Multistorey Multistorey BuildingBuilding

Introduction

Multistorey BuildingMultistorey Building

Multistorey BuildingMultistorey 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.

Multistorey BuildingMultistorey 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.

Multistorey BuildingMultistorey 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.

Multistorey BuildingMultistorey 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.

Sections of multistory Sections of multistory BuildingBuilding

Structural AnalysisStructural 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 followsi. Load bearing wall systemsii. Building with flexural systemsiii.Moment resisting frame systemiv.Dual frame systemv. Tube systems

i.i. Load bearing wall Load bearing wall systemsystem

• 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.

ii.ii. Building with flexural Building with flexural wall systemwall 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.

iii.iii. Moment resisting Moment resisting frame systemsframe 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 R=5. the frame should be detailed conforming to IS 13290:1993 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.

iv.iv. Flexural shear (wall) Flexural shear (wall) systemssystems

• 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.

v.v. Dual frame systemsDual frame systems• It is structural system with the following features:i. Moment resisting frame providing support for

gravity loads.ii. Resistance resisting loads is provided by :

a) Specially detailed moment resisting frame which is capable of resisting at least 25% of the base shear including torsion effects

b) Flexural walls must resist total required lateral force in accordance with relative stiffness considering interaction of walls and frames as single systems.

vi.vi. Space frameSpace 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.

vii.vii. Tube systemTube 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.

Stiffness ElementsStiffness 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.

Regularity 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.

Vertical Structural Vertical Structural IrregularityIrregularity

• 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.

Plan Structural Plan Structural IrregularityIrregularity

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.

NEED FOR NEED FOR REDUNDANCYREDUNDANCY

• 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.

PARTITION WALLS OR PARTITION WALLS OR INFILL WALLSINFILL 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.

MEMBER STIFFNESSMEMBER 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.

Modulus of elasticityModulus 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.

Moment of inertiaMoment 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.

Moment of inertiaMoment 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.

LOADSLOADS• 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 %.

LOADSLOADS

Wind LoadsWind LoadsWind 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.

• 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.

• 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 heightK1= probability or risk factor

k2 = terrain, height, and structure size factor

k3 =local topography factor

Effect of Sequence of Effect of Sequence of ConstructionConstruction

• 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.

• 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.

ANALYSIS FOR LATERAL ANALYSIS FOR LATERAL

LOADSLOADS• 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.

Portal methodPortal 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.

• 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.

Cantilever methodCantilever methodIn 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.

TORSION IN BUILDINGSTORSION 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.

TORSION IN BUILDINGSTORSION IN BUILDINGS

Steps in torsional Steps in torsional analysisanalysis

• 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.

• 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.

Steps in torsional analysisSteps 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.

Monolithic Beam To Column Monolithic Beam To Column

JointsJoints

• 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.

The shear in jointThe shear in joint