Special metals for seismic retrofitting of steel buildings

Special metals for seismic retrofittingof steel buildingsL Di Sarno1 and A S Elnashai2

1 University of Naples, Italy2 University of Illinois at Urbana-Champaign, USA

SummaryNovel metals such as aluminium alloys, stainlesssteels and shape memory alloys can be used forthe retrofitting of steel buildings in seismic areas.Therefore, it is useful to investigate theirmechanical and physical properties along with thekey issues of the material modelling. The presentpaper focuses on the mechanical response of suchmetals which are inherent to the seismic design.Furthermore, it compares their mechanical

characteristics in order to assess (i) the relativemerits; and (ii) the cost-effectiveness in practicalapplications. Analytical formulations employedfor either refined or simplified modelling arecritically reviewed; advantages and disadvantagesof each scheme are highlighted. Finally, severalexamples of practical applications of these novelmetals in seismic retrofitting are discussed andfurther developments outlined.

Key words: retrofitting; aluminium; stainless steels; shape memory alloys; steel structures; modelling

Prog. Struct. Engng Mater. 2003; 5:60–76 (DOI: 10.1002/pse.143)

1 Introduction

Recent earthquakes, in Northridge, California, 1994,Hyogoken-Nanbu, Japan, 1995 and Chi-Chi, Taiwan,1999, led to unexpected damage to steel structures.The damage was widespread and occurred in low-to-high-rise framed structures[1–3]. As a result severalresearch projects were undertaken world-wide,resulting in new design guidelines for seismicrehabilitation[4].

Strategies for seismic retrofitting may be eithertraditional or unconventional[5]. Local and globalinterventions are effective methodologies to enhancethe energy dissipation capacity of building structures.However, novel materials, special metals, and/ortechnologies, base isolation and supplementaldamping are nowadays available for steel frames.

Innovative metal materials which can be used forretrofitting of steel structures are:

* aluminium alloys (AAs);* stainless steels (SSs);* shape memory alloys (SMAs).

These metals possess peculiar characteristics thatrender them suitable in the field of seismicrehabilitation. These characteristics include:(i) mechanical properties; (ii) corrosion resistance inharsh environments; (iii) heat resistance;(iv) weldability; (v) chemical-physical compatibility

with other materials; (vi) life cycle cost; and(vii) recyclability. The mechanical properties of suchnovel metals are summarized in Table 1. Mild steel isalso included in Table 1 and used as a benchmark.

The table shows that the density of all but SSs isgenerally lower than mild steels; AAs havesignificantly reduced weight (one-third that of mildsteel). As a result, the latter is a viable solution whenthe minimization of added masses is of primaryconcern. However, this is not usually the case forresidential and/or commercial buildings, but it can becrucial for other constructions (historic buildings,bridges, roofs, etc.). Moreover, AAs and SMAs are lessrigid (about one-third as rigid as steels); therefore, thestructural design is generally governed by buckling ordeformation limits. SSs generally have lower yieldstrengths than mild steels, but higher strainhardening, for example, ductility ratios (2.22compared with 1.58). AAs exhibit a wide range ofvariability for the yield strength (20–360MPa). This isalso the case for SMAs. However, the variability is lesswithin a single phase, e.g. martensite (70–140MPa)and austenite (195–690MPa).

The values of ultimate elongation (elongation atfracture) show that SSs may undergo higher plasticdeformations than mild steels (50% compared with28%). Material overstrength, which is a measure of theplastic redistribution, is high for AAa and SSs andexceptionally high for SMAs (up to 10–20).

Earthquake Engineering and Structural Dynamics

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SSs possess a coefficient of thermal expansionsimilar to that of carbon steel: 17–19� 10�6 8C�1 forstainless steels compared with 12–15� 10�6 8C�1 inmild steels. Different coefficients of expansioncharacterise AAs (24–25� 10�6 8C�1) and SMAs (6.6–10� 10�6 8C�1). Thus, welding between SMAs andordinary steels should be assessed accurately in thedesign of unconstrained components. By contrast, inconstrained elements the residual stresses for bothAAs and SMAs are about two-thirds of than those insteel structures. Residual stresses increase linearlywith the Young’s modulus E; the coefficient of thermalexpansion (a) is the factor of proportionality.

Strength-to-weight ratios show that special metalalloys, particularly SMAs and AAs, are extremelyefficient. Therefore, they may be adequately exploitedas suitable materials for retrofitting applications. Thechoice of any such metal alloy for retrofitting shoulddepend primarily upon (i) mechanical properties(strength, stiffness, ductility), (ii) compatibility, (iii)corrosion and heat resistance and (iv) life cycleassessment. A comparison of the approximate cost ofdifferent materials is provided in Fig. 1. It may beobserved that the cost of raw materials for AAs ishigher than SSs and that it is (about four times) higherthan for carbon steel. However, as far as seismicretrofitting is concerned, the choice of designsolutions should be performed on the basis of cost–benefit analysis accounting for life cycle costs;judgment of simple initial costs is, indeed, restrictiveand unreliable.

An overview of the innovative metal alloys isprovided herein. Special emphasis is placed on theirengineering properties that render them suitable forapplications in seismic retrofitting of steel structures.Issues concerning mechanical modelling are brieflyaddressed and examples of practical applications areprovided.

2 Aluminium alloys

The elevated strength-to-weight ratio (Table 1), widerange of yield strength, significant strain hardening,good ductility, ease of manufacture for components,either simple or with complex shapes (via extrusion),and weldability, render aluminium an attractive metal

for the improvement of existing structures in seismicareas. Indeed, components in low-yielding ductileAAs may function as a fuse, limiting the maximumlateral force transmitted to primary structuralmembers and providing significant energydissipation. The mechanical properties of AAs arediscussed in Section 2.1.

2.1 MECHANICAL PROPERTIES

New AAs with relatively high strength, ductility, lightweight and good corrosion resistance are constantlybeing developed[6]. The use of such metals forstructural retrofitting has already been proven,especially to enhance the seismic resistance of shearlinks in braced frames[7] or to rehabilitate historic andmonumental structures[8]. Therefore, they representan attractive solution for the retrofitting of steelstructures.

AAs are obtained by adding to aluminium (Al)several chemical elements, such as copper (Cu),magnesium (Mg), manganese (Mn), silicon (Si) or zinc(Zn), to increase its strength. Indeed, pure aluminiumhas good ductility properties, but generally low proofstress (s0.2). As a result, several alloys are available,and their mechanical properties vary as a function ofthe chemical composition. For example, amongwrought alloys, Al–Mg alloys (5000 series) exhibitrelatively low strengths (s0:2 ¼ 100MPa), high work-hardening (the strength can be increased tos0:2 ¼ 2002300MPa), sufficient ductility (ultimateelongation 10–15%) along with good corrosionresistance. By contrast, series 6000 and 7000, i.e.

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Table 1 Mechanical properties of steel and special metal alloys

Density(g/cm3)

Young’sModulus(GPa)

YieldStrength(MPa)

UltimateStrength(MPa)

Elongation atFracture(%)

MaterialOver-strength

Yield strength-to-weight ratio(� 104 cm)

Mild steels 7.9 205 215–355 340–510 10–28 1.44–1.58 27–45Aluminium alloys 2.7 65–73 20–360 50–410 2–30 1.14–2.50 7–133SMAs (Ni–Ti) 6.5 28–41m 70–140m 1900w 5–10w 13.57–27.14m 11–22m

70–83a 195–690a 895f 25–50f 1.30–4.59a 30–106a

Stainless steels 8.0 193 180–480 400–660 35–50 1.38–2.22 23–60

a ¼ austenite; m ¼ martensite; f ¼ fully annealed; w ¼ work-hardened; material overstrength ¼ ultimate/yield strength

0.0

1.0

2.0

3.0

Glass Mild steel Stainless steel Galvanised steel Aluminum alloys

Cos

t (E

uro

/ kg)

Fig. 1 Approximate costs of some materials used in theconstruction industry

SEISMIC RETROFIT WITH SPECIAL METALS 61

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Al–Si–Mg and Al–Zn–Cu alloys, have high strength(s0:2 ¼ 2002300MPa for series 6000 ands0:2 ¼ 4002500MPa for series 7000) and relativelyreduced corrosion resistance and ductility[9]. Thesealloys are suitable for extrusion and hot-rolledsections and can be used for either welded or boltedconnections. By alloying aluminium through Cu, Mgand Mn the strength and ductility are enhanced, butthe corrosion resistance drops. In seismic retrofittingof steel buildings the former are thought to be ofparamount importance, hence the lower corrosionresistance can be accepted. Moreover, alloyingaluminium with other chemical elements should bepreferred to cold-working processes to improve thestrength because such processes drastically reducethe material ductility (up to one-tenth of the initialvalue).

The stress–strain response for AAs is highlynonlinear and does not exhibit a well-defined yieldpoint. Generally 0.20% offset permanent strain (proofstress), is employed (Fig. 2). The strain hardening isalso significant. Material overstrength, i.e. ultimate-to-yield stress, may be as high as 2.50, thus giving rise tolarge plastic redistributions[10]. The overstrengthvaries with the alloying elements. These mechanicalproperties are similar to those of SSs, as discussed inSection 3.1.

Unpinched and full-hysteresis loops (metallichysteresis) may be found either in normal or shearstresses[7], provided that buckling phenomena areprevented. Owing to the high deformability of AAs,cross-sections and structural members are likely toexperience local and global buckling, respectively.However, adequate design rules to prevent suchphenomena are available[10].

Finally, AAs do not exhibit a transition temperatureas for mild steels, i.e. aluminium is less susceptiblethan ordinary steels to brittle fracture, either at low orroom temperature. Therefore, they can be candidatesfor applications in seismic rehabilitation, where thetoughness is of paramount importance.

2.2 MODELLING

Numerical analyses performed using finite elementmethods (FEM) in the inelastic regime generallyemploy simplified uniaxial stress–strain formulations.

The most common models comprise linear elasticperfectly plastic (LEPP), linear elastic strain hardening(LESH), linear elastic nonlinear hardening (LENLH)and the Ramberg–Osgood model (ROM). The uniaxialstress–strain response for mild steel is usuallymodelled via LEPP, LESH or LENLH, while AAs maybe reliably modelled via ROM, which is based on thefollowing equation:

e ¼ ee þ ep ¼ sE0

þ 0:002ss0:2

� �n(1)

where e is the total strain, expressed as the sum of theelastic ee and plastic part ep, s is the actual stress, E0

the elastic (initial) modulus (E0¼ 70GPa), s0.2 is theproof stress while n is a model constant. The lattershould be calibrated through tests on compression ortensile coupons, or more reliably from stub columnsby curve fitting. The values of the exponent n vary asa function of the alloy type: generally for non-heat-treated alloys n510220, and for heat-treated alloys420–40. However, the analytical expression for n is asfollows:

n ¼ log 0:002=e1ð Þlog s0:2=s1ð Þ (2)

in which s1 and e1 are arbitrary stress and strainvalues, the stress s1 may be assumed to correspond tothe 0.1% strain offset e1.

Consequently, the tangent Et and the secant Es

moduli are given by:

Et ¼s0:2E0

s0:2 þ 0:002nE0 s=s0:2ð Þn�1(3:1)

Es ¼E0

1þ 0:002 E0 sn�1=sn0:2� � (3:2)

The Ramberg–Osgood curve is capable of closelyapproximating stress–strain curves for a wide rangeof AAs. However, difficulties arise when ROM is usedfor practical applications and experimental data arenot available. Design standards[10] provide only thevalues of the stress s0.2 and the Young’s modulus E0,therefore the constant n can not be determined bymeans of eq. (2). In such cases approximate methodsavailable in the literature may be utilised[9]. Thesimplest expression is as follows:

n ¼ s0:210

(4)

Multiaxial models for metal plasticity are morereliable when cyclic loads are considered[11]. Thematerial can be modelled either as elastoplastic withisotropic linear elasticity (von Mises yield criterion)and isotropic hardening or by using more advancedformulations. For example, a multiaxial formulationwith strain hardening based on the true stress–straincurve has been proposed[6] as follows:

seq ¼ Y0 þQ 1� e�Cep� �

(5)

where seq is the equivalent stress, ep the plastic strain.Y0, Q and C are material properties; Y0 corresponds toFig. 2 Stress–strain curves for aluminium (A) and steel (S)

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS62


the proof stress, while Q and C determine themagnitude of the strain hardening and the shape ofthe curve, respectively. According to availableexperimental tests[6,11,12] suitable values for C are10–20, whereas factor Q varies depending on the alloy,normally ranging between 80MPa (low hardening) and200MPa (high hardening).

2.3 APPLICATIONS FOR SEISMIC DESIGN

Recently, AAs (3003 and 6061) have been used[7] toenhance the energy dissipation of shear links(dissipative zones) in eccentric braced frames (EBFs).Such alloys are very attractive for shear links becauseof (i) low yield strengths; (ii) high metallic damping;(iii) high strain hardening; and (iv) low strain-rateeffects. The low yield strength allows the use ofthicker webs which in turn prevents web buckling,while strain hardening in shear modes is favourablefor plastic redistribution within the dissipative zonesof the frame. Moreover, soft alloys undergo manylarge plastic deformation cycles without tearing; Fig. 3illustrates an aluminium specimen after large sheardeformations and a typical hysteresis loop. Therefore,hybrid braced frames with aluminium shear linksrepresent a viable alternative to traditional EBFs.However, to enhance the energy dissipation it isadvisable to use softer alloys (3003), for the link websand stronger alloy (6061), for the flanges.

The shear resistance Vw of the aluminium link to beused for capacity checks is given by:

Vw ¼ 1:9s0;2g0:2Aw (6:1)

where s0.2 is the proof stress and Aw is the horizontalweb area:

Aw ¼ ltw (6:2)

with l the link length and tw the web thickness. Thesize of shear links may be determined by calculatingthe area Aw to resist the design storey shear Vdi:

Aw ¼ Vdi

1:64 f0:2(6:3)

in which the shear stress (1.64 s0.2) corresponding tostrains equal to 0.10 is assumed.

Transverse stiffeners are required to avoid webbuckling and to ensure ductile shear failure. Theirdesign should be based on stability and strengthchecks. Minimum thickness should be 10mm andthey should be placed on both sides of the link.

Adequate stiffness is ensured by assuming themoment of inertia of stiffeners Ist about the centroidalaxis parallel to the web as:

Ist54jat3w (7:1)

where the coefficient j is given by:

j ¼ 2:5a

tw

� �2�2

" #50:50 (7:2)

The minimum strength of the stiffeners may beevaluated assuming that each stiffener behaves like astrut with an axial force equal to one-third of theexpected shear in eq. (7.2).

The spacing a of transverse stiffeners to avoid webbuckling and to ensure ductile shear failure shouldsatisfy the following equation:

9:37ks

b2¼ 0:20 (8:1)

where the plate buckling coefficient ks, assumesclamped end conditions for the web panel, is givenby:

ks ¼5:6þ 9:0

a2a41

9:0þ 5:6

a2a41

8>><>>: (8:2)

where b is the web panel depth-to-thickness ratio anda the panel aspect ratio, defined as:

a ¼ a

d� 2tf(8:3)

with d the total depth of the link and tf the thickness ofthe flanges. Intermediate stiffeners may be omittedwhen web depth-to-thickness ratio is not greater than20, while end stiffeners are necessary for the ductileresponse of the link.

Fig. 3 Aluminium shear links: (a) test specimen; (b) typical hysteretic loop[7]



The inherent mechanical properties of AAs,especially the low proof stress and significant strainhardening, render these alloys suitable to be used foralternative dissipative elements in seismicrehabilitation, such as diagonal bracings and metalshear walls. However, further experimental andnumerical work is needed to assess the feasibility andthe cost-effectiveness of such applications.

Finally, it is instructive to note that the corrosionproblems that may arise on joining aluminium to adifferent metal can be easily solved. Indeed,bi-metallic (galvanic) corrosion can be preventedeither by coating the carbon steel contact surface witha protective layer or by sealing the joint, thus avoidingthe contact between the electrolyte and the metals ofthe connection.

3 Stainless steels

SSs are metal alloys which contain a high percentageof chromium (Cr). Normal grades are obtained byadding at least 12% by weight to low-alloy carbonsteel. The presence of Cr allows the formation of aprotective oxide on the material surface (stainlessmetal). Furthermore, Cr is employed in theclassification[13] of SS groups (Fig. 4), based on theirmicro-structure, as follows:

* austenitic (ASS);* ferritic (FSS);* austenitic–ferritic (AFSS) or duplex;* martensitic (MSS);* precipitation hardening (PHSS);

It should be pointed out that the choice of the mostsuitable type and grade of SS relies fundamentallyupon the required corrosion resistance for the ambientconditions, namely the ‘service environment’[14]. ForSSs, life expectancy[15] may not be treated separatelyfrom structural design as in mild steel, but it is strictly

related to (i) the initial selection of material grade;(ii) the design process; (iii) the fabrication route; and(iv) the surface finish and maintenance. Therefore,among the aforementioned sub-groups, ASSs andAFSSs are usually employed for structuralapplications. So far, AFSSs have been the mostsuccessfully used, owing to the wide range ofavailable industrial products (structural profiledsections, nuts, bolts, etc.) manufacturedfrom them.

It is noteworthy that the application of SS inordinary structural systems was prompted by recentanalytical and experimental studies carried outworld-wide[16–19]. Design procedures have alreadybeen implemented[14,15], although furtherdevelopments as well as improvements are requiredto achieve the desired reliability and cost-effectiveness.

The mechanical properties which are essential forseismic retrofitting are discussed in Section 3.1. Thenkey issues relative to the material modelling will beaddressed.


The stress–strain response for SS shows a gradualtransition from the elastic to the plastic branch.Therefore, it does not exhibit a well-defined yieldpoint (round house response). As a consequence, a 0.20%offset permanent strain is generally employed as yieldstrength s0.2 (proof stress) as for AAs (see Section 2.1).Fig. 5 illustrates these properties by contrasting thestress-strain response of two types of SS, austeniticand austenitic–ferritic (duplex 2205), to the mild steel.Moreover, the mechanical response is stronglydependent on the material composition[19].

SSs exhibit higher ultimate-to-yield stress (su/s0.2)ratios than mild steels (1.8–2.0 compared with1.2–1.5), thus leading to a larger spread of plasticityalong the member length. Fig. 6 shows, for example,the su/s0.2 ratios for hot-rolled plates as a function ofthe thickness of two common SS grades, austenitic 304(S220) and 316 (S240). Furthermore, predefinedmaterial overstrength may be more easily achieved by

Fig. 4 Schaeffler diagram for stainless steel[13]

0

250

500

750

1000

0 10 20 30 40 50

0.2% Proof Stress

0.2% Offset Strain

Strain (%)

Stre

ss (

MP

a)

Austenitic-Ferritic(Duplex 2205)

Austenitic (304-316)

Carbon Steel

Exaggerated

Fig. 5 Typical stress–strain curve for stainless and mild steels



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manufacturers because of tighter quality controls.However, these improvements, ranging between fourand six times, are achieved for SSs with highermaterial initial cost compared with ordinary carbonsteels.

In addition, SSs show high values of elongation-to-fracture eu, and this increases with the thickness: forASS (S220 and S240) the values vary between 35%(S240) and 37% (S220), for a thickness less than 3mm,while a value of 40% was found for greater thickness.These figures are, however, the lower bounds. Thus,the higher ultimate elongation has a beneficialinfluence on the application of SS in seismic designand/or retrofitting. Moreover, experimental testsperformed on SS beam–columns[16] showed excellentenergy absorption capacity (ductility), thus promotingthe efficiency of SS in seismic applications. Inaddition, it was found that the ductility increases as afunction of the ratio of Ni/Cr (see Fig. 5), thereforeASSs can be used efficiently.

SSs generally exhibit rather high increases instrengths at fast rates of loading[14], whereas the effectof strain rate on the initial tangent elasticity modulusis negligible. Annealed types of ASS exhibit a proofstress reduction of 15 and 30% for tests conductedwith a strain rate from 10�3 to 10�5 s�1 and from 10�3

to 10�8 s�1, respectively. More recently, dynamic testson SS[20] were performed over a range of strain ratesfrom 1.4� 10�4 to 8.0 sec�1 for a total of 54 dynamictensile tests. It has been confirmed that the initialstress state of the material has an effect on the strainrate. Typical strain-time curves show that the strainrate can be idealised as two discrete slopes,representing the pre- and post-yield strain rates, ’eeyand ’eeu respectively. The influence of the materialstrain rate sensitivity decreases with an increase instrain, i.e. ’eey5’eeu. The transition between the twoslopes occurs in the yield region and depends uponthe change in stiffness of the material from elastic toplastic behaviour. As a consequence, the ultimatetensile strength for dynamic loading conditions isenhanced to a lesser extent than the yield stress for thesame strain rate. A modified expression of the

Cowper-Symonds empirical formula may be used toevaluate the dynamic proof stress syd:

syd � s0:2s0:2

¼ ’eeD

� �1=q(9)

where the constants D and q may be determined froma least-mean-squares fit when plotting the data on alog–log diagram with axes corresponding to log[(syd/s0.2)�1] (abscissa) and log ð’eeÞ (ordinate). It is advisedto use at ’ee ¼ 0:1 s�1for austenitic grades (S220 andS240) the constants D ¼ 2002300 s�1 and q ¼ 425,and D ¼ 550026000 sec�1 and q ¼ 627 for duplex2500[20]. Therefore, it is confirmed that the dynamicproof stresses syd (overstress) are dependent upon theSS grades; the higher the grade the higher theoverstress.

ASS and AFS possess greater toughness than mildsteel[15] and may be assumed not to be susceptible tobrittle fracture for service temperatures down to�408C. Furthermore, recent fatigue tests[21] basedupon constant amplitude axial tension loadingshowed that longitudinal and transverse non-load-carrying fillet welds for SS behave much better thanequivalent welds in ordinary steels. Thus referenceS-N curves for mild steel[13] underestimate the actualresponse of SS for the same fatigue classes.Nonetheless, it is thought that higher fatigue classescannot be reliably used yet for designing constructionin stainless steels, because of the limited experimentaldata. Therefore, further experimental work is requiredto validate the higher performance of SS. It has beenobserved, however, that there are no significantchanges of fatigue strength with thickness, at least forthickness of between 8 and 12mm, unlike mild steelfor which the behaviour generally deteriorates withincreasing thickness.

The main reasons behind the use of SS for seismicrehabilitation may be summarized as follows:

* the manufacturing processes are amenable totighter control of the variation of yield strength andhence of the stress ratio su/s0.2;

Fig. 6 Material overstrength for austenitic stainless steels: (a) grade 304; (b) grade 316



* they offer high durability and adequatedeformation capacity;

* the ductility is higher than ordinary carbon steels,e.g. ultimate elongation eu ¼ 50260% (SSs)compared with eu ¼ 20230%(mild steels);

* they have excellent properties for bucklingphenomena, such as local buckling, and thestrength reduction after buckling is much smallerthan that of ordinary mild steels.

3.2 MODELLING

Material modelling for SSs is generally cumbersomesince it should be based upon multiaxial models forcyclic plasticity. A two-surface-based formulationwith distortional rules has been proposed for SSs[18].This model (Fig. 7) enables the plastic threshold forloading steps to be achieved by means ofmodifications applied to the earlier material model(elastic inner and memory outer surfaces). Moreover,under stress reversals the stress vector is not cut off bythe elastic limit surface. This specific feature does notapply for standard incremental plasticity-basedmodels for continua. Such a two-surface modelprovides results in agreement with experimental testson SS both for uniaxial and biaxial stress states. Sincethe initial yielding criteria for the ASS grade arealmost isotropic, the formulation (von Mises criterion)is well suited to define the mechanical response of theASS rather than the AFSS grades.

The reduction of the yield strength in the directionopposite to the initial loading (Bauschinger effect), aswell as the increased yield strength in the directiontransverse to the initial loading, can be representedthrough a distortional hardening rule. However, areliable choice of the proof stress value is necessary. Itis advisable for numerical modelling of materials withno distinct yield point, such as AAs and SSs, toemploy the proportional limit (s0.01) rather than the0.2% offset stress (s0.2).

The two-surface constitutive model (Fig. 7) iscomprised of a memory surface and one elastic limitsurface bounding the region in the stress space,assumed completely elastic. The memory surfacecontrols the largest effective stress (se) and the relativeplastic modulus, and is also used to compute thedirection of the plastic flow. A simple von Misessurface with its centre in the origin of the referencesystem and based on an isotropic hardening rule issufficiently accurate as the memory surface. Theelastic limit surfaces comprise two differentboundaries; a von Mises surface with mixedhardening in the region of the stress point at initialloading, and a distorted surface in the oppositedirection are used for the inner surfaces. Theanalytical formulations of such surfaces are asfollows:

Surface relative to the initial loading:

FI ¼ 32 s̄ijs̄ij � %ss2e ¼ 0 (10:1)

Surface relative to the loading in the oppositedirection:

FII ¼ 32 s̄ij Iijkl þCaijakl

� �s̄kl � %ss2e ¼ 0 (10:2)

where the deviatoric stresses s̄ij and sij are given as:

s̄ij ¼ sij � aij (10:3)

s̄ij ¼ sij � 13 skkdij (10:4)

with aij is the current centre of the yield surface.Moreover, the von Mises effective stress %sseis:

%sse ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi32 s̄ij � s̄ij

q(10:5)

and the scalar function C depends upon the deviatorytensor aij:

C ¼ ca20 þ aijaij

(10:6)

which implies that the distortion is introduced as soonas plastic strains are produced. The distortionparameter c varies between 2.5 and 3.0 as a functionof the grades, while a0 ¼ 0:001 for all SSs.Furthermore, the two surfaces FI and FII share thesame centre aij and size %sse.

On the other hand, the uniaxial stress–strainresponse for SS is generally used for FEMcalculations; in such cases the ROM is employed.However, the latter model is characterized by aprogressive decrease of the plastic modulus and isunsuitable when employed for a limited strain rangein the SS uniaxial response. Nonetheless,experimental investigations[22] showed that the ROMcurve matches perfectly the actual (experimental)stress strain relationship up to the equivalent yieldpoint (s0.2). Beyond the stress s0.2 the mismatch tendsto diverge and hence an improvement of the original

Fig. 7 Translation elastic limit surface combined with expansionof memory surface[18]



formula is required. Therefore, a composite Ramberg–Osgood formula may be used, as follows:

for s4s0:2 e ¼ sE0

þ epyss0:2

� �n(11:1)

for s4s0:2 e ¼ s� s0:2E0:2

þ epus� s0:2su � s0:2

� �n0þet;0:2

(11:2)

where n and n0 are parameters to be calibrated byfitting the experimental curves; their values can beassumed to be 5–6 (n) and 3–4 (n0). epy and epu are theplastic strains corresponding to the 0.2% proof stress(s0.2) and ultimate strength (su), respectively, whileet,0.2 is the total strain corresponding to e0.2. E0 and E0.2

are the initial and the proof stress moduli. It is worthnoting that the second branch of the curve has beenderived by employing translation of the coordinatesystem from the origin to the 0.2% stress point andexpressing the basic formula in the new referencesystem.

In several practical applications it may beconvenient and adequate to model the materialresponse for SSs by means of uniaxial stress–strainrelationships of the Petersson and Popov multi-surface formulation[23,24]. The latter employs a mixedisotropic and kinematic hardening rule and has beensuccessfully adopted for several studies[25,26]. Its mainadvantage with respect to other simplified models,such as bilinear with or without hardening, wasobserved particularly in the large strain cyclicamplitudes. Moreover, the multi-surface model givesa reliable estimate of the plastic hinge length asopposed to an overestimate of up to 50%, whenemploying simplified piecewise models, includingbilinear ones. Therefore, to obtain a realisticprediction of the system ductility as well as to achievea rational representation of the structural (rather thannumerical) collapse, the multi-surface model is areliable formulation for structural assessment.


SSs used for structural components exhibit sufficientplastic deformation capacity and excellent energyabsorbing ability. Moreover, SSs have excellentproperties for buckling phenomena; so they aresuitable for seismic retrofitting. However, fewexamples exist world-wide of framed structures withbeams and columns in SSs; they refer mainly to newoffice buildings (Fig. 8), cultural facilities andswimming pool buildings and roofs[16].

Tubular sections are more common than wideflange profiles. Tubes may be formed from plate andseam welding. They have also been produced bycentrifugal casting to provide a wide range ofrequired thicknesses[27]. Tubular components can beused in space frames, trusses, bracings and endframes. Rolled angles, bars, rods and fabricatedcomponents can be used for the strengthening ofstructural components and systems.

Recent analytical studies[19] performed on a set of 50carbon steel (CS), SS and hybrid (CS and SS) moment-resisting frames (MRFs) as in Fig. 9 have shown thatSS in seismic design may be beneficial, but it is subjectto a number of constraints and design considerations.Static inelastic analyses (pushovers) were carried outon regular (RMRFs) and irregular MRFs in elevation(IMRFs, i.e. with soft storey, and SET1, SET2 and SET3with setbacks). The distribution of SS within the MRFsis summarized in Table 2. It is worth noting that therelative merits and the cost-effectiveness of SSs at thebeam ends (dissipative zones) and beam-to-columnconnections (Christmas tree) have been investigated forseismic retrofitting applications.

Indeed, the results of the performed analyses haveshown that for RMRFs and frames with setbacks(SET1, SET2 and SET3) there is quite a wide range ofvariability in terms of improved energy dissipationcapacity, e.g. behaviour factor supply[28]. Nevertheless,the higher the amount of SS in the columns the higherthe behaviour factors (Table 3).

It is worth mentioning that the spreading of suchmetal alloy gives rise to a higher reserve of global

Fig. 8 Structural applications of stainless steel: (a) tubular trusses for skylight supports; (b) for mega-bracing; (c) filled with water forexternal fire protection system[27]




resistance capacity (Fig. 10), thus implying a saferdesign with regard to CS. Similarly, the computedvalues of global ductility confirm the enhancedperformance of hybrid frames. At yield limit state theCS benchmark frames exhibit lower interstorey drifts(d/h) than for hybrid and SS MRFs. By contrast, theformer possesses higher d/h at the ultimate limit state,which corresponds to the onset of 4% storey drift. Anupper limit for the beneficial effects of hybridbuilding structures was observed for SS beam-to-column joints. The optimal configuration correspondsto the MRFs with SS at column ends (spanning 20% ofthe length at each member).

Further experimental and analytical work iscertainly required to investigate possible uses of SS in

Fig. 9 Geometric layout of the assessed set of MRFs

.......................................................................................................................................................

.......................................................................................................................................................

.......................................................................................................................................................

Table 2 Distribution of SS (% of member length) within the MRFs

Frame RMRFs & IMRFs SET1 SET2 SET3

Designation Type Beams Columns Total Beams Columns Total Beams Columns Total Beams Columns Total

C100bc BCS10b H 20.0 12.0 20.0 11.8 20.0 11.5 20.0 11.2CS20b H 40.0 24.0 40.0 23.6 40.0 22.9 40.0 22.4CS10c H 20.0 8.0 20.0 8.2 20.0 8.5 20.0 8.8CS20c H 40.0 16.0 40.0 16.4 40.0 17.0 40.0 17.6CS10bc H 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0CS20bc H 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0CS100b H 100.0 60.0 100.0 58.9 100.0 57.5 100.0 56.0CS100c H 100.0 40.0 100.0 41.1 100.0 42.5 100.0 44.0S100bc B 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

B ¼ benchmark; H ¼ hybrid

............................................

.........................................................................

.........................................................................

Table 3 Mean values and coefficients of variations (COVs) ofbehaviour factors

q*

Frame Type Mean COV

C100bc 5.41 0.21CS10b 5.70 0.23CS20b 5.76 0.23CS10c 6.17 0.21CS20c 6.65 0.16CS10bc 6.53 0.23CS20bc 7.08 0.17CS100b 5.73 0.24CS100c 6.61 0.16S100bc 7.03 0.19

q* ¼ VU/VY; VU and VY ultimate and yield base shear



other structural systems, including concentric andeccentric braced frames and structural sub-assemblages, such as beam-to-column connectionsand shear links. Moreover, the dynamic buckling ofextremely slender profiles requires more theoreticaland experimental developments, particularly undertransient loading, as in earthquakes.

4 Shape memory alloys

SMAs are special metal alloys with superelasticproperties, which can undergo large strains with noresidual deformation after unloading. Thismechanism is based upon reversible solid-to-solid

phase transformation (austenite to martensite), whichcan be either thermal- or stress-induced. Theaustenite-to-martensite transformation increasesdeformations for constant stress. Dissipative capacityof SMAs depends upon the hysteretic loop generatedupon unloading, because of the chemical instability ofthe martensite which switches to austenite at lowstresses. Mechanical properties of SMAs are discussedin Section 4.1 along with issues related to materialmodelling in Section 4.2.


SMAs comprise binary or ternary metallic alloyscapable of undergoing thermo-elastic martensitic

Fig. 10 Pushover curves for the assessed set of MRFs: regular (MRFs), irregular (IMRFs) and with setbacks (SET1 and SET2)



transformations. Such alloys have attracted extensiveinterest in seismic retrofitting in the past decadebecause of their novel properties[29–31]. Indeed, SMAsare metallic materials which may undergo largedeformations (strains up to 10%!) while recoveringtheir initial configuration, without any residualdeformation, at the end of cyclic loading. Thus, unlikecommon plastically deforming metals, such as AAsand SSs, nonlinear deformations are metallurgicallyreversible for such novel alloys. This is a result of amartensitic phase change which can be eithertemperature-induced or stress-induced. SMAs aretwo-phase metals that may exist either in austenitic orin martensitic form. The former has a stiffermetallographic structure that gives rise to high yieldstrength, while the latter exhibits lower yield and isless rigid. Thus, phase type and its transformation areof paramount importance for mechanical properties ofthese alloys.

In thermally induced transformations at constantstress, SMAs are characterized by four temperatures:Ms and Mf during cooling, As and Af during heating(Fig. 11). Ms and Mf correspond to the temperatures atwhich the transformation from the parent phase(austenite or beta-phase) into martensite starts andfinishes, respectively. Typical values of Ms and Mf forNiTi alloy are �13 and �388C, respectively. On theother hand, As and Af are the temperatures at whichthe reverse transformation (martensite to beta-phase),starts and finishes. For Ni–Ti, the values for As and Af

are 22 and 378C, respectively. Therefore, martensite-to-austenite transformation occurs over a relativelynarrow temperature range, between �100 and 1008C,as a function of the alloy composition. However, thebeginning and end of the transformation duringheating or cooling extends over a much larger thermalrange.

The overall metallurgical transformation describesa hysteresis loop (thermal hysteresis) of the order of10–508C corresponding to T1 in Fig. 11. T1 varies as a

function of the alloying system[32]. It is worthmentioning that the thermal or transformationhysteresis is defined as the temperature differencebetween a phase transformation upon heating andcooling. In Ni–Ti alloys, for example, it is usuallymeasured as the difference between Ap and Mp. Ap

(Mp) is the temperature at which a shape memoryalloy is about 50% transformed to austenite(martensite) upon heating (cooling).

In stress-induced isothermal transformations,austenite transforms to martensite at a critical stress, sswhich varies as a function of the temperature[33]. Thehigher the applied stress the higher is the transitiontemperature. Under uniaxial load, stress in austeniteremains almost constant until the entire phase is fullytransformed, although deformations increase. Furtherstraining causes elastic loading of martensite. Byunloading, a reverse transformation occurs;unstressed martensite is unstable at suchtemperatures. The inverse transformation takes placeat a lower stress level, and hysteresis occurs(mechanical hysteresis). The stress ss at which thetransformation starts for Ni–Ti is about 120MPa and itends at a stress sf of 210MPa.

Depending on the material temperature, greater orlower than austenitic finish temperature Af, SMAsexhibit two different mechanical properties (Fig. 12).If the temperature is greater than Af, strains attainedon loading (even 8–10%) are completely andspontaneously recovered after unloading. Thisprocess leads to significant energy-absorbing capacitywith zero residual strain (superelasticity orpseudoelasticity). This effect is called superelasticbecause it is characterized by the impressive amountof possible elastic strain, which is more than 20 timeshigher than in conventional materials. For example,mild steels show values of yield strains of 0.12–0.20%.By contrast, if the material temperature is less than Af,residual strains remain at the end of unloading, butthey may be recovered by heating above Af (shapememory effect). It is worth noting that the residualstrain is very large if the temperature is less than As,or if the material phase is fully martensitic.

During thermal- and/or stress-induced phasetransformations, the modulus of elasticity of SMAsvaries significantly (thermo-elasticity), for example forNi–Ti alloy it changes by a factor of 2–4 (70GPa foraustenite compared with 300GPa for martensite).Similar changes may occur in yield strength, namely500MPa (austenite) and 300MPa (martensite). Yet,damping characteristics undergo significant changeswith temperature. It is instructive to note thatequivalent mechanical damping xeq of these metalalloys, expressed as a percentage of the critical value,is typically much higher than the steel counterpart,even when SMA material is near its activationtemperature. Values of xeq for these special metals areof the order of 15–20% in comparison with 0.1–0.2%generally used for mild steel[34]. The significant

Fig. 11 Typical transformation temperature curve for a SMAspecimen (constant stress)



damping level is due to the large hysteresis loopinvolved in the loading and unloading process.

Five groups of SMAs are of interest for seismicrehabilitation[31]: Ni–Ti, Fe–Mn–Si, two copper alloys(Cu–Zn–Al and Cu–Al–Ni) and some special stainlesssteel formulations. Although Ni–Ti SMAs aremore expensive and more difficult to machine thanCu-based SMAs, they are extensively used forstructural applications. Such metals allow higherworking stresses and strains, and generally exhibithigher stability under cyclic loads. Other mechanicalcharacteristics that render SMA; especially Ni–Tialloys, desirable for seismic protection ofstructures[33], include: (i) hysteretic damping;(ii) highly reliable energy dissipation based on arepeatable solid-state phase transformation; (iii) self-centring capability; (iv) excellent low- and high-cyclefatigue properties; (v) excellent corrosion resistance;and (vi) no degradation due to ageing.

Many advances have occurred recently in themodelling of shape memory materials; nevertheless,such modelling is not yet as mature as that of otherengineering solids. Section 4.2 discusses the availableformulations and provides the main advantages anddisadvantages of each of them in practicalapplications.

4.2 MODELLING

As far as modelling is concerned, a thermodynamicformulation was proposed[35] for the constitutive lawof SMAs; the latter was derived in regime of planestrains. A large number of analytical constitutivemodels have been proposed. An extensive review ofthese models can be found in the literature[36].However, such models are mainly mechanical and donot capture the rate dependence of the responseunder transient loading, e.g. earthquakes. Moreover,the latter are complex and difficult to implement inFEM codes for structural analysis. As a consequence,simplified formulations have been adopted forseismic engineering applications[29,37]. They consist ofone-dimensional stress–strain relationships capable ofdescribing the behaviour of superelastic alloys under

seismic excitations. The applicability of suchmathematical models has been verified throughexperimental tests[29]. The dependence of the stress-strain response to the loading rate and the consequenttemperature changes can also be adequatelyaccommodated. The analytical formulation ispresented in a uniaxial context because most of thepractical applications to seismic devices, such asbracings and isolation devices, are made directly orindirectly by the use of wires or their assembly. Theconstitutive laws (s–e curves) used in seismicapplications have the following expression:

’ss ¼ E ’ee� ’eej j s� bY

� �n� �(12:1)

b ¼ Ea ein þ ft ej jcerf aeð Þ u �’eeeð Þ½ ��

(12:2)

in which b is back-stress, Y is the SMAyield stress, i.e.the beginning of the stress-induced transition fromaustenite to martensite, and n is the overstress power.The constant a, given by Ey/(E�Ey) controls the slopeof the s–e curve; the quantities E and Ey are theaustenitic elastic modulus and the slope afteryielding, respectively. The post-yielding modulus Ey

may be assumed not greater than 0.10E.Moreover, inelastic strains ein are computed as

follows:

ein ¼ e� sE

(13)

while the error function erf(x) is given as:

erf xð Þ ¼ 2

p

Z x

0

e�x2dx (14)

and u(x) is the unit step function:

u xð Þ ¼0 x50

1 x50

((15)

The constants ft, c, and a are functions of thematerial; they control the recovery of the elastic strainduring unloading.

The mathematical model expressed in eqs (12.1)and (12.2) has been extended[37] to represent thehardening of SMAs after the transition to martensite iscompleted. Such model describes the material

(a)(b)

Fig. 12 Stress–strain relationship (a) shape memory effect; (b) superelasticity



https://www.researchgate.net/publication/238166637_Base_isolation_system_with_shape_memory_alloy_device_for_elevated_highway_bridges?el=1_x_8&enrichId=rgreq-2f72939127bb108c2e4de30a393400b8-XXX&enrichSource=Y292ZXJQYWdlOzIyNzYyOTY4OTtBUzoxMDEwODIyNjkyMjQ5NjdAMTQwMTExMTI5OTk1Ng==


https://www.researchgate.net/publication/245371876_Review_of_Mechanics_of_Shape_Memory_Alloy_Structures?el=1_x_8&enrichId=rgreq-2f72939127bb108c2e4de30a393400b8-XXX&enrichSource=Y292ZXJQYWdlOzIyNzYyOTY4OTtBUzoxMDEwODIyNjkyMjQ5NjdAMTQwMTExMTI5OTk1Ng==

behaviour over a wider range of strains. This is usefulespecially in the case of base isolation with SMAdevices. The extended model replaces eq. (12.1) withthe following:

’ss ¼E ’ee� ’eej j s� bY

� �n� �uI eð Þ þ Em’eeuII eð Þ

þ 3a1’eee2 þ 2a2sign eð Þ’eeeþ a3’eeuII eð Þ� �

(16:1)

with:

uIðeÞ ¼ 1� uIIðeÞ � uIIIðeÞð Þ (16:2)

uIIðeÞ ¼0 ej j5em1 ej j5em

((16:3)

uIIIðeÞ ¼1 e’ee40 and e15 ej j5em0 otherwise

((16:4)

The elastic behaviour of martensite depends uponthe term Em’eeuII eð Þ. This response starts if strains arehigher than em (Fig. 13), which corresponds to thecompletion of the phase transformation fromaustenite to martensite. The transition from thestiffness Ey to Em is smooth and is obtainedmathematically by means of the last bracketed term ineq. (16.1); this term is computed only during loadingand for strains e15 ej j5em. The curvature of thetransition depends upon the constants a1, a2 and a3,the values of which are chosen in such a way that theslope of the function in the last bracketed term in eq.(16.1), at e1 and em, is consistent with: (i) the slope ofSMA plastic behaviour; and (ii) elastic response ofmartensite. The slope evaluated in e2 controls thesmoothness of the transition.

For SMAs with perfect superelastic behaviour thevalues of the parameters controlling the shape ofloops are[37]: a ¼ 900, C ¼ 0:001, ft¼ 0.08, a ¼ 0:019and n ¼ 1. The limit of the superelastic range isem¼ 0.08, while the points defining the transition fromthe slope Ey to Em are e1¼ 0.05 and e2¼ 0.065. Thelatter is the mean of e1 and em. The elastic modulus ofmartensite Em is generally 30–35% lower than theelastic modulus of SMA austenite state E, and they

depend upon the alloy chemical composition. This isalso the case for the yield stress Y.


SMAs possess enhanced re-centring properties alongwith high low-cyclic fatigue resistance and low lifecycle cost; therefore, they have all the attributes forseismic retrofitting applications. Moreover,experimental tests[31,38] have shown that Ni–Ti alloysperform better than other alloys (Cu–Al–Zn, Cu–Al–Ni, Fe–Mn and Mn–Cu). They have superiorsuperelastic properties and low sensitivity totemperature in the range 5–358C for buildings and�5–458C for bridges. Significant fatigue and corrosionresistance are shown by either austenite andmartensite. Furthermore, an enhanced stability ofcyclic response has been observed experimentally andnumerically along with negligible degradation forenvironmental actions[37]. SMAs are thus used indissipative devices for innovative seismic protectionstrategies either in the form of bracing or baseisolators, with re-centring and/or energy dissipationcapacities[39].

SMA devices consist of bars and wires which differin diameter, stress-state during service life and phase.Wires are generally manufactured up to 2mmdiameter, primarily as austenite phase. By contrast,bars may have diameters up to 8mm and can beeither austenite or martensite. Special bars aremanufactured to 50mm. Generally, wires are used forpure axial loads, while bars are suitable for bendingand/or shear and/or torsion.

Martensite bars, under cyclic bending and torsiondissipate large amounts of energy (equivalent viscousdamping up to 15–20%). They have high fatigueresistance and mechanical behaviour not dependentupon temperature on load frequency. However, theyexhibit residual deformations upon unloading. Bycontrast, austenite bars possess lower energydissipation (equivalent viscous damping is 5–10%)with no residual deformations (superelasticity).

SMA dampers may be used for seismicapplications, especially for retrofitting of steel,composite and reinforced concrete framedstructures[30,31,40]. Braces with martensite bars underbending are very effective in mitigating seismicvibrations. Pretensioned austenite wires are usuallycombined with martensite bars to enhance mechanicalperformance of the dampers (re-centring group).Manufacturing of bending bars is usually easier thantorsion counterparts; moreover, they are compact andeasy to install into the device. Therefore, bending barsare more common for practical applications. Braceswith martensite bars in double-bending orpretensioned superelastic austenite wires representenergy-dissipating SMA groups; similarly, for baseisolation devices employing SMAs.Fig. 13 Cyclic stress–strain curves for SMAs





SMA dampers are based upon re-centring and high-energy dissipation of Ni–Ti alloys. However, thehigher the re-centring, the lower the dissipation. There-centring capability may be obtained by employingaustenitic wires. On the other hand, enhanced energydissipation is provided by martensitic bars subjectedto flexure and/or torsion. Austenitic superelasticpretensioned wires show high energy dissipation. Inthis case, the wires act as a double counteractingsystem of springs.

Ni–Ti alloys are still expensive (about 200 h/kg),thus the use is optimized by loading them mainly intension. Therefore, wires are initially pretensioned byimposing strains epret which are half the strains emrelative to austenite–martensite transformation, i.e.epret¼ 1/2 em. Pretension may also prevent buckling ofwires under compression.

SMA dampers may be arranged as in Fig. 14; theyconsist of two co-axial pipes with two groups of bolts:three plus three are placed laterally (dissipative group)and two on top (re-centring group). The dissipativegroup has two bolts connected to the internal pipewhile the third bolt is connected to the external pipe.The re-centring group has bolts connected to the innerand outer pipe, respectively.

Thus, the re-centring group forms a parallel systemwith the dissipative group. The former exhibits rigid-hardening behaviour while the latter behaves as aCoulomb-type system. As a consequence ofcombining re-centring (rigid–plastic with hardening)and dissipative groups (Coulomb’s constitutive law),a flag-shaped symmetric hysteretic loop isobtained.

Three types of SMA devices may be thusimplemented, as shown in Fig. 15 where the

relevant hysteretic force–displacement loops are alsoincluded:

* re-centring devices (SRCDs);* dissipative devices (NRCDs);* re-centring and dissipative devices (RCDs).

Optimal devices for seismic applications are RCDs.They show relatively low residual deformations andsignificant dissipative capacity. Moreover, theequivalent viscous damping (xeq) of RCDs withaustenite wires (re-centring group) and martensitebars (dissipative group) ranges between 4 and 12%.Using austenite wires for re-centring and austenitegroups, xeq increases to 12–18%. SRCDs haverelatively small xeq, between 2 and 8%. By contrast,ordinary equivalent damping for NRCDs is of theorder of 40% when pretensioned austenite wires areused. Therefore, to design SMA dampers, it isessential to choose adequate numbers and types ofwires and bars, and calibrate the pretension. Thedesign should be targeted to achieve high re-centringcapacity, high stiffness for small displacements andelevated energy dissipation.

The effectiveness of base isolation devices in SMAshas been compared with that of rubber systems. Thesedevices consist of a SMA wire re-centring and/ordissipating device based on the same scheme as thebraces and with three sliding steel–Teflon bearings(Fig. 16). Alternatively, U-shaped SMA bars or steelplates can be introduced in the bearings as energydissipation groups. Extensive numerical andexperimental tests performed in Europe[31] haveshown that the displacements of the isolation systemand the interstorey displacements (superstructure) aresignificantly smaller for the SMA-based device. These

Fig. 14 SMA damper (working mechanism) [31]



reductions vary with the intensity of the groundmotion: the higher the base acceleration, the higherthe reduction (40–50% for 0.35 g compared with 70–80% for 0.60 g). Therefore, SMA-based devices forseismic isolation are highly efficient in improving thestructural performance and represent a viable strategyfor the rehabilitation of steel buildings.

It is worth noting that, comparing the costs for SMApassive control systems (base isolation and bracings)with the traditional counterparts, there is no

significant increase in the cost if Ni–Ti is used as thekernel component of the device.

Finally, an innovative steel semi-rigid connectionwith Ni–Ti–SMA tendons has been recently tested toretrofit beam-to-column connections[41,42]. Such ascheme relies upon the mechanical properties ofSMAs, i.e. shape memory effects and superelasticeffects (See Section 4.2). In the pseudoelastictemperature range, Ni–Ti components not onlydissipate energy, but also provide the connection with

-10

-5

0

5

10

-8 -6 -4 -2 0 2 4 6 8

Displacement (mm)

For

ce (

kN)

-10

-5

0

5

10

-8 -6 -4 -2 0 2 4 6 8

Displacement (mm)

For

ce (

kN)

-10

-5

0

5

10

-8 -6 -4 -2 0 2 4 6 8

Displacement (mm)

Forc

e (k

N)

(a)(b) (c)

Fig. 15 SMA damper for steel brace: (a) re-centring (SCRD); (b) dissipative (NRCD); (c) re-centring-dissipative (RCD) [31]

Fig. 16 Layout of the isolation system with SMAs [31]



restoring forces. SMA tendons, e.g. rods of 20–40mmdiameter and 400–500mm length, may be connectedto the column from the top and bottom flanges of thebeam (Fig. 17).

Experimental tests showed that the connectionbehaviour is stable with significant energy dissipation(no pinching). Moreover, the tendons may recover byheating the original shape, even after largedeformations, and the connection dissipativecapacities are preserved. Butane torches are veryeffective in providing high levels of heat at a rapidrate. By contrast, heat tape has the ability to wraparound the tendon and thus heat it uniformly. Therate of heat flow and the maximum temperature aremore limited, 1408C (heat tape) compared with 2888C(butane torches).

Further experimental and numerical tests arerequired to ascertain the feasibility of the applicationof SMAs to retrofit beam-to-column connections forsteel buildings.

5 Conclusions

This study has shown that novel metals such asaluminium alloys (AAs), stainless steels (SSs) andshape memory alloys (SMAs) exhibit: (i) strength-to-weight ratio fy/g; (ii) material overstrength fu/fy; (iii)elongation at fracture eu; (iv) equivalent damping xeq;and (v) fatigue and corrosion resistance which aresuperior to traditional mild steels. Therefore, suchmetals are attractive for seismic retrofitting of existingsteel buildings. Indeed, they are suitable fordissipative zones, e.g. plastic hinge zones, diagonalbracings, shear links and metal shear walls, owing totheir enhanced ductility (for example eu¼ 50–60% forSSs) and hence energy absorption (for examplexeq¼ 8–16% for SMAs). Moreover, reliable analytical

formulations for material modelling are available foreither simple or complex loading conditions, such asuniaxial and multiaxial stress states. However, thematerial costs remain prohibitive when comparedwith traditional mild steels. The higher costsexpressed in h/kg range between 4 and 6 times forAAs and SSs and are much higher (about 200 times)for the SMAs. Thus, in order to minimize the volumeof material for structural components, an ad hocdesign guide should be formulated. Further analyticaland experimental work is therefore required to assessthe viability and cost-effectiveness of their use inpractical applications

Acknowledgements

This work was supported in part by the EarthquakeEngineering Research Centers Program of theNational Science Foundation under NSF Award EEC97-01785. Any opinions, findings and conclusions orrecommendations expressed are those of the authorsand do not necessarily reflect those of the NationalScience Foundation.

References and recommended reading

[1] Mahin SA. Lessons from damage to steel buildings during the Northridge

earthquake. Engineering Structures 1998: 20(4–6): 261–270.

[2] Watanabe E, Sugiura K, Nagata K & Kitane Y. Performances and

damages to steel structures during 1995 Hyogoken-Nanbu earthquake. Engineering

Structures 1998: 20(4–6): 282–290.

[3] Naeim F, Lew M, Huang CH, Lam HK & Carpernter LD. The

performance of tall buildings during the 21 September 1999 Chi-Chi earthquake

Taiwan. The Structural Design of Tall Buildings 2000: 9(2): 137–160.

[4] Di Sarno L & Elnashai AS. Seismic retrofitting of steel and composite

building structures. Mid-America Earthquake Center Report, CD Release 02-01,

University of Illinois at Urbana-Champaign, IL, USA. 2002.

Fig. 17 Partially restrained connection with SMA tendons: (a) experimental sub-assemblage; (b) moment–rotation diagram[41]








[5] Eurocode 8. Design of Structures for Earthquake Resistance. Part 3:

Strengthening and repair of buildings. Brussels: European Commission for Standardiza-

tion. 2002.

[6] Tryland T, Clausen AH & Remseth S. Effect of material and geometry

variations on beam under patch loading. Journal of Structural Engineering (ASCE) 2001:

127(8): 930–939.

[7] Rai DC & Wallace BJ. Aluminium shear-links for enhanced seismic

resistance. Earthquake Engineering and Structural Dynamics 1998: 27(4): 315–342.

[8] Mazzolani FM & Mandara A. Modern trends in the use of special metals

for the improvement of historical and monumental structures. Engineering Structures

2002; 24(7): 834–856.

[9] Mazzolani FM. Aluminium Alloy Structures. 2nd Edn. London: E&FN Spon.

1995.

[10] Eurocode 9. Design of Aluminium Alloy Structures. Part 1.1: General Rules and

Rules for Buildings. Brussels: European Commission for Standardization. 1999.

[11] Moen L, Hopperstad OS & Langseth M. Rotational capacity of

aluminum beams under moment gradient. I: Experiments. Journal of Structural

Engineering, ASCE, 1999: 125(8): 910–920.

[12] De Matteis G, Moen LA, Langseth M, Landolfo R, Hopperstad OS

& Mazzolani FM. Cross sectional classification for aluminium beams. Parametric

study. Journal of Structural Engineering (ASCE) 2001: 127(3); 271–279.

[13] Eurocode 3. Design of Steel Structures. Part 1.1: General Rules and Rules for

Buildings. Brussels: European Commissions for Standardization. 1993.

[14] Euro Inox. Design Manual for Structural Stainless Steel. European Stainless

Steel Development & Information Group, Nickel Development Institute, Toronto.

1994.

[15] Eurocode 3. Design of Steel Structures. Part 1.4: General Rules}Supple-

mentary Rules for Stainless Steel. Brussels: European Commission for Standardization.

1996.

[16] Aoki H. Establishment of design standards and current practice for

stainless steel structural design in Japan. Journal of Constructional Steel Research 2000:

54(1): 191–210.

[17] Burgan BA, Baddoo NR & Gilsenan KA. Structural design of stainless

steel members: Comparison between Eurocode 3, Part 1.4 and tests results. Journal

of Constructional Steel Research 2000: 54(1): 51–73.

[18] Johansson B & Olsson A. Current design practice and research on

stainless steel structures in Sweden. Journal of Constructional Steel Research 2000:

54(1): 3–29.

[19] Di Sarno L, Elnashai AS & Nethercot DA. Seismic performance

assessment of stainless steel frames. Journal of Constructional Steel Research 2003:

in press.

[20] Jones N & Birch RS. Dynamic and Static Tensile Tests on Stainless Steel for

The Steel Construction Institute. Confidential Report, Ascot, Berkshire, UK, 1998.

[21] The Steel Construction Institute. Development of the use of stainless

steel in construction. Workpage No. 7 ‘Fatigue’. Final Report to European Coal and

Steel Community, Ascot, Berkshire, UK. 2000.

[22] Mirambell E & Real E. On the calculation of deflections in structural

stainless beams: an experimental and numerical investigation. Journal of Constructional

Steel Research 2000: 54(1): 109–133.

[23] Petersson H & Popov EP. Constitutive relations for generalized

loadings. Journal of the Engineering Mechanics Division (ASCE) 1977: 103(EM4);

611–627.

[24] Popov EP & Petersson H. Cyclic metal plasticity: experiments and

theory. Journal of the Engineering Mechanics Division (ASCE) 1978: 104(EM6);

1371–1388.

[25] Mizuno E, Kato M & Fukumoto Y. Multi-surface model application to

beam-columns subjected to cyclic loads. Journal of Constructional Steel Research 1987:

7(4): 253–277.

[26] Elnashai AS & Izzuddin BA. Modelling of material non linearities in

steel structures subjected to transient dynamic loading. Earthquake Engineering and

Structural Dynamics 1993: 22(6): 509–532.

[27] Specialty Steel Industry of North America. Stainless Steel for

Structural Applications. Design Handbook. Ontario, SSINA. 1999.

[28] Borzi B & Elnashai AS. Refined force reduction factor for seismic

design. Engineering Structures 2000: 22(10): 1244–1260.

[29] Graesser E & Cozzarelli F. Shape memory alloys as new materials

for aseismic isolation. Journal of Engineering Mechanics (ASCE) 1991: 117(11):

2590–2608.

[30] Housner GW, Bergman LA, Caughey TK, Chassiakos AG, Claus

RO, Masri SF, Skelton RE, Soong TT, Spenser BF Jr, Yao TP. Structural

control: past, present, and future. Journal of Engineering Mechanics, (ASCE) 1997:

123(9): 897–971.

[31] Dolce M, Cardone D & Marnetto R. Implementation and testing of

passive control devices based on shape memory alloys. Earthquake Engineering and

Structural Dynamics 2000: 29(7): 945–968.

[32] Van Humbeeck J. Shape memory alloys: a material and a technology.

Advanced Engineering Materials 2001: 3(11): 837–850.

[33] Duerig TW, Melton KN, Stockel D & Wayman CM. Engineering

aspects of shape memory alloys. London: Butterworth Heinemann. 1990.

[34] Bachmann H, Ammann WJ, Deischl F, Eisenmann J, Floegl I,

Hirsch GH, Klein GK, Lande GJ, Mahrenholtz O, Natke HG, Nussbaumer

H, Pretlove AJ, Rainer JH, Saemann EU & Steinbeisser L. Vibration Problems

in Structures. Practical Guidelines. Basel: Birkhauser. 1995.

[35] Achenbach M, Atanochovic T & Muler I. A model for memory alloys

in plane strain. International Journal of Solids and Structures 1986: 22(2): 171–193.

[36] Birman V. Review of mechanics of shape memory alloy structures. Applied

Mechanics Review 1997: 50(11): 629–645.

[37] Wilde K, Gardoni P & Fujino Y. Base isolation system with shape

memory alloy device for elevated highway bridges. Engineering Structures 2000: 22(3);

222–229.

[38] Des Roches R & Delemont M. Seismic retrofit of simply supported

bridges using shape memory alloys. Engineering Structures 2002: 24(3): 325–332.

[39] Bruno S & Valente C. Comparative response analysis of conventional

and innovative seismic protection strategies. Earthquake Engineering and Structural

Dynamics 2002: 31(5): 1067–1092.

[40] Soong TT & Spenser BF. Supplemental energy dissipation: state-of-the-

art and state-of-practice. Engineering Structures 2002: 24(3): 243–259.

[41] DesRoches R, Leon R, Hess G & Ocel J. Innovative beam-column joint

connections using shape memory alloy components. Proceedings of the SPIE Smart

Systems for Bridges, Structures, and Highways Conference, New Port Beach, CA,

2001: Paper n. 4330–27.

[42] Ocel J, Leon RT, DesRoches R, Krumme R, Hayes J & Sweeney S.

Full-scale testing of nitinol based semi-rigid connections, Proceedings of the 12th

European Conference on Earthquake Engineering, London, 2002: Paper 614.

LDi SarnoDepartment of Structural Analysis and Design,University of Naples, Federico II,Naples, Italy(currently post-doctoral fellow atMid-America Earthquake Center),University of Illinois at Urbana-Champaign,USAE-mail: [email protected]

ASElnashaiNewmark Civil Engineering Laboratory,Department of Civil and Environmental Engineering,University of Illinois at Urbana-Champaign,USA






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Special metals for seismic retrofitting of steel buildings

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