CHAPTER-1

INTRODUCTION

1.1 General:

Mankind has always had a fascination for height and throughout our history, we

have constantly sought to metaphorically reach for the stars. From the ancient pyramids to

today’s modern skyscraper, a civilization’s power and wealth has been repeatedly

expressed through spectacular and monumental structures. Today's the symbol of economic

power and leadership is the skyscraper. There has been a demonstrated competitiveness

that exists in mankind to proclaim to have the building in the world.

This undying quest for height has laid out incredible opportunities for the building

profession. From the early moment frames to today's ultra-efficiency mega-braced

structures, the structural engineering profession has come a long way. The recent

development of structural analysis and design software coupled with advances in the finite

element method has allowed the creation of many structural and architecturally innovative

forms. However, increased reliance on computer analysis is not the solution to the

challenges that lie ahead in the profession. The basic understanding of structural behavior

while leveraging on computing tools are the elements that will change the way structures

are designed and built.

The design of skyscrapers is usually governed by the lateral loads imposed on the

structure. As buildings have gotten taller and narrower, the structural engineering has been

increasingly challenged to meet the imposed drift requirements while minimizing the

architectural impact of the structure. In response to this challenge, the profession has

proposed a multitude of lateral schemes that are now expressed in tall buildings across the

globe.

This study seeks to understand the evolution of the different lateral system that has

emerged and its associated structural behavior, for each lateral scheme examined, its

advantages and disadvantages will be looked at. The lateral schemes explored are the

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moment frames, the braced frames, braced-rigid frame and the B – frames with outriggers.

1.2 Structural Concept:

The key idea in conceptualizing the structural system for a narrow tall building is to

think of it as a beam cantilevering from the earth (fig1.1). The lateral directed force

generated, either due to wind blowing against or due to the inertia forces induced by

ground shaking, tends both to snap it (shear), and push it over (bending).

Fig. 1.1 Structural concept of tall building

Therefore, the building must have a system to resist shear as well as bending. In

resisting shear forces, the building must not break by shearing off (fig1.2a) and must not

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strain beyond the limit of elastic recovery (fig 1.2b).

Fig 1.2 Building shear resistance; (a) Building must not break (b) Building

must not deflect excessively in shear

Similarly, the system resisting the bending must satisfy three needs (fig 1.3).The

building must not overturn from the combined forces of gravity and lateral loads due to

wind or seismic effects; it must not break by premature failure of columns either by

crushing or by excessive tensile forces: its bending deflection should not exceed the limit

of elastic recovery.

In addition, a building in seismically active region must be able to resist realistic

earthquake forces without losing its vertical load carrying capacity.

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Fig 1.3 Bending resistance of building (a) Building must not overturn; (b) Columns

must not fail in tension or compression; (c) Bending deflection must not be excessive.

In the structure's resistance to bending and shear, a tug-of-war ensues that sets the

building in motion, thus creating a third engineering problem; motion perception or

vibration. If the building sways too much, human comfort is sacrificed, or more

importantly, non-structural elements may break resulting in expensive damage to the

building contents and causing danger to the pedestrians.

A perfect structural form to resist the effects of bending, shear and excessive

vibration is a system possessing vertical continuity ideally located at the farthest extremity

form the geometric center of the building. A Concrete chimney is perhaps an ideal, if not

an inspiring engineering model for a rational super-tall structural form. the quest for the

best solution lies in translating the ideal form of the chimney into a more practical skeletal

structure.

With the provision that a tall building is beam cantilevering from earth, it is evident

that all the columns should be at the edges of the plan, thus the plan shown in fig 1.4 (b)

would be preferred over the plan in fig 1.4 (a). Since the arrangement is not always

possible, it is of interest to study how the resistance to bending is affected by the

arrangement. of columns in plan. We will use two parameters, Bending Rigidity Index BRI

and Shear Rigidity Index SRI, first published in Progressive Architecture, to explain the

efficiency of structural systems.

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Fig 1.4 Building plan forms; (a) Uniform distribution of columns

(b) Columns concentrated at the edges.

The Ultimate possible bending efficiency would be manifest in a square building

which concentrates all the building columns into four corner columns as shown in fig 1.5

(a) since this plan has maximum efficiency it is assigned the ideal Bending Rigidity Index

(BRI) of 100.The BRI is the total moment of inertia of all building columns about the

centroidal axes participating as an integrated system.

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The traditional tall building of the past, such as Empire State building, used all

columns as part of the lateral resisting system. For columns arranged with regular bays, the

BRI is 33 (fig 1.5b).

Fig 1.5 Column Layout and bending rigidity index (BRI); (a) Square building with

Corner columns BRI=100; (b) Traditional building of 1930's BRI = 33.

A modern tall building of the 1980'd and 90’s have closely spaces exterior columns

and long clear span to the elevator core in an arrangement called a "tube". If only perimeter

columns are used to resist the lateral loads, the BRI is 33. An example of this plan type is

the World Trade Center in New York City fig 1.5 (c). The seat Tower in Chicago uses all

its columns as part of the lateral system in a configuration called a "bundled tube". It also

has a BRI of 33 (fig 1.5d).

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Fig 1.5 Column Layout and bending rigidity index (BRI); (c) Modern tube building

BRI=100; (d) Sear Tower BRI = 33.

The Citicorp tower fig 1.5 (e), uses all of its columns as part of its lateral system,

but because columns could not be placed in the corner, its BRI is reduced to 31. If the

columns were moved to the corners, the BRI would be increased to 56 (fig 1.5f). Because

there are eight columns in the core supporting the loads, the BRI falls short of 100.

Fig 1.5 Column Layout and bending rigidity index (BRI); (e) City Corp Tower

BRI=31; (f) Building with corner and core columns BRI = 56, (g) Southwest tower

BRI=63.

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The plan of Bank of southwest tower, a proposed tall building in Houston, Texas,

approaches the realistic ideal for bending with a BRI of 63 (fig 1.5f). The corner columns

are split and displaced from the corners to allow generous views from office interiors.

In order for the columns to work as elements of an integrated system, its necessary

to interconnect hem with an effective shear-resisting system. Let us look at some of the

possible solutions and their relative Shear Rigidity Index (SRI).

The ideal shear system is a plate or wall without openings with an ultimate Shear

Rigidity Index (SRI) of 100 (fig 1.6a). The second-best shear system is a diagonal web

system at 45 degree angles which has an SRI of 62.5 (fig 1.6b). A more typical bracing

system which combines diagonals and horizontals but use more material is shown in (fig

1.6c). Its SRI depends on the slope of the diagonals and has a value of 31.3 for the most

usual brace angle of 45 degrees.

The most common shear systems are rigidity joined frames as shown in (fig 1.6d-g).

The efficiency of the frame as measured by its SRI depends on the proportions of

member’s lengths and depths. A frame with closely spaced columns, like used in all four

faces of a square building has high shear rigidity and doubles up as an efficient bending

configuration, The resulting configuration is called as "tube” and is the basis of

innumerable tall building includes the world's two most famous buildings, the Sears tower

and the World trade center.

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Fig 1.6 Tall Building Shear System; (a) Shear wall system; (b) Diagonal web system;

(c) Web system with diagonal and horizontals; (d)-(f) Rigid Frames.

In designing the lateral bracing system for building it is important to distinguish

between a "wind design" and "seismic design". The building must be designed for

horizontal forces generated by wind or seismic loads, whichever is greater, as prescribed by

the building code or site-specific study accepted by the building Official However, Since

the actual Seismic forces, when they are occur, are likely to be significantly larger then

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code-prescribed forces, seismic design requires material limitations and detailing

requirements in addition to strength requirements. Therefore, for buildings in high-seismic

zones, even when wind forces govern the design, the detailing and proportioning

requirements of seismic resistance must also be satisfied. The requirements get

progressively higher.

CHAPTER-2

LITERATURE REVIEW

2.0 General:

As the height of the building increases the effect of lateral loads (seismic and wind

loads) become very predominant. This chapter will discuss the previous work done on this

subject. Many of the scholars have studies on performance of RC frame with different type

of bracings, shear walls etc. Some of the papers are discussed below.

2.1 Literature Review:

A brief literature review is presented on this topic as follows.

Wang et. al (2012), explored the effect of different types of bracing like steel bracing and

bracing with concrete filled steel tube struts are introduced in RC frame structures to

evaluate the seismic performance of building. These models are analyzed with base-shear

method, superposition of modal responses method and time history method respectively.

The results show that the steel-stiffness and the top displacement of the fame structure

decreases significantly. The models are analyzed in Etabs software.

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Jiang et. al (2012), Conducted seismic performance evaluation of a steel-concrete hybrid

frame tube in high rise building. In this study a non linear time history analysis is done on a

tall building with the hybrid frame-tube structure. The analytic model of the structure is

established with the aid of PERFORM_3D program. The 61 storey office building with the

seismic intensity of eight is taken foe analysis. The hybrid superstructure consists of an

outer steel reinforced concrete frame and a steel reinforced concrete core tube. The elastic

dynamic characteristics, the global displacement responses, the performance levels and the

deformation demand-to-capacity ratios of structural components under different levels of

earthquake are presented. Numerical analysis results indicate that the hybrid structure has

good seismic performance.

Richards (2011), has studied seismic behavior of irregular high-rise RC structure using

eccentrically braces. In this study, an anti-seismic analysis of two structures is performed to

evaluate their torsion vibration response in earthquake. The self-vibration character and

relative displacement between different floors are compared. A 25 storey multi-functioned

building is considered under seismic intensity 7 and soil type III, the earthquake resistance

rank is II level. The eccentricity braces are made of Q235 rolled wide flange H-beam, and

welded with embedded parts in reinforced concrete members. It is found that eccentrically

braces properly can reduce the response of torsional vibration and other seismic response of

the structures efficient. It is verified that this method is a simple and economic one.

Ali and Moon (2007), Presented a study of structural development in tall buildings, in this

paper reviews of evolution of tall building developments for the primary structural systems,

a new classification-interior structures and exterior structures are presented. While most

representative structural systems for tall buildings are discussed, the emphasis in this

review paper is on current trends such as outrigger systems and diagrid structures.

Auxiliary damping aerodynamic and twisted forms, which directly or indirectly affect the

structural performance of tall buildings, are reviewed. Finally, the future of structural

developments in tall buildings is envisioned briefly.

Kim and Choi (2004), Has compared the Special Concentric Braced Frames (SCBFs) and

Ordinary Concentric Braced Frames (OCBFs) for evaluating the over strength, ductility

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and the response modification factor by performing pushover analysis of model structures

with various storey’s and span lengths. The results were compared with those from

nonlinear incremental dynamic analysis. According to the analysis results, the response

modification factors of model structures computed from pushover analysis were generally

smaller than the values given in the design codes except in low-rise SCBFs. The generally

incremental dynamic analysis generally matched well with those obtained from pushover

analysis.

Maheri and Akbari (2003), has explained the seismic behavior factor, R, for steel X-

braced and knee braced RC buildings. The R factor components including ductility

reduction factor and over strength factor are extracted from inelastic pushover analysis of

brace-frame system of different heights and configurations. The effects of some parameters

influencing the value of R factor, including the higher of the frame, shear of bracing system

from the applied load and the type of building system are investigated. It is found that the

two latter parameters have a more localized effect on the R values and their influence does

not warrant generalization at this stage. However, the height of this type of lateral load-

resisting system has a profound effect on the R factor, as it directly affects the ductility

moment-resisting RC frame dual system for different ductility demands.

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CHAPTER-3

METHODOLOGY

3.1 Loading and Design Criteria:

In this study an office building of 10 storey’s and 30 storey’s having same plan

dimension and column arrangement is selected. The building is 33m X 33m in plan with

columns spaced at 5.5m from center to center. A floor to floor height 3.3m is assumed. The

location of the building assumed to be at imphal. An elevation and plan view of a typical

structure is shown in fig 2.1 (a) and 2.1 (b). The facade system of the structure is also

assumed to transfer the wind loading applied to the main lateral load carrying system (e.g.

moment frame, bracing) as point loads. This allowed the application of the wind loading to

node points in the Etabs model and eliminated local deformation that might occur at the

windward face columns.

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Fig 3.1 (a) Building plan dimension (Common to all floors, all models; units 'm')

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Fig 3.1 (b) Storey Height (Common to all models; unit 'm')

3.2 Live load:

Live load is assumed as per IS 875 (part 2-imposed loads) table 1.Since the building

is assumed to be a office building the live load was taken as KN/m2 (office building with

no separate storage) for all floors except the top floor where the live load is taken as

2KN/m2. Apart from live load a uniform cladding load of 7KN/m is assumed for all floors

for peripheral beams only. Also a slab dead load is applied assuming a 125mm thick

concrete slab on all floors (to avoid complicated load calculations involving composite

floor system). Those slabs panels are assumed as rigid diaphragm. Also a SDL of 2KN/m 2

is assumed on all floors to take care of furnishing and other things.

3.3 Wind load:

Wind load in this study is established in accordance with IS 875 (part 3-wind

loads). The location selected is Imphal. The basic wind speed as per the code is Vb=47m/s.

The coefficient K1 and K2 are taken as 1.0. The terrain category is taken as category 4 with

structure class B for 10 storey models and class C for thirty storey models. Taking internal

pressure coefficient as +0.2 the net pressure coefficient Cp (windward) works out as +0.9

and Cp (leeward) as -0.05 based on h/w and l/w ratio of table 4 of IS 875 (part 3). Using

the above data the ETABS automatically interpolates the coefficient K3 and eventually

calculates lateral wing load at each storey. Same load is applied along positive and negative

X & Y axis one direction at a time to determine the worst loading condition.

3.4 Quake load:

Quake load in this study is established in accordance with IS 1893 (part 1)-2002.

The seismic zone of the previously selected location in zone 5 (Z=0.36). The importance

factor (I) of the building is taken as 1.0. The site is assumed to be hard/rocky site (type I).

The response reduction factor R is taken as 5.0 for all frames.

The fundamental time period (Ta) of all frames was calculated as per clause 7.6.1 of

the before mentioned code.

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Ta =0.085 * h0.75 .........................................Eq. 3.1

Based on the above data the Etabs calculates the design horizontal seismic

coefficient (Ah) using the Sa/g value from the appropriate response spectrum. The Ah value

calculated is utilized in calculating the design seismic base shear (VB) as,

VB= Ah * W .........................................Eq. 3.2

Where, W=Seismic weight of building.

The design seismic bear shear so calculated is distributed along the height of the

building as per the expression,

Qi = VB * (Wi * hi2) * (Wj * hj

2)-1 .........................................Eq. 3.3

Where, Qi = Design lateral force at floor i.

Wi = Seismic weight of the floor i.

hi = height of the floor I measured from base

j= 1 to n, n being no. of floors in building at which masses are located.

3.5 Building Design and Optimizing Criteria:

The structural component of the building viz. beams, columns and braces are

designed as per IS 800-1984. The following load combinations are used to determine the

maximum stress in the steel sections.

i. DL+LL

ii. DL+LL+WL(x or y)

iii. DL+LL+EL(x or y)

iv. DL+WL(x or y)

v. DL+EL(x or y)

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A stress ration limit of 0.9 is used in design of all the members to ensure safe design.

The following limitations are used for optimization of structure:

The lateral displacement on any floor in case of wind loads does not exceed H/500.

The lateral displacement on any floor in case of quake loads does not exceed H/250.

The stress ratio shall be lie between 0.7-0.9 in case of members designed for

strength.

3.6 Optimization procedure:

After modeling the structure and appropriate loads in Etabs, the members are

assigned with initial sections for analysis. After running the analysis for first time accurate

forces in each member is known. The structure is then designed as per IS 800-1984. The

members initially assigned may or may not satisfy the above guidelines, therefore, the

member sections are either increased or decreased suitably to meet lateral displacement and

stress ratio criterion. The second iteration of analysis is then performed with new set of

sections to find new forces in members. The iteration involved in analysis and subsequent

design are repeated number of times till the lateral displacement and stress ratio is satisfied.

In some type of structures like moment frames, the strength design of members is not

sufficient to limit the lateral displacement. It requires a stiffness design wherein the

members are ensured sufficient stiffness to ensure lateral displacements are within the

limits. In such case the stress ratio limit of 0.7-0.9 cannot be satisfied, therefore, this

guideline is omitted

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CHAPTER-4

LATERAL SYSTEMS

4.1 Rigid frames:

A frame is considered rigid when its beam-to column connection has sufficient

rigidity to hold virtual unchanged the original angles between intersecting members. A

rigid frame high-rise structure typically comprises of parallel or orthogonally arranged

bents consisting of columns and girders with moment resistant joints. Resistance to

horizontal loading is provided by the bending resistance of columns, girders and joints. The

continuity of the frame also assist in assisting gravity loading more efficiently by reducing

the positive moment in the center span of girders.

Typical deformations of a moment resistant frame under lateral are indicated in (fig

4.1). The point of contra flexure is normally located near the mid height of the columns and

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mid-span of the beams. The lateral deformation of a frame as will be seen shortly is partly

due to frame racking, which might be called shear sway, and partly to column shortening.

The shear-sway component constitutes approximately 80 to 90 percent of the overall lateral

deformation of the frame. The remaining component of deformation is due to column

shortening, also called cantilever or chord drift component.

Fig 4.1 (a) Response of rigid frame to lateral loads; (b) flexural deformation of beams

and columns due to non deformability of connections.

The size of member in a moment-resisting frame is often controlled by stiffness

rather than strength to control drift under lateral loads. The lateral drift is a function of both

the column stiffness and beam stiffness. In a typical application, the beam spans are 6m to

9m while the storey heights are usually between 3.65m to 4.27m. Since the beam spans are

greater that the floor heights, the beam moment of inertia needs to be greater than the

column inertia by the ratio of beam span to story heights for an effective moment-resisting

frame.

Moment-resisting frames are normally efficient for building upto 20 stories in

height. The lack of efficiency for taller buildings is due to the moment resistance derived

primarily through flexure of its members.

The connections in steel moment resisting frames are important design elements.

Joint rotation can account for a significant portion of the lateral away. The strength and

ductility of the connection are also important considerations especially for frames designed

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to resist seismic loads.

4.1.2 Deflection Characteristics:

The lateral deflection components of rigid frame can be thought of as being caused

by two components similar to the deflection components of prismatic cantilever beam. One

component can be likened to the bending deflection and other to the shear deflection.

Normally for prismatic members when the span-to-depth ratio is greater than 10 or so, the

bending deflection is by far the more predominant component. Shear deflections contribute

a small portion to over all deflection and are therefore generally neglected in calculating

deflections. The deflection characteristics of a rigid frame, one the other hand, are just

opposite; the component analogue to the beam shear deflection dominates the deflection

picture and many amounts to as much as 80% of the total deflection, while the remaining

20% come from the bending component. The bending and shear components of deflection

are usually referred to as the cantilever bending and frame racking each with its own

distinct deflection mode.

A) Cantilever bending component:

This phenomenon is also known as chord-drift. The wind load acting on the vertical

face of the building causes an overall bending moment on any horizontal cross-section of

the building. This moment, which reaches its maximum value at the base of the building,

causes the building to rotate about the leeward columns and is called the overturning

moment. In resisting the overturning moment, the frame behaves as a vertical cantilever

responding to bending through the axial deformation of columns resulting in compression

in the leeward columns and tension or uplift in the windward columns. The columns

lengthen on the windward face of the building and shorten on the leeward face. This

Column length change causes the building to rotate and results in the chord drift

component of the lateral deflection, as shown in (fig 4.2a).

Because of the cumulative rotation up the height, the storey drift due to overall 20

bending increasing with height, while that due to racking tends to decrease. Consequently

the contribution to storey drift from overall bending may, in the uppermost stories, exceed

that from racking. The contribution of overall bending to the total drift, however, will

usually not exceed 10 to 20 percent of that of racking, except in very tall, slender, rigid

frames. Therefore the overall deflected shape of medium-rise frame usually has a shear

configuration.

For normally proportioned rigid frame, as a first approximation, the total lateral

deflection can be thought of as a combination of three factors.

1. Deflection due to axial deformation of columns (15 to 20 %).

2. Frame racking due to beam rotation (50 to 60 %).

3. Frame racking due to column rotation (15 to 20 %).

In addition to the above, there is a fourth that contributes to the deflection of the

frames which is due to deformation of the joint. In a rigid frame, since the size of joint are

relatively small

compared to column

and beam length, it is

a common practice to

ignore the effect of

joint

deformation. However, its contribution buildings drift in very tall buildings consisting of

closely spaced columns and deep spandrels could be substantial, warranting a close study.

This effect is called panel zone deformation.

B) Shear racking component:

This phenomenon is analogous to the shear defection in a beam and is caused in

rigid frame by the bending of beam and columns. The accumulated horizontal shear above

any storey of rigid frame is resisted by shear in the columns of that storey (fig 4.3b). The

shear causes the storey-height columns to bend in double curvature with points of contra

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flexure at approximately mid-storey--height level the moment applied to join from the

column above and below are resisted by the attached girders, which also bend in double

curvature, with points of contra flexure at approximately mid-span. Those deformations of

columns and girders allow racking of the frame and horizontal deflection in each storey.

The overall reflected shape of a rigid frame structure due to racking has a shear

configuration with the concavity upwind, a maximum inclination near the base and a

minimum inclination at the top, as shown in the (fig 4.2b).

Fig 4.2 Rigid frame deflection: (a) forces and deformation caused by external

overturning moment; (b) Forces and deformation caused by external shear.

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This mode of deformation accounts for about 80% of the total sway of structure. In

a normally proportioned rigid-frame building with columns spacing at about 10.6m to

12.2m and a storey height of 3.65m to 4m beam flexural contributes about 50 to 65% of the

total sway. The column rotation, one the other hand, contributes about 10 to 20 % of the

total deflection. This is because in most unbraced frames the ratio of columns stiffness to

girder stiffness is very high, resulting in larger joint rotations of girders. So generally when

it is desired to reduce the deflection of unbraced frames, the place to start adding stiffness

is in the girders. However, in non-typical frames, such as those that occur in framed tubes

with column spacing approaching floor-to-floor height, it is necessary to study the relative

girder and column stiffness before making adjustments in the member properties.

4.1.3 Calculation of drift:

Calculation of drift due to the lateral loads is a major task in the analysis of tall

building frames. Although it is convenient to consider the lateral displacements to be

composed of two distinct components, whether or not the cantilever or the rocking

component dominates the deflection is dependent on factors such as height-to-width ratio

of the building and the relative rigidity of column to girder. Unless the building is very tall

or very slender, it’s usually the racking component that dominates the deflection picture. A

simple method for determining the deflection of a tall building is to assume that the entire

structure acts as a vertical cantilever in which the axial stress in each column is

proportional to its distance from the centroidal axis of the frame. This approach assumes

that the frame is infinitely stiff with respect to the longitudinal shear and hence

underestimates the deflection.

However, the above tedious calculation can be minimized using a simple stick

model. In this method a single cantilever is modeled equal to the height of the given

structure, having same number of storey. The moment of inertia of each storey in the stick

model is set equal to the sum of second moment of all column cross sections presenting the

actual model.

For example, if a1,a2,......an represents the cross sectional area of all the columns in the

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given storey similarly if d1,d2,......dn, represents the distance of these columns from the neutral

axis of the structure, then M.I. of a storey in stick model is given by;

I = a1*d12+a2*d2

2+a3*d32+...........................+an*dn

2

The calculated 'I' values for each storey using the above formula are used for stick

model in Etabs. The lateral loads either wind or seismic, whichever is critical are also

modeled at respective storey. An analysis performed with this data will yield in chord drift

component of the moment frame. The shear racking component due to combined column

and girder flexure can also be estimated using the same technique. However, instead of

using the 'I' value, shear areas Av are used calculated following formula.

Av=30*[H*(1/{I/H) col.+1/{I/L}gir.)]-1

4.2 Braced Frames:

Rigid frame systems are not efficient for buildings taller than about 30 stories

because the shear racking components of deflection due to the bending of columns are

girders causes the drift to be too large. A braced frame attempts to improve upon the

efficiency of rigid frame by virtually eliminating the bending of columns and girders. This

is achieved by adding web members such as diagonals or chevron braces. The horizontal

shear is now primarily absorbed by the web & not by the columns. The webs carry the

lateral shear predominantly by the horizontal component of axial action allowing for nearly

a pure cantilever behavior.

4.2.1 Physical Behavior:

In simple term, braced frames may be considered as cantilevered vertical trusses

resisting lateral loads primarily through the axial stiffness of columns and braces. The

columns act as a chord in resisting the overturning moment, with tension in the windward

column and compression in the leeward column. The diagonals and the girders work as the

web members in resisting the horizontal shear, with diagonals in axial compression are

tension depending upon their direction inclination. The girders act axially, when the system

is a fully triangulated truss. They undergo bending also when the braces are eccentrically

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connected to them. Because the lateral load on the building is reversible, braces are

subjected in turn, to both compression and tension; consequently, they are most often

designed for more stringent case of compression.

The effect of the chords axial deformations on the lateral deflection of the frame is

to tend to cause a "flexural" configuration of the structure, that is, with concavity download

and a maximum slope at the top (fig 4.3a). The effect of the web member deformations,

however, is to tend cause a "shear" configuration of the structure (i.e., with downwind and

a maximum slope at the top; (fig 4.3b). The resulting deflected shape serves with a

resultant configuration depending on their relative magnitudes, as determined mainly by

the type of bracing; nevertheless, it is the flexural deflection that most often dominates the

deflection characteristics.

Fig 4.3 Braced frame deformation: (a) Flexural deformation;

(b) Shear deformation; (c) Combined configuration

The role of web members in resisting shear can be demonstrated by following the

path of the horizontal shear down the braced bent. Consider the typical braced frames,

shown in (fig 4.4 a-e), subjected to an external shear force at the top. In (fig 4.4a), the

diagonal in each storey is in compression, causing the beam to be in axial tension;

therefore, the shortening of the diagonal and extension of the braces connecting to each

beam end are in equilibrium horizontally when the beam carrying insignificant axial load.

In (fig 4.4c), half of each beam is in compression while the other half is in tension.

In (fig 4.4d), the braces are alternately in compression and tension while the beams remain

basically unstressed. And finally in (fig 4.4e), the end parts of the beam are in compression

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and tension with the entire beam subjected to double curvature bending, observed that with

a reversal in the direction of the horizontal load, all actions and deformations in each

member will also be reserved.

Fig 4.4 Load path for horizontal shear through web numbers: (a) single diagonal

bracing (b) X-bracing; (c) chevron bracing; (d) single-diagonal, alternate direction

bracing; (e) Knee bracing.

Fig 4.5 Gravity Load path: (a) single diagonal single direction bracing (b) X-bracing;

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In braced frame the principal function of web members is to resist the horizontal

shear forces. However, depending upon the configuration of the bracing, the web members

may pick up substantial compressive forces as the columns shorten vertically under gravity

loads. Consider for example, the typical bracing configuration shown in (fig 4.5). As the

columns in (4.5 a,b), shorten, the diagonals are subjected to compression forces because the

beams at each end of the braces are effective in resisting the horizontal component of the

compressive forces in the diagonal. At a first glance this may appear to be the case for the

frame shown in (fig 4.4 c). However, the diagonal shown in (fig 4.5 c) will not attract

significant gravity forces because there is no triangulation at the ends of beams where

diagonals are not connected (nodes A and D, in fig 4.5c). The only horizontal resistant at

the beam end is by the bending resistance of columns, which usually is of minor

significance in the overall behavior, similarly in (fig 4.5 d), the vertical restraint from the

bending stiffness of the beam is not large; therefore as in previous case, the diagonal

experience only negligible gravity forces.

4.2.2 Calculation of Drifts:

In considering the deflected shape of a braced frame, it is important to appreciate

the relative influence of the flexure and shear mode contributions, due to column axial

deformations whereas shear deformations occur due to diagonal and girder deformations.

4.2.3 Calculation of Flexural Component:

The flexural component can be calculated using the same computer model

discussed earlier in chapter 3. the only change that is to be incorporated is that previously

in moment frame the entire column structure contributed to lateral resistance, however, in

case of braced frames only the column attached to braces core provides lateral resistance.

Thus only second moment of c/s area of columns attached to brace core is considered rather

than the complete structure.

4.2.4 Calculation of shear component:

The following table 4.1 shows the formulas to be used for calculating the shear

deformations due to girder and diagonal deformations. It should be noticed that some forms 27

of bracing arrangement induce axial forces or moments in girders, while some leave the

girders significantly unstressed.

Table 4.1 Shear deformation formulas

Type of brace Shear deflection per storey

Single Diagonal

(Alternate)

V d3

E L2 * Ad

Double Diagonal V d3

2E L2 * Ad

4.3.1 Rigid-Braced Frames:

Even for building in the range of 10-15 stories unreasonably heavy columns result if

lateral bracing is confined to the building service core because the available depth for

bracing is usually limited. In addition, high uplift forces that may occur at the bottom of

core columns can present foundation problems. In such instances an economical structural

solution can be arrived at by using rigid frames in conjunction with the core bracing

system. Although deep girders and moment connections are required for frame actions,

rigid frame are often preferred because they are least objectionable from the interior space

planning consideration. Often times, architecturally, it may be permissible to use the

spandrels and closely spaced columns on the building because usually the column will not

interfere with the space planning and the depth of spandrel need not be shallow for passage

of air-conditioning duct. A schematic floor plan of a building use these concept is shown if

(fig 5.1 a).

28

Fig

4.6

Types of rigid brace frames; (a) braced core and perimeter frames.

For slender building with the height-width ratios in excess of 5, an interacting

system of moment frame and the braces becomes uneconomical if braces are placed within

the building core. In such situation, a good structural solution is to be separate the bracing

of the full width of the building facades if such a system does not compromise the

architecture of the building. If it does, then a possible solution is to be moved the full depth

bracing to the interior of the building. Such a bracing concept is shown in (fig 4.6 d), in

which moment frames located at the building facade interact with interior-braces bends.

Those bend stretch out for the full width of the building form giant K braces, resisting,

overturning the shear force by developing predominantly axial forces.

29

Fig 4.6 (d) Full-depth interior bracing and exterior frames,

All of the bracing systems and any number of their vibrations can be used either

singly or in combination and can be made interact with the moment-connected frames. The

magnitude of their interaction can be controlled by the varying the relative stiffness of the

various structural elements to achieve an economical structural system.

4.3.2 Physical Behavior:

If the lateral deflection patterns of braced and un-braced frames are similar, the

lateral loads can be distributed between the two systems according to their relative

stiffness. However, in normally proportioned buildings the un-braced and braced frames

deform with their own characteristic shapes, necessitating that we study their behavior as a

unit.

Insofar as the lateral-load-resistance in concerned, the rigid and braced frames can

be considered as two distinct units. The basis of the classification is the mode of

deformation of unit when subjected to lateral loading. The deflection characteristics of

braced framed are similar to those of a cantilever beam. Near the bottom the vertical truss

is very stiff; therefore the floor-floor deflection will be less than half the values near the

top. Near the top the floor-floor deflection increase rapidly maintained due to the

cumulative effect of chord drift. The column strains at the bottom of the building produce a

deflection at the top; and since this same effect occurs at every floor, the resulting drift at

the top is cumulative. This type of deflection often referred to chord drift is difficult to

control requiring material quantities well in excess required for gravity needs.

Rigid frame deforms predominantly in a shear mode. The relative storey deflection

depends primarily on the magnitude of the shear applied at each storey level. Although near

the bottom deflections are large, and near the top smaller as compared to the braced frame,

the floor-floor deflection can be consider more nearly uniform. When the two systems, the

braced and rigid frames are connected by rigid floor diaphragms, a non-uniform shear force

develops between the two. The resulting interaction helps in extending the range od

application of the two system to buildings up to about 40 stories in height.

30

(Fig 4.5a) shows the individual deformation pattern of a braced and un-braced

frame subjected to lateral loads. Also shown are the horizontal shear forces between the

two frames connected by rigid floor slabs. Observe that the braced frame acts as a vertical

cantilever beam, with the slope of the deflection greatest at the top of the building,

indicating that in this region the braced frame contributes the least to the lateral stiffness.

The rigid frame has a shear mode deformation, with the slope of deformation

greater at the base of the structure where the maximum shear is acting. Because of the

different lateral deflection characteristics of two elements, the frame tends to pull back the

brace in the upper portion of the building while pushing it forward in the lower portion. As

a result, the frame participates more effectively in the upper portion of the building where

lateral shears are relatively less. The braced frame carries most of the shear in the lower

portion of the building. Thus, because of the distinct difference in the deflection

characteristics, the two systems help each other a great deal. The frame tends to reduce the

lateral deflection of the trusted core at the top, while the trussed core supports the frame

near the base. A typical variation of horizontal shear carried by each frame is shown in (fig

4.2 b) in which the length of arrow conceptually indicated the magnitude of interacting

shear forces.

31

Fig 4.7 Interaction between braced and unbraced frames; (a) Characteristic

deformation shapes; (b) Variation of shear forces resulting from interaction.

Although the framed part of a high rise structure is usually more flexible in

comparison to the braced part, as the number of stories increases, its interaction with the

braced frame becomes more significant, contributing greatly to the lateral resistance of the

building. Therefore, when the frame part is fairly rigid by itself, its interaction with the

braced portion of the building can result in a considerably more rigid and efficient design.

4.4.1 Outrigger and Belt truss system:

Innovative structural schemes are continuously being sought in the design of high

rise structures with the intention of limiting the wind drift to acceptable limits without

paying a high premium in steel tonnage. The savings in steel tonnage and cost can be

dramatic if certain techniques are employed to utilize the full capacities of the structural

elements. Various wind-bracing techniques have been developed to this end; this section

deals with one such system, namely, the belt truss system, also known as the core-out-

trigger system in which the axial stiffness of the perimeter columns or the columns in line

with core bracing (outrigger system) is invoked for increasing the resistance to overturning

moments.

This efficient structural form consists of a central core, comprising of braced

frames, with horizontal cantilever "outrigger" trusses or girders connecting the code to the

outer columns. The core may be centrally located with outriggers extending on both sides

(fig 4.8 a) or it may be located on one side of the building with outriggers extending to the

building columns on one side (fig 4.8 b).

32

Fig 4.8 (a) Outrigger system with a central core (b) outrigger system with offset core.

When horizontal loading acts on the building, the column restrained outrigger resist

the rotation of the core, causing the lateral deflections and moments in the core to be

smaller than if the free-standing core alone resisted the loading. The resulting is to increase

the effective depth of the structure when it flexed as a vertical cantilever, by inducing

tension in the windward columns and compression in the leeward columns.

In addition to those columns located at the end of the outriggers, it is usual to also

mobilize other peripheral columns to assist in restraining the outrigger. This is achieved by

including a deep spandrel girder, or a "belt-truss", around the structure at the levels of the

outriggers.

To make the outriggers and belt truss adequately stiff in flexure and shear, they are

made at least one and often 2 stories deep. It is also possible to use diagonals extending

through several floor to act as outrigger as shown in (fig 4.8 c). And finally girders at each

floor may be transformed into outrigger system is very effective in increasing the structure

flexural stiffness; it does not increase its resistance to shear, which has to be carried mainly

by the core.

Fig 4.8 (c) Diagonals acting as outriggers;

In the flowing sub-section the stiffness effect of a single outrigger located at the top

of the structure is examined first. Next, the effect of lowering the truss along the height is

33

studied with the object of finding the most optimum location for minimizing the building

drift.

4.4.2 Behavior:

To understand the behavior of an outrigger system, consider a building stiffness by

a story high outrigger at top, as shown in (fig 4.9). Because the outrigger is at the top, the

system is often referred to as a cap or hat truss system. The tie-down action of the cap truss

generates a restoring couple at the building top, resulting in point of contra flexure in its

deflection curve. This reversal in curvature reduces the bending moment in the core and

hence, the bending drifts.

Although the belt truss shown in (fig 4.10) functions as a horizontal stiffener

mobilizing other exterior column, for analytical simplicity we will assume that the

cumulative effect the exterior columns may be represent by to equivalent columns, one at

each end of the outrigger (fig 4.9 c). This idealization is not necessary in developing the

theory, but the explanation simple.

The core may be considered as single-redundant cantilever with rotation restrain at

the top by stretching and shorting of windward and leeward columns. The result of tensile

and compressive forces is equivalent to restoring couple opposing the rotation of core.

Therefore, the cap truss may be conceptualized as a restraining spring located at the top of

the cantilever. Its rotational stiffness may defined as the restoring couple due to a unit

rotation of the core at the top.

34

Fig4.9 Belt truss system (a) Building plan with cap truss, (b) cantilever bending of

core; (c) Tie-down action of cap truss.

Assuming the cap truss is infinitely rigid, the axial elongation and shortening of

columns is equal to the rotation of core multiplied by their respective distances from the

center of core. If the distance of the equivalent column is d/2 from the center of the core,

the axial deformation of the column is than equal to d/2,where is d is the rotation of the

core. Since the equivalent spring stiffness is calculated for unit rotation of the core (i.e.,

=1), the axial deformation of equivalent columns is equal to

1*d/2=d/2 units.

The corresponding axial load is given by

AEdP= 2L

Where,

P = axial load in the columns.

A = area of columns.

E = modulus of elasticity.

d = distance between the exterior columns.35

L = height of the building.

The resorting couple, that is, the rotational stiffness of the cap truss, is given by the

axial load in the equivalent columns multiplied by their distance from the center of the cre.

Using the notation K for the rotational stiffness, and noting that there are two equivalent

columns, each located at distance d/2 from the core, we get

dK = P* * 2 = Pd

2The reduction on drift depends on the stiffness K and the magnitude of rotation at

the top.

4.4.3 Calculation of displacements:

The cantilever bending and shear racking component can be easily determined

using the formulas and techniques mentioned in chapter-4 (Braced frames). The negative

displacement caused due to the presence of outrigger can be calculated using the procedure

mentioned below.

The structural parameters for one outrigger-braced frame are obtained as follows.

The flexural stiffness associated with the columns of the braced frame is given by,

E * Aa * c2

EIt = 2

The racking shear stiffness of the braced frames with 2 bays and 2 double diagonal

braced can be obtained from below equation,

2a2 * h * E * (Ad1+Ad2)GAt =

d3

The flexural stiffness of the outrigger structure is given by equation,

E * Ab * h2

EIo = 2

The racking shear stiffness of outrigger with segment is given by,

a2 * h * E * (Ad1+Ad2+.........+Adn)GAo =

d3

36

The global 2nd moment of area of the exterior columns can be obtained from

equation,

EIc = 2 * E * Ac * l2

The characteristic parameters Sv and Sh are given by equations,

H H 1 b 1 1St = + ; Sh = + + EIt EIc hGAo hGAt

The characteristic non-dimensional parameters for the structure can now be

obtained from following equation;

GAt

βH = H ; √ EIt

Sh

ω = Sv

Where,

E = Modulus Elasticity of steel

Aa = c/s area of the column attached to braced frame.

c = Total bay length of braced core.

Ab = c/s area of top and bottom chords of outriggers

h = Height of the outrigger.

Ac = c/s area of columns attached to outrigger.

Ad1 ..........Adn = c/s area of diagonals

l = Length of outrigger from center of braced core.

b = Length of outrigger from the face of BF.

a = Horizontal component of diagonal length.

d = Length of diagonal

H = Total height of the building

x = Location if mid-height of outrigger from top.

However, the practical optimum location of a single outrigger lie at the location

slightly higher than the value obtained from the above fig. The reason for this variation is

due to certain assumptions made during the derivation of the formulas discussed

previously. They are, 37

1. The lateral does not remain constant up the building height. It varies in a trapezoidal

or triangular manner, the former representative of wind loads and the later seismic

loads.

2. The c/s areas of both the exterior and interior columns typically reduce up the

building height. A linear variation is perhaps more representative of practical

building column.

3.

Fig. 4.10 Optimum location of outriggers

4. As the area of the core columns decreases the height, so does the moment of inertia

of core. Therefore, a linear variation M.I of the core, up the height is more

appropriate.

Incorporating the aforementioned modifications aligns the analytical model close to the

practical structure, but renders the hand calculation all but impossible.

4.4.4 Step wise Calculation:

E = 2 X 108 KN/m2

38

Aa = 8.712 X 10-3m2 (designation - 2512)

c = 11m

Ab = 7.65 X 10-3m2 (designation - 1716)

h = 3.3m

Ac = 7.92 X 10-3m2 at16.5 and 7.16 X 10-3m2 at 11m

(Note: Above values are avg. areas of all columns below the outrigger level)

l = 16.5m

a = 5.5m

d = 6.414m

H = 33m

x =?

E * Aa * c2

EIt = = 2 x 108 x 8.712 x 10-3 x112/2 = 105.42 x 106Kn-m2 2

2a2 * h * E * (Ad1 + Ad2)GAt = = 2 x 5.52 x 3.3 x 2 x 108 x (10.1+5.8) x10-3 x 6.414-3

d3

=2.41 x 106 Kn

E * Ab * h2

EIo = = 2 x 108 x 7.65 x 10-3 x 3.32/2 = 8.33 x 106Kn-m2 2

a2 * h * E * (A1 + A2+....... An)GAo = d3

= 2 x 5.52 x 3.3 x 2 x 108 x (14.9+6.6+2x6.4) x10-3 x 6.414-3

=2.6 x 106 Kn

EIc = 2 * E * Ac * l2 = 2 x 2 x 108 x (7.92 x 16.52 + 7.16 x 112) x 10-3 = 1209.83 x 106Kn-m2

Sv = 33 x ((105.42 x 106)-1 + (1209.83 x 106)-1) = 3.4 x 10-7

39

Sh = 1.5-2 (11 x (24x8.33x106)-1 + (3.3x2.6x106)-1 + (3.3x2.41x106)-1 = 1.32 x 10-7

Therefore, from fig 4.10, optimum location of outrigger is X = 11.55m

CHAPTER-5

40

RESULTS AND DISCUSSUIONS

TABLE-5.1 MI and Lateral Load Values Of 10 Storey Model for Moment Frame Building.

Storey M.I. (m4) F (KN)10 47.49 375.939 59.29 393.098 57.45 315.667 65.22 242.096 71.15 178.315 79.45 125.654 85.97 79.973 85.97 45.232 92.49 20.111 101.98 5.07

The above table shows the moment of inertia and lateral load values of 10 storey model of moment frame building ,here we observe that MI decreases the height of the building increases and shear force increases with the increases in the height of building.

TABLE -5.2 Chord Drift Component of 10 Storey Moment Frame Building

Storey d. (mm)10 0.819 0.698 0.577 0.466 0.355 0.254 0.173 0.092 0.041 0.01

From the above table it can be observe that the chord drift values are insignificant.

TABLE-5.3 Column and Beam ROTATION Components Due To ELY

41

Storey c. (mm) b. (mm)10 69.15 57.269 63.76 53.368 56.67 47.437 48.06 40.916 38.88 33.875 30.79 26.804 23.02 20.003 16.59 13.632 10.02 7.781 5.72 2.56

The above table shows column and beams rotation components due to earthquake loading in Y direction, while comparing it can be seen that the rotation due to beams members is lesser than column members.

TABLE-5.4 % CONTRIBUTION OF EACH COMPONENT DUE TO ELY

Storey C.B. % CR % BR % Total (mm) Limit

10 0.64 55.36 45.01 127.23 1329 0.59 55.12 45.3 117.83 118.88 0.55 55.13 45.31 105.69 105.67 0.52 53.74 45.74 89.45 92.46 0.49 53.18 46.33 73.11 79.25 0.44 53.23 46.33 57.86 664 0.4 53.3 46.31 43.21 52.83 0.33 55.71 45.96 30.33 39.62 0.25 56.17 43.57 17.86 26.41 0.16 65.68 35.16 7.31 13.2

AVG. 0.44 55.16 45.4

From the above table, we can see that from all the models the deflection values due to

earthquake load is in the limits as per IS code.

Table- 5.5 Chord Drift Components of single diagonal braced frame.

42

Storey M.I. (m4) ELY (KN)10 0.20 371.659 0.24 391.788 0.51 310.397 0.48 238.236 0.86 175.425 0.84 122.004 1.24 78.213 1.22 45.092 1.57 19.621 1.67 5.92

From the above table shows the moment of inertia and earthquake loading in y

direction for 10 storey model, it can be seen that the lateral load caused due to earthquake

is maximum in top storey.

Table - 5.6 Displacement values obtained using E-tabs.

Storey CB (mm)10 61.959 51.678 41.727 32.456 25.115 16.864 10.843 6.092 2.661 0.65

The above table value of deflection for the cross brace building model can be

viewed, as the deflection is maximum in the top storey when compared with other stories.

Table - 5.7 Displacement values of 10 storey-braced frame model.

43

Storey M.I. (MF) m4 M.I. (BF) m4 ELY (KN)10 29.75 0.17 368.829 39.76 0.26 388.548 48.23 0.48 309.547 56.58 0.64 237.886 65.06 0.87 175.945 68.15 1.1 121.824 72.4 1.13 79.253 71.76 1.4 45.62 77.16 1.67 19.861 77.16 1.67 5.98

The above table reflects the value of moment of inertia, for moment frame building

model, braced frame building model, while comparing both we can see the moment of

inertia is maximum in moment frame model, then the earthquake load in y direction can

also be viewed for the same 10 storied building models.

Table - 5.8 Displacement for 10 storey model with outrigger at top

Storey CB (mm)10 55.859 53.78 46.837 40.116 32.625 25.94 18.533 11.852 7.331 2.560 0

The total of the deflection caused due to the 10 storey models with outrigger at top

is viewed from the above table.

Table - 5.9 Displacement Components WLY.

44

Storey CB CR BR CB % CR % BR % Total Limit30 19.8 95.5 78.31 10.23 49.33 40.45 193.6 19829 18.86 94.76 77.27 9.88 49.64 40.48 190.9 191.428 17.93 92.69 75.38 9.64 49.83 40.53 186 184.827 16.99 89.29 72.51 9.5 49.94 40.56 178.8 178.226 16.06 84.58 68.66 9.49 49.96 40.55 169.3 171.625 15.14 78.59 64.98 9.54 49.52 40.94 158.7 16524 14.22 75 61.79 9.41 49.67 40.92 151 158.423 13.3 70.79 58.51 9.33 49.64 41.03 142.6 151.822 12.4 66.5 55 9.26 49.66 41.08 133.9 145.221 11.51 62.15 51.24 9.21 49.76 41.03 124.9 138.620 10.63 57.33 47.94 9.17 49.47 41.36 115.9 13219 9.77 54.1 45.04 8.97 49.67 41.36 108.9 125.418 8.92 50.58 42 8.79 49.83 41.38 101.5 118.817 8.1 46.79 38.82 8.64 49.93 41.42 93.7 112.216 7.3 43.08 35.62 8.49 50.2 41.42 86 105.615 6.52 39.14 32.54 8.34 50.05 41.61 78.2 9914 5.78 36.14 29.88 8.04 50.34 41.62 71.8 92.413 5.06 32.98 27.16 7.76 50.59 41.65 65.2 85.812 4.38 29.67 24.35 7.5 50.8 41.7 58.4 79.211 3.74 26.51 21.65 7.2 51.08 41.72 51.9 72.610 3.13 23.22 19.05 6.9 51.15 41.95 45.4 669 2.57 20.66 16.77 6.44 51.64 41.92 40 59.48 2.06 18 14.43 5.98 52.19 41.84 34.5 52.87 1.6 15.27 12.13 5.52 52.67 41.81 29 46.26 1.19 12.73 9.88 5.01 53.47 41.52 23.8 39.65 0.84 10.13 7.84 4.46 53.86 41.68 18.8 334 0.54 8.06 6 3.72 55.19 41.09 14.6 26.43 0.31 5.95 4.24 2.95 56.66 40.38 10.5 19.82 0.14 4 2.56 2.1 59.64 38.26 6.7 13.21 0.04 2.01 0.96 1.19 66.96 31.84 3 6.6

AVG % 7.42 51.74 40.84

From the above table all models is compared for the wind loading in x direction

which has increased from 0.44% to 7.42%. The remaining displacement is shared almost

equally by both beam and column.

It is observed that in case of most moment frame, the building undergoes double 45

curvature i.e., the inter storey displacements decreases as we move away from the base. It

can be said that the efficiency of moment frames is more in top floors when compared to

the bottom floors.

Table- 5.10 Displacement components WLX.

Storey CB CR BR CB % CR % BR % Total Limit30 19.8 40.21 97.49 12.57 25.53 61.9 157.50 198.0029 18.86 39.88 96.15 12.18 25.75 62.07 154.90 191.428 17.93 39.05 93.63 11.90 25.93 62.17 150.60 184.8

46

27 16.99 37.70 89.71 11.77 26.11 62.13 144.40 178.226 16.06 35.84 84.69 11.76 26.24 62.00 136.60 171.625 15.14 33.52 80.05 11.76 26.04 62.20 128.70 16524 14.22 32.08 76.20 11.60 26.19 62.20 122.50 158.423 13.3 30.41 71.98 11.50 26.29 62.22 115.70 151.822 12.4 28.68 67.22 11.45 26.48 62.07 108.30 145.221 11.51 26.9 62.10 11.45 26.76 61.79 100.50 138.620 10.63 24.94 57.33 11.44 26.84 61.71 92.90 13219 9.77 23.58 53.15 11.29 27.26 61.45 86.50 125.418 8.92 22.11 48.67 11.20 27.74 61.06 79.70 118.817 8.1 20.53 43.97 11.16 28.28 60.56 72.60 112.216 7.3 18.97 39.24 11.14 28.96 59.9 65.5 105.615 6.52 17.32 35.26 11.04 29.30 59.67 59.10 9914 5.78 16.03 32.39 10.66 29.58 59.76 54.20 92.413 5.06 14.68 29.56 10.26 29.79 59.95 49.30 85.812 4.38 13.27 26.55 9.91 30.03 60.06 44.20 79.211 3.74 11.91 23.45 9.56 30.46 59.98 39.10 72.610 3.13 10.5 20.67 9.14 30.61 60.25 34.30 669 2.57 9.36 18.26 8.53 31.00 60.48 30.20 59.48 2.06 8.19 15.85 7.90 31.36 60.74 26.10 52.87 1.6 6.98 13.42 7.28 31.71 61.01 22.00 46.26 1.19 5.84 10.87 6.66 32,61 60.73 17.90 39.65 0.84 4.68 8.68 5.90 32.96 61.13 14.20 334 0.54 3.72 6.63 4.98 34.16 60.86 10.90 26.43 0.31 2.75 4.74 3.97 35.25 60.78 7.80 19.82 0.14 1.84 2.82 2.93 38.35 58.73 4.80 13.21 0.04 0.92 0.94 1.88 48.44 49.68 1.90 6.6

AVG % 9.49 29.87 60.64The above table shows the lateral deformation values due to wind load in x

direction, it is observed that contribution of chord drift has further increased to 9.49%

compared to previous value of 7.42%. Also the beam rotation contributes almost twice

when compared to column rotation.

Table - 5.11 Displacement and % contributions of single diagonal braced frame

Storey Flexural Shear Flexure % Shear % Total Total % Limit

10 58.08 24.52 70.32 29.68 82.60 62.58 132.00

47

9 48.55 23.25 67.62 32.38 71.80 60.44 118.8

8 39.37 21.33 64.86 35.14 60.70 57.48 105.6

7 30.78 18.42 62.57 37.43 49.20 53.25 92.40

6 23.02 16.48 58.27 41.73 39.50 49.87 79.20

5 16.25 13.25 55.08 44.92 29.50 44.70 66.00

4 10.55 11.15 48.61 51.39 21.70 41.10 52.80

3 6.02 7.48 44.58 55.42 13.50 34.09 39.60

2 2.70 5.50 32.99 67.01 8.20 31.06 26.40

1 0.70 2.00 25.86 74.14 2.70 20.45 13.20

AVG % 53.08 46.92 45.5

From the above table it is observed that the avg. % contribution of both flexure and

shear components is approximately same and the pattern in which the flexure component

vary is reverse of that observed in shear.

DISPLACEMENT ELY

DISPLACEMENT (mm)

Chart 5.1 - Displacement component in a single diagonal braced frame

The chart shows storey vs. displacement for the avg. % contribution of both

48

flexure and shear components. We can see that shear is lesser than flexure.

Table 5.12 Displacements and % contributions of double diagonal braced frame

Storey Flexural Shear Flexure % Shear % Total Total % Limit

10 61.95 12.55 83.16 16.84 74.5 56.44 132.00

9 51.67 12.42 80.61 19.39 64.09 53.95 118.8

8 41.72 11.68 78.13 21.87 53.39 50.56 105.6

7 32.45 10.54 75.48 24.52 42.99 46.53 92.40

6 24.11 9.28 72.21 27.79 33.39 42.16 79.20

5 16.86 8.13 67.47 32.53 24.99 37.86 66.00

4 10.84 6.55 62.32 37.68 17.39 32.94 52.80

3 6.09 5.1 54.39 45.61 11.19 28.26 39.60

2 2.66 3.43 43.69 56.31 6.09 23.07 26.40

1 0.65 1.74 27.02 72.98 2.39 18.1 13.20

AVG % 64.45 35.55 38.99

From the above table it is observed that due to presence of double diagonals the

shear displacements due to diagonal deformation has reduced considerably and so has the

overall displacement. Also the percentage average of the displacements from all the

floors has reduced to 38.99% compared to 45.5% observed in single diagonal frame.

DISPLACEMENT ELX

49

DISPLACEMENT (mm)

Chart 5.2 displacement components of 10 storey double diagonal braced frame

The above chart shows storey vs. displacement in which shear displacements have

been reduced.

Table- 5.13 displacements and % contributions of double diagonal braced frame along X

direction.

Storey Flexure Shear Flexure % Shear % Total Limit

30 117.69 16.11 91.69 8.31 193.8 198

29 169.72 16.18 91.3 8.7 185.9 191.4

28 161.76 16.14 90.93 9.07 177.9 184.8

27 153.79 16.01 90.57 9.43 169.8 178.2

26 145.84 15.66 90.3 9.7 161.5 171.6

25 137.91 15.19 90.08 9.92 153.1 165

50

24 129.99 14.71 89.84 10.16 144.7 158.4

23 122.12 14.08 89.66 10.34 136.2 151.8

22 114.28 13.52 89.42 10.58 127.8 145.2

21 106.51 12.89 89.21 10.79 119.4 138.6

20 98.82 12.28 88.95 11.05 111.1 132

19 91.22 11.68 88.65 11.35 102.9 125.4

18 83.74 10.96 88.42 11.58 94.7 118.8

17 76.39 10.31 88.1 11.9 86.7 112.2

16 69.19 9.61 87.81 12.19 78.8 105.6

15 62.18 9.02 87.33 12.67 71.2 99

14 55.38 8.32 86.94 13.06 63.7 92.4

13 48.81 7.69 86.39 13.61 56.5 85.8

12 42.51 6.99 85.87 14.13 49.5 79.2

11 36.50 6.3 85.28 14.72 42.8 72.6

10 30.82 5.68 84.44 15.56 36.5 66

9 25.50 5.1 83.33 16.67 30.6 59.4

8 20.58 4.52 81.98 18.02 25.1 52.8

7 16.09 3.91 80.43 19.57 20 46.2

6 12.06 3.34 78.34 21.66 15.4 39.6

5 8.55 2.85 75.01 24.99 11.4 33

4 5.58 2.32 70.69 29.31 7.9 26.4

3 3.20 1.7 65.4 34.6 4.9 19.8

2 1.45 1.15 55.88 44.12 2.6 13.2

1 0.37 0.53 41.16 58.84 0.9 6.6

AVG 83.11 16.89

Table 5.13 and table 5.14 gives the complete set of displacements and their %

contributions to overall displacement along X and Y direction.

DISPLACEMENT WLX

51

Chart 5.3 Displacement components of 30 storey’s DDBF in X-direction.

DISPLACEMENT WLY

Chart 5.4 Displacement

components of 30 storeys

DDBF in Y- direction.

The above charts show

storey vs. displacement.

In case of 30 storey braced

frame the cantilever

effect is observed to huge and a

single braced core placed at the

center of the building is found to be inefficient. A single braced core causes huge

moments to be concentrated at the base and requires very large sections.

Table-5.14 displacements and % contributions of double diagonal braced framed

along Y direction.

52

Storey Flexure Shear Flexure % Shear % Total Limit30 177.69 12.91 93.23 6.77 190.6 19829 169.72 13.08 92.85 7.15 182.8 191.428 161.76 13.24 92.43 7.57 175.0 184.827 153.79 13.21 92.09 7.91 167.0 178.226 145.84 13.06 91.78 8.22 158.9 171.625 137.91 12.79 91.51 8.49 150.7 16524 129.99 12.51 91.22 8.78 142.5 158.423 122.12 12.08 90.99 9.01 134.2 151.822 114.28 11.72 90.7 9.3 126 145.221 106.51 11.19 90.5 9.5 117.7 138.620 98.82 10.68 90.25 9.75 109.5 13219 91.22 10.18 89.96 10.04 101.4 125.418 83.74 9.56 89.75 10.25 93.3 118.817 76.39 9.01 89.45 10.55 85.4 112.216 69.19 8.51 89.05 10.95 77.7 105.615 62.18 7.92 88.7 11.3 70.1 9914 55.38 7.42 88.18 11.82 62.8 92.413 48.81 6.79 87.79 12.21 55.6 85.812 42.51 6.29 87.1 12.9 48.8 79.211 36.5 5.7 86.49 13.51 42.2 72.610 30.82 5.18 85.61 14.39 36.0 669 25.5 4.7 84.44 15.56 30.2 59.48 20.58 4.22 82.97 17.03 24.8 52.87 16.09 3.71 81.24 18.76 19.8 46.26 12.06 3.24 78.85 21.15 15.3 39.65 8.55 2.75 75.67 24.33 11.3 334 5.58 2.22 71.59 28.41 7.8 26.43 3.2 1.7 65.4 34.6 4.9 19.82 1.45 1.15 55.88 44.12 2.6 13.21 0.37 0.53 41.16 58.84 0.9 6.6

AVG. 84.23 15.77Table 5.15 displacements and % contributions of 10 storey integrated system in Y direction.

Storey CB-MF

CB-BF Shear CB-MF%

CB-BF%

Shear% Total Total% Limit

10 0.97 52.49 4.67 1.66 90.3 8.03 58.12 44.03 1329 0.83 43.91 6.22 1.62 86.17 12.21 50.96 42.89 118.8

53

8 0.69 35.68 7.16 1.58 81.98 16.45 43.52 41.21 105.67 0.55 28.02 7.5 1.53 77.69 20.78 36.07 39.04 92.46 0.43 21.09 7.46 1.47 72.78 25.75 28.97 36.58 79.25 0.31 14.99 6.92 1.4 67.46 31.14 22.22 33.67 664 0.21 9.81 6.13 1.29 60.74 37.97 16.14 30.57 52.83 0.12 5.68 5.06 1.13 52.31 46.56 10.87 27.44 39.62 0.06 2.65 3.54 0.92 42.41 56.68 6.25 23.69 26.41 0.02 0.69 1.91 0.57 26.53 72.9 2.62 19.83 13.2

AVG 1.32 65.84 32.85 33.9

The above table gives the complete set of displacements along with their %

contributions to overall displacement. From the above table it is clear that it is clear that

the chord drift offered by the moment frame is negligible, whereas, that offered by the

braced frame from the significant part of the overall displacement.

DISPLACEMENT ELY

Chart 5.5

Displacement components in 10 storey integrated system the chart shows.

54

The chart shows storey vs. displacement. It is observed that overall displacements

are much lesser compared to both moment and braced frame.

Table-5.16 comparison of lateral displacements

Storey MF BF MBF Limit30 193.6 193.8 191.76 19829 190.9 185.9 186.52 191.428 186 177.9 180.13 184.827 178.8 169.8 172.56 178.226 169.3 161.5 163.75 171.625 158.7 153.1 154.34 16524 151 144.7 146.37 158.423 142.6 136.2 138.01 151.822 133.9 127.8 129.54 145.221 124.9 119.4 120.93 138.620 115.9 111.1 112.37 13219 108.9 102.9 104.84 125.418 101.5 94.7 97.12 118.817 93.7 86.7 89.3 112.216 86 78.8 81.58 105.615 78.2 71.2 73.95 9914 71.8 63.7 67.07 92.413 65.2 56.5 60.24 85.812 58.4 49.5 53.41 79.211 51.9 42.8 46.88 72.610 45.4 36.5 40.54 669 40 30.6 34.95 59.48 34.5 25.1 29.5 52.87 29 20 24.26 46.26 23.8 15.4 19.4 39.65 18.8 11.4 14.95 334 14.6 7.9 11.14 26.43 10.5 4.9 7.62 19.82 6.7 2.6 4.6 13.21 3 0.9 1.93 6.60 0 0 0 0

55

The above table gives the comparison between moment frame, braced frame and

moment braced frame. The moment braced frame is having less displacement and is more

efficient when compared to the other two frames.

COMPARISION OF LATERAL DISPLACEMENT

Chart 5.6 Comparison of lateral displacements between MF, BF and MBF

Chart 5.6 comparison of lateral displacements shows MBF has less displacement

and it is preferable than the other two.

TABLE-5.17 Displacement components of different models

Storey CB DD OTD Total Total% Limit10 84.71 18.29 -48.99 54.01 40.92 1329 71.21 12.39 -37.19 46.41 39.07 118.88 58.08 7.5 -27.02 38.55 36.51 105.67 45.58 4.39 -19.58 30.4 32.9 92.46 33.93 2.33 -12.3 23.96 30.25 79.25 23.55 1.62 -2.59 22.57 34.2 664 14.95 0.83 1.03 16.82 31.85 52.83 8.26 0.37 2.43 11.07 27.95 39.62 3.6 0.15 3.14 6.89 26.11 26.41 0.92 0.03 1.43 2.37 17.99 13.2

AVG% 31.78

56

From the above table it can be observed that an outrigger reduces the total displacement

by pushing the structure in opposite direction to that of lateral loads. This is achieved by

generating a restoring moment which can be calculated as below.

DISPLACEMENT ELX

Chart 5.7-Displacement components in a single outrigger structure

From the above graph it can be see that the structure undergoes sudden change in

displacement at the level of outrigger. A part from that it can be seen that the total

displacements at all floors are further reduced when compared to the outrigger placed at

top level.

Table 5.18 displacements for outrigger at different location.

Storey Top Middle Bottom10 55.85 56.01 77.99 53.7 46.11 66.58 46.83 38.55 55.97 40.11 30.4 436 32.62 23.96 33.25 25.9 32.57 23.34 18.53 16.82 15.93 11.85 11.07 8.4

57

2 7.33 6.89 3.61 2.56 2.37 2.60 0 0 0

The table 5.18 gives the comparison of final displacements for outrigger placed at top,

middle and bottom location. We can observe that displacement at top is less than middle

and bottom.

DISPLACEMENT ELX

DISPLACEMENT (mm)

Chart 5.8 Displacements due to outrigger at top, middle and bottom location

Given in chart 5.10 is the comparison of displacements for various outrigger

locations. From the chart it can be seen that there is sudden change in displacement at the

outrigger location in all three cases. This is due to the restoring effect caused by the

presence of outrigger.

58

Table- 5.19 Displacement components in 30 storey outrigger model.

Storey CB DD OTD Total Limit30 865.79 11.34 -680.5 195.62 19829 825.61 11.2 -645.42 191.38 191.428 785.44 9.96 -612.22 182.18 185.827 745.29 8.88 -575.04 178.14 178.226 705.2 7.97 -540.64 171.53 171.625 665.19 7.16 -506.93 165.42 16524 625.33 6.37 -472.77 157.93 158.423 5858.66 5.75 -439.27 151.14 151.822 545.26 5.15 -406.32 145.09 145.221 506.21 5.6 -375.97 135.85 138.620 467.6 5.13 -345.17 127.57 13219 429.53 3.71 -313.88 119.36 125.418 392.12 3.32 -285.14 111.3 118.817 355.47 2.97 -255.87 103.57 112.216 319.72 2.66 -226.09 96.29 105.615 285.01 2.49 -197.81 89.69 9914 251.49 2.34 -166.62 87.2 92.413 219.32 2.1 -140.92 80.5 85.812 188.66 1.87 -117.43 73.11 79.211 159.7 1.66 -96.11 65.25 72.610 132.6 1.44 -76.96 57.08 669 107.58 1.21 -59.97 48.82 59.48 85.82 1.03 -45.17 40.68 52.87 65.54 0.88 -32.55 32.86 46.26 46.94 0.75 -22.06 25.62 39.65 32.24 0.64 -13.8 19.08 334 20.68 0.52 -0.95 13.45 26.43 11.87 0.41 -7.75 8.64 19.82 5.38 0.28 -3.63 5.7 13.21 1.37 0.14 -0.95 1.73 6.60 0 0 0 0 0

The table above gives the complete set of displacement due to wind load in Y direction.

59

DISPLACEMENT WLY

DISPLACEMENT (mm)

Chart 5.9 Displacement components in 30 storey outrigger model.

The above chart shows storey vs. displacement for 30 storey outrigger model in

case of belt truss system it is found that by addition of few diagonals at outrigger level

the lateral displacements at all floors are reduced considerably, with little change in the

weight of the structure. The reduction in lateral displacement is due to increased flexural

rigidity to the structure when compared to simple outrigger system.

60

Table-5.20 lateral displacements due to wind load in OBT model.

Outrigger belt system

Outrigger system

Storey UX(mm) UY(mm) UX(mm) UY(mm) Limit30 125.55 171.43 193.87 195.62 19829 123.52 169.49 190.64 191.38 191.428 120.09 165.41 185.57 182.18 185.827 116.15 160.76 177.61 178.14 178.226 111.8 155.44 171.01 175.53 171.625 107.22 149.67 165.95 165.42 16524 102.45 143.34 158.1 157.93 158.423 97.55 136.43 150.78 151.14 151.822 92.55 129.07 142.81 145.09 145.221 87.47 121.43 135.65 135.85 138.620 82.39 113.67 126.45 127.57 13219 77.38 106.2 118.33 119.36 125.418 72.46 99.16 110.37 111.3 118.817 67.71 92.67 102.73 103.57 112.216 63.25 86.63 95.37 96.29 105.615 59.11 81.14 88.79 89.69 9914 57.88 79.42 86.22 87.2 92.413 53.71 73.75 79.63 80.5 85.812 49.15 67.49 72.32 73.11 79.211 45.19 60.63 75.54 65.25 72.610 38.98 53.38 56.47 57.08 669 33.74 46.04 48.34 48.82 59.48 28.47 38.93 40.28 40.68 52.87 23.29 32.13 32.54 52.86 46.26 18.33 25.7 25.38 25.62 39.65 13.69 19.75 18.89 19.02 334 9.51 15.3 13.31 13.45 26.43 5.92 9.54 8.54 8.64 19.82 3.06 5.44 5.63 5.7 13.21 1.04 2.23 1.69 1.73 6.6

61

Apart from reduced displacements the axial force at the base of core due to wind

load is reduced from 10244 KN to 9581 KN. This difference is distributed proportionally

to the newly activated columns due to presence of belt truss.

DISPLACEMENT WLX

DISPLACEMENT (mm)

Chart 5.10 displacements in simple outrigger and outrigger belt truss system in X

direction.

DISPLACEMENT WLY

DISPLACEMENT (mm)

Chart 5.11 Disp in simple outrigger and outrigger belt truss system in Y- direction.62

From the above charts 5.10 and 5.11 the storey vs. displacement charts it is

concluded that among two outrigger system it is preferable to use combined outrigger and

belt truss System as it also reduces the forces at the base of core which otherwise may

yield to complications in the foundation design.

Table-5.21 comparison of lateral displacements obtained with each system

Storey MF BF MBF OT OBT Limit30 193.6 193.8 193.6 195.62 171.43 19829 190.9 185.9 190.9 191.38 169.49 191.428 186 177.9 186 182.18 165.41 185.827 178.8 169.8 178.8 178.14 160.76 178.226 169.3 161.5 169.3 175.53 155.44 171.625 158.7 153.1 158.7 165.42 149.67 16524 151 144.7 151 157.93 143.34 158.423 142.6 136.2 142.6 151.14 136.43 151.822 133.9 127.8 133.9 145.09 129.07 145.221 125.9 119.4 125.9 135.85 121.43 138.620 115.9 111.1 115.9 127.57 113.67 13219 108.9 102.9 108.9 119.36 106.2 125.418 101.5 94.7 101.5 111.3 99.16 118.817 93.7 86.7 93.7 103.57 92.67 112.216 86 78.8 86 96.29 86.63 105.615 78.2 71.2 78.2 89.69 81.14 9914 71.8 63.7 71.8 87.2 79.42 92.413 65.2 56.5 65.2 80.5 73.75 85.812 58.4 49.5 58.4 73.11 67.49 79.211 51.9 42.8 51.9 65.25 60.63 72.610 45.4 36.5 45.4 57.08 53.38 669 40 30.6 40 48.82 46.04 59.48 35.5 25.1 35.5 40.68 38.93 52.87 29 20 29 52.86 32.13 46.26 23.8 15.4 23.8 25.62 25.7 39.65 18.8 11.4 18.8 19.02 19.75 334 15.6 7.9 15.6 13.45 15.3 26.43 10.5 4.9 10.5 8.64 9.54 19.82 6.7 2.6 6.7 5.7 5.44 13.21 3 0.9 3 1.73 2.23 6.6

63

From the above table it can be seen that most efficient system with respect to reduction in

lateral displacement is a combined outrigger and belt truss system. However, in case of

both outrigger and belt truss system two outriggers are used, one at top level and another

at mid level, requiring at least two service floors. It should also be kept in mind that the

level at which the outriggers are placed are not the optimum locations.

DISPLACEMENT ELY

DISPLACEMENT (mm)

Chart 5.12 comparisons of displacements from all 30 storey models.

The chart 5.12 gives the comparison of all the lateral systems used in the present study.

The above chart storey vs. displacement gives the comparison of lateral systems from 30

storey models. It is conclude that outrigger system is preferable from all.

DISCUSSIONS:

64

These are from the analyses result of models using Etabs.

MI decreases as the height of the building increases and shear force increases with

the increase in height of the building.

The chord values are insignificant in case of 10 storey moment frame building the

moment of inertia and earthquake loading in Y direction for 10 storey model, it

can be seen that the lateral load caused due to earthquake is maximum in top

storey when compared with other stories.

The efficient of moment frames is more in top floors when compared to the

bottom floors. Due to the diagonal deformation has reduced considerably in

DDBF.

That contribution of chord drift has further increased to 9.49% compared to

previous value of 7.42%. Also the beam rotation contributes almost twice when

compared to column rotation in single diagonal frame.

In case of 30 storey braced frame the cantilever effect is observed to b huge and a

single braced core placed at the center of the building is found to be insufficient.

For 30 storey outrigger model in case of belt truss system it is found that by

addition of few diagonals at outrigger level the lateral displacement at all floors

are reduced considerably, with little change in weight of the structure.

The reduction in lateral displacements is due to increased flexural rigidity of the

structure when compared to simple outrigger system.

Among two outrigger systems it is preferable to use combined outrigger and belt

truss system as it also reduces the forces at the base of core which otherwise may

yield to complications in foundation design.

From all the models outriggers belt truss system has less displacement and more

control over drift moment frame and braced has displacements nearly equal.

Moment-braced frame has less displacement than the two.

CHAPTER -6

65

CONCLUSION

1. The most efficient system with respect to steel tonnage once again works out be

“integrated rigid-braced frame systems”, however the differences this time is much more

significant when compared to simple double diagonal braced frame system.

2. The 30 storey rigid brace frame in the present study is subjected to much rigorous

optimization, hence the least steel tonnage achieved. However, rigorous optimization

means that the sections used are not consistent.

3. It should be kept in mind that a moment frame involves a more detail design of the

joints to achieve the required portal frame effect. The additional steel required for the

joints is much more when compared to the amount of steel required for simple shear

connections used in braced and outrigger systems.

4. The most efficient system with respect to reduction in lateral displacement is a

combined outrigger and belt truss system . However, in case of both outrigger and belt

truss system two outriggers are used , one at top level and another at mid level, requiring

at least two service floors. It should also be kept in mind that the level at which the

outriggers are placed are not the optimum locations.

5. From the above discussion it can be concluded that even though integrated systems has

least steel tonnage, it requires additional steel for rigid joint, which will bring the steel

tonnage close to that of outrigger systems. Among two outrigger systems it is preferable

to use combined outrigger and belt truss system as it also reduces the forces at the base of

core which otherwise may yield to complications in the foundation design.

SCOPE FOR THE FUTURE WORK

66

Future work can be carried out for across earthquake response of the tall buildings

with respect to structural systems. The different type of systems may be introduces for

resisting the lateral forces

Lateral systems along with the different type of combinations may be used for

resisting the lateral forces. Analysis using better techniques, a detail dynamic analysis can

be carried out, collecting the response of the tall building at every mode. A study can be

done to these lateral systems for making more effective in earthquake as well as wind

forces resisting designs. Any how many new techniques are now available to make the

structures stiff against the lateral forces. A study can be done by providing the base

isolation techniques with these lateral system or the springs may to provided with these

systems, also we can make an investigation of dampers with these systems.

REFERENCES

67

Literature & Books:

1. Zhixin Wang, Haitao Fan and Haungjuan, “Analysis of the seismic

performance of RC frame structure with different types of bracing” Applied

mechanics and material vols, 166-169, pp 2209-2215, May 2012.

2. Huanjun jiang, Bo Fu and Laoer Liu, “Seismic performance evolution of a

steel concrete hybrid frame-tube high-rise building structure” Applied Mechanics

and materials vol. 137, pp 149-153, Oct 2011.

3. Paul W. Richards, P.E., M.ASCE, “Seismic column demands in ductile braced

frames” Journal of structure engineering, vol. 135,No.1, ISSN 0733-9445/2009/1-

33-41, January 2009.

4. Mir M. Ali and Kyoung Sun Moon, “Structural development in tall building;

current trends and future prospects” architectural science review, Vol. 50.3, pp

205-223, June 2007.

5. Jinkoo Kim, Hyunhoon Choi, “ Response modification factors of chevron-

braced frames” Engineering structures, Vol. 27, pp 285-300, October-2004.

6. Mahmood R. Maheri, R. Akbari, “Seismic behavior factor, R for steel X-braced

and Knee-braced RC buildings” Engineering structure, Vol. 25 pp 1505-1513,

May 2003.

7. V. Kapur and Ashok K. Jain, “Seismic response of shear wall frame versus

braced concrete frames” university of Roorkee, Roorkee, 247 672, April 1983.

8. Taranth B.S., “Structural analysis and design of tall buildings” McGraw-Hill

Book company, 1988.

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