Seismic Design Of Reinforced Concrete Structures

10. Seismic Design of Reinforced Concrete StructuresFigure 10- 1. Components of and considerations inearthquake-resistant building design10.1.5The Need for a Good DesignConcept and Proper DetailingBecause of the appreciable forces anddeformations that can be expected in criticalregions of structures subjected to strong groundmotions and a basic uncertainty concerning theintensity and character of the ground motions ata particular site, a good design concept isessential at the start. A good design conceptimplies a structure with a configuration thatbehaves well under earthquake excitation anddesigned in a manner that allows it to respondto strong ground motions according to apredetermined pattern or sequence of yielding.The need to start with a sound structuralconfiguration that minimizes “incidental” andoften substantial increases in member forcesresulting from torsion due to asymmetry orforceconcentrationsassociatedwithdiscontinuities cannot be overemphasized.Although this idea may not be met with favorby some architects, clear (mainly economic)benefits can be derived from rity, and the avoidance of severediscontinuities in mass, geometry, stiffness, orstrength. A direct path for the lateral (inertial)forces from the superstructure to anappropriately designed foundation is verydesirable. On numerous occasions, failure totake account of the increase in forces anddeformations in certain elements due to torsionor discontinuities has led to severe structural467distress and even collapse. The provision ofrelative strengths in the various types ofelements making up a structure with the aim ofcontrolling the sequence of yielding in suchelements has been recognized as desirable fromthe standpoint of structural safety as well asminimizing post-earthquake repair work.An important characteristic of a good designconcept and one intimately tied to the idea ofductility is structural redundancy. Sinceyielding at critically stressed regions andsubsequent redistribution of forces to lessstressed regions is central to the ductileperformance of a structure, good practicesuggests providing as much redundancy aspossible in a structure. In monolithically castreinforced concrete structures, redundancy isnormally achieved by continuity betweenmoment-resisting elements. In addition tocontinuity, redundancy or the provision ofmultiple load paths may also be accomplishedby using several types of lateral-load-resistingsystems in a building so that a “backup system”can absorb some of the load from a primarylateral-load-resisting system in the event of apartial loss of capacity in the latter.Just as important as a good design conceptis the proper detailing of members and theirconnections to achieve the requisite strengthand ductility. Such detailing should aim atpreventing nonductile failures, such as thoseassociated with shear and with bond anchorage.In addition, a deliberate effort should be madeto securely tie all parts of a structure that areintended to act as a unit together. Becausedynamic response to strong earthquakes,characterized by repeated and reversed cyclesof large-amplitude deformations in criticalelements, tends to concentrate deformationdemands in highly stressed portions of yieldingmembers, the importance of proper detailing ofpotential hinging regions should command asmuch attention as the development of a gooddesign concept. As with most designs but moreso in design for earthquake resistance, wherethe relatively large repeated deformations tendto “seek and expose,” in a manner of speaking,weaknesses in a structure—the proper fieldimplementation of engineering drawings

468Chapter 10ultimately determines how well a structureperforms under the design loading.Experience and observation have shown thatproperly designed, detailed, and constructedreinforced-concrete buildings can provide thenecessary strength, stiffness, and inelasticdeformation capacity to perform satisfactorilyunder severe earthquake loading.10.1.6Accent on Design for StrongEarthquakesThe focus in the following discussion willbe on the design of buildings for moderate-tostrong earthquake motions. These casescorrespond roughly to buildings located inseismic zones 2, 3 and 4 as defined in theUniform Building Code (UBC-97).(10-1) Byemphasizing design for strong ground motions,it is hoped that the reader will gain anappreciation of the special considerationsinvolved in this most important loading case.Adjustments for buildings located in regions oflesser seismic risk will generally involverelaxation of some of the requirementsassociated with highly seismic areas.Because the requirement for greater ductilityin earthquake-resistant buildings represents theprincipal departure from the conventionaldesign for gravity and wind loading, the majorpart of the discussion in this chapter will bedevoted to considerations associated withproviding ductility in members and structures.The discussion in this chapter will beconfined to monolithically cast reinforcedconcrete buildings.10.2DUCTILITY INEARTHQUAKERESISTANT DESIGN10.2.1Design ObjectiveIn general, the design of economicalearthquake resistant structures should aim atproviding the appropriate dynamic andstructural characteristics so that acceptablelevels of response result under the designearthquake. The magnitude of the maximumacceptable deformation will vary dependingupon the type of structure and/or its function.In some structures, such as slender, freestanding towers or smokestacks or suspensiontype buildings consisting of a centrally locatedcorewall from which floor slabs are suspendedby means of peripheral hangers, the stability ofthe structure is dependent on the stiffness andintegrity of the single major element making upthe structure. For such cases, significantyielding in the principal element cannot betolerated and the design has to be based on anessentially elastic response.For most buildings, however, andparticularly those consisting of rigidlyconnected frame members and other multiplyredundant structures, economy is achieved byallowing yielding to take place in somecritically stressed elements under moderate-tostrong earthquakes. This means designing abuilding for force levels significantly lowerthan would be required to ensure a linearlyelastic response. Analysis and experience haveshown that structures having adequate structuralredundancy can be designed safely to withstandstrong ground motions even if yielding isallowed to take place in some elements. As aconsequence of allowing inelastic deformationsto take place under strong earthquakes instructures designed to such reduced forcelevels, an additional requirement has resultedand this is the need to insure that yieldingelements be capable of sustaining adequateinelastic deformations without significant lossof strength, i.e., they must possess sufficientductility. Thus, where the strength (or yieldlevel) of a structure is less than that whichwould insure a linearly elastic response,sufficient ductility has to be built in.10.2.2Ductility vs. Yield LevelAs a general observation, it can be statedthat for a given earthquake intensity andstructure period, the ductility demand increasesas the strength or yield level of a structuredecreases. To illustrate this point, consider two

10. Seismic Design of Reinforced Concrete Structuresvertical cantilever walls having the same initialfundamental period. For the same mass andmass distribution, this would imply the samestiffness properties. This is shown in Figure 102, where idealized force-deformation curves forthe two structures are marked (1) and (2).Analyses(10-2, 10-3) have shown that the maximumlateral displacements of structures with thesame initial fundamental period and reasonableproperties are approximately the same whensubjected to the same input motion. Thisphenomenon is largely attributable to thereduction in local accelerations, and hencedisplacements, associated with reductions instiffness due to yielding in critically stressedportions of a structure. Since in a verticalcantilever the rotation at the base determines toa large extent the displacements of points abovethe base, the same observation concerningapproximate equality of maximum lateraldisplacements can be made with respect tomaximum rotations in the hinging region at thebases of the walls. This can be seen in Figure10-3, from Reference 10-3, which shows resultsof dynamic analysis of isolated structural wallshaving the same fundamental period (T1 1.4sec) but different yield levels My. The structureswere subjected to the first 10 sec of the east—west component of the 1940 El Centro recordwith intensity normalized to 1.5 times that ofthe north—south component of the same469record. It is seen in Figure 10-3a that, except forthe structure with a very low yield level (My 500,000 in.-kips), the maximum displacementsfor the different structures are about the same.Thecorrespondingductilitydemands,expressed as the ratio of the maximum hingerotations, θmax to the corresponding rotations atfirst yield, θy, are shown in Figure 10-3b. Theincrease in ductility demand with decreasingyield level is apparent in the figure.Figure 10-2. Decrease in ductility ratio demand withincrease in yield level or strength of a structure.Figure 10-3. Effect of yield level on ductility demand. Note approximately equal maximum displacements for structureswith reasonable yield levels. (From Ref. 10-3.)

470A plot showing the variation of rotationalductility demand at the base of an isolatedstructural wall with both the flexural yield leveland the initial fundamental period is shown inFigure 10-4.(10-4) The results shown in Figure10-4 were obtained from dynamic inelasticanalysis of models representing 20-storyisolated structural walls subjected to six inputmotions of 10-sec duration having differentfrequency characteristics and an intensitynormalized to 1.5 times that of the north—southcomponent of the 1940 El Centro record.Again, note the increase in ductility demandwith decreasing yield level; also the decrease inductility demand with increasing fundamentalperiod of the structure.Chapter 10The above-noted relationship betweenstrength or yield level and ductility is the basisfor code provisions requiring greater strength(by specifying higher design lateral forces) formaterials or systems that are deemed to haveless available ductility.10.2.3Some Remarks about DuctilityOne should note the distinction betweeninelastic deformation demand expressed as aductility ratio, µ (as it usually is) on one hand,and in terms of absolute rotation on the other.An observation made with respect to onequantity may not apply to the other. As anexample, Figure 10-5, from Reference 10-3,Figure 10-4. Rotational ductility demand as a function of initial fundamental period and yield level of 20-story structuralwalls. (From Ref. 10-4.)

10. Seismic Design of Reinforced Concrete Structuresshows results of dynamic analysis of twoisolated structural walls having the same yieldlevel (My 500,000 in.-kips) but differentstiffnesses, as reflected in the lower initialfundamental period T1 of the stiffer structure.Both structures were subjected to the E—Wcomponent of the 1940 El Centro record. Eventhough the maximum rotation for the flexiblestructure (with T1 2.0 sec) is 3.3 times thatof the stiff structure, the ductility ratio for thestiff structure is 1.5 times that of the flexiblestructure. The latter result is, of course, partlydue to the lower yield rotation of the stifferstructure.rotation per unit length. This is discussed indetail later in this Chapter.Another important distinction worth notingwith respect to ductility is the differencebetween displacement ductility and rotationalductility. The term displacement ductility refersto the ratio of the maximum horizontal (ortransverse) displacement of a structure to thecorresponding displacement at first yield. In arigid frame or even a single cantilever tion, the lateral displacement of thestructure is achieved by flexural yielding atlocal critically stressed regions. Because of this,it is reasonable to expect—and results ofanalyses bear this out(10-2, 10-3, 10-5)—thatrotational ductilities at these critical regions aregenerally higher than the cement ductility ratios of 3 to 6 mayimply local rotational ductility demands of 6 to12 or more in the critically stressed regions of astructure.10.2.4The term “curvature ductility” is also acommonly used term which is defined asResults of a Recent Study onCantilever WallsIn a recent study by Priestley and Kowalskyon isolated cantilever walls, it has beenshown that the yield curvature is not directlyproportional to the yield moment; this is incontrast to that shown in Figure 10-2 which intheir opinions leads to significant errors. In fact,they have shown that yield curvature is afunction of the wall length alone, for a givensteel yield stress as indicated in Figure 10-6.The strength and stiffness of the wall varyproportionally as the strength of the section ischanged by varying the amount of flexuralreinforcement and/or the level of axial load.This implies that the yield curvature, not thesection stiffness, should be considered thefundamental section property. Since wall yieldcurvature is inversely proportional to walllength, structures containing walls of differentlength cannot be designed such that they yieldsimultaneously. In addition, it is stated that walldesign should be proportioned to the square of(10-6)Figure 10-5. Rotational ductility ratio versus maximumabsolute rotation as measures of inelastic deformation.471

472Chapter 10wall length, L2, rather than the current designassumption, which is based on L3 .It should be noted that the above findingsapply to cantilever walls only. Further researchin this area in various aspects is currentlyunderway at several institutions.M1MIn certain members, such as conventionallyreinforced short walls—with height-to-widthratios of 2 to 3 or less—the very nature of theprincipal resisting mechanism would make ashear-type failure difficult to avoid. Diagonalreinforcement, in conjunction with horizontaland vertical reinforcement, has been shown toimprove the performance of such members (10-7).10.3.2M2M3yFigure 10-6. Influence of strength on moment-curvaturerelationship (From Ref. 10-6).10.3BEHAVIOR OFCONCRETE MEMBERSUNDER EARTHQUAKETYPE LOADING10.3.1General Objectives of MemberDesignA general objective in the design ofreinforced concrete members is to so proportionsuch elements that they not only possessadequate stiffness and strength but so that thestrength is, to the extent possible, governed byflexure rather than by shear or bond/anchorage.Code design requirements are framed with theintent of allowing members to develop theirflexural or axial load capacity before shear orbond/anchorage failure occurs. This desirablefeature in conventional reinforced concretedesign becomes imperative in design forearthquake motions where significant ductilityis required.Types of Loading Used inExperimentsThe bulk of information on behavior ofreinforced-concrete members under load has‘generally been obtained from tests of full-sizeor near-full-size specimens. The loadings usedin these tests fall under four broad categories,namely:1. Static monotonic loading—where load inone direction only is applied in increments untilfailure or excessive deformation occurs. Datawhich form the basis for the design ofreinforced concrete members under gravity andwind loading have been obtained mainly fromthis type of test. Results of this test can serve asbases for comparison with results obtained fromother types of test that are more representativeof earthquake loading.2. Slowly reversed cyclic (“quasistatic”)loading—where the specimen is subjected to(force or deformation) loading cycles ofpredetermined amplitude. In most cases, theload amplitude is progressively increased untilfailure occurs. This is shown schematically inFigure 10-7a. As mentioned earlier, much of thedata upon which current design procedures forearthquake resistance are based have beenobtained from tests of this type. In a few cases,a loading program patterned after analyticallydetermined dynamic response(10-8) has beenused. The latter, which is depicted in Figure 107b, is usually characterized by large-amplitudeload cycles early in the test, which can produceearly deterioration of the strength of aspecimen.(10-9) In both of the above cases, theload application points are fixed so that themoments and shears are always in phase—acondition, incidentally, that does not alwaysoccur in dynamic response.

10. Seismic Design of Reinforced Concrete Structures473Figure 10-7. Two types of loading program used in quasi-static tests.This type of test provides the reversingcharacter of the loading that tional static loading. In addition, therelatively slow application of the load allowsclose observation of the specimen as the testprogresses. However, questions concerning theeffects of the sequence of loading as well as thephase relationship between moment and shearassociated with this type of test as it is normallyconducted need to be explored further.3. Pseudo-dynamic tests. In this type of test,the specimen base is fixed to the test floor whiletime-varying displacements determined by anon-line computer are applied to selected pointson the structure. By coupling loading rams witha computer that carries out an incrementaldynamic analysis of the specimen response to apreselected input motion, using measuredstiffness data from the preceding loadingincrement and prescribed data on specimenmass and damping, a more realistic distributionof horizontal displacements in the test structureis achieved. The relatively slow rate at whichthe loading is imposed allows convenientinspection of the condition of the structureduring the progress of the test.This type of test, which has been usedmainly for testing structures, rather thanmembers or structural elements, requires afairly large reaction block to take the thrustfrom the many loading rams normally used.4. Dynamic tests using shaking tables(earthquake simulators). The most realistic testconditions are achieved in this setup, where aspecimen is subjected to a properly scaled inputmotion while fastened to a test bed impelled bycomputer-controlled actuators. Most currentearthquake simulators are capable of impartingcontrolled motions in one horizontal directionand in the vertical direction.The relatively rapid rate at which theloading is imposed in a typical dynamic testgenerally does not allow close inspection of thespecimen while the test is in progress, althoughphotographic records can be viewed after thetest. Most currently available earthquakesimulators are limited in their capacity to smallscale models of multistory structures or nearfull-scale models of segments of a structure oftwo or three stories. The difficulty of viewingthe progress of damage in a specimen as theloading is applied and the limited capacity ofavailable (and costly) earthquake simulators hastended to favor the recently developed pseudodynamic test as a basic research tool for testingstructural systems.The effect of progressively increasing lateraldisplacements on actual structures has beenstudied in a few isolated cases by means offorced-vibration testing. These tests haveusually been carried out on buildings orportions of buildings intended for demolition.

47410.3.3Chapter 10Effects of Different Variables onthe Ductility of ReinforcedConcrete MembersFigure 10-8 shows typical stress—straincurves of concrete having different compressivestrengths. The steeper downward slope beyondthe point of maximum stress of curvescorresponding to the higher strength concrete isworth noting. The greater ductility of the lowerstrength concrete is apparent in the figure.Typical stress-strain curves for the commonlyavailable grades of reinforcing steel, withnominal yield strengths of 60 ksi and 40 ksi, areshown in Figure 10-9. Note in the figure thatthe ultimate stress is significantly higher thanthe yield stress. Since strains well into thestrain-hardening range can occur in hingingregions of flexural members, stresses in excessof the nominal yield stress (normally used inconventional design as the limiting stress insteel) can develop in the reinforcement at theselocations.Figure 10-8. Typical stress-strain curves for concrete ofvarying compressive strengths.Rate of Loading An increase in the strainrate of loading is generally

10. Seismic Design of Reinforced Concrete Structures 465 10.1 INTRODUCTION 10.1.1 The Basic Problem The problem of designing earthquake-resistant reinforced concrete buildings, like the design of structures (whether of concrete, steel, or other material) for other loading