Chapter 1

INTRODUCTION

1.1 General

In recent years, Bangladesh has a growing trend towards construction of 15 to 30 storied

buildings, almost all of these are being situated in Dhaka. The taller and more slender a

building is, the more important the structural factors become and the more necessary it is to

choose an appropriate structural form. In addition to satisfy nonstructural requirements, the

principal objectives in choosing a building’s structural form is to arrange to support the

gravity, dead and live load and to resist at all levels the external horizontal load and shear,

moment and torque with adequate strength and stiffness. These requirements should be

achieved as economically as possible. A major step forward in reinforced concrete high-rise

structural form comes with the introduction of shear walls for resisting horizontal load. The

structural form of the tall building is concerned mainly with the arrangement of the primary

vertical components and their interconnections. The column spacing is usually governed by

the car parking requirement at ground level. The columns are connected by rigid beams. 125

mm / 250 mm thick brick walls are used as partition wall between two flats in apartment

buildings. Generally there are no openings in these walls and hence it may be replaced by

reinforced concrete shear wall. A numerical comparative study of different structural system

is done using finite element package program. To calculate the design wind pressure and

earthquake base shear, the loads are taken from method proposed in BNBC. For quick

estimation of design wind pressure and earthquake force for specific criteria some graphs are

presented. Any necessary value or interpolated value is taken from the graph directly.

1.2 Objectives of the Study

A 16-storied building is selected to study the behaviour of different structural models under

lateral loads. For simplicity of 2-D analysis, a typical transverse bay is considered for

analysis. The specified bay is idealized as different models and a comparative performance is

carried out. The main objectives of the research may be stated as follows:

To determine the efficient structural system against lateral loads.

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To study the effect of different parameters on model frames due to wind pressure and

earthquake forces.

To study different modeling techniques for high rise building structures.

To study the effect of column size, shear wall thickness, coupling beam size etc. on

lateral drift.

To study the stresses in infilled material.

1.3 Scope of the Study

The project work has been aimed to determine the efficient structural system due to lateral

loads on high rise building. The study has been performed through a set of structural models

with the elastic analyses by a professional structural software, STAAD –III. This is

performed only on the basis of some limited criteria, these are relative stiffness of model

frames, bending moments in connecting beams and stresses in infill material of different

model frames. For these purpose only, the typical bay of a 16-storied building is modelled by

different alternately adopted structural systems. These are Rigid Frame model, Infill Frame

model, Coupled Wall model (with auxiliary beam connection), Coupled Wall model (without

auxiliary beam connection) and Equivalent Wide Column model.

1.4 Methodology

To study the behaviour of 16-storied high rise building against lateral loads, a typical bay is

studied by alternative structural systems. The following items are executed on the specified

typical bay consideration.

a. A limited parametric study is carried out to control the lateral sway of the high rise

building. The top deflection of the structure and the stresses in the structural members

for various structural forms are presented graphically in detail.

b. A short direction bay of a 16-storied office building is considered for lateral load

analysis. Wind load and Earthquake load are taken as lateral loads.

The specified bay is modeled by three structural systems,

1. Rigid Frame model

2. Infilled Frame model

3. Coupled Wall model

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The Coupled Wall is modeled into three structural sub models as

i. Coupled Wall model (without auxiliary beam)

ii. Coupled Wall model (with auxiliary beam)

iii. Equivalent Wide Column model

The total five models are then analyzed with the aforesaid software.

c. A shear panel element is used to enable modelling of shear wall. Axial, shear and

bending deformation are considered during the analysis. Modeling of shear wall in 2-D

analysis is done using the concept of rigid end condition between columns and beams.

d. The parameters that are varied in structural system are, coupling beam size, column

size, inclusion of infill material (Brick masonry) in modelling rigid frame structures etc.

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Chapter 2

LITERATURE REVIEW

2.1 Introduction

Recently there has been being a considerable increase in the number of tall buildings both

residential and commercial. The modern trend is towards taller and more slender structures.

Thus, the effects of lateral load like wind load and earthquake load etc. are attaining

increasing importance and almost every designer is faced with the problem of providing

adequate strength and stability against lateral loads. This is a new development in

Bangladesh, as the earlier building designers usually designed for the vertical loads only and

as an afterthought checked, the final design for the lateral loads as well.

Tall building is analyzed by idealizing the structure into simple two-dimensional or more

refined three-dimensional continuums. In two-dimensional methods several approximations

are made and particular column line is chosen to analyze the building, in which total

effectiveness of the building is not achieved. On the other hand, in three-dimensional

analysis, the whole building is taken into consideration and thus, the structure is modeled

more realistically.

Several commercial software are available for two and three-dimensional analysis of

structures. Where as software for two-dimensional analysis are usually inexpensive, the same

for the three-dimensional analysis may be very expensive and not quite easy to use. Since

designers of moderately high rise buildings very often adopt two-dimensional analysis

methods in the design office for simplicity and for comprehensive analysis three-dimensional

method is obvious.

In the following section, the details of literature review of followings are stated:a. Structural Systemsb. Lateral Loadsc. Method of Analysisd. Modeling Techniquee. Driftf. P-Delta Effect

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2.2 Structural System

From the structural engineer’s point of view, the determination of the structural system of a

high rise building is ideally involved only the selection and arrangement of the major

structural elements to resist most efficiently the various combinations of gravity and

horizontal loads. In reality, however, the choice of structural system is usually strongly

influenced by other than structural considerations. Several factors have to be taken into

account in deciding the structural systems. These include the internal planning, the material

and method of construction, the external architectural treatment, location and routing of the

service systems, the nature and the magnitude of the horizontal loads, the height and the

structural system etc. The taller is the building, it is more critical to choose an appropriate

structural system.

A major consideration affecting the structural system is the function of the building. Modern

office buildings call for large open spaces that can be subdivided with lightweight

partitioning to suit the individual tenant’s needs. Consequently, main vertical components are

generally arranged, as far as possible, around the perimeter of the plan and, internally, in

group around the elevator, stair, and service lifts. The floor areas between the exterior and

interior components, leaving large column free areas available for office planning. The

services are distributed horizontally in each story above the partitioning and are usually

concealed in a ceiling space. The extra depth required by this space causes typical story

height in an office building to be 3000 mm or more.

A major step forward in reinforced concrete high rise structural system comes with the

introduction of shear walls for resisting horizontal load. This is the first in a series of

significant developments in the structural systems of concrete high rise buildings, freeing

them from the previous 20 to 25 story height limitations of the rigid frame and flat plate

systems. The innovation and refinement of these new systems, together with the development

of higher strength concrete, has allowed the height of concrete buildings to reach within

striking distance of 100 stories.

2.2.1 Rigid Frame

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

consisting of columns and beams with moment resistance joints (Fig. 2.1). The lateral

stiffness of a rigid frame bent depends on the bending stiffness of the columns, beams, and

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connections in the plane of bent. The rigid frame’s principal advantage is its open rectangular

arrangement, which allows freedom of planning and easy fitting of doors and windows. If

used as the only source of lateral resistance in a building, in its typical 6m to 9m bay size,

rigid framing is economical only for buildings up to 25 stories. Above that the relatively high

lateral flexibility of the frame calls for uneconomically large members in order to control the

drift.

Rigid frame construction is ideally suited for reinforced concrete buildings because of the

inherent rigidity of reinforced concrete joints. The rigid frame system is also used for steel

buildings, but moment resistant connections in steel tend to be costly. The sizes of the

columns and beams at any level of rigid frame are directly influenced by the magnitude of

the external shear at that level, and they therefore increase toward the base.

Column

Beam

Fig. 2.1 Rigid frame

Gravity load also is resisted by the rigid frame action. Negative moments are induced in the

beams adjacent to the columns reducing the mid-span positive moment significantly

compared to a simply supported span. In structures in where gravity loads dictate the design,

economies in member sizes from this effect tend to be offset by the higher cost of the rigid

joints. While rigid frames of a typical scale that serve alone to resist lateral load have an

economic height limit of about 25 stories. Smaller scale rigid frames in the form of perimeter

tube, or typically scaled rigid frames in combination with shear wall or braced bent, can be

economic up to much greater heights.

2.2.1.1 Behaviour of Rigid Frame Structure under Lateral Load

The horizontal stiffness of a rigid frame is governed mainly by bending resistance of the

beams, the columns, and their connections and in tall frame, by the axial rigidity of the

columns. The accumulated horizontal shear above any story of a rigid frame is resisted by

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shear in the columns of that story. The shear causes the story height columns to bend in

double curvature with points of contra-flexure at approximately mid story height levels. The

moments applied to a joint from the columns above and below are resisted by the attached

beams, which also bend in double curvature, with points of contra-flexure at approximately

mid span.

The overall moment of the external horizontal load is resisted in each story level by the

couple resulting from the axial tensile and compressive forces in the columns on opposite

sides of the structure. The extension and shortening of the columns cause overall bending and

associated horizontal displacements of the structure. Because of the cumulative rotation up

the height, the story drift due to overall bending increases with height, while that due to

racking tends to decrease.

Consequently the contribution to story 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% than of that racking, except in very tall, slender, rigid

frames. Therefore the over all deflected shape of a high rise rigid frame usually has a shear

configuration.

2.2.2 Shear Wall

A shear wall structure is considered to one whose resistance to horizontal load is provided

entirely by shear wall (Fig. 2.2). The walls are part of a service core or a stair well, or they

serve as partitions between accommodations. They are usually continuous down to the base

to which they are rigidly attached to form vertical cantilever.

Shear wall

Fig. 2.2 Plan of shear wall

Their high inplane stiffness and strength makes them well suited for bracing buildings up to

about 35 stories, while simultaneously carrying gravity loads. It is usual to locate the walls

on plan, so that, they attract an amount of gravity dead load sufficient to suppress the

maximum tensile bending stresses in the wall caused by lateral load. In this situation, only

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minimum wall reinforcement is required. The term “shear wall” is in some way a misnomer

because the walls deform predominately in flexure. Shear walls are planar, but are often of L,

T, I or U shaped section to better suit the planning and to increase their flexural stiffness.

2.2.2.1 Behaviour of Shear Wall Structure under Lateral Load

High rise building typically comprises an assembly of shear walls whose length and

thickness changes or not. It is discontinued or not through the height. The effect of such

variations creates complex redistribution of the moments and shears between the walls, with

associated horizontal interactive forces in the connecting beams and slabs. To understand the

behaviour of shear wall structures, they are classified as proportionate and non-proportionate

systems.

A proportionate system is one in which the ratios of the flexural rigidities of the walls remain

constant through the height. As for example, two walls connected by beams whose lengths do

not change throughout the height, but whose changed walls thickness are same at any level,

is proportionate. Proportionate systems of walls do not cause any redistribution of shears and

moments at the changed levels. The statically determinacy of proportionate systems allows

the analysis is done by consideration of equilibrium. The external moment and shear on non-

twisting structures are distributed between the walls simply in proportion to the flexural

rigidities.

A non-proportionate system is one in which the ratios of the walls flexural rigidities are not

constant through the height. At levels where the rigidities change, redistribution of the wall

shear and moments occur, corresponding horizontal interactions in the connecting beams and

the possibility of very high local shears in the walls. Non proportionate structures are

statically indeterminate. Hence it is more difficult to visualize the behaviour and analyze.

2.2.3 Shear Wall-Frame

A structure whose resistance to horizontal load is provided by a combination of shear walls

and rigid frames may be categorized as a wall-frame structure. The shear walls are often parts

of the elevator and service cores while the frames are arranged in plan, in conjunction with

the walls, to support the floor system.

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When a wall-frame structure is loaded laterally, the different free deflected forms of the walls

and the frames cause them to interact horizontally, through the floor slabs. Consequently, the

individual distribution of lateral load on the wall and the frames are very different from the

distribution of the external load. The horizontal interaction is effective in contributing to

lateral stiffness to the extent that wall-frame of up to 50 stories or more are economical. If the

wall-frame structures that do not twist and, therefore, that is analyzed as equivalent planar

models which are mainly plan-symmetric structures, subjected to symmetric load. Structures

that are asymmetric about the axis of loading inevitably twist.

The potential advantages of a wall-frame structure depend on the amount of horizontal

interaction, which is governed by the relative stiffness of the walls and frames, and the height

of the structure. The taller the building and, in typically proportioned structures, the stiffer

the frames, the greater is the interaction. It is used to be common practice in the design of

high rise structure to assume that the shear walls or cores resist all lateral loads, and to design

the frames for gravity load only. This assumption would incur little error for buildings of less

than 20 stories with flexible frames.

The principal advantages of accounting for the horizontal interaction in designing a wall-

frame structure are as follows (Coul, 1991):

i. The estimated drift is significantly less than if the walls alone are considered to resist

the horizontal load.

ii. The estimated bending moments in the walls or cores are less.

iii. The columns of the frames are designed as fully braced.

iv. The estimated shear in the frames in many cases is approximately uniform throughout

the height.

2.2.3.1 Behaviour of Shear Wall-Frame under Lateral Load

Considering the separate horizontal stiffness at the top of a typical 10-storied elevator core

and typical rigid frame of the same height, the core is 10 or more times as stiffer as the

frame. If the same core and frame are extended to a height of 20 stories, the core is then only

approximately three times as stiffer as the frame. At 50 stories the core is reduced to being

only half as stiff the frame. The change in the relative top stiffness with the total height,

occurs because of the top flexibility of the core. It behaves as a flexural cantilever, is

proportioned to the cube of the height, where as the flexibility of the frame, which behaves as

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shear cantilever, is directly proportioned to its height. Consequently, height is a major factor

in determining the influence of the frame on the lateral stiffness of the wall-frame.

A further understanding of the interaction between the wall and the frame in a wall-frame

structure is given by the deflected shapes of the shear wall and a rigid frame subjected

separately to horizontal load, Fig. 2.3 and 2.4.

Flexural shape Shear shape

Shear shape

Point of contra- flexure

Flexural shape

(a) (b) (c)(a) Wall subjected to uniformly distributed horizontal load

(b) Frame subjected to uniformly distributed horizontal load (c) Wall-frame structure subjected to horizontal load

Fig. 2.3 Deflected shape of wall-frame structure.

Interaction forces

(a) (b) (c)

(a) Rigid frame (b) Shear wall (c) Interconnected Frame and shear mode bending mode shear wall (Equal deflection at each deformation deformation story level)

Fig. 2.4 Interaction of forces between wall and frame.

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The wall deflects in a flexural mode with concavity downward and a maximum slope at the

top, while the frame deflects in a shear mode with concavity upward and a maximum slope at

the base. When the wall and frame are connected together by a pin ended links and subjected

to horizontal load, the deflected shape of the composite structure has a flexural profile in the

lower part and a shear profile in the upper part.

2.2.4 Coupled Shear Wall

In many practical situations, however, walls are connected by moment resisting members.

Walls in residential buildings are perforated by vertical rows of openings that are required for

windows on external gable walls or for doorways or corridors in internal walls.

Wall centroidal axisShear wallCoupling beam

Fig.2.5 Coupled shear wall

The walls are connected by beam or floor slabs serve as connecting beams to produce a shear

interaction between the two in plane cross walls (Fig. 2.5). Such structures, which consist of

walls that are connected by bending resistant elements, are termed “Coupled shear wall,” in

which the presence of the moment resisting connections greatly increases the stiffness and

efficiency of the wall system.

2.2.4.1 Behaviour of Coupled Shear Wall Structures under Lateral Load

The coupled walls when deflect under the action of the lateral loads, the connecting beam’s

ends are forced to rotate and displace vertically, so that the beams bend in double curvature

and thus resist the free bending of the walls. The bending action induce shears in the

connecting beams, which exert bending moments on each walls, tensile in the wind ward

wall and compressive in the leeward wall. The wind moment M at any level is then resisted

by the sum of the bending moments M1 and M2 in the two walls (Fig. 2.5) at that level. The

moment of the axial force is Nl, where N is the axial force in each wall at that level and l is

the distance between their centroidal axes.

M = M1 + M2 + Nl (2.1)

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The last term represents the reverse moment caused by the bending of the connecting beams,

those oppose the free bending of the individual walls. This term is zero in the case of linked

walls, and reaches a maximum when the connecting beams are infinity rigid.

The action of the connecting beams is then to reduce the magnitudes of the moments in the

two walls by causing a proportion of the applied moment to be carried by axial forces.

Because of the relatively larger lever arm l involved, a relatively small axial stress gives rise

to a disproportionally larger moment of resistance. The maximum tensile stress in concrete is

greatly reduced. This makes it easier to suppress the wind or earthquake local tensile stresses

by gravity load compressive stresses.

2.2.5 Infilled-Frame

In many countries infilled frame (Fig.2.6a) is the most usual form of construction for high

rise buildings of up to 30-stories height. Column and beam framing of reinforced concrete, or

sometimes steel, is infilled by panels of brickwork, block work, or cast-in-place concrete.

When an infilled frame is subjected to lateral load, the infill behaves effectively as a strut

along its compression diagonal to brace the frame, Fig. 2.6b.

The infills serve also as an external wall or internal partitions, the system is an economical

way of stiffening and strengthening the structure.

Shear deformation of infill

Leeward column in compression

Frame bearing on infill Windward column

in tension Equivalent diagonal strut

(a) (b)

(a) Interaction between frame and infills (b) Analogous braced frame

Fig. 2.6 Idealization of Frame-Infill interaction behaviour

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In non-earthquake regions where the wind forces/earthquake forces not severe, the masonry

infilled concrete frame is one of the most common structural forms for high rise construction.

The infilled are presumed to contribute sufficiently to the lateral strength of the structure for

it to withstand the horizontal load. The simplicity of construction with skilled expertise in

building such type of structures have made the infilled frame one of the most rapid and

economical structural forms for tall buildings. Their use in earthquake regions, therefore, is

provided with the additional provision that the walls are reinforced and anchored into the

surrounding frame with sufficient strength to withstand their own transverse infilled forces.

2.2.5.1 Behaviour of Infiled Frames under Lateral Load

Masonry use in infill to brace a frame combines some of the desirable structural

characteristics of each, while overcoming some of their deficiencies. Due to high in-plane

rigidity of the masonry wall, it gives more stiffness to the wall than relatively flexible frame.

The ductile frame contains the brittle masonry and when it cracks up to certain loads and

displacement much larger than it is achieved without the masonry infill. The result is,

therefore, a relatively stiff and tough bracing system. The wall braces the frame partly by its

behaviour as a diagonal bracing strut in the frame (Fig. 2.6). Three potential modes of failure

of the wall arise as a result of its interaction with the frame. The first is a shear failure

stepping down through the joints of the masonry and precipitated by the horizontal shear

stresses in the bed joints. The second is a diagonal crack of the wall through the masonry

along a line, or lines, parallel to the leading diagonal and caused by the tensile stresses

perpendicular the leading diagonal. The “perpendicular” tensile stresses are caused by the

divergence of the compressive stress trajectories on opposite sides of the load diagonal as

they approach the middle region of the infill. The diagonal crack is initiated at and spreads

from the middle of the infill, where the tensile stresses are a maximum, tending to stop near

the compressive corners, where the tension is suppressed. In the third mode of failure, a

corner of the infill at one of the ends of the diagonal strut some times is crushed against the

frame due to the high compressive stresses in the corner. The nature of the forces in the

frame can be understood by referring to the analogous braced frame Fig. 2.6b. The forward

column is in tension and the leeward column is in compression.

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2.2.5.2 Stresses in Infill

When the lateral loads are subjected on the Infill frame, stresses are generated in the infill

materials. Mainly three types of stresses are formed. They are shear stress, tensile stress and

compressive stress. Shear stress is related to combination of shear stress and normal stress

and it follows Coulomb’s Law up to certain normal stress. Diagonal deformation of block

bounded by beam and column produces diagonal tension in the infill that causes failure in

tension. Mortar goes more strain than brick in masonry by compressive force that causes

tensile stress in brick. Ultimately the corner block fails in tension.

a. Shear Failure

Shear failure of the infill is related to the combination of shear and normal stresses induced at

points in the infill when the frame bears on it as the structure is subjected to the external

lateral shear. Lot of series of plane-stress membrane finite element analyses have shown that

the critical values of this combination of stresses occur at the center of the infill and they are

expressed empirically, given by Coull (1991)

Shear stress, (2.2)

Vertical compressive stress, (2.3)

Where, Q is the horizontal shear load applied by the frame to the infill of the length L, height

h, and thickness t.

b. Diagonal Tensile Failure

Consequently, diagonal crack of the infill is related to the maximum value of the diagonal

tensile stress in the infill. It also happens at the center of the infill and based on the results of

the analysis, it is expressed empirically as diagonal tensile stress,

(2.4)

These stresses are governed mainly by the properties of the infill material. They are little

influenced by the stiffness properties of the frame because, it occurs at the center of the infill

away from the region of contact with the frame.

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c. Compressive Failure of the Corners

Experiment on model infilled frames have shown that the length of bearing of each story-

height column against its adjacent infill is governed by flexural stiffness of the column

relative to the in-plane bearing stiffness of the infill. The stiffer the column, the longer the

length of bearing and the lower the compressive stresses at this interface. The length of

column bearing is estimated by, (2.5a)

(2.5b)

Where,

Em is the elastic modulus of the masonry and EI is the flexural rigidity of the column.

The parameter expresses the bearing stiffness of the infill relative to the flexural rigidity of

the column. The stiffer the column, the smaller the value of and the longer the length of

bearing.

It is considered that when the corner of the infill crushes, the masonry bearing against the

column within the length is at the masonry ultimate compressive stress f’m, then the

corresponding ultimate horizontal shear Q’c on the infill is given by,

(2.6a)

If the allowable horizontal shear is Qc on the infill, and consider a value for E/Em is 3 for

reinforced concrete frame. The allowable horizontal shear Qc for a reinforced concrete

framed infill is,

(2.6b)

Where, fm is allowable compressive stress of infill.

From above equation it is shown that the masonry compressive strength and the wall

thickness have the most direct influence on the infill strength while the column inertia and

infill height less effect on the infill strength because of their fourth root.

d. Code Provisions for Infilled Material

BNBC (1993),

For clay units,Allowable shear stress, < 0.40 N/ mm2

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Allowable compressive stress, axial, N / mm2

Allowable compressive stress, flexural, Fb = 0.33 f’m 10 N / mm2

Direct tensile stress, Ft = 0.35 N/ mm2 (51 psi )

Allowable bond shear stress, N / mm2 ( psi )

Modulus of Elasticity Em =750 f’m 15,000 N / mm2

Shear Modulus G = 0.4 Em

UBC (1997),

Allowable bond shear stress, N / mm2 ( psi )

Allowable compressive stress, N / mm2

Allowable tensile stress

Normal to bed joint, Ft=0.17 N/mm2 (24 psi)

Normal to head joint, Ft=0.34 N/mm2 (48 psi)

Modulus of Elasticity, Em = N/mm2

Hendry, A.W. and Davies, S. R. (1981),

Direct tensile stress, Ft = 0.40 N/ mm2 (58 psi)

Modulus of Elasticity Em = 700 f’m N / mm2

Flexural tensile strength Ftb = 0.80 to 2 N / mm2

Shear strength Fv = 0.3 N / mm2

Compressive strength N / mm2

2.3 Review of Lateral Loads

Loads on high rise buildings differs from loads on low rise buildings in its accumulation into

much larger structural forces, in the increased significance of wind load, and in the greater

importance of dynamic effect. The collection of gravity load over a large number of stories in

a high rise building produces column loads of an order higher than low-rise buildings. Wind

load on a high rise building acts not only over a very large building surface, but also with

greater intensity at the greater heights and with a large moment arm about the base than on a

low-rise building. Although wind load over a low-rise building usually insignificant

influence on the design of the structure, wind on a high rise building has a dominant

influence on its structural arrangement and design. In an extreme case of a very slender or

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flexible structure, the motion of the building in the wind is considered in assessing the load

applied by the wind.

In earthquake regions, any internal loads from the shaking of the ground well exceed the load

due to wind, therefore, be dominant in influencing the building’s structural system, design,

and cost. As an internal problem, the building’s dynamic response plays a large part in

influencing, and in estimating, the effective load on the structure.

With the exception of dead load, the loads on a building are not assessed accurately. While

maximum gravity live loads are anticipated approximately from previous field observations,

wind and earthquake loads are random in nature, more difficult to measure from past events,

and even more difficult to predict with confidence. The application of probabilistic theory

has helped to rationalize, if not in every case to simply, the approaches to estimate wind and

earthquake loads.

2.3.1 Wind load A mass of air moving at a certain velocity has a kinetic energy, equal to ½ MV2, where M

and V are the mass and velocity of air in motion. When an obstacle like a building is met in

its path, a part of the kinetic energy of air in motion gets converted to potential energy of

pressure. The actual intensity wind pressure depends on a number of factors like angle of

incidence of the wind, roughness of surrounding area, effects of architectural features, i,e.

shape of the structure etc. and lateral resistance of the structure. Apart from these, the

maximum design wind load pressure depends on the duration and amplitude of the gusts and

the probability of occurrence of an exceptional wind in the lifetime of building. It is possible

to take into account the above factors in determining the wind pressure.

The lateral load due to wind is the major factor that causes the design of high rise buildings

to differ from those of low rise to medium rise buildings. For buildings of up to about 10

storied and of typical properties and the design is rarely affected by the wind loads. Above

this height, however, the increase in size of the structural members, and the possible

rearrangement of the structure to account for wind load, incurs a cost premium that increases

progressively with height. With innovations in architectural treatment, increase in the

strengths of materials, and advances in method of analysis, tall building structures become

more efficient and lighter and, consequently, more prone to deflect and even to sway under

wind load.

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Along wind Gust pressure

Mean pressure

Across wind Wind

Fig. 2.7 Simplified two dimensional flow of wind. Fig. 2.8 Schematic representation of mean wind and gust velocity

2.3.1.1 Determination of Design Wind Load

Wind is the general word for air naturally in motion, which by virtue of the mass and velocity

possesses kinetic energy. If an obstacle is placed in the path of the wind so that the moving

air is stopped or deflected from its path, then all or part of the kinetic energy of the moving

air is transformed into pressure (Fig. 2.7 & 2.8). The intensity of pressure at any point on an

obstacle depends on the shape of the obstacle, the angle of the incidence of the wind, the

velocity and density of the air, and the lateral stiffness of the engaged structure.

Under the action of a natural wind, a tall building is continually buffeted by gusts and others

aerodynamic forces. The structure deflects about a mean position and will oscillate

continuously.

If the wind energy that is absorbed by the structure is larger than the energy dissipated by the

structural damping, then the amplitude of oscillation continues to increase and finally leads to

destruction and the structure comes aerodynamically unstable.

These factors have increased the importance of wind as a design consideration. For

estimations of the overall stability of a structure and of the local pressure distribution on the

building, knowledge of the maximum steady or time averaged wind loads is usually

sufficient.

2.3.1.2 Methods for Determining Wind Load

Here, two methods are described. The first method is Quasi-Static method (static approach),

in that it assumes the building is fixed rigid body in the wind. Quasi-Static method is

appropriate for tall building, slenderness or susceptibility to vibration in the wind. The

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second method is Dynamic Method. It is appropriate for exceptionally tall, slender or

vibration-prone building. The two methods are described in UBC.

a. Quasi-Static Method

The quasi-static method has generally proved satisfactory. However, in very tall and slender

buildings, aerodynamics instability may develop. This is because of the fact that during a

windstorm and the building is constantly buffeted by gusts and starts vibrating in its

fundamental mode. If the energy absorbed by the building is more than the energy it can

dissipate by structural damping, the amplitude of the vibration goes on increasing till failure

occurs. A detailed study supported by wind tunnel experiments is often necessary in this

case.

It is representative of modern static methods of estimating wind load in that it accounts for

the effects of gust and for local extreme pressures over the faces of the building. It also

accounts for local differences in exposure between the open country side and a city center, as

well as allowing for vital facilities such as hospitals, state bank, power station, and fire and

police stations, whose safety must be ensured for use after an extreme wind storm.

The determination of wind design forces on a structure is basically a dynamic problem.

However, for reasons of tradition and for simplicity, it has been used practice to use a quasi-

static approach and treat wind as a statically applied pressure, neglecting its dynamic nature.

The wind has calculated as per following section, 2.3.2.

Some of the considerations that enter into the choice of design wind pressure are,

The anticipated life time of the structure and its relation to the return period of maximum

wind velocity

The duration of gusts

The magnitude of gusts

Variation of wind speed with height

Angle of inclination of the wind

Influence of the ground

Influence of the architectural features

Influence of the internal pressure

Lateral resistance of structure

19

b. Dynamic Method

If the building is exceptionally slender or tall, if it is located in extremely severe exposure

condition, the effective wind load on the building is increased by dynamic interaction

between the motion of the building and the gust of the wind. If it is possible to allow for it in

the budget of the building, the best method of assessing such dynamic effects is by wind

tunnel tests. For buildings that are not so extreme as to demand a wind tunnel test, but for

which the simple design procedure is inadequate, alternative dynamic methods of estimating

the wind load by calculation have been developed.

i. Wind Tunnel Experimental Method

Wind tunnel tests to determine load is quasi steady for determining the static pressure

distribution on a building. The pressure coefficients so developed are then used in calculating

the full-scale load through on of the prescribed method. This approach is satisfactory for

building whose motion is negligible and therefore has little effect on the wind load.

If the building slenderness or flexibility is such that its response to excitation by the energy

of the gusts may significantly influence the effective wind load, the wind tunnel test is a fully

dynamic one. In this case, the elastic structural properties and the mass distribution of the

building as well as the relevant characteristics of the wind are modeled.

Building models for wind tunnel test are constructed with a scale of 1:400 being common

(Coull, 1991). Tall buildings typically exhibit a combination of shear and bending behaviour

that has a fundamental sway mode comprising a flexurally shaped lower region and a

relatively linear upper region. This is represented approximately in wind tunnel tests by a

rigid model with flexurally sprung base. It is not necessary in such a model to represent the

distribution of mass in the building, but only its moment of inertia about the base.

The wind characteristics that are generated in the wind tunnel are the vertical profile of the

horizontal velocity, the turbulence intensity and the power spectral density of the longitudinal

component, special “ boundary layer” wind tunnels have been designed to generate those

characteristics. Some use long working sections in which the boundary layer develops

naturally over a rough floor, others shorter ones include grids, fences, or spires at the test

section entrance together with a rough floor, while some activate the boundary layer by jets

or driven flops. The working sections of the tunnel are up to a maximum of about 1.8 sq. m

(20 sq.ft) and it operates at atmospheric pressure.

20

ii. Analytical MethodWind tunnel testing is a highly specialized, complex, and expensive procedure, and is

justified only for very high cost projects. To bridge up the gap between those buildings that

require only a simple approach to wind load and those that clearly demand a wind tunnel

dynamic test, more detailed analytical methods have been developed that allow the dynamic

wind load. The method described here is based on the pioneering work of Davenport and is

now included in the National Building Code of Canada (NBCC).

The external pressure or suction P on the surface of the building is obtained using the basic

equation.

p = qCcCGCp (2.7)

q = wind dynamic pressure for a minimum basic 50 years wind speed at a height of 10m

above ground

Cc = exposure factor is based on a mean wind speed vertical profile

CG = gust effect factor is the ratio of the expected peak loading to the mean loading effect.

Cp = external pressure coefficient averaged over the area of the surface considered.

2.3.2 Code Provisions for Wind Load

The minimum design wind load on buildings and components is determined based on the

velocity of the wind, the shape and size of the building and the terrain exposure condition of

the site. Provision to the calculation of design wind loads for the primary framing system and

for the individual structural components of the buildings. Provisions are included for forces

due to along-wind (Fig. 2.7) response of regular shaped building, caused by the common

wind-storms including cyclones, thunder-storms and norwesters.

a. Basic Wind Speed

The basic wind speed for the design is taken from basic wind speed map of Bangladesh

(BNBC,1993), where it is in km/h for any location in Bangladesh, having isotachs

representing the fastest-mile wind speed at 10 meters above the ground with terrain exposure

B for a 50 years recurrence interval. The minimum value of the basic wind speed set in the

map is 130 km / h and maximum is 260 km / h.

21

b. Exposure Category

Exposure A: Urban and sub-urban areas, industrial areas, wooded areas, hilly or other

terrain covering at least 20 percent of the area with obstructions of 6 meters or more in height

and extending from the site at least 500 meters or 10 times the height of the structure, which

ever is greater.

Exposure B: Open terrain with scattered obstruction having heights generally less than 10

m extending 800 m or more from the site in any full quadrant. This category includes

airfields, open park land, sparely built up out skirts of towns, flat open country and grass

land.

Exposure C: Flat and unobstructed open terrain, coastal areas and riversides facing large

bodies of water, over 1.5 km or more in width. Exposure C extends inland from the shoreline

400 m or 10 times the height of structure, whichever greater. The basic wind speed for

selected locations in Bangladesh are given in Appendix A, Table A.4.1

c. Sustained Wind Pressure

The sustained wind pressure, qz on a building surface at any height z above the ground can be

calculated from the following relation,

qz = CcCICzVb2 (2.8)

qz = sustained wind pressure at height z , kN / m2

CI = structural importance coefficient as given in Appendix A, Table A.4.2

Cc = velocity to pressure conversion coefficient = 47.2 x 10 -6

Cz= combined height and exposure coefficient, Table 3.2 and Fig. 3.2

Vb = basic wind speed in km/h obtained from Appendix A, Table A.4.1

d. Design Wind Pressure

The design wind pressure, Pz for a structure or an element of a structure at any height z

above mean ground level is determined from relation,

Pz = CGCpqz (2.9)

Pz = design wind pressure at height z, kN / m2

CG = gust coefficient which is either Gz , or Gh to be from Table 3.3

e. Gust Response Factor, Gh for Non-slender Buildings (BNBC, 1993)

For the main wind force resisting system of non-slender buildings and structures, the value of

the gust response factor, Gh is determined from Table 3.3 and Fig. 3.3 evaluated at height h

22

above mean ground level of the building or structure. Height h, is defined as the mean roof

level or the top of the parapet, whichever is greater.

f. Gust Response Factor, Gz for Building Components

For components and cladding of all buildings and structures, the value of Gz is determined

from Table 3.3 and Fig. 3.3 evaluated at height z above the ground, where the component or

cladding under consideration is located on the structure.

Cp = Overall pressure coefficient for structure or component as in Table 3.1 and Fig. 3.1

g. Codes Approach for Wind Load

In Uniform Building Code (1994), building having a height greater than 123 m (400 ft) or a

height greater than five times their width, or with structures sensitive to wind excited

oscillations, dynamic wind load has to be calculated based National Building Code of Canada

(NBCC). Details of Dynamic Wind Load method is described in its supplement.

ANSI standard A58.1 (1982) contains the most comprehensive provisions concerning wind

load on structure.

The UBC and NBCC both assume that wind and earthquake loads need not are taken to act

simultaneously. The UBC considers the improbability of extreme gravity and wind or

earthquake, loads acting simultaneously allowing for the combination a one-third increase in

stress or 25% reduction in the sum of the gravity and wind load or earthquake load.

The NBCC approach allows for the improbability of the loads acting simultaneously. It

applies a reduction factor to the combined loads rather than to increase in the permissible

stresses, with greater reductions for the greater number of load types combined.

The ACI Code approach allows of a load factor of 1.7 for wind load in USD method and a

reduction factor of 0.75 when gravity and wind load is permitted together.

2.3.3 Earthquake Load

Earthquake load consists of the inertial forces of the building mass that result from the

shaking of its foundation by a seismic disturbance. Two methods are described here. The first

approach, termed the Equivalent Lateral Force method. It is simple estimate of the structure’s

fundamental period and the anticipated maximum ground acceleration or velocity, together

with relevant factors to determine a maximum base shear. The design forces used in the

equivalent static analysis are less than the actual forces imposed on the buildings by the

corresponding earthquake. The justification for using lower design forces includes the

23

potential for greater strength of the structure provided by the working stress level, the

damping provided by the building components.

The second method is Modal Method. The equivalent static method is suitable for the

majority of high-rise building. If the lateral load resisting elements or the vertical distribution

of mass are significantly irregular over the height of the building, or setbacks, an analysis

that takes greater consideration of the dynamic characteristics of the building is made. In

such cases, a modal method for analysis is appropriate.

a. Equivalent Lateral Force Method

This method is the most common approach, in this, the earthquake forces are treated as static

forces and the resulting stresses are calculated and checked against specified safe values.

This method is used for calculation of seismic lateral forces for all structural system. The

lateral forces specified in BNBC (1993), UBC (1994), ANSI are intended to be used as

equivalent static loads.

Determination of the Minimum Base Shear

This is an approximate method, which has evolved because of the difficulties involved in

carrying out realistic dynamic analysis. Code practices inevitably rely mainly on the simpler

static force approach and incorporate varying degrees of refinement in an attempt to simulate

the real behaviour of the structures. Basically, it gives a crude means of determining the total

horizontal force (base shear) V on a structure.

UBC (1994) uses equivalent horizontal static forces to design the building for maximum

earthquake motion. Using Newton’s second law of motion, the total lateral seismic force,

also called the base shear, is determined by the relation (Newton’s law),

V = Ma = F1 +F2 + F3 = m1a1 + m2a2 + m3a3 (2.10)

(2.11)

(2.12)

W = building weight

g = acceleration due to gravity

V = total horizontal seismic force over the height of the building

M = mass of the building

a = the maximum acceleration of the building

24

(2.13)

“C” seismic coefficient, which represents the ratio of maximum earthquake acceleration to

the acceleration due to gravity (Taranath, 1988) but in BNBC it refers as “Z”.

An important feature of equivalent static load requirements in most codes of practice till

2000, is the fact that the calculated seismic forces are considerably less than those which is

actually occur in the large earthquakes in the area concerned.

b. Modal Method

This method is based on linear elastic structural behaviour, employs the superposition of a

number of modal peak responses, as determined from a prescribed response spectrum. In a

modal analysis a lumped mass model of the building with horizontal degrees of freedom at

each floor is analyzed to determine the modal shapes and modal frequencies of vibration. The

results are then used in conjunction with an earthquake design response spectrum and

estimates of the modal damping to determine the probable maximum response of the

structure from the combined effect of its various modes of oscillation.

2.3.4 Code Provisions for Earthquake Load

The UBC states that the structure is designed for a minimum total lateral seismic load V,

which is assumed to act non concurrent in orthogonal directions parallel to the main axes of

the structure, where V is the calculated from the formula, UBC (1994), BNBC (1993) as

(2.14)

(2.15)

T = Ct hn3/4 (2.16)

V = base shear, Z = seismic zone coefficient, I = structural importance coefficient

R =response modification coefficient for structural systems, C = Numerical coefficient

W = total dead load + 25% live load in storage and warehouse occupancies

S = site coefficient for soil, T = fundamental period of vibration

Ct = 0.073 for reinforced concrete moment resisting frames and eccentrically braced steel

frames and 0.049 for all other structural systems

25

hn = height in meters above the base to level n.

The design base shear equation provides the level of the seismic design loading for a given

structural system, assuming that the structure undergoes inelastic deformation during a major

earthquake.

a. Vertical Distribution of Lateral Forces

The total design base shear V, is distributed over the height of the structure as described

below,

(2.17)

Ft is the concentrated lateral force applied at the top of the structure,

Ft = 0.07TV 0.25V (2.18)

= 0 for T 0.7 sec. (2.19)

The remaining portion of the base shear is distributed over the height of the structure,

including the top level n, according to the expression.

(2.20)

Wx wi = portion of W at x, i level, hx hi = height to x, i level

The design shear at any story, Vx equals the sum of the forces, Fi and Fx above that story. For

a building with a uniform mass distribution over the height, the lateral forces and story shears

are distributed as shown in fig. 2.9

F t F t + F n

F n

hn Level x hx

D v

Structure Lateral Load Story shearFig. 2.9 Typical distribution of Code specified static forces and story shears in a building with uniform mass distribution

26

b. Limitation of Height and Fundamental Time Period in Code Provisions for Earthquake Analysis

The main restriction that has been imposed by different codes to the Quasi-static method is

structural height. In every code regular and irregular structures of certain height is analyzed

by Quasi-static method. The height restriction is given by different codes.

UBC (1994) 73 m (240’-0”)

IS (1984) 90 m (295’- 0”)

BSLJ (1987) 60m (197’-0”)

Table 2.1 Fundamental time period T, in different codes

Code Formula Suggested

UBC (1994)

T = Cthn3/4

hn = Height in feet above the base to level n

Ct = 0.035 for steel moment resisting frames

Ct = 0.03 for reinforced concrete moment resisting frames and eccentrically braced frames

Ct = 0.02 for all other buildings

NBCC (1995)

T = 0.1 N ( lateral force resisting system consists of a moment resisting space frame )

T = 0.09hn / Ds ( other structures)

N = total number of stories above exterior grade to level n

hn = height above the base to level n in meter

Ds = maximum base dimension of building in meter in direction parallel to the applied seismic

force

IS (1984)

T = 0.1 n ( moment resisting frames without bracing or shear walls for resisting the lateral loads)

T = 0.09H / d ( all others)

n = number of stories including basement stories

H = total height of the main structure of the building in meters

d = maximum base dimension of building in meters in direction parallel to the applied seismic

force

BSLJ (1987)

T = h ( 0.02 + 0.01)

T = the fundamental natural period of the building in seconds

h = the height of the building in meters

= the ratio of the total height of stories of steel construction to the height of the building

BNBC(1993)

T = Ct hn3/4

hn = Height in meters above the base to level n

Ct = 0.083 for steel moment resisting frames

Ct = 0.073 for reinforced concrete moment resisting frames and eccentrically braced steel frames

Ct = 0.049 for all other structural systems

c. Codes Approach for Earthquake Load

27

The principal design document in the United States for regions of high seismicity is the

Uniform Building Code (1994), which incorporates design criteria developed by the

Structural Engineers Association of California. The UBC (1994) allows structures to be

designed based on either equivalent static lateral loads or time history analysis of the

dynamic response of the structure. The method used to determine the loads depends on the

seismic zone and the type of structure. The simpler of two equivalent static loading method is

specified by the UBC under criteria for “minimum design lateral forces,” where as the more

complex equivalent static loading method, as well as the time history analyses, are specified

under “dynamic lateral force procedures.”

The ACI Code approach allows a load factor of 1.87 for earthquake load in USD method and

allowing a reduction factor 0.75 when gravity and earthquake load is permitted together in

USD and WSD method.

2.4 Methods of Analysis

The coupled shear wall structure is analyzed some times by either approximate method or

more accurate techniques. The frames are easy and more flexible to hand calculation, but

tend to be restricted to regular or quasi irregular structures and load systems. It deals with

irregular structures and complex loading, but require the services of a digital computer. The

method employed, generally depends on the structural layout and on the degree of accuracy

required.

The methods of analysis are detailed as follows:

i. Continuous Medium method

ii. Finite Element method

iii. Equivalent Wide Column Frame method

2.4.1 Continuous Medium Method

This is approximate method and it shows a wide understanding the behavior of coupled wall

structure and, at concurrently, gives a better qualitative and quantitative understanding of the

relative influence of the walls and the connecting beams or slab resisting horizontal loads.

The basic assumption made in the analysis are as follows (Coull, 1991):

28

i. The properties of the walls and connecting beams do not change over the height, and

the story heights are constant.

ii. Plane section before bending remains plane after bending for all structural members.

iii. The discrete set of connecting beams, each of flexural rigidity Eib, may be replaced

by an equivalent continuous connecting medium of flexural rigidity Eib/h per unit height,

where h is the story height, the inertia of the top beam should be half of the other beams.

d1 b/2 b/2 d2

Q

q n q M1 M2

N N

Wall 1 Wall 2

Fig. 2.10 Internal forces in coupled shear walls

iv. The walls deflect equally horizontally, as a result of the high in plane rigidity of the

surrounding floor slabs and the axial stiffness of the connecting beams. It follows that the

slopes of the walls are everywhere equal along the height, and thus, using a straight forward

application of the slope deflection equations. The connecting beams, and hence the

equivalent connecting medium, deforms with a point of contra flexure at mid span. It also

follows from this assumption that the curvature of the walls are equal throughout the height,

and also the bending moment in each wall is proportional to its flexural rigidity

v. The discrete set of axial forces, shear forces, and bending moments in the connecting

beams then is placed by equivalent continuous distributions of intensity n, q and m

respectively, per unit height (Fig. 2.10).

N= qdz (2.21)

(2.22)

29

Axial Force in Wall,

(2.23)

Shear in Connecting Members,

(2.24)

Wall Moments,

(2.25)

(2.26)

Deflection,

(2.27)

Significance of Structural Parameter kH,

(2.28)

(2.29)

(2.30)

A = cross sectional area of two walls, I = moment of inertia of two walls

A1 = cross sectional area of wall w1, A2 = cross sectional area of wall w2

L = center distance of walls, h = each floor height

b = width of opening, Ib = moment of inertia of connecting beam

Ic = effective moment of inertia of connecting beam

30

l = distance between centroids of walls 1 and 2

= Poisson’s ratio (0.15) for concrete

d = total depth of coupling beam

(2.31)

For a given set of walls, with fixed dimensions, the value of kH is a measure of the stiffness

of the connecting beams, and it increases if either l, is increased or the clear span b is

decreased. If the connecting beams have negligible stiffness (kH=0) then the applied

moment M is resisted entirely by bending moments in the walls, and the axial force N is

negligible. If the connecting beams are rigid (kH = ), the structure behaves as a single

composite doweled beam, with a linear bending stress distribution across the entire section,

and zero stress at the neutral axis, which is situated at the centroid of the two walls elements.

The value of kH is thus define the degree of composite action and indicates the mode of

resistance to applied moments. If kH is large, say greater than 8, the beams are classed as

stiff and the structure tends to act like a composite cantilever. In between these values the

mode of action varies with the level concerned.

2.4.2 Finite Element Method

In coupled shear wall structures analysis, the most suitable method is equivalent frame

technique and it is the most versatile and accurate analytical method. But sometimes it

becomes difficult to model the structure with any degree of confidence using a frame of

beams and columns where notably with very irregular openings, or with complex support

conditions. The use of membrane finite elements is the only feasible alternative here. In this

technique, the surface concerned is divided into a series of elements, generally rectangular,

triangular, or quadrilateral in shape, connected at a discrete set of nodes on their boundaries.

Explicit or implicit forms of the corresponding stiffness matrices for different element shapes

are presented in the literature, enabling the structure stiffness matrices to be set up and solved

to give all nodal displacements and associates forces. A finite element analysis, rectangular

elements should be as square as possible, triangular elements should be equilateral, and

31

quadrilateral elements should be parallelograms with square sides, to achieve most accurate

results.

In a sense, it is consider the finite elements as pieces of the actual structure if recognizes that

the elements are connected to each other not only at the nodes but also at the sides. It is east

to see that if the pieces are held together only at the nodes, the structure is greatly weakened

because the elements separates along the mesh lines. Clearly, the actual structure does not

perform this way, so a finite element must deform in certain restricted ways. In formulating

this behavior, it is necessary to assure that adjacent elements do not behave as if saw cuts

were placed between them until only wisps of material at the nodes hold the pieces together.

a. The finite element method essentially consists of

i. Idealization of the structure into an assemblage of discrete elements

ii Selection of displacement function

iii Evaluation of stiffness of each element from its geometric and elastic properties

iv Assembly of the overall stiffness matrix from individual element stiffness matrices

v Modification of the stiffness matrix to take into account the boundary conditions

vi Solution of resulting equilibrium equations to obtain nodal displacements.

b. Calculation of Stresses

The method is now well established and documented as software i,e. STAAD –III, ANSYS

etc. is used for practical structural analysis .

In analysis by software, Particular problems arise when using the technique for structures

such as coupled walls where relatively slender components such as coupling beams which

are connected to relatively massive components, shear walls. Although it is perfectly

acceptable to model the walls by rectangular membrane finite element with two degree of

freedom at each node, it is inappropriate to use such elements for the connecting beams. This

is required the use of high aspect ratio (length: depth) elements, which might lead to

computational errors. In addition, a minimum of three elements would be required to model

the double curvature form of bending in the connecting beams, which would increase

considerably the size of the structure stiffness matrix and cost of solution. It is sufficiently

accurate, and much more convenient, to model a beam by a standard line element, but in that

case the node at the wall-beam junctions would have to have three degrees of freedom

32

associated with it (two translation and one rotation). It would not then be possible to ensure

compatibility with the adjoining node of a plane stress element with only two degrees of

freedom (two translations). Some other devices are then required to achieve proper

compatibility between beams and walls, and this is achieved in different techniques.

For example, it is possible to use special elements with as additional rotational degree of

freedom at each node. Such special elements are still rarely available in general purpose in

programs, and they increase the number of degrees of freedom by 50%, although they avoid

the necessity of horizontally long thin wall elements.

A easy alternative is to add a fictitious, flexurally rigid, auxiliary beam to the edge wall

element at the beam-wall junctions. The fictitious beam is used connected to two adjacent

wall nodes, either in the direction of or normal to the beam. This allows the rotation of the

wall, as defined by the relative transverse displacements of the ends of the auxiliary beam,

and the moment, to be transferred to the beam. A similar device is used to connect a column

to a wall if the structure is modeled by a combination of a frame and plane stress finite

elements.

2.4.3 Equivalent Wide Column Frame Method

The most suitable approach is, by the use of a frame analogy, which is a very versatile and

economic approach and is used for the most of the practical purposes.

The analysis requires the modeling of the interaction between the vertical shear walls and the

horizontal connecting beams. Over the height of a single story, a wall panel appears a very

broad, but when viewed in the context of the entire height it appears as a slender cantilever

beam. When subjected to lateral forces, the wall is dominated by its flexural behavior, and

shearing effects is generally insignificant.

Flexible column at wall center line Stiff wide column arm

Flexible beam

Fig. 2.11 Equivalent wide-column model

33

In the easy analogous frame model, the wall presented by an equivalent column. It is located

at the centroidal axis (Fig. 2.11), to which is assigned the axial rigidity EA and the flexural

rigidities EI of the wall. The condition that plane sections remain plane is incorporated by

means of stiff arms located at the connecting beam levels, spanning between the effective

column and the external fibers. The rigid arms ensure that the correct rotations and vertical

displacements are produced at the edges of the walls. The connecting beams is represented as

line elements in the conventional manner, and assigned the correct axial, flexural, and if

necessary, shearing rigidities. Generally, shearing deformations is included if the beam’s

length/depth ratio is less than about 5.

2.4.4 Analogous Frame Method

In conventional stiffness method, the analogous frame is analyzed most conveniently.

General purpose, frame analysis programs are now widely available to carry out the matrix

operations required on both micro and main frame computers. These require no more of the

engineer than a specification of the geometric and structural data, and the applied load.

Different approaches are possible for modeling the rigid ended connecting beams in the

analytical model, depending on the facilities and options available in the program used. The

most important techniques are as follows,

a. Direct Solution of the Analytical Model

A direct application of the stiffness method will require a series of nodes at the junctions

between the stiff arms and the connecting beams in the wide column model, as well as at the

column story levels. The rigidities of the wide column arms are simulated by assigning very

high numerical values of axial areas and flexural rigidities to the members concerned. In

practice, a value of 1,000 to 10,000 times the corresponding values for the flexible

connecting beams has been found to provide results of accuracy without causing numerical

problems in the solution.

b. Use of Stiffness Matrix for Rigid Ended Beam Element

Because of the rigid connecting elements, simple relationships exist between the actions at a

column node and those at the adjacent wall beam junction node. It is possible to derive a

composite stiffness matrix for the complete beam segment between column nodes that

incorporates the influence of the stiff end segments.

34

The required stiffness matrix for the line element with rigid arms is derived either by

transforming the effects at the wall beam junctions i and j to the nodes at the wall centroidal

axes 1 and 2 by a transformation matrix.

c. Use of Haunched Member Facility

A haunched member option is used to represent the rigid arms if specific large stiffness vales

are given to the cross sectional area and flexural rigidity of the haunched ends. These values

are sufficiently large for the resulting deformations to be negligible, but not sufficiently large

to cause computational problems from ill conditioned equations.

The stiffness of the end segments depends on the length as well as the cross sectional

properties and the choice of the rigidities EA and EI for the stiff segments. It reflects the

effect of the ratio of the length of the arm to the span of the flexible connecting beam. End

values of the order of 10,000 times the connecting beam values are generally found

acceptable.

d. Use of Equivalent Uniform Connecting Beams

In a symmetrical coupled wall structure, in which axial deformations of the connecting

beams are assumed negligible, the rotation of the walls at any level is equal. The rotation of

the stiff ended beams are equal, and, consequently, it possible to replace the stiff ended beam

by an equivalent uniform beam with an effective second moment of inertia Ic, thereby,

treating the wide column frame as a normal plane frame of beams and columns.

(2.32)

Ib = real moment of inertia of flexural beam

b= width of connecting beam

l= connecting beam length

The coupled shear wall structure is then, presented by a frame having uniform beams of

length l and flexural rigidities EIc.

If the connecting beams are relatively deep, so that the effects of shearing deformation are

significant, the effective second moment of inertia is assigned may be further modified to

include this effect. The values of Ic must be then replaced I’c, where,

(2.33)

35

(2.34)

A = cross sectional are of beam

G = modulus of shear rigidity of beam

GA = shear rigidity

= cross sectional shape factor for shear, equal to 1.2 for rectangular section.

2.5 Modelling Technique

The response of a building to horizontal load is governed by the components that are stressed

as the building deflects. Really, for ease and accurate structural analysis, the participating

components includes only the main structural elements such as slabs, beams, girders,

columns, walls, and cores etc. In reality, however, other, nonstructural elements are stressed

and contribute to the building’s behavior; these include, for example, the staircases, partition,

and cladding etc.

To make the problem ideal, it is usual necessary in modeling a building for analysis, to

include only the main structural members and to assume that the effects of the nonstructural

components are small and save guard.

To identify the main structural elements, it is necessary to recognize the dominant modes of

action of the proposed building structure and to assess the extent of the various members’

contribution to them. Then, by neglecting consideration of the nonstructural components, and

the less essential structural components, the problem of analyzing a tall building structure is

reduced to a more viable size.

2.5.1 Modelling for Preliminary Analysis

The aim of preliminary analyses, for the early stages of design, to compare the performance

of alternative proposals for the structure, or to determine the deflections and major member

forces in a chosen structure from which the size of structure’s elements to be properly

proportioned. The formation of the model and the procedure for a preliminary analysis is

rapid and produce results that are dependable approximations. The model and its analysis is

therefore represent fairly well, if not absolutely accurately, the principal modes of action and

interaction of the major structural elements. The most complete approach to satisfying the

36

above requirements is a three dimensional stiffness matrix analysis of a fully detailed finite

element model of the structure. The columns, beams, and bracing members are represented

by beam elements, while shear wall and core components is represented by assemblies of

membrane elements (Coull,1991, P-81).

Sometimes, certain reduction in the size or complexity of the model is acceptable. While

allowing it to still in accuracy as a final analysis; for example, if the structure and load are

symmetrical, a three dimensional analysis of a half structure model, or even a two

dimensional analysis of a fully interactive two-dimensional model, is acceptable.

2.5.2 Modelling for Accurate AnalysisIt is important for the intermediate and final stages of design to obtain a reasonably accurate

estimate of the structure deflections and member forces. With the wide availability of the

structural analysis software, it is now possible to solve very large and complex structural

models.

In preliminary analysis, it is necessary some of the more gross approximations. The structural

model for an accurate analysis is represented in a more detailed manner where exist all the

major active components of the prototype structure. The principal elements are columns,

walls, and cores, and their connecting slabs and beams.

The major structural analysis programs typically offer a variety of finite elements for

structural modeling. As an absolute minimum for accurately representing high rise structure,

a three dimensional program with beam element and quadrilateral membrane element is used

to suffice. Beam elements are used to represent beams and columns and by making their

inertias negligibly small or by releasing their end rotations, which are used for shear walls

and wall assemblies, preferably includes an incompatible mode option to better allow for the

characteristic in-plane bending of shear walls.

a. Connection of Beam Element to Membrane Element

When modeled membrane elements, shear walls with in-plane frame connecting beams

require special consideration. Membrane elements do not have a degree of freedom to

represent in-plane rotation of these corners. Therefore, a beam element is connected to node

of a membrane element is effectively connected only by a hinge.

37

Auxiliary beam Connecting beam

Wall element

Fig. 2.12 Connection of beams to wall element for shear wall

A remedy for this deficiency is to add a fictitious, flexurally rigid, auxiliary beam to the

edge wall element (Fig. 2.12). The adjacent ends of the auxiliary beam and the external beam

are both constrained to rotate with the wall-edge node. Consequently, the rotation of the wall,

as defined by the relative transverse displacements of the ends of auxiliary beam, and a

moment are transferred to the external beam (Coull, 1991).

b. High Rise Behaviour

A more accurate assessment of a proposed high rise structure’s behaviour is necessary to

form a properly representative model for analysis. A high rise structure is essentially a

vertical cantilever that is subjected to axial load by gravity and to lateral load by wind or

earthquake.

Lateral load exerts at each level of a building a shear, a moment, and some times, a torque,

which have maximum values at base of the structure that increase rapidly with the building

height. The response of a structure to lateral load, in having to carry the external shear,

moment, and torque, is more complex than its first order response to gravity load.

The recognition of the structure’s behaviour under lateral load and the formation of the

corresponding model are usually the dominant problems of analysis. The principal criterion

of a satisfactory model is that under lateral load it deflects similarly to the prototype

structure.

2.6 Drift of Structure

Drift is the magnitude of displacement at the top of a building relative to its base. The ratio of

the total lateral deflection to the building height, or the story deflection to story height, is

referred to as the “ Deflection Index.” The imposition of a maximum allowable lateral sway

(drift) is based on the need to limit the possible adverse effects of lateral sway on the stability

38

of individual columns as well as the structure as a whole. And also, on the excessive crack

and consequent loss of stiffness and the integrity of nonstructural partitions, glazing and

mechanical elements in the building.

Crack associated with the lateral deflections of nonstructural elements such as partitions,

windows, etc, cause serious maintenance problems. Therefore, a drift limitation is selected to

minimize such crack also second order p-delta effects due to gravity load being of such a

magnitude as to precipitate collapse.

In the absence of code limitation in the past, buildings are designed for wind load with

arbitrary values of drift, ranging from about 1/300 to 1/600 of their height, depending on the

judgement of the Engineer. Deflections based on drift limitation of about 1/300 used several

decades ago and computed, assuming the wind force is resisted by the structural frame alone.

In reality, the heavy masonry partitions and exterior cladding common to buildings of that

period considerably increased the lateral stiffness of such structures.

To date (2000) only the UBC (1994), BOCA and NBCC (1980), among North American

model building codes, specify a maximum value of the deflection index of 1/500,

corresponding to the design wind load. Also, ACI Committee 435 recommends a drift limit

1/500. In recent years many engineering offices, owing to competitive pressures, have

somewhat relaxed the drift criterion by allowing an overall in any one story not to exceed

H/400. Also, in cases where wind tunnel studies indicate wind forces in the building to be

smaller than those specified in the code, designers take the liberty of applying the H/500

criterion to the smaller (wind tunnel) wind forces.

The performance of modern reinforced concrete buildings designed in recent years to meet

this criterion appears to have been satisfactory with respect to the stability of the individual

columns and the structure as a whole, the integrity of nonstructural elements, and the comfort

of the occupants of such buildings.

Most of the modern high rise reinforced concrete buildings containing shear walls have

computed deflections ranging between H/800 and H/1200 due to inherent rigidity of the wall-

frame interaction.

To establish of a drift index limit is a major design decision, but, unfortunately, there are no

unambiguous or widely accepted values, or even, in some of the National Codes concerned,

any firm guidance. As the height of the building increases, drift index coefficients is

39

decreased to the lower end of the range to keep the top story deflection to a suitably low

level.

Excessive drift of a structure is reduced by change the geometric configuration of the

building. That is to alter the mode of lateral load resistance, to increase the bending stiffness

of the horizontal members, to add additional stiffness by the inclusion of stiffer wall or core

members, achieving stiffer connections, and even by sloping the exterior columns.

In dynamic response the minimum tolerable values of acceleration for the typical or normal

person needs further studies. It is obvious that the acceptability of a design with respect to

perception of sway motion. It is assessed by a dynamic analysis of the building under a set of

a probable range of wind exposures. No perceptible motion has been reported in concrete

buildings to date. The supplement to the National Building Code of Canada (1980), contains

expressions by which peak along-wind and across-wind acceleration of buildings is

calculated. According to the supplement, “ it appears that when the amplitude of acceleration

is in the range of 0.5 % to 1.5 % of the acceleration due to gravity, movement of the building

becomes perceptible to most people.” Based on this and other information, a tentative

acceleration limitation of 1 to 3 % of gravity once every 10 years is recommended for use in

conjunction with the expressions for computation of acceleration. The lower value is thought

suitable for apartment buildings, and the higher value for office buildings.

2.7 P-Delta Effect

A first order computer analysis of a building structure for simultaneously applied gravity and

horizontal loading results in deflections and forces that are a direct superposition of the

results for the two types of load considered separately. Any interaction between the effects of

gravity load and horizontal load is not account for by the analysis.

In reality, when horizontal load acts on a building and causes it to drift the resulting

eccentricity of the gravity load from the axes of the walls and columns produces additional

moments to which the structure responds by drifting further. The additional drift induces

additional internal moments sufficient to equilibrate the gravity load moments. The effect of

gravity load P acting on the horizontal displacements is known as the P-Delta effect.

The second order P- Delta additional deflections and moments are small for typical high rise

structure, with a magnitude usually of less than 5% (Coull,1991) of the first order values. If

40

the structure is exceptionally flexible, however, the additional forces is sufficient to require

consideration in the member’s design, or the additional displacement causes unacceptable

total deflections that require the structure is stiffened. In an extreme case of lateral flexibility

combined with exceptionally heavy gravity load, the additional forces from the P-Delta effect

might cause the strength of some members are exceeded with the possible consequence

collapse. Or, the additional P-Delta external moments is some times exceed the internal

moments and the structure is capable of mobilizing by drift, in which case the structure

collapses through instability. Such failures occur at gravity loads less than the critical overall

buckling load.

2.8 STAAD-III

STAAD-III is a comprehensive Structural Engineering Software that addresses all aspects of

engineering-model development, analysis, design, verification and visualization.

2.8.1 Type of Structures in STAAD–III EnvironmentA Structure is as an assemblage of elements. STAAD-III is capable of analyzing and

designing structures consisting of both frame and plate/shell elements. Almost any type of

structure can be analyzed by STAAD-III. Most general is the SPACE structure, which is

three-dimensional frame and shear wall structure with loads applied in any direction.

a. Plate/Shell Element

The plate/shell finite element is based on the hybrid element formulation. The element can be

3-noded or 4-noded (quadrilateral). If all the four nodes of a quadrilateral element do not lie

on the same plane, it is advisable to model them as triangular elements. “Surface structures”

such as wall, slabs, plates and shells can be modeled using finite elements. The user may also

use the element for “Plane Stress” action only. The “Element Plane Stress” command should

be used for this purpose.

b. Geometric Modelling Considerations

The program automatically generates a fifth node “O” at the element center. While assigning

nodes to an element in the input data. Element aspect ratio should not excessive. They should

be on the order of 1:1 and preferably less than 4:1.

41

c. Theoretical Basis

The STAAD-III plate finite element is based on hybrid finite element formulations. A

complete quadratic stress distribution is assumed for plane stress action (Fig.2.13) and plate

bending action.

x y Fy

xy yx Fxy

yx xy

y x Fx

(a) (b)

Fig. 2.13 (a) Plane stress distribution, (b) Sign convention of element forces

d. Distinguishing Features of Finite Element

Displacement compatibility between the plane stress component of one element and the plate

bending component of an adjacent element which is at an angle to the first is achieved by the

elements. This compatibility is usually ignored in most flat shell/plate elements. The out of

plane rotational stiffness from the plane stress portion of each element is usefully

incorporated and not treated as a dummy as is usually done in most commonly available

commercial software. These elements are available as triangles and quadrilaterals, with

corner nodes only, with each node having six degrees of freedom. These elements may be

connected to plane /space frame members with full displacement compatibility. No additional

restraints/release are required. The plate bending portion can handle thick and thin plates,

thus extending the usefulness of the plate elements into a multiplicity of problems. The

triangular shell element is very useful in problems with double curvature where the

quadrilateral element may not be suitable.

2.9 Summary

The structural system of high rise building is influenced strongly by its function while having

to satisfy the requirements of strength and serviceability under all probable conditions of

gravity and lateral loads. The taller a building, the more important it is economically to

select an appropriate structural system. The flexural continuity between the members of a

42

structure, enables the structure to resist horizontal load as well as to assist in carrying gravity

load. Lateral load causes rack of the frame due to double bending of the columns and beams,

resulting in an overall shear mode of deformation of the structure. The lateral displacement

of the rigid frames subjected to horizontal load is due to three modes of member deformation,

beam flexure, column flexure, and axial deformation of columns. The lateral displacements

in each story attributable to three components is calculated separately and summed to give

the total drift. If the total drift, or the drift within any story, exceeds the allowable values, an

inspection of the components of drift indicates which members is increased in size to most

effectively control the drift.

Wind load becomes significant for buildings over 10 stories high and progressively more so

with increased height. For buildings that are not very tall or slender, the wind load is

estimated by a static method. The static method depends on location, effects on gust and the

importance of the building. For very tall building, it is recommended that a wind tunnel test

on a model is made.

For structural analysis, the intensity of an earthquake is usually described in terms of the

ground acceleration as a fraction of the acceleration of gravity, i,e. 0.1, 0.2 or 0.3g. Although

peak acceleration is an important analysis parameter, the frequency characteristics and

duration of an earthquake motion is to the natural frequency of a structure and the longer

duration of the earthquake, the greater the potential for damage. The zone coefficient Z in

UBC method corresponds numerically to the effective peak ground acceleration (EPA) of a

region, and is defined for Bangladesh by a map that is divided into three regions which are,

zone 1, zone 2 and zone 3. The places are situated in zone 1, are Barisal, Khulna, Jessore,

Rajshahi etc, in zone 2 are, Chittagong, Commila, Dhaka, Jaypurhat and Phanchaghar etc.

and in zone 3, are Sylhet, Brahmanbaria, Jamalpur and Lalmonirhat (BNBC, 1983) etc. The

values of Z =0.075, 0.15 and 0.25 for zone 1, zone 2 and zone 3 respectively. The coefficient

C represents the response of the particular structure to the earthquake acceleration. A

maximum limit on C=2.75 for any structure and soil condition. The structural system factor

R is a measure of the ability of the structural system to sustain cyclic inelastic deformations

without collapse. The magnitude of R depends on the ductility of the type materials of the

structure. A lower limit of C/R = .075 is prescribed.

43

Continuous medium method is an approximate method for analysis of coupled shear wall. It

is suitable for hand calculation. But the coupled shear wall is analyzed by Equivalent Wide

Column Frame method in which an equivalent column located at the centroidal axis, to

which is assigned the axial rigidity EA and the flexurial rigidities EI of the wall. The

connected beams are represented as line elements in the conventional manner. This method is

the most versatile and accurate analytical method.

Regular frame is analyzed by hand calculation both in Continuous medium method and

Equivalent frame method but irregular frames and walls with varying openings and sizes, it is

difficult to analysis, then the most suitable method of Finite element is alternative. In this

technique, the surface concerned is divided into a series of elements, generally rectangular,

triangular, or quadrilateral in shape, connected at a discrete set of nodes on their boundaries.

Explicit or implicit forms of the corresponding stiffness matrices for different element shapes

are presented in the literature, enabling the structure stiffness matrices to be set up and solved

to give all nodal displacements and associates forces. A finite element analysis, rectangular

elements are as square as possible, triangular elements are equilateral, and quadrilateral

elements are parallelograms with square sides, to achieve most accurate results.

In modeling a structure for analysis it is usually to represent only the main structure members

and to assure that the effects of nonstructural members are small and conservative.

Additional assumptions are made with regard to the linear behavior of the material, the in-

plane rigidity of the floor slabs, and then neglect of certain member stiffness and

deformations, in order to further simplification the model for analysis.

In accurate modeling, the columns and beams of frames are represented individually by beam

finite elements and shear wall is represented by assemblies of membrane finite element.

Drift is the magnitude of displacement at the top of a building relative to its base. In the

absence of code limitation in the past, buildings is used to design for wind load with arbitrary

values of drift, ranging from about 1/300 to 1/600 of their height. To date (2000) only the

UBC (1994), BOCA and NBCC (1980), among North American model building codes,

specify a maximum value of the deflection index of 1/500, corresponding to the design wind

load. Also, ACI Committee 435 recommends a drift limit 1/500. Also, in cases where wind

tunnel studies indicate wind forces in the building is smaller than those specified in the code,

designers take the liberty of applying the H/500 criterion to the smaller (wind tunnel) wind

44

forces. Most of the modern high rise reinforced concrete buildings containing shear walls

have computed deflections ranging between H/800 and H/1200 due to inherent rigidity of the

wall-frame interaction.

When horizontal load acts on a building and causes it to drift the resulting eccentricity of the

gravity load from the axes of the walls and columns produces additional moments to which

the structure responds by drifting further. The additional drift induces additional internal

moments sufficient to equilibrate the gravity load moments. The effect of gravity load P

acting on the horizontal displacements is known as the P-Delta effect.

The second order P- Delta additional deflections and moments are small for typical high rise

structure, with a magnitude usually of less than 5% (Coull,1991) of the first order values. If

the structure is exceptionally flexible, however, the additional forces is sufficient to require

consideration in the member’s design, or the additional displacement causes unacceptable

total deflections that require the structure to be stiffened.

45

Chapter 3

GRAPHICAL PRESENTATION OF LATERAL LOADS

3.1 Introduction

The wind and earthquake load design data are presented in BNBC in tabular form. In design

calculation, the required coefficients would be taken from table value (whichever is required

from BNBC) and intermediate value by interpolation from the given data. In graphical form,

the behaviour of data is easy to understand at a glance and their trend is well known by this

form. All of them are not presented in this limited study. Some of them which are generally

required, these are represented in graphical form in this chapter.

3.2 Graphical Presentation of Wind Load

Wind load parameters are taken from BNBC (1993) for load calculation. These values are

presented in tabular form in Code. For easy calculation and to understand the behaviour in

load analysis, tabular values are represented in graphical form here. The graphs are produced

these are,

i. Cp vs. (Fig. 3.1)

ii. z vs. Cz (Fig. 3.2)

iii. z vs. Gh , Gz (Fig. 3.3)

iv. z vs. (Fig. 3.4, 3.5 & 3.6)

h = height of building

L = length of building parallel to wind in consideration

B= width of building perpendicular to wind

z= height above ground level

46

Table 3.1 Overall pressure coefficient, Cp

L/B Cp

h/B 0.5 h/B=10 h/B=20 H/B 400.1 1.4 1.55 1.8 1.950.5 1.45 1.85 2.25 2.5

0.65 1.55 2 2.55 2.8

1 1.4 1.7 2 2.2

2 1.15 1.3 1.4 1.6 3 1.1 1.15 1.2 1.25

h = building height in meter

B = building width normal to wind in meter

L = building length parallel to wind in meter

47

h/B 40

h/B = 20

h/B = 10

h/B 0.5

48

Fig. 3.1 Evaluation of overall pressure coefficient , Cp

Table 3.2 Combined height and exposure coefficient, Cz Height above ground level,

Cz

z (meter) Exposure A Exposure B Exposure C0 0.368 0.801 1.196

4.5 0.368 0.801 1.196

6 0.415 0.866 1.263

9 0.497 0.972 1.37

12 0.565 1.055 1.451

15 0.624 1.125 1.517

18 0.677 1.185 1.573

21 0.725 1.238 1.623

24 0.769 1.286 1.667

27 0.81 1.33 1.706

30 0.849 1.371 1.743

35 0.909 1.433 1.797

40 0.965 1.488 1.846

45 1.017 1.539 1.89

50 1.065 1.586 1.93

60 1.155 1.671 2.002

70 1.237 1.746 2.065

49

80 1.313 1.814 2.12

90 1.383 1.876 2.171

100 1.45 1.934 2.217

110 1.513 1.987 2.26

120 1.572 2.037 2.299

130 1.629 2.084 2.337

140 1.684 2.129 2.371

150 1.736 2.171 2.404

A B C

50

Fig. 3.2 Evaluation of combined height and exposure coefficient , Cz

Table 3.3 Gust response factors, Gh and Gz

Height above ground level,

Gh and Gz

z (meter) Exposure A Exposure B Exposure C0 1.654 1.321 1.154

4.5 1.654 1.321 1.154

6 1.592 1.294 1.14

9 1.511 1.258 1.121

12 1.457 1.233 1.107

15 1.418 1.215 1.097

18 1.388 1.201 1.089

21 1.363 1.189 1.082

24 1.342 1.178 1.077

27 1.324 1.17 1.072

30 1.309 1.162 1.067

35 1.287 1.151 1.061

40 1.268 1.141 1.055

45 1.252 1.133 1.051

50 1.238 1.126 1.046

60 1.215 1.114 1.039

70 1.196 1.103 1.033

80 1.18 1.095 1.028

51

90 1.166 1.087 1.024

100 1.154 1.081 1.02

110 1.144 1.075 1.016

120 1.134 1.07 1.013

130 1.126 1.065 1.01

140 1.118 1.061 1.008

150 1.111 1.057 1.005

A B C

52

Fig. 3.3 Evaluation of gust response factors, Gh and Gz

Design Wind Pressure, Pz is written as,

Pz = CGCpCcCICzVb2 (3.1)

From above equation it is written as, (3.2)

For different exposure conditions and places the value of is calculated in Table 3.4

to 3.6 and then represented in Fig. 3.4 to 3.6

From the figure value of at different height z for different exposure conditions and

places the value of design pressure, Pz is calculated easily by multiplying the figure value to

Gh Cp CI

For example,

Z = 30 m

Zone =Dhaka

Exposure =B

Then value of is 2.854 (Table 3.4, Fig. 3.4)

Therefor, Pz = 2.854GhCpCI

Where,

Gh = constant for specified building height (Fig. 3.3)

Cp = pressure coefficient for specified building (Fig. 3.1)

53

CI = importance coefficient for specified building (Table C.2)

Table 3.4 Design pressure component, for Dhaka

Height above ground level, Kpa

z (meter) Exposure :A Exposure: B Exposure: C

0 0.766 1.668 2.49

4.5 0.766 1.668 2.49

6 0.864 1.803 2.63

9 1.035 2.024 2.852

12 1.176 2.197 3.021

15 1.299 2.342 3.158

18 1.411 2.467 3.275

21 1.509 2.578 3.379

24 1.601 2.677 3.471

27 1.686 2.769 3.552

30 1.768 2.854 3.629

35 1.893 2.984 3.741

40 2.009 3.098 3.843

45 2.117 3.204 3.935

50 2.217 3.302 4.018

60 2.405 3.48 4.168

70 2.575 3.635 4.299

80 2.734 3.777 4.414

54

90 2.879 3.906 4.52

100 3.019 4.027 4.616

110 3.15 4.137 4.705

120 3.273 4.241 4.787

130 3.392 4.339 4.866

140 3.506 4.433 4.936

150 3.614 4.52 5.005

A B C

55

Fig. 3.4 Value of for different exposure conditions for Dhaka

Table 3.5 Design pressure component, for Chittagong

Height above ground level,

KPa

z (meter) Exposure :A Exposure: B Exposure: C

0 1.174 2.556 3.816

4.5 1.174 2.556 3.816

6 1.324 2.763 4.03

9 1.586 3.102 4.372

12 1.803 3.367 4.63

15 1.991 3.59 4.841

18 2.16 3.781 5.019

21 2.313 3.95 5.179

24 2.454 4.104 5.319

27 2.585 4.244 5.444

30 2.709 4.375 5.562

35 2.901 4.573 5.734

40 3.079 4.748 5.891

45 3.245 4.911 6.031

50 3.398 5.061 6.159

60 3.686 5.332 6.388

56

70 3.947 5.571 6.589

80 4.19 5.788 6.765

90 4.413 5.986 6.928

100 4.627 6.171 7.074

110 4.828 6.341 7.212

120 5.016 6.5 7.336

130 5.198 6.65 7.457

140 5.374 6.794 7.566

150 5.54 6.928 7.671

A B C

Fig. 3.5 Value of for different exposure conditions for Chittagong

Table 3.6 Design pressure component, for Khulna

Height above ground level, kPa

z (meter) Exposure :A Exposure: B Exposure: C0 0.984 2.142 3.198

4.5 0.984 2.142 3.198

6 1.11 2.316 3.377

9 1.329 2.599 3.663

12 1.511 2.821 3.88

57

15 1.669 3.008 4.056

18 1.81 3.169 4.206

21 1.939 3.31 4.34

24 2.056 3.439 4.458

27 2.166 3.556 4.562

30 2.27 3.666 4.661

35 2.431 3.832 4.805

40 2.58 3.979 4.936

45 2.719 4.115 5.054

50 2.848 4.241 5.161

60 3.088 4.468 5.353

70 3.308 4.669 5.522

80 3.511 4.851 5.669

90 3.698 5.016 5.805

100 3.877 5.172 5.928

110 4.046 5.313 6.043

120 4.204 5.447 6.148

130 4.356 5.573 6.249

140 4.503 5.693 6.34

150 4.642 5.805 6.428

A B C

58

Fig. 3.6 Value of for different exposure conditions for Khulna

3.3 Graphical Presentation of Earthquake Load

Earthquake load parameters are taken from BNBC (1993) for Earthquake load calculation.

These values are presented in tabular form in Code and intermediate value can be calculated

by interpolation. For any height of structure, easy calculation of required values and to

understand the trend of value is found from the presented graphs in load analysis. For this

reason, tabular values have represented in graphical form here. The graphs are produced

these are,

i. hn vs. & T (Fig. 3.7 )

ii. hn vs. (Fig. 3.8 )

iii. hn vs. (Fig. 3.9 )

iv. hx vs. (Fig. 3. 10)

59

a. Graphical presentation of fundamental period of vibration, T and ratio of

numerical coefficient, C and site coefficient, S from building height for moment

resisting frame

We know for all buildings the value of fundamental period, T may be approximated by the

following formula

T = Cthn3/4, (3.3)

Ct = 0.073 for reinforced concrete moment resisting frames and eccentrically braced steel

frames and Numerical coefficient given by the following relation

C = (3.4)

From above equations it can be written for reinforced concrete moment resisting frames and

eccentrically braced steel frames as,

(3.5)

T = 0.073 hn3/4 (3.6)

Above values is calculated for different building height as in Table 3.7 and presented in Fig.

3.7

Table 3.7 Evaluation of fundamental period of vibration, T and ratioof numerical coefficient, C and site coefficient, S from building height for moment resisting frame (RC)

Building heightabove base, hn

(meter)T in sec

5.5 0.019

3 4.13 0.166

6 2.92 0.28

9 2.39 0.38

12 2.07 0.47

15 1.85 0.556

18 1.69 0.638

21 1.56 0.716

24 1.46 0.792

27 1.38 0.865

60

30 1.31 0.936

35 1.21 1.05

40 1.13 1.161

50 1.01 1.373

60 0.92 1.574

70 0.86 1.766

80 0.8 1.953

90 0.75 2.133

100 0.72 2.308

110 0.68 2.48

120 0.65 2.647

130 0.63 2.81

140 0.6 2.971

150 0.58 3.129

T

61

Fig. 3.7 Variation of ratio and fundamental time period, T with building height for

MRF

b. Graphical Presentation of Base Shear

Design Base Shear, (3.7)

(derived earlier) (3.8)

Putting the value of for MRF in above equation, it is written as,

(3.9)

For different building height and R values the LHS of above equation is calculated in Table

3.8 and presented in Fig. 3.8, from which the base shear is easily calculated.

For example,

Building height = 24 m

R value = 6 (C.6)

62

Therefore,

V = 0.243ZIWS

Where,

Z = seismic zone coefficient

I = structure importance coefficient

W = seismic dead load

S = site coefficient for soil

Table 3.8 Evaluation of base shear for MRF

Building height

above base, hn

(meter)R=5 R=6 R=7 R=8 R=9 R=10

1 1.100 0.917 0.786 0.688 0.611 0.550

3 0.826 0.688 0.590 0.516 0.459 0.413

6 0.584 0.487 0.417 0.365 0.324 0.292

9 0.478 0.398 0.341 0.299 0.266 0.239

12 0.414 0.345 0.296 0.259 0.230 0.207

15 0.370 0.308 0.264 0.231 0.206 0.185

18 0.338 0.282 0.241 0.211 0.188 0.169

21 0.312 0.260 0.223 0.195 0.173 0.156

24 0.292 0.243 0.209 0.183 0.162 0.146

63

27 0.276 0.230 0.197 0.173 0.153 0.138

30 0.262 0.218 0.187 0.164 0.146 0.131

35 0.242 0.202 0.173 0.151 0.134 0.121

40 0.226 0.188 0.161 0.141 0.126 0.113

50 0.202 0.168 0.144 0.126 0.112 0.101

60 0.184 0.153 0.131 0.115 0.102 0.092

70 0.172 0.143 0.123 0.108 0.096 0.086

80 0.160 0.133 0.114 0.100 0.089 0.080

90 0.150 0.125 0.107 0.094 0.083 0.075

100 0.144 0.120 0.103 0.090 0.080 0.072

110 0.136 0.113 0.097 0.085 0.076 0.068

120 0.130 0.108 0.093 0.081 0.072 0.065

130 0.126 0.105 0.090 0.079 0.070 0.063

140 0.120 0.100 0.086 0.075 0.067 0.060

150 0.116 0.097 0.083 0.073 0.064 0.058

64

10 9 8 7 6 5

Fig. 3.8 Evaluation of base shear (kN) for MRF

c. Graphical Presentation of Base Shear for Dhaka

(3.10)

Z = 0.15 (C.4)

S = 1.50 (A soil profile 21 meters or more in depth and containing more than 6 meters of soft

to medium stiff clay, C.5)

I = 1.0 (standard occupancy structure, C.3)

Above equation is written as,

(3.11)

For different building height and R values the LHS of above equation is calculated in Table

3.9 and presented in Fig. 3.9, from which the base shear is easily calculated.

For example,

65

Building height = 24 m

Zone = Dhaka

R value = 6

Therefore,

(Fig. 3.9)

V = 0.055W

Where,

W = weight for specified building as per BNBC

Table 3.9 Evaluation of base shear for MRF for Dhaka city

Building height

above base, hn

(meter)R=5 R=6 R=7 R=8 R=9 R=10

1 0.322 0.268 0.192 0.120 0.067 0.033

3 0.186 0.155 0.111 0.069 0.038 0.019

6 0.131 0.109 0.078 0.049 0.027 0.014

9 0.107 0.089 0.064 0.040 0.022 0.011

12 0.093 0.078 0.055 0.035 0.019 0.010

15 0.083 0.069 0.049 0.031 0.017 0.009

18 0.076 0.063 0.045 0.028 0.016 0.008

21 0.070 0.058 0.042 0.026 0.014 0.007

24 0.066 0.055 0.039 0.025 0.014 0.007

66

27 0.062 0.052 0.037 0.023 0.013 0.006

30 0.059 0.049 0.035 0.022 0.012 0.006

35 0.054 0.045 0.032 0.020 0.011 0.006

40 0.051 0.043 0.030 0.019 0.011 0.005

50 0.046 0.038 0.027 0.017 0.010 0.005

60 0.042 0.035 0.025 0.016 0.009 0.004

70 0.038 0.032 0.023 0.014 0.008 0.004

80 0.036 0.030 0.021 0.013 0.007 0.004

90 0.034 0.028 0.020 0.013 0.007 0.004

100 0.032 0.027 0.019 0.012 0.007 0.003

110 0.031 0.026 0.018 0.012 0.006 0.003

120 0.029 0.024 0.017 0.011 0.006 0.003

130 0.028 0.023 0.017 0.010 0.006 0.003

140 0.027 0.023 0.016 0.010 0.006 0.003

150 0.026 0.022 0.015 0.010 0.005 0.003

67

10 9 8 7 6 5

Fig. 3.9 Evaluation of base shear ( kN) of MRF for Dhaka City

d. Vertical Distribution of Lateral ForcesIn the absence of a more rigorous procedure, the total lateral forces, which is the base shear

V, can be distributed along the height of the structure as below,

(3.12)

Where,

Fi = Lateral force applied at story level i

Ft = Concentrated lateral force considered at the top of the building in addition to the force Fn

The concentrated force, Ft acting at the top of the building can be determined as follows,

Ft = 0.07 TV 0.25V when T > 0.70 second (3.13)

Ft = 0.0 when T 0.70 second

The remaining portion of the base shear (V-Ft), is distributed over the height of the building

including level n, according to relation,

(3.14)

68

At each story level x, the force Fx is applied over the area of the building in proportion to the

mass distribution at that level.

Considering the equal mass at every level, then the equation can be written as

(3.15)

(3.16)

For different story building the base shear is distributed in Table 3.10 and presented in Fig.

3.10.

For example,

At height = 24 m, Building = 16-storied

Fx = 0.0588(V-Ft)

Where, V = base shear

Table 3.10 Distribution of base shear for 15 to 20- storied building

Building height

above base, hx

(meter)15-storeied 16-storeied 17-storeied 18-storeied 19-storeied 20-storeied

3 0.830 0.740 0.650 0.580 0.530 0.480

6 1.670 1.470 1.310 1.170 1.050 0.950

9 2.500 2.210 1.960 1.750 1.580 1.430

12 3.330 2.940 2.610 2.390 2.110 1.900

15 4.170 3.660 3.270 2.920 2.630 2.380

18 5.000 4.410 3.920 3.510 3.160 2.850

21 5.830 5.150 4.580 4.090 3.680 3.330

24 6.670 5.880 5.230 4.600 4.210 3.810

69

27 7.500 6.620 5.880 5.260 4.740 4.290

30 8.330 7.350 6.540 5.850 5.260 4.760

33 9.170 8.090 7.190 6.430 5.790 5.240

36 10.000 8.820 7.840 7.020 6.320 5.710

39 10.830 9.560 8.500 7.600 6.840 6.190

42 11.670 10.290 9.150 8.190 7.370 6.670

45 12.500 11.030 9.800 8.770 7.890 7.140

48 11.760 10.460 9.360 8.420 7.620

51 11.110 9.940 8.950 8.090

54 10.530 9.470 8.570

57 10.000 9.050

60 9.520

20 19 18 17 16 15

70

Fig. 3.10 Distribution of base shear for different storied building

3.4 Summary

In this chapter, generally required data in design calculation for wind and earthquake loads

are presented in graphical form. Any required data or intermediate data are directly taken

from the graph value. To facilitate wind load and earthquake load calculation, generally

required graphs are presented in this chapter as follows:

Wind load,

i. Cp vs. (Fig. 3.1)

ii. z vs.Cz (Fig. 3.2)

iii. z vs. Gh and Gz (Fig. 3.3)

iv. z vs. (Fig. 3.4 to 3.6)

Earthquake load,

i. hn vs. & T (Fig. 3.7)

71

ii. hn vs. (Fig. 3.8)

iii. hn vs. (Fig. 3.9)

iv. hx vs. (Fig. 3.10)

Chapter 4

MODELLING OF THE STRUCTURES

4.1 Introduction

The modelling of a high rise building structure for analysis is

dependent to some extent on the approach to analysis, which is

related to the type and size of structure. This section describes

the finite element model for simulating model behaviour of high

rise structure. STAAD-III professional purpose Finite Element

software has been employed for this purpose. The developed

model uses beam elements with two nodes and finite element

model with four nodes for modelling the structure. It is assumed

that the load is such that the stress level of all materials is within

the elastic range.

72

4.2 Description of Model Building

In order to study the effect of different models, beam sizes, column sizes, auxiliary beam,

and brick masonry on bending moment, deflection, stiffness and stress in brick masonry

hence a 16-storied high rise building is given. Such as a typical floor plan, elevation, and

alternately adopted model plans of the building for this study is shown in Fig. 4.1a and 4.1b.

Coupled-Wall Plan,

Rigid Frame Plan

Typical Floor Plan (16-storied) Infilled Frame Plan

Fig. 4.1a Model plans of structure

73

Fig. 4.1b Elevation of structure

The columns, beams, shear walls, and infills are kept constant cross section and floor height

throughout the building. The uniformity and symmetry used in this example is adopted

primarily for simplicity. The member dimensions used in this example are within practical

range.

The beam width is kept 300 mm constant and the depth is varied 450 mm, 600 mm, 750 mm,

and 900 mm. The shear wall is taken 300x3650 mm and the thickness of infill is 250 mm.

The variable column sizes considered in this study are 300x450 mm, 300x600 mm, 300x750

and 300x900 mm.

Brick masonry crushing strength is taken, 12.50 MPa, poison’s ratio for concrete is, 0.15,

poison’s ration of brick masonry is, 0.20.

On this basis of the given data of the building, the lateral forces are presented in appendix,

Table A.1 and A.2. Considering the critical direction of the building, which is transverse

direction and adopted in this study.

4.3 Loads Considered for Analysis

A brief calculation of wind and earthquake load is given here. Location of building is

considered at Dhaka city, where exposure condition is A, and Earthquake zone is 2.

Only three load cases have been considered in this study. Following the cases, the horizontal

concentrated load at top, the wind load and earthquake load calculations have made along

with gravity load.

Load case: 1 D + L + H

74

Load case: 2 0.75(D + L + W)

Load case: 3 0.75(D + L + E)

D = dead load, L = gravity live load, H = horizontal concentrated load at top

W = wind load, E =earthquake load

To calculate the wind load, basic wind velocity of 210 km / h is considered.

The gravity, wind and earthquake loads are calculated and shown in appendix A and

presented in Table A.1 and A.2.

4.4 Modelling used for the Study

In this study, during 2-D analysis, building is idealized as an assemblage of vertical Rigid

frame, Shear wall, Infilled frame systems interconnected by horizontal rigid beams. A shear

panel element (Seraj, 1996, PP.199) is used to enable modelling of shear wall. Axial, shear

and bending deformations are considered during the analysis, modelling of shear wall in 2-D

analysis is done using the concept of rigid end condition between columns and beams.

For the analysis, only one direction, that is, short direction of building has been selected.

Two-dimensional analysis is conducted using the STAAD-III package software.

The analysis is divided into two phases. In the first phase, the relative stiffness of the systems

considered is calculated considering a 100 kN load at the top of model frames.

In the second phase, wind and earthquake loads are applied for the systems, then limited

parametric studies conducted by adopting two-dimensional analysis. Several parameters are

varied in order to determine their effects on moments, stresses, and deflections of model

frames.

Three different structural systems for the same bay are selected alternatively to carry out the

study of the 16-storied reinforced concrete building. The structural systems considered are,

i. Coupled Shear Wall

ii. Rigid Frame

iii. Infilled Frame

Again Coupled Shear Wall is subdivided into three structural models, as

a. Coupled-Shear Wall model with auxiliary beam

b. Coupled-Shear Wall model without auxiliary beam

c. Equivalent Wide Column model

75

4.4.1 Basic Model under Lateral Load Study

The basic models used for the numerical analysis under lateral loads for this study are given

in this article. The total five structural models are given on the following page in STAAD

geometric forms (Fig. 4.2 to 4.6). Member numbers and element numbers are given on

geometry but node numbers are not shown on geometry. Due to column sizes variation in

Rigid Frame model and Infill Frame model, hence four types of dimension are shown on the

top of model frames. Fig. 4.2 is used as Coupled Wall model with finite element, Fig. 4.3 is

used as Coupled Wall model by finite element without auxiliary beam, Fig. 4.4 is used as

Rigid Frame model by beam element, Fig. 4.5 is used as Infilled Frame model by finite

element and beam element. Fig.4.6 is used as Equivalent Wide Column Frame model by

beam element. The different types of input data file are given in appendix B

76

Fig. 4.2 Coupled Wall model , Finite element method (with auxiliary beam)

77

Fig. 4.3 Coupled Wall model , Finite element method (without auxiliary beam)

78

Fig. 4.4 Rigid Frame model

79

Fig. 4.5 Infilled Frame model

80

Fig. 4.6 Equivalent Wide Column Frame model

4.5 Summary

A typical 2-D bay of 16-storied RC building is taken for study problem in which columns,

beams and walls are maintained uniform size over the height for specified set of analysis.

From practical point of view, the gravity loads are taken in association with lateral loads in

the analysis to get real value of stresses. BNBC wind load is adopted where the wind design

parameters are, “210 km/h” for basic wind speed, “A” for exposure condition and “Dhaka

City” for location.

In earthquake load calculation, BNBC earthquake load is applied where the earthquake

design parameters are, Z =0.15 for earthquake zone 2, S=1.5 for site soil coefficient, I=1.0

(standard occupancy) for importance coefficient, R=5 for structural modification coefficient.

Three structural systems for the same bay are selected alternatively to carry out the study.

81

Chapter 5

RESULTS AND DISCUSSIONS

5.1 Introduction

Frames are the most widely used structural system in building construction but frames alone

are not always suitable to resist lateral loads. Equivalent static force method is allowed in

design codes to represent earthquake loads for such structures up to certain height. For tall

building structure, other building system should be adopted to resist lateral loads. These are

Frame-Wall, Coupled Wall, Infilled Frame, Tube system etc.

A short direction bay of a 16-storied office building is considered for lateral load analysis

here.

Wind load and Earthquake load are taken as lateral loads.

The specified bay is modeled by three structural systems, as

a. Rigid Frame structure (RF)

82

b. Infilled Frame structure (IF)

c. Coupled Wall structure (CW).

The Coupled Wall structure is idealized as,

i. Wall model without auxiliary beam (CW)

ii. Wall model with auxiliary beam (CWAB) and

iii. Equivalent Wide Column model (EWC).

The total five models are then analyzed by STAAD-III, computer software package program.

Effect of different parameters are studied to assess their influence on the behavior of high

rise structure. For the purpose of analysis, a bisymmetric 16-storied building is considered.

Parameters of study are:

Structural system

Beam size

Column size

All of them are analyzed with STAAD-III, a professional software package program. The

results of different models are presented in tabular and graphical form in this chapter.

The analyses of model frames are done for concentrated load at top end, wind and earthquake

loads. Deflections of model frames, their relative stiffness, moment in connecting beams and

stresses in infill materials are also calculated. These are presented in Tables 5.1 to 5.22 and

Fig. 5.1 to 5.15

5.2 Deflection of Different Structural System for Concentrated Load at Top

The concentrated load is applied at top to assess the relative deflection characteristics of

different model frames. Two types of deflection are associated in model frames. Bending

deflection and shear deflection. The bending mode of deflection is a result of axial

deformation of columns. It is generally neglected in frame structure. As the height to width

ratios of the structure increases, the effect of column axial deformation becomes more

dominant. For relatively short frames with height to width ratios less than 3, the deflection

due to axial shortening of columns can be neglected and the deflection of the frame can be

assumed to be entirely due to shear mode deflection. This mode of deflection occurs in frame

structures due to story sway associated with double bending of columns and beams. The

greater the slenderness of the frame, the more critical it becomes to instability in the flexural

83

deflection as opposed to the shear deflection. The greater the beam stiffness, the frame tends

to less shear deflection (Tables 5.1 to 5.4 and Fig. 5.1 to 5.4). The smaller the beam stiffness

associated, the frame tends to deflect as flexural deflection as a result the rigid frame goes to

largest deflection (Fig. 5.1).

In Fig. 5.1 to 5.4 and Tables 5.1 to 5.4, the Coupled Wall Model Frame without auxiliary

beam (AB) shows free cantilever deflection and the deflection of model can not be reduced

by increasing beam stiffness due to hinge connection of beam element to wall element. In

Table 5.1, the maximum deflection is found due to minimum beam stiffness compared to

others and minimum deflection is achieved by increasing beam stiffness (Table 5.4). Also it

is found that the deflection is decreased by increasing column size (Tables 5.5 to 5.7).

Finally, it is seen that the deflections are decreased with increased beam stiffness and column

stiffness for Infilled Frame, Rigid Frame, Coupled Wall (CWAB) and Wide Column model,

but deflection remains unaltered for Coupled Wall model (without auxiliary beam) where it

deflects as a free cantilever.

From maximum to gradual minimum deflections are found in Coupled Wall (without

auxiliary beam), Rigid Frame, Infilled Frame, Coupled Wall (with auxiliary beam) and Wide

Column Model respectively.

Table 5.1 Deflections (mm) of structure for different structural systems due to 100 kN load at top

Height, m Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide column

0 0.00 0.00 0.00 0.00 0.00

3 1.49 0.46 0.29 0.42 0.22

6 4.31 1.44 0.96 1.51 0.83

9 7.72 2.89 2.02 3.35 1.77

12 11.52 4.79 3.42 5.76 3.00

15 15.65 7.00 5.12 8.62 4.51

18 20.06 9.48 7.09 12.11 6.24

21 24.72 12.28 9.29 16.11 8.17

24 29.60 15.32 11.69 20.52 10.28

27 34.66 18.57 14.28 25.23 12.53

30 39.88 21.99 17.00 30.34 14.90

84

33 45.23 25.55 19.87 35.75 17.38

36 50.68 29.23 22.82 41.37 19.93

39 56.21 32.99 25.86 47.11 22.54

42 61.78 36.81 28.94 53.50 25.19

45 67.31 40.65 32.05 59.16 27.85

48 72.41 44.45 35.16 65.12 30.50

[Beam size: 300 x 450, column size: 300 x 600, wall size: 300 x 3650 mm]

EWC

CWAB

IF CW

RF

Beam size: 300x 450 mmColumn size: 300 x 600 mmWall size: 300 x 3650 mmAuxiliary beam: 300x450 mm

85

Floor level height: 3000 mmLoad at top: 100 kN

Fig. 5.1 Deflected shapes of structure for different structural systems due to concentrated load at top

Table 5.2 Deflections (mm) of structure for different structural systems due to 100 kN load at top

Height, m Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide column

0 0.00 0.00 0.00 0.00 0.00

3 1.18 0.33 0.21 0.42 0.21

6 2.83 1.02 0.77 1.51 0.65

9 4.84 1.95 1.45 3.35 1.22

12 7.12 3.06 2.37 5.76 2.07

15 9.51 4.34 3.46 8.62 3.06

18 12.12 5.85 4.79 12.11 4.16

21 14.93 7.43 6.12 16.11 5.12

24 17.74 9.22 7.63 20.52 6.75

27 20.73 11.04 9.22 25.23 8.11

30 23.72 12.91 10.91 30.34 9.52

33 26.83 15.02 12.75 35.75 11.03

86

36 30.04 17.05 14.54 41.37 12.67

39 33.23 19.13 16.33 47.11 14.18

42 36.44 21.24 18.21 53.50 15.79

45 39.61 23.32 20.05 59.16 17.22

48 42.62 25.43 21.96 65.12 18.83

[Beam: 300 x 600 mm, column size: 300 x 600 mm, wall size: 300 x 3650 mm]

EWC CWAB

IF RF

CW

Beam size: 300 x 600 mmColumn size: 300 x 600 mmWall size: 300 x3650 mm Auxiliary beam: 300x600 mmFloor level height: 3000 mmLoad at top: 100 kN

87

Fig. 5.2 Deflections of different structural systems due to concentrated load at top

Table 5.3 Deflections (mm) of different structural systems due to 100 kN load at top

Height, m Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide Column

0 0.00 0.00 0.00 0.00 0.00

3 0.88 0.32 0.18 0.42 0.12

6 2.23 0.90 0.55 1.51 0.43

9 3.82 1.72 1.10 3.35 0.89

12 5.60 2.75 1.80 5.76 1.47

15 7.54 3.86 2.62 8.62 2.15

18 9.61 5.12 3.55 12.11 2.91

21 11.80 6.49 4.57 16.11 3.73

24 14.09 7.94 5.66 20.52 4.60

27 16.45 9.47 6.80 25.23 5.52

30 18.88 11.06 8.00 30.34 6.46

33 21.36 12.69 9.23 35.75 7.44

88

36 23.89 14.36 10.50 41.37 8.42

39 26.44 16.04 11.78 47.11 9.42

42 29.01 17.74 13.08 53.50 10.42

45 31.58 19.43 14.39 59.16 11.41

48 33.98 21.07 15.69 65.12 12.36

[Beam: 300 x 750 mm, column size: 300 x 600 mm, wall size: 300 x 3650 mm]

EWC CWAB

IF RF

CW

Beam size: 300 x 750 mmColumn size: 300 x 600 mmWall size: 300 x 3650 mmAuxiliary beam: 300x750 mmFloor level height: 3000 mmLoad at top: 100 kN

89

Fig. 5.3 Deflected shape of different structural systems due to concentrated load at top

Table 5.4 Deflections (mm) of different structural systems due to 100 kN load at top

Height, m Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide Column

0 0.00 0.00 0.00 0.00 0.00

3 0.78 0.29 0.16 0.42 0.10

6 1.91 0.78 0.45 1.51 0.34

9 3.23 1.46 0.89 3.35 0.70

12 4.70 2.30 1.43 5.76 1.13

15 6.30 3.19 2.06 8.62 1.64

18 8.00 4.19 2.77 12.11 2.20

21 9.80 5.27 3.54 16.11 2.80

24 11.67 6.41 4.35 20.52 3.44

27 10.61 7.61 5.21 25.23 4.10

30 15.60 8.85 6.09 30.34 4.79

33 17.64 10.12 7.80 35.75 5.49

90

36 19.71 11.42 7.94 41.37 6.20

39 21.80 12.73 8.89 47.11 6.92

42 23.91 14.05 9.85 53.50 7.63

45 26.01 15.35 10.81 59.16 8.34

48 28.00 16.62 11.76 65.12 9.00

[Beam: 300 x 900 mm, column size: 300 x 600 mm, wall size: 300 x 3650 mm]

EWC CWAB

IF RF

WC

91

Beam size: 300 x 900 mmColumn size: 300 x 600 mmWall size: 300 x 3650 mmAuxiliary beam: 300x900 mmFloor level height: 3000 mmLoad at top: 100 kN

Fig. 5.4 Deflected shape of different structural systems due to concentrated load at top

Table 5.5 Deflections (mm) of different structural systems due to 100 kN load at top

92

[Beam: 300 x 600 mm, column size: 300 x 450 mm, wall size: 300 x 3650 mm]

EWC CWAB

IF RF CW

Height, m Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide

Column

0 0.00 0.00 0.00 0.00 0.00

3 1.82 0.42 0.21 0.42 0.21

6 4.43 1.01 0.77 1.51 0.65

9 7.26 2.05 1.45 3.35 1.22

12 10.37 3.36 2.37 5.76 2.07

15 13.72 4.78 3.46 8.62 3.06

18 17.21 6.35 4.79 12.11 4.16

21 20.85 8.12 6.12 16.11 5.12

24 24.62 10.01 7.63 20.52 6.75

27 28.53 12.15 9.22 25.23 8.11

30 32.56 14.26 10.91 30.34 9.52

33 36.61 16.17 12.75 35.75 11.03

36 40.71 18.69 14.54 41.37 12.67

39 44.92 20.92 16.33 47.11 14.18

42 49.15 23.21 18.21 53.50 15.79

45 53.46 25.63 20.05 59.16 17.22

48 57.32 27.72 21.96 65.12 18.83

93

Beam size: 300 x 600 mmColumn size: 300 x 450 mmWall size: 300 x 3650 mmAuxiliary beam: 300x600 mmFloor level height: 3000 mmLoad at top: 100 kN

Fig. 5.5 Deflected shape of different structural systems due to concentrated load at top

Table 5.6 Deflections (mm) of different structural systems due to 100 kN load at top

Height, m Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide Column

0 0.00 0.00 0.00 0.00 0.00

3 0.82 0.35 0.21 0.42 0.21

6 2.25 0.92 0.77 1.51 0.65

9 3.97 1.83 1.45 3.35 1.22

12 5.86 2.91 2.37 5.76 2.07

15 7.94 4.15 3.46 8.62 3.06

18 10.12 5.56 4.79 12.11 4.16

21 12.53 7.01 6.12 16.11 5.12

24 14.95 8.72 7.63 20.52 6.75

27 17.56 10.56 9.22 25.23 8.11

94

30 20.21 12.33 10.91 30.34 9.52

33 22.92 14.26 12.75 35.75 11.03

36 25.67 16.29 14.54 41.37 12.67

39 28.45 18.25 16.33 47.11 14.18

42 31.32 20.22 18.21 53.50 15.79

45 34.14 22.27 20.05 59.16 17.22

48 36.73 24.25 21.96 65.12 18.83

[Beam: 300 x 600 mm, column size: 300 x 750 mm, wall size: 300 x 3650 mm]

EWC CWAB

IF RF CW

95

Beam size: 300 x 600 mmColumn size: 300 x 750 mmWall size: 300 x 3650 mmAuxiliary beam: 300x600 mmFloor level height: 3000 mmLoad at top: 100 kN

Fig. 5.6 Deflected shape of different structural systems due to concentrated load at top

Table 5.7 Deflections (mm) of different structural systems due to 100 kN load at top

Height, m Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide Column

0 0.00 0.00 0.00 0.00 0.00

3 0.61 0.32 0.21 0.42 0.21

6 1.83 0.91 0.77 1.51 0.65

9 3.34 1.75 1.45 3.35 1.22

12 5.12 2.82 2.37 5.76 2.07

15 7.05 4.03 3.46 8.62 3.06

18 9.16 5.34 4.79 12.11 4.16

21 11.23 6.87 6.12 16.11 5.12

24 13.52 8.55 7.63 20.52 6.75

27 15.98 10.22 9.22 25.23 8.11

96

30 18.45 12.01 10.91 30.34 9.52

33 21.01 13.91 12.75 35.75 11.03

36 23.52 15.83 14.54 41.37 12.67

39 26.23 17.80 16.33 47.11 14.18

42 28.82 19.75 18.21 53.50 15.79

45 31.46 21.76 20.05 59.16 17.22

48 33.85 23.73 21.96 65.12 18.83

[Beam: 300 x 600 mm, column size: 300 x 900 mm, wall size: 300 x 3650 mm]

EWC CWAB

IF RF CW

Beam size: 300 x 600 mm

97

Column size: 300 x 900 mmWall size: 300 x 3650 mmAuxiliary beam: 300x600 mmFloor level height: 3000 mmLoad at top: 100 kN

Fig. 5.7 Deflected shape of different structural systems due to concentrated load at top

5.3 Relative Stiffness of Model Frames for Concentrated Load at Top

The relative stiffness of different model frames is presented in Tables 5.8

to 5.11. The analyses are carried out for 100 kN lateral loads at top of the

model frames. Relative stiffness of the model frames is defined, as the

lateral load required for unit deflection. Here 100 kN is adopted instead of

1 kN load, then the load is divided by total drift to get stiffness of the

model frames.

From Tables 5.8 to 5.11, among five models, the maximum stiffness is

found for Wide Column model. Although the Wide Column and Coupled

Wall (with AB) model are of same configuration, nevertheless the stiffness

is somewhat different. Because in Wide Column model, the coupling beam

acts perfectly rigid joint, so that it gives higher stiffness than Coupled Wall

model. In Coupled Wall model, the coupling beams are connected to nodal

98

points of shear wall with auxiliary beams which lacks full rigidity, as a

result the stiffness is somewhat lower than Wide Column model.

In Infilled Frame model, the stiffness is considerably higher than Rigid Frame model (Tables

5.8 to 5.11). With respect to the shear configuration of a laterally loaded rigid frame model

without Infill, an Infill deflects in a flexural mode (Fig. 5.1 to 5.7). This difference in

deflected shape occurs in between Infilled Frame and Rigid Frame because the infill greatly

reduces the shear mode deformation which increase the stiffness of the Infilled Frame model.

Without auxiliary beam connection in Coupled wall model, the stiffness becomes lower than

other models because the coupled wall deflects as free cantilever, as a result the stiffness is

considerably less. It is shown in Tables 5.8 to 5.11 that the stiffness of models can be

increased with increased beam or column sizes.

From above discussions it is clear that the stiffness of buildings can be increased by different

modifications of structural systems, by increasing beam or column sizes. Comparing the

relative stiffness of model frames, it can be suggested that which one the structural system is

more efficient. Here, Coupled Wall model (reinforced concrete shear wall) is more efficient

than the others in terms of lateral sway of model frames and hence it is the most stiff system.

However, the Infilled Frame gives considerable stiffness than all others except Coupled wall

model. Coupled wall model is expensive in construction. In terms of economy this system is

not always efficient one. Where as the stiffness of Infilled model is close to Coupled Wall

model and construction cost is much less than coupled wall system. If the infill stresses are

within allowable limit due to lateral loads, then Infillled structural system is quite efficient

structural system and economically acceptable too.

Table 5.8 Stiffness of models (N/mm) , column size: 300 x 450 mm, wall size: 300 x 3650 mm

Beam size, mm Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide Column

300 x 450 1204 2444 2844 1536 3279

300 x 600 1745 3593 4415 1536 5371

300 x 750 2158 4794 6373 1536 8091

300 x 900 2456 5907 8503 1536 11111

99

Table 5.9 Stiffness of models (N/mm), column size: 300 x 600 mm, wall size: 300 x 3650 mm

Beam size, mm Rigid Frame Infilled Frame Coupled WallAB Coupled Wall Wide Column

300 x 450 1487 2643 2844 1536 3255

300 x 600 2350 3934 4554 1536 5311

300 x 750 3126 5336 6373 1536 8091

300 x 900 3750 6658 8503 1536 11111

Table 5.10 Stiffness of models( N/mm), column size: 300 x 750 mm, wall size: 300 x 3650 mm

Beam size, mm Rigid Frame Infilled Frame

Coupled WallAB Coupled Wall Wide Column

300 x 450 1655 2756 2844 1536 3279

300 x 600 2729 4134 4415 1536 5371

300 x 750 3815 5718 6373 1536 8091

300 x 900 4778 7273 8503 1536 11111

Table 5.11 Stiffness of models( N/mm), column size: 300 x 900 mm, wall size: 300 x 3650 mm

Beam size, mm Rigid Frame Infilled Frame

Coupled Wall AB Coupled Wall Wide Column

300 x 450 1762 2811 2844 1536 3279

300 x 600 2957 4228 4415 1536 5371

300 x 750 4270 5949 6373 1536 8091

300 x 900 5528 7716 8503 1536 11111

100

5.4 Deflection of Different Structural System for Lateral Load

The wind and earthquake loads are calculated according to BNBC (1993). The wind load

base shear is found greater than earthquake base shear (Tables A.1 and A.2). Exposure

condition “A” for wind and zone “2” for earthquake are considered for Dhaka City. The base

shear due to wind load is found 35 % higher than the base shear due to earthquake.

Deflection of the structure, modeled as different structural systems, due to both earthquake

and wind forces are presented in Tables 5.12a, 5.12b and plotted in Fig. 5.8. From the limited

study, it is found that the deflections of every system due to wind load are greater than the

deflection due to earthquake load. The differences between top deflections due to lateral

loads are small (not more than 16 %) though the wind load base shear is greater by 35 % than

earthquake load. The greater intensity of load at top and the concentrated load at top of the

model frames due to earthquake makes the difference less. The distinctive feature of wind

and earthquake forces is, that the wind load is external forces the magnitudes of which are

proportional to the exposed surface, while the earthquake force is inertial force depending

primarily on the mass and the stiffness properties of the model structure.

101

In Fig. 5.8, the Rigid Frame model undergoes combined flexural-shear deflection. Rigid

Frame model and Coupled Wall model without auxiliary undergoes excess deflection than

allowable limit, 96mm (Fig. 5.8) due to less stiffness of beams and columns according to

ACI Committee 435. But generally in rigid frame, the deflection is shear mode deflection.

The shear mode of deflection occurs in rigid frame by the double bending of columns and

beams which occurs in the upper part. The beam-column joint in upper part of the model acts

as rigid joint and stresses are in elastic range. The joint deformations are negligible. But in

lower part of model frame, the flexural mode of deflection takes place (Fig. 5.12). The

flexural mode of deflection happens when the beam undergoes joint deformation. At the

lower part of frame, the stress in beams exceeds the elastic range and it acts as semi rigid or

hinge joint. Hence the frame undergoes flexural mode of deflection at the lower part.

The Wide Column model deflects less than all other models. Coupled Wall model (without

AB) deflects more due to hinge connection between finite membrane element and finite

beam element. As a result, the system deflects as free cantilever as shown in Fig. 5.8. For

this reason it is not possible to lower the deflection values with increased beam size.

Decreased deflection is increasing wall inertia, which is uneconomical.

The deflections of Wide Column model and Coupled Wall model (with AB) are close

although the same configuration between them exists. Because the auxiliary beam connection

to nearest node of element makes the system close to rigid joint. At least the same size of

auxiliary should be connected to get reliable result that is somewhat conservative.

The deflection due to wind of Infill Frame model is found 15 % greater than Coupled Wall

model (with AB) and 34 % less than Rigid Frame model (Fig. 5.8). It is seen that the infill

contributes sufficient stiffness to withstand lateral loads. The stiffening effect of the infill

panel on the frame represents fairly well by a diagonal strut having the same thickness as the

panel (Mark Fintel, 1974, PP.358). An effective width depends on many factors. The

effective width of the strut increases with increasing column stiffness and panel height to

length ratio and decreases with increasing value of the load and modulus of elasticity of the

infill material. The effect of infill walls can be well observed on the response of structures

subjected to earthquake motion. Walls filling the space between frame members not only

tend to increase the stiffness, but it altogether alters the mode of response of the frame. The

frame changes into a shear wall and as a result, it changes the entire structure and the

102

resulting distribution of lateral forces among the frame components (Mark Fintel, 1974).

Virtually the wind and earthquake load is dynamic and reversible one. At one stage an infill

panel acts in one diagonal direction in compression (as a strut) and in other diagonal

direction in tension. The compression and tension diagonals are reversed when the horizontal

load comes from other direction. As a result in severe lateral load, the infill fails out of plane

and makes the infill frame into frame only, which may result greater in deflection under

severe lateral load.

In Fig. 5.9 and 5.10, the deflections are presented for various beam and column sizes. The

lateral deflection caused by lateral force decreases with increased beam or column sizes.

These merely due to increase in flexural stiffness of beams or columns.

In Fig. 5.11, the deflections of Wide Column model are presented for various beam sizes. In

this model, it is shown that the lateral deflection decreases with increased beam sizes. At

certain stiffness of beam, the model frame starts to deflect in flexural mode (for beam,

300x450 mm).

Table 5. 12a Deflections (mm) of different structural systems due to wind load.

Height, m Rigid Frame Infilled Frame Wide Column Coupled WallAB Coupled Wall

0 0.00 0.00 0.00 0.00 0.003 3.50 1.43 0.76 0.89 1.576 10.29 4.35 2.69 2.96 5.66

9 18.35 8.25 5.52 6.02 12.0512 27.03 12.88 9.03 9.82 20.46

15 36.02 18.00 13.04 14.29 30.6318 45.15 23.52 17.37 19.13 42.31

21 54.24 29.29 21.95 24.25 55.2524 63.18 35.21 26.60 29.51 69.25

27 71.84 41.17 31.25 34.83 84.09

30 80.14 47.09 35.84 40.12 99.60

33 88.00 52.90 40.21 45.83 115.6236 95.35 58.55 44.61 50.41 131.20

39 102.16 64.00 48.74 55.35 148.6142 108.39 69.26 52.70 60.14 165.36

45 114.04 74.34 56.52 64.81 182.2048 119.34 79.31 60.26 69.42 198.98

[Beam size: 300 x 600 mm, Column size: 300 x 750 mm ]

Table 5.12b Deflections (mm) of different structural systems due to EQ load.

103

Height, m Rigid Frame Infilled Frame Wide Column Coupled WallAB Coupled wall

0 0 0 0 0 03 2.56 1.07 0.61 0.74 1.366 7.66 3.34 2.20 2.46 4.94

9 13.87 6.45 4.57 5.04 10.58

12 20.71 10.20 7.55 8.32 18.08

15 27.97 14.43 11.00 12.14 27.20

18 35.48 19.04 14.79 16.39 37.77

21 43.13 23.95 18.83 20.93 49.57

24 50.79 29.05 23.00 25.67 62.42

27 58.37 34.27 27.24 30.52 76.1430 65.77 39.52 31.48 35.52 90.57

33 72.93 44.74 35.67 40.30 105.54

36 79.75 49.89 39.78 45.13 120.94

39 86.20 54.93 43.76 49.88 136.6342 92.22 59.84 47.63 54.54 152.50

45 97.77 64.63 51.40 59.10 168.45

48 103.00 69.36 55.11 63.62 184.41 [Beam size: 300 x 600 mm, Column size: 300 x 750 mm]

1: EQ load on WC model 6: Wind load on IF model

2: Wind load on WC model 7: EQ load on RF model

3: EQ load on CW/AB model 8: Wind load on RF model

4: EQ load on IF model 9: EQ load on CW model

5: Wind load on CW/AB model 10: Wind load on CW model

1

2 7 8

3

4 9 10

5

6

104

allowable limit of Deflection (96 mm)

(ACI Committee 435)

Beam size: 300x 600 mm Column size: 300x750 mm

Wall size: 300x 3650 mm Auxiliary beam: 300x600 mm

Floor level height: 3000 mm Wind and EQ load: BNBC

Fig. 5.8 Deflections of different structural systems due to wind and earthquake load.

Table 5.13 Deflections (mm) of Rigid Frame model due to wind load for variable beam sizes

Height, m Beam,300x450 Beam,300x600 Beam,300x750 Beam,300x900

0 0.00 0.00 0.00 0.00

3 4.97 3.36 2.57 2.14

6 15.59 9.88 7.17 5.72

9 28.75 17.63 12.53 9.85

12 43.07 25.96 18.29 14.29

15 57.91 34.60 24.27 18.90

18 72.87 43.36 30.34 23.59

21 87.70 52.08 36.40 28.27

24 102.2 60.65 42.35 32.86

27 116.20 68.96 48.11 37.30

30 129.58 76.92 53.63 41.55

33 142.20 84.45 58.83 45.56

105

36 153.98 91.50 63.64 49.30

39 164.84 98.02 68.17 52.76

42 174.73 103.98 72.27 55.92

45 183.69 109.40 75.98 58.78

48 192.05 114.47 79.47 61.43

[Beam size: 300 x 450 mm, 300 x 600, 300 x 750 mm, 300 x 900 mm, Column size: 300 x 900 mm]

1

2

3

4

4 3 2 1

106

Fig. 5.9 Deflections of Rigid Frame model due to wind load

Table 5.14 Deflection (mm) of Rigid Frame model due to wind load for variable column sizes

Height, m Col,300x450 Col,300x600 Col,300x750 Col,300x900

0 0.00 0.00 0.00 0.00

3 10.70 6.16 4.32 3.36

6 25.19 15.89 12.02 9.88

9 40.47 26.56 20.79 17.63

12 56.07 37.65 30.07 25.96

15 71.73 48.92 39.59 34.60

18 87.23 60.19 49.18 43.60

21 102.35 71.30 58.69 52.08

24 116.94 82.00 67.98 60.65

27 130.83 92.47 76.95 68.96

30 143.90 102.32 85.52 76.92

33 156.02 111.53 93.58 84.45

36 167.11 120.05 101.08 91.50

39 177.09 127.83 107.96 98.02

42 185.93 134.83 114.25 103.98

45 193.59 141.02 119.88 109.40

48 200.24 146.62 125.07 114.47

107

[Column size: 300 x 450 mm, 300 x 600, 300 x 750 mm, 300 x 900 mm, Beam size: 300 x 600 mm]

1

108

2

3

4

4 3 2 1

Beam 300x600 mm

Fig. 5.10 Deflections of Rigid Frame model due to wind load

Table 5.15 Deflections (mm) of Wide Column model due to wind load for variable beam sizes

Height, m Beam,300x450 Beam,300x600 Beam,300x750 Beam,300x900

109

0 0.00 0.00 0.00 0.00

3 0.98 0.76 0.62 0.52

6 3.54 2.69 2.13 1.74

9 7.41 5.52 4.29 3.45

12 12.34 9.03 6.91 5.48

15 18.09 13.04 9.83 7.71

18 24.48 17.39 12.95 10.06

21 31.33 21.95 16.15 12.44

24 38.49 26.50 19.36 14.81

27 45.49 31.25 22.52 17.11

30 53.26 35.84 25.57 19.33

33 60.67 40.31 28.49 21.43

36 68.01 44.61 31.25 23.40

39 75.23 48.74 33.84 25.23

42 82.33 52.70 36.28 26.93

45 89.32 56.52 38.58 28.53

48 96.24 60.26 40.81 30.06

[Beam size: 300 x 450 mm, 300 x 600, 300 x 750 mm, 300 x 900 mm, Wall size: 300x3650 mm]

2

3

1

110

4 3 2 1

Wall 300x3650 mm

Fig. 5.11 Deflections of Wide Column model due to wind load

111

5.5 Moment in Beams of Different Structural System for Lateral LoadWind loads are applied on different model frames to observe the model connecting beam

moments at various floor levels. The beam and column sizes are kept constant and then

lateral loads are applied on different model system. The moments of different model frames

due to both wind and earthquake loads are presented in Table 5.16 and 5.17. They are plotted

in Fig. 5.12.

From the limited study, it is found that the moments in beams of every system caused by

wind load are greater than the moments in beams caused by earthquake load. But the

differences between moments caused by these two different types of lateral loads are small

(not more than 12 % for max value) though the wind load is greater by 35 % than earthquake

load. The greater intensity of load at top and the top load of earthquake makes the difference

less.

The connecting beam moments in wide column model are less than all other models and

coupled wall model (without AB) gives very less moments due to hinge connection between

membrane element and beam element. As a result the moments linearly decrease as shown in

Fig. 5.12.

It is shown in Fig. 5.12 that the maximum moment is developed in connecting beam for

Rigid frame, Infilled Frame, Wide Column, Coupled Wall (AB) and Coupled Wall system at

a level of (z / H) 0.44, 0.56, 0.56, 0.56 and base level respectively.

The moments in beams in wide column model and coupled model (with AB) are somewhat

different although the same configuration between them exists. Because the beam-column

joints in wide column model are rigid and the auxiliary beam connection in coupled wall

model to nearest node of element makes the system close to rigid joint.

For different beam sizes and fixed column sizes, the variation of beam moment in connecting

beams are studied for rigid frame model (Tables 5.18, Fig. 5.13) and wide column model

(Tables 5.20, Fig. 5.15) due to wind load.

In rigid frame model, the upper parts of all the curves concave downward gradually. The

curve concave downward more due to greater beam size. At a certain height from base level,

the maximum bending moment occurs. Below certain height, the beam goes to higher stress

due to lateral loads and the beam-column joint deformation happens, as a result the joint does

112

not act fully as a rigid joint, hence the rotation takes place and the bending moment decreases

and the curve concave upward. The greater beam size can take more stress, so that the

maximum bending moment occurs at lower height close to base level (Fig. 5.13). The lower

parts of the same curves (Fig. 5.13 and 5.14) repeat and it happens in another beam.

In wide column model the upper parts of all the curves concave downward gradually. The

concavity is more due to greater beam size. At a certain height from base level, the maximum

bending moment occurs. Below certain height, the beam experiences higher stress due to

lateral loads and the beam-column joint deformation happens, as a result the joint does not

act as a fully rigid joint. The rotation takes place and the bending moment decreases and the

curve tends to go concave upward. The greater beam size can take more stress and the

maximum bending moment occurs at lower levels. In Fig. 5.15, the broken line curve shows

the variation of maximum bending moment due to beam size variation, which is

progressively concave upward.

The stiffness of model frame is increased due to increase of beam size, so that the model has

less deflection but the bending moment increases in beams (Tables 5.18 and 5.20) due to

higher stiffness of beam.

In the Infill Frame model, the bending moment in beams are quite less (about 15%) than the

rigid frame model. The infill acts as diagonal bracing for the frame, which reduces bending

moment in beams.

Table 5.16 Bending moment (kN-m) in beams for different structural systems due to wind load.

Height, m Rigid Frame Infilled Frame Wide Column Coupled WallAB Coupled Wall

3 283 179 143 133 73

113

6 338 226 197 181 699 340 260 238 218 6412 358 292 268 244 58

15 368 304 288 263 53

18 371 318 300 276 4821 369 325 306 283 4324 363 327 307 286 3827 354 326 303 285 3430 341 321 296 281 2933 327 314 287 275 2536 311 306 277 268 2139 294 297 266 260 1842 277 289 256 251 1445 262 282 248 239 1248 239 265 243 165 7

[Connecting beam size : 300x600 mm, Column size: 300 x750mm]

Table 5.17 Bending moment (kN-m) in beams for different structural systems due to EQ load.

Height, m Rigid Frame Infilled

Frame

Wide Column Coupled WallAB Coupled Wall

3 214 162 131 122 68.676 262 203 176 163 62.469 290 233 211 195 56.4612 309 264 239 218 51.42

15 321 276 258 237 46.59

18 329 290 272 251 42.2321 332 300 280 260 38.26

24 331 305 284 265 34.5827 327 307 284 267 31.11

30 321 306 281 266 27.80

33 312 303 275 264 24.6036 301 298 269 260 21.50

39 288 292 261 254 18.53

42 275 285 254 248 15.75

45 263 280 247 237 13.3648 238 264 243 164 8.86

[Connecting beam size: 300x600 mm, Column size: 300x750 mm]

1: EQ load on CW model

114

2: Wind load on CW model Beam size: variable

3: EQ load on CW/AB model Column size: 300x750mm

4: EQ load on WC model Wall size: 300x 3650 mm

5: Wind load on CW/AB model Auxiliary beam: variable

6: EQ load on IF model Floor level height: 3000 mm

7: Wind load on WC model Wind load: BNBC

8: Wind load on IF model

9: EQ load on RF model

10:Wind load on RF model

1 2 3 4 5 6 7 8 9 10

Fig. 5.12 Bending moment in beams for different structural systems due to wind and EQ load.

Table 5.18 Bending moment (kN-m) in beams for Rigid Frame model of different beam sizes due to wind load.

Height, m Beam,300x450 Beam,300x600 Beam,300x750 Beam,300x900

115

3 301 340 365 385

6 351 363 371 383

9 348 350 381 414

12 333 358 399 431

15 315 365 406 436

18 315 366 405 432

21 312 362 397 419

24 307 353 384 401

27 298 341 366 378

30 288 326 345 351

33 275 309 322 322

36 262 290 297 292

39 247 271 272 262

42 232 252 248 234

45 219 236 228 209

48 196 203 191 171

[Column size: 300x600 mm]

116

1

2

3

4

1 2 3 4

Column: 300x600 mm

Fig. 5.13 Bending moment in beams for Rigid Frame model of different beam sizes due to wind load.

Table 5.19 Bending moment (kN-m) in beams for Rigid Frame model of different column sizes due to wind load.

Height, m Col, 300x450 Col, 300x600 Col, 300x750 Col, 300x900

117

3 375 340 308 278

6 380 363 349 333

9 365 350 341 335

12 355 358 356 352

15 361 365 364 361

18 361 366 366 365

21 355 362 363 363

24 345 353 356 357

27 332 341 346 348

30 315 326 332 336

33 296 309 316 321

36 276 290 299 306

39 256 271 281 289

42 235 252 263 272

45 218 236 248 258

48 183 203 221 236

[Beam size: 300x600 mm]

118

1

1 2 3 4 2

3

4

Fig. 5.14 Bending moment in beams for Rigid Frame model of different column sizes due to wind load.

Table 5.20 Bending moment (kN-m) in beams for Wide Column model of different beam sizes due to wind load.

119

Height, m Beam,300x450 Beam,300x600 Beam,300x750 Beam,300x900

3 112 143 178 213

6 145 197 251 304

9 172 238 303 362

12 194 268 337 396

15 210 288 356 412

18 222 300 365 415

21 231 306 365 408

24 236 307 358 393

27 239 303 346 373

30 239 296 330 349

33 237 287 311 322

36 235 277 292 295

39 232 266 273 269

42 228 256 255 245

45 225 248 241 225

48 223 243 232 212

[Column size: 300x600 mm]

120

1234

1

2

3 4

Column: 300x600 mm

Fig. 5.15 Bending moment in beams for Wide Column model of different beam sizes due to wind load.

5.6 Stresses in Infill Material of Infilled Frame (Wind Load) The infill is brick masonry. The properties of brick masonry are described in art. 2.2.5.2.

Lateral loads are applied to Infilled Frame model and calculated infill stresses due to wind

121

load for the model frame upto 8th story because more stress at lower portion. The stresses are

presented in Tables 5.21 and 5.22. The maximum compressive stress is found in infilled

material is 2332 kN/sq.m which is 4.5% less than allowable limit [2442 kN/sq.m, (BNBC)]

and the maximum tensile stress found in infilled material is 282 kN/sq.m which is 19.5 %

less than allowable limit [350 kN/sq.m, (BNBC)].

The shear strength of brick masonry is represented in Codes of Practice by a static friction

type of equation (Coull, 1991)

fs = fbs + c (5.1)

together with a maximum limiting value (0.40 N/mm2, BNBC).

Where,

fbs = bond shear stress = 0.025 f’m N/mm2 (5.2)

c = compressive force

This relationship holds good up to value of c = 2 N/mm2 (2000 kN/ m2)

= 0.40 (average value)

The maximum shear stress found in infilled material is 540 kN/sq.m, which is 35 % greater

than allowable limit [400 kN/sq.m (BNBC)].

From above results, it is found that the shear stress has exceeded the allowable limit. Hence,

the use of infill masonry in high rise building is limited. When it is used as infill to the frame,

the stresses in infill are to be carefully checked against lateral loads. For over stresses in

brick infill, reinforced may be used as infill which allowed by ACI and UBC [The crushing

strength (f’m) of brick masonry is taken 12.5 kN/sq.m (1813 psi)].

From the analysis of structural models, it is found that if the rigid frame model is filled by

brick masonry then the moments in connecting beam substantially reduces at lower level of

building height (Table 5.16 and 5.17) and the stiffness of Infilled model increases (about

40%). The brick masonry is cheap and easy in construction than RC work. It can be used

economically as structural system if the stresses in infill material do not exceed the allowable

limits.

Table 5.21 Infilled masonry normal stress due to wind loadFloor Fx, kN/sq.m, parallel to bed joint Fy, kN/sq.m, normal to bed joint

Level 300x600 mm 300x750 mm 300x900 mm 300x600 mm 300x750 mm 300x900 mm

122

1 98 -355 98 -363 97 -371 70 -2078 260 -2332 163 -2284

2 154 -401 137 -399 124 -399 282 -1490 138 -2106 32 -2053

3 160 -392 132 -390 114 -391 170 -1726 40 -1894 0 -1853

4 132 -390 142 -383 127 -385 32 -1554 0 -1703 0 -1671

5 143 -345 124 -345 112 -348 0 -1374 0 -1502 0 -1479

6 149 -319 132 -321 122 -325 0 -1222 0 -1337 0 -1323

7 147 -297 132 -299 124 -303 0 -1080 0 -1181 0 -1175

8 142 -274 130 -276 123 -280 0 -941 0 -1031 0 -1031

[+ve value in tension and –ve value in compression, beam size in mm, column size 300x750 mm]

Table 5. 22 Infilled masonry shear stress due to wind load

Floor Shear stress, Fxy in kN / sq.m

Level 300 x 600 mm 300 x 750 mm 300 x 900 mm

1 492 467 450

2 540 497 467

3 518 478 452

4 495 458 436

5 436 404 387

6 405 377 364

7 377 354 344

8 347 328 321

[Column size: 300 x 750 mm, Variable beam size: 300x600, 300x750, 300x900 mm]

5.7 Summary

A short direction bay of a 16-storied office building is considered for lateral load analysis.

Wind load and Earthquake load are considered as lateral loads.

123

The specified bay is modeled by three structural systems, namely, a. Rigid Frame structure,

b. Infilled Frame structure, c. Coupled Wall structure.

The Coupled Wall Structure is modeled into three structural models as i. Wall Element

model ii. Wall Element model with auxiliary beam iii. Equivalent Wide Column model. The

total five models are then analyzed by STAAD-III, a package program.

The maximum to gradually minimum stiffness is found in Equivalent Wide Column,

Coupled Wall (with auxiliary beam), Infilled Frame, Rigid Frame and Coupled Wall

respectively.

When the Coupled wall system is modeled by membrane finite elements, then shear wall’s

(in-plane frame) connecting beams require a special consideration. Membrane elements do

not have a degree of freedom to represent an in-plane rotation of these corners, therefore, a

beam element connected to node of a membrane element is effective only by a hinge. As a

result the walls deflect as free cantilever.

When the relative stiffness is greater, there exists larger bending moment in the connecting

beams. Maximum bending moment develops in beams along building height at nearly H/3

for Rigid Frame for different beam and column sizes. There is no considerable change in

maximum beam moments due to changes of beam and column sizes (Fig. 5.10 and 5.11). In

Wide Column and Coupled Wall model, the maximum bending moment develops at nearly

H/3 along building height and gradually increases along height with increased beam size

(Fig. 5.12).

For Infilled Frame analyzed under wind load, it is found that the stresses of different types

are close to allowable limit for the frame under consideration. The maximum compressive

stress in infilled material is found to be 4.5% less than allowable limit. The maximum shear

stress, however, found exceed the allowable limit by about 35%. The maximum tensile stress

found in the infilled material is again about 19.5% less than the allowable limit.

124

Chapter 6

CONCLUSION & SUGGESTION6.1 General

The ability to model high rise buildings successfully for analysis requires an understanding

of their behavior under lateral loads. A good grasp of the techniques of modeling serves as an

aid in generally assessing high rise building behaviour and subsequent selection and

development of structural forms for such buildings.

In modeling a structure for analysis, only the main structural members are idealized and it is

assumed that the effects of nonstructural members are small and conservative. Additional

assumptions are made with regard to the linear behavior of the materials, and the neglect of

certain member stiffness and deformations, in order to further simplify the model for

analysis. In more accurate modeling, the columns and beams of frames are represented

individually by beam elements. Shear walls are represented by assemblage of membrane

finite elements. Certain reductions of a detailed model are possible while still producing an

acceptable accurate solution. These reductions include halving the model to allow for

symmetrical or anti symmetrical behavior or representing the structure by a planar model and

conducting a two dimensional analysis.

6.2 Conclusions

A typical bay of a high rise building is considered for lateral load analysis. Wind and

earthquake loads are imposed on the model frame as lateral loads. The loads are adopted in

analysis as it is considered in design. The specified bay is modeled by three structural

systems. They are a. Rigid Frame model, b. Infilled Frame model and c. Coupled Wall

model. The Coupled Wall is modeled into three structural sub models, which are i. Wall

Element model ii. Wall Element model with auxiliary beam and iii. Equivalent Wide Column

model.

On the basis of results of analysis the following conclusions are made,

The lateral deflection of the model is found minimum in Equivalent Wide Column model

and the deflection value gradually increases for Coupled Wall model, Infilled Frame

model, Rigid Frame model and Coupled Wall model (without auxiliary beam)

respectively.

125

Maximum bending moment in connecting beam develops in between H/3 to H/2 along

model height from base level for different model with different member sizes.

Stiffness of model increases with increased beam sizes or column sizes or both.

Compressive stress, tensile stress and shear stress decrease in infilled material with

increased beam size.

In finite element method of analysis for Coupled Wall model, the finite membrane

element and finite beam element connection is such that either it is a hinge or rigid joint.

In rigid connection (actual case), auxiliary beam must be considered in the connection of

the model. If the auxiliary beam is not considered, the wall behaves as a free cantilever

under lateral load, which is not representative of the real response.

The maximum compressive stress and maximum tensile stress in infill brick masonry are

found somewhat below the allowable limits as per BNBC values. However, the

maximum shear stress is exceeded the allowable limit by 12.5% in infill brick masonry.

Hence, the brick masonry wall may need strengthening with wire mesh (retro-fitting) or

reinforced masonry may be used instead of masonry infilled frame can be used in high

rise buildings of reasoned height as shear wall with proper analysis and design.

Shear stress in infill material is critical in high rise building compared to tension in lateral

load analysis.

For severe lateral loads caused by wind load and or earthquake load, the reinforced shear

wall is obvious. Because, it produces less deflection and less bending moment in

connecting beams under lateral loads than all others structural system.

The stiffness of Rigid Frame model found in the analysis is 42% to 65% of Coupled Wall

and stiffness of Infilled Frame model found in the analysis is 86% to 91% of Coupled

Wall.

The maximum moment in connecting beam of Rigid Frame model found in analysis is

31% greater than Coupled Wall model and the maximum moment in connecting beam of

Infilled Frame is 15.5% greater than Coupled Wall model. The robust construction cost

of RC wall makes the building cost higher. The efficient structural system is infilled

rigid frame structure if the stresses are within the allowable limits, whether it is

reinforced plaster or reinforced masonry.

126

6.3 Recommendations for Future Study

The following recommendations are made for future study on the basis of lateral load analysis of a 2-D bay for16-storied high rise building as follows, In order to establish the influence of floor height of building, a similar investigation

should be carried out in future.

Three dimensional models study can be carried out for similar investigation.

Dynamic earthquake study can be carried out for similar frames.

The study is performed only with uniform beam and column along height but it can be

proposed to further investigations with various sizes along height.

The investigation can be extended for cross bracing for every floor of a rigid frame and in

filled frame in building.

Laboratory investigation for infilled frame can be made, where the column and beam cast

against infill and the column and beam cast prior to infill.

References

Aktan, A. E., Bertero, V. V. and Sakino, K. (1985), “Lateral Stiffness Characteristics of RC Frame-Wall Structures,” ACI Pub. SP 86-10, Detroit.

127

Amanat, K. M. and Enam, B. (1999), “Study of the Semi-Rigid Properties of Reinforced Concrete Beam-Column Joints,” JCE (IEB), Vol.CE27, No.1.

Basu, A. K. and Nagpal, A. K. (1980), “Frame-Wall Systems with Rigidly Joint Link Beams,” Journal of Structural Engineering, ASCE 106(5).

Coull, A. and Stafford, S. B. (1991), “Tall Building Structures, Analysis and Design,” John Wiley and Sons, Inc.

Clough, R.W. and Penzien, J. (1993), “Dynamics of Structures,” McGraw-Hill Book Company, New York.

Coull, A. and Chowdhury (1967), “Analysis of Coupled Shear-Walls,” ACI Journal, Proceedings, Vol.64.

Fintel, M. (1974), “Handbook of Concrete Engineering,” 2nd. Edition, CBS Publishers & Distributors, India.

Fintel, M. (1975), “Deflection of High-Rise Concrete Buildings,” ACI Journal, Proceedings, Vol.72, No.7.

Gaiotti, R. and Smith, B. S. (1989), “P-Delta Analysis of Building Structures,” ASCE, Journal of Structural Engineering, Vol. 115, No. 4.

Ghos, S.K. and Domel, A.W. (1992), “ Design of Concrete Buildings for Earthquake and Wind Forces,” International Conference of Building Officials, California, USA.

Hendry, A. W. (1981), “Structural Brick work,” The Macmillan Press Ltd. London.

Hendry, A. W. and Davies, S. R. (1981), “An Introduction to Load Bearing Brick Work Design,” Ellis Horwood Limited, England.

Housing and Building Research Institute, Bangladesh Standards and Testing Institution (1993), “Bangladesh National Building Code (BNBC),” Dhaka.

ICBO (1995), “Uniform Building Code,” International Conference of Building Officials, Chapter 23, Part-III, Earthquake Design, USA.

Jones, S. W., Kirby, P.A. and Nethercot, D.A. (1982), “Columns with Semi-Rigid Joints,” American Society of Civil Engineers, (ASCE), Journal of Structural Engineering, Vol. 108, pp-361-372.

Khan, F.R. and Sbarounis, J.A. (1964), “Interaction of Shear Walls and Frames,” Proceeding, ASCE, Vol. 90 (ST3), Part 1.

Kazimi, S. M.A. and Chandra, R. (1976), “Analysis of Shear-Walled Buildings,” Tor-Steel Research Foundation, India.

Macleod, I. A. (1970), “Shear Wall-Frame Interaction,” Portland Cement Association, PCA.

Macleod, I.A.(1969), “New Rectangular Finite Element for Shear Wall Analysis,” ASCE 95(3), pp. 399-409,

128

Moudrres, F.R. and Coull, A. (1986), “Stiffening of Linked Shear Wall,” ASCE 112(3)

Munaj, A. N. and Salek, M. S. (1996), “Comparison of Two and Three Dimensional Analysis of Moderately Sized Tall Buildings under Wind Loads,” JCE (IEB), Vol. CE24, No. 2. Nilson, A. and Darwin, D. (1997), “Design of Concrete Structures,” 12th edition, The McGraw-Hill Companies, Inc.

Pauly, T. and Priestly, M.J.N. (1992), “Seismic Design of Reinforced Concrete and MasonryBuildings,” John Wiley and Sons, Inc, New York,

Pauley, T. (1971), “Coupling Beams of Reinforced Concrete Shear Walls,” Proceedings, ASCE, V97.

Research Engineers Pvt. Ltd. (1996), “STAAD-III, Structural Analysis and Design Software,” Rev. 22, Research Engineers, Inc.

Seraj, S. M., Ansary, M. A. and Noor, M.A (1997), “Critical Evaluation and Comparison of Different Seismic Code Provision,” JCE (IEB), Vol. CE25.No.1.

Tahur, A. (1984), “Simplified Analysis of Wall-Frame Structure with Columns and Girders of Unequal Lateral Dimension,” M. Sc. Engg. (Civil), Thesis, BUET.

Romstad, K. M. and Subramanian, C. V. (1970), “Analysis of Frames with Partial Connection Rigidity,” ASCE, Journal of Structural Engineering, Vol. 100.

Smith, C. S. and Carter, C. (1969), “A Method of Analysis for Infilled Frame,” Proceedings Inst. of Civil Engg. London, V.44.

Taranath, B. S. (1988), “Structural Analysis and Design of Tall Building,” McGraw-Hill Book Company.

Wolfgang, S. (1961), “High-Rise Building Structures,” John Wiley & Sons.

129

Appendix A

CALCULATION OF GRAVITY, WIND AND EARTQUAKE LOADS

A.1 Introduction

The P-delta effect is not considered in analysis. Hence, the gravity load has insignificant effect on deflection of model frames and moments in vertical members.

Gravity load, Wind load and Earthquake load are calculated for the model frames as follows: Superimposed load are taken, 5.25 kPa for dead load and 2.85 kPa for live load, 6 kN/m for facade dead load, 24 kN/m3 for unit weight of concrete,19 kN /m3 for unit weight of masonry, 1 kN / m2 for floor finish, 0.25 kN / m2 for ceiling plaster, 1 kN / m2 for light weight partition wall, wind load, earthquake load is taken as per BNBC, ultimate crushing strength of concrete is taken 21 Mpa.

A.2 Gravity Load Dead load (DL)i. 125 mm thick slab load = 3 kN / m2

ii. Floor finish = 1

iii. Ceiling plaster = 0.25

iv. Partition wall = 1

Total = 5.25 kN / m2

Others load as, Beam, Columns, Infill walls, Facade loads, i.e rise, drop, windows etc. are

calculated as below and converted as kN / m2 on floor load

a. Beams (Transverse) = 4x6’x0.3x0.5x23.60 = 84.56 kN

b. Beams (Along) = 1x6.40x0.3x0.50x23.60 =22.66 kN

c. Columns = 4x0.30x0.60x3.00x23.60 =51.83 kN

d. Infills =2x3.05xx19x0.25 = 70.54 kN

e. Façade = 2 x6 x 6 = 70.20 kN

Total = 300.19 kN

Load per sq.m = 300.19 / 6x 13.7 = 3.65 kN / m2

Influenced area = 13.7 x 6 = 82.20 sq. m

Total DL = 82.20 x 5.25 = 431.55 kN

DL per m = 431.55 / 13.7 = 31.50 kN

130

Total LL = 82.20 x 2.85 = 234.27 kN

LL per m = 234.27 / 13.70 = 17.10 kN

A.3 Wind Load

Location Dhaka

Exposure A

Basic wind velocity 210 km /h (Table C.1)

For value Cp,

H = 48 m, B = 30 m, L = 13.70 m

H / B = 48 / 30 = 1.60, L/B= 13.70 / 30 = 0.46

Hence, Cp (Fig. 3.1) = 1.45

Design wind pressure, Pz values for different height are calculated from Fig. 3.4 and presented in

Table A.1 GhCpCI is constant for specified building,

Gh = 1.22 (Fig. 3.3), CI = 1 (Table C.2), Hence, GhCpCI = 1.77

Pz = 1.77 x (Fig. 3.4 values against height), these are presented in Table A.1

Table A.1 Design wind pressure at floor level as follows

H in

meter ( From Graph 2.4 ) Pz in kN/m2

Pz in kN at floor node

131

3

6

9

12

15

18

21

24

27

30

33

36

39

42

45

48

0.76

0.85

1.05

1.20

1.25

1.40

1.50

1.60

1.65

1.80

1.85

1.94

2.00

2.05

2.15

2.20

1.35

1.51

1.86

2.13

2.22

2.49

2.66

2.84

2.93

3.20

3.29

3.45

3.55

3.64

3.82

3.91

24.71

27.63

34.04

38.98

40.63

45.57

48.68

51.97

53.62

58.56

60.21

63.14

64.97

66.61

69.91

71.55

Total = 820.18 kN

A.4 Earthquake Load

Earthquake load has been calculated from the consideration as follows;

Location Dhaka

Zone = 2

Zone coefficient, Z = 0.15

Site Coefficient factor, S = 1.50

Importance Coefficient, I = 1

Response Modification Coefficient, R= 5 (Table C.6)

Building 16-storied

Building height, H = 48 m

Bay width = 6 m

Bay length = 13.7 m

Floor area under bay consideration = 82.20 sq.m

132

Total DL per floor area = 3.65 + 5.25 = 8.90 kN /m2

Total DL for one floor under bay considered = 8.90 x 6 x 13.70 = 731.58 kN

Total DL for 16 floors under bay considered = 731.58 x 16 = 11705.28 kN

Live Load (LL) = 2.85 kN /m2

Total LL for one floor = 2.85 x 6 x 13.70 = 234.27 kN

Total LL for 16 floors under bay considered = 234.27 x 16 = 3748.32 kN

Total load, W under bay consideration =Total DL + 25% Gravity LL

= 11705.26 + 0.25 x 3748.32

= 12642.34 kN

V / W (Fig. 3.9) =0.048

V (base shear) = 0.048 x W = 0.048x 12642.34

=606.83 kN

Building height, H = 48 m

Hence, T = 1.35 sec. (Fig. 3.7)

Ft = 0.07TV 0.25V, T 0.7 sec.

Ft = 0 T 0.7 sec.

Ft = 0.07 x 1.35 x 606.83 = 57.35 kN

V-Ft = 549.48 kN

wx= total floor load at every floor

Considering equal wx at every floor

Hence, the floor distribution comes, as (A.2.1)

(A.2.2)

Loads, Fx are presented in Table A.2

Table A.2 Earthquake load in kN at every floor level

hx in m Fx / ( V-Ft) % Fx in kN

3 0.65 4.04

133

6

9

12

15

18

21

24

27

30

33

36

39

42

45

48

1.52

2.2

3.0

3.60

4.40

5.20

6.00

6.80

7.40

8.20

8.90

9.70

10.40

11.20

11.70

8.05

12.12

16.16

20.21

24.25

28.29

32.30

36.37

40.41

44.45

48.49

52.53

56.56

60.62

64.66

V - Ft = 549.57 kN

Appendix B

STAAD-III SCRIPT FILES

B.1 Introduction

Input data files of 2D analysis for different model frames are appended in

the following sub articles. These are Rigid Frame model, Infill Frame

134

model, Equivalent Wide Column model, Coupled Wall Frame model

(considering with auxiliary beam) and Coupled Wall Frame model

(considering without auxiliary beam). These frame models are analyzed

with different loads, different beam and column sizes for concentrated

load at top, wind and earthquake load. Only one type of these is written in

each data file. Output results are directly compiled in tables through

chapter 5.

B.2 Input FilesFor different model frames only one set of input file of each has been given below through B.2.1 to B.2.10. B.2.1 STAAD PLANE

RIGID FRAME model

Wind load analysis

UNIT KNS MMS

JOINT COORDINATE

1 0 0 ; 2 2744 0 ; 3 10061 0 ; 4 12805 0

REPEAT ALL 16 0 3050

MEMBER INCIDENCE

1 5 6 ; 2 6 7 ; 3 7 8

REPEAT ALL 15 3 4

100 1 5 115 1 4 ; 116 2 6 131 1 4

132 3 7 147 1 4 ; 148 4 8 163 1 4

UNIT MMS

MEMBER PROPERTY

1 TO 48 PRI YD 750 ZD 300

100 to 115 148 to 163 pri yd 900 zd 300

116 TO 147 PRI YD 750 ZD 300

CONSTANT

E CONCRETE

POI CONCRETE

DEN CONCRETE

SUPPORT

1 TO 4 FIXED

Unit METRE

LOAD 1 : SELF WT

SELF Y -1

Load 2 : Floor DL

Member load

1 to 48 uni y -16.10

Load 3 : Floor LL

Member load

1 to 48 uni y -8.78

135

LOAD 4 : Wind LOAD

JOINT LOAD

5 FX 21.94

9 FX 32.26

13 FX 41.96

17 FX 45.17

21 FX 49.04

25 FX 52.91

29 FX 55.49

33 FX 58.07

37 FX 60.03

41 FX 61.94

45 FX 63.90

49 FX 65.19

53 FX 67.77

57 FX 69.69

61 FX 70.98

65 FX 72.94

LOAD COMB 5

1 .75 2 .75 3 .75 4 .75

PERFORM ANALYSIS

Load list 4 5

PRINT JOINT DISPLACEMENT LIST 68

PRINT JOINT DISPLACEMENT LIST 5 TO 65 BY 4

Print Member force List 1 to 48

Plot displacement file

FINISH

B.2.2 STAAD PLANE

RIGID FRAME model

Earthquake load analysis

UNIT KNS MMS

JOINT COORDINATE

1 0 0 ; 2 2744 0 ; 3 10061 0 ; 4 12805 0

REPEAT ALL 16 0 3050

MEM INCI

1 5 6 ; 2 6 7 ; 3 7 8

REPEAT ALL 15 3 4

100 1 5 115 1 4 ; 116 2 6 131 1 4

132 3 7 147 1 4 ; 148 4 8 163 1 4

UNIT MMS

MEM PRO

1 TO 48 PRI YD 750 ZD 300

100 to 115 148 to 163 pri yd 900 zd 300

116 TO 147 PRI YD 750 ZD 300

CONSTANT

E CONC

136

POI CONC

DEN CONC

SUPPORT

1 TO 4 FIXED

Unit MET

LOAD 1 : SELF WT

SELF Y -1

Load 2 : Floor DL

Mem load

1 to 48 uni y -16.10

Load 3 : Floor LL

Mem load

1 to 48 uni y -8.78

LOAD 4 : Wind LOAD

JOINT LOAD

5 FX 5.12

9 FX 10.19

13 FX 15.31

17 FX 20.38

21 FX 25.37

25 FX 30.57

29 FX 35.69

33 FX 40.76

37 FX 45.92

41 FX 50.95

45 FX 56.07

49 FX 61.19

53 FX 66.26

57 FX 71.33

61 FX 76.50

65 FX 81.57

65 FX 71.73

LOAD COMB 5

1 .75 2 .75 3 .75 4 .75

PERFORM ANALYSIS

Load list 4 5

PRINT JOINT DISPLACEMENT LIST 68

PRINT JOINT DISPLACEMENT LIST 5 TO 65 BY 4

Print Mem force List 1 to 48

Plot disp file

FINISH

B.2.3 STAAD PLANE

INFILLED (MASONRY WALL) FRAME model

wind load analysis

137

UNIT KNS MMS

JOINT COORDINATE

1 0 0 ; 2 2744 0 ; 3 10060 0 ; 4 12805 0

REPEAT ALL 16 0 3050

MEM INCI

1 5 6 ; 2 6 7 ; 3 7 8

REPEAT ALL 15 3 4

100 1 5 115 1 4 ; 116 2 6 131 1 4

132 3 7 147 1 4 ; 148 4 8 163 1 4

ELEMENT INCIDENT

536 19 20 24 23

537 23 24 28 27

538 27 28 32 31

539 31 32 36 35

540 35 36 40 39

541 39 40 44 43

542 43 44 48 47

543 47 48 52 51

544 51 52 56 55

545 55 56 60 59

546 59 60 64 63

547 63 64 68 67

DEFINE MESH

A JOINT 1

B JOINT 5

C JOINT 9

D JOINT 13

E JOINT 17

F JOINT 21

G JOINT 25

H JOINT 29

I JOINT 33

J JOINT 37

K JOINT 41

L JOINT 45

M JOINT 49

N JOINT 53

O JOINT 57

P JOINT 61

Q JOINT 65

R JOINT 2

S JOINT 6

T JOINT 10

U JOINT 14

V JOINT 18

W JOINT 22

X JOINT 26

138

Y JOINT 30

Z JOINT 34

a JOINT 38

b JOINT 42

c JOINT 46

d JOINT 50

e JOINT 54

f JOINT 58

g JOINT 62

h JOINT 66

i JOINT 3

j JOINT 7

k JOINT 11

l JOINT 15

m JOINT 19

n JOINT 4

o JOINT 8

p JOINT 12

q JOINT 16

r JOINT 20

GENERATE ELEMENT RECT

MESH ARSB 3 3

MESH BSTC 3 3

MESH CTUD 3 3

MESH DUVE 3 3

MESH EVWF 3 3

MESH FWXG 3 3

MESH GXYH 3 3

MESH HYZI 3 3

MESH IZaJ 3 3

MESH JabK 3 3

MESH KbcL 3 3

MESH LcdM 3 3

MESH MdeN 3 3

MESH NefO 3 3

MESH OfgP 3 3

MESH PghQ 3 3

MESH inoj 3 3

MESH jopk 3 3

MESH kpql 3 3

MESH lqrm 3 3

UNIT NEW MMS

MEM PRO

1 TO 48 PRI YD 750 ZD 300

100 TO 115 148 to 163 PRI YD 900 ZD 300

116 TO 147 PRI YD 750 ZD 300

ELEMENT PRO

139

548 TO 727 536 TO 547 TH 250

CONSTANT

E 24828 MEM 1 TO 48 100 TO 163

POI 0.15 MEM 1 TO 48 100 TO 163

DEN .000024 MEM 1 TO 48 100 TO 163

E 4483 MEM 548 TO 727 536 TO 547

POI .25 MEM 548 TO 727 536 TO 547

DEN .000019 MEM 548 TO 727 536 TO 547

SUPPORT

1 TO 4 69 70 231 232 FIXED

Unit KNS MET

LOAD 1 : SELF WT

SELF Y -1

Load 2 : Floor DL

Mem load

1 to 48 uni y -16.06

Load 3 : Floor DL

Mem load

1 to 48 uni y -8.76

LOAD 4 : Wind LOAD

JOINT LOAD

5 FX 21.94

9 FX 32.26

13 FX 41.96

17 FX 45.17

21 FX 49.04

25 FX 52.91

29 FX 55.49

33 FX 58.07

37 FX 60.03

41 FX 61.94

45 FX 63.90

49 FX 65.19

53 FX 67.77

57 FX 69.69

61 FX 70.98

65 FX 72.94

LOAD COMB 5

1 .75 2 .75 3 .75 4 .75

Perform analysis

Load List 4 5

PRINT JOINT DISPLACEMENT LIST 68

PRINT JOINT DISPLACEMENT LIST 5 to 65 by 4

Print mem force list 1 to 48

Print element forces list 548 to 727 536 to 547

FINISH

140

B.2.4 STAAD PLANE

INFILLED (MASONRY WALL) FRAME model

Earthquake load analysis

UNIT KNS MMS

JOINT COORDINATE

1 0 0 ; 2 2744 0 ; 3 10060 0 ; 4 12805 0

REPEAT ALL 16 0 3050

MEM INCI

1 5 6 ; 2 6 7 ; 3 7 8

REPEAT ALL 15 3 4

100 1 5 115 1 4 ; 116 2 6 131 1 4

132 3 7 147 1 4 ; 148 4 8 163 1 4

ELEMENT INCIDENT

536 19 20 24 23

537 23 24 28 27

538 27 28 32 31

539 31 32 36 35

540 35 36 40 39

541 39 40 44 43

542 43 44 48 47

543 47 48 52 51

544 51 52 56 55

545 55 56 60 59

546 59 60 64 63

547 63 64 68 67

DEFINE MESH

A JOINT 1

B JOINT 5

C JOINT 9

D JOINT 13

E JOINT 17

F JOINT 21

G JOINT 25

H JOINT 29

I JOINT 33

J JOINT 37

K JOINT 41

L JOINT 45

M JOINT 49

N JOINT 53

O JOINT 57

P JOINT 61

Q JOINT 65

R JOINT 2

S JOINT 6

T JOINT 10

U JOINT 14

141

V JOINT 18

W JOINT 22

X JOINT 26

Y JOINT 30

Z JOINT 34

a JOINT 38

b JOINT 42

c JOINT 46

d JOINT 50

e JOINT 54

f JOINT 58

g JOINT 62

h JOINT 66

i JOINT 3

j JOINT 7

k JOINT 11

l JOINT 15

m JOINT 19

n JOINT 4

o JOINT 8

p JOINT 12

q JOINT 16

r JOINT 20

GENERATE ELEMENT RECT

MESH ARSB 3 3

MESH BSTC 3 3

MESH CTUD 3 3

MESH DUVE 3 3

MESH EVWF 3 3

MESH FWXG 3 3

MESH GXYH 3 3

MESH HYZI 3 3

MESH IZaJ 3 3

MESH JabK 3 3

MESH KbcL 3 3

MESH LcdM 3 3

MESH MdeN 3 3

MESH NefO 3 3

MESH OfgP 3 3

MESH PghQ 3 3

MESH inoj 3 3

MESH jopk 3 3

MESH kpql 3 3

MESH lqrm 3 3

UNIT NEW MMS

MEM PRO

1 TO 48 PRI YD 750 ZD 300

142

100 TO 115 148 to 163 PRI YD 900 ZD 300

116 TO 147 PRI YD 750 ZD 300

ELEMENT PRO

548 TO 727 536 TO 547 TH 250

CONSTANT

E 24828 MEM 1 TO 48 100 TO 163

POI 0.15 MEM 1 TO 48 100 TO 163

DEN .000024 MEM 1 TO 48 100 TO 163

E 4483 MEM 548 TO 727 536 TO 547

POI .25 MEM 548 TO 727 536 TO 547

DEN .000019 MEM 548 TO 727 536 TO 547

SUPPORT

1 TO 4 69 70 231 232 FIXED

Unit KNS MET

LOAD 1 : SELF WT

SELF Y -1

Load 2 : Floor DL

Mem load

1 to 48 uni y -16.05

Load 3 : Floor DL

Mem load

1 to 48 uni y -8.76

LOAD 4 : Wind LOAD

JOINT LOAD

5 FX 5.12

9 FX 10.19

13 FX 15.27

17 FX 20.38

21 FX 25.37

25 FX 30.57

29 FX 35.69

33 FX 40.76

37 FX 45.92

41 FX 50.95

45 FX 56.07

49 FX 61.19

53 FX 66.26

57 FX 71.33

61 FX 76.50

65 FX 81.57

65 FX 71.73

LOAD COMB 5

1 .75 2 .75 3 .75 4 .75

Load List 4 5

PRINT JOINT DISPLACEMENT LIST 68

PRINT JOINT DISPLACEMENT LIST 5 to 65 by 4

PRINT material pro list 1

143

Print mem force list 1 to 48

Print element stress list 548 to 727 536 to 547

FINISH

B.2.5 STAAD PLANE

EQUIVALENT WIDE COLUMN model

WIND LOAD ANALYSIS

UNIT KNS MMS

JOIN COOR

1 0 0 ; 2 10061 0

R A 16 0 3050

MEM INCI

1 3 4 16 1 2

50 1 3 65 1 2

70 2 4 85 1 2

MEMB OFFSET

1 TO 16 START 6

1 TO 16 END -6

UNIT MMS

MEM PRO

1 TO 16 PRI YD 512 ZD 300

50 TO 65 70 TO 85 PRI YD 3659 ZD 300

CONS

E CONC

POI CONC

DEN CONC

SUPPORT

1 2 FIXED

UNIT FT

LOAD 1 :

SELF Y -1

LOAD 2 : FLOOR D LOAD

MEM LOAD

1 TO 16 UNI Y -16.10

LOAD 3 : FLOOR L LOAD

MEM LOAD

1 TO 16 UNI Y -8.78

LOAD 4 : WIND LOAD

JOINT LOAD

3 FX 21.94

5 FX 32.26

7 FX 41.96

9 FX 45.17

11 FX 49.04

13 FX 52.91

15 FX 55.49

17 FX 58.07

144

19 FX 60.03

21 FX 61.94

23 FX 63.90

25 FX 65.19

27 FX 67.77

29 FX 69.69

31 FX 70.98

33 FX 72.94

LOAD COMB 5 :

1 .75 2 .75 3 .75 4 .75

PER ANA

Load list 4 5

PRINT JOINT DISP LIST 34

PRINT JOINT DISP LIST 3 TO 33 BY 2

Print mem force list 1 to 16

PLOT DISP FIL

FIN

B.2.6 STAAD PLANE

EQUIVALENT WIDE COLUMN model

EARHQUAKE LOAD ANALYSIS

UNIT KNS MMS

JOIN COOR

1 0 0 ; 2 10061 0

R A 16 0 3050

MEM INCI

1 3 4 16 1 2

50 1 3 65 1 2

70 2 4 85 1 2

MEMB OFFSET

1 TO 16 START 6

1 TO 16 END -6

UNIT MMS

MEM PRO

1 TO 16 PRI YD 512 ZD 300

50 TO 65 70 TO 85 PRI YD 3659 ZD 300

CONS

E CONC

POI CONC

DEN CONC

SUPPORT

1 2 FIXED

UNIT FT

LOAD 1 :

SELF Y -1

LOAD 2 : FLOOR D LOAD

MEM LOAD

145

1 TO 16 UNI Y -16.10

LOAD 3 : FLOOR L LOAD

MEM LOAD

1 TO 16 UNI Y -8.78

LOAD 4 : EQ LOAD

JOINT LOAD

3 FX 5.12

5 FX 10.19

7 FX 15.31

9 FX 20.38

11 FX 25.37

13 FX 30.57

15 FX 35.69

17 FX 40.76

19 FX 45.92

21 FX 50.95

23 FX 56.07

25 FX 61.19

27 FX 66.26

29 FX 71.33

31 FX 76.50

33 FX 81.57

33 FX 71.73

LOAD COMB 5 :

1 .75 2 .75 3 .75 4 .75

PER ANA

PRINT SUPPORT REACTION

Load list 4 5

PRINT JOINT DISP LIST 34

PRINT JOINT DISP LIST 3 TO 33 BY 2

print mem force list 1 to 16

PLOT DISP FILE

FIN

B.2.7 STAAD PLANE

STAAD PLANE

COUPLED WALL FRAME model (considering auxiliary beam)

Wind load analysis

UNIT KNS MMS

JOINT COORDINATE

1 0 0 ; 2 1829 0 ; 3 3659 0

REPEAT ALL 32 0 1524

200 10061 0 ; 201 11890 0 ; 202 13720 0

REPEAT ALL 32 0 1524

MEM INCI

200 9 206 215 1 6

AUXILIARY BEAMS

146

216 8 9;217 14 15;218 20 21;219 26 27;220 32 33;221 38 39;222 44 45

223 50 51;224 56 57;225 62 63;226 68 69;227 74 75;228 80 81;229 86 87

230 92 93;231 98 99;232 206 207;233 212 213;234 218 219;235 224 225

236 230 231;237 236 237;238 242 243;239 248 249;240 254 255;241 260 261

242 266 267;243 272 273;244 278 279;245 284 285;246 290 291;247 216 217

ELE INCI

1 4 5 2 1 TO 63 2 3 ; 2 5 6 3 2 TO 64 2 3

101 203 204 201 200 TO 163 2 3

102 204 205 202 201 TO 164 2 3

UNIT MMS

MEM PRO

200 TO 215 PRI YD 550 ZD 300

AUXILIARY BEAM

216 TO 247 pri yd 550 zd 300

ELE PROPERTY

1 TO 64 101 TO 164 TH 300

CONSTANT

E CONC

POI CONC

DEN CONC

SUPPORT

1 TO 3 200 TO 202 FIXED

UNIT MET

LOAD 1 : SELF WT

SELF Y -1

Load 2 : Floor DL

Mem load

200 to 215 uni y -16.10

Load 3 : Floor LL

Mem load

200 to 215 uni y -8.78

LOAD 4 : Wind LOAD

JOINT LOAD

7 FX 21.94

13 FX 32.26

19 FX 41.96

25 FX 45.17

31 FX 49.04

37 FX 52.91

43 FX 55.49

49 FX 58.07

55 FX 60.03

61 FX 61.94

67 FX 63.90

73 FX 65.19

79 FX 67.77

85 FX 69.69

147

91 FX 70.98

97 FX 72.94

LOAD COMB 5 :

1 .75 2 .75 3 .75 4 .75

PER ANA

LOAD LIST 4 5

PRINT JOINT DISP LIST 97

PRINT JOINT DISP LIST 202 to 298 by 6

PRINT MEM FORCES LIST 200 TO 215

PRINT ELEMENT STRESSES LIST 1 TO 64 101 TO 164

PLOT DISP FILE

FIN

B.2.8 COUPLED WALL FRAME model (considering auxiliary beam)

Earthquake load analysis

UNIT KNS MMS

JOINT COORDINATE

1 0 0 ; 2 1829 0 ; 3 3659 0

REPEAT ALL 32 0 1524

200 10061 0 ; 201 11890 0 ; 202 13720 0

REPEAT ALL 32 0 1524

MEM INCI

200 9 206 215 1 6

AUXILIARY BEAMS

216 8 9;217 14 15;218 20 21;219 26 27;220 32 33;221 38 39;222 44 45

223 50 51;224 56 57;225 62 63;226 68 69;227 74 75;228 80 81;229 86 87

230 92 93;231 98 99;232 206 207;233 212 213;234 218 219;235 224 225

236 230 231;237 236 237;238 242 243;239 248 249;240 254 255;241 260 261

242 266 267;243 272 273;244 278 279;245 284 285;246 290 291;247 216 217

ELE INCI

1 4 5 2 1 TO 63 2 3 ; 2 5 6 3 2 TO 64 2 3

101 203 204 201 200 TO 163 2 3

102 204 205 202 201 TO 164 2 3

UNIT MMS

MEM PRO

200 TO 215 PRI YD 550 ZD 300

AUXILIARY BEAM

216 TO 247 pri yd 550 zd 300

ELE PROPERTY

1 TO 64 101 TO 164 TH 300

CONSTANT

E CONC

POI CONC

DEN CONC

SUPPORT

1 TO 3 200 TO 202 FIXED

UNIT MET

148

LOAD 1 : SELF WT

SELF Y -1

Load 2 : Floor DL

Mem load

200 to 215 uni y -16.10

Load 3 : Floor LL

Mem load

200 to 215 uni y -8.78

LOAD 4 : EQ LOAD

JOINT LOAD

7 FX 5.12

13 FX 10.19

19 FX 15.31

25 FX 20.38

31 FX 25.37

37 FX 30.57

43 FX 35.69

49 FX 40.76

55 FX 45.92

61 FX 50.95

67 FX 56.07

73 FX 61.19

79 FX 66.26

85 FX 71.33

91 FX 76.50

97 FX 81.57

97 FX 71.73

LOAD COMB 5:

1 .75 2 .75 3 .75 4 .75

PER ANA

LOAD LIST 4 5

PRINT JOINT DISP LIST 97

PRINT JOINT DISP LIST 202 to 298 by 6

PRINT MEM FORCES LIST 200 TO 215

PRINT ELEMENT STRESSES LIST 1 TO 64 101 TO 164

PLOT DISP FILE

FIN

B.2.9 STAAD PLANE

COUPLED WALL FRAME model

WIND LOAD ANALYSIS

UNIT KNS MMS

JOINT COORDINATE

1 0 0 ; 2 1829 0 ; 3 3659 0

REPEAT ALL 32 0 1524

200 10061 0 ; 201 11890 0 ; 202 13720 0

149

REPEAT ALL 32 0 1524

MEM INCI

200 9 206 215 1 6

ELE INCI

1 4 5 2 1 TO 63 2 3 ; 2 5 6 3 2 TO 64 2 3

101 203 204 201 200 TO 163 2 3

102 204 205 202 201 TO 164 2 3

UNIT MMS

MEM PRO

200 TO 215 PRI YD 550 ZD 300

ELE PROPERTY

1 TO 64 101 TO 164 TH 300

CONSTANT

E CONC

POI CONC

DEN CONC

SUPPORT

1 TO 3 200 TO 202 FIXED

UNIT MET

LOAD 1 : SELF WT

SELF Y -1

Load 2 : Floor DL

Mem load

200 to 215 uni y -16.10

Load 3 : Floor LL

Mem load

200 to 215 uni y -8.78

LOAD 4 : Wind LOAD

JOINT LOAD

7 FX 21.94

13 FX 32.26

19 FX 41.96

25 FX 45.17

31 FX 49.04

37 FX 52.91

43 FX 55.49

49 FX 58.07

55 FX 60.03

61 FX 61.94

67 FX 63.90

73 FX 65.19

79 FX 67.77

85 FX 69.69

91 FX 70.98

97 FX 72.94

LOAD COMB 5 :

1 .75 2 .75 3 .75 4 .75

150

PER ANA

LOAD LIST 4 5

PRINT JOINT DISP LIST 97

PRINT JOINT DISP LIST 202 to 298 by 6

PRINT MEM FORCES LIST 200 TO 215

PRINT ELEMENT STRESSES LIST 1 TO 64 101 TO 164

PLOT DISP FILE

FIN

B.2.10 STAAD PLANE

COUPLED WALL FRAME model

Earthquake LOAD ANALYSIS

UNIT KNS MMS

JOINT COORDINATE

1 0 0 ; 2 1829 0 ; 3 3659 0

REPEAT ALL 32 0 1524

200 10061 0 ; 201 11890 0 ; 202 13720 0

REPEAT ALL 32 0 1524

MEM INCI

200 9 206 215 1 6

ELE INCI

1 4 5 2 1 TO 63 2 3 ; 2 5 6 3 2 TO 64 2 3

101 203 204 201 200 TO 163 2 3

102 204 205 202 201 TO 164 2 3

UNIT MMS

MEM PRO

200 TO 215 PRI YD 550 ZD 300

ELE PROPERTY

1 TO 64 101 TO 164 TH 300

CONSTANT

E CONC

POI CONC

DEN CONC

SUPPORT

1 TO 3 200 TO 202 FIXED

UNIT MET

LOAD 1 : SELF WT

SELF Y -1

Load 2 : Floor DL

Mem load

200 to 215 uni y -16.10

Load 3 : Floor LL

Mem load

200 to 215 uni y -8.78

LOAD 4 : EQ LOAD

JOINT LOAD

7 FX 5.12

151

13 FX 10.19

19 FX 15.31

25 FX 20.38

31 FX 25.37

37 FX 30.57

43 FX 35.69

49 FX 40.76

55 FX 45.92

61 FX 50.95

67 FX 56.07

73 FX 61.19

79 FX 66.26

85 FX 71.33

91 FX 76.50

97 FX 81.57

97 FX 71.73

LOAD COMB 5

1 .75 2 .75 3 .75 4 .75

PER ANA

LOAD LIST 4 5

PRINT JOINT DISP LIST 97

PRINT JOINT DISP LIST 202 to 298 by 6

PRINT MEM FORCES LIST 200 TO 215

PRINT ELEMENT STRESSES LIST 1 TO 64 101 TO 164

PLOT DISP FILE

FIN

Appendix CTABLES (BNBC, 1993)

C.1 Introduction and Tables

Some tables from Bangladesh National Building Code (BNBC) are appended here to

facilitate load calculation. These are Basic Wind Speed Vb, Structural Importance factor CI

152

for wind, Structural Importance factor for Earthquake I, Seismic Zone Coefficient Z, Site

Coefficient S and Response Modification Coefficient R.

Table C.1 Basic wind speed for selected location in Bangladesh, Vb

Location Basic Wind Speed km/h Location Basic Wind Speed km/hAngarpotaBagherhatBandarbanBargunaBarisalBholaBograBrahmanbariaChandpurChapai NawabgonjChittagongChuadangaComillaCox’s BazarDahagramDhakaDinajpurFaridpurFeniGaibandaGazipurGopalgonjHabigonjHatiyaIshurdiJoypurhatJamalpurJessoreJhalakatiJhenaidahKhagracharriKhulnaKutubdiaKishoregonjKurigramKushtiaLakshmipur

150252200260256225198180160130260198196260150210130202205210215242172260225180180205260208180238260207210215162

LalmonirhatMadaripurMaguraManikgonjMeherpurMoheshkhaliMoulibazarMunshigonjMymensinghNaogaonNarailNarayangonjNarsinghdiNatoreNetrokonaNilphamariNoakhaliPabnaPanchagarhPatuakhaliPirojpurRajbariRajshahiRangamatiRangpurSatkhiraShariatpurSherpurSirajganjSrimangalSt.Martin’s islandSunamgonjSylhetSandwipTangailTeknafThakurgaon

204220208185185260168184217175222195190198210140184202130260260188155180209183198200160160260195195260160260130

Table C.2 Structural importance coefficient, CI for wind load

Structural Importance Category Structural Importance Coefficient ,CI

I Essential facilities

II Hazards facilities

1.25

1.25

153

III Special occupancy structures

IV Standard occupancy structures

V Low risk structures

1.00

1.00

0.80

Table C.3 Structural importance coefficient, I for earthquake

Structural Importance Category Structural Importance Coefficient, I

I Essential facilities 1.25

II Hazard Facilities 1.25

III Special Occupancy Structures 1

IV Standard Occupancy Structures 1

V Low Risk Structures 1

Table C.4 Seismic zone coefficient, Z

Selected Seismic Zone Zone Coefficient

Zone-1 Chapai Nawabganj, Rajshahi, Pabna, Kusthia, Jessore, Faridpur, Khulna, Faridpur, Barisal 0.075

Zone-2 Dhaka, Chittagong, Cox’s Bazar, Commila, Tangail, Nagaon, Joypuhat,Rangpur,Panchagar 0.15

Zone-3 Sylhet, Shrimongal, Mymensingh, Bogra, Lalmonirhat,Netrokona,Gibandah,Brahmanbaria 0.25

Table C.5 Site coefficient, S for seismic lateral forces

Type Site Soil Characteristics Coefficient, S

S1 A soil profile either :

a) a rock like material characterized by a shear wave

1

154

velocity greater than 762 m/s or by other suitable

means of classification, or

b) Stiff or dense soil condition where the soil depth is

less than 61 m

S2 A soil profile with dense or stiff soil conditions, where

the soil depth exceeds 61 m1.2

S3 A soil profile 21 m or more in depth and containing

more than 6 m of soft to medium stiff clay but not more

than 12 m of soft clay

1.5

S4 A soil profile containing more than 12 m of soft clay

characterized by a shear wave velocity less than 152 m/s 2

Table C.6 Response modification coefficient for structural systems, R (BNBC, 1993)

Basic Structural System Description of Lateral Force Resisting System Ra. Bearing Wall System 1. Light framed walls with shear panels

i) Plywood walls for structures, 3 story or less

ii) All others light framed walls

2. Shear walls

i) Concrete

8

6

6

155

ii) Masonry

3. Light steel framed bearing walls with tension only bracing

4. Braced frames where bracing carries gravity loads

i) Steel

ii) Concrete

iii) Heavy timber

6

4

6

4

4

b. Building Frame System 1. Steel eccentric braced frame (EBF)

2. Light framed walls with shear panels

i) Plywood walls for structures 3 stories or less

ii) All others light framed walls

3. Shear walls

i) Concrete

ii) Masonry

4. Concentric braced frames (CBF)

i) Steel

ii) Concrete

iii) Heavy timber

10

9

7

8

8

8

8

8

c. Moment Resisting Frame

system

1. Special moment resisting frame (SMRF)

i) Steel

ii) Concrete

2. Intermediate moment resisting frame (IMRF), concrete

3. Ordinary moment resisting frame (OMRF)

i) Steel

ii) Concrete

12

12

8

6

5

d. Dual System 1. Shear walls

i) Concrete with steel or concrete SMRF

ii) Concrete with steel OMRF

iii) Concrete with concrete IMRF

iv) Masonry with steel or concrete SMRF

v) Masonry with steel OMRF

vi) Masonry with concrete IMRF

2. Steel EBF

i) With steel SMRF

ii) With Steel OMRF

3. Concentric braced frame (CBF)

i) Steel with steel SMRF

ii) Steel with steel OMRF

iii) Concrete with concrete SMRF

iv) Concrete with concrete IMRF

12

6

9

8

6

7

12

6

10

6

9

6

ACKNOWLEDGEMENT

156

The Author wishes to express his deepest gratitude to Dr. Md. Shafiul Bari, Professor,

Department of Civil Engineering, BUET for his continuous guidance, invaluable suggestions

and affectionate encouragement at every stage of this study.

The author also gratefully appreciate the help in conducting the AutoCAD graphics rendered

by A. Shadat and Tuhin Ahmed, AutoCAD operator, Union Technical Consult Ltd, House

no. G-22, Pallabi extension R/A, Mirpur, Dhaka-1221.

DECLARATION

157

I do hereby declare that the Project work reported therein, has been performed by me and this

work has neither been submitted nor is being concurrently submitted in consideration for any

degree at any other University.

Author

ABSTRACT

158

In recent years Bangladesh has witnessed a growing trend towards construction of 15-30 storied buildings. All most all of these are being situated in Dhaka City. The tallest building in Bangladesh to date is the 30-storied (with one basement) Bangladesh Bank Annex Building. No extensive study has been conducted to compare the different techniques available for the analysis of tall buildings with different structural system. A limited parametric study is carried out to search suitable structural system of the high rise building. A short direction bay of a 16-storied building is considered for lateral load analysis by 2D. Wind and earthquake loads are considered as lateral loads. The specified bay is modeled by three structural systems, namely, i) Rigid Frame structure, ii) Infilled Frame structure, iii) Coupled Wall structure. The Coupled Wall structure is again modeled in three forms as, i) Finite Element model without auxiliary beam, ii) Finite Element model with auxiliary beam, and iii) Equivalent Wide Column model. The parameters that are varied in structural system are, beam size, column size, inclusion of infill material (brick masonry) in modeling rigid frame structures etc. To conduct the parametric study, professional software (STAAD-III) is employed. To calculate the design wind pressure and earthquake base shear, the loads are estimated as per specification of Bangladesh National Code (BNBC-1993). Any necessary value or interpolated value is taken from the graph directly. The analysis results are presented in tabular and graphical form and discussed in detail.

SYMBOLS AND NOTATIONS

a the maximum acceleration of the building

A1 cross sectional area of wall w1

A2 cross sectional area of wall w2

B width of opening

b width of connecting beam

C seismic coefficient,

159

structural flexibility coefficient, numerical coefficient

Cc velocity to pressure conversion coefficient

Cz combined height and exposure coefficient

CG gust effect factor

Cp external pressure coefficient averaged over the area of the surface

considered.

CI structural importance coefficient

d total depth of coupling beam

Ec modulus of elasticity of concrete

Em modulus of elasticity of brick masonry

f’c crushing strength of concrete

f’b crushing strength of brick

F’c uniaxial cylinder strength of concrete

Fv allowable shear stress of masonry

f’m crushing strength of Brick masonry

fm allowable strength of Brick masonry

fbc allowable bond shear stress of masonry

g acceleration due to gravity

G modulus of rigidity

GA modulus of shear rigidity of beam

hn height of structure in meter above the base to level n.

h each floor height

H total building height, height from base level to specified level

Ib moment of inertia of connecting beam

I structural importance coefficient, moment of inertia of two walls

Ic effective moment of inertia of connecting beam

l distance between centroids of walls 1 and 2

160

M1 bending moment in wall W1

M2 bending moment in wall W2

N axial force in coupled wall

Q horizontal shear load

Q’c ultimate horizontal shear on the infill

q uniformly distributed horizontal load on walls, wind dynamic pressure

qz sustained wind pressure

R structural system coefficient

S site coefficient for soil

T fundamental period of vibration

Vb basic wind speed

V base shear

W building weight

Z seismic zone coefficient

poison ratio of concrete

unit weight of concrete

’ crushing strength of mortar

d diagonal tensile stress of brick masonry

y vertical compressive stress of brick masonry

x principal stress

m unit weight of brick masonry

m poison ratio of brick masonry

cross sectional shape factor for shear, equal to 1.2 for rectangular

section.

xy shear stress

ABBREVIATIONS

AB Auxiliary Beam

ACI American Concrete Institute

ANSI American National Standard Institute

161

ASCE American Society of Civil Engineers

ATC Applied Technology Council

BNBC Bangladesh National Building Code

BOCA Building Officials and Code Administration International

BSLJ Building Standard Law of Japan

CW Coupled Wall without auxiliary beam

CWAB Coupled Wall with auxiliary beam

EWC Equivalent Wide Column

IEB Institution of Engineers, Bangladesh

IF Infilled Frame

IMRF Intermediate Moment Resisting Frame

IS Indian Standard

JCE Journal of Civil Engineering

LHS Left Hand Side

MRF Moment Resisting Frame

NABC North American Building Code

NBCC National Building Code of Canada

OMRF Ordinary Moment Resisting Frame

RF Rigid Frame

SMRF Special Moment Resisting Frame

UBC Uniform Building Code

WC Wide Column, Equivalent Wide Column

TABLE OF CONTENTS

162

PageACKNOWLEDGEMENT i

DECLARATION ii

ABSTRACT iiiSYMBOLS & NOTATIONS iv

ABBREVIATIONS vi

Chapter 1 INTRODUCTION

1.1 General 1

1.2 Objectives of the Study 1

1.3 Scope of the Study 2

1.4 Methodology 2

Chapter 2 LITERATURE REVIEW

2.1 Introduction 4

2.2 Structural System 5

2.2.1 Rigid Frame 5

2.2.1.1 Behaviour of Rigid Frame Structure under Lateral Load 6

2.2.2 Shear Wall 7

2.2.2.1 Behaviour of Shear Wall Structure under Lateral Load 8

2.2.3 Shear Wall-Frame 9

2.2.3.1 Behaviour of Shear Wall-Frame under Lateral Load 9

2.2.4 Coupled Shear Wall 11

2.2.4.1 Behaviour of Coupled Shear Wall Structure under Lateral Load 11

2.2.5 Infilled Frame

12

2.2.5.1 Behaviour of Infilled Frames under Lateral Load 13

2.2.5.2 Stresses in Infill 14

2.3 Review of Lateral Loads 16

2.3.1 Wind Load 17

2.3.1.1 Determination of Design Wind Load 18

2.3.1.2 Methods for Determining Wind Load 18

163

2.3.2 Code Provisions for Wind Load 21

2.3.3 Earthquake Load 23

2.3.4 Code Provisions for Earthquake Load 25

2.4 Method of Analysis 28

2.4.1 Continuous Medium Method 28

2.4.2 Finite Element Method 31

2.4.3 Equivalent Wide Column Frame Method 33

2.4.4 Analogous Frame Method 34

2.5 Modelling Technique 36

2.5.1 Modelling for Preliminary Analysis 36

2.5.2 Modelling for Accurate Analysis 37

2.6 Drift of Structure 39

2.7 P-Delta Effect

40

2.8 STAAD-III 41

2.9 Summary 42

Chapter 3 GRAPHICAL PRESENTATION OF LATERAL LOADS

3.1 Introduction 46

3.2 Graphical Presentation of Wind load 46

3.3 Graphical Presentation of Earthquake load 59

3.4 Summary 71

Chapter 4 MODELLING OF THE STRUCTURES

4.1 Introduction 72

4.2 Description of Model Building 72

4.3 Loads Considered for Analysis 74

4.4 Modelling used for the Study 74

4.4.1 Basic Model under Lateral Load Study 75

164

4.5 Summary 81

Chapter 5 RESULTS AND DISCUSSIONS

5.1 Introduction 82

5.2 Deflections of Different Structural System for Concentrated Load at Top 83

5.3 Relative Stiffness of Model Frames for Concentrated Load at Top 98

5.4 Deflection of Different Structural System for Lateral Load 100

5.5 Moment in Beams of Different Structural System for Lateral Load 110

5.6 Stresses in Infill Material of Infilled Frame (Wind Load) 120

5.7 Summary 122

Chapter 6 CONCLUSION & SUGGESTION

6.1 General 123

6.2 Conclusions 123

6.3 Recommendations for Future Study 125

References 126

Appendix A CALCULATION OF GRAVITY, WIND AND EARTHQUAKE LOADS

A.1 Introduction 128

A.2 Gravity Load 128

A.3 Wind Load 129

A.4 Earthquake Load 130

Appendix B STAAD SCRIPT FILES

B.1 Introduction 133

B.2 Input Files 133

Appendix C TABLES (BNBC, 1993)

C.1 Introduction and Tables 151

165

ANALYSIS ON THE BEHAVIOUR OF HIGH RISE BUILDING

SITUATED ON SMALL AREA

UNDER LATERAL DIFLECTION DUE TO EARTH QUAKE AND WIND

PRESSURE

A Project Work Submitted by

RABBE KHAN MD. IBRAHIM S M TANVIR FAYSAL ALAM CHOWDHOURY

In partial fulfillment of the requirement for the degree of

HOUNERS OF ENGINEERING IN CIVIL ENGINEERING (Structural)

AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGYDhaka 1000.

and

October, 2011

Department of Civil Engineering

166

CERTIFICATION

The project titled “ANALYSIS ON THE BEHAVIOUR OF HIGH RISE BUILDING SITUATED ON SMALL

AREA

UNDER LATERAL DIFLECTION DUE TO EARTH QUAKE AND WIND PRESSURE ‘’

Submitted by: RABBE KHAN, MD. IBRAHIM , S M TANVIR FAYSAL ALAM CHOWDHOURY. SESSON-2011-12. has been accepted by the Examination Committee as satisfactory in partial fulfillment for the requirement of Master of Engineering in Civil Engineering (Structural) held on AUGUST 25, 2011.

Dr. Md. Mahmudur RAhman

Professor (Supervisor)Department of Civil EngineeringAUST, Dhaka-1000

167