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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
3
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 Systems b. Lateral Loads c. Method of Analysis d. Modeling Technique e. Drift f. 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 nontwisting 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 wallframe 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 contraflexure 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) (a) Rigid frame shear mode deformation
(b)
(c)
(b) Shear wall bending mode deformation
(c) Interconnected Frame and shear wall (Equal deflection at each 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 axis Shear wall Coupling 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 (a)
Equivalent diagonal strut (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) Q τxy = 1.43 Lt Shear stress, 0.8h − 0.2)Q σy = L Lt
(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,
σd =
0.58 Q Lt
(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 storyheight 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 π column bearing α is estimated by, α = (2.5a) 2λ λ =4
Emt 4EIh
(2.5b)
Where, Em is the elastic modulus of the masonry and EI is the flexural rigidity of the column. The parameter λ expresses the bearing stiffness of the infill relative to the flexural rigidity of the column. The stiffer the column, the smaller the value of λ 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 λ is at the masonry ultimate compressive stress f’m, then the corresponding ultimate horizontal shear Q’c on the infill is given by,
Q ' c = f ' m t.
π 2
.4
4 EIh Emt
(2.6a)
If the allowable horizontal shear is Qc on the infill, and consider a value for E/E m is 3 for reinforced concrete frame. The allowable horizontal shear Qc for a reinforced concrete framed infill is, Qc = 2.9 fm 4 lhr
(2.6b)
3
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, Fy = 0.025
f 'm
< 0.40 N/ mm2
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Allowable compressive stress, axial,
h' 3 f ' m 1 − 42 t Fa = 5
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,
Fbs = 0.025
Modulus of Elasticity
Em =750 f’m ≤ 15,000 N / mm2
Shear Modulus
G = 0.4 Em
f 'm
N / mm2 ( 0.3 f ' mpsi )
UBC (1997), Allowable bond shear stress, Allowable compressive stress, Allowable tensile stress
Fbs = 0.025
fm =
f ' mN
m / mm2 ( 0.3 f 'psi )
f ' m N / mm2 3
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 = 2000
f 'm
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 Compressive strength
Fv = 0.3 N / mm2 2 Fb = f b N / mm
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. 2.3.1.1
Fig. 2.8 Schematic representation of mean wind and gust velocity 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 quasistatic 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
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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.
21
ii. Analytical Method Wind 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.
22
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
23
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
24
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 M = V =
W g
Wa = WC g
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
(2.10) (2.11) (2.12)
25
C=
a g
(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 ZICW R
(2.14)
1.25 S 2/3 T
(2.15)
V =
C=
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
26
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)
n
V = Ft + ∑Fi i =1
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. Fx =
(V − Vt )Wxhx
(2.20)
n
∑W h i
i
i =1
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 Ft
Ft+Fn Fn
hn
Level x hx
D
v
Structure Lateral Load Story shear Fig. 2.9 Typical distribution of Code specified static forces and story shears in a building with uniform mass distribution
27
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 T = Cthn3/4
UBC (1994)
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 T = 0.1 N ( lateral force resisting system consists of a moment resisting space frame )
NBCC (1995)
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 T = 0.1 n ( moment resisting frames without bracing or shear walls for resisting the lateral loads)
IS (1984)
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 T = h ( 0.02 + 0.01α )
BSLJ (1987)
T = the fundamental natural period of the building in seconds h = the height of the building in meters α = the ratio of the total height of stories of steel construction to the height of the building T = Ct hn3/4
BNBC (1993)
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
28
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):
29
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 M1 N
Wall 1
Fig. 2.10
q
n
q M2 N
Wall 2
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 q=
dN dz
(2.21) (2.22)
30
Axial Force in Wall,
wH 2 1 z 2 1 N = 2 (1 − ) + H (kα H ) 2 k l 2
coshkα z + kα H sinhkα ( H − z ) 1 − coshkα H
(2.23)
Shear in Connecting Members, q=
wH z l sinh kαz − kαz cosh kα ( H − z ) 1− + 2 cos kαH k l H kαH
(2.24)
Wall Moments, I1 1 z 2 M 1 = w H (1 − ) 2 − Nl I 2 H M2 =
(2.25)
I 2 1 z wH 2 (1 − ) 2 − Nl I 2 H
(2.26)
Deflection, 4 4 wH 1 z z Y = 1 − + 4 − 1 EI 24 H H
−
}+
1 k2
1 2( kαH ) 2
4 2 z z 2 1 z z − ( ) − 1 − + 4 − 1 H H 24 H H
1 [1 + kαH sinh kαH − cosh kαz − kαH sinh kα ( H − z 4 ( kαH ) cosh kαH
) ]} ]
Significance of Structural Parameter kα H, AI k 2 =1+ A1 A2 l 2
α2 = Ic =
12 I c l 2 b 3 hI
(2.27)
(2.28) (2.29)
Ib
{1 + 2.4( d / b) (1 + υ )} 3
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
(2.30)
31
l = distance between centroids of walls 1 and 2 ν = Poisson’s ratio (0.15) for concrete d = total depth of coupling beam 12 I l 2 kαH = 3 c b hI
1/ 2
AI 2 1 + H A1 A2
(2.31)
For a given set of walls, with fixed dimensions, the value of kα H 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 (kα H=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 (kα H = ∝), 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 kα H is thus define the degree of composite action and indicates the mode of resistance to applied moments. If kα H 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
32
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
33
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
34
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.
35
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. 3
l Ic = Ib b
(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, 3
I I l I 'c = c = Ib 1 + r 1 + r b
(2.33)
36
12 EI b λ GAb 2 A = cross sectional are of beam r=
(2.34)
G = modulus of shear rigidity of beam GA = shear rigidity λ = 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
37
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 Analysis It 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.
38
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
39
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 wallframe 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
40
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
41
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 Environment A 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.
42
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. σx
σy
Fy
τ xy
τ yx
τ yx
Fxy
τ xy
σy
σx
Fx
(a) Fig. 2.13 d.
(a) Plane stress distribution,
(b) (b) Sign convention of element forces
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
43
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.
44
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 inplane 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
45
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.
46
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, L B
i.
Cp vs.
ii.
z vs. Cz
(Fig. 3.2)
iii.
z vs. Gh , Gz
(Fig. 3.3)
iv.
z vs.
Pz Gh C p C I
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
Table 3.1
Overall pressure coefficient, Cp
(Fig.
3.1)
(Fig. 3.4, 3.5 & 3.6)
47
L/B
Cp h/B=10 1.55 1.85 2 1.7 1.3 1.15
h/B ≤ 0.5 1.4 1.45 1.55 1.4 1.15 1.1
0.1 0.5 0.65 1 2 ≥ 3
h/B=20 1.8 2.25 2.55 2 1.4 1.2
h = building height in meter B = building width normal to wind in meter L = building length parallel to wind in meter h/B=.5 h/B=10 h/B=20 h/B=40 3 2.8 2.6
Overall presure coefficient , Cp
2.4 2.2 2 1.8 1.6 1.4 1.2 1 0
0.4
0.8
1.2
1.6
2
2.4
2.8
L/B
h/B ≥ 40
h/B = 20
h/B = 10 h/B ≤ 0.5
3.2
H/B ≥ 40 1.95 2.5 2.8 2.2 1.6 1.25
48
Fig. 3.1 Evaluation of overall pressure coefficient , Cp
Table 3.2
Combined height and exposure coefficient, Cz
Height above ground level, z (meter) 0
Exposure A 0.368
Exposure B 0.801
Exposure C 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
Cz
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 Exposure A Exposure B Exposure C
96 90 84 78
z =Height above ground level in m
72 66 60
A
B
C
54 48 42 36 30 24 18 12 6 0 0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
Combined height and exposure coefficient, Cz
2.7
3
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, z (meter) 0
Gh and Gz Exposure A 1.654
Exposure B 1.321
Exposure C 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
Exposure A Exposure B Exposure C 90 84 78
A
z =Height above ground level in meter
72
B
C
66 60 54 48 42 36 30 24 18 12 6 0 0.6
0.8
1
1.2
1.4
1.6
Gh and Gz
1.8
2
2.2
2.4
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, Pz 2 = C c C zVb Gh C p C I
(3.2)
Pz For different exposure conditions and places the value of G C C is calculated in Table 3.4 h p I to 3.6 and then represented in Fig. 3.4 to 3.6 Pz From the figure value of G C C at different height z for different exposure conditions and h p I places the value of design pressure, Pz is calculated easily by multiplying the figure value to G h Cp CI For example, Z = 30 m Zone =Dhaka Exposure =B Then value of
Pz Gh C p C I
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) CI = importance coefficient for specified building (Table C.2)
53
Table 3.4
Design pressure component,
Height above ground level,
Pz Gh C p C I
for Dhaka Pz Gh C p C I
= C c C z Vb
2
Kpa
z (meter) 0
Exposure :A 0.766
Exposure: B 1.668
Exposure: C 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
90
2.879
3.906
4.52
54
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
Exposure :A Exposure: B Exposure: C
90 84 78 72
z = Height in m from ground level
66
A
B
C
60 54 48 42 36 30 24 18 12 6 0 0
0.5
1
1.5
2
2.5
3
3.5
Pz/Gh CpCI in kPa
4
4.5
5
5.5
6
55
Fig. 3.4 Value of
Pz for different exposure conditions for Dhaka Gh C p C I
Pz
Table 3.5
Design pressure component, Pz
Height above ground level, z (meter)
Gh C p C I
for Chittagong
GhC p C I
= C c C z Vb
2
KPa
0
Exposure :A 1.174
Exposure: B 2.556
Exposure: C 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
70
3.947
5.571
6.589
80
4.19
5.788
6.765
56
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
Exposure :A 7.671 Exposure: B Exposure: C
90 84
A
B
C
78
z = Height in m from ground level
72 66 60 54 Pz
48 3.5 Value of Fig. GhC p C I
42 Table 3.6
for different exposure conditions for Chittagong Pz
Design pressure component, Pz
Height 36 above ground level,
30 z (meter) 0
Gh C p C I
for Khulna
Gh C p C I
= C c C z Vb
2
kPa
Exposure :A 0.984
Exposure: B 2.142
Exposure: C 3.198
0.984
2.142
3.198
618
1.11
2.316
3.377
9
1.329
2.599
3.663
12
1.511
2.821
3.88
15 6
1.669
3.008
4.056
18 0
1.81
3.169
4.206
24
4.5
12
1
1.4 1.8 2.2 2.6
3
3.4 3.8 4.2 4.6
Pz/Gh CpCI in kPa
5
5.4 5.8 6.2 6.6
7
57
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
60
3.088
4.468
Exposure :A 5.161 Exposure: B 5.353 Exposure: C
7090
3.308
4.669
5.522
8084
3.511
4.851
5.669
90
3.698
5.016
5.805
100
3.877
5.172
5.928
11072
4.046
5.313
6.043
12066
4.204
5.447
6.148
130
4.356
5.573
6.249
140
4.503
5.693
6.34
4.642
5.805
6.428
z = Height in m from ground level
78
60 54
150
48 42 36 A
30
B
C
24 18 12 6 0 0
0.5
1
1.5
2
2.5
3
3.5
Pz/Gh CpCI in kPa
4
4.5
5
5.5
6
58
Fig. 3.6 Value of 3.3
Pz GhC p C I
for different exposure conditions for Khulna
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, C
i.
hn vs.
&T
(Fig. 3.7 )
ii.
V hn vs. ZISW
(Fig. 3.8 )
iii.
hn vs. W
iv.
hx vs. V − F t
S
V
Fx
(Fig. 3.9 ) %
(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 = 1.25 S (3.4) T 2/3 From above equations it can be written for reinforced concrete moment resisting frames and eccentrically braced steel frames as, C S
=
7.156 1/ 2 h n
(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 ratio of numerical coefficient, C and site coefficient, S from building height for moment resisting frame (RC) Building height above base, hn (meter)
C S
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
90 110
0.68
2.48
120
0.65
2.647
81 130
0.63
2.81
140
0.6
2.971
150
0.58
3.129
72
hn= Building height in meter
63
54
45 C S
36
T
27
18
9
0 0
0.2
0.4 0.6
0.8
1
1.2 1.4
1.6 1.8
C/S and T value in second
2
2.2
2.4 2.6
2.8
3
61
Fig. 3.7 Variation of C ratio and fundamental time period, T with building height for S
MRF
b. Graphical Presentation of Base Shear Design Base Shear, C = S
7.156 hn
V =
ZICW R
(derived earlier)
1/ 2
(3.7) (3.8)
Putting the value of C for MRF in above equation, it is written as, S
V ZIWS
=
(3.9)
7.156 hn
1/ 2
R
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 Therefore, V ZIWS
= 0.243
(C.6)
62
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
V
=
7.156
above base, hn (meter) 1
R=5
R=6
hn R=7
1.100
0.917
3
0.826
6
ZIWS
1/ 2
R
R=8
R=9
R=10
0.786
0.688
0.611
0.550
0.688
0.590
0.516
0.459
0.413
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
27
0.276
0.230
0.197
0.173
0.153
0.138
63
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
R=5 0.068
84 120
0.130
0.108
0.093
0.081
0.072
0.065 R=7
130
0.126
0.105
0.090
0.079
0.070
R=8 0.063
140
0.120
0.100
0.086
0.075
0.067
0.060 R=10
0.116
0.097
0.083
0.073
0.064
0.058
90
78 72
150
R=6
R=9
hn = Building height in meter
66 60 54 48 42 36 30 24 18 12 6 0 0.00
0.10
0.20
0.30
0.40
0.50
0.60
V / (ZISW)
0.70
0.80
0.90
1.00
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 V
ZIWS
=
7.156 hn
1/ 2
R
(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, 1.61 V = 1/ 2 W hn R
(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, Building height = 24 m
65
Zone = Dhaka R value = 6 Therefore, V W
= 0.055
(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
V
=
1.61
R=7
R=9
R=10
0.268
0.192
0.120
0.067
0.033
0.186 0.131 0.107
0.155 0.109 0.089
0.111 0.078 0.064
0.069 0.049 0.040
0.038 0.027 0.022
0.019 0.014 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
27
0.062
0.052
0.037
0.023
0.013
0.006
above base, hn (meter) 1
R=5
R=6
0.322
3 6 9
hn
1/ 2
R R=8
W
66
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
0.038
0.032
0.023
0.014
0.008
0.004
0.036
0.030
0.021
0.013
0.007
0.004
R=5
0.034
0.028
0.020
0.013
0.007
0.004
R=7
0.032
0.027
0.019
0.012
0.007
0.003
R=8
0.031
0.026
0.018
0.012
0.006
0.003
R=10
0.029
0.024
0.017
0.011
0.006
0.003
0.028
0.023
0.017
0.010
0.006
0.003
0.027
0.023
0.016
0.010
0.006
0.003
0.026
0.022
0.015
0.010
0.005
0.003
70
90
80 84
90 100
78
110 72
120 130
66
140 60
hn = Building height in meter
150
R=6
R=9
54
48
42
36
30
24
18
12
6
0 0.00
0.02
0.04
0.06
V/W
0.08
0.10
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 Forces In 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, n
V = Ft + ∑ Fi Where,
(3.12)
i =1
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)
when T ≤ 0.70 second
Ft = 0.0
The remaining portion of the base shear (V-Ft), is distributed over the height of the building including level n, according to relation, wh Fx = (V − F ) t n x x ∑ wi hi i =1
(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 h Fx = (V − F ) t n x ∑ hi
(3.15)
i =1
Fx h = nx V − Ft ∑ hi
(3.16)
i =1
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 % = 5.88 V − Ft 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 15-storeied 16-storeied (meter) 3 0.830 0.740
Fx % V − Ft
17-storeied
18-storeied
19-storeied
20-storeied
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
12.500
11.030
9.800
8.770
7.890
7.140
11.760
10.460
9.360
8.420
7.620
11.110
9.940
8.950
17-storeied 8.090
10.530
9.470
8.570
10.000
9.050 20-storeied
45 48 51 54 57 60
60 57 54 51 48
15-storeied 16-storeied 18-storeied 19-storeied
9.520
45 42
hx = Floor height in m
39 36 33 30 27 24 21 18 15 12 9
20 19 18
17
16
15
6 3 0 0.00
1.60
3.20
4.80
6.40
8.00
Fx / (V -Ft)%
9.60
11.20
12.80
14.40
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.
L
(Fig. 3.1)
ii.
Cp vs. B z vs.Cz
iii.
z vs. Gh and Gz
(Fig. 3.3)
iv.
Pz z vs. Gh C p C I
(Fig. 3.2) (Fig. 3.4 to 3.6)
Earthquake load, i.
hn vs.
C &T S
(Fig. 3.7)
71
ii.
hn vs.
V ZISW
(Fig. 3.8)
iii.
hn vs.
V W
(Fig. 3.9)
iv.
Fx hx vs. V − F % x
(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
84
30
39.88
21.99
17.00
30.34
14.90
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
Rigid Frame [Beam size: 300 x 450, column size: 300 x 600, wall size: 300 x 3650 mm] Infilled Frame Coupled Wall/AB Coupled Wall Wide column 48 45 42 39 36 33
H= height in m
30 27 24 21 18
EWC CWAB IF
15
CW
12
RF
9 6
Beam size: 300x 450 mm Column size: 300 x 600 mm Wall size: 300 x 3650 mm
3 0 0
10
20
30
40
50
Deflection in mm
60
70
80
90
85
Auxiliary beam: 300x450 mm Floor level height: 3000 mm Load 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]
Rigid Frame Infilled Frame Coupled Wall/AB Coupled Wall Wide column 48 45 42 39 36 33
H= height in m
30 27
EWC CWAB IF
24
RF CW
21 18
Beam size: 300 x 600 mm Column size: 300 x 600 mm Wall size: 300 x3650 mm Auxiliary beam: 300x600 mm Floor level height: 3000 mm Load at top: 100 kN
15 12 9 6 3 0 0
4
8
12
16 20 24
28 32
36 40
Deflection in mm
44 48 52
56 60
64 68
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]
Rigid Frame Infilled Frame Coupled Wall/AB Coupled Wall Wide column
48 45 42 39 36 33 H = height in m
30 27 24 EWC CWAB
21
IF
18
RF CW
15 12
Beam size: 300 x 750 mm Column size: 300 x 600 mm Wall size: 300 x 3650 mm Auxiliary beam: 300x750 mm Floor level height: 3000 mm Load at top: 100 kN
9 6 3 0 0
4
8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 Deflection in mm
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
Rigid Frame
[Beam: 300 x 900 mm, column size: 300 x 600 mm, wall size: 300 x 3650 mm]
Infilled Frame Coupled W all/AB Coupled W all W ide column
48 45 42 39 36 33
H= height in m
30 27 24 21 18 EWC CWAB
15
IF
12
RF WC
9 6 3 0 0
4
8
12
16
20
24
28
32
36
40
Deflection in mm
44
48
52
56
60
64
68
91
Beam size: 300 x 900 mm Column size: 300 x 600 mm Wall size: 300 x 3650 mm Auxiliary beam: 300x900 mm Floor level height: 3000 mm Load 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] Height, m
Rigid Frame
Infilled Frame
Coupled WallAB
Coupled Wall
Wide Col um n
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
Rigid Frame Infilled Frame Coupled Wall/AB Coupled Wall Wide column 48 45 42 39
EWC CWAB
36
IF
33
RF CW
H= height in m
30 27 24 21
Beam size: 300 x 600 mm Column size: 300 x 450 mm Wall size: 300 x 3650 mm Auxiliary beam: 300x600 mm Floor level height: 3000 mm Load at top: 100 kN
18 15 12 9 6 3 0 0
4
8
12
16 20 24
28 32
36 40
Deflection in mm
44 48 52
56 60
64 68
94
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
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]
95
Rigid Frame Infilled Frame Coupled Wall/AB Coupled Wall Wide column 48 45
EWC CWAB IF
42
RF CW
39 36 33
H= height in m
30 27 24 21 18
Beam size: 300 x 600 mm Column size: 300 x 750 mm Wall size: 300 x 3650 mm Auxiliary beam: 300x600 mm Floor level height: 3000 mm Load at top: 100 kN
15 12 9 6 3 0 0
4
8
12
16 20 24
28 32
36 40
44 48 52
56 60
64 68
Deflection in mm
Fig. 5.6 Deflected shape of different structural systems due to concentrated load at top
96
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
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]
97
Rigid Frame Infilled Frame Coupled Wall/AB Coupled Wall Wide column 48 45
EWC CWAB IF
42
RF CW
39 36 33
H= height in m
30
Beam size: 300 x 600 mm Column size: 300 x 900 mm Wall size: 300 x 3650 mm Auxiliary beam: 300x600 mm Floor level height: 3000 mm Load at top: 100 kN
27 24 21 18 15 12 9 6 3 0 0
4
8
12
16 20 24
28 32
36 40
Deflection in mm
44 48 52
56 60
64 68
98
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 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
99
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 450 300 x 600 300 x 750 300 x 900
1204 1745 2158 2456
2444 3593 4794 5907
2844 4415 6373 8503
1536 1536 1536 1536
3279 5371 8091 11111
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 450 300 x 600 300 x 750 300 x 900
1487 2350 3126 3750
2643 3934 5336 6658
2844 4554 6373 8503
1536 1536 1536 1536
3255 5311 8091 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
300 x 450 300 x 600 300 x 750 300 x 900
1655 2729 3815 4778
Infilled Frame 2756 4134 5718 7273
Coupled WallAB
Coupled Wall
Wide Column
2844 4415 6373 8503
1536 1536 1536 1536
3279 5371 8091 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
300 x 450 300 x 600 300 x 750 300 x 900
1762 2957 4270 5528
Infilled Frame 2811 4228 5949 7716
Coupled Wall AB
Coupled Wall
Wide Column
2844 4415 6373 8503
1536 1536 1536 1536
3279 5371 8091 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
101
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. 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
102
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 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 0 3 6 9 12 15 18 21
Rigid Frame 0.00 3.50 10.29 18.35 27.03 36.02 45.15 54.24
Infilled Frame 0.00 1.43 4.35 8.25 12.88 18.00 23.52 29.29
Wide Column 0.00 0.76 2.69 5.52 9.03 13.04 17.37 21.95
Coupled WallAB 0.00 0.89 2.96 6.02 9.82 14.29 19.13 24.25
Coupled Wall 0.00 1.57 5.66 12.05 20.46 30.63 42.31 55.25
103
24 27
63.18 71.84
35.21 41.17
26.60 31.25
30 80.14 47.09 35.84 33 88.00 52.90 40.21 36 95.35 58.55 44.61 39 102.16 64.00 48.74 42 108.39 69.26 52.70 45 114.04 74.34 56.52 48 119.34 79.31 60.26 [Beam size: 300 x 600 mm, Column size: 300 x 750 mm ]
29.51 34.83
69.25 84.09
40.12 45.83 50.41 55.35 60.14 64.81 69.42
99.60 115.62 131.20 148.61 165.36 182.20 198.98
Table 5.12b Deflections (mm) of different structural systems due to EQ load. Height, m
Rigid Frame
Infilled Frame
Wide Column
Coupled WallAB
Coupled wall
0 3 6 9
0 2.56 7.66 13.87
0 1.07 3.34 6.45
0 0.61 2.20 4.57
0 0.74 2.46 5.04
0 1.36 4.94 10.58
12 15
20.71 27.97
10.20 14.43
7.55 11.00
8.32 12.14
18.08 27.20
18 21
35.48 43.13
19.04 23.95
14.79 18.83
16.39 20.93
37.77 49.57
50.79 58.37 65.77 72.93
29.05 34.27 39.52 44.74
23.00 27.24 31.48 35.67
25.67 30.52 35.52 40.30
62.42 76.14 90.57 105.54
79.75 86.20 92.22 97.77
49.89 54.93 59.84 64.63
39.78 43.76 47.63 51.40
45.13 49.88 54.54 59.10
120.94 136.63 152.50 168.45
48 30 103.00 69.36 55.11 [Beam size: 300 x 600 mm, Column size: 300 x 750 mm] 27
63.62
184.41
Height in m
48 24 27 45 30 42 33 39 36 39 36 42 33 45
RF-W IFR-W WC-W
24
CW/AB-W
21
CW-W
181: EQ load on WC model
6: Wind load on IF model
RF-EQ
2: Wind load on WC model 15 3: EQ load on CW/AB model 12 4: EQ load on IF model 95: Wind load on CW/AB model
7: EQ load on RF model
IFR-EQ
8: Wind load on RF model
WC-EQ
9: EQ load on CW model
CW/AB-EQ
10: Wind load on CW model
CW-EQ
6 3 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Deflection in mm
104
1 2
7
8
3 4
9
10
5 6
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 sizes
for variable beam
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
105
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
33
142.20
84.45
58.83
45.56 Beam,300x750
36
153.98
91.50
63.64
Beam,300x900 49.30
98.02
68.17
52.76
103.98
72.27
55.92
48
39
164.84
45
42
174.73
Beam,300x450
41.55
Beam,300x600
45
42
183.69
109.40
75.98
58.78
48
39192.05
114.47
79.47
61.43
[Beam size: 300 x36450 mm, 300 x 600, 300 x 750 mm, 300 x 900 mm, Column size: 300 x 900 mm]
Floor Height in meter
33 30 27 24 21 18 15 12 9
1
6 3
2 3
0 0
20
40
60
80
100
120
Deflection in mm
140
160
180
200
106
4
4
3
2
1
Column 300x900 mm
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
107
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
108
Col,300x450 Col,300x600 Col,300x750 Col,300x900 48 45 42 [Column size: 300 x 450 mm, 300 x 600, 300 x 750 mm, 300 x 900 mm, Beam size: 300 x 600 mm] 39 36
Floor Height in meter
33 30 27 24 21 18
1 2
15
3 4
12 9 6 3 0 0
20
40
60
804
3100
2 120
Deflection in mm
140
1 160
180
200
109
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
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
110
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
48
96.24
60.26
40.81
B eam , 3 0 0 x 4 5 0
28.53
B eam , 3 0 0 x 6 0 0
30.06
B eam , 3 0 0 x 7 5 0
[Beam size: 300 x 450 mm, 300 x 600, 300 x 750 mm, 300 x 900 mm, Wall size: 300x3650 B eam , 3 0 0mm] x900 48
45
42
39
36
33
2 30
3
ert e 2 7m ni t h ige H 2 4ro lo F
1
21
18
4
15
3
2
1
12
9
6
3
0 0
10
20
30
40
50
D ef lect io n in m m
60
70
80
90
100
111
Wall 300x3650 mm
Fig. 5.11 Deflections of Wide Column model due to wind load
5.5 Moment in Beams of Different Structural System for Lateral Load Wind 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
112
(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 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
113
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 3 6 9 12
Rigid Frame 283 338 340 358
Infilled Frame 179 226 260 292
Wide Column 143 197 238 268
15 368 304 288 18 371 318 300 21 369 325 306 24 363 327 307 27 354 326 303 30 341 321 296 33 327 314 287 36 311 306 277 39 294 297 266 42 277 289 256 45 262 282 248 48 239 265 243 [Connecting beam size : 300x600 mm, Column size: 300 x750mm]
Coupled WallAB 133 181 218 244
Coupled Wall 73 69 64 58
263 276 283 286 285 281 275 268 260 251 239 165
53 48 43 38 34 29 25 21 18 14 12 7
114
Table 5.17 Bending moment (kN-m) in beams for different structural systems due to EQ load.
Infilled
Rigid Frame
Height, m
Wide Column
Coupled WallAB
Coupled Wall
Fra me 3 6 9 12
214 262 290 309
162 203 233 264
131 176 211 239
122 163 195 218
68.67 62.46 56.46 51.42
15 18 21 24 27
321 329 332 331 327
276 290 300 305 307
258 272 280 284 284
237 251 260 265 267
46.59 42.23 38.26 34.58 31.11
30 33 36 39 42 45 48
321 312 301 288 275 263 238
306 303 298 292 285 280 264
281 275 269 261 254 247 243
266 264 260 254 248 237 164
27.80 24.60 21.50 18.53 15.75 13.36 RF-W 8.86 IFR-W
48
45 [Connecting beam size: 300x600 mm, Column size: 300x750 mm] 42
WC-W CW/AB-W
39
CW-W
36
RF-EQ
33
IFR-EQ WC-EQ
Height in meter
1: EQ load30on CW model
CW/AB-EQ
2: Wind load 27 on CW model
Beam size: variable
3: EQ load on CW/AB model 24 4: EQ load on WC model 21 on CW/AB model 5: Wind load
Column size: 300x750mm
6: EQ load18on IF model
Floor level height: 3000 mm
7: Wind load 15 on WC model
Wind load: BNBC
CW-EQ
Wall size: 300x 3650 mm Auxiliary beam: variable
8: Wind load on IF model 12 9: EQ load on RF model 9 10:Wind load on RF model 6 3 0 0
50
100
150
200
250
300
Bending moment in kN-m in beam
350
400
115
1 2
3
456 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 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
116
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]
48 Beam,300x450
45
Beam,300x600 Beam,300x750
42
Beam,300x900 39 36
Floor Height in meter
33 30 27 24
1 2
21
3 18
4
15 12 9 6 3 0 0
50
100
150
200
250
300
Moment in kN-m
350
400
450
500
117
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
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
118
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]
48 Col,300x450
45
Col,300x600 Col,300x750
42
Col,300x900 39 36
Floor Height in meter
33 30 27
1 1
24
2 3 4
2 3
21
4
18 15 12 9 6 3 0 150
200
250
300
Moment in kN-m
350
400
119
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. 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
120
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]
Beam,300x450
48
Beam,300x600
45
Beam,300x750 Beam,300x900
42 39 36 33 re 30 te m n i 27 th g ie 24 H r o o l 21 F
1 2 3 4
1
18
2
15
3
12
4 9 6 3 0 0
50
100
150
200 Moment250 in kN-m 300
350
400
450
121
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 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 + µ σ (5.1)
c
122
together with a maximum limiting value (0.40 N/mm2, BNBC). Where, fbs = bond shear stress = 0.025 √f’m N/mm2 σ
c
(5.2)
= compressive force
This relationship holds good up to value of σ c = 2 N/mm2 (2000 kN/ m2) µ = 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 load Floor Level
Fx, kN/sq.m, parallel to bed joint
Fy, kN/sq.m, normal to bed joint
300x600 mm 300x750 mm 300x900 mm
300x600
mm
300x750 mm
300x90 mm 0
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
123
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. 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.
124
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.
Chapter 6 CONCLUSION & SUGGESTION
6.1 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.
125
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. ♦ 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.
126
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. 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.
127
♦ 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 FrameWall Structures,” ACI Pub. SP 86-10, Detroit. 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.
128
Coull, A. and Chowdhury (1967), “Analysis of Coupled Shear-Walls,” ACI Journal, Proceedings, Vol.64. Fintel, M. (1974), Distributors, India.
“Handbook of Concrete Engineering,” 2nd. Edition, CBS Publishers &
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, 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 Masonry Buildings,” John Wiley and Sons, Inc, New York,
129
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.
130
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 = 5.25 kN / m2
Total
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
Load per sq.m
= 300.19 kN = 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
131
DL per m
= 431.55 / 13.7
= 31.50 kN
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,
H / B = 48 / 30 = 1.60,
L = 13.70 m
L/B= 13.70 / 30 = 0.46
Hence, Cp (Fig. 3.1) = 1.45 Design wind pressure, Pz Pz values for different height are calculated from Fig. 3.4 and presented in Gh C p C I
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
Pz ( From Graph 2.4 ) Gh C p C I
Pz in kN/m2
Pz in kN at floor node
132
meter 3
0.76
1.35
24.71
6
0.85
1.51
27.63
9
1.05
1.86
34.04
12
1.20
2.13
38.98
15
1.25
2.22
40.63
18
1.40
2.49
45.57
21
1.50
2.66
48.68
24
1.60
2.84
51.97
27
1.65
2.93
53.62
30
1.80
3.20
58.56
33
1.85
3.29
60.21
36
1.94
3.45
63.14
39
2.00
3.55
64.97
42
2.05
3.64
66.61
45
2.15
3.82
69.91
48
2.20
3.91
A.4
71.55 Total = 820.18 kN
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
=6m
Bay length
= 13.7 m
Floor area under bay consideration
= 82.20 sq.m
133
Total DL per floor area
= 8.90 kN /m2
= 3.65 + 5.25
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
Total load, W under bay consideration
=Total DL + 25% Gravity LL
= 3748.32 kN
= 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
Fx =
Fx =
(V − Fx ) hx
n
∑w h i =1
n
∑h i =1
(V − Fx ) wx hx i
i
(A.2.2)
i
Loads, Fx are presented in Table A.2 Table A.2 Earthquake load in kN at every floor level hx in m
(A.2.1)
Fx / ( V-Ft)
%
Fx in kN
134
3
0.65
4.04
6
1.52
8.05
9
2.2
12.12
12
3.0
16.16
15
3.60
20.21
18
4.40
24.25
21
5.20
28.29
24
6.00
32.30
27
6.80
36.37
30
7.40
40.41
33
8.20
44.45
36
8.90
48.49
39
9.70
52.53
42
10.40
56.56
45
11.20
60.62
48
11.70
64.66 V - Ft
= 549.57 kN
135
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 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 Files For 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 156;267;378 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
136
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 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 156;267;378 REPEAT ALL 15 3 4
137
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 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
138
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 UNIT KNS MMS JOINT COORDINATE 1 0 0 ; 2 2744 0 ; 3 10060 0 ; 4 12805 0 REPEAT ALL 16 0 3050 MEM INCI 156;267;378 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
139
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 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
140
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 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
141
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 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 156;267;378 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
142
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 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
143
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 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
144
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 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
145
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 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
146
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 : 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
147
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 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
148
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 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
149
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 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
150
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 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
151
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 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
152
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
153
Appendix C TABLES (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 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 Angarpota Bagherhat Bandarban Barguna Barisal Bhola Bogra Brahmanbaria Chandpur Chapai Nawabgonj Chittagong Chuadanga Comilla Cox’s Bazar Dahagram Dhaka Dinajpur Faridpur Feni Gaibanda Gazipur Gopalgonj Habigonj Hatiya Ishurdi Joypurhat Jamalpur Jessore Jhalakati Jhenaidah Khagracharri Khulna Kutubdia Kishoregonj Kurigram Kushtia Lakshmipur
Basic Wind Speed km/h 150 252 200 260 256 225 198 180 160 130 260 198 196 260 150 210 130 202 205 210 215 242 172 260 225 180 180 205 260 208 180 238 260 207 210 215 162
Location Lalmonirhat Madaripur Magura Manikgonj Meherpur Moheshkhali Moulibazar Munshigonj Mymensingh Naogaon Narail Narayangonj Narsinghdi Natore Netrokona Nilphamari Noakhali Pabna Panchagarh Patuakhali Pirojpur Rajbari Rajshahi Rangamati Rangpur Satkhira Shariatpur Sherpur Sirajganj Srimangal St.Martin’s island Sunamgonj Sylhet Sandwip Tangail Teknaf Thakurgaon
Basic Wind Speed km/h 204 220 208 185 185 260 168 184 217 175 222 195 190 198 210 140 184 202 130 260 260 188 155 180 209 183 198 200 160 160 260 195 195 260 160 260 130
154
Table C.2
Structural importance coefficient, CI for wind load
Structural Importance Category I Essential facilities
Structural Importance Coefficient ,CI 1.25
II Hazards facilities
1.25
III Special occupancy structures
1.00
IV Standard occupancy structures
1.00
V Low risk structures
0.80
Table C.3
Structural importance coefficient, I for earthquake
Structural Importance Category I Essential facilities II Hazard Facilities III Special Occupancy Structures IV Standard Occupancy Structures V Low Risk Structures
Table C.4
Structural Importance Coefficient, I 1.25 1.25 1 1 1
Seismic zone coefficient, Z Zone Coefficient
Selected Seismic Zone 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 Type
Site coefficient, S for seismic lateral forces Site Soil Characteristics
Coefficient, S
155
S1
A soil profile either : a) a rock like material characterized by a shear wave velocity greater than 762 m/s or by other suitable means of classification, or
1
b) Stiff or dense soil condition where the soil depth is S2
less than 61 m A soil profile with dense or stiff soil conditions, where
S3
the soil depth exceeds 61 m A soil profile 21 m or more in depth and containing more than 6 m of soft to medium stiff clay but not more
S4
than 12 m of soft clay A soil profile containing more than 12 m of soft clay characterized by a shear wave velocity less than 152 m/s
Table C.6 a.
1.2
1.5
2
Response modification coefficient for structural systems, R (BNBC, 1993)
Basic Structural System Bearing Wall System
Description of Lateral Force Resisting System 1.
2.
R
Light framed walls with shear panels i)
Plywood walls for structures, 3 story or less
8
ii)
All others light framed walls
6
Shear walls
156
b.
Building Frame System
Concrete
6
ii)
Masonry
6
3.
Light steel framed bearing walls with tension only bracing
4.
Braced frames where bracing carries gravity loads Steel
6
ii)
Concrete
4
1. 2.
Light framed walls with shear panels
4.
1.
system
Dual System
Plywood walls for structures 3 stories or less
9
ii)
All others light framed walls
7
Shear walls i)
Concrete
8
ii)
Masonry
8
Concentric braced frames (CBF) i)
Steel
8
ii)
Concrete
8
iii) Heavy timber Special moment resisting frame (SMRF)
8
i)
Steel
12
ii)
Concrete
12
2.
Intermediate moment resisting frame (IMRF), concrete
3.
Ordinary moment resisting frame (OMRF)
1.
2.
3.
4 10
i)
i)
d.
4
i)
iii) Heavy timber Steel eccentric braced frame (EBF)
3.
c. Moment Resisting Frame
i)
Steel
8 6
ii) Concrete Shear walls
5
i)
Concrete with steel or concrete SMRF
12
ii)
Concrete with steel OMRF
6
iii)
Concrete with concrete IMRF
9
iv)
Masonry with steel or concrete SMRF
8
v)
Masonry with steel OMRF
6
vi)
Masonry with concrete IMRF
7
i)
With steel SMRF
12
ii)
With Steel OMRF
6
Steel EBF
Concentric braced frame (CBF) i)
Steel with steel SMRF
10
ii)
Steel with steel OMRF
6
iii)
Concrete with concrete SMRF
9
iv)
Concrete with concrete IMRF
6
ACKNOWLEDGEMENT
157
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
158
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
159
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 (BNBC1993). 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 coefficien t, structural
160
flexibility coefficien t, numerical coefficien t 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
M1
bending moment in wall W1
161
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
ν
poison ratio of concrete
γ
unit weight of concrete
σ’
crushing strength of mortar
σ
d
diagonal tensile stress of brick masonry
σ
y
vertical compressive stress of brick masonry
σ
x
principal stress
γ
m
unit weight of brick masonry
ν
m
poison ratio of brick masonry
λ
cross sectional shape factor for shear, equal to 1.2 for rectangular section.
τ
xy
shear stress
ABBREVIATIONS AB
Auxiliary Beam
ACI
American Concrete Institute
ANSI
American National Standard Institute
162
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
163
Page ACKNOWLEDGEMENT
i
DECLARATION ABSTRACT
Chapter 1
Chapter 2
ii iii
SYMBOLS & NOTATIONS
iv
ABBREVIATIONS
vi
INTRODUCTION 1.1
General
1
1.2
Objectives of the Study
1
1.3
Scope of the Study
2
1.4
Methodology
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
7
Shear Wall
2.2.2.1 Behaviour of Shear Wall Structure under Lateral Load
8
2.2.3
9
Shear Wall-Frame
2.2.3.1 Behaviour of Shear Wall-Frame under Lateral Load
9
2.2.4
11
Coupled Shear Wall
2.2.4.1 Behaviour of Coupled Shear Wall Structure under Lateral Load 2.2.5
11
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
164
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
Chapter 3
Chapter 4
2.8
STAAD-III
41
2.9
Summary
42
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
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
165
4.5 Chapter 5
Summary
81
RESULTS AND DISCUSSIONS 5.1
Introduction
82
5.2
Deflections of Different Structural System for Concentrated Load at Top
83
Relative Stiffness of Model Frames for Concentrated Load at Top
98
5.3 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
123
General 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.3 129
Wind Load
166
A.4
Appendix B
Earthquake Load
130
STAAD SCRIPT FILES B.1
Introduction
133
B.2
Input Files
133 Appendix C
TABLES (BNBC, 1993) C.1
Introduction and Tables
151
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
167
In partial fulfillment of the requirement for the degree of HOUNERS OF ENGINEERING IN CIVIL ENGINEERING (Structural)
AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY Dhaka 1000. and October, 2011
Department of Civil Engineering
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.
168
Dr. Md. Mahmudur RAhman Professor Department of Civil Engineering AUST, Dhaka-1000
(Supervisor)
