Gioncu [Framed Structures. Ductility and Seismic Response - 2000]

Journal of Constructional Steel Research 55 (2000) 125–154www.elsevier.com/locate/jcsr

Framed structures. Ductility and seismicresponse

General Report

V. Gioncu *

Department of Architecture, Politehnica University Timisoara, 1900 Timisoara, Romania

Abstract

The purpose of this general report is to review the state-of-the art research works for ductilityrelated to seismic response of framed structures. The required ductility is determined at thelevel of full structure behaviour, while the available ductility is obtained as local behaviourof node (joint panel, connections or member ends). The checking for ductility may be perfor-med for monotonic or seismic loads. For monotonic loads, the push-over method is developedin simplified form proposed by Mazzolani and Piluso, on the basis of a rigid plastic globalmechanism. The result is the required ductility. In the same way, a local plastic mechanismis used for determining the available ductility. For seismic loads, the differences between near-source and far-source earthquakes are emphasized, which induces some important modificationon required ductility. The factors regarding seismic actions, such as velocity and cycling load-ing, reduce the available ductility. Finally using these results, the designer is able to verify ifthe available ductility is greater than the required ductility. 2000 Elsevier Science Ltd. Allrights reserved.

Keywords:Available ductility; Required ductility; Push-over method; Time-history method; Standardbeam; Component method

1. Introduction

In the design of framed structures for static and seismic actions engineers haverecognized the need to account for different purposes the plastic design. The staticanalysis is accounted with the inelastic force redistribution in the calculations of loadeffects. For the seismic analysis, the interest is intended on dissipation of input seis-

* Tel.: +40-56-203125; fax:+40-56-203125, 192998.

0143-974X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.PII: S0143 -974X(99)00081-4

126 V. Gioncu / Journal of Constructional Steel Research 55 (2000) 125–154

mic energy. The basic design parameter in both approaches is theductility, con-sidered as the ability of the structure to undergo large plastic deformations withoutlosing strength. In the design practice it is generally accepted that steel is an excellentmaterial for these due to performance in terms of ductility. But in the last decadesspecialists have recognized that so-called good ductility of steel structures may be,in some particular conditions, only a dogma, which is derived by the reality. In fact,the recent earthquakes of Mexico City (1985) Loma Prieta (1989) Northridge (1994)and Kobe (1995) have seriously compromised this idyllic image of steel as a perfectmaterial for seismic areas. In some cases the performance of steel joints and memberswas very bad and large damage was produced, showing that in special conditions,the present design concepts are not sufficiently, being too vague for a proper design:“When plastic global analysis is used, the members shall be capable of formingplastic hinges with sufficient rotation capacity to enable the required redistributionof bending moment to develop” (EUROCODE 3, Section 5.3.1). “Sufficient localductility of members or parts of members in compression shall be assured”(EUROCODE 8, Section 3.5.3.1). These two examples show some very indefiniteprovisions of codes, for the structural designer it is essential to have a clear definitionof what “sufficient rotation capacity” or “sufficient local ductility” means. Aimingto supply these lacks, the codes contain some constructional rules, considering thatthe fulfill of them assures a good ductility. But the above mentioned bad behavioursof steel structures have shown that this conception is not proper and the verificationof structure ductility must be quantified at the same level as the strength and stiffness.

In the past, a great amount of research works were devoted to the developmentof a transparent methodology that takes into account therequired ductility, in func-tion on the main characteristics of ground motions and full structure behaviour, andthe available ductility, given by the local behaviour of the nodes (joint panels, con-nections and member ends). The design objective for ductility is to verify if theavailable ductility is greater than the required ductility.

2. Basic design philosophy for ductility

Before the 1960s the ductility notion has been used only for characterizing thematerial behaviour, after Baker’s studies in plastic design and Housner’s researchworks in earthquake problems, this concept has been extended at the level of structureand is associated with the notions of strength and stiffness of the whole structure.But after years of using this concept today it continues to be an ambiguous parameter.In the practice of plastic design of structures, ductility defines the ability of a struc-ture to undergo deformations after its initial yield without any significant reductionin ultimate strength. The ductility of a structure allows prediction of the ultimatecapacity of a structure, which is the most important criterion for designing structuresunder conventional loads. In the practice of earthquake resistant design, the termductility is used for evaluating the seismic performance of structures, by indicatingthe quantity of seismic energy which may be dissipated through plastic deformations.The use of ductility concept gives the possibility to reduce seismic design forces

127V. Gioncu / Journal of Constructional Steel Research 55 (2000) 125–154

and allows the production of some controlled damage in the structure, also in caseof strong earthquakes.

The following ductility types are widely used in literature (Fig. 1):

O material ductility, or axial ductility, which characterizes the material plastic defor-mations;

O cross-section ductility, or curvature ductility, which refers to the plastic defor-mations of cross-section, considering the interaction between the parts composingthe cross-section itself;

O member ductility, or rotation ductility, when the properties of member are con-sidered;

O structure ductility, or displacement ductility, which considers the behaviour of thewhole structure.

In Fig. 1 the subscriptu refers to the ultimate deformation (strain, curvature, rotation

Fig. 1. Ductility types.


or displacement), while subscripty indicates the corresponding deformation for firstyielding. Referring to the ultimate deformation, the collapse of an element can bereached by plastic deformations limited by buckling (Fig. 2(a)) or by fracture (Fig.2(b)) of some components. So, the ductility can be:

O deformation ductility, when the collapse is due to buckling of a compressedelement;

O fracture ductility, when the collapse is the result of the fracture of a tensionedelement.

There are many disputable problems in the above definitions, due to the fact thatthey have precise definition and quantitative meaning only for the case of monotoneand linear elasto-perfectly plastic behaviour. Their use in actual cases, where thestructural behaviour significantly differs from the idealized ones, leads to much ambi-guity and confusion [1]. One of the most significant confusions is to judge the steelstructure ductility according to the material ductility, obtained by an uniaxial tensiontest for monotoning loading. One must be aware of the fact that the result obtainedfrom axial tests never represents the actual behaviour of steel in a structure. Fornon-normal conditions, as uncontrolled random variability of yield stress, reducedtemperatures, shock-loading, earthquake attack, many of the good performance ofsteel may be lost by an erosion of the native properties (Fig. 3). The factors influenc-ing this erosion are presented in Fig. 4, being divided in element factors (material,cross-section, members) and joint factors (panel zones, column flanges,connections) [2].

For assessment ofrequired ductility it is necessary to gather information oncharacteristics of possible earthquake on the site of the structure. Due to the coinci-dence or near-coincidence of the natural periods of ground motions and fundamentalperiods of structure, an amplification of required ductility occurs (Fig. 5). A signifi-cant progress has recently been made in the development and application of innov-

Fig. 2. Deformation and fracture ductilities.


Fig. 3. Erosion of native steel properties.

Fig. 4. Factors influencing the available ductility.

ative systems for seismic protection, reducing this amplification. The factors influ-encing the amplification of ground motions are presented in Fig. 6. The requiredductility is directly influenced by ground motions (source, distance from source, siteconditions) and structural systems (foundations, structure types, non-structuralelements).


Fig. 5. Amplification of required ductility.

Fig. 6. Factors influencing the required ductility.

Ductility of a structure is provided by satisfying the limit state criterion:

Da

gm$gFDr (1)

whereDa is the available ductility determined from the local plastic deformation andDr, is the required ductility obtained from the global plastic behaviour of structure.The partial safety factorsgm for available ductility andgF for required ductility must


be determined considering the scatter of data with a mean plus one standard variationand the uncertainties in available and required capacities. Values ofgm=1.3 andgF=1.2 are proposed for this verification, if the ductility is obtained by deformationductility. If the available ductility results from fracture, a greater value forgF mustbe used (i.e.gF=1.5).

In an effort to develop methods based on ductility it is clear that the evaluationof the inelastic response is required. For moment resisting frames (MRFs) inelasticdeformations correspond to the formation of plastic hinges at localized positions.Available ductility is therefore associated with the rotation capacity of plastic hinges.This one may be localized in one of the node components: panel zone, connectionsor member ends. Due to the multitude of influencing parameters a macroscopic viewof the node by subdividing it into individual basic components has proved to bemost appropriate. This approach for determining the local ductility is known as thecomponent method[3]. The assumption considered in this method allows us to deter-mine the overall rotation as the sum of the all components and the node ductilityby the ductility of the weaker component (Fig. 7).

Required ductility on the other hand is associated with the global behaviour whichis a function of the member of plastic hinges as well as the amount of plastic rotationthey undergo. For plastic analysis of a moment resisting frame, the methods availableto the designer are either monotonic static nonlinear analyses (push-over type) ordynamic time-history analyses (Fig. 8). Of course the last ones are more effective,but they require special computer programs which are not available for all designoffices. At the same time the time-history methods are large computation time con-sumer and they are very expensive. The push-over methods, if the conditions ofloads and local behaviour are proper designed, may provide sufficient informationin the expected behaviour for design purposes.

Fig. 7. Component methodology.


Fig. 8. Push-over and time-history analyses.

3. Ductility under monotonic loading

Checking the structure ductility, there are three problems which must be solved:(i) the global behaviour determined by push-over analysis, in which the requiredductilities of components are obtained; (ii) the calculation of available ductilities ofcomponents; (iii) evaluation of required/available ductility ratios for all components.

3.1. Required ductility

For determining therequired ductilitypush-over analysis is used. The structure issubjected to incremental lateral loads, using one or more predetermined load patternsof horizontal forces. These load patterns are supposed to bind the lateral load distri-butions that will occur when the structure is subjected to earthquakes that causesignificant inelastic deformations. The determining of this pattern is a very difficulttask, because it depends on the influence of superior vibration modes and the pro-gressive plastic hinge formation. For any given distribution the static behaviour isdefined by the pattern of loading,a, which increases monotonically, and the topsway displacement,d [4]. The response of structure under monotonic horizontal iscompletely described by the behavioural curvea–d (Fig. 9). The behavioural curvecomprises four branches. The first part represents the phase of elastic behaviour,extended from the origin until the point of first yielding is reached, for the parametersay, anddy. The second part is a nonlinear one due to the process of plastic hingeformation and the plastic redistribution capacity until the maximum multiplieramax

and the corresponding displacementdmax are reached. The third part is a softening


Fig. 9. Structure behaviour under monotonic loading.

branch and it is characterized by the fact that the structure is still indeterminate andthe process of plastic hinge formation is in progress until a kinematic mechanism isformed, corresponding to the displacementdmax. This part is strictly related to thetype of collapse mechanism and the magnitude of vertical loads. The ultimate partdescribes the collapse of structure. After reaching first yielding, a plastic rotation ofsuccessively formed plastic hinges is developed. All these plastic hinges must besupervised because in many cases other than the first one develops the maximumvalue.

A simplified methodology for push-over analysis based on the rigid plastic collapse


mechanism is developed by Mazzolani and Piluso [5], by substituting the actualcurve with a tri-linear one (Fig. 10). The first part is an elastic one and correspondsto linear behaviour. The equilibrium curve of collapse mechanism is determined bysecond-order rigid-plastic analyses and can be described by the following relation-ship:

a5a02gsd (2)

in which a0, is the collapse multiplier of the seismic horizontal forces, obtained bya rigid-plastic analysis andgs is the slope of the liniarized mechanism equilibriumcurve, determined in function of mechanism type. The cusp produced by the intersec-tion of elastic curve and mechanism equilibrium curve is cut by a horizontal straightline, corresponding to a point of the mechanism equilibrium curve with a sway dis-placement equal to 2.5 times the elastic displacement. The required rotation of plastichinges can be determined by the relationship:

qpr51

H0(du2dy) (3)

whereH0 is the sum of the interstory heights of stroreys involved in the collapsemechanism. The ultimate displacement value can be determined at same level ofultimate loads, corresponding to different performance criteria (operational, life safe,near collapse).

Concerning the collapse mechanisms of frames under horizontal forces Mazzolani

Fig. 10. Tri-linear simplified force-displacement curve.


Fig. 11. Plastic mechanism types.

and Piluso [6] have established three main types (Fig. 11), the global plastic mech-anism being a particular case of second type mechanism. In this figure is also shownthe active height part of structure. In the aim to obtain one of the three plasticmechanisms the design philosophy must consider that inelastic deformations occurin beams or columns. In function, the position of plastic hinges results in the casesof strong column–weak beam design (SC–WB, the beam being detailed to be weakerthan the adjoining columns) and weak column–strong beam design (WC–SB, thecolumn being considered the members to undergo plastic deformation). For a distri-bution of seismic loads corresponding to the first vibration mode, the required duc-tilities for the two mechanism types are plotted in Fig. 12 (after Bertero and Bertero

Fig. 12. Required ductilities for SC–WI3 and WC–SB.


[7]). One can see that the WC–SB system gives very large required ductilities,especially for structures with large vibration periods.

The push-over method is relatively simple to implement, but contains a great num-ber of assumptions and approximations that may be reasonable in some cases andunreasonable in others. Especially, in the case where superior vibration modes haveimportant effects, the obtained results can be very far from the actual behaviour ofstructures. Thus, the interpretation of results must be done within the context of usedassumptions [8].

3.2. Available ductility

For available ductility, obtained as a local ductility, the design philosophy mustconsider that the inelastic deformations occur in one or more of the three componentsof a node i.e. beam or column ends, connections and panel zones (Fig. 13). Moderncodes impose that plastic deformation must occur only at the beam ends and thecolumn bases, without considering the joint panels, even if it is well-known thatthese show a stable behaviour under plastic shear deformations. But in reality therequired conditions (the joint capacity must be 20% stronger than the adjacentmembers) do not assure the elastic behaviour of joints and as a consequence, thepanel zone can be in some cases the weakest component of joint. Results of so calledweak panel zone–strong column system (WP–SC), in which the panel zones aredesigned to be the weakest element of the node and the inelastic deformations areexpected to occur in panel zones. Fig. 14 shows the developing process of plastichinge in a frame in the function of the panel joint and members moment ratios [9].The white circles indicate that the the yields occur at joint panels and blank circlesthe development of plastic hinges in members. Taking into account the variabilityof material qualities the case of reduced plastic moment of joint panels is expected.

Fig. 13. Components of frame nodes.


Fig. 14. Plastic hinges in joint panels and member ends.

So, one can see that the neglection of plastic deformations of joint panels in theframe analysis is a miscalculation.

The ductility of membersis an other dispute between the code provisions andresearchers, concerning the use of ductility determined at the level of cross-section(as in EUROCODE 3) or it is necessary to use the ductility of members as proposedby Mazzolani and Piluso [10] and Gioncu and Mazzolani [11]. The code provisionsare particularly qualitative, so this procedure is inadequate for a methodology inwhich the available ductility is compared with the required one. A proper availableductility must be determined taking into account that the members and joints belongto a structure with a complex behaviour. But this is a very difficult task due to thegreat number of factors influencing the behaviour of the actual member and joint.Thus it is important to simplify the analysis by using for actual elements a simplesubstitute with a similar behaviour [12]. For a member, this is thestandard beam,determined in a structure by the position of inflection points (Fig. 15). Thus, actualstructure can be replaced by a combination of standard beams for which the ductilitycan be separately determined. There are two standard beam types, the first, SB1,with a central concentrated load for the beams under moment gradient, and thesecond, SB2, with the distributed load for quasi-uniform moment. The member duc-tility is determined by the rotation capacity of a standard beam using the momentrotation curve (Fig. 16(a)). The formulae to calculate the available rotation capacityis given by:

Ra5qrp

qp

5qr

qp

21 (4)

whereqrp is the ultimate plastic rotation;qp is the rotation corresponding to the firstplastic hinge andqr is the total ultimate rotation. The problem of evaluating therotation capacity has recently been of primary interest, as testified by the numerouspublished papers, presenting different methods which can be classified into the theor-etical methods (based on using FEM, or integrating the moment-curvature


Fig. 15. Standard beams.

Fig. 16. Rotation capacity of standard beam.


relationship), approximate methods (based on the use of the collapse plasticmechanism), and empirical methods (based on statistical analysis of experimentaltests). Between these methods, the method of collapse of the plastic mechanismseems to be the most adequate one for design purposes. Based on this methodology acomputer program DUCTROT (DUCTility of ROTation) was developed at INCERCTimisoara [13]. Fig. 16(b) shows two of the plastic mechanisms used for determiningthe rotation capacities. The comparison of theoretical and experimental data showsa good correspondence [12]. The use of this computer program allows framing themembers in the member ductility classes as the proposals of Mazzolani and Piluso[10]; high ductility R$7.50, medium ductility 4.5,R,7.50, low ductility1.5#R,4.5. Fig. 17 shows the classification of an I-profile in function on cross-section classes and member classes. It is very clear that a good correspondence doesnot exist between these two classifications.

The joint ductility depends on the importance of all component behaviours (Fig.18). For welded joints the ductility is given by the plastic shear deformation, bycrushing of web of joint panel or weld fracture, while for bolted joints the ductilityresults from plastic deformations until fracture of the column flanges, connectionelements (i.e., end plates) or by fracture of bolts or welds. The ductility of jointscan also be determined using the local plastic mechanisms (Fig. 19). An extensionof DUCTROT computer program, to include the ductility of joints, is now working.

Fig. 17. Influence of geometrical parameters on rotation capacity.


Fig. 18. Joint collapse types.

Fig. 19. Local plastic mechanism for joint collapse.

The node ductilityresults from the comparison of member and joint components.The weakest of them decides the node ductility. A comparison between momentcapacities of the joint panel and beam is shown in Fig. 20. The beam is realized ofIPE profiles, the columns, of HEB profiles. The figure gives the possibility to decidewhich one, the beam or the panel, is the weakest component and characterizes thenode ductility.


Fig. 20. Node collapse.

The last great seismic events have shown that the concentration of plastic hingesinto joints leads to a brittle fracture of welds or bolts. Therefore, great efforts in thelast period are devoted to define adequate different detailing of joints able to providea more satisfactory behaviour [14]. Fig. 21(a) shows the new type of joint in whichtwo solutions are proposed, both of them based on the idea to move the plastic hingeaway from the column-beam interface, in the field where the weldings or bolts donot determine the node behaviour. This solution can be obtained by weakening thespecific beam near to connection by trimming the beam flanges (dog–bone solution,[15]) or by strengthening the specific beam near to the connection by adding verticalribs or cover plates. The increasing ductility in these two solutions are presented inFig. 21(b). The weakening of the beam gives the possibility to reduce the dimensionsof columns, while strengthening requires the increase of these dimensions [16], (Fig.21(c)), showing the superiority of the dog–bone solution.

3.3. Required/available ductility ratios

For evaluation ofrequired/available ductility ratiosthe frames analysed by Maz-zolani and Piluso [5] are used. The plastic rotation of plastic hinges for beams andcolumns are determined. Two required ductilities are determined for live safe andnear collapse, on the basis of the design philosophy of performance based earthquakedesign. The analysed frames are: G–MRF which has been demonstrated by meansof second order plastic design to form global mechanism, and S–MRP, which hasbeen sized on the basis of member hierarchy criterion. One can see, (Fig. 22) thatthe required ductilities for beams are smaller in all cases than the available ductilities.


Fig. 21. Weakening and strengthening the beam ends.


Fig. 21. (continued)


Fig. 22. Required and available ductilities.

In exchange for columns, in the case of G–MRF the condition (1) is satisfied onlyfor life safe and in case of S–MRF the available ductility is smaller than the requiredductility for both levels of verification.

4. Ductility under seismic loading

For the checking of relationship (1) in the conditions of seismic loading someimportant modifications for the required and available ductilities must be considered.For the required ductility, an amplification of static determined values may occurwhile for static available ductility an erosion must be determined in function ofground motion characteristics.


4.1. Required ductility

For required ductility, some very important new information was obtained duringthe last few years. Due to the development of a large network of instrumentationall over the world, especially in the seismic affected countries and due to someearthquakes that occurred near very dense populated areas (Imperial Valley, 1979,Wittier Narrows, 1987, Loma Prieta, 1989, Northridge, 1994, Kobe, 1995) there area large amount of measurements of ground motion for different distances from thesources and for different site conditions. This new situation offers a possibility toreveal a new concept in structural design, which was neglected in the current concept:the differences in ground motion and in behaviour of the structures between near-source and far-source fields [17], (Fig. 23(a)). For Europe’s earthquakes, over 60percent are situated in the range of 4–14 km and the actions of near-source earth-quake type is of first importance for structural design. Unfortunately the groundmotions and the design methods adopted in codes are mainly based on accelerationrecords obtained from the far-source field, being incapable to describe in a propermanner the earthquake action in the near-source field. So, in this respect, a structuremay be situated in three different positions, which produced different amplificationof ductilities, near-site, intermediate-site or far-site, (Fig. 23(b)). The differences in

Fig. 23. Earthquake types and required ductilities.


main characteristics of near-source and far-source are presented in Fig. 24: directionof fault rupture propagation vs site stratification, velocity pulse vs cyclic loading,important vertical components vs moderate ones, high velocity of ground motionsvs moderate ones.

As a consequence of these differences in the ground motions, then are someimportant modifications in the required ductilities for near and far field earthquakes,(Fig. 25) [17]: influence of higher vibration modes vs first vibration mode, increasingof axial forces due to vertical components vs negligible increasing, higher ductility

Fig. 24. Near and far-source earthquake, main characteristics.


Fig. 25. Near and far-source structure behaviour.

demands for the upper part of structure vs ductility demands in the lower part,increasing of storey drifts due to high velocities vs normal values.

The influence of velocity pulse type of near-source earthquakes is studied usingan artificial generated accelerogram characterized by the accelerations, pulse periodand number of pulses [18]. Fig. 26 shows the spectra for horizontal motion, comparedwith an EC8 spectrum. One can see that the EC8 values do not cover the highamplification in the range of reduced structure periods. In exchange, these valuesare too large for medium and high structure periods as the one of steel structures.

Influence of impulse period on the ductility demands is studied in Fig. 27, [18].


Fig. 26. Spectra for velocity impulse earthquakes.

Fig. 27. Influence of velocity impulse periods.


The natural period periods of analysed structures is:T1=1.72 s,T2=0.61 s,T3=0.35s. The structure was analysed for a level of acceleration ofag=0.35 g with theDRAIN–2D computer program. One can see very clearly the influence of differentvibration modes: for the pulse periods near to second vibration mode, the requiredductility is concentrated at the top of structure, while for pulse periods near to firstvibration mode, the maximum ductility demands occurs at the first level. The requiredductilities resulting from the second vibration mode are more reduced than the onesobtained from the first vibration mode. Taking into account that the pulse groundmotions in near-source regions are generally between 0.3…0.6 s, results are that, forthe flexible frames, the second vibration modes may have a very great influence onthe structure behaviour. This consideration is confirmed by the results obtained usingrecorded accelerogrames in near and far-field [18].

For near-source earthquakes a very important factor affecting the required ductilityis the increasing of axial forces in columns due to the vertical components of groundmotions, which can be grater than the horizontal components. The increasing of axialforces in the first level columns is presented in Fig. 28, in function of a number ofstoreys, after Papaleontiou and Roesset [19] and Papazoglou and Elnashai [20], forLoma Prieta Capitola records withav/aH=1.11.

4.2. Available ductility

For available ductility it is possible to use the values determined for monotonicloading, but introducing some corrections which consider the erosion due to seismic

Fig. 28. Influence of vertical components.


loading characteristics, (Fig. 29). The main factors which may reduce the monotonicductility are presented in Fig. 30. One of the main factors is the velocity of groundmotions, which can be very high in a near-source zone. The high velocities producean increasing of strain-rate, with the effect of increasing of yield ratio [21]:

ry5fyfu

(5)

For very high strain-rates this ratio is close to 1 and the elements have no condition

Fig. 29. Erosion of available ductility.


Fig. 30. Factors of ductility erosion.

to develop plastic hinges. Thus, brittle fractures may occur in a members or joints.One other important factor influencing the ductility is the seismic cycling loading.In comparison with the monotonic loads the envelope of cyclic loads shows adecrease of rotation capacity as the effect of accumulation of plastic deformations[12]. The number of plastic excursions plays an important role in the erosion ofmonotonic determined ductility. It is very well known that in the case of a near-source area the first or second cycle is the most devastating one [22] while for far-source areas, especially for soft soils, there are 5–10 cycles with plastic deformationsin structures, producing an accumulation of plastic deformations or residual stresses,phenomenon which induces an important reduction of local ductility.

4.3. Comparison of required and available ductilities

The checking for ductility of beams is generally an ordinary operation withoutspecial problems. Difficulties occur at the checking for ductility of the columns. Foran ordinary moment-resisting frames in case that the effect of first vibration modeis determinant, the variation of bending moment is presented in Fig. 31(a), with adouble-curvature variation on the height of the storeys. The available ductilityincreases at each level, due to decreasing the effect of axial forces, while the requiredductility has the maximum value at the first storey, due to the shear type deformation.So, the disagreement between required and available ductilities may occur at theFrame first storeys. For special moment-resisting frames, the dimensions of columnsare increased to obtain a global mechanism. This over-strength of the column mayintroduce some adversary effects, by reducing the available ductility of columns due


Fig. 31. Required and available ductilities.

to the one curvature moment variation, Fig. 31(b). So, if due some differencesbetween design and actual hypothesis, (i.e. about the distribution of horizontal forceswhich produces the global mechanism) the plastic hinges may occur in the columns,and they are less ductile than ordinary frames, being a potential source of structurecollapse. In these cases, the second vibration interacts with the first mode (the caseof near-source earthquakes) the diagram of bending moment shows irregularities ofvariation at the middle frame height [23], which induce a dramatic reduction ofavailable ductility in this region. Because just in this place the required ductility hasa maximum, the collapse of the building may occur due to lack of sufficient ductility.This was a common phenomenon during the Kobe earthquake, where, many build-ings were damaged on the storeys situated at the middle height of structure.


5. Conclusions

Today code provisions for ensuring a sufficient structure ductility are based onthe compliance of some constructive rules. So, the level of ductility achieved is notformally calculated and the inherent ductility is not recognized. Due to this fact,during the last severe earthquakes many steel structures were damaged, the detailingrule being insufficient to ensure a general good ductility.

Recent development of advanced design concept is based on the objective to pro-vide a structure with sufficient ductility, in the same way as for strength and stiffnessusing a quantitative methodology. The developed method is based on the checkingthat the available ductility, determined from the local ductility, is greater than therequired ductility, obtained from the global behaviour of structure.

This paper presents the main problems of this checking, showing the factors influ-encing the required and available ductilities, defined for monotonic and seismic load-ings.

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Documents

Gioncu [Framed Structures. Ductility and Seismic Response - 2000]