ANALYSIS AND DESIGN OF STRUCTURES IVNAVEEN KUMAR S ACE10UAR021SEM 8 ACE,HOSURINNOVATIVE WORKSELL STRUCTURE & FOLDED PLATES ?Thinshellisdefinedasashellwithathicknesswhichissmallcomparedtoitsotherdimensionsandinwhichdeformationsarenotlargecomparedtothicness.Aprimarydifferencebetweenashellstructureandaplatestructureisthat,intheunstressedstate,theshellstructurehascurvatureasopposedtoplatesstructureswhichareflat.Membraneactioninashellisprimarilycausedbyin-planeforces(planestress),thoughtheremaybesecondaryforcesresultingfromflexuraldeformationsFolded PlatesBarrel VaultsShort ShellsDomes of RevolutionFolded Plate DomesIntersection ShellsWarped SurfacesCombinationsShell ArchesTYPESCYLINDRICAL BARREL VAULTSBarrelvaultsareperhapsthemostusefuloftheshellstructuresbecausetheycanspanupto150feetwithaminimumofmaterial.Theyareveryefficientstructuresbecausetheusethearchformtoreducestressesandthicknessesinthetransversedirection.BarrelvaultsareessentiallydeepconcretebeamswithverythinwebmembersandmaybedesignedassuchbytheordinarymethodsofreinforcedconcreteThecurveofthecrosssectionofthebarrelisusuallyacircle.However,anyotherformmaybeused,suchastheellipse,aparabola,orafunicularcurvewhichfitsthethrustlineoftheappliedload.Eachcurvehasitsparticularstructuralandestheticqualities.Anumberoftermshavebeendevelopedtodescribecylindricalshells.Ifthespanislargeincomparisontothewidth,theformiscalledalongshell.Ifthelengthisshort,itiscalledashortshell.Anarbitraryratioforlongshellsisaspan/radiusratioof5.Ashortshellhasaspan/radiusrationlessthan1andshellsbetweentheselimitsarecalledintermediateshells.Elements of Barrel VaultsMultiple Barrels - Outside StiffenersELEMENTSOFBARRELVAULTSStiffenersarerequiredatcolumns.Theydonotnecessarilyhavetobecompletediaphragms,asshownhere,butmaybearcheswithahorizontaltie.Incontrasttofoldedplateswherethethicknessisbasedonthedesignofaslabelement,thethicknessofthebarrelshellisusuallybasedontheminimumthicknessrequiredforcoveringthesteelforfireproofing,plusthespacerequiredforthreelayersofbars,plussomespacefortolerance.Ifthesebarsareallhalfinchrounds,apracticalminimumwouldbe31/4inches.Nearthesupportsthethicknessmaybegreaterforcontainingthelargerlongitudinalbars.MULTIPLEBARRELS-OUTSIDESTIFFENERSCorrugated CurvesBarrel with Unstiffened EdgesEdge Supported ShellsUNSTIFFENEDEDGESCORRUGATEDCURVESThe Lazy STHELAZYSEdge MembersEDGEMEMBERSEDGESUPPORTEDSHELLSNorth Light ShellsNORTHLIGHTSHELLSButterfly ShellsBUTTERFLYSHELLSTYPESRigid FramesSHORT SHELLS barrelvaultsweredescribedhavingalengthofbarrelwhichislongincomparisontothewidth.theshortshellstructureisacylindricalshellhavingalargeradiusincomparisontothelength.Thetwotypesofshellshaveuseswhicharealtogetherdifferentandthearchitecturalandengineeringproblemsrequireadifferentapproach.Thereare,ofcourse,borderlinecaseswhereitisdifficulttodistinguishbetweenthelonganshortshell.Basic elements of Short ShellsBASICELEMENTSOFSHORTSHELLS1)theshellspanningbetweenarches,and2)thearchstructure.Inthisstructure,theedgebeamsareprovidedatthelowestpointoftheshellandthearchisplacedontopoftheshellsothatformsmaybemovedthroughthebarrel.Insmallstructures,theedgebeamcanbeomittediftheshellisthickened.Thecurveoftheshellisdeterminedbythepropershapeofthearchandmaybeacircleforsmallstructuresormayconformtothethrustlineofthearchforongspanstructures.:Pure Arch and ShellPUREARCHANDSHELLMassive AbutmentsMASSIVEABUTMENTSRIGIDFRAMESShortshellsmaybeusedwithconcreterigidframesastheprinciplestructuralelement.Therigidframewithoutahorizontaltieatthelowpointoftheshellissuitableonlyforshortspansbecauseofthemassiveproportionsrequiredforthknees.Itisnotnecessarytohavethespansofalltherigidframesequal,andthebendingmomentsintheframesmaybereducedifshortersidespansareused.Skylightsmaybeusedinashortshellandtheymaybecontinuoustransverselyiftheyareplacedineveryotherspansotheshelloneachsideoftheskyligtcantileversoutfromtheadjacentspan.Rigidframesareusuallybuiltwithtierodsconnectingthebaseofthecolumns,especiallyifsoilconditionswillnotpermitlateralloadsonthesoilmaterial.DomesTheprimaryresponseofadometoloadingisdevelopmentofmembranecompressivestressesalongthemeridians,byanalogytothearch.Thedomealsodevelopscompressiveortensilemembranestressesalonglinesoflatitude.Theseareknownashoopstressesandaretensileatthebaseandcompressivehigherupinthedome.C:\SAP2000N\tom\half dome example.emfMeridional Compressive StressCircumferential Hoop Stress (comp.)Circumferential Hoop Stress (tens.)SPHERESEGMENT-COLUMNSUPPORTSIfadomeisbuiltaslessthanahalfsphere,atensionringofsteelbars,plates,orwiresisrequiredatthebasetocarrythethrustsoftheshell.Inthiscase,theringhasbeenmadebigenoughsothatitassistsindistributingthereactionofthecolumnsintothedome.Thedirectstressesintheshellaremostlycompressiveinthisstructureandaresosmallthatthestresscalculationsarehardlynecessary.Therearebendingstressesintheshellwallduetorestraintofthethrustringandtochangeintemperature.Therefore,thethicknessoftheshellisincreasedinthevicinityofthethrustring.Otherwise,theshellthicknessisaminimumandmaybe21/2to3inchesforspansupto150ft.Multiple DomesMULTIPLEDOMESShallow Square Intersection ShellINTERSECTIONSHELLScombiningportionsoftheprevioustypesarrangedtoformmorestablecombinationsthantheindividualelementsalone.Themostappropriatenameis"intersectionshell"becausethesurfacesthatproducetheshellappeartomeetatanintersection.Anyofthebasictypesmaybeusedinthismannerbutthebarrelshellisthemostfamiliaranduseful.Thestructuralefficiencyoftheintersectionshelldependsontheangleoftheintersectionofthesurfaces.Iftheangleissmall(calledherefordescriptivepurposes,sharp),thenanaturalribisformedbytheadjacentelementsofthebasicshellswhichismuchstifferthantheadjacentshellsoneachside.Anitersectionforwhichtheangleisverylargeiscalledhereashallowintersection.Anintersectionof90degreesistheoptimumvaluebecauseitgivesastiffrib.C:\SAP2000N\tom\folded plate example.emfFolded PlatesFolded plates are assemblies of flat plates rigidly connected together along their edges.in such a way so as to make the structural system capable of carrying loads without .the need for additional supporting beams along mutual edges.Types of folded plates :1-Prismatic : if they consist of rectangular plates.2-Pyramidal : when non-rectangular plates are used.3-Prismoidal, triangular or trapezoidal.Perpendicular to the main span, the shell acts as short span plates in transverse bendingIn the main span direction, the shell develops membrane tension at the top and compression at the bottom, in analogy to a beam in bendingclassified as:single.Multiple.Symmetrical.Unsymmetrical.Simple.Continuous.Folded plates with simple joints.Folded plates with multiple joints.Folded plates with opened cross sectional.Folded plates with closed cross sectional.FoldedPlateBehaviors:Eachplateisassumedtoactasabeaminitsownplane,thisassumptionisjustifiedwhentheratioofthespan"length"oftheplatetoitsheight"width"islargeenough.Butwhenthisratioissmall,theplatebehavesasadeepbeam.Assumptions For the analysis of Folded Plates :1-Material is homogenous, elastic, isotropic, Hook's Law is valid, thickness of plate is small when compared to plate dimensions.2-Problem will be treated as one-dimension if plate is assumed to behave in beam action, but in two dimensions if based on the theory of elasticity.3-Joints are assumed to be rigid enough.NOTE :The main problem of folded plates is the analysis, not the design.When can ridge displacements be neglected ?Ridge displacements be neglected if there is no ridge displacement such as: -closed systems.-If the folded plate system is under symmetrical loading.-In folded plate systems with interior symmetrical planes, subjected to symmetrical loads. But in other cases ridge displacements may take place, yet they are such a small order of magnitude that their effects can be neglected, as folded plate system provided with adequate number of intermediate diaphragms.Folded Plates With Simple JointWhen the folded plate is that with simple joint , which mean that no more than 2 elements are connected to the joint. But when more than 2 elements are connected to the joint, it can be named as multiple joint. The width of any plate should not be larger than 0.25 its length to be considered to act as beam. Actions of Folded plate due to loads :1-Slab action : loads are transmitted to ridges by the bending of plates normal to their planes.2-Beam action : Loads are transmitted through plates in their planes to diaphragms.TAPERED FOLDED PLATESBASIC ELEMENTSThe principle components in a folded plate structure are illustrated in the sketch above. They consist of, 1) the inclined plates, 2) edge plates which must be used to stiffen the wide plates, 3) stiffeners to carry the loads to the supports and to hold the plates in line, and 4) columns to support the structure in the air. A strip across a folded plate is called a slab element because the plate is designed as a slab in that direction. The span of the structure is the greater distance between columns and the bay width is the distance between similar structural units. The structure above is a two segment folded plate. If several units were placed side by side, the edge plates sould be omitted except for the first and last plate. If the edge plate is not omitted on inside edges, the form should be called a two segment folded plate with a common edge plate.The structure above may have a simple span, as shown, or multiple spans of varying length, or the folded plate may cantilever from the supports without a stiffener at the end.FOLDED PLATE RIGID FRAMEREINFORCEMENT DETAIL OF FLAT SLAB ?SPACING:The spacing of bars in a flat slab, shall not exceed 2 times the slab thickness.AREA OF REINFORCEMENT :When the drop panels are used, the thickness of drop panel for determining area of reinforcementshall be the lesser of the following:(a) Thickness of drop, and(b) Thickness of slab plus one quarter the distance between edge of drop and edge of capital. The minimum percentage of the reinforcement is same as that in solid slab i.e., 0.12 percent if HYSD bars used and 0.15 percent, if mild steel is used.MINIMUM LENGTH OF REINFORCEMENT :At least 50 percent of bottom bars should be from support to support. The rest may be bent up. The minimum length of different reinforcement in flat slabs should