Multistorey Building

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Multistorey Building

• Introduction

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Multistorey Building
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Multistorey Building

• Reinforced concrete buildings consist of floor
  slabs, beams, girders and columns continuously
  placed to form a rigid monolithic system as shown
  in Fig. 19.1. Such a continuous system leads to
  greater redundancy, reduced moments and
  distributes the load more evenly. The floor slab
  may rest on a system of interconnected beams.
  Interior beams B4, B5, B6 are supported on the
  girders, whereas, the exterior beams BI, B2, B3
  are directly supported by the columns. Girders
  such as GI, G2, G3 are also supported directly by
  the columns. Beams BI, B2, B3 and girders GI, G2
  and 03 are not only continuous but are also
  monolithic with upper and lower columns.

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Multistorey Building

• Thus, a building frame is a three-dimensional
  structure or a space structure. It is idealized
  as a system of interconnected two-dimensional
  vertical frames along the two mutually
  perpendicular horizontal axes for analysis. These
  frames are analyzed independently of each other.
  In frames where the columns are arranged on a
  rectangular grid, loading patterns giving biaxial
  bending need not be considered except for corner
  columns.

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Multistorey Building

• The degree of sophistication to which a
  structural analysis is carried out depends on the
  importance of the structure. A wide range of
  approaches have been used for buildings of
  varying heights and importance, from simple.
  approximate methods which can be carried out
  manually, or with the aid of a pocket calculator,
  to more refined techniques involving computer
  solutions. Till a few years ago most of the
  Multistorey buildings were analyzed by
  approximate methods such as substitute frame,
  moment distribution, portal and cantilever
  methods.

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Multistorey Building

• The recent advent of personal computers (PC's)
  and the abundance of ready-made computer package
  programs has reduced the use of approximate
  methods which at present are useful for
  preliminary analysis and verification. The
  application of computers is not restricted merely
  to analysis they are used in almost every phase
  of concrete work from analysis to design, to
  plotting, to detailing, to specification writing,
  to cost estimating etc.

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Sections of multistory Building
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Structural Analysis

• A building is subjected to various load such as
  dead load, live load, lateral load such as wind
  load or earthquake load.
• A structural systems may be classified as follows
• Load bearing wall systems
• Building with flexural systems
• Moment resisting frame system
• Dual frame system
• Tube systems

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i. Load bearing wall system

• Walls provide support for all gravity load s as
  well as resistance to lateral loads
• There are no columns
• The walls and partition wall supply in-plane
  lateral stiffness and stability to resist end and
  earthquake loading.
• This systems lacks in providing redundancy for
  the vertical and lateral load supports, that is,
  if the walls fail, the vertical loads as well as
  lateral loads carrying capacity is eliminated to
  instability.

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ii. Building with flexural wall system

• The gravity load is carried primarily by a frame
  supported on columns rather than bearing walls.
• Some minor portion of the gravity load can be
  carried on bearing walls but the amount so
  carried should not should not represent more than
  a few of the building area.
• The resistance to lateral loads is provided by
  nominal moment resistance be incorporated in the
  vertical load frame design.

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iii. Moment resisting frame systems

• If the system in which members and joints are
  capable of resisting vertical and lateral loads
  primarily by flexural.
• To qualify for a response reduction factor R5.
  the frame should be detailed conforming to IS
  132901993 to provide ductility excepts in
  seismic zone2.
• In moment resistant frame, relative stiffness of
  girders and columns is very important.
• A frame may be designed using weak column- strong
  girder proportions or strong column-weak girder
  proportions.

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iv. Flexural shear (wall) systems

• It is reinforced concrete wall designed to resist
  lateral forces parallel to the plane of the wall
  and detailed to proved ductility conforming to IS
  13290-1993.
• The international building code of America IBC
  2000 permits the use of flexural shear wall
  systems up to height of about 45m.
• However, it can be used up to height of 70m, if
  and only if flexural walls in any plane do not
  resist more than 33 of the earthquake design
  force including torsional effects.

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v. Dual frame systems

• It is structural system with the following
  features
• Moment resisting frame providing support for
  gravity loads.
• Resistance resisting loads is provided by
• Specially detailed moment resisting frame which
  is capable of resisting at least 25 of the base
  shear including torsion effects
• Flexural walls must resist total required lateral
  force in accordance with relative stiffness
  considering interaction of walls and frames as
  single systems.

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vi. Space frame

• It is three dimensional structural systems
  without shear or bearing walls composed of
  interconnected members laterally supported so as
  to function as complete self contained unit with
  or without aid of horizontal diaphragm of floor
  systems.

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vii. Tube system

• If consisting of closely spaced exterior columns
  tied at each floor level with relatively deep
  spandrel beams.
• Thus it creates the effect of hollow concrete
  tube perforated by opening for the windows.
• The exterior columns are generally spaced between
  1.2m to 3m.
• The spandrel beams interconnecting the closely
  spaced columns have a depth varying from 60cm to
  1.25m and width from 25cm to 1m.
• Such building has very high moment of inertia
  about the two orthogonal axes in controlling
  lateral displacements in very tall building.

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Stiffness Elements

• In tall buildings stiffness elements are required
  so as to control the lateral drift from
  serviceability considerations.
• Stiffness may be provided through walls, wall
  panels or diagonal bracing members.

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Regularity

• Regularity of a building can significantly affect
  its performance during a strong earthquake.
• Past earthquakes have repeatedly shown that
  buildings having irregular configurations suffer
  greater damage than buildings having regular
  configurations.
• Regular structures have no significant physical
  discontinuities in plan or vertical configuration
  or in their lateral force systems.
• Whereas irregular structures have significant
  physical discontinuities in configuration or in
  their lateral force resisting systems.
• They may have either vertical irregularity or
  plan irregularity or both.

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Vertical Structural Irregularity

• Stiffness soft- storey- a soft storey is one in
  which the lateral stiffness is less than 70 of
  that in the storey above or less than 80 of
  average stiffness of the three storeys above.
• Strength weak storey- a weak storey is one in
  which the storey strength is less than 80 if
  that in the storey above. The storey strength is
  the total strength of all seismic force resisting
  elements sharing the storey shear for the
  direction under consideration.
• Vertical geometry
• In plane discontinuity and
• Weight or mass - A mass irregularity is
  considered to exist where the effective mass of
  any storey is more than 150 of the effective
  mass of an adjacent storey. A roof which is
  lighter than the floor below need not be
  considered.

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Plan Structural Irregularity

• It may be caused on account of the following
  aspects
• (1) Torsional irregularity,
• (2) Re-entrant corners,
• (3) Diaphragm discontinuity,
• (4) Out-of-plane offsets, and
• (5) Non-parallel systems.

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NEED FOR REDUNDANCY

• It is strongly 'recommended that the lateral
  force resisting system be made as redundant as
  possible within the functional parameters of the
  building because of many unknowns and
  uncertainties in the magnitude and
  characteristics of the earthquake loading, in the
  materials systems of construction, and in the
  method of analysis.
• Redundancy plays an important role in
  determining the ability of the building to resist
  earthquake forces. In a statically determinate
  system every component must remain operative to
  preserve the integrity of the structure.
• On the contrary, in a highly indeterminate
  system, one or more redundant components may fail
  and still leave a structural system which retains
  its integrity and continue to resist the
  earthquake forces although with reduced
  effectiveness.
• It is, therefore, preferable to provide multiple
  lines of bracing to perimeter bracing, and
  multiple bents or bays of bracing in each bracing
  line than a single braced bay. Good torsional
  stiffness is also essential. The objective is to
  create a system that will have its inelastic
  behavior distributed nearly uniformly throughout
  the plan and elevation of the system. The back up
  system can prevent progressive or catastrophic
  collapse if distress occurs in the primary system.

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PARTITION WALLS OR INFILL WALLS

• Brick masonry is a highly non-homogeneous and
  orthotropic material and it is difficult to model
  its behavior and properties. The behavior of a
  framed building with masonry infill's is quite
  complex. There are several problems associated
  with the masonry panels during earthquakes. Soft
  storey effect is the most serious. The presence
  of windows and absence of any rigid contact
  between the masonry panel and the beam above and
  below further complicates the problem. The
  infill's are brittle and weak compared to the
  concrete members. The infill's contribute to the
  stiffness of the building during the initial
  stage of loading but fail much earlier before the
  ultimate capacity of the frame is reached.
  Similarly, they do not contribute to the strength
  and ductility of the frame. The usual practice is
  to ignore the strength and stiffness of the
  infill's but to consider its mass and design the
  bare frame for earthquake load.
• It is desirable to provide a 10-20 mm clear gap
  between the masonry panel and the adjoining beam
  and columns. The gap may be filled with weak
  mortar. The intention is to let the infill panel
  separate from the moment resisting frame during
  an earthquake and let the moment resisting frame
  resist the earthquake force through ductile
  behavior. It is recommended that for such ductile
  moment resisting frames with infill wall panels a
  R value equal to 4 should be taken instead of as
  implied in the. IS 1893-2001.

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MEMBER STIFFNESS

• Stiffness of a member in elastic analysis is
  defined as EI/L were E is modulus of elasticity
  of concrete, I is moment of inertia and L is
  center to center length of a member.
• The codes generally allow the use of any
  reasonable assumption when computing the
  stiffness for use in a frame analysis provided
  the assumptions made are consistent throughout
  the analysis.
• Ideally, the member stiffness El should reflect
  the degree of cracking and inelastic action which
  has occurred along each member immediately prior
  to the onset of yielding.
• The value of El varies along the length of a
  member and is also a function of stress level.
• The exact determination of El is quite complex,
  hence simple assumptions are required to define
  the flexural stiffness for practical analysis.
  The results of an analysis obviously depend on
  the values of El.

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Modulus of elasticity

• A suitable value of the modulus of elasticity of
  concrete is required if a building frame is to be
  analyzed by the stiffness method using a
  computer. The modulus of elasticity of concrete
  is considerably more variant than its compressive
  strength.

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Moment of inertia

• The moment of inertia of a section can be
  determined on the basis of any one of the
  following cross-sections throughout the building
• (a) Gross concrete section -'the cross-section of
  the member ignoring reinforcement,
• (b) Gross equivalent section - the concrete
  cross-section plus the area of reinforcement
  transformed on the basis of modular ratio.
• (c) Cracked section - the area of concrete in
  compression plus the area of reinforcement
  transformed on the basis of modular ratio.
• For the purpose of computing the moment of
  inertia, the value of modular ratio may be taken
  as 15 irrespective of the grade of concrete in
  the absence of better information. A consistent
  approach should be used for all elements of the
  structure.

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Moment of inertia

• The moment of inertia of beams/girders and
  columns is generally calculated on the basis of
  gross-section with no allowance made for
  reinforcing steel. There is a difficulty involved
  in the determination of moment of inertia to be
  used in continuous T-beams. The moment of inertia
  is much greater where there is sagging moment
  with the flanges in compression than where there
  is hogging moment with the flanges cracked due to
  tension. Thus, there is a need to use an
  equivalent value which is constant throughout its
  length. A general practice is to assume
  equivalent moment of inertia equal to twice the
  moment of inertia of the web. The depth of web is
  taken as the overall depth of the beam.

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LOADS

• The dead load on a frame is calculated floor-wise
  and consists of weight of floors, girders,
  partition walls, false ceiling, parapets,
  balconies, fixed or permanent equipment and half
  the columns above and below a floor. The load
  acting on a column is calculated from all the
  beams framing into it.
• Live loads the magnitude of live load depends
  upon the type of occupancy of the building. IS
  875-1987 (part 2) has specified certain minimum
  values of live loads (or imposed loads) for
  specific purpose as given in Appendix C. l. The
  live load distribution varies with time. Hence,
  each member is designed for the worst combination
  of dead and live loads. A reduction in live load
  is allowed for a beam if it carries load from an
  area greater than 50 m2. The reduction is 5 for
  each 50 m2 area subject to a maximum reduction of
  25 .

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LOADS
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Wind Loads

• Wind is essentially a random phenomenon. In the
  past it was considered sufficient to the highest
  wind speed that had been recorded at the
  meteorological stations nearest concerned place.
  The corresponding wind pressure was applied
  statically. This was erroneous practice since
  wind loading varies with time. Moreover, the wind
  speed )depends on several factors such as
  density of obstructions in the terrain, size of
  gust, return period, and probable life of
  structure etc. Thus no deterministic method can
  do Lice with wind loading.

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• The wind loads in IS 875-1987. (Part 3) are
  based on two considerations
• (1)The statistical and probabilistic approach to
  the evaluation of wind loads, and
• (2)Due recognition to the dynamic component of
  wind loading and its interaction with the dynamic
  characteristics of the structure.

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• The design wind speed Vz at any given height and
  at a given site is expressed as a product of four
  parameters
• Vz Vbk1k2k3
• Where
• Vb basic wind speed in meter/sec at 10 m height
• K1 probability or risk factor
• k2 terrain, height, and structure size factor
• k3 local topography factor

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Effect of Sequence of Construction

• Most computer softwares for the analysis of
  building frames are based on the stiffness matrix
  method. They require input of the building
  geometry and loading before beginning the
  analysis. The quantum of data depends whether the
  analysis is 2-D or 3-D. In actual practice, a
  building is built up gradually, hence dead load
  is also built up gradually. In a 15- storey
  building, at the time 6th floor is being raised,
  there is only a 6- storey frame and not a 15-
  storey frame. Hence, the dead load of 6- storey
  frame is resisted by a 6- storey frame and not a
  15- storey frame. The procedure of simultaneous
  analysis of a complete frame for dead and live
  loads may lead to erroneous results.

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• The simultaneous analysis of a complete frame is
  correct only for live loads. It is correct for
  dead loads if all columns have identical stress
  level or axial deformations. If the adjoining
  columns have differential elastic shortening, the
  analysis may show significant positive bending
  moments over the highly stressed column. In fact,
  by the time 7-th storey is being raised, the
  elastic axial shortening in the 6- storey frame
  due to dead loads has already taken place and,
  there won't be any positive moment over the
  highly stressed column. A similar situation may
  arise in a shear wall-frame structure near top
  region of the shear wall.

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ANALYSIS FOR LATERAL LOADS

• A building should be carefully designed for
  lateral forces because not only must buildings
  have sufficient lateral resistance to prevent
  overturning, hence failure, but they also must
  have sufficient lateral resistance to deflections
  so as to satisfy the limit state of
  serviceability. Approximate analysis, of building
  frames can be carried out either.by portal method
  or by cantilever method. The portal method is
  supposed to be satisfactory for most buildings
  upto about 25 storeys, whereas, the cantilever
  method is good enough for about 35 storeys.

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Portal method

• In this method, the following assumptions are
  made
• (1) There is a point of inflection at the centre
  of each girder.
• (2) There is a point of inflection at the centre
  of each column.
• (3) The total horizontal shear on each storey is
  divided between the columns of that storey so
  that each interior column carries twice as much
  shear as each exterior column.

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• These assumptions reduce a highly statically
  indeterminate structure to a statically
  determinate one. The method neglects the effect
  of axial deformations in the columns. he
  assumptions associated with the portal method
  results in errors in the vicinity of the base and
  top of the frame, and at set backs or locations
  where significant changes in ember stiffness
  occur.

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Cantilever method

• In this method, the following assumptions are
  made
• 1) There is a point of inflection at the centre
  of each girder.
• 2) There is a point of inflection at the centre
  of each column.
• 3) The intensity of axial stress in each column
  of a storey is proportional to horizontal
  distance of that column from the centre of
  gravity of all the columns of the storey under
  consideration.
• It is suggested that if height of the building is
  more than five times its least lateral dimension,
  a more precise method of analysis should be used.

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TORSION IN BUILDINGS

• There are series of frames in orthogonal
  directions x and y to resist gravity loads and
  lateral loads. A floor is generally quite rigid
  in its own plane. Each frame may have a different
  stiffness distribution and mass distribution. At
  each floor, it is possible to centre of rigidity
  due to lateral stiffness and centre of mass. If
  the building is symmetric with respect to lateral
  stiffness and mass, the two entre would coincide.
  Otherwise, there will be an eccentricity in the
  two directions.

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TORSION IN BUILDINGS
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Steps in torsional analysis

• Step I Arrange all the frames in the building
  along the y-direction interconnected through
  axially rigid links at the floor levels, apply
  the lateral loads and carry out a plane frame
  static analysis. The frame shears computed by
  analyzing this hypothetical building are taken as
  the relative stiffnesses of the lateral load
  resisting elements.

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• Step 2 Arrange all the y-direction frames in the
  building along the y-direction interconnected
  through axially rigid links at the floor levels,
  apply the lateral loads and carry Out a plane
  frame static analysis. The frame shears computed
  by this analysis are used to compute the
  x-coordinates of the reference centers (shear
  centre by the storey eccentricity approach and
  centre of rigidity by the floor eccentricity
  approach Another such analysis in the x-direction
  gives the y-coordinates of the reference centers.
• Step 3 Compute the, torsional stiffness K9 of the
  building with reference to the reference centres
  computed in Step 2 using the relative stiffnesses
  of the frames computed in the Step 1. The values
  of K9 are different for the two sets of reference
  centres.

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Steps in torsional analysis

• Step 4 Compute the location of the reference
  centres of mass. In the case of storey
  eccentricity approach these are the cumulative
  centres of mass while in the case of floor
  eccentricity approach these are the nominal
  centres of mass. Then compute the eccentricity at
  each floor.
• Step 5 Compute the design torsional moments
  corresponding to eda for y-direction loading and
  compute the frame shears.

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Monolithic Beam To Column Joints

• A beam-column joint is a very critical element in
  reinforced concrete construction where the
  elements intersect In all the three directions.
• Floor slab has been removed for convenience.
  Quite often in design the details of joint are
  simply ignored. Joints are most critical because
  they insure continuity of a structure and
  transfer forces that are present at the ends of
  members into and though the joint.
• Frequently joints are points of weakness due to
  lack of adequate anchorage for bars entering the
  joint from the columns and beams.

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The shear in joint