Drift analysis and Comparison due to rigid frame structure

STAMFORD UNIVERSITY BANGLADESH
DEPARTMENT OF CIVIL ENGINEERING
DRIFT ANALYSIS AND COMPARISON DUE TO
LATERAL LOAD ON RIGID FRAME STRUCTURE
Farok Ahmed
ID: CEN 05208211
Md.Suhaeb Mia
ID: CEN 05208217
Md. Rafiqul Islam Liton
ID: CEN 05208160
Md.Shamsuddin Rony
ID: CEN 05107929
MAY 2017

DRIFT ANALYSIS AND COMPARISON DUE TO
LATERAL LOAD ON RIGID FRAME STRUCTURE
A project & Thesis by
Farok Ahmed
ID: CEN 05208211
Md.Suhaeb Mia
ID: CEN 05208217
ID: CEN 05208160
Md.Shamsuddin Rony
ID: CEN 05107929
Supervised by
Abdur Rahman
Assistant professor
Department of Civil Engineering
In partial fulfillment of the requirements for the degree of Bachelor
of Science (B.Sc.) in Civil Engineering
MAY 2017

STAMFORD UNIVERSITY BANGLADESH
DEPARTMENT OF CIVIL ENGINEERING
51, SIDDESWARI ROAD, DHAKA - 1217
The project and thesis titled “Drift Analysis and Comparison Due to Lateral Load on
Rigid Frame Structure” submitted by Farok Ahmed ID: CEN 0528211, Md.Suhaeb Mia
ID: CEN 05208217, Md. Rafiqul Islam Liton ID: CEN 05208160, Md.Shamsuddin Rony
ID: CEN 05107929 Batch: 51(C) of the Department of Civil Engineering has been
examined thoroughly and accepted in partial fulfillment of the requirements for the degree
of Bachelor of Science in Civil Engineering on 09 May 2017.
________________________________
(Abdur Rahman)
Supervisor
Assistant Professor
Department of Civil Engineering
Stamford University Bangladesh

DECLARATION
We, Farok Ahmed, Md.Suhab Mia, Md. Rafiqul Islam Liton and Md.Shamsuddin Rony are
the student of B.Sc. in Civil Engineering of Stamford University Bangladesh here by
solemnly declare that the works presented in this thesis & project has been carried out by
us and has not previously been submitted to any other University/College/Organization for
any academic qualification/certificate/diploma/ degree etc. We warrant that the present
work does not breach any copyright law. We further undertake to indemnify the University
against any loss or damage arising from breach of the foregoing obligations.
___________________
Farok Ahmed
ID: CEN 05208211
Batch: 52(B)
________________
Md.Suhaeb Mia
ID: CEN 05208217
Batch: 52(C)
_____________________
ID: CEN 05208160
Batch: 52(C)
_____________________
Md.Shamsuddin Rony.
ID: CEN 05107929
Batch: 51(C)

DEDICATION
We would like to dedicate this thesis to our sweet and lovely parents. We would also like
to dedicate our work to our mentor Abdur Rahman, Assistant Professor, Department of
Civil Engineering, Stamford University Bangladesh.

TABLE OF CONTENTS
TITLE PAGE
ACKNOWLEDGEMENT I
ABSTRACT II
LIST OF SYMBOLS III
LIST OF FIGURE IV
LIST OF TABLES VII
CHAPTER 1: INTRODUCTION
1.1 Background of the study 1
1.2 Objective of the Study 5
CHAPTER 2: LITERATURE REVIEW
2.1 Rigid frame structural system 6
2.1.1 Introduction 6
2.1.2 Mechanical behavior 7
2.1.3 Vertical load resistance 8
2.1.4 Stability 9
2.1.4.1 Second order analysis 9
2.1.4.2 P- analysis 10
2.1.5 Joints in continuous frames
2.1.5.1 Rotational stiffness in joints
2.1.5.2 Semi-rigid joints
2.1.5.3 Seismic performance of moment resistant steel joints
10
11
11
12

2.1.6 Continuum model of rigid frame structures
2.1.7 Robustness of the rigid frame system
12
15
2.2 Lateral loads on tall Buildings 17
2.2.1 Nature of earthquake 18
2.2.2 Design considerations 18
2.2.3 Tall buildings behavior during Earthquake 20
2.2.4 Damping and seismic separation 21
2.3 Analysis for drift due to lateral load 22
2.3.1 Introduction 22
2.3.2 Analysis for Drift 22
2.3.3 Components of Drift 23
2.3.3.1 Story Drift due to Girder Flexure 24
2.3.3.2 Story Drift due to Column Flexure 25
2.3.3.3 Total Drift 26
2.3.4 Correction of Excessive Drift 26
CHAPTER 3: METHODOLOGY OF THE STUDY
3.1 Introduction 28
3.2 Select building plan 28
3.2.1 Building plan 28
3.2.2 Beam & Column layout 29
3.2.3 Front elevation 29
3.3 Collection Design data and materials properties 30
3.4 Analysis of the structure 31
3.4.1 By using ETABS software 31
3.4.1.1 Grid system names 31

3.4.1.2 Define material property data 31
3.4.1.3 Define load patterns 32
3.4.1.4 Frame in ETABS 32
3.4.1.5 Load case and combination 33
3.4.1.6 Check model in ETABS 33
3.4.1.7 Run analysis after ETABS 34
3.4.1.8 Base reaction in ETABS 34
3.4.1.9 Maximum story drift earthquake Y direction (short direction) 35
3.4.1.10 Maximum story drift earthquake X direction (long direction) 35
3.4.2 By using Programming Language C++ 36
3.4.2.1 Earthquake load calculation 36
3.4.2.2 Earthquake load at the story level 38
3.4.2.3 Calculate story girder drift 39
3.4.2.4 Calculate story column drift 40
3.4.2.5 Calculate story total drift 41
3.4.2.1 Create a new project in Code Blocs 41
3.4.2.2 Write equation in different terms names in Code Blocks 42
3.4.2.3 Build and run program 42
3.4.2.4 input equation value in Code Block 42
3.4.2.5 Output equation value in Code Block 43
3.4.2.6 Equation drift with respect to height 43
CHAPTER 4: RESULTS AND DISCUSSION
4.1 Introduction 44
4.2 Results 44

4.2.1 Story drift table and curve by ETABS Software 44
4.2.2 Variation of drift with height of Building By Programming language 48
4.2.3 Comparison drift Programming language & ETABS 48
4.2.4 Variation of drift with Building height
49
4.2.5 Variation of drift with number of span
49
4.2.6 Variation of drift with dimension beam and column
50
4.2.7 Variation of drift with shear value beam and column
50
4.2.8 Variation of drift with height of Building By Programming
language and ETABS
51
4.3 Discussion 51
CHAPTER 5: CONCLUSIONS & RECOMMENDATIONS
5.1 General 52
5.2 Conclusions 52
5.3 Recommendations 52
REFERENCES 53
APPENDIX 54

I
ACKNOWLEDGEMENT
The research works Drift Analysis and Comparison Due to Lateral Load on Rigid Frame
Structure has been conducted in partial fulfillment of the requirements for the degree
of Bachelor of Science (B.Sc.) in Civil Engineering. This critical works became
possible for us due to the unconditional help and co-operation in different ways by
many people. We express our gratefulness and thanks to them for their assistance in
preparation of this project and thesis.
First of all, we like to show our highest gratitude to the Almighty Allah for His kindness
on us that make it possible to complete the study and preparation of this project
and thesis.
The work presented here was carried out under the supervision of Abdur Rahman,
Assistant Professor of the Department of Civil Engineering, Stamford University
Bangladesh. The author wishes to express his deep gratitude to him for his patient
guidance and affectionate encouragement from the starting till the end of the thesis.
Without his inspiration, constant guidance and invaluable suggestions at all phases, the
work could hardly be materialized.
The author wishes to convey his thanks to the teachers, friends and well-wishes, who have
helped me, suggested me with a view to accomplishing the project work.

II
ABSTRACT
An analytical study has been performed for the effect of lateral loading on tall structure
buildings. This paper mainly deals with the drift analysis on tall structure buildings by the
action of lateral loads. This study a differential equation is formed and solved to determine
the drift of the building.
A program is also developed with the help Visual Basic Language to analysis the drift. The
analytical results are presented in tabular from and as well as in graphical form. Recently
there has been a considerable increase in the number of tall buildings, both residential and
commercial, and the modern trend is towards taller and more slender structures. Thus the
effects of lateral loads like winds loads, earthquake forces are attaining increasing
importance and almost every designer is faced with the problem of providing adequate
strength and stability against lateral loads. For this reason in recent years wind and
earthquake loading have become determining factors in high-rise building design. This
lateral loads are mainly responsible for drift. So the design of tall structures must take into
consideration of the drift. Although there are no specific requirements in the effects of drift,
it is an important issue which may significantly impact the buildings structural behavior
and economy. This paper aims to analyze the drift for lateral loads and comparison on drift
for earthquake and wind loads on tall structures. To analyze the drift, we used programming
Language C++ (Code Blocks). Mainly we analyzed three types of high rise structures such
as rigid frame, couple shear wall and wall frame structures. Strength, serviceability and
stability in tall structures have to include in design criteria. Strength is satisfied by limit
stresses, while serviceability is satisfied by drift limits in the range of H/500 to H/1000 .On
the other hand stability is satisfied by sufficient factor of safety against buckling and P-
Delta effects.

III
LIST OF SYMBOLS:
Symbol Specification unit
Z Seismic zone coefficient
I Structural Importance coefficient
R Response modification coefficient
C Seismic coefficient
S Site coefficient for soil characteristics
T Fundamental period of vibration
hn Building height in meter above base level [ft]
Q Shear force [kip]
h Height of the story [ft]
Ig Moment if inertia of girder [in4]
Ic Moment of inertia of Column [in4]
L Clear distance between two column [ft]
δg Deflection of girder
δc Drift of column
δs Story Drift
E Modulus of Elasticity [k/in2]
Qi+1 upper story shear force [kip]
Qi-1 lower story shear force [kip
h i+1 upper story height [ft]
h i-1 lower story height [ft]
Fn Concentrated lateral force considered at the top of the building
in addition to the force
[k]

IV
LIST OF FIGURE
Page
Figure 1.1 : Maximum story drift at different floor level (longitudinal
direction)
2
Figure 1.2: Maximum story drift at different story level (longitudinal
direction)
3
Figure 1.3: Comparison different type story drift at different story level. 3
Figure 1.4: Comparison different structure type story drift at different story
level.
4
Figure 1.5: Maximum story drifts at different story level in ETABS. 4
Figure 1.6: Comparison different structure Model type story drift at
different story level.
5
Figure 2.1: The economical height for different types of framework in steel
construction.
6
Figure 2.2: The main deflection components on rigid frames. 8
Figure 2.3: Example of different vertical load patterns on the girders 8
Figure 2.4: Variables for second order analysis in rigid frame building 9
Figure 2.5: Illustration of the P-effect 10
Figure 2.6: model of a bolted joint connection in analysis software 11
Figure 2.7: Rotational stiffness of bolted joint connection displayed in
figure 2.6
12
Figure 2.8: Moment connection between I-beam and RHS-profile using
blind bolted extended endplate
12
Figure 2.9: The continuum model of a one-bay framework with steps a) to
d)
13
Figure 2.10: Vertical displacement components 1 2 and 3 at contra flexure
points in a one bay example of continuum method frame
reduction
14

V
Figure 2.11: Column reduction using continuum method on multi-bay rigid
frame structure
15
Figure 2.12: Principle on how the rigid frame can remain stable after loss of
columns
16
Figure 2.13: The simple method in analyzing progressive collapse visualized 16
Figure 2.14: Story building frame models analyzed for robustness. 17
Figure 2.15: Schematic representation of seismic force (Taranath, 1998) 21
Figure 2.16: Rigid frame with setback 22
Figure 2.17: setback structure separated for analysis 22
Figure 2.18: Deflection of portal frame a) Frame subjected to lateral loads
b) Typical story segment
23
Figure 2.19: joint rotation due to girder flexure 23
Figure 2.20: story drift due to girder flexure 24
Figure 2.21: story drift due to column flexure 24
Figure 3.1: Building plan of 14 story 28
Figure 3.2: Beam and Column Layout plan 29
Figure 3.3: Front Elevation 29
Figure 3.4: Grid system names 31
Figure 3.5: Define material property data 31
Figure 3.6: Define load patterns 32
Figure 3.7: Frame in ETABS 32
Figure 3.8: Load case and combination 33
Figure 3.9: Load case and combination 33
Figure 3.10: Run analysis after ETABS 34
Figure 3.11: Story response plots 35
Figure 3.12: Maximum story drift earthquake in Y direction 35
Figure 3.13: Create a new project in Code Blocks 41

VI
Figure 3.14: Write equation in different terms names in Code Blocks 42
Figure 3.15: Build and run program 42
Figure 3.16: Input equation value in Code Block 42
Figure 3.17: Output equation value in Code Block 43
Figure 4.1: Story drift curve ETABS 45
Figure 4.2: Variation of drift with height of Building by using ETABS 47
Figure 4.3: Variation of drift with height of Building by using
Programming language
48
Figure 4.4: Variation of drift with Building height 49
Figure 4.5: Variation of drift with number of span 49
Figure 4.6: Variation of drift with dimension beam and column 50
Figure 4.7: Variation of drift with shear value beam and column 50
Figure 4.8: Variation of drift with height of Building for Equation and
ETABS
51

VII
LIST OF TABLES
Page
Table 1: Materials Properties For this Research Design data were
collected from related consultant firm
30
Table 2: Base Reactions 34
Table 3: Seismic Zone Coefficient, Z ( BNBC, Table- 6.2.22) 36
Table 4: Structure Importance Coefficient, I &I' ( BNBC, Table-6.2.23) 36
Table 5: Earthquake load at the story level (zone-II). 38
Table 6: Similarly same Equation 2nd to 14th
stories calculate girder
drift.
39
Table 7: Similarly same Equation 2nd to 14th
stories calculate column
drift
40
Table 8: Story drift and Total Drift: 41
Table 9: Equation drift with respect to height 43
Table 10:
Story drift in ETABS (Y Direction):
44
Table 11: Story drift in ETABS (X Direction) 46
Table 12: Story drift in programming Language and ETABS value 48

1
Drift Analysis and Comparison Due to Lateral Load on Rigid Frame Structure
1.1 BACKGROUND OF THE STUDY
The tallness of a structure is relative and cannot be defined in absolute terms either in
relation to height or the number of stories. The council of Tall Buildings and Urban
Habitat considers building having 9 or more stories as high-rise structures. But, from a
structural engineer's point of view the tall structure or multi-storied building can be
defined as one that, by virtue of its height, is affected by lateral forces due to wind or
earthquake or both to an extent. Lateral loads can develop high stresses, produce sway
movement or cause vibration. Therefore, it is very important for the structure to have
sufficient strength against vertical loads together with adequate stiffness to resist lateral
forces. So lateral forces due to wind or seismic loading must be considered for tall
building design along with gravity forces. Tall and slender buildings are strongly wind
sensitive and wind forces are applied to the exposed surfaces of the building, whereas
seismic forces are inertial (body forces), which result from the distortion of the ground
and the inertial resistance of the building. These forces cause horizontal deflection in a
multi-story building called drift. Lateral deflection is the predicted movement of a
structure under lateral loads and story drift is defined as the difference in lateral deflection
between two adjacent stories. Lateral deflection and drift have three effects on a structure;
the movement can affect the structural elements (such as beams and columns); the
movements can affect non-structural elements (such as the windows and cladding); and
the movements can affect adjacent structures .Without proper consideration during the
design process, large deflections and drifts can have adverse effects on structural
elements, nonstructural elements, and adjacent structures. When the initial sizes of the
frame members have been selected, an approximate check on the horizontal drift of the
structures can be made. The drift in the non-slender rigid frame is mainly caused by
racking. This racking may be considered as comprising two components: the first is due
to rotation of the joints, as allowed by the double bending of the girders, while the second
is caused by double bending of the columns. If the rigid frame is slender, a contribution
to drift caused by the overall bending of the frame, resulting from axial deformations of
the columns, may be significant. If the frame has a height width ratio less than 4:1, the
contribution of overall bending to the total drift at the top of the structure is usually less
than 10% of that due to racking. The following method of calculation for drift allows the
separate determination of the components attributable to beam bending, and overall

2
cantilever action. In most tall rigid frame buildings, the depth and thereby stiffness of
members in a rigid frame building are determined by stiffness rather than ultimate
strength. The most common challenge in using rigid frame building system is controlling
lateral drift. Additionally, the reliability of rigid beam-column joints is hard to verify in
the building system. In steel buildings, the rotational stiffness of a bolted joint relies
mostly on empirical studies and experimental data rather than analytical results. Most tall
buildings in Finland include some other kind of lateral stiffness providing sys-tem than a
rigid frame. Precast concrete buildings, a common type of building in Finland, have joints
that are non-rigid by definition. Cast-in-place building frames can be cast continuously
and therefore naturally be used as rigid frames.
When it comes to steel frames, welding provide a rigid joint between columns and beams
in most cases. A bolted joint can also be made moment resisting but the rotational
stiffness of the steel bolted joint is hard to analyze and the behavior of the joint needs to
be mapped in order to determine whether the joint can be applied.
We are previous studies different types of drift curve respect to building height given
bellow:
Figure 1.1: Maximum story drift at different floor level (longitudinal direction)

3
Figure 1.2: Maximum story drift at different story level (longitudinal direction)
Figure 1.3: comparison different type story drift at different story level.

4
Figure 1.4: comparison different structure type story drift at different story level.
Figure 1.5: Maximum story drifts at different story level in ETABS.

5
Figure 1.6: comparison different structure Model type story drift at different story level.
1.2 OBJECTIVE OF THE STUDY
The objectives of the study are as follows:
 To analysis the horizontal displacement on high-rise structure due to earthquake
loads.
 To observe the longitudinal impact on high rise structure.
 The analysis of drift of different types of tall structures and also calculation of
drift by hand and programming Language C++ (code blocks).
 To compare the value of drift from programming with C++ (code blocks) for
different types of tall buildings.

6
2.1 RIGID FRAME STRUCTURAL SYSTEM
2.1.1 Introduction
The main purpose of the structural system is to provide a feasible way to carry vertical
and lateral loads. The type of structural system is chosen according to its architectural
characteristics, loading, purpose and structural characteristics. Rigid frame building
system is generally used for buildings comprising up to 25 stories. As seen in figure 2.1,
taller buildings generally contain other building systems.
Figure 2.1: The economical height for different types of framework in steel construction
The uniqueness of the rigid frame building system lies in its lateral load resistance. Both
beams and columns participate in transferring the load to the foundation. This also makes
the rigid frame system challenging to analyze. Because beams also participate in the
lateral stiffness, they need to be designed for lateral stability along with their ability to
carry vertical loads. Because of the lack of bracing structural elements in the building
plane, the rigid frame delivers open plane solutions with architectural flexibility in
placement of windows and other surface elements. The rigid frame building system, the
girders in the structure do not provide any lateral stiffness. This makes it easier to
calculate the forces in them and the same dimensions and lengths of the girders can be

7
used throughout the building. One way to include both the advantages from a rigid frame
and a tubular structure is to create a framed-tube structure. The framed tube structural
system comprise a tube, created from columns and beams placed close to each other. The
beam column joints are moment resistant. Because of the geometry and the placing of the
columns, the building can be analytically calculated as a tubular structure.
2.1.2 Mechanical behavior
The rigid frame construction system incorporates columns and beams that are rigidly, or
at least semi-rigidly, connected to one another. The joint between them are made moment
resistant, meaning the moment is transferred from columns to beams This feature, called
the rigid frame action, provides the lateral force resistance in the building system. When
designing buildings, especially tall buildings, this action plays the greatest role in
determining the height and other dimensions of the columns and girders.
In figure 2.2, the response to lateral force is illustrated along with the deflection
characteristics of the system. As seen there, the lateral force on the building creates
flexure in the members. This flexure is transferred between columns and beams by the
rigidity of the column-beam joints. Ultimately, the force is transferred to the ground. The
continuity in the joints usually make the sagging moment due to gravity loads in the
girders smaller than if the girders were simply supported. However, the pattern of the life
load needs more consideration than in the simply supported alternative. This because all
joints transfer moments and this can lead to large hogging moments at the supports.
Because of the high robustness of a rigid frame, accurate analysis on the structure can be
done after the member properties have been assigned.
The deflection characteristics for rigid frame construction system consist of 2 main
components, cantilever bending and frame racking. Cantilever bending usually represent
10-15% of the total lateral displacement. Frame racking forms the main component of
deflection and accounts for 70% of the total deflection in a rigid frame. These deflection
types are illustrated in fig 2.12. The story drift, the lateral displacement of a floor
compared to the floor below, is greatly affected by the frame racking deflection
component. A limit from 500
l
to 400
l
is usually set for rigid frame buildings, and this is
generally the limiting factor in tall rigid frame buildings.

8
Figure 2.2: The main deflection components on rigid frames.
2.1.3 Vertical load resistance
The pattern of the vertical live load plays a more important part in a rigid frame than in a
simple connected frame. The continuity of the girders over its spans make the maximum
moment in them very sensitive to different patterns of vertical loading. This effect
provide additional design challenges in the building. Examples on this effect is illustrated
in figure 2.2.There pattern (a) provides maximum positive moment at bays AB and CD
while providing maximum negative moment at point A. The (b)-labeled pattern however
provide maximum negative moment at point B.
Figure 2.3: Example of different vertical load patterns on the girders

9
2.1.4 Stability
The rigid joints in a rigid frame provide the need for special consideration. Because of
them, no individual compression member can fail independently from the members
connected to it. For this reason the rigid frame needs to be analyzed both as an entire
structure as well as a combination of single members to acquire the stability of the
building. The critical load for a simple one-bay one-story frame and structures of similar
complexity can be calculated by solving the systems characteristic differential equation,
solving slope deflection equations (for frames with more degrees of freedom) or by
matrix analysis. These methods, however, can prove to be difficult if even possible to
solve when the structure at hand is a multistory multi-bay rigid frame.
2.1.4.1 Second order analysis
Figure 2.4: Variables for second order analysis in rigid frame building
This thesis focuses on the second order effects that occur when movement, based on
elastic theory increase the loading on the elements. Tall building frames experience both
local. Second order effects, affecting the elements of the building) and global second
order effects (affecting the entire building as one unit).
Since the rigid frame provides its own stability system and is a sway frame, second order
analysis is required by Euro code in building design. The sensitivity of the second-order
effects in a multi-story rigid frame depends on the stiffness of the beams and columns,
and also on the stiffness of the joints.

10
2.1.4.2 P-analysis
The second order effects of an entire building can prove troublesome to obtain, especially
if it comprises asymmetric geometry and non-prismatic design. For these cases, the P -
analysis provide a useful tool in approximating the second order effects of the structure.
When the structure, modeled as a column in figure 2.15, is subjected to both vertical load
and horizontal load (V) it undergoes drift in the horizontal direction. This results in an
eccentricity of the vertical load which creates an additional bending moment on the
structure. This additional moment in turn increases the lateral displacement on top of the
structure and the cycle is repeated. Through repetition of these cycles lateral displacement
is accumulated in the structure, see 1 and 2 in figure 2.15
Figure 2.5: Illustration of the P-effect
2.1.5 Joints in continuous frames
In order to acquire stiffness from frames, moment forces need to be transferred from the
columns to the beams in the frame. This interaction requires the column-beam joints to
be rigid or at least semi rigid. This requirement can be fulfilled in different ways for
different frame materials and geometry.

11
2.1.5.1 Rotational stiffness in joints
Joints can be classified by their stiffness and by their strength. The code recognizes 3
types of joints, when classified by stiffness:
• Nominally pinned joints
• Rigid joints
• Semi-rigid joints
2.1.5.2 Semi-rigid joints
Semi-rigid joints are inter-element joints that are neither nominally pinned nor nominally
fixed. In practice, most steel construction joints are semi-rigid. The deflection of semi-
rigid frames can be modeled using 2 no dimensional parameters.
In designing rigid frames, the joints are often assumed to be semi-rigid by creating the
joints as rotational springs.
Figure 2.6: model of a bolted joint connection in ANSYS software
FE-models can prove efficient in analyzing the rotational stiffness properties. Figure 2.19
shows a FE-model of a bolted top angle joint in steel. The rotational stiffness of the joint
in the figure is analyzed in ANSYS fem-software in a study, with the result plotted in
figure 2.20. Result from the FE-model is compared to experimental testing of the joint at
hand as well as empirical results. The results in figure 2.20 are correlated in this case.
The study concluded that the FE-approach can be applied in analysis of steel joint
rotational behavior under moment load

12
Figure 2.7: Rotational stiffness of bolted joint connection displayed in figure 2.6
2.1.5.3 Seismic performance of moment resistant steel joints
Studies like [27] divide welded moment resistant joints in steel as pre- or post-Northridge.
This division refers to the types of welded steel joints used in buildings that did
experience damage in the 1994 Northridge earthquake. The damage to moment frame
steel buildings usually occurred in welded connections between wide-flanged beams and
columns. The failure of these connections were often of a brittle character, as in the case
illustrated in figure 2.23. Joints including full-penetration field welding in top and bottom
flange of the beam were found to develop large inelastic rotations under seismic loading.
One way to improve the safety of steel joints under seismic loading is to design the beams
connected so that plastic hinges form in the beams rather than in the joints
Figure 2.8: Moment connection between I-beam and RHS-profile using blind bolted ex-
tended endplate
2.1.6 CONTINUUM MODEL OF RIGID FRAME STRUCTURES
The rigid frame building system is often more complicated to analyze analytically than
other building system because of the fact that the same elements that provide vertical load

13
resistance also provide the lateral stiffness of the building. In order to approximate the
lateral deflection and story drift of the structure, reduction of the frame can be done to
acquire a mathematical model easier to analyze than the structure itself. The continuum
method was developed to be an approximate method of calculating the drift in the rigid
frame. It involves reducing the frame to a cantilever beam with loads applied to it. The
load applied to the column represent the frame action. This method is recommended for
use with rigid frame structures rising to at least 4 stories. The beams are also assumed to
be of sufficient amount to form a continuous connecting medium between the columns.
The method is exact when the structure to be analyzed is symmetrical, and thereby having
the contra flexure point in the center of the beam. Additionally the amount of beams in
the frame need to be sufficient to provide a continuous connecting medium between the
columns. With a continuum model of the structure, a basic understanding in the
displacements, deformations and internal bar forces of the structure. This can be of good
service in the first stages of the design process.
Formulas and reduction steps for this method is listed in appendix C. the basic steps
carried out in the continuum reduction method
Figure2.9: The continuum model of a one-bay framework with steps a) to d)
Step b) in figure 2.25 includes cutting the beams in the frame in their contra flexure points
and applying compensation forces at the location of the cuts with qh-forces, the shear
flow compensation force. Into the next step, step c) in figure 2.25, the beams are removed
and compensation forces from their forces are applied to the columns. The columns then
experience normal forces (N) and moments in the locations of the beams. Ultimately the

14
two columns in figure 2.25 are replaced with one column, representing the mechanical
properties of the structure.
When the beams are cut, the ends of the beams move vertically in relation to each other.
This type of vertical deflection at contra flexure point in the beams can be divided into 3
Components; 1, 2 and 3. A visual representation of these deflection components in a one
bay rigid frame example is on display in figure 2.26. The calculation of the -values is
outlined in C.
b)
(a) Vertical displacement due to deflection of the columns (b) Vertical displacement due
to axial deformation of the columns
c)
(c) Vertical displacement due to bending
moment in the beams
Figure 2.10: Vertical displacement components 1 2 and 3 at contra flexure points in a one
bay example of continuum method frame reduction.
The continuum model rigid frame reduction method can also be applied to multi-bay rigid
frame structures, as shown in figure 2.27. The beams in the multi-bay example has the
same load configuration and similar contra flexure point locations, where they are cut.

15
The model, in that stage consisting of a row of columns is then reduced to a single column
in the same way as with the one-bay structure derived in C
Figure 2.11: Column reduction using continuum method on multi-bay rigid frame
structure
2.1.7 ROBUSTNESS OF THE RIGID FRAME SYSTEM
A buildings systems ability to withstand unforeseen action is referred to as the robustness
of the building. There are few tools developed for designing rigid frame structure. Several
tools are available for designing braced frames, but the rigid frame offers other
difficulties that are harder to address as a designer. One of these challenges lies in fire
dimensioning of rigid frame structures with composite elements. When designing for
accidental loads the focus need to be set on the avoidance of progressive collapse of the
building frame. The robustness of the rigid frame can prove useful in these situations. A
study made by CTBUH investigated a 27 story steel frame building experiencing loss of
columns due to a potential plane crash into the building or an explosion. The building
frame investigated as the target building comprise a moment frame. Columns in the
moment frame are rectangular hollow steel section elements and the beams are built up
I-beams, much like the target building analyzed in this study
The principle on how the rigid frame redistribute loads in the case of loss of columns in
a potential accidental situation is illustrated in figure 2.28. As seen in the picture, the
remaining frame members carry the now redistributed load, and the building remains
stable. The result from loss of columns was tested both starting from center columns and
starting from corner columns, both at bottom floor and 20th floor. At bottom floor the

16
frame remained stable after the loss of 6 center columns, and likewise after loss of 5
corner columns. At the 20th floor the frame remained stable after the loss of 8 center
columns or the loss of 7 corner columns.
Figure 2.12: Principle on how the rigid frame can remain stable after loss of columns
Semi-rigid frames are also able to provide some robustness in the case of lost columns.
A study compared the performance of a moment frame and a simple braced frame under
accidental loads and lost columns in different locations in the building. The study showed
that simple braced frames are more likely to progressively collapse than a moment frame
Figure 2.13: The simple method in analyzing progressive collapse visualized
Under column loss. Additionally the study proved the corner column being more critical
to lose than a perimeter column, this because the corner columns have less connected
members and thus less ability to redistribute load [30]. The study [30] analyzed 2 different
frames under the situation of lost columns. Both frames, as seen in figure 2.30, include a
rigid frame skeleton, with the difference being that one also includes the composite slab
in the building floors. The study revealed that the model with slab included reduced the
frame deflection in the case with lost columns by 50 % compared to the model with only
rigid frame skeleton included. [30]. this indicates that additional robustness to a rigid
frame can be provided through the use of composite slabs in the intermediate floors.

17
Figure 2.14: 9-story building frame models analyzed for robustness. (b) FE-model
includes the columns and beams while (b) includes the frame as well as the column
composite slab
2.2 LATERAL LOADS EFFECT ON TALL BUILDING
As earthquakes can happen almost anywhere, some measure of earthquake resistance in
the form of reserve ductility and redundancy should be built into the design of all
structures to prevent catastrophic failures. Moreover, during the life of a building in a
seismically active zone, it is usually expected that the building will be subjected to many
small earthquakes, including some moderate ones, one or more large ones, and possibly
a very severe one.
Building massing, shape and proportion, ground acceleration, and the dynamic response
of the structure, influences the magnitude and distribution of earthquake forces. On the
other hand, if irregular forms are inevitable, special design considerations are necessary
to account for load transfer at abrupt changes in structural resistance.
Therefore, two general approaches are utilized to determine the seismic loading, which
take into consideration the properties of the structure, and the past record of earthquakes
in the region. When compared to the wind loads, earthquake loads have stronger intensity
and shorter duration. The general philosophy of earthquake-resistant design for buildings
is based on the principles that they should (Smith and Coull, 1991):

18
• resist minor earthquakes without damage;
• resist moderate earthquakes without structural damage but accepting the probability of
non-structural damage:
• Resist average earthquakes with the probability of structural as well as non-structural
damage, but without collapse.
2.2.1 Nature of earthquake
The earth’s outer layer is composed of plates ranging in thickness from 32 to 241 km.
The plates are in constant motion, riding on the molten mantle below, and normally
traveling at the rate of a millimeter a week, which is equivalent to the growth rate of a
fingernail. Hence, this motion causes continental drift and the formation of mountains,
volcanoes, and earthquakes. As a complex phenomenon, earthquake has just begun to be
understood. Thanks to the analytical studies of earthquake response of buildings,
experimental studies performed both in the laboratory and in the field, much of
destruction and loss of life resulting from earthquake are tried to be prevented.
2. 2.2 Design considerations
The intensity of vibration of the earth’s surface at the building site depends on following
factors (Taranath, 1998):
• amount of energy released;
• distance from the center of the earthquake to the structure;
• Character and the thickness of foundation material.
During an earthquake, the magnitude of seismic loads on the structure depends on the
following factors (Taranath, 1998):
• building mass;
• the dynamic properties of the building;
• The intensity, duration and frequency content of ground motion and soil structure
interaction.
Although, the magnitude of earthquake can be predicted on a regional basis from the
probability theories, there are too many unknowns to be able to predict quantitatively and
with any degree of certainty the ground vibration of some unknown future earthquake.

19
Moreover, despite the advancements in earthquake engineering during the last three
decades, many uncertainties still exist.
The plan layout of a building plays a vital role in its resistance to lateral forces and the
distribution of earthquake forces. Experience has shown that the buildings with an
unsymmetrical plan have a greater vulnerability to earthquake damage than the
symmetrical ones (Taranath, 1998). Therefore, symmetry in both axes, not only for the
building itself but also for the arrangement of wall openings, columns, and shear walls is
very important. For a building with irregular features, such as asymmetry in plan or
vertical discontinuity, assumptions different from the buildings with regular features
should be used in developing seismic criteria.If irregular features are inevitable, special
design considerations should be used to account for the unusual dynamic characteristics,
and the load transfer and stress concentrations that occur at abrupt changes in structural
resistance. Asymmetry in plan can be eliminated or improved by separating L-, T-, and
U-shaped buildings into distinct units by use of seismic joints at junctions of the
individual wings.15Considering the effect of lateral forces on the structural system from
the start of the layout could save substantial time and money without detracting
considerably from the building usefulness or appearance.
The systems to provide resistance to seismic lateral forces, rely basically on a complete,
three-dimensional space frame; a coordinated system of moment frames, shear walls or
braced frames with horizontal diaphragms. The local soil condition is also an important
factor for the seismic motion. For instance, harder soils and bedrock will effectively
transmit short-period vibrations while filtering out longer-period vibrations as opposite
to softer soils which will transmit longer-period vibrations (Taranath, 1998).
A list of features that can be utilized to minimize the earthquake damage is as follows
(Taranath, 1998):
1) Provide details which allow structural movement without damage to non-structural
elements, such as piping, glass, plaster, veneer, partitions and like. To minimize this
type of damage, special care in detailing, either to isolate these elements or to
accommodate the movement, is required.

20
2) Breakage of glass windows can be minimized by providing adequate clearance at edges
to allow for frame distortions.
3) Damage to rigid non-structural partitions can be largely eliminated by providing a
detail at the top and sides which will permit relative movement between the partitions
and the adjacent structural elements.
4) In piping installations, the expansion loops and flexible joints used to accommodate
temperature movement and are often adaptable to handling the relative seismic
deflections between adjacent equipment items attached to floors.
5) Fasten free-standing shelving to walls to prevent toppling.
In the earthquake-resistant design, because of quite low probability, there is no need to
consider the simultaneous action of wind and earthquake loads. Furthermore, there is no
record that an extreme wind and earthquake loads stroke a building at the same time. It
is expected, as in the case of wind loads, that under the action of moderate earthquake
loads, the building structure will remain within the elastic range.
2.2.3 Tall building behavior during earthquakes
Since the seismic motions of the ground result in vibration in the structure, the behavior
of a tall building can be described as a vibration problem during an earthquake. The
damage in a building results from the inertial forces caused by the vibration of the
building mass. An increase in the mass has two adverse effects for the earthquake design.
First, it causes an increase in the force, and second, it can result in buckling and crushing
of vertical elements such as columns and walls. On the other hand, even though the
duration of strong motion is a significant measure, it is not explicitly utilized as a design
criterion at present. In order to prevent distress in structural members and architectural
components lateral deflections resulting from seismic loads should be limited. For the
design of the non-structural elements, sufficient clearance or flexible supports are
important criteria to accommodate the predictable movements.
Seismic motion response of tall buildings is to some extent generally different than low-
rise buildings. The magnitude of inertia forces generated by an earthquake depends on
the building mass, ground acceleration, the nature of foundation, and the dynamic

21
characteristics of the structure (Figure 2.34). Although tall buildings are more flexible
than low-rise buildings, and usually experience accelerations much less than low-rise
ones, a tall building subjected to ground motions for a prolonged period may experience
much larger forces if its natural period is near that of the ground waves (Taranath, 1998).
Figure 2.15 Schematic representation of seismic force (Taranath, 1998)
2.2.4 Damping and seismic separation
The conventional approach to improving the safety and serviceability of structures is to
increase the structure’s capacity by enlarging the member section and providing sufficient
ductility for the structure. Utilization of damping devices is another method to mitigate
the dynamic response of the building. Based on external energy requirement, damping
devices used in earthquake engineering can be classified in two broad categories: active
and passive devices. While in the passive devices, no external energy supply is required
and the control mechanisms move along with the main structures, in the active devices,
the dynamic responses of the structures are controlled with the introduction of external
energy into the structure. Besides this, the degree of damping depends on the construction
materials, type of connections and the presence of non-structural elements. In addition,
seismic separation approach can also be utilized. Because of different modes of response,
adjoining buildings or adjoining sections of the same building can strike each other. In
such cases, building separations or joints should be used to allow adjoining buildings to
respond independently to earthquake induced motion.

22
2.3 ANALYSIS FOR DRIFT DUE TO LATERAL LOAD
2.3.1 Introduction
As building heights increase, the forces of nature begin to dominate the structural system
and take on importance in the overall building system. The analyses and design of tall
building are affected by lateral loads, particularly drift or sway caused by such loads.
Drift or sway is the magnitude of the lateral displacement at the top of the building
relative to its base.
2.3.2 Analysis for Drift
When the initial sizes of the frame members have been selected, an approximate check
on the horizontal drift of the structure can be made. The drift in a non-slender rigid frame
is mainly caused by racking.
The racking may be considered as comprising two components: the first is due to rotation
of the joints, as allowed by the double bending of the girders (Fig.-2.19), while the second
is caused by double bending of the columns (Fig.-2.20). If a rigid frame is slender, a
contribution to drift caused by the overall bending of the frame, resulting from axial
deformations of the columns, may be significant (Fig.-2.21). If the frame has a height
width ratio less than 4:1, the contribution of overall bending to the total drift at the top of
the structure is usually less than 10% of that due to racking. The following method of
calculation for drift allows the separate determination of the components attributable to
beam bending, column bending, and overall cantilever action.
Figure 2.16-Rigid frame with setback Figure 2.17- setback structure separated
for analysis

23
2.3.3 Components of Drift
It is assumed that the drift analysis that points of contra-flexure occur in frame at the mid
story level of the columns and the mid span of the girders. This is a reasonable assumption
for high-rise frames for all stories except near the top and bottom.
Figure 2.18 -Deflection of portal frame. a) Frame subjected to lateral loads b) typical
story segment
Figure 2.19- joint rotation due to girder flexure

24
1.3.............
jointstheofstiffnessrotationalTotal
jointsby thecarriedmomentTotal
gi

2.3.....................
2
1
12
momentTotalThe



ih
i
QihiQ
    
3
3
3
3
2
2
2
2
1
1
1
1
6
L
gI
L
gI
L
gI
L
gI
L
gI
L
gI
E 
Figure 2.20 - story drift due to girder flexure
Figure 2.21- story drift due to column flexure
2.3.3.1 Story Drift due to Girder Flexure
Consider a story-height segment of a frame at floor level i consisting of a line of girders
and half story-height columns above and below each joint (Fig.-2.19). To isolate the
effect of girder bending, assume the columns are flexurally rigid.
The average rotation of the joints can be expressed approximately as
And the total rotation stiffness

25
  3.3..................................................................112
L
gI
E
  4.3................................
1)(24
11



L
gI
E
ihiQihiQ
ig
  5.3..........................................112 iihi
ih
ig  

   
 6.3..........
)(24
11
1)(24
11
2



 

iL
gI
E
ihiQihiQ
iL
gI
E
ihiQihiQih
ig
7.3..............................
)(12
2


iL
gI
E
ihiQ
ig

From Eqs. (3.1) to (3.3)
A similar expression may be obtained for the average joint rotation in the floor i-1 below,
but with subscripts (i+1) replaced by i, and I by (i-1).Referring to Fig.-2.20, the drift in
story i due to the joint rotations is
That is
Assuming that the girders in floors i-1 and i are the same, the story heights are the same,
and the average of Qi+1 and Qi-1 is equal to Qi
2.3.3.2 Story Drift due to Column Flexure
Referring to (Fig-2.19+2.20+2.10) in which the drift due to bending of the columns is
isolated by assuming the girders are rigid, the drift of the structure in story I is
𝛿𝑖𝑐 =
(𝑄𝑖𝑐ℎ𝑖2
12𝐸 ∑ 𝐼𝑖
… … … … … … . .3.8

26
  11.3.............................
)(12
2
)(12
2




ih
cI
E
ihiQ
iL
gI
E
ihiQ
S

From which,
𝛿𝑖𝑐 =
(𝑄𝑖𝑐ℎ𝑖2
12𝐸 ∑ (
𝐼 𝑐
ℎ
) 𝑖
… … … … … … . .3.9
2.3.3.3 Total Drift
The resulting drift in a single story i is the sum of the components.
S
 = g
 + C
 …………………………………………. 3.10
2.3.4 Correction of Excessive Drift
The typical proportioning of member size in tall rigid frame is such that girder flexure is
the major cause if drift, with column flexure a close second. Therefore increasing the
girder stiffness is usually the most effective and economical way of correcting excessive
drift. If the girder in any single bay is substantially smaller than the others level. It should
be increased first.
An estimate of the modified girder sizes required at level i to correct the drift in that story
can be obtained by neglecting the contribution due to overall bending and rewriting Eq.
(3.12) in the from

12.3..........................................
)(12
)(12
)(





ih
cI
E
ihiQ
L
iE
ihiQ
ih
Ig

In which ∂i is assigned the value of the allowable story drift. If the frame is un-usually
proportioned so that column
Flexure contributes a major part of the drift, Eq. (3.12) may be rewritten to allow an
estimate of the required size by interchanging ∑ (Ig/L)i and ∑(Ic/L)i.

27
A relative simple check on whether girders or columns should be adjusted first has been
proposed as follows (7.85).Compute for each joint across the floor levels above and
below the story whose drift is critical. The value of a parameter  where
13.3................................................................./)(
L
gI
h
iI

In which ∑ (Ig/L) refers to the girder connecting into the joint.
If a scan of the resulting value of  indicates that
1.  >> 0.5, adjust the girder sizes;
2.  << 0.5, adjust the column sizes;
3.  = 0.5, adjust both column and girder sizes.
This test should preferably be accompanied by an inspection of the drift components of
Eq. (3.11) to ascertain whether the allowable story drift is exceed by any one component
alone, as might occur in a grossly undersized initial design .If it is exceed by any one
component, whether as a result of undersized columns re of undersize beams, that
component must be remedied first.

28
3.1 INTRODUCTION
This chapter provides a detailed methodology of the whole structure of rigid frame
structure. The procedure use to a continuous medium method to analysis. The main
features can be summarized as below:
3.2 SELECT BUILDING PLAN
3.2.1 Building plan
A 70’ by 35’ and 15 story building structure was considered for this study. The height
of GF 12’ and remain each story is taken as 10’ making the total height of the structure
142’.
Figure 3.1- 14 Story building plan

29
3.2.2 Beam and Column Layout plan
Beam and Column layout sample picture is shown from the step in the analysis
Figure 3.2- Beam and Column Layout plan
3.2.3 Front Elevation
Figure 3.3- 14 Story Front Elevation

30
3.3 COLLECTION DESIGN DATA AND MATERIALS PROPERTIES
Table 1: Materials Properties For this Research Design data were collected from related
consultant firm
Length x Width ( 70 x 35 ) feet
No. of stores 14
Story height 1st
story 12 feet and remain story10 feet
Beam 01 ( 12 x 18 ) inch
Beam 02 ( 12 x 20 ) inch
Column 01 ( 1st
– 14th
storied ) ( 18 x 24 ) inch
Column 02 ( 1st
– 14th
Column 03 ( 1st
– 14th
Slab thickness 5 inch
Wind Load 210 Km/hr. for Dhaka city
Support condition Fixed
Per floor area 2450 Sft
Dead Load 100 Psf
Live Load 40 Psf
Wind Load From calculation ( by BNBC )
Beam clear cover 1.5 inch
Column clear cover 1.5 inch
Load combination .75(1.4DL+1.7LL+1.7WL)
Column type Tied
Thickness of al wall 5 inch
Yield strength of reinforcing bars, fy 60,000 psi
Concrete compressive strength, f’
c 4,000 psi
Normal density concrete having wc 150 pcf
Design code
Bangladesh National Building Code (
BNBC ), 2006
American Concrete Institute ( ACI )
Building Design Code, 2008

31
3.4 ANALYSIS OF THE STRUCTURE
3.4.1 By using ETABS software
Extended 3D analysis of Building System (ETABS) is an nonlinear analysis software
specially designed for building frame system. Dating back more than 30 years to the
original development of ETABS, structural analysis for buildings is easy and simple for
both lateral and gravity loads. In this chapter, a brief description about planning,
modeling, analysis and design of the twenty storied residential building is provided.
3.4.1.1 Grid system names:
Figure 3.4- Grid system names
3.4.1.2 Define material property data:
Figure3.5- Define material property data

32
3.4.1.3 Define load patterns:
Figure 3.6- Define load patterns
3.4.1.4 Frame in ETABS:
Figure3.7- Frame in ETAB

33
3.4.1.5 Load case and combination:
Figure 3.8- Load case and combination
3.4.1.6 Check model in ETABS:
Figure 3.9- Load case and combination

34
3.4.1.7 Run analysis after ETABS:
Figure 3.10 Run analysis after ETABS
3.4.1.8 Base reaction in ETABS:
TABLE 2: Base Reactions
Load Case/Combo FX FY FZ MX MY MZ
kip kip kip kip-ft kip-ft kip-ft
Dead 0.002 22.475 6757.024 118861.4674 -234805 772.6353
Live 0.002 29.967 1628.485 24298.1669 -56588.1257 1030.1804
FF 0 0 922.469 16127.9741 -32056.4231 0.000004256
PW 0 0 1844.939 32255.9483 -64112.8463 0.000008512
WALL 0 0 4004 71270.8335 -139139 -0.000047
Comb1 0.004 52.442 15156.917 262814.3902 -526702 1802.8157
EX X Max 0.007 75.094 10.572 5984.0332 370.7088 2600.6647
EX Y Max 0.007 75.094 10.572 5984.0332 370.7088 2600.6647
WIND X -365.969 0 0 -0.000003244 -34913.0259 6183.3669
WIND Y 0 -718.551 0 666735 0.00002452 -24970.2975

35
3.4.1.9 Maximum story drift earthquake Y direction (short direction)
Figure 3.11- Maximum story drift earthquake Y direction (short direction)
3.4.1.10 Maximum story drift earthquake in X (long direction)
Figure 3.12 Maximum story drift earthquake X direction (long direction)

36
3.4.2 By using Programming Language C++
C++ is a general purpose programming language that supports various computer
programming models such as object-oriented programming and generic programming. It
was created by Bjarne Stroustrup and, “Its main purpose was to make writing good
programs easier and more pleasant for the individual programmer.”
3.4.2.1 Earthquake load calculation
Calculate load from ETABS:
Total Load= DL+LL+FF+PW+WALL
= 6757.024+1628.485+922.469+1844.939+4004
= 15156.917 kip
=15157 kip
Earthquake Load Calculation:
Table 3: Seismic Zone Coefficient, Z ( BNBC, Table- 6.2.22)
Seismic Zone Zone Coefficient
1 0.075
2 0.15
3 0.25
Table 4: Structure Importance Coefficient, I &I' ( BNBC, Table-6.2.23)
Structure importance categories
Structure Importance Coefficient
I I'
Essential facilities 1.25 1.50
Hazardous facilities 1.25 1.50
Special occupancy structures 1.00 1.00
Standard occupancy structures 1.00 1.00
Low-risk structures 1.00 1.00

37
   
ih
ihtFV
ihiW
ihiWtFV
iF






W
R
ZIC
V 
3/2
25.1
T
S
Design base shear ,
Where
Z = Seismic zone coefficient = 0.15 [for zone-2]
I = Structural Importance coefficient = 1
R = Response modification coefficient = 12
C = Seismic coefficient =
In which S = Site coefficient for soil characteristics = 1.5
T = Fundamental period of vibration = 4
3
nt
hC
Where Ct = 0.073 [for RCC moment resisting frame]
hn= Building height in meter above base level = 160ft = 48.78 m
sec35.14
3
)48.78(073.04
3

n
h
t
CT [T > 0.7]
And
75.253.1
3/235.1
5.125.1
3/2
25.1



T
S
C (Ok)
Design base shear (for Dhaka) 29015157
12
53.1115.0



R
ZIC
V kips
Vertical distribution of lateral force:
Lateral force applied at story level i,
Since T > 0.7, Additional force to be add at roof, Ft =0.07TV = 0.07× 1.35 × 290 = 27.41
kip 0.25 V = (0.25×290) = 72.5kip (ok)

38
Where Ft = Concentrated lateral force considered at the top of the building in addition to
the force Fn = 27.41kip
i
h
ih
ih
iVF
i
F
22.0
12)13121110987654321(10
41.27290







3.4.2.2 Earthquake load at the story level
Table 5: Earthquake load at the story level (zone-II).
Story Height (Ft) F (kip)
1st
12 0.22×12 =2.64
2nd
22 0.22×22 =4.84
3rd
32 0.22×32 =7.04
4th
42 0.22×42 =9.24
5th
52 0.22×52 =11.44
6th
62 0.22×62 =13.64
7th
72 0.22×72 =15.84
8th
82 0.22×82 =18.04
9th
92 0.22×92 =20.24
10th
102 0.22×102 =22.44
11th
112 0.22×112 =24.64
12th
122 0.22×122 =26.84
13th
132 0.22×132 =29.04
14th
142 0.22×142 =31.24

39

    



 

iL
gI
E
ihiQihiQ
iL
gI
E
ihiQihiQih
ig
)(24
11
1)(24
11
2

3.4.2.3 Calculate story girder drift
Story drift due to girder flexure:
For 1st story
    12*
17.10
12
18*12
*30000*24
22*84.412*64.2
17.10
12
18*12
*30000*24
12*64.20*0
2
12
42.12
12
18*12
*30000*24
22*84.412*64.2
42.12
12
18*12
*30000*24
12*64.20*0
2
12
1 3333








    12*
58.9
12
18*12
*30000*24
22*84.412*64.2
58.9
12
18*12
*30000*24
12*64.20*0
2
12
58.9
12
18*12
*30000*24
22*84.412*64.2
58.9
12
18*12
*30000*24
12*64.20*0
2
12
3333








    12*
17.10
12
18*12
*30000*24
22*84.412*64.2
17.10
12
18*12
*30000*24
12*64.20*0
2
12
42.12
12
18*12
*30000*24
22*84.412*64.2
42.12
12
18*12
*30000*24
12*64.20*0
2
12
3333








=0.0000427634
Similarly same Equation 2nd to 14th stories calculate girder drift.
Table 6: Similarly same Equation 2nd to 14th stories calculate girder drift.
Story Height Girder Drift
2nd
22 0.000216919
3rd
32 0.000634582
4th
42 0.00140676
5th
52 0.00264424
6th
62 0.0044578

40
7th
72 0.00695824
8th
82 0.0102563
9th
92 0.0144629
10th
102 0.0196886
11th
112 0.0260444
12th
122 0.033641
13th
132 0.0425892
14th
142 0.0378555
3.4.2.4 Calculate story column drift
Story drift due to column flexure:
 


ih
cI
E
ihiQ
ic
)(12
2

For 1st story
  12*
12
12
324*20
*30000*12
212*64.2
1 
=0.0000066
Similarly same Equation 2nd to 14th stories calculate column drift
Table 7: Similarly same Equation 2nd to 14th stories calculate column drift
Story Height Column Drift
2nd
22 0.0000745607
3rd
32 0.000333748
4th
42 0.000990412
5th
52 0.00232719
6th
62 0.00470312
7th
72 0.0085536
8th
82 0.0143905
9th
92 0.0228019
10th
102 0.0344524
11th
112 0.0500831
12th
122 0.0705112
13th
132 0.0966306
14th
142 0.129411

41
3.4.2.5 Calculate story total drift
Table 8: Story drift and Total Drift
Story Height Total Drift (in)
1st
12 0.0000493634
2nd
22 0.000291479
3rd
32 0.00096833
4th
42 0.00239717
5th
52 0.00497143
6th
62 0.00916092
7th
72 0.0155118
8th
82 0.0246468
9th
92 0.0372647
10th
102 0.0541411
11th
112 0.0761275
12th
122 0.104152
13th
132 0.13922
14th
142 0.167267
3.4.2.1 Create a new project in Code Blocs:
Figure 3.13- Create a new project in Code Blocs

42
3.4.2.2 Write equation in different terms names in Code Block:
Figure3.14- Write equation in different terms names in Code Block
3.4.2.3 Build and run program:
Figure 3.15- Build and run program
3.4.2.4 Input equation value in Code Block
Figure 3.16- Input equation value in Code Block

43
3.4.2.5 Output equation value in Code Block:
Figure 3.17- Output equation value in Code Block
3.4.2.6 Equation drift with respect to height:
Table 9: Equation drift with respect to height:
Story Height(ft) Equations Drift (in)
GF 0 0
1st
12 0.0000493634
2nd
22 0.000291479
3rd
32 0.00096833
4th
42 0.00239717
5th
52 0.00497143
6th
62 0.00916092
7th
72 0.0155118
8th
82 0.0246468
9th
92 0.0372647
10th
102 0.0541411
11th
112 0.0761275
12th
122 0.104152
13th
132 0.13922
14th
142 0.167267

44
4.1 INTRODUCTION
Tall buildings can be analyzed by idealizing the structure into simple two-dimensional
or more refined three-dimensional continuums. Drift is an important consideration
for tall structure design and often dictates the selection of the structural system. In
the present study, three types of tall structures were analyzed for lateral loads, with
the parameters varied being a number of bays, bay width, the number of stories and
stiffness (e.g., dimensions of beams and columns).A structure whose resistance to
horizontal loading is provided by a combination of shear walls and rigid frames
categorized as a wall-frame structure. For wall-frame structures, the drift is depended
on total building height, the length of span, the dimension of the cross section of
beam and column, the intensity of load. Variation of Drift with the different
properties of wall and loading condition are rapid calculated by Microsoft excel. The
result variation of drift for different input value and their relationship given below:
4.2 RESULTS
4.2.1 Story drift table and curve by ETABS Software
Table 10: Story drift in ETABS (Y Direction):
Story Elevation(ft) Location Y-Dir(in)
ROOF 142 Top 0.942171
STOREY13 132 Top 0.903068
STOREY12 122 Top 0.857204
STOREY11 112 Top 0.804756
STOREY10 102 Top 0.746385
STOREY9 92 Top 0.682807
STOREY8 82 Top 0.614817
STOREY7 72 Top 0.543265
STOREY6 62 Top 0.469058
STOREY5 52 Top 0.393151
STOREY4 42 Top 0.316543
STORET3 32 Top 0.240254
STOREY2 22 Top 0.165268
STOREY1 12 Top 0.092219
GF 0 Top 0

45
Story Response - Maximum Story Displacement
Summary Description
This is story response output for a specified range of stories and a selected load case or
load combination.
Input Data
Name StoryResp2
Display Type Max story displ Story Range User Specified
Load Case EQ+Y Top Story ROOF
Output Type Not Applicable Bottom Story GF
Figure 4.1- Variation of drift with height of Building by using ETABS(Y Direction)

46
Table 11: Story drift in ETABS (X Direction)
Story Response Values
Story Elevation(ft) Location X-Dir(in)
ROOF 142 Top 0.692195
STOREY13 132 Top 0.674531
STOREY12 122 Top 0.650283
STOREY11 112 Top 0.619637
STOREY10 102 Top 0.583092
STOREY9 92 Top 0.541191
STOREY8 82 Top 0.494514
STOREY7 72 Top 0.443655
STOREY6 62 Top 0.389224
STOREY5 52 Top 0.331842
STOREY4 42 Top 0.272139
STORET3 32 Top 0.21074
STOREY2 22 Top 0.148208
STOREY1 12 Top 0.08474
GF 0 Top 0

47
Story Response - Maximum Story Displacement
Summary Description
This is story response output for a specified range of stories and a selected load case or
load combination.
Input Data
Name StoryResp2
Display Type Max story displ Story Range User Specified
Load Case EQ+X Top Story ROOF
Output Type Not Applicable Bottom Story GF
Figure 4.2- Variation of drift with height of Building by using ETABS(X Direction)

48
4.2.2 Variation of drift with height of Building by using programming Language
Figure 4.3- Variation of drift with height of Building by using programming Language
4.2.3 Comparison drift programming Language & ETABS:
Table 12: Story drift in programming Language and ETABS value:
Story Height Total Equations Drift (in) ETABS Drift (in)
GF 0 0 0
1st
12 0.0000493634 0.08474
2nd
22 0.000291479 0.148208
3rd
32 0.00096833 0.21074
4th
42 0.00239717 0.272139
5th
52 0.00497143 0.331842
6th
62 0.00916092 0.389224
7th
72 0.0155118 0.443655
8th
82 0.0246468 0.494514
9th
92 0.0372647 0.541191
10th
102 0.0541411 0.583092
11th
112 0.0761275 0.619637

49
12th
122 0.104152 0.650283
13th
132 0.13922 0.674531
14th
142 0.167267 0.692195
4.2.4 Variation of drift with Building height
Figure 4.4: Variation of drift with Building height
4.2.5 Variation of drift with number of span
Figure 4.5: Variation of drift with number of span

50
4.2.6 Variation of drift with dimension beam and column
Figure 4.6: Variation of drift with dimension beam and column
4.2.7 Variation of drift with shear value beam and column
Figure 4.7: Variation of drift with shear value beam and column

51
4.2.8 Variation of drift with height of Building by programming Language and ETABS:
Figure 4.8- Variation of drift with height of Building by programming Language and
ETABS
4.3. DISCUSSION
Considering all result and variation of drift we get different relationship between the
section properties and loading condition on building
Behold when
 Increase the height of Building increase the drift.
 Increase the load intensity on building increase the drift of building.
 increase the building length decrease the drift of building
 increase the width of building decrease the drift of building
We also know the allowable drift is (H/500) or (H/1000) this the height of building.

52
5.1 GENERAL
According to the specialist, there is possibility to occurrence of earthquake. In our
country, the numbers of high rise building is increasing here day by day due to
increasing population. Drift is a common phenomenon for high rise and this may
hamper the integrity of the structure and cause serious loss of life and properties in case
of a major earthquake. So every high rise structure should consider the effect of drift.
Then the loss of life and property will be attenuated. In these study regular shaped
structures has been considered only. Estimation of drift is carried out for rigid frame
structure, coupled shear wall structure and wall frame structure. This study indicates
that the drift on high rise structures has to be considered as it has a notable magnitude.
So every tall structure should include the drift due to earthquake load as well as wind
load. This chapter presents the answers to the main research questions and thereby
the conclusions to this research.
5.2 CONSOLATIONS
A theoretical investigation has been made to study the drift. The following conclusions
can be drawn from this theoretical study:
The drift of the structure increases with increase in the height of the structure. The drift
of 7-storey, 10-storey and 13-storey is increased due to increase in the height of the
structure. The drift at the same level increases with increase in the total height of the
structure.The drift of the structure decreases with the increase in the width of the structu
re.The earthquake acceleration increases with increase in the total height of the
structure. The earthquake acceleration increases with the increase in the width of the
structure at the along direction. The earthquake acceleration decreases with the
increase in the width of the structure at the width direction.
5.3 RECOMMENDATIONS
In this theoretical study only wind loads is considered. The following should be kept in
mind for further study. The drift and dynamic response due to seismic load should be
considered. The differential equation is only formed for coupled shear wall and wall-
frame structure, this equation should be formed for all type of structural system. The
program is only applicable for coupled shear wall; it should be modified for all type of
tall structure.

53
REFERENCES:
Page
1. https://www.researchgate.net/publication/265281589_Analysis_of_drift_
due_to_
wind_loads_and_earthquake_loads_on_tall_structures_by_programming
_language_c
1
2. https://aaltodoc.aalto.fi/bitstream/handle/123456789/23993/master_Holm
g%C3%A5rd_ Nicklas_2016.pdf?sequence=1&isAllowed=y 6
3. Taranath B.S. (1988), “Structural Analysis and Design of Tall
Buildings”.McGraw-Hill
Book Company 6
4. https://etd.lib.metu.edu.tr/upload/12607000/index.pdf 15
5. [Stafford Smith Bryan & Alex Coul, Tall Building Structures: Analysis
and Design. John Wiley & Sons, INC, pp. 148-149, 1991
22
6. https://www.scribd.com/doc/34629522/Thesis-on-Tall-Building 22

54
APPENDIX
#include <iostream>
#include <cmath>
using namespace std;
main()
{
float GL,Gd,Cd,CL,H,Q,QU,QL,HU,HL,Ig,Ic,L,L1,L2,L3,L4,L5,L6,L7,L8,L9;
double Dg,Dc,Td,E=30000;
cout << "Total drift calculate"<< endl;
cout << "structural type Rigid frame for girder"<< endl;
cout << "enter your choice the numbers of span L"<< endl;
cin >> L;
if (L==1)
{
cout << "Enter the value of shear force,Q=";
cin >> Q;
cout << "Enter the value of story height,H=";
cin >> H;
cout << "Enter the value of upper story shear force QU=";
cin >> QU;
cout << "Enter the value of lower story shear force,QL=";
cin >> QL;
cout << "Enter the value of upper story height,HU=";
cin >> HU;
cout << "Enter the value of lower story height,HL=";
cin >> HL;
cout << "Enter the cross sectional length of girder, GL=";
cin >> GL;
cout << "Enter the cross sectional width of girder Gd=";
cin >> Gd;

55
cout << "Enter the cross sectional length of column CL=";
cin >> CL;
cout << "Enter the cross sectional width of column Cd=";
cin >> Cd;
cout << "Enter the value of clear distance,L1=";
cin >> L1;
Ig=(GL*Gd*Gd*Gd)/12;
Ic=(CL*Cd*Cd*Cd)/12;
Dg=((H/2)*((QL*HL+Q*H)/(24*E*(Ig/L1))+(Q*H+QU*HU)/(24*E*(Ig/L1))))*12;
Dc=(((Q*(H*H))/(12*E*(Ic/H))))*12;
Td= Dg+Dc;
cout << " Girder drift =" <<Dg<<endl;
cout << " Column drift =" <<Dc<<endl;
cout << " Total drift of rigid frame structure=" <<Td<<endl;}
else if (L==2)
{
cin >> Q;
cin >> H;
cin >> QU;
cin >> QL;
cin >> HU;
cin >> HL;
cin >> GL;
cin >> Gd;

56
cin >> CL;
cin >> Cd;
cin >> L1;
cin >> L2;
Dg=((H/2)*((QL*HL+Q*H)/(24*E*(Ig/L1))+(Q*H+QU*HU)/(24*E*(Ig/L1))))*12+((
H/2)*((QL*HL+Q*H)/(24*E*(Ig/L2))+(Q*H+QU*HU)/(24*E*(Ig/L2))))*12;
Dc=((Q*(H*H))/(12*E*(Ic/H)))*12;
Td= Dg+Dc;
else if (L==3)
{
cin >> Q;
cin >> H;
cin >> QU;
cin >> QL;
cin >> HU;
cin >> HL;
cin >> GL;

57
cin >> Gd;
cin >> CL;
cin >> Cd;
cin >> L1;
cin >> L2;
cin >> L3;
H/2)*((QL*HL+Q*H)/(24*E*(Ig/L2))+(Q*H+QU*HU)/(24*E*(Ig/L2))))*12+((H/2)*(
(QL*HL+Q*H)/(24*E*(Ig/L3))+(Q*H+QU*HU)/(24*E*(Ig/L4))))*12;
Dc=((Q*(H*H))/(12*E*(Ic/H)))*12;
Td= Dg+Dc;
else if (L==4)
{
cin >> Q;
cin >> H;
cin >> QU;
cin >> QL;

58
cin >> HU;
cin >> HL;
cin >> GL;
cin >> Gd;
cin >> CL;
cin >> Cd;
cin >> L1;
cin >> L2;
cin >> L3;
cin >> L4;
(QL*HL+Q*H)/(24*E*(Ig/L3))+(Q*H+QU*HU)/(24*E*(Ig/L3))))*12+((H/2)*((QL*H
L+Q*H)/(24*E*(Ig/L4))+(Q*H+QU*HU)/(24*E*(Ig/L4))))*12;
Dc=((Q*(H*H))/(12*E*(Ic/H)))*12;
Td= Dg+Dc;

59
else if (L==5)
{
cin >> Q;
cin >> H;
cin >> QU;
cin >> QL;
cin >> HU;
cin >> HL;
cin >> GL;
cin >> Gd;
cin >> CL;
cin >> Cd;
cin >> L1;
cin >> L2;
cin >> L3;
cin >> L4;
cin >> L5;

60
L+Q*H)/(24*E*(Ig/L4))+(Q*H+QU*HU)/(24*E*(Ig/L4))))*12+((H/2)*((QL*HL+Q*
H)/(24*E*(Ig/L5))+(Q*H+QU*HU)/(24*E*(Ig/L5))))*12;
Dc=((Q*(H*H))/(12*E*(Ic/H)))*12;
Td= Dg+Dc;
else if (L==6)
{
cin >> Q;
cin >> H;
cin >> QU;
cin >> QL;
cin >> HU;
cin >> HL;
cin >> GL;
cin >> Gd;
cin >> CL;

61
cin >> Cd;
cin >> L1;
cin >> L2;
cin >> L3;
cin >> L4;
cin >> L5;
cin >> L6;
H)/(24*E*(Ig/L5))+(Q*H+QU*HU)/(24*E*(Ig/L5))))*12+((H/2)*((QL*HL+Q*H)/(24
*E*(Ig/L6))+(Q*H+QU*HU)/(24*E*(Ig/L6))))*12;
Dc=((Q*(H*H))/(12*E*(Ic/H)))*12;
Td= Dg+Dc;
else if (L==7)
{
cin >> Q;
cin >> H;

62
cin >> QU;
cin >> QL;
cin >> HU;
cin >> HL;
cin >> GL;
cin >> Gd;
cin >> CL;
cin >> Cd;
cin >> L1;
cin >> L2;
cin >> L3;
cin >> L4;
cin >> L5;
cin >> L6;
cin >> L7;

63
*E*(Ig/L6))+(Q*H+QU*HU)/(24*E*(Ig/L6))))*12+((H/2)*((QL*HL+Q*H)/(24*E*(Ig
/L7))+(Q*H+QU*HU)/(24*E*(Ig/L7))))*12;;
Dc=((Q*(H*H))/(12*E*(Ic/H)))*12;
Td= Dg+Dc;
cout << " Enter the value of Td=" <<Td <<endl;}
else if (L==8)
{
cin >> Q;
cin >> H;
cin >> QU;
cin >> QL;
cin >> HU;
cin >> HL;
cin >> GL;
cin >> Gd;
cin >> CL;

64
cin >> Cd;
cin >> L1;
cin >> L2;
cin >> L3;
cin >> L4;
cin >> L5;
cin >> L6;
cin >> L7;
cin >> L8;
*E*(Ig/L6))+(Q*H+QU*HU)/(24*E*(Ig/L6))))*12+((H/2)*((QL*HL+Q*H)/(24*E*(Ig
/L7))+(Q*H+QU*HU)/(24*E*(Ig/L7))))*12+((H/2)*((QL*HL+Q*H)/(24*E*(Ig/L8))+
(Q*H+QU*HU)/(24*E*(Ig/L8))))*12;
Dc=((Q*(H*H))/(12*E*(Ic/H)))*12;
Td= Dg+Dc;
cout << " Total drift of rigid frame structure=" <<Td<<endl;} }

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