Some Concepts In Earthquake Behaviour Of Buildings
Some Concepts inEarthquake Behaviour of BuildingsC. V. R. MurtyRupen GoswamiA. R. VijayanarayananVipul V. MehtaGujarat State Disaster Management AuthorityGovernment of Gujarat
Some Concepts inEarthquake Behaviour of BuildingsΔHStrengthDeformabilityDesign Lateral Force HStiffnessInelastic EnergyLateral Deformation ΔC. V. R. MurtyRupen GoswamiA. R. VijayanarayananVipul V. MehtaGujarat State Disaster Management AuthorityGovernment of Gujarat
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PrefaceThis book explains concepts in behaviour of buildings during earthquakes. The book dwellson basic concepts in earthquake resistant design of buildings, first describes these at a conceptuallevel and then articulates further with numerical examples. It is an attempt to respond to some ofthe frequently asked questions by Architects and Structural Engineers regarding behaviour ofReinforced Concrete (RC) and Steel buildings under the action of lateral loads, especially duringearthquakes. Since most buildings built in India are made of RC, the dominant set of examples usedis of RC buildings. But, with no loss of generality, the broad concepts discussed in this documentare valid for both RC and Steel buildings. Also, the discussion is limited to normal buildingswithout any special devices, like base isolation and other energy absorbing or dissipating devices. Also,specialised systems (like post-tensioning slab systems and nuclear power plants) are not in focus.This book employs exaggerated deformation shapes to emphasise deformations, and thereby,to develop the most needed intuition of structural behaviour of buildings during earthquakes andits consequences on earthquake-resistant design. The book contains animations related to behaviourof the various buildings models used in this work. Those readers seeing the electronic copy of thisbook should make special note of those pages titled Animation Set ., to capture the hyperlinks andreach the said animations.The target audience of the book is practicing seismic structural engineers and architects, inaddition to students and teachers of engineering and architecture colleges striving to understand seismicbehaviour, analysis and design of buildings.iii
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AcknowledgementsThe authors are grateful to the Gujarat State Disaster Management Authority (GSDMA),Government of Gujarat, Gandhinagar (Gujarat, India), for readily agreeing to support thepreparation of this book; the generous financial grant provided by GSDMA towards this effort isgratefully acknowledged. Ms. Alpa R. Sheth, Managing Director, Vakil Mehta Sheth ConsultingEngineers Private Limited, Mumbai, and Seismic Advisor, GSDMA, Gandhinagar, Gujarat, hasprovided unstinted support to the project. Her technical inputs have been invaluable at all stages ofthe project - the proposal review, intermediate feedback during development and technical reviewat the end. The authors are indebted to her for this proactive role in the development of the book,and thank her sincerely for the same. The authors sincerely thank Mr. Birju Patel, Deputy Director,GSDMA, Gandhinagar, for timely action and administrative support from GSDMA side.The authors extend their appreciation to Dr. R. Bannerji, IAS, Chief Executive Officer,GSDMA, Dr. V. Thiruppugazh, IAS, Additional Chief Executive Officer, GSDMA and Mr. S. I. Patel,Additional Chief Executive Officer, GSDMA for their invaluable inputs and guidance during thecourse of preparing and finalizing this book.Mr. Arvind Jaiswal, Chief Consulting Engineer, EON Designers and Architects Limited,Secunderabad, read in detail the manuscript of this book and offered critical technical comments;the authors offer him their most sincere gratitude for this special contribution towards improvingthe usefulness of this book. CSI India, New Delhi, provided the nonlinear structural analysis tools,e.g., SAP2000, ETABS and PERFORM 3D, to undertake numerical work for the preparation of thisbook; this contribution is sincerely acknowledged. Professors Devdas Menon and A. Meher Prasad atIIT Madras provided resources during the early days of the work and offered continuedencouragement during the entire course of this work; the authors are indebted to them for thisaffection and support. M.Tech. (Civil Engineering) students at IIT Madras, Mr. DeepanShanmugasundaram, Mr. Arun Mathews and Mr. K. Rajgopal, prepared the input files for manybuilding analyses as part of their research assistantship; their contribution is sincerelyacknowledged. The authors acknowledge with thanks the support offered by various sections ofIIT Madras in administering this book writing project. In particular, the authors gratefullyacknowledge support offered by Mrs. S. Kavita, Project Assistant, Department of Civil Engineering,and of Mrs. C. Sankari and Mr. Anand Raj of the Structural Engineering Laboratory of the Institute.The authors remain indebted to their parents and family members for the unconditionalsupport and understanding throughout the development of the book This book is dedicated to allthe people of India, who lost their lives in RC building collapses during past earthquakes in thecountry v
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iivviix1Earthquake-Resistant Buildings1.11.21.31.41.5Basics of Earthquake-Resistant Design and ConstructionBasic Aspects of Seismic DesignThe Four Virtues of Earthquake Resistant Buildings1.3.1 Characteristics of Buildings(a) Seismic Structural Configuration(b) Structural Stiffness, Strength and Ductility1.3.2 What are the Four Virtues?(a) Who Controls the Four Virtues?(b) How to Achieve the Four Virtues?Earthquake Demand versus Earthquake CapacityForce-based Design to Displacement-based Design2Earthquake Demand on Buildings2.12.2Seismic Design ForceDynamic Characteristics of Buildings2.2.1 Natural Period(a) Fundamental Natural Period of Building(b) Factors influencing Natural Period(1) Effect of Stiffness(2) Effect of Mass(3) Effect of Building Height(4) Effect of Column Orientation(5) Effect of Unreinforced Masonry Infill Walls in RC Frames(6) Effect of Cracked Sections on Analysis of RC Frames(c) Design Practice2.2.2 Mode Shape(a) Fundamental Mode Shape of Oscillation(b) Factors influencing Mode Shapes(1) Effect of Flexural Stiffness of Structural Elements(2) Effect of Axial Stiffness of Vertical Members(3) Effect of Degree of Fixity at Member Ends(4) Effect of Building Height(5) Effect of Unreinforced Masonry Infill Walls in RC Frames(c) Design Practice2.2.3 DampingGround Motion Characteristics2.3.1 Accelerograms2.3.2 Response Spectrum of a Ground Motion(a) Acceleration Response Spectrum of a Ground Motion(b) Design 27292932323436384044454747495152
page3Earthquake Capacity of Buildings – Elastic Behaviour3.13.2Elastic BehaviourConfiguration3.2.1 Overall Geometry(a) Plan Shape(1) Buildings with different shapes, but same Plan Area(2) Buildings with different projections, but same Plan Shape(b) Plan Aspect Ratio(1) Buildings with distributed LLRS in plan and cut-outs(2) Buildings with regular plan shape, but of large plan size and with cut-outs(c) Slenderness Ratio3.2.2 Structural Systems and Components(a) Moment Frame Systems(b) Structural Wall-Frame Systems(c) Braced Frame Systems(d) Tube System(e) Tube-in-Tube and Bundled Tube Systems(f) Flat Slab Building3.2.3 Load Paths(a) Frames(b) Structural WallsMass3.3.1 Mass Asymmetry in Plan3.3.2 Mass Irregularity in ElevationInitial Stiffness3.4.1 Stiffness Irregularity in Plan3.4.2 Stiffness Irregularity in Elevation(a) Open or Flexible Storey in Buildings(b) Plinth and Lintel Beams in Buildings(c) Buildings on Slope(d) Set-back and Step-back Buildings3.4.3 Adjacency3.4.4 Soil Flexibility3.33.44Earthquake Capacity of Buildings – Inelastic Behaviour4.14.2Inelastic BehaviourStrength4.2.1 Strength Hierarchy(a) Beam-Column Joints4.2.2 Structural Plan Density4.2.3 Strength Asymmetry in Plan4.2.4 Strength Discontinuity in Elevation(a) Open/ Flexible/ Weak Storeys in a Building(b) Discontinuous Structural Walls in a Building(c) Short Column EffectDuctility4.3.1 Definitions of Ductility(a) Contributors to Ductility in Reinforced Concrete Buildings(b) Achieving Ductility in Reinforced Concrete Buildings(c) Assessing Ductility available in Buildings4.3.2 Strength Provided in Building and Overall Ductility 3174180183186190192196200205205205216216220
page4.44.3.3 Capacity Design of Buildings(a) Displacement Loading(b) Capacity Design Concept4.3.4 Distribution of Damage in Buildings(a) The Open Ground Storey Buildings(b) Strong Column - Weak Beam Design(c) Excessive ductility demands owing to Pounding from Adjacent Building /Adjacent Part of same BuildingModeling of Buildings5Earthquake-Resistant Design of Buildings5.15.25.3IntroductionEarthquake-Resistant Design MethodsEarthquake-Resistant Design Procedure5.3.1 Stiffness Design Stage5.3.2 Strength Design Stage5.3.3 Ductility Design StageClosing 22222224227228232237238
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Symbolsag (t)fcfnmuuuyvuvyGround accelerationGrade of concretenth Fundamental natural frequency of buildingSeismic massUltimate plastic displacement of a frame member in tension/compressionIdealized yield displacement of a frame member in tension/compressionUltimate plastic shear displacementIdealised yield shear TnTx1Ty1Tz1Tθ1VBVjhVjvVnGross cross-sectional area of RC sectionDesign horizontal base shear coefficientArea resisting shearBreadth of buildingModulus of elasticityLateral forceShear modulusHeight of buildingLateral base shear force of the buildingPeak lateral strengthImportance factorEffective moment of inertia of beamGross moment of inertia of beamMoment of inertia of a beamMoment of inertia of a columnEffective moment of inertia of a cracked RC columnGross moment of inertia of an un-cracked RC columnGross moment of Inertia of an RC sectionInitial lateral stiffnessLength of buildingDepth of a frame memberLength of a frame memberDesign flexural moment capacity of beamOverstrength flexural moment capacity of beamDesign flexural moment capacity of columnPlastic moment capacity of a frame memberMaximum overstrength-based plastic moment capacity of a frame memberAxial load applied on of a frame memberCritical axial load of a frame memberDesign axial load capacity of column in pure axial compressionResponse Reduction FactorStrength RatioDesign acceleration spectrum valueFundamental translational natural period of the buildingnth Fundamental natural period of the buildingFundamental translational natural period along X-directionFundamental translational natural period along Y-directionFundamental vertical natural period along Z-directionFundamental torsional natural period about Z-axisDesign base shearHorizontal shear force in beam-column jointVertical shear force in beam-column jointNominal shear capacity of RC sectionxi
VΩWZZpMaximum overstrength-based equilibrium compatible shear demandSeismic weight of buildingSeismic Zone FactorPlastic Section ModulusβμmμsνξσcrΩsRatio of pure flexural translational stiffness to pure shear translational stiffnessImposed deformation during earthquakeUltimate rotational capacityIdealized yield rotationMaterial ductilityMember ductilityStructure ductilityPoisson ratioDampingCritical axial stress in compressionOverstrength factor for steel barsΔmaxΔRoofΔYMaximum lateral deformationDisplacement at roof levelIdealized yield deformationδθuθyμxii
Chapter 1Earthquake-Resistant Buildings1.1 DYNAMIC ACTIONS ON BUILDINGS – WIND versus EARTHQUAKEDynamic actions are caused on buildings by both wind and earthquakes. But, design for windforces and for earthquake effects are distinctly different. The intuitive philosophy of structuraldesign uses force as the basis, which is consistent in wind design, wherein the building is subjectedto a pressure on its exposed surface area; this is force-type loading. However, in earthquake design,the building is subjected to random motion of the ground at its base (Figure 1.1), which inducesinertia forces in the building that in turn cause stresses; this is displacement-type loading. Anotherway of expressing this difference is through the load-deformation curve of the building – thedemand on the building is force (i.e., vertical axis) in force-type loading imposed by wind pressure,and displacement (i.e., horizontal axis) in displacement-type loading imposed by earthquake shaking.Wind force on the building has a non-zero mean component superposed with a relativelysmall oscillating component (Figure 1.2). Thus, under wind forces, the building may experiencesmall fluctuations in the stress field, but reversal of stresses occurs only when the direction of windreverses, which happens only over a large duration of time. On the other hand, the motion of theground during the earthquake is cyclic about the neutral position of the structure. Thus, the stressesin the building due to seismic actions undergo many complete reversals and that too over the smallduration of earthquake.ΔroofFwag(t)(a)(b)Figure 1.1: Difference in the design effects on a building during natural actions of (a) EarthquakeGround Movement at base, and (b) Wind Pressure on exposed areatime(a)time(b)Figure 1.2: Nature of temporal variations of design actions: (a) Earthquake Ground Motion – zero mean,cyclic, and (b) Wind Pressure – non-zero mean, oscillatory
1.2 BASIC ASPECTS OF SEISMIC DESIGNThe mass of the building being designed controls seismic design in addition to the buildingstiffness, because earthquake induces inertia forces that are proportional to the building mass.Designing buildings to behave elastically during earthquakes without damage may render theproject economically unviable. As a consequence, it may be necessary for the structure to undergodamage and thereby dissipate the energy input to it during the earthquake. Therefore, thetraditional earthquake-resistant design philosophy requires that normal buildings should be able toresist (Figure 1.3):(a) Minor (and frequent) shaking with no damage to structural and non-structural elements;(b) Moderate shaking with minor damage to structural elements, and some damage to non-structuralelements; and(c) Severe (and infrequent) shaking with damage to structural elements, but with NO collapse (to savelife and property inside/adjoining the building).Therefore, buildings are designed only for a fraction ( 8-14%) of the force that they wouldexperience, if they were designed to remain elastic during the expected strong ground shaking(Figure 1.4), and thereby permitting damage (Figure 1.5). But, sufficient initial stiffness is requiredto be ensured to avoid structural damage under minor shaking. Thus, seismic design balancesreduced cost and acceptable damage, to make the project viable. This careful balance is arrivedbased on extensive research and detailed post-earthquake damage assessment studies. A wealth ofthis information is translated into precise seismic design provisions. In contrast, structural damageis not acceptable under design wind forces. For this reason, design against earthquake effects iscalled as earthquake-resistant design and not earthquake-proof design.(a)(b)(c)Figure 1.3: Earthquake-Resistant Design Philosophy for buildings: (a) Minor (Frequent) Shaking –No/Hardly any damage, (b) Moderate Shaking – Minor structural damage, and some non-structuraldamage, and (c) Severe (Infrequent) Shaking – Structural damage, but NO collapseH, ΔroofLateral Force HMaximum Force,if the structure remains elasticElastic StructureActual StructureReduction in Design Forcewhen some damage can be allowedMinimum Design Force,that codes require to be usedLateral Deflection Δroof0Figure 1.4: Basic strategy of earthquake design: Calculate maximum elastic forces and reduce by afactor to obtain design forces.2
(a)(b)Figure 1.5: Earthquake-Resistant and NOT Earthquake-Proof: Damage is expected during anearthquake in normal constructions (a) undamaged building, and (b) damaged building.The design for only a fraction of the elastic level of seismic forces is possible, only if thebuilding can stably withstand large displacement demand through structural damage withoutcollapse and undue loss of strength. This property is called ductility (Figure 1.6). It is relativelysimple to design structures to possess certain lateral strength and initial stiffness by appropriatelyproportioning the size and material of the members. But, achieving sufficient ductility is moreinvolved and requires extensive laboratory tests on full-scale specimen to identify preferablemethods of detailing.In summary, the loading imposed by earthquake shaking under the building is ofdisplacement-type and that by wind and all other hazards is of force-type. Earthquake shaking requiresbuildings to be capable of resisting certain relative displacement within it due to the imposeddisplacement at its base, while wind and other hazards require buildings to resist certain level offorce applied on it (Figure 1.7a). While it is possible to estimate with precision the maximum forcethat can be imposed on a building, the maximum displacement imposed under the building is notas precisely known. For the same maximum displacement to be sustained by a building (Figure1.7b), wind design requires only elastic behaviour in the entire range of displacement, but inearthquake design there are two options, namely design the building to remain elastic or toundergo inelastic behaviour. The latter option is adopted in normal buildings, and the former inspecial buildings, like critical buildings of nuclear power plants.HH, ΔroofGood DuctilityStrengthMedium DuctilityPoorDuctility0DeformabilityΔFigure 1.6: Ductility: Buildings are designed and detailed to develop favorable failure mechanismsthat possess specified lateral strength, reasonable stiffness and, above all, good post-yielddeformability.3Δ
ΔroofFwHForce LoadingWind Demandag(t)Δ0Earthquake DemandDisplacement Loading(a)HWind DesignEarthquake DesignOption 2Earthquake DesignOption 10ΔEarthquake Design(b)Figure 1.7: Displacement Loading versus Force Loading: Earthquake shaking imposes displacementloading on the building, while all other hazards impose force loading on it4Δ
1.3 THE FOUR VIRTUES OF EARTHQUAKE RESISTANT BUILDINGSFor a building to perform satisfactorily during earthquakes, it must meet the philosophy ofearthquake-resistant design discussed in Section 1.2.1.3.1 Characteristics of BuildingsThere are four aspects of buildings that architects and design engineers work with to createthe earthquake-resistant design of a building, namely seismic structural configuration, lateral stiffness,lateral strength and ductility, in addition to other asepcts like form, aesthetics, functionality andcomfort of building. Lateral stiffness, lateral strength and ductility of buildings can be ensured bystrictly following most seismic design codes. But, good seismic structural configuration can beensured by following coherent architectural features that result in good structural behaviour.(a) Seismic Structural ConfigurationSeismic structural configuration entails three main aspects, namely (a) geometry, shape andsize of the building, (b) location and size of structural elements, and (c) location and size ofsignificant non-structural elements (Figure 1.8). Influence of the geometry of a building on itsearthquake performance is best understood from the basic geometries of convex and concave lensesfrom school-day physics class (Figure 1.9). The line joining any two points within area of the convexlens, lies completely within the lens. But, the same is not true for the concave lens; a part of the linemay lie outside the area of the concave lens. Structures with convex geometries are pref
1.2 Basic Aspects of Seismic Design 2 1.3 The Four Virtues of Earthquake Resistant Buildings 5 1.3.1 Characteristics of Buildings 5 (a) Seismic Structural Configuration 5 (b) Structural Stiffness, Strength and Ductility 8 1.3.2 What are the Four Virtues? 9 (a) Who Controls the Four Virtues? 9 (b) How to Achieve the Four Virtues? 10
This earthquake was as big as:This earthquake was as big as: 500 Hiroshima bombs Half the eruption of Mt. St. Helens 11 Cape Mendocino earthquakes 1992 CAPE MENDOCINO RUPTURE 2004 Indonesian earthquake 1906 earthquake 1906 earthquake 2004 Indonesia How big was the 1906 Earthquake?
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