Behaviour ofSteel Structuresin Seismic AreasSTESSA ’94

Proceedings of the International Workshop,organised by the European Conventionfor Constructional Steelwork

Timisoara, Romania26 June — 1 July 1994

Edited byFEDERICO MAZZOLANIProfessor of Structural Engineering,University ‘Federico II’ ofNaples, Italy

and

VICTOR GIONCUProfessorfor Design of Structures,Department ofArchitecture,Technical University of Timisoara, Romania

E & F N SPONAn Imprint of Chapman & HallEL London - Glasgow - Weinheim - New York - Tokyo - Melbourne - Madras

5 DAMAGE ASSESSMENT IN STEELMEMBERS UNDER SEISMIC LOADING

G. BALLIO and C. A. CASTIGLIONIDepartment of Structural Engineering, Milan Polytechnic, Milan,Italy

AbstractA method is presented trying to unify both design and damage assessment methods forhigh and low cycle fatigue, based on the results of an extensive experimental researchprogramme. Interpreting the stress range A0 as associated to the real strain range Ac inan ideal perfectly elastic material, high and low cycle fatigue test data can be fitted by thesame Wohler (S-N) lines usually given in Recommendation for (high cycle) fatigue designof steel structures. Local buckling can be regarded as a notch effect, intrinsic to thevarious shapes, and related to their geometrical properties (ctf and a’/tw slendernessratios ofthe flanges and the web). In the case of variable amplitude loading histories, alinear damage accumulation rule together with the previously defined S-N cun/es canlead to a reliable collapse criterion also for members under seismic loading.Keywords: Damage assessment, damage accumulation models, local buckling, S-Ncurves.

1. Introduction

Eurocode-3 (CEN I993), defines fatigue as "damage in a structural part, through gradualcrack propagation caused by repeated stress fluctuations".Depending on a number of factors, these load excursions may be introduced either understress or strain controlled conditions. Depending on the number of cycles sustainable tofailure, and on their amplitude, we can distinguish failure for high or low cycle fatigue.

Failure by high cycle fatigue is characterised by a large number of withstandable cycleswith a nominal stress range A0 in the elastic range (i.e. with Ao<2f}, , fy being the yieldstress of the material). This is a well known effect, and was studied since 19th centuryfor mechanical engineering applications (Wohler, 1860). Although only a limited numberof typologies of connections and of structural details can be considered at presentthoroughly investigated, the general aspects of this problem, and in particular the basicmethodologies for assessment and design, can be considered well established.Low cycle fatigue is characterised by a small number of cycles to failure, with large

plastic deformations (i.e. with strain range As >21-3), =2f), /E, E being the Young modulusof the material). In general, low cycle fatigue problems in civil engineering stmcturesarise either under seismic loading or in pressure vessels or under severe thermal cycling.Cycles with large amplitudes in the plastic range are usually connected with local

Behaviour of Steel Structures in Seismic Areas. Edited by F. M. Mazzolani and V. Gioncu.Published in 1995 by E & FN Spon, 2-6 Boundary Row, London SE1 8HN. ISBN: 0 419 19890 3.

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buckling in structural members. At present, knowledge of low cycle fatigue behavior ofcivil engineering connections is not jet as well established as the high cycle fatigue one.In particular, there is no generally recognised design or damage assessment method forlow cycle fatigue, and a clear definition ofa collapse criterion is lacking.In this paper a procedure is described, trying to unify design and damage assessmentmethods for structural details under high and low cycle fatigue. After discussing theproposed approach, its experimental validation based on constant and variable amplitudecyclic test results will be presented. By transforming the nominal strain range As in anequivalent stress range (A0*=Ae E) computed by considering the material as indefinitelylinear elastic, the experimental test data obtained under cycles with a constant amplitudein the plastic range can be interpolated by the same Stress range-Number of cycles tofailure (S-N) lines usually given in recommendations for the (fatigue) design of steelstructures (e.g. Eurocode-3). Furthermore, a linear damage accumulation model (Miner'srule), together with the rainflow cycle counting method, can be adopted for the damageassessment under variable amplitude loading.

2. The proposed approach

The proposed approach to unify the design and damage assessment procedures for steelstructures under low and/or high cycle fatigue, originally proposed by Ballio &Castiglioni (l994a) is based on the two following assumptions:

1. To know, for a given structural detail (cycled under strain controlled conditions),the relationships between the number of cycles to failure Nf and the cycle amplitudeAs, expressed in terms of generalised displacement components (i.e. ofdisplacements Av or of rotation Ad) or of deformation As). These relationships havethe same meaning in high and in low cycle fatigue with the following difference:

o in high cycle fatigue the component is subjected to cycles in the elastic range, with acycle amplitude As < 2 s where sy is the value of the displacement componentcorresponding at first yieldyin the material;

~ in low cycle fatigue the component is subjected to cycles in the plastic range, i.e.with an amplitude As > 2 sy .

2. Damage accumulation in a structural detail is a linear function of the number ofcycles sustained by the component itself. This means to assume that Miner's rule,usually applied in high cycle fatigue damage assessment, can be applied also in lowcycle fatigue.

Immediate consequence of the second assumption is the definition of a unified failurecriterion for both high and low cycle fatigue: a structural component fails when Miner'sdamage index reaches unity. Of course, the problem of the definition of the failureconditions is transposed to that of the identification of appropriate S-N curvescorresponding to the desired safety level.Consequence of the first assumption is the possibility to interpret low cycle fatigue withthe same laws commonly accepted for high cycle fatigue.

Damage assessment In S[€€l members ()5

In fact, in high cycle fatigue (under stress controlled conditions):- a structural component is subjected to load cycles having a constant amplitude AF;- the maximum value of the load excursion AF must be lower than the value Fy

associated with the attainment of the yield stress in the material. Fy may betheoretically computed or experimentally evaluated;

o the nominal stress induced by the external load F may computed either theoreticallyor with conventional methods, leading to a relationship of the type o=o(F);

o the stress range A0=Ac5(AD is finally correlated to the number of cycles to failureNf, independently from the yield strength ofthe material.

In order to generalise this approach, under the assumption of indefinitely linear elasticmaterial, it can be written:

AFA0-§o"(Fy) (1)

In low cycle fatigue (under strain controlled conditions):- a structural component is subjected to displacement cycles having a constant

amplitude As;o the maximum value of the excursion As of the generalised displacement component

s is greater than the value sy associated with the attainment of the yield stress in thematerial. sy may be theoretically computed or experimentally evaluated;

o if the material can be regarded as an elastic perfectly plastic one (as in the case ofsteel), and the hypothesis of concentrated plastic hinge can be considered realistic(as shown by Ballio & Castiglioni (l994b) for steel members under seismic loading),it can conventionally be assumed that strains are proportional to the generaliseddisplacement component s, and it can be stated that:

A525 (2)8 Sy y p

This equation defines the nominal strain range in a particular way, as discussed indetail by Ballio & Castiglioni (l994a), taking into account the local reduction ofstiffness at plastic hinge location by an equivalent uniform reduction of stiffnessalong the total beam length.

~ For an ideally linear elastic material, the relationship between strains and the loadcausing the displacement s can be written as: i

E8=6(19 (3)

Es}, = cs (Fy) (4)~ The value EAe, which can be interpreted as the stress range associated in an ideally

linear elastic material to the strain range Ae, can be finally correlated to the numberof cycles to failure Nf .

it follows that, at yield:

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~ Equation (5) is similar to equation (1), that is valid for high cycle fatigue. Thedifference consists in having considered cyclic displacements instead of cyclicforces. ,

3. Experimental validation

In order to experimentally validate the proposed approach, tests were performed byBallio & Castiglioni (l994b) at the Structural Engineering Department of Politecnico diMilano, on full scale cantilever members 1.6 m long (fig.l), of the commercial shapesHE22OA, HE22OB and IPE300, using an equipment designed by Ballio and Zandonini(1985), capable of applying horizontal cyclic actions in a quasi-static way. Presently, thetesting programme is continuing, in order to enlarge the data-base; tests are carried outalso considering the presence of an axial load, on both HE220A and HEl20A specimens,characterised by different slenderness ratios of both the flanges and the web with respectto HE220A (tab. 1).

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Table l- Geometrical propenies of specimen shapes

3.1 Constant amplitude tests

3.1.1 Description of the test results

To date, 37 tests were performed (11 on HE2?-.0A shapes, 12 on HE22OB and ll onIPE300, 3 on HEIZOA) imposing to the specimens displacement cycles with a constantamplitude. Furthermore, 8 tests were performed on HEZZOA specimens, subjected to anaxial load; three values ofthe axial load P were considered: PP, = 0.05, 0.10 and 0.125,P}, =f,.A being the plastic strength ofthe cross section.In addition to the usual hysteresis loops in terms of force applied on the top vs. topdisplacements, for each specimen the experimental measurements obtained by means ofaset of displacement transducers positioned as shown in fig. 1, were processed followingthe ECCS (1986) Recommended procedures in order to obtain informations regarding

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Damage assessment in steel members 67

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resistance ratio, rigidity ratio,cumulative energy ratio andbuckle size which were plottedvs. the number of appliedcycles.Before any comment, itis important to remember that,according to the definitions

given in EC-3, HE22OAprofile has a c/gr ratio of theflanges (10.0) larger than thatof HEZZOB (6.9), of IPE3OO(7.0) and of HE12OA (7.5),while its width to thicknessratio for the web (d/t,,,= 21.7)is intermediate between thoseof HE120A (14.8), which issimilar to that of I-1E22OB(ai/tw =16.0), and of IPE3OO(d/r,,,=35.1) (tab. 1).

Based on the test results byBallio Castiglioni (l994a) thefollowing considerations canbe drawn, having a generalvalidity, for the shapesexamined in this study:

1. Deterioration effects,fig, 1 Specimen Setup causing a reduction in load

carrying capacity, stiffnessand hysteresis loops

area begin earlier in HEA specimens (having larger c/rfratio) than in both IPE andHEB ones. IPE beams, characterised by larger d/tw ratios, although initiallyfollowing an intermediate behavior between HEA and HEB, experience much fasterdegradation;

Local buckling starts a few cycles earlier in IPE beams than in I-{EA ones, whilstHEB specimens can sustain a larger amount of cycles without buckling. A majorrole in governing local buckling effects is played by the web slenderness ratio d/tw.Buckling develops completely within a few cycles, whose number seems to dependon the c/tfratio, then stabilisation of the buckles size occurs.For all types of profile, once local buckling takes place and buckle size stabilisationoccurs, also the hysteresis loops stabilise, and the rate of reduction in load carryingcapacity decreases with increasing the number of cycles imposed to the specimen,until a final stage is reached, when the deterioration rate suddenly increases againand the specimen collapses after a few cycles. In particular, both IPE and HEAbeams clearly evidence this type of behavior, while HEB specimen show a smoothertransition from the (longer) phase of cycle stabilisation to that leading to collapse;

68 Ballio and Castiglioni

4. These differences in behavior at the final stage, between HEB specimens and HEAand IPE ones is associated with a difference in their failure modes. HEA and IPEbeams generally collapse by steady crack propagation due to low-cycle fatigueeffects; the HEB specimens, on the contrary, evidence some kind of brittle fractureofboth the flange and the web, either at the specimen-to-base welds or at the plastichinge where, due to large localised distortions, surface cracks usually develop a fewcycles after local buckling ofthe flange plates.

3.1.2 Reprocessing the test data

When test data are re-processed according to equation (5), the following parametersmust be defined: the number of cycles to failure Nf, the values of the generaliseddisplacement component (sy) and ofthe stress level (o (Fy)) corresponding at first yield.Of course, various operative choices are available for the definition of these parameters;in order to clearly identify the consequences of these operative choices, the followingconsiderations should be taken into account.

~ To define the number of cycles to failure Nf, a collapse criterion must be adopted,either assumed conventionally a-priori, or identified test by test corresponding tofailure. In the first case, for example, failure might be associated with the reductionof the load carrying capacity to a given percentage y of the yield strength (e.g. y=50%, or y=70%). In the second case, for example, as a consequence of the lasttwo considerations of the previous paragraph, the number of cycles to failure Nfcan be assumed either as the one corresponding to complete separation of oneflange (generally this is the case for HEB shapes) or as the one corresponding to thesudden (final) increase in the deterioration trend after cycle stabilisation (generallyapplicable to HEA and IPE shapes).

- The generalised displacement component can be assumed either as a displacement vor as a rotation ¢. Accordingly, the value corresponding to first yield can bedefined as the yield displacement V (or the yield rotation ¢ ,), and can betheoretically computed or conventionally defined reprocessing test data, for exampleadopting the ECCS (1986) Recommended procedures.

- The nominal stress level (<3 (Fy)) associated to an external load (Fy) causing firstyield in the material can be determined experimentally, by means of tensile tests, ortheoretically, by applying conventional methods of structural mechanics. In the firstcase, cs (F,)= In order to apply the second procedure, both the yield strength(F)-) shoufid be determined (e.g. according to ECCS Recommended procedures)and, for flexural members, the dimension of the plastic hinge.

Once determined the number of cycles to failure ]\/Jr, test data can be re-processed to plotin a log-log scale Nfvs. Ao* given by eq. (5). The domain log (Ao*=EAe) vs. /0g N isthe usual domain for the Wohler (1960) (S-N) curves adopted by various InternationalCodes and Standards for (high cycle) fatigue design of steel structures. In fact, the strainrange As (having the same physical meaning in both high and low cycle fatigue) has beencorrelated to the number of cycles to failure Nf and is then multiplied by the Youngmodulus E in order to deal with the same parameters commonl_v used by designers

Damage assessment in steel members 69

dealing with high cycle fatigue. For high cycle fatigue design, the most commonstructural details have been grouped into a number of categories (a same category fordifferent details having similar fatigue strength), and to each category has been associatedan S-N curve. It has recently been recognised the possibility to unify the slope of suchcurves which, in the most recent Recommendations (eg. EC-3, ECCS 1985) are definedby an equation ofthe type:

NAO3 =/1 (6)A being a constant assuming different values for each S-N curve.

In order to verify the first assumption introduced in the previous point 2 of this paper(equivalence of EAe- Nfcuryes for high and low cycle fatigue), it is tried to interpret theexperimental test data ofthe low cycle fatigue tests performed during the present study,by means of the S-N curves proposed by Eurocode-3, whose validity is extrapolated inthe low cycle fatigue range (i.e. for number of cycles N ranging from 10 to 500, andcorresponding stress ranges EAe = Ao*> 2fy) by means of eq. (5).

In high cycle fatigue, strength categories implicitly account for different notch effects,i.e. for different local stress concentrations due to geometry of the detail and/or defectscaused by fabrication procedures. It is supposed that the same consideration holds also inthe case of low cycle fatigue: local buckling can in fact be regarded as a notch effect,because it induces local stress concentrations in the buckled area (at plastic hingelocation).In fact, as already discussed, and in good agreement with previous results byYamada (Yamada, 1969; Yamada & Shirakawa, 1971, Yamada et al. 1988), the differentgeometries of the cross sections make the specimens more or less vulnerable by localbuckling effects. This means that each shape, as a function of its geometrical properties,can be considered as belonging to a definite fatigue strength category, becauseintrinsically affected by a more or less pronounced notch effect.Ifthis assumption is true, it must be expected that the different shapes considered in this

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Damage assessment in steel members 71

specimens failed at weldings fatigue strength than HE22OA, because ofthe lower c//f andti/t,,... ratios. Furthermore, the tested specimens evidenced two different failure modes: bycracking in the base material at the plastic hinge locations, or by cracking at the weldingof the reinforcement plates to the specimens. It must than be expected that differentfatigue strength curves apply to the different failure modes.

The following figures 2-4 respectively show the test data for HE220A, HE220B andIPE3OO specimens failed for cracking in the base material at plastic hinge locations, fittedby the S-N lines of Eurocode-3.As expected, test data for HE220B can be fitted by EC-3 line for category 80, and thosefor IPE3OO by that for category 63; those for HE220A specimens can be fitted by the linefor category 71, intermediate between the two previous ones, while HE12OA specimenscan be fitted by line for category 80.Figure 5 refers to test data for specimens failed at weldings; HE22OA and HE220Bspecimens can be fitted by category 63 line, while IPE300 specimens, despite the samewelded detail was adopted for all shapes, are fitted by line 56 and show a lower fatiguestrength. This is probably caused by the formation ofthe plastic hinge nearer to the base(i.e. nearer to the weldment) in IPE specimens rather than in HE ones. This fact seemsagain to confirm the hypothesis that local buckling can be considered as a notch effectreducing the fatigue strength ofthe profile.However, independently on the category of fatigue resistance pertinent to each shape, itis important to notice that the slope of the line fitting (in a log-log plot) the low cyclefatigue test data, reprocessed according to eq. (5), is nearly -3. This is in good agreementwith the results of research on high cycle fatigue. It follows that both high and low cyclefatigue test data can be fitted by S-N lines having the same slope -3, the fatigue categorydepending on the notch effect associated with the various structural details.

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fig. 7 Effect of assumed failure condition ondamage assessment

deterioration rate (leading to failure)~ based on a condition defined a-priori, associated to a reduction of the load carrying

capacity to a given percentage of the yield strength F,,.F/F,,=0.95 leads to conservative assessments of the’ fatigue strength, as well as toscattering ofresults, while assuming as failure condition a reduction of strength to 0.50F,,leads to assessments similar to those based on test evidence. V

Fig. 8 shows the effects of the definition ofthe stress range Ao* (i.e. ofthe definition ofthe yield stress and of the assumed generalised displacement component s) on theassessment of the fatigue strength of HE220A specimens, in the case of a failurecondition assumed a-priori corresponding to a reduction of the specimen strength F to0.50F,,_. It can be noticed that scattering in the results is connected to the definition ofthe yield strength, while smaller is the influence ofthe assumed displacement component;in fact, if top displacements v or rotations at plastic hinge location (I5 are assumed asgeneralised displacement component s in eq. 5, a small scattering can be noticed in theresults. On the contrary, if the stress level corresponding at yield (o(F,_,)) is definedthrough a tensile test (i.e. coincident with f,,) or by means of structural mechanics (i.e. asF},L'/W, where W is the section modulus and L'= L-(Q11/2) the cantilever member lengthminus halfthe dimension ofthe plastic hinge), due to the uncertainties connected withthe latter definitions of both L‘ and F,.’ a larger scatter in the results can be noticed. Fig.8.1, 8.2 and 8.3 respectively refer’ to different values of parameter Q (respectivelyassumed equal 1.0, 1.5 and 2.0). It can be noticed how scattering of the results isstrongly influenced by this parameter.

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Damage assessment in steel members 73

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Hence, in order to avoid biased results from re-processing test data, extreme accuracyand consistency must be adopted when defining the various parameters. In particular.when possible, the yield strength should be determined by tensile tests.

3.2 Variable amplitude tests

~The second assumption, previously introduced in chapter 2, deals with the possibility oradopting Miner's rule for defining an acceptable failure criterion in low cycle fatigue.

Some random displacement histories were numerically obtained by means of a dynamicnumerical simulation code by Ballio, Castiglioni and Perotti (1988), adopting artificialaccelerograms obtained on the basis of Eurocode-8 (1988) recommended spectra.Various oscillograms were numerically obtained under increasing values of the peakground acceleration, and Miner's damage index was computed using the Rainflowmethod for cycle counting. When a time history giving a Miner's damage index greaterthan 1 (i.e. indicating failure) was obtained as output ofthe numerical simulation, such adisplacement history was imposed in a quasi-static way to the specimens under testing.At present, a total of ll random tests have been performed (4 on HE22OA shapes, 4 onIPE3OO and 3 on HE220B). The experimental results were re-processed by means oftherainflow cycle counting method and Miner's damage index associated with collapse ofeach specimen was computed, based on the transformation given by equation (5) and onthe EC-3 fatigue strength lines previously identified for the various profiles. Theobtained results are summarised in table 2 where the failure mode (S= at plastic hinge,W= at welding) and the damage index corresponding to the EC-3 lines are given.

TEST' _ EC-3 FATIGUE CURVE

90 “ so 71 as 1 Failure1 HEA1 1* 0.542 0.772 1%-=‘-1*-=1:10'4 “ 1.580 5 s

HEA9 if 0.854 1.202 {$71110 ' 2.489 SHEA10 ' 0.599 1 0.853 111.220" 1. 4 1.746 (I)

1 HEAH 1.040 l;~;.: 1.490 . 2.135 (I)HEB1 -"-3"“? 52I!3,()'€?§Z§5'i§=§f§?§§'5z: 2.900 1 4.152 C/2HEBIZ

1 0.773

1 0 717 1 1.020 ' ' .-..<<: €1 HEBl3 111 0.523 0.744 'i;§;;?5.21'-t €1 IPE‘) 0.461 ' 0.657 0.939 1 ~1' .3411 (/2

1' IPE 10 1 0.385 1 0.547 ' 0.783 .-i=ii-si§'lf§i"lj'=2.0 U1lPE11 0.460 0.660 11-II I346 Cl)

1 lPEl5 1 0.478 0.6800.9400.973 1 1:594 (/1

Table 2 - Damage indexes corresponding to specimen collapse in \'Z1flZ1blC amplitude tests

The following considerations can be drawn:o Miner's rule gives damage index values with scatters similar to those commonly

accepted in random high cycle fatigue.~ For HEA specimens Miner's rule correctly allows prediction of failure in association

with EC-3 line for fatigue strength category 71.

Uamage ClSS€SSm€fZl' U1 steel members '/D

o For HEB specimens, depending on the failure mode, Miner's rule leads to a correctprediction of failure respectively in association with EC-3 lines for fatigue strengthcategories 80 and 63. In particular, the adopted fatigue strength lines lead todamage assessments largely on the safe side; increasing the fatigue strength ofHjE220B specimens by one category results in damage index values nearer to unity.

- For IPE specimens, Miner's mle correctly allows prediction of failure in associationwith EC-3 line for fatigue strength category 63.

4. Conclusions

The obtained results show the validity of the two assumptions on which the proposedapproach is based:1. the same S-N curves are valid in high and low cycle fatigue, if an equivalent stress

range A o*=EAe is considered, associated with an ideal indefinitely elastic behaviorofthe material; in particular, the slope ofthese S-N curves in a (log-log) plot is -3.

2. Miner's rule can be adopted, together with the previously defined S-N curves andwith a cycle counting method (e.g. Rainflow) to define a unified collapse criterion,valid for both high and low cycle fatigue.

The application of these results and of the proposed method for damage assessment, tosteel structures under seismic loading, may lead to an overcoming of seismic designmethods based on the behavior factor, as shown by Ballio & Castiglioni (19940).

5. References

Ballio G., Castiglioni CA. (l994a) A unified approach for the design of steel structuresunder low and/or high cycle fatigue, to appear on Jour. of Constr. Steel Research.

Ballio G., Castiglioni C.A. (l994b) Seismic behavior of steel sections", Journal ofConstructional Steel Research, 1994, n.29

Ballio G., Castiglioni CA. (1994c) An approach to the seismic design of steel structuresbased on cumulative damage criteria, to appear on Earthquake Engineering &Structural Dynamics.

Ballio G., Castiglioni C.A., Perotti F. (1988) On the assessment of structural designfactors for steel structures, IX W.C.E.E., Tokyo, 5, 1167-1171.

Ballio G., Zandonini R. (1985) An experimental equipment to test steel structuralmembers and subassemblages subject to cyclic loads, Ingegneria sismica, 2, 25-44.

CEN (1992), Eurocode-3: Design of Steel Structures - Part 1-1: General rules andrules for buildings, ENV 1993-1-l:l992 E.

ECCS (1985), Recommendations for the fatigue design of structures, lst Ed.ECCS, T.C.l, T.W.G. 1.3, (1986) Recommended testing procedure for assessing the

behavior of structural steel elements under cyclic loads, Rept. n. 45.Eurocode-8 (1988), Design of structures in seismic regions, Part 1: General rules and

rules for buildings.Wohler A. (1860), Zeitschrift fiir Bauwesen, vol. 10.Yamada M.,(l969), Low cycle fatigue fracture limits of various kinds of stmctural

members subjected to alternately repeated plastic bending under axial compression as

/0 DUHZU ana L,ClS[lgll()I'll

an evaluation basis or design criteria for aseismic capacity, IV W.C.E.E., Santiago,Chile, Vol.1, B-2, Jan. 69, 137-151.

Yamada M., Kawamura l—I., Tani A., et al. (1988), Fracture ductility of structuralelements and of structures, IX W.C.E.E., Tokyo, IV, IV219-IV224.

Yamada M. Shirakawa H. (1971), Elasto-plastic bending deformation of wide-flangesteel beam-columns subjected to axial load, Pan II, Stahlbau, 40,H.3 65-74, H.5143-151