3. Multistorey BuildingMultistorey Building• Reinforced concrete buildings consist of floor slabs,beams, girders and columns continuously placed toform a rigid monolithic system as shown in Fig. 19.1.Such a continuous system leads to greaterredundancy, reduced moments and distributes theload more evenly. The floor slab may rest on asystem of interconnected beams. Interior beams B4,B5, B6 are supported on the girders, whereas, theexterior beams BI, B2, B3 are directly supported bythe columns. Girders such as GI, G2, G3 are alsosupported directly by the columns. Beams BI, B2, B3and girders GI, G2 and 03 are not only continuousbut are also monolithic with upper and lowercolumns.
4. Multistorey BuildingMultistorey Building• Thus, a building frame is a three-dimensionalstructure or a space structure. It is idealized as asystem of interconnected two-dimensional verticalframes along the two mutually perpendicularhorizontal axes for analysis. These frames areanalyzed independently of each other. In frameswhere the columns are arranged on a rectangulargrid, loading patterns giving biaxial bending neednot be considered except for corner columns.
5. Multistorey BuildingMultistorey Building• The degree of sophistication to which a structuralanalysis is carried out depends on the importanceof the structure. A wide range of approaches havebeen used for buildings of varying heights andimportance, from simple. approximate methodswhich can be carried out manually, or with the aidof a pocket calculator, to more refined techniquesinvolving computer solutions. Till a few years agomost of the Multistorey buildings were analyzed byapproximate methods such as substitute frame,moment distribution, portal and cantilever methods.
6. Multistorey BuildingMultistorey Building• The recent advent of personal computers (PCs)and the abundance of ready-made computerpackage programs has reduced the use ofapproximate methods which at present are usefulfor preliminary analysis and verification. Theapplication of computers is not restricted merely toanalysis; they are used in almost every phase ofconcrete work from analysis to design, to plotting,to detailing, to specification writing, to costestimating etc.
7. Sections of multistorySections of multistoryBuildingBuilding
8. Structural AnalysisStructural Analysis• A building is subjected to various load such as deadload, live load, lateral load such as wind load orearthquake 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
9. i.i. Load bearing wall systemLoad bearing wall system• Walls provide support for all gravity load s as well asresistance to lateral loads• There are no columns• The walls and partition wall supply in-plane lateralstiffness and stability to resist end and earthquakeloading.• This systems lacks in providing redundancy for thevertical and lateral load supports, that is, if the wallsfail, the vertical loads as well as lateral loadscarrying capacity is eliminated to instability.
10. ii.ii. Building with flexural wallBuilding with flexural wallsystemsystem• The gravity load is carried primarily by a framesupported on columns rather than bearing walls.• Some minor portion of the gravity load can becarried on bearing walls but the amount so carriedshould not should not represent more than a few %of the building area.• The resistance to lateral loads is provided bynominal moment resistance be incorporated in thevertical load frame design.
11. iii.iii. Moment resisting frameMoment resisting framesystemssystems• If the system in which members and joints arecapable of resisting vertical and lateral loadsprimarily by flexural.• To qualify for a response reduction factor R=5. theframe should be detailed conforming to IS13290:1993 to provide ductility excepts in seismiczone2.• In moment resistant frame, relative stiffness ofgirders and columns is very important.• A frame may be designed using weak column-strong girder proportions or strong column-weakgirder proportions.
12. iv.iv. Flexural shear (wall)Flexural shear (wall)systemssystems• It is reinforced concrete wall designed to resistlateral forces parallel to the plane of the wall anddetailed to proved ductility conforming to IS 13290-1993.• The international building code of America IBC 2000permits the use of flexural shear wall systems up toheight of about 45m.• However, it can be used up to height of 70m, if andonly if; flexural walls in any plane do not resist morethan 33% of the earthquake design force includingtorsional effects.
13. v.v. Dual frame systemsDual frame systems• It is structural system with the following features:i. Moment resisting frame providing support for gravityloads.ii. Resistance resisting loads is provided by :a) Specially detailed moment resisting frame which is capable of resisting atleast 25% of the base shear including torsion effectsb) Flexural walls must resist total required lateral force in accordance withrelative stiffness considering interaction of walls and frames as singlesystems.
14. vi.vi. Space frameSpace frame• It is three dimensional structural systems withoutshear or bearing walls composed of interconnectedmembers laterally supported so as to function ascomplete self contained unit with or without aid ofhorizontal diaphragm of floor systems.
15. vii.vii. Tube systemTube system• If consisting of closely spaced exterior columns tiedat each floor level with relatively deep spandrelbeams.• Thus it creates the effect of hollow concrete tubeperforated by opening for the windows.• The exterior columns are generally spaced between1.2m to 3m.• The spandrel beams interconnecting the closelyspaced columns have a depth varying from 60cmto 1.25m and width from 25cm to 1m.• Such building has very high moment of inertiaabout the two orthogonal axes in controlling lateraldisplacements in very tall building.
16. Stiffness ElementsStiffness Elements• In tall buildings stiffness elements are required so asto control the lateral drift from serviceabilityconsiderations.• Stiffness may be provided through walls, wall panelsor diagonal bracing members.
17. RegularityRegularity• Regularity of a building can significantly affect itsperformance during a strong earthquake.• Past earthquakes have repeatedly shown that buildingshaving irregular configurations suffer greater damage thanbuildings having regular configurations.• Regular structures have no significant physical discontinuitiesin plan or vertical configuration or in their lateral forcesystems.• Whereas irregular structures have significant physicaldiscontinuities in configuration or in their lateral force resistingsystems.• They may have either vertical irregularity or plan irregularity orboth.
18. Vertical StructuralVertical StructuralIrregularityIrregularity• Stiffness soft- storey- a soft storey is one in which the lateralstiffness is less than 70% of that in the storey above or less than80% of average stiffness of the three storeys above.• Strength weak storey- a weak storey is one in which the storeystrength is less than 80% if that in the storey above. The storeystrength is the total strength of all seismic force resistingelements sharing the storey shear for the direction underconsideration.• Vertical geometry• In plane discontinuity and• Weight or mass - A mass irregularity is considered to existwhere the effective mass of any storey is more than 150% ofthe effective mass of an adjacent storey. A roof which islighter than the floor below need not be considered.
19. Plan Structural IrregularityPlan Structural IrregularityIt may be caused on account of the followingaspects:(1) Torsional irregularity,(2) Re-entrant corners,(3) Diaphragm discontinuity,(4) Out-of-plane offsets, and(5) Non-parallel systems.
20. NEED FOR REDUNDANCYNEED FOR REDUNDANCY• It is strongly recommended that the lateral force resisting system be made asredundant as possible within the functional parameters of the building because ofmany unknowns and uncertainties in the magnitude and characteristics of theearthquake loading, in the materials & systems of construction, and in the methodof analysis.• Redundancy plays an important role in determining the ability of the building toresist earthquake forces. In a statically determinate system every component mustremain operative to preserve the integrity of the structure.• On the contrary, in a highly indeterminate system, one or more redundantcomponents may fail and still leave a structural system which retains its integrityand 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 thatwill have its inelastic behavior distributed nearly uniformly throughout the plan andelevation of the system. The back up system can prevent progressive orcatastrophic collapse if distress occurs in the primary system.
21. PARTITION WALLS ORPARTITION WALLS ORINFILL WALLSINFILL WALLS• Brick masonry is a highly non-homogeneous and orthotropic material and it isdifficult to model its behavior and properties. The behavior of a framedbuilding with masonry infills is quite complex. There are several problemsassociated with the masonry panels during earthquakes. Soft storey effect isthe most serious. The presence of windows and absence of any rigid contactbetween the masonry panel and the beam above and below furthercomplicates the problem. The infills are brittle and weak compared to theconcrete members. The infills contribute to the stiffness of the building duringthe initial stage of loading but fail much earlier before the ultimate capacityof the frame is reached. Similarly, they do not contribute to the strength andductility of the frame. The usual practice is to ignore the strength and stiffnessof the infills but to consider its mass and design the bare frame for earthquakeload.• It is desirable to provide a 10-20 mm clear gap between the masonry paneland the adjoining beam and columns. The gap may be filled with weakmortar. The intention is to let the infill panel separate from the momentresisting frame during an earthquake and let the moment resisting frame resistthe earthquake force through ductile behavior. It is recommended that forsuch ductile moment resisting frames with infill wall panels a R value equal to 4should be taken instead of as implied in the. IS: 1893-2001.
22. MEMBER STIFFNESSMEMBER STIFFNESS• Stiffness of a member in elastic analysis is defined as EI/L wereE is modulus of elasticity of concrete, I is moment of inertiaand L is center to center length of a member.• The codes generally allow the use of any reasonableassumption when computing the stiffness for use in a frameanalysis provided the assumptions made are consistentthroughout the analysis.• Ideally, the member stiffness El should reflect the degree ofcracking and inelastic action which has occurred along eachmember immediately prior to the onset of yielding.• The value of El varies along the length of a member and isalso a function of stress level.• The exact determination of El is quite complex, hence simpleassumptions are required to define the flexural stiffness forpractical analysis. The results of an analysis obviously dependon the values of El.
23. Modulus of elasticityModulus of elasticity• A suitable value of the modulus of elasticity ofconcrete is required if a building frame is to beanalyzed by the stiffness method using a computer.The modulus of elasticity of concrete is considerablymore variant than its compressive strength.
24. Moment of inertiaMoment of inertia• The moment of inertia of a section can be determined on the basisof any one of the following cross-sections throughout the building:(a) Gross concrete section -the cross-section of the memberignoring reinforcement,(b) Gross equivalent section - the concrete cross-section plus thearea of reinforcement transformed on the basis of modular ratio.(c) Cracked section - the area of concrete in compression plusthe area of reinforcement transformed on the basis of modularratio.• For the purpose of computing the moment of inertia, the value ofmodular ratio may be taken as 15 irrespective of the grade ofconcrete in the absence of better information. A consistentapproach should be used for all elements of the structure.
25. Moment of inertiaMoment of inertia• The moment of inertia of beams/girders and columns isgenerally calculated on the basis of gross-section with noallowance made for reinforcing steel. There is a difficultyinvolved in the determination of moment of inertia to be usedin continuous T-beams. The moment of inertia is much greaterwhere there is sagging moment with the flanges incompression than where there is hogging moment with theflanges cracked due to tension. Thus, there is a need to usean equivalent value which is constant throughout its length. Ageneral practice is to assume equivalent moment of inertiaequal to twice the moment of inertia of the web. The depthof web is taken as the overall depth of the beam.
26. LOADSLOADS• The dead load on a frame is calculated floor-wise and consists ofweight of floors, girders, partition walls, false ceiling, parapets,balconies, fixed or permanent equipment and half the columnsabove and below a floor. The load acting on a column is calculatedfrom all the beams framing into it.• Live loads the magnitude of live load depends upon the type ofoccupancy of the building. IS 875-1987 (part 2) has specified certainminimum values of live loads (or imposed loads) for specific purposeas given in Appendix C. l. The live load distribution varies with time.Hence, each member is designed for the worst combination of deadand live loads. A reduction in live load is allowed for a beam if itcarries load from an area greater than 50 m2. The reduction is 5 % foreach 50 m2 area subject to a maximum reduction of 25 %.
28. Wind LoadsWind LoadsWind is essentially a random phenomenon. In the pastit was considered sufficient to the highest wind speedthat had been recorded at the meteorologicalstations nearest concerned place. The correspondingwind pressure was applied statically. This waserroneous practice since wind loading varies withtime. Moreover, the wind speed )depends on severalfactors such as : density of obstructions in the terrain,size of gust, return period, and probable life ofstructure etc. Thus no deterministic method can doLice with wind loading.
29. • The wind loads in IS: 875-1987. (Part 3) are based ontwo considerations:(1)The statistical and probabilistic approach to theevaluation of wind loads, and(2)Due recognition to the dynamic component ofwind loading and its interaction with the dynamiccharacteristics of the structure.
30. • The design wind speed Vz at any given height andat a given site is expressed as a product of fourparameters• Vz = Vbk1k2k3WhereVb = basic wind speed in meter/sec at 10 m heightK1= probability or risk factork2 = terrain, height, and structure size factork3 =local topography factor
31. Effect of Sequence ofEffect of Sequence ofConstructionConstruction• Most computer softwares for the analysis of buildingframes are based on the stiffness matrix method.They require input of the building geometry andloading before beginning the analysis. The quantumof 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- storeyframe. Hence, the dead load of 6- storey frame isresisted by a 6- storey frame and not a 15- storeyframe. The procedure of simultaneous analysis of acomplete frame for dead and live loads may leadto erroneous results.
32. • The simultaneous analysis of a complete frame iscorrect only for live loads. It is correct for deadloads if all columns have identical stress level oraxial deformations. If the adjoining columns havedifferential elastic shortening, the analysis may showsignificant positive bending moments over thehighly stressed column. In fact, by the time 7-thstorey is being raised, the elastic axial shortening inthe 6- storey frame due to dead loads has alreadytaken place and, there wont be any positivemoment over the highly stressed column. A similarsituation may arise in a shear wall-frame structurenear top region of the shear wall.
33. ANALYSIS FOR LATERALANALYSIS FOR LATERALLOADSLOADS• A building should be carefully designed for lateralforces because not only must buildings havesufficient lateral resistance to prevent overturning,hence failure, but they also must have sufficientlateral resistance to deflections so as to satisfy thelimit state of serviceability. Approximate analysis, ofbuilding frames can be carried out either.by portalmethod or by cantilever method. The portalmethod is supposed to be satisfactory for mostbuildings upto about 25 storeys, whereas, thecantilever method is good enough for about 35storeys.
34. Portal methodPortal method• In this method, the following assumptions are made:• (1) There is a point of inflection at the centre ofeach girder.• (2) There is a point of inflection at the centre ofeach column.• (3) The total horizontal shear on each storey isdivided between the columns of that storey so thateach interior column carries twice as much shear aseach exterior column.
35. • These assumptions reduce a highly staticallyindeterminate structure to a statically determinateone. The method neglects the effect of axialdeformations in the columns. he assumptionsassociated with the portal method results in errors inthe vicinity of the base and top of the frame, andat set backs or locations where significant changesin ember stiffness occur.
36. Cantilever methodCantilever methodIn this method, the following assumptions are made:•1) There is a point of inflection at the centre of eachgirder.•2) There is a point of inflection at the centre of eachcolumn.•3) The intensity of axial stress in each column of astorey is proportional to horizontal distance of thatcolumn from the centre of gravity of all the columns ofthe storey under consideration.•It is suggested that if height of the building is morethan five times its least lateral dimension, a moreprecise method of analysis should be used.
37. TORSION IN BUILDINGSTORSION IN BUILDINGS• There are series of frames in orthogonal directions xand y to resist gravity loads and lateral loads. A flooris generally quite rigid in its own plane. Each framemay have a different stiffness distribution and massdistribution. At each floor, it is possible to centre ofrigidity due to lateral stiffness and centre of mass. Ifthe building is symmetric with respect to lateralstiffness and mass, the two entre would coincide.Otherwise, there will be an eccentricity in the twodirections.
38. TORSION IN BUILDINGSTORSION IN BUILDINGS
39. Steps in torsional analysisSteps in torsional analysis• Step I : Arrange all the frames in the building alongthe y-direction interconnected through axially rigidlinks at the floor levels, apply the lateral loads andcarry out a plane frame static analysis. The frameshears computed by analyzing this hypotheticalbuilding are taken as the relative stiffnesses of thelateral load resisting elements.
40. • Step 2 Arrange all the y-direction frames in thebuilding along the y-direction interconnectedthrough axially rigid links at the floor levels, apply thelateral loads and carry Out a plane frame staticanalysis. The frame shears computed by this analysisare used to compute the x-coordinates of thereference centers (shear centre by the storeyeccentricity approach and centre of rigidity by thefloor eccentricity approach Another such analysis inthe x-direction gives the y-coordinates of thereference centers.• Step 3 Compute the, torsional stiffness K9 of thebuilding with reference to the reference centrescomputed in Step 2 using the relative stiffnesses ofthe frames computed in the Step 1. The values of K9are different for the two sets of reference centres.
41. Steps in torsional analysisSteps in torsional analysis• Step 4 Compute the location of the referencecentres of mass. In the case of storey eccentricityapproach these are the cumulative centres of masswhile in the case of floor eccentricity approachthese are the nominal centres of mass. Thencompute the eccentricity at each floor.• Step 5 : Compute the design torsional momentscorresponding to eda for y-direction loading andcompute the frame shears.
42. Monolithic Beam To Column JointsMonolithic Beam To Column Joints• A beam-column joint is a very critical element inreinforced concrete construction where theelements intersect In all the three directions.• Floor slab has been removed for convenience.Quite often in design the details of joint are simplyignored. Joints are most critical because they insurecontinuity of a structure and transfer forces that arepresent at the ends of members into and thoughthe joint.• Frequently joints are points of weakness due to lackof adequate anchorage for bars entering the jointfrom the columns and beams.