SEISMIC ANALYSIS OF BRACED STEEL

FRAMES
Thesis submitted in partial fulfillment of the requirements for the degree of
BACHELOR OF TECHNOLOGY
in
CIVIL ENGINEERING
by
RATNESH KUMAR
Roll no. 110CE0075
Under the guidance of
Prof.K.C.Biswal

DEPARTMENT OF CIVIL ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA, ORRISA – 769008
May, 2014
 NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA – 769008, ORISSA
INDIA
CERTIFICATE

This is to certify that the thesis entitled “SEISMIC ANALYSIS OF BRACED STEEL
FRAMES” submitted by Mr. RATNESH KUMAR in partial fulfilment of the requirements for
the award of Bachelor of Technology Degree in Civil Engineering with specialization in
Structural Engineering at the National Institute of Technology Rourkela is an authentic work
carried out by him under my supervision.
To the best of my knowledge, the matter embodied in the thesis has not been submitted to any
other University/Institute for the award of any degree or diploma.

Place: NIT Rourkela

Date: May 12, 2014
Prof. K.C.BISWAL
Department of Civil Engineering
NIT Rourkela, 769008
 ACKNOWLEDGEMENT

I am thankful to the Dept. of Civil Engineering, NIT ROURKELA, for giving me the
opportunity to execute this project, which is an integral part of the curriculum in B.Tech
program at the National Institute of Technology, Rourkela.
I am thankful to my project guide Prof. K.C.BISWAL, whose encouragement, guidance and
support from the initial to the final level enabled me to develop an understanding of the subject.
I am thankful to Prof N.Roy, Head of Civil Engineering Department, for all the facilities
provided to successfully complete this work. I am also very thankful to all the faculty members
of the department, especially Structural Engineering specialization for their constant
encouragement, invaluable advice, inspiration and blessing during the project.
I thank Dr. Robin Davis, Associate Professor, Dept of Civil Engineering, for all the advice and
help he provided for my project.
I would like to thank Dr. Pradip Sarkar, Associate Professor, Dept of Civil Engineering, for all
his support and encouragement throughout my stay here.
I also thank Dr. Asha patel, Associate Professor, Dept of Civil Engineering, for all the advice
and suggestions she provided for my project work.
Last but not the least, I take this opportunity to extend my deep appreciation to my family and
friends, for all that they meant to me during the crucial times of the completion of my project.

RATNESH KUMAR
 ABSTRACT

The study of braced steel frame response is widely studied in many branches of Structural
engineering. Many researchers have been deeply studying these structures, over the years,
mainly for their greater capacity of carrying external loads. Every Special moment resisting
frames undergo lateral displacement because they are susceptible to large lateral loading. The
problems associated with this are the P-∆ effect and the ductile and brittle failure at beams and
columns connections . As a consequence, engineers have increasingly turned to braced steel
frames as a economical means for earthquake resistant loads.
The present study consist of two models. Model 1 is a Steel Moment Resisting Frame (SMRFs)
with concentric bracing as per IS 800-2007. Cross bracing, diagonal bracing and an unbraced
frame is considered for study. Model 2 consist of two Steel Moment Resisting Frame with
similar V type bracing and Inverted V (Chevron bracing) configuration, but with varying height.
Performance of each frame is studied through Equivalent static analysis, Response Spectrum
analysis, and linear Time History analysis.
 TABLE OF CONTENTS
Title Page No
Acknowledgements ………………………………………………………………
Abstract…………………………………………………………………………...
Tables of Contents………………………………………………………………..
List of Figures…………………………………………………………………….
List of Tables……………………………………………………………………..
CHAPTER 1. INTRODUCTION TO THESIS
1.1 Introduction 1
1.2 Objectives 2
1.3 Methodology 2
1.4 Scope of the present study 2
1.5 Organization of the thesis 3
CHAPTER 2. LITERATURE REVIEW
2.1 General 4
2.2 Literature review 4-5
CHAPTER 3. A REVIEW OF ANALYSIS
3.1 Equivalent static analysis 6-8
3.2 Response spectrum analysis 8-9
CHAPTER 4. STRUCTURAL MODELLING
4.1 Introduction 10
4.2 Frame geometry 10-12
4.3 Frame designs 12-14
CHAPTER 5. STRUCTURAL RESPONSE
5.1 MODEL 1 15-25
5.1.1 Lateral load profile 15
5.1.2 Base shear comparison 15
5.1.3 Peak story shear 16
5.1.4 Story drift of the model 16-19
 5.1.5 A comparison of shear force, bending moment and axial force
5.1.5.1 Shear force 19-21
5.1.5.2 Bending moment 21-22
5.1.5.3 Axial force 22-23
5.2 MODEL 2
5.2.1 Base shear comparison 23
5.2.2 Story drift of the model 23-24
CHAPTER 6. SUMMARY AND CONCLUSION 25-26
Reference 27
 LIST OF FIGURES
Fig no. page.
1.1 Inelastic response of steel moment resisting frame 1
3.1 Seismic zones of India 6
3.2 A graph representing Average response spectral coefficient 10
3.3 A graph representing Maximum Modal response vs modal frequency 10
4.1 Plan of Model 1 11
4.2 Front elevation of Model 1 with X bracing system 11
4.3 Side elevation of Model 1 with X bracing system 11
4.4 3D view of Model 1 with single Diagonal bracing system 12
4.5 Model 2 plane frame larger height 12
4.6 Model 2 plane frame smaller height 12
4.7 A graph representing ground acceleration for Imperial earthquake 14
4.8 A graph representing ground acceleration used by IS Code 14
4.9 A graph representing ground acceleration for San Franscisco earthquake 14
5.1 A graph representing Lateral load profile for Model 1 15
5.2 A graph representing story drift of model 1 for Equivalent static analysis 16
5.3 A graph representing story drift of model 1 for response spectrum analysis 17
5.4 A graph representing a comparision of story drift of model 1, without bracing
for all three earthquake loading 17
5.5 Two graphs representing a comparision of story drift of model 1, all bracing
configuration for IS code and San franscisco earthquake loading 18
5.6 A graph representing Shear force in columns under response spectrum analysis 19
5.7 A graph representing shear force in columns under IS code earthquake loading 20
5.8 A graph representing bending moment in columns under response spectrum analysis 21
5.9 A graph representing bending moment in columns under IS code earthquake loading 22
5.10 A graph representing maximum axial force at column ends under IS code
 Earthquake loading 23
5.11 A graph representing comparision of base shear in model 2 24
5.12 A graph representing story drift of model 2 for response spectrum analysis 24
5.13 A graph representing story drift of model 2 for IS code earthquake loading 25
 LIST OF TABLES
Table no page no.
4.1 Different parameters of the three earthquake loading used for
Time History analysis 13
5.1.2 Base shear comparison as calculated by IS code 1893:2002 and
modal analysis 16
5.1.3 Peak storey shear for Response spectrum analysis 17
5.1.4 Story drift for Time history analysis 18
5.1.5.1 Shear force in columns for Time history analysis 20
5.1.5.2 Bending moment in columns for Time history analysis 22
5.1.5.3 Axial force in columns for Time history analysis 23
5.2.2 Story drift for Time history analysis 24
CHAPTER 1

INTRODUCTION

OBJECTIVES

METHODOLOGY

SCOPE OF PRESENT STUDY

ORGANIZATION OF THE THESIS

1.INTRODUCTION
In the present time, Steel structure plays an important role in the construction industry. Previous
earthquakes in India show that not only non-engineered structures but engineered structures need
to be designed in such a way that they perform well under seismic loading. Structural response
can be increased in Steel moment resisting frames by introducing steel bracings in the structural
system. Bracing can be applied as concentric bracing or ecentric bracing. There are ‘n’ number
of possibilities to arrange steel bracings, such as cross bracing ‘X’, diagonal bracing ‘D’, and ‘V’
type bracing.
Steel moment resisting frames without bracing, inelastic response failure generally occurs at
beam and column connections. They resist lateral forces by flexure and shear in beams and
columns i.e. by frame action. Under severe earthquake loading ductile fracture at beams and
columns connections are common. Moment resisting frames have low elastic stiffness. P-∆ effect
is an another problem associated with such structures in high rise buildings.

FIG 1.1 (ref. B.Tech thesis 2012, Praval Priyaranjan,dspace@nitrkl.ac.in)

So, to increase the structure response to lateral loading and good ductility properties to perform
well under seismic loading concentric bracings can be provided. Beams, columns and bracings
are arranged to form a vertical truss and then lateral loading is resisted by truss action. Bracings
allow the system to obtain a great increase in lateral stiffness with minimal added weight. Thus,
they increase the natural frequency and usually decrease the lateral drift. They develop ductility
through inelastic action in braces. Failure occurs because of yielding of truss under tension or
buckling of truss under compression. These failures can be compensated by use of Buckling
Reinforced Braced frame (BRBs) or Self Centering Energy Dissipating frames (SCEDs).
The present study will clearly estimate the advantage of concentrically braced steel frames over
Steel moment resisting frames. A simple computer based modeling in Staad Pro. Software is

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performed for Equivalent static analysis, Response spectrum analysis, and linear Time history
analysis subjected to earthquake loading.

1.1 OBJECTIVES

Following are the main objective of the present study:

a) To investigate the seismic performance of a multi-story steel frame building
• When unbraced and then with different bracing arrangement such as cross bracing
‘X’ and diagonal bracing using Equivalent Static analysis, Response Spectrum
analysis and linear Time History analysis.
• Under different earthquake loading and loading combinations.
b) To investigate the seismic response of a multi story steel frame building
• Under same bracing configuration but with varying number of story i.e. with
varying height of the building.

1.2 METHODOLOGY

a) A thorough literature review to understand the seismic evaluation of building structures

and application of Equivalent Static analysis, Response Spectrum analysis, and linear
Time History analysis.
b) Seismic behaviour of steel frames with various concentric bracings and ecentric bracing
geometrical and structural details.
c) Modeling the steel frame with various concentric bracing by computer software Staad
pro.
d) Carry out Equivalent Static analysis, Response Spectrum analysis and linear Time
History analysis on the models and arrive at conclusion.

1.3 SCOPE OF THE PRESENT STUDY

In the present study, modeling of the steel frame under the three analysis mentioned above
using Staad Pro software is done and the results so obtained are compared. Conclusions are
drawn based on the tables and graphs obtained .

1.4 ORGANIZATION OF THE THESIS

The thesis is organized as per detail given below:

Chapter 1: Introduces to the topic of thesis in brief.

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Chapter 2 : Discusses the literature review i.e. the work done by various researchers.

Chapter 3 : Equivalent Static analysis, Response Spectrum analysis, and linear Time History
analysis have been discussed briefly.

Chapter 4 : Modeling the structure under loading as prescribed in IS 1893-2002.

Chapter 5 : Results and discussion.

Chapter 6 : Conclusion.

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CHAPTER 2

LITERATURE REVIEW
 LITERATURE REVIEW

2.1 INTRODUCTION
This chapter deals with a brief review of the past and recent study performed by researchers on
seismic analysis of braced steel frames. A detailed review of each literature would be difficult to
address in this chapter. The literature review focusses on concentrically braced frames, failure
mode generally observed in moment resisting frames and bracings, brace to frame connections,
local buckling and plastic hinge formation. The recent study of use of Buckling reinforced
bracing (BRBs) and Self centered energy dissipating frames (SCEDs) is also mentioned.
2.2 LITERATURE REVIEWS
 Tremblay et al. ,(ASCE)0733-9445(2003)

Tremblay et al. performs an experimental study on the seismic performance of

concentrically braced steel frames with cold-formed rectangular tubular bracing system.
Analysis is performed on X bracing and single diagonal bracing system. One of the
loading sequence used is a displacement history obtained from non linear dynamic
analysis of typical braced steel frames. Results were obtained for different cyclic
loading and were used to characterize the hysteretic response, including energy
dissipation capabilities of the frame. The ductile behaviour of the braces under different
earthquake ground loading are studied and used for design applying the codal
procedures. Simplified models were obtained to predict plastic hinge failure and local
buckling failure of bracing as a ductility failure mode. Finally, Inelastic deformation
capabilities are obtained before failure of moment resisting frame and bracing members.

 Khatib et al. (1988)

The failure mode generally observed in special moment resisting frames with bracing
system is fracture of bracings at the locations of local buckling or plastic hinges.
Significant story drift can occur at a single story and this research shows how the
failure mode occurs and how the failure is concentrated entirely on single floor . So, this
is one of the limitations of using moment resisting frames with bracing system.

 Seismic response of Steel braced reinforced concrete frames by K.G.Vishwanath in

International journal of civil and structural engineering (2010)
A four storey building was taken in seismic zone 4 according to IS 1893:2002 . The
performance of the building is evaluated according to story drift. Then the study is
extended to eight story and twelve story. X type of steel bracing is found out to be most
efficient.

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 Seismic response assessment of concentrically braced steel frame buildings (The 14th
World conference on earthquake engineering October 12-17, 2008, Beijing, China)
Improvement of performance based design and analysis procedure for better
understanding of conventionally used concentrically braced frame and buckling
restrained braced frames is discussed.

 Hanson and Martin (1987); Kelly et al. (2000)

The typical failure mode experienced by special moment resisting frames with bracing
ie. Damage to braces, brace to frame connections, columns and with base plates were
studied.

 Ghobarah A. et al., (1997)

The study shows that the inter story drift can also be considered as a means to provide
uniform ductility over the stories of the building. A story drift may result in the
occurrence of a weak story that may cause catastrophic building collapse in a seismic
event. Uniform story ductility over all stories for a building is usually desired in seismic
design.

 Christopoulus et al. (2008)

An advanced cross bracing system has been used in University of Toronto called
(SCEDs) Self centering energy dissipating frames. Alike, Special moment resisting
frames and Buckling reinforced braced frames, they also dissipate energy, but they have
self centering capabilities which reduce residual building deformation after major
seismic events.

 Tremblay et al. (2008)

An extensive analytical study is performed to compare the Buckling restrained braced
frames with self centering energy dissipating frames . According to the results, the
residual deformation of SCED brace frame systems is negligible under low and
moderate hazard levels and is reduced significantly under MCE or maximum
consudered earthquake level.

5
Chapter 3

A REVIEW OF ANALYSIS

Equivalent Static Analysis

Response Spectrum Analysis

Time History Analysis

3.1 EQUIVALENT STATIC ANALYSIS – AN OVERVIEW
The equivalent static method is the simplest method of analysis. Here, force depend upon the
fundamental period of structures defined by IS Code 1893:2002 with some changes. First, design
base shear of complete building is calculated, and then distributed along the height of the
building, based on formulae provided in code. Also, it is suitable to apply only on buildings with
regular distribution of mass and stiffness.
Following are the major steps in determining the seismic forces:
Determination of Base shear
For determination of seismic forces, the country is classified in four seismic zones:
Fig 3.1 shows seismic zones of India (ref., IS 1893:2002)

The total design lateral force or design base shear along any principal direction is determined by
the expression:

6
 V = AW (3.1)
Where,
A = design horizontal seismic coefficient for a structure
W = seismic weight of building
The design horizontal seismic coefficient for a structure A is given by :
A = (ZISa)/ 2Rg (3.2)
Z is the zone factor in Table 2 of IS 1893:2002 (part 1). I is the importance factor,
R is the response reduction factor, Sa/g is the average response acceleration coefficient for rock
and soil sites as given in figure 2 of IS 1893:2002 (part 1). The values are given for 5% damping
of the structure.

FIG 3.2
T is the fundamental natural period for buildings calculated as per clause 7.6 of IS 1893:2002
(part1).
Ta = 0.075h0.75 for moment resisting frame without brick infill walls
Ta = 0.085h0.75 for resisting steel frame building without brick infill walls
Ta = 0.09h/√d for all other buildings including moment resisting RC frames
h is the height of the building in m and d is the base dimension of building at plinth level in m.

Lateral distribution of base shear

The total design base shear has to be distributed along the height of the building. The base shear
at any story level depends on the mass and deformed shape of the building. Earthquake forces
tend to deflect the building in different shapes, the natural mode shape which in turn depends
upon the degree of freedom of the building. A lumped mass model is idealized at each floor,

7
which in turn converts a multi storyed building with infinite degree of freedom to a single degree
of freedom in lateral displacement, resulting in degrees of freedom being equal to the number of
floors.
The magnitude of lateral force at floor (node) depends upon:
• Mass of that floor
• Distribution of stiffness over the height of the structure
• Nodal displacement in given mode
IS 1893:2002 (part 1) uses a parabolic distribution of lateral force along the height of the
building. Distribution of base shear along the height is done according to this equation:
Qi = Wi hi2 / ∑j=1n (Wjhj2) (3.3)

Where:
Qi = design lateral force at floor i
Wi = seismic weight at floor i
hj = height of floor I measured from foundation
n = number of stories in the building or the number of levels at which masses are located.

3.2 RESPONSE SPECTRUM ANALYSIS - AN OVERVIEW

Response spectrum analysis is a procedure for calculating the maximum response of a structure
when applied with ground motion. Each of the vibration modes that are considered are assumed
to respond independently as a single degree of freedom system. Design codes specify response
spectra which determine the base acceleration applied to each mode according to its period (the
number of seconds required for a cycle of vibration).
Having determined the response of each vibration mode to the excitation, it is necessary to obtain
the response of the structure by combining the effects of each vibration mode because the
maximum response of each mode will not necessarily occur at the same instant, the statistical
maximum response, where damping is zero, is taken as sum of squares (SRSS) of the individual
responses.

8
The results of response spectrum are all absolute extreme values and so they need to be
combined as they do not correspond to any equilibrium state nor they take place at the same
time. There are several methods to execute this , one of them being the (SRSS) method, Square
root of sum of squares method. In this method , the maximum response in terms of given
parameter, G (displacement, acceleration, velocity) may be estimated through the square root of
sum of m modal response squares, contributing to global response:
G = ∑mn=1 (Gn)2

3.3 TIME HISTORY ANALYSIS- AN OVERVIEW

It is a linear or non linear analysis of dynamic structural response under the loading which may
differ according to specified time function. The basic governing equation for the dynamic
equation for dynamic response of multi degree of freedom system is given by equation 3.4.
The given equation can be solved by numerical integration method such as Runge-kutta method,
Newmark integration method and wilson – Ɵ method. The staad pro. Software calculates the
structural responses at each time step and thus solves the governing time equation.

9
Chapter 4

STRUCTURAL MODELLING

Introduction

Frame Geometry

Frame Design
 STRUCTURAL MODELLING
4.1 INTRODUCTION
The study in this thesis is based on basically on linear time history analysis of steel frames
with concentric bracing models. Different configurations of frames are selected such as cross
bracing, diagonal bracing and V and inverted V bracing and analyzed. This chapter presents a
summary of various parametres defining the computational models, the basic assumptions and
the steel frame geometry considered for this study.
4.2 FRAME GEOMETRY
Model 1 is an asymmetric plan . Model 2 is a symmetric plan and hence a single plane
frame is considered to be representative of building in one direction.
For Model 1, plan is represented in fig4.1.

And the front elevation for Cross bracing model is represented in fig4.2.

10
Side elevation for the model is represented as FIG 4.3:

A 3D view of the typical steel frame with diagonal bracing is represented as FIG 4.4

11
Model 2 is a symmetric plan, and hence plane frame used for analysis. Variation is both the
brame is height of the building.

FIG 4.5 FIG 4.6

The bay width is 2m and the story height is 3m at each floor level.

12
 4.3 FRAME DESIGN
The building frame used in this study is assumed to be located in Indian seismic zone IV
with medium soil conditions. Seismic loads are estimated as per IS 1893:2002 and design of steel
elements are carried as per IS 800 (2007) standards. The characterstic strength of steel is
considered 415 Mpa. The gravity loading consists of the self weight of the structure, a floor load
of 3kN/m2 on every floor except the roof , the roof floor load is taken 2kN/m2. The design
horizontal seismic coefficient (Ah ) is calculated as per IS 1893:2002
Ah = ZI/2R,
Where, seismic zone factor, Z = 0.24, Importance factor I = 1.0, Response reduction factor, R =
3.0.The design base shear (VB) is calculated as per IS 1893:2002
VB = Ah.Sa/g.W
Period for analysis = 0.085H0.75 , which is found to be 0.647 sec.
Estimated design base shear from above formula is found to be 18.12 kN for without bracing. By
SRSS method, in response spectrum analysis, the total base shear was found to be 22.84
considering 6 modes of participation for without bracing. A comparision between them will be
shown later.
Every beam used in the both the models is ISMC 200. Every column used in the model is ISMC
300 and for bracings angle section are used. Every bracing is an angle section IS 75x75x5.

TIME HISTORY LOADING

The three earthquake used for analysis are as follows:
Table 4.1
Records Component Magnitude Epicentral Duration Time step PGA PGV PGA/PGV
distance (s) for response (g) (m/s)
(km) computation
(s)
1979 HVP 225 6.53 19.81 37.745 0.005 0.2476 0.4765 0.519
Imperial
valley – 06
IS code - - - 40.0 0.01 1.0 1.0405 0.961
1987 San GGP010 5.28 11.13 39.725 0.005 0.1073 0.0377 2.846
Franscisco

13
 FIG 4.7

FIG

FIG 4.9

14
 CHAPTER 5

STRUCTURAL RESPONSE under

different bracing
configuration and loading

Model 1

Model 2
 SEISMIC RESPONSE OF STEEL FRAME UNDER DIFFERENT
BRACING CONFIGURATION AND LOADING

5. 1 MODEL 1
5.1.1 LATERAL LOAD PROFILE

FIG 5.1
Cross bracing have the highest lateral stiffness as compared to diagonal bracing, and obviously
to frame without bracing. A increase in stiffness attracts larger inertia force and this is evident
from the graph.

5.1.2 BASE SHEAR COMPARISION OF MODAL ANALYSIS (RESPONSE SPECTRUM

ANALYSIS) WITH IS CODE 1893:2002 CALCULATED DESIGN BASE SHEAR
EQUIVALENT STATIC RESPONSE SPECTRUM
ANALYSIS (kN) ANALYSIS (kN),
Modal participation factor
considered till 6th mode,
SRSS method

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 WITHOUT BRACING 18.12 22.84

WITH DIAGONAL BRACING 22.24 23.99

WITH CROSS BRACING 24.64 24.27

From table, it is evident that the design base shear provided by the code is less as compared to by
modal analysis. A 26% increase in design base shear is observed in moment resisting frame
without bracings. It can also be concluded that by increasing the lateral stiffness of the steel
frame, base shear of the frame will obviously increase.
5.1.3 PEAK STORY SHEAR FOR RESPONSE SPECTRUM ANALYSIS
FLOORS WITHOUT WITH DIAGONAL WITH CROSS
BRACING BRACING BRACING
5 5.97 6.06 6.41
4 12.75 13.25 13.89
3 17.97 18.79 19.40
2 21.43 22.41 22.82
1 22.84 23.99 24.27
BASE 22.84 23.99 24.27

5.1.4 STORY DRIFT OF THE MODEL

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 FIG 5.2
On an average, 87% decrement in story drift is observed by installing cross or diagonal bracing
on the model as compared to that of the model without bracing. Now, cross bracing and diagonal
bracing undergo almost same drift. This is because, one of the diagonal of cross bracing remains
inactive during the analysis.

FIG 5.3
A decrease in the story drift is observed in both the analysis in upper floors. This can be infered
from that the loading profile of the model. The roof load is lower as compared to the load on
other floors. Hence the loading profile shows an increment till the 4th floor and then falls on the
5th floor leading to a decrement of drift on the upper floors.
On an average, 28% decrement is observed by installing cross bracing instead of diagonal
bracing. Cross bracing is obviously more laterally stiffer than diagonal bracing, and hence the
decrement is observed.
Table 5.1.4 Story drift in X direction in mm for Time History analysis
Earthquake Imperial IS code San franscisco

Bracing X D W X D W X D W

Base 0 0 0 0 0 0 0 0 0

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Story 1 0.018 0.044 2.482 1.207 1.933 9.788 0.096 0.187 1.189

Story 2 0.042 0.096 6.466 2.831 4.369 25.72 0.225 0.421 3.129

Story 3 0.067 0.142 10.062 4.54 6.664 40.51 0.361 0.640 4.933

Story 4 0.091 0.176 12.626 7.455 8.577 51.44 0.488 0.821 6.256

Story 5 0.111 0.198 14.039 8.609 9.919 57.65 0.591 0.948 7.021

FIG 5.4
Time history is a linear analysis and hence the effect of decreased roof loading doesn’t affect the
final drift profile. IS code ground loading has the highest peak ground acceleration as compared
to the other two earthquake loadings. Therefore, highest story drift is observed in IS Code as
compared to the other two earthquake loading.

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 X D W

FIG 5.5
Cross bracing has the most lateral stiffness and hence in both the earthquake loading it shows
least story drift.

5.1.5 A COMPARISION OF SHEAR FORCE, BENDING MOMENT AND AXIAL

FORCE AT THE CORNER COLUMNS
Bracings change the stiffness of the moment resisting frames. Hence, it has a significant effect
on the shear force and bending moment of columns as they take most of the lateral loading acting
as a truss member i.e, they can take only tension or compression. Here, the values of shear force,
bending moment and axial force of the corner columns at the 1st bay is observed and discussed.
5.1.5.1 Shear force comparision

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 W X

FIG 5.6
Table 5.1.5.1 A COMPARISION OF SHEAR FORCE IN COLUMNS UNDER TIME
HISTORY ANALYSIS (values in kN)
EARTHQUAKE IMPERIAL IS CODE SAN FRANSCISCO
BRACING X D W X D W X D W
COLUMN AT BASE 1.02 1.67 3.73 1.62 4.00 17.06 0.51 0.70 1.51
COLUMN@1ST 0.80 1.14 2.29 0.30 2.07 13.33 0.70 0.75 0.67
FLOOR
COLUMN @2ND 0.87 1.15 1.61 0.10 2.08 11.04 0.72 0.77 0.37
FLOOR
COLUMN@3RD 0.77 1.06 0.76 0.28 1.77 6.35 0.73 0.77 0.03
FLOOR
COLUMN@4TH 0.89 0.89 0.68 0.8 1.20 1.10 0.87 0.93 0.87
FLOOR

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 X

FIG 5.7
Both the graphs, represent a lower value of shear force for cross bracing as compared to diagonal
bracing and frame without bracing. For both the analyses, it can be concluded that by increasing
the bracing, or by increasing the lateral stiffness shear force in columns tend to decrease.

5.1.5.2 Bending moment comparision

FIG 5.8

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Table 5.1.5.2 A COMPARISION OF BENDING MOMENT IN COLUMNS BY TIME
HISTORY ANALYSIS
EARTHQUAKE IMPERIAL IS CODE SAN FRANSCISCO
BRACING TYPE X D W X D W X D W
COLUMN AT 1.61 3.17 10.32 4.62 8.77 43.19 0.40 0.84 4.68
BASE
COLUMN AT 1ST 1.16 1.64 3.69 0.35 3.10 21.44 1.00 1.04 1.15
FLOOR
COLUMN AT 2ND 1.29 1.62 1.50 0.05 2.87 10.74 1.05 1.09 0.16
FLOOR
COLUMN AT 3RD 1.22 1.40 0.30 0.66 0.41 4.48 1.11 1.14 0.75
FLOOR
COLUMN AT 4TH 1.16 1.18 0.20 0.56 0.35 3.34 1.09 1.12 0.65
FLOOR

FIG 5.9
Both the graphs, represent a lower value of bending moment for cross bracing as compared to
diagonal bracing and frame without bracing. So, by increasing the lateral stiffness of the moment
resisting frame, increasing the bracing bending moment force applied at the columns tend to
decrease.

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5.1.5.3 Axial force comparision
EARTHQUAKE IMPERIAL IS CODE SAN FRANSCISCO
BRACING TYPE X D W X D W X D W
COLUMN AT BASE 76.36 33.5 34.17 171.14 114.77 61.28 49.25 48.27 41.98
COLUMN AT 1ST 60.62 28.7 23.09 138.18 88.53 38.78 40.97 40.50 34.70
FLOOR
COLUMN AT 2ND 43.54 23.4 23.06 96.81 50.0 17.71 31.38 31.37 26.57
FLOOR
COLUMN AT 3RD 26.07 16.5 15.86 56.30 4.24 2.89 20.28 20.86 17.41
FLOOR
COLUMN AT 4TH 9.43 7.6 6.71 20.69 2.87 2.66 8.06 9.03 7.20
FLOOR

FIG 5.10
The graph represent a higher value for axial force at column ends for cross bracings followed by
diagonal bracing and frame without bracing. So, with increase in bracing axial forces in the
columns tend to increase.

5.2 MODEL 2
5.2.1 BASE SHEAR COMPARISION FOR BOTH THE MODELS WITH VARYING HEIGHT
UNDER RESPONSE SPECTRUM ANALYSIS (SRSS METHOD)

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 FIG 5.11
1 represents smaller height of building and 2 represents larger height. The total base shear found
out is smaller for smaller height building as compared to larger height. This can again be
attributed to the fact that the larger ht. model is more stiffer than than the smaller ht. and hence
the variation is expected.
5.2.2 STORY DRIFT COMPARISION FOR RESPONSE SPECTRUM ANALYSIS

FIG 5.12
Table 5.2.2 STORY DRIFT FOR TIME HISTORY ANALYSIS

MODEL SMALLER HEIGHT LARGER HEIGHT

EARTHQUAKE IS IMPERIAL SAN IS IMP SAN

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BASE 0 0 0 0 0 0
1 STORY 1.424 0.262 0.146 2.090 0.093 0.225
2 STORY 3.058 0.562 0.311 4.575 0.200 0.490
3 STORY 5.043 0.928 0.503 7.005 1.463 0.745
4 STORY 7.404 1.366 0.718 10.113 2.106 1.063
5 STORY 8.854 1.636 0.718 14.354 2.977 0.346
17.905 3.710 0.435
20.216 4.172 0.498

FIG 5.13
From the graph it is evident that at the same floor level the story drift of larger height model is
found to be greater than that of the smaller. This can also be attributed to the fact that the larger
ht. model is more stiffer than the smaller one, and hence the variation.

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CHAPTER 6
SUMMARY

CONCLUSION
 SUMMARY AND CONCLUSION
SUMMARY
The selected frame models were analysed using response spectrum and non linear time history
analysis. The 1st model was an asymmetric plan with a without braced moment resisting frame
and then it was braced with diagonal bracing and cross bracing. The bracings increased the
stiffness and the frequency of the frame. Cross bracing is more stiffer than diagonal bracing.
Hence, for cross bracing maximum base shear was obtained as compared to diagonally braced
model and model without bracing. Bracing decrease the lateral displacement of the moment
resisting frame. More stiffer the frame least is the story drift. Bracings also increase the shear
force and bending moment capacity of the columns. In a laterally more stiff frame, the columns
are subjected to less shear force and bending moment and an increased axial force at their ends.
Model 2 was a symmetric plan and a plane frame was used for analysis was performed. The
frame had same V and inverted V bracing configuration but varied in height. A larger height
model was more stiffer as compared to smaller one and hence had more base shear. Also at the
same story, it was observed that the story drift in the larger height building was much more
compared to smaller height. Larger height building is more stiffer and hence the variation. So, as
the height of the model is increased, a bracing system will decrease the story drift but an
increased height will increase the story drift leading to the problems like P-∆ effect.

CONCLUSION
• Braced steel frame have more base shear than unbraced frames.
• Cross bracing undergo more base shear than diagonal bracing.
• Bracings reduce the lateral displacement of floors.
• Cross bracing undergo lesser lateral displacement than diagonal bracing.
• Cross braced stories will have more peak story shear than unbraced and diagonal braced
frames.
• Axial forces in columns increases from unbraced to braced system.
• Shear forces in columns decrease from unbraced to braced system. Diagonal braced
columns undergo more shear force than cross braced.
• Bending moment in column decreases from unbraced to braced system. Diagonal braced
column undergo more bending moment than cross braced frame.
• Under the same bracing system and loading, system with larger height or more number of
storys will have more base shear than the smaller one.
• Under the same bracing system and loading, system with larget height or more number of
storys will undergo large lateral displacement on the same storys than the smaller one.

26
 REFRENCES

• Tremblay, R.; et al., Performance of steel structures during the 1994 Northridge
earthquake, Canadian Journal of Civil Engineering, 22, 2, Apr. 1995, pages 338-360.
• Khatib, I. and Mahin, S., Dynamic inelastic behavior of chevron braced steel frames,
Fifth Canadian Conference on Earthquake Engineering, Balkema, Rotterdam, 1987,
pages 211-220.
• AISC (American Institute of Steel Construction), Seismic Provisions for Structural Steel
Buildings, Chicago, 1997.
• AISC (American institute of Steel Construction).(1999), load and resistance factor design
specification for structural steel buildings, chicago.
• A. Meher Prasad: “Response Spectrum”, Department of Civil Engineering, IIT Madras.
• David T. Finley, Ricky A. Cribbs: “Equivalent Static vs Response Spectrum – A
comparision of two methods”.
• IS 1893 (Part 1):2002, “Criteria for Earthquake Resistant Design of Structures”.
• Hassan, O.F., Goel, S.C.(1991).”Modelling of bracing members and seismic behaviour of
concentrically braced steel frames”.
• Tremblay, R.,Timler,P.,Bruneau,M.,and Filiatrault,A. (1995). “Performance of steel
structures during 17 january,1994 Northridge earthquake.”

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