and Non Linear Analysis of
Steel Frame with Increasing of Distributed
Load at Upper Half Portion of the Building
75
5.1.8 Case 7 – Linear and Non Linear Analysis of
Steel Frame with Decreasing of Distributed
Load at Upper Half Portion of the Building
78
5.1.9 Case 8 - Linear and Non Linear Analysis of
Steel Frame with Increasing of Column Size
at Lower Portion of the Building
81
5.2 Discussion of the Results 84
5.2.1 Analysis 1 – Comparison of Wind Effect for
Linear and Non Linear Analysis
84
5.2.2 Analysis 2 – Comparison of Sway
Prediction from Linear and Geometric Non
Linear Analysis
86
x
5.2.3 Analysis 3 - Approach Applied to Study
Sway Effect
87
5.2.4 Analysis 4 - The SAP2000 Software
Checking
92
CHAPTER 6 CONCLUSIONS AND
RECOMMENDATIONS
93
6.0 Introduction 93
6.1 Conclusions 93
6.2 Recommendations 94
REFERENCES 95
xi
LIST OF TABLES
TABLE NO. TITLE PAGE
4.1 Topography factor, S1 39
4.2 Ground roughness, building size and height above ground,
factor S2
40
4.3 Force coefficients Cf for rectangular clad buildings with flat
roofs (acting in the direction of the wind)
42
4.4 Wind calculation result using CP3, Chapter V ( Part 2 ) 44
5.1 Sway for linear and non linear analysis of steel frame
without wind load - Case 1
58
5.2 Sway for linear and non linear analysis of steel frame with
the consideration of wind load - Case 2
61
5.3 Sway for non linear analysis of steel frame with the
maximum consideration of wind load - Case 2(a)
64
5.4 Sway for linear and non linear analysis of steel frame with
fully bracing - Case 3
66
5.5 Sway for linear and non linear analysis of steel frame with
bracing system placed at half of building ( top side ) - Case 4
69
5.6 Sway for linear and non linear analysis of steel frame with
alternate bracing - Case 5
72
5.7 Sway for linear and non linear analysis of steel frame with
increase distributed load at half building ( top side ) - Case 6
75
5.8 Sway for linear and non linear analysis of steel frame with
xii
decrease distributed load at half building ( top side ) - Case 7 78
5.9 Sway for linear and non linear analysis of steel frame by
increasing of column size at lower half portion of the
building - Case 8
81
5.10 Sway value due to wind and no wind effect predicted from
linear analysis
85
5.11 Sway value due to wind and no wind effect predicted from
linear analysis
85
5.12 Sway result of steel frame structure from linear and
geometric non linear analysis prediction ( Case 2 )
86
5.13 Comparison of sway for several methods of bracing system 88
5.14 Higher and lower distributed load on a beam 89
5.15 Comparison of sway due to standard and higher column size 91
xiii
LIST OF FIGURES
FIGURE NO. TITLE PAGE
2.1 Instability of frame structure under horizontal loads 7
2.2 Pictorial representation of bar with second order effect 8
2.3 Load deformation curves of one storey frame 13
2.4 Deformation of a brace 14
2.5 A wind load assume to hit the building 16
3.1 Arrangement of number for calculation at a trial steel frame
structure
19
3.2 A trial steel frame structure illustrate in SAP2000 33
3.3 Result of displacement, U1 at top joint at left hand in unit
millimeter
34
4.1 The plan view of building to be calculated for distributed
load
36
4.2 The frame model to be analyzed 38
4.3 The plan shape of the steel frame structure that hit by the
wind
43
4.4 New model form 45
4.5 Joint restraint 46
4.6 Load Case Data form 47
4.7 Analytical model for Case 1 48
4.8 Analytical model for Case 2 49
xiv
4.9 Analytical model for Case 3 : Steel frame structure with fully
braced
50
4.10 Analytical model for Case 4 : Partially braced steel frame
structure
51
4.11 Analytical model for Case 5 : Steel frame structure with
alternate bracing system
52
4.12 Analytical model for Case 6 : Higher value of distributed
load
53
4.13 Analytical model for Case 7 : Lower value of distributed
load
54
4.14 Analytical model for Case 8 : Higher stiffness of the column
base
55
5.1(a) Sway at different level of steel frame structure without wind
load ( linear analysis )
59
5.1(b) Sway at different level of steel frame structure without wind
load ( non linear analysis )
60
5.2(a) Sway at different level of steel frame structure with wind
load consideration ( linear analysis )
62
5.2(b) Sway at different level of steel frame structure with wind
load consideration ( non linear analysis )
63
5.2(c) Sway at different level of steel frame structure with
maximum wind load consideration ( non linear analysis )
65
5.3(a) Sway at different level of steel frame structure with fully
bracing ( linear analysis )
67
5.3(b) Sway at different level of steel frame structure with fully
bracing ( non linear analysis )
68
5.4(a) Sway at different level of steel frame with half of top side of
the building be placed with bracing system ( linear analysis )
70
5.4(b) Sway at different level of steel frame with half of top side of
the building be placed with bracing system ( non linear
xv
analysis ) 71
5.5(a) Sway at different level of steel frame with alternate bracing
( linear analysis )
73
5.5(b) Sway at different level of steel frame with alternate bracing
( non linear analysis )
74
5.6(a) Sway at different level of steel frame structure with
increasing of applied distributed load acted at upper of the
building ( linear analysis )
76
5.6(b) Sway at different level of steel frame structure with
increasing of applied distributed load acted at upper of the
building ( non linear analysis )
77
5.7(a) Sway at different level of steel frame structure with
decreasing of applied distributed load acted at upper of the
building ( linear analysis )
79
5.7(b) Sway at different level of steel frame structure with
decreasing of applied distributed load acted at upper of the
building ( non linear analysis )
80
5.8(a) Sway at different level of steel frame structure by increasing
the stiffness of the column at lower portion ( linear analysis )
82
5.8(b) Sway at different level of steel frame structure by increasing
the stiffness of the column at lower portion ( non linear
analysis )
83
5.9 Comparison between the Results from Linear and Geometric
Non Linear Analysis
87
5.10 Comparison of Sway Prediction ( Geometric Non Linear
Analysis ) due to Different Type of Bracing System
88
5.11 Comparison of Sway due to Different Distributed Load from
Geometric Non Linear Analysis
90
5.12 Comparison of Sway for Standard Column Size and Higher
Column Size ( Non Linear Analysis Prediction )
91
xvi
NOTATIONS
P - Axial load
P – delta - Non linear effect
A - Area
I - Moment of inertia
Φ - Angle
2D - Two dimensional
BS - British Standard
V - Wind speed
Vs - Design wind speed
S1 - Topography factor
S2 - Ground roughness, building size and height above ground
S3 - Exposure to wind
q - Dynamic pressure of wind
k - Wind coefficient
Wk - Wind load
Cf - Force coefficient
ke - Linear elastic stiffness matrix
kg - Geometric stiffness matrix
Γ - Diagonal matrix
xvii
Ke - Global linear elastic stiffness matrix
T - Transform
u - Member displacement for local
v - Member displacement for global
Q - Member force
E - Modulus of elasticity
W - Distributed load
L - Length
U1 - Displacement value in X direction
U2 - Displacement value in Y direction
U3 - Displacement value in Z direction
R1 - Rotation value in X direction
R2 - Rotation value in Y direction
R3 - Rotation value in Z direction
CHAPTER 1
INTRODUCTION
There are several types of structure in this modern world. Most of the
structures behaves like linear elastic under a service loads. Slender structures such as
suspension systems, arches and tall buildings can be considered as non linear elastic. In
general, buildings having 30 to 50 stories can be classified as tall buildings. While, for
buildings with 50 stories or more can be considered as super tall buildings.
Tall building is the most structure that requires stability because it consist a lot of
frame structure with different width and height. Building will be unstable if inadequate
of lateral support and may resulted to collapse. Buildings and structures are considered
stable with lateral supports by using either bracing system or shear system or both such
as wall to ensure the stability of the building. Moreover, the important thing to consider
are the software to be used to analysis the tall building structure and a wind speed at
construction area to avoid any problem in future.
2
1.1 Statement of Problems
There are several problems that require scientific explanation in this study:
1. A linear analysis is more prefer as compare to non linear analysis in
structural design. This is because it can be simplify by design, time and
cost saving, and at the same time it does not require the use of computer
software for non linear case. Furthermore, a non linear analysis is more
complicated than linear analysis in structural problem solving. Therefore it
is important to understand the difference between both non linear and linear
analysis and able to justify the application of these approach. At the same
time the verification of the software is necessary to identify the reliability
of the tool.
2. The wind speed in Malaysia is less than 35 km/h at 10 m height refer to
Malaysia Standard. Eventhough the wind speed is small, it can still give
adverse effect to the tall building. Therefore, the identification of suitable
wind speed is important to ensure the stability of the steel frame.
3. Client or project initiator always focuses on capital cost and not the quality
of the building construction. Intergration of additional structure such as
bracing may increase the operation cost but at the same time it will improve
the sway and crack and therefore increase the life time of the building.
Hence, it is important to identify the requirement and the positioning of the
braces in steel frame structure.
3
1.2 Objectives of Study
The objectives of this study are:
1. To analyze the steel frame structure subjected to wind and without wind
load by using linear and geometric non linear analysis and to observe the
effect.
2. To compare the difference of lateral displacement or sway values between
linear and geometric non linear analysis prediction.
3. To observe if there is an alternative approach to decrease sway for steel
frame that being idealized as tall building.
4. To verify whether SAP2000 software is reliable tool for the evaluation of
tall building structure.
1.3 Scope of the Study
The scope of works in this research includes:
1. A six storey building which made up of steel material and was analyzed by
using SAP2000 software for linear and geometric non linear analysis.
2. The atmospheric wind speeds which will be use to study the wind behavior.
The evaluation will be based on data from Malaysia Standard and wind
calculation by using CP3, Chapter V ( Part 2 ).
4
1.4 Significance of the Study
This study can be used as a reference to other researchers and designers to
explore the stability in frame structure and design application. It can also provide a good
design, more stable and longer last tall building which able to provide better service to
consumers.
95
REFERENCES
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[7] Emil Simiu and Robert H. Scanlan (1996). Wind Effects on Structures, 1996, John
Wiley & Sons Publication.
[8] Seshasayee Ankireddi and Henry T. Y. Yang (1996). Simple ATMD Control
Methodology for Tall Buildings Subject to Wind Load, Journal of Structural
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96
[11] K. C. Mehta, J. E. Minor and T. A. Reinhold (1983). Wind Speed Damage
Correlation in Hurricane Frederic, Journal of Structural Engineering, Volume
109, No. 1 - 4.
[12] W F Chen (1999). Practical Analysis for Semi-Rigid Frame Design, World
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[14] Malaysia Standard (2002). Code of Practice on Wind Loading for Building
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