Evaluation of Structural Robustness of Members and Connections

L. Simões da Silva, L. Neves University of Coimbra, Portugal

L. Baniotopoulos1, P. Perdikaris2, M. Zygomalas1 Aristotle University of Thessaloniki, University of Thessaly, Greece

V. Bosiljkov Slovenian National Building and Civil Engineering Institute, Slovenia

H. Bouchair CUST – Lermes Blaise Pascal University, France

G. De Matteis University of Naples Federico II, Italy

D. Dubina “Politehnica” University of Timisoara, Romania

P. Haller1, U. Kuhlmann2, F. Kühnemund2, H. Stangenberg3 TU Dresden, University of Stuttgart, University of Aachen, Germany

G. Huber Aste Engineering, Innsbruck, Austria

A. Koslowski Rzeszow University of Technology/Universidade da Beira Interior, Poland/Portugal

F. Wald Czech Technical University in Prague, Czech Republic

ABSTRACT: A state-of-the-art review of the evaluation of the ductility of structural members and connections in view of robustness is presented in this paper, focussing on the specific contributions of the COST C12 members. Firstly, a general methodology common to all structural materials is presented for both members and connections. Next, specific aspects for the various materials are described, together with reference to available experimental, numerical and analytical work.

1 INTRODUCTION

Robustness of a structure represents the ability of the structure not to suffer a major collapse due to minor accidental damage. According to Bertero (1997), a robust steel structure should be provided with balanced stiffness, strength and ductility be-tween its members, connections and supports. Be-cause the issue of ductility is still the most difficult to establish, special emphasis in this paper will be devoted to the description of the various methodolo-gies and current developments (analytical, numerical and experimental) for the evaluation of ductility for the various structural materials. 2 GENERAL METHODOLOGY

2.1 MEMBERS 2.1.1 Introduction

The evaluation of the ductility of structural mem-

bers was a topic of several research programs in the last years. The determination of available rotation capacity for plastic distribution in structural systems

was predominant in that research work. These re-sults are important for the examination of structural robustness both in general and also for exceptional loading.

Subsequently the testing procedure for the deter-mination of the ductility of structural members is il-lustrated, followed by the respective definition for the available deformation capacity. Different authors recalculated the test behaviour using numerical or mechanical models. These models are introduced with references for further study.

Different concepts for the check of sufficient ro-tation capacity are followed by the codes or re-searchers, respectively. A short overview over these procedures closes this state-of-the–art review.

2.1.2 Tests 2.1.2.1 Testing procedure and test results

The ductility of structural members was investi-gated in three-point-bending tests. Figure 1 shows the principle of the corresponding test set up. From

the measured beam end rotation the angle of rotation φ as shown in Figure 1 could be derived.

The typical result of these tests is a non-linear moment-rotation curve with a stable increasing branch, a maximum bearing moment capacity and a post critical decreasing part. The plotted rotation is not a physical value, but derived from the measured end rotation. It characterises the ductility of the beam including the plastic curvature in the yield zone.

Μ

Μ

φφφφ

φ

Figure 1. Principle of test set up and test result of a three point bending test.

2.1.2.2 Definition of the members ductility Up to now, the ductility of members is mainly

dealt in view of the available rotation capacity. It characterises the ability of a plastified section to ro-tate while maintaining its design moment resistance. Due to strain-hardening effects the real moment ex-ceeds the ideal plastic moment Mpl. With increasing rotations the moment graph passes a maximum value and decreases until it reaches the level of the ideal plastic moment Mpl again.

The available rotation capacity φavail of a member is defined as the rotation from the point Mpl is first reached (under assumption of ideal-elastic/ideal-plastic behaviour) to the point the real M-φ-curve reaches the level of Mpl again (see Figure 1).

2.1.3 Models for the determination of ductil-ity

2.1.3.1 Models for I-shape sections Kuhlmann (1986, 1987a,b) developed a numerical

procedure to calculate the moment-rotation-behaviour of I-shaped beams considering local buck-ling in the plastic range. The behaviour of the beams in the post critical part of the moment-rotation-relationship is considered by a yield line model for the buckled web and flange parts (see Figure 2). Feldmann (1994) uses a similar model for represen-tation of the post critical buckling behaviour of I-shape beams. Spangemacher bases his investigation on numerical simulations of I-shaped beams. Axhag (1998) presented in his thesis a cross section model, which predicts the moment-rotation relationship for slender I-shaped girders made of high strength steel.

Figure 2. Yield line model for the post buckling behaviour of a beam flange from Kuhlmann (1987a).

2.1.3.2 Models for hollow sections Research work of Stranghöhner (1995) focuses on

the ductility behaviour of hollow sections. She fol-lows a similar procedure as the researches men-tioned above. Tests are compared to results of nu-merical and mechanical modelling. The decreasing branch of the respective moment-rotation-curve is represented by a corresponding yield line model for the webs of the hollow section.

2.1.4 Concepts for check of sufficient ductil-ity

2.1.4.1 General demand The application of plastic hinge theory requires

sufficient rotation capacity of those sections, where plastic hinges occurs, except for the section forming the final hinge. Consequently the available rotation capacity of the section φavail must be larger than or equal to the required rotation φreq as demanded from the structural system. Equation (1) has to be ful-filled.

reqavail φφ ≥ (1)

2.1.4.2 Deemed-to-satisfy-criteria For practical design rules should be simple to use.

Eurocode 3 (1992) replaces the explicit check of suf-ficient rotation capacity by the check of profile slen-derness values. From thorough scientific investiga-tions boundary values are derived due to flange and web slenderness and stress distribution in the cross section. The rotation capacity of members is limited among others by local buckling. In dependence of the slenderness values of its parts Eurocode 3 (1992) classifies the sections to allow for different kinds of design methods. In case the slenderness values ac-cording to class 1 are satisfied no further check of rotation capacity is necessary.

2.1.4.3 Explicit check of sufficient rotation capacity Feldmann (1994) and Spangemacher (1992) fol-

low a different path for the check of the sufficient rotation capacity. For the determination of the avail-able rotation capacity of I-Shaped sections a formula is given, which is based on tests as well as on nu-

merical and mechanical parameter studies. By that the field of application is extended, e.g. also on the check of the ductility capacity for plastic design of structures under cyclic loading from earthquakes. However for each case the required rotation capacity has to be determined in dependence of the structural system and on the relevant level of sophistication.

Further investigations on the required values of rotation capacity also incorporating the joint behav-iour are necessary.

2.2 CONNECTIONS 2.2.1 Introduction

Conventionally, connections are treated either as nominally pinned or as fully continuous. A modern approach is to develop efficient connection types first and then to take their realistic behaviour into consideration within the frame analysis. An accurate representation of the joint behaviour forms the basis for a correct and safe structural design, where the available joint properties have to be compared with the requirements from the structure at serviceability and ultimate limit states.

Connections have to transfer moments and forces between members with an adequate margin of safety. Their behaviour obviously influences the dis-tribution of forces within the structure. The connec-tion’s representation can be subdivided into the four steps: characterisation, classification, idealisation and modelling. This complex process allows finally to establish adequate procedures to ensure that equa-tion (1) is satisfied, and is described below in more detail.

2.2.2 Characterisation That means the determination of the joint’s mo-

ment-rotation curves (Fig. 1); or, at least, the deter-mination of the corresponding key values (initial ro-tational stiffness, moment resistance and rotation capacity). This can be achieved with different ap-proaches: (i) experimental, using full-scale joint tests (Huber 2000, chapter 3.6), (ii) numerical, based on finite element calculations and (iii) analytical.

In the following the component method will be used as the analytical tool to determine the joint re-sponse, especially its ductility. An analytical de-scription of the behaviour of a joint has to cover all sources of deformabilities, local plastifications, plas-tic redistribution of forces within the joint itself and local instabilities. Due to the multitude of influenc-ing parameters, a macroscopic inspection of the complex joint by subdividing it into components has proved to be most appropriate. The components can be modelled by translational springs with non-linear force-deformation response. The joint characterisa-tion basing on the component method therefore starts with the identification of the contributing

components, followed by their characterisation (de-termination of their structural properties as force-deformation curves) and ending up with the assem-bly of the component properties or curves to those of the joint.

actual curve

M

φ

actual initial stiffness

actual plastic moment resistance

actual rotation capacity

from quasi-static teststatistical evaluation

M

φ

initial stiffness

characteristic plastic

rotation capacity

from several tests

moment resistance

Fig. 1 Joint characteristics

Attention should be paid to the delicate wording when talking about rotations (Fig. 2). φpl is the (overall) rotation capacity, whereas (φpl - φel) should be named the plastic rotation capacity (necessary for global redistribution). So this plastic rotation capac-ity of joints corresponds to the rotation capacity of members (beams and columns). However whereas in the case of plastic hinges within members only this plastic rotation appears between the axis of the adja-cent members (the elastic rotation only leads to a common curvature), within a joint both the elastic and the plastic rotation can be observed as an angle between the connected elements.

M

φφel φpl

φpl ... (overall) rotation capacity

... plastic rotation capacityφpl φel−

φpl/φel ... rotation capacity factor

φ =redist

φ redist

Fig. 2 Proposed terms in view of rotations

2.2.2.1 Component identification According to the Eurocodes a (basic) component

of a joint is a specific part that makes an identified contribution to one or more of its structural

1

2

3

4

5

6

7

8,9,10

11 12

13

16

b j

h jz

1415

No. component1 interior steel web panel

2 concrete encasement3 exterior steel web panel (column flange+local effects)

4 effect of concrete encasement on exterior spring5 beam flange (local effects), contact plate, end plate

6 steel web panel incl. part of flange, fillet radius

7 stiffener in tension

8 column flange in bending (stiffened)

9 end plate in bending , beam web in tension

10 bolts in tension

11 reinforcement (within panel) in tension12 slip of composite beam (due to incomplete interaction)13 redirection of unbalanced forces14 steel web panel in shear

15 steel web panel in bending

16 concrete encasement in shear Fig. 3 Component model (spring model)

properties. When identifying the contributing com-ponents within a joint one can distinguish between components loaded in tension (or bending), com-pression and shear. Apart from the type of loading one can distinguish between components linked to the connecting elements, those linked to load-introduction into the column web panel and the component ”column web panel in shear”. The nodal subdivision leads to the component model (spring model, Fig. 3).

2.2.2.2 Component characterisation The component model is based on known force-

deformation curves of the individual contributing components, which have to be derived within the component characterisation (components’ key val-ues or even full curves). Again this can be done at different levels of accuracy using different tools, such as component tests (experimental approach), finite element simulations (numerical approach) or analytical mechanical models.

Sophisticated mechanical models describing the basic components’ response have been developed at several research centres and have been validated against component test results and numerical simula-tions. With the help of comprehensive parameter studies the sophisticated and relatively complex formulae describing the stiffness, resistance and de-formation capacity of each basic component could be reduced to easy-to-handle formats. Such simpli-fied formulae are integrated into the codes.

2.2.2.3 Component assembly The transfer from force-deformation curves of the

individual joint components to the moment-rotation curves of the full joint has to be done based on the component model fulfilling the requirements of compatibility and equilibrium. Doing so it is assured that the joint model behaves exactly in the same way as the complex component model with respect to applied moments.

Depending on the intended level of accuracy a more sophisticated or a simplified component model (different modelling of the components’ interplay) can be chosen (Fig. 4). Furthermore the assembly can be done for the main rotational key values only (initial rotational stiffness, plastic moment resis-tance, rotation capacity) or for the full shape of the resulting M-φ curves. Depending on those choices the assembly either has to be done by an iterative computational procedure or can be solved by a sim-ple calculation adding up the individual springs step by step parallel or in series. Especially for the de-termination of the joint’s failure mode and the resulting rotation capacity (ductility) a simplified analytical approach for a hand calculation could not yet be provided. The codes are therefore only giving rough guidelines.

Sophisticated Simplified

Fig. 4 Different accuracy levels of assembly

Two different tools have been provided by the au-thors for the assembly of component F-∆ curves to the joint’s M-φ curve. In (Silva and Girão, 2000) formulae are developed on the basis of an energy formulation that enable the evaluation of the M-φ curve. Alternatively, a computational tool is de-scribed in (Huber 2000, chapter 4.3) which is based on an iterative approach for the non-linear branches (Fig. 5) covering both the sophisticated and the sim-plified component model.

Fig. 5 CoBeJo program for component assembly

2.2.3 Classification, Idealisation The classification is a possible but not obligatory

tool for simplification of modelling providing boundary conditions defining the limits for the use of conventional types of modelling (nominally con-tinuous or nominally pinned). In view of the drastic increase of frame software capability the use of ad-vanced joint models will become more and more natural. When still aiming at conventional rigid or hinged joint models the joint characteristics in view of stiffness, strength and rotation capacity have to be compared to classification boundaries. Depending on the method of global analysis either all or only one of the classification checks becomes decisive.

In the following the required rotation for full re-distribution within the frame (“ductile” joints) will be provided: In systems where the first plastic hinges form in the joints (due to partial strength Mj,Rd<MRd, simultaneously at both beam ends), the joints have to provide sufficient overall rotation ca-pacity φpl for plastic redistribution within the beam. This required overall rotation φpl can be shared into a part φel (ideal elastic=Mj,Rd/S), the elastic rotation until the hinge in the joint has formed, and a part

φredist, the further rotation necessary to allow for a fi-nal plastic hinge at midspan due to global redistribu-tion. The ratio between φel and φredist obviously de-pends on the joint stiffness S, however the overall required rotation φpl= φel + φredist is independent of the joint’s stiffness (Fig. 6).

In contrast to its independence from the joint’s stiffness the required rotation indeed depends on the joint’s strength: φpl decreases - following nearly a linear function - with increasing moment resistance of the joints. In other words the required rotation of a high strength joint is lower than that of a hinge (Fig. 7). Details can be taken from (Huber 2000, chapter 3.10)

ΕΙL

p

M

S S

Φ

LS ⋅Ι⋅Ε=γ

)21(12LpM

2

hog γ+⋅⋅

−=

γ+γ+

⋅ΕΙ⋅

⋅=

21101

384Lpw

4

( )γ+⋅=−⋅

= 612

MM

8LpM hog

hog

2

sag

SM

M21M

3L hog

hogsag =

−⋅

ΕΙ⋅=φ

independent from S( )M5.0ME3L

hogRd,sagredist elpl ⋅−⋅Ι

=φ+φ=φ

0redist =φ( )M5.0ME3L

hogRd,sagel ⋅−⋅Ι

=φMM Rdj,hog =MM Rdsag,sag =5.0

MM

1LE3S

Rd,j

Rd,sag −⋅

Ι=

ME3L

Rd,sagredist ⋅Ι

=φ0el =φ0Mhog =MM Rdsag,sag =0S =

MM joint) strength (partial MM0 Rd,jhogRdRd,j ≤≤≤

Fig. 6 Required rotation capacity for full redistribution

Fig. 7 Proposal for ductility boundaries

Idealisation means the conversion of non-linear moment-rotation curves into simplified (linearised) ones. Depending on the available software either the full non-linear shape of the joint-curves or simplifi-cations of them can be assigned to the respective joint springs.

2.2.4 Modelling Modelling is the reproduction of the connection

behaviour within the structural analysis. Linked to the joint characteristics there are three types of joint modelling which are closely linked to the method of global analysis and to the classification of the joint: A continuous joint ensures full rotational continuity,

a semi-continuous joint provides only partial rota-tional continuity and a simple joint prevents any ro-tational continuity between the connected members (Fig. 8).

rigid, full-strength

pinned (hinged) = simple

= continuous

= semi-continuousfull or partial strength,specific rotation capacity

rigid or semi-rigid,

(sufficient rotation capacity) Fig. 8 Types of joint modelling

2.2.5 Conclusion Comprehensive knowledge is available on the

field of the analytical derivation of the joint’s stiff-ness and resistance whereas the determination of the rotation capacity still needs further research work. On the one hand only little information exists at pre-sent in view of the components’ deformation capac-ity and on the other hand comprehensive parameter studies will then be necessary to evaluate the inter-play of different components in view of the overall rotation capacity. Special attention will have to be paid to the fact that already a slight overstrength of a ductile component may change the failure mode to the second weakest and maybe brittle component! That can result in a completely different rotation ca-pacity of the whole joint.

These effects are being studied at different re-search centres under the umbrella of the actual COST-C12 project. The comparison between re-quired and available ductility values should finally lead to a classification system for joints hopefully as simple as that for beams where width-to-thickness ratios lead to 4 cross section classes. 3 CONCRETE STRUCTURES Recently, in relation to the “displacement-based” seismic design of new R/C structures and the evalua-tion and retrofitting of existing R/C structures, there has been an increased interest in estimating the de-formation-capacity of R/C members. The 1997 NEHRP Guidelines for the Seismic Rehabilitation of Buildings (FEMA-273/274 1997, FEMA-356 2000) evaluate a member by comparing the seismic de-mand and the member’s capacity in terms of defor-mations. In order the performance-based design of reinforced concrete structures subjected to earth-quake loads to result in improved structural per-formance, aside of other criteria such as specifying realistic demands, the capacity and ductility of com-ponent members and connections need to be evalu-ated and/or predicted with as much certainty as pos-sible. The local moment-, rotational- and ductility-capacity of R/C beam and column components (and connections) or the global drift-capacity of the struc-tural system under earthquake-type loads on the one

hand, and their shear strength on the other hand, are of major importance. This is true for either designing new structures or repairing existing ones. This phase of the design process, which may be associated with either primary or secondary structural components, refers to either strength or stiffness (deformation) evaluation at different performance levels. The force reduction or response modification factors, R, as-signed to different structural and material types by different design codes effectively reflect the per-ceived available ductility of a structural system (Paulay & Priestley 1992), although sometimes ac-count for effects additional to ductility. Models which consider the effects of inclined cracking, bond-slip law at the concrete-steel interface, the con-tribution of concrete in tension and a more appropri-ate ó-å diagram for the steel reinforcement have been for example proposed to determine the plastic rotation capacity of beams under monotonic loading (CEB 1993,1998). Because of the rather complex phenomena involved during the inelastic response of R/C members, in addition to the on-going needed re-search investigations on the development of more advanced models for determining the load- and de-formation- capacity, further experimental research is needed especially under cyclic loading to determine their true inelastic response and validate the pro-posed models. Based on a large database of mainly cyclic test re-sults on R/C beams, columns and walls it was con-cluded (Panagiotakos & Farthis 2001) that: (a) steel reinforcement ductility (high-ductility steel vs. cold-worked steel or tempcore steel) influence strongly the R/C member’s deformation capacity, (b) load cycling appears to be important in reducing substan-tially the deformation capacity only if it is applied fully at the maximum deformation, while the number and magnitude of deformation cycles before ultimate is unimportant, (c) the most important parameter in increasing the member’s deformation capacity ap-pears to be the shear-span ratio, (d) the effect of con-fining reinforcement on ductility is not as high as expected, (e) for values of concrete strength up to 120 MPa, the increase in ductility is equally positive

Figure 1. Experimental setup for the beam-column specimen.

as the compression-to-tension steel ratio, (f) increas-ing the applied axial load from zero to that at bal-ance results in an almost linear decrease in deforma-tion capacity to about 50% and (g) all other geometric and mechanical parameters being equal, shear walls failing either in flexure or shear-flexure exhibit deformation capacities of about 30% of that of a beam or a column member.

A current experimental research effort (Kotsovos

& Perdikaris 2001) at the National Technical Uni-versity in Athens and the University of Thessaly in Volos is underway to investigate the available strength and ductility in R/C members at the so-called “critical locations” and determine the appro-priateness of the design requirements and procedures of various design codes, which may result in grossly under- or over-estimating the load and ductility ca-pacity of R/C members. The main objective of this project is not only an improved design procedure for new R/C structures that insures the desired ductility but also for repairing and strengthening damaged R/C structures. Two-span (1.20-m and 1.95-m long) continuous 15-cm (wide) x 30-cm (high) R/C pris-matic beam-column specimens are tested under a concentrated monotonic and cyclic transverse load-ing applied at midspan of the 1.95–m long span for various levels of constant axial load (see Figures 1-2). The concrete specimens are reinforced with S500-2Ö14 steel rebars on each top and bottom face and appropriate number and distribution of S320-Ö6 closed steel stirrups according to the current Greek design code for R/C structures (EKOS 2000) and the “compressive-force path” concept (Kotsovos & Pav-lovic 1999). The applied transverse load and support

Figure 2. Photo of the experimental setup.

system used for the tests result in the formation of two plastic hinges (underneath the applied load and at the middle support) and an inflection point be-tween the load-point and the middle support, a common condition for a column member of a build-ing subjected to lateral seismic loads. Representative load-displacement loops under monotonic and cyclic transverse load application for a constant axial load equal to N=315 kN (about 44% of the axial load at

the balanced condition) are shown in Figures 3a and 3b.

0

50

100

150

200

250

0 20 40 60 8

DISPLACEMENT (mm)

LOA

D (k

N)

0

(a) Monotonic Loading

-200-150-100-50

050

100150200250

-40 -20 0 20 40

DISPLACEMENT (mm)

LOA

D (k

N)

(b) Cyclic Loading

Figure 3. Load-displacement loops for a specimen de-

signed according the current design code for R/C struc-tures in Greece.

4 STEEL STRUCTURES

4.1 Robustness: Redundancy, Overstrength and Ductility

A robust steel structure should be provided with balanced stiffness, strength and ductility between its members, connections and supports (Bertero, 1997). Conceptually, Seismic Resistant Steel (SRS) struc-tures are always redundant, because redundancy is the inherent condition of the reliability of structural systems. Therefore, in the American Design Codes (UBC, 1997, AISC, 1997), redundancy (or reliabil-ity) coefficient is a component of reduction factor R (corresponding to q-factor in Eurocode 8). Bertero R & Bertero V (1999) have shown the redundancy is dependent of overstrength and ductility of structural system. In fact, to take advantage of redundancy, it is necessary: 1) to decrease the coefficient of varia-tion, (COV), of the demand relatively to the COV of the supplied capacity (Nakashima, 1998); 2) to pro-vide the necessary overstrength of structural compo-nents in order to assure the yielding of dissipative-designed zones (Calderoni et al, 1996, Ohi, 1998); 3) to increase the plastic rotation capacity, i.e. duc-tility (Gioncu, 2000); 4) to guarantee a minimal rota-tion capacity in all members of the structural system so that they can follow the displacement of the struc-ture without failure and allow other elements to dis-

sipate the earthquake input energy. Therefore, struc-tural robustness means redundancy, overstrength and ductility.

As a measure of redundancy (overall overstrength) can be taken the ratio 1ααu ; uα - the ultimate mul-tiplier of seismic action; 1α - the multiplier of seis-mic action corresponding to the first plastic hinge. This definition is used in Eurocode 8(1994) to define the reduction factor; for MRS frames, for instance,

15 ααuq ×= . Dubina et al (1999) suggested as a measure of structural redundancy the Seismic Per-formance Factor (SPF):

s

u

EPAEPA

SPF = (1)

EPAu = Ultimate Effective Peak Acceleration, corre-sponding to the seismic input, evaluated for the most unfavorable failure criteria: drift, plastic rotation ca-pacity for members and joints and plastic instability (collapse);

EPAs = Effective Peak Acceleration induced by seismic excitation SPF > 1, and can take different values, according to the performance objectives of design. A special MRS frame designed according to SCWB philosophy (Strong Column Weak Beam), and based on the AISC-1997 provisions, is an example of a re-dundant structure. Such a frame, well designed, is capable to withstand ground motions of twice the design level very little likelihood of collapse, whereas a frame designed according to the WCSB approach (Weak Column Strong Beam), is ill-conditioned and may develop a collapse mechanism at an excitation level well below twice the design level (Biddah A &Heidebrecht, 1999). However, the WCSB traditional philosophy must nowadays be re-vised to account for the performances of Partial Moment (PR) Frames (Elnashai, 1998 and Salazar &Halder, 2001) and also for the Reduced Beam Sec-tion Moment (RBSM) Frames (Uang & Fan, 2000). In fact, in these cases, the redundancy and ductility of structure is obtained by weakness (thus not over-strength, obviously!) of beam-to-column joints and beam-to-joint zones, respectively.

4.2 Performance based design: Methodology and Modeling

Robustness of a SRS structure, e.g. redun-dancy/overstrength and ductility, must be designed to satisfy specific performance objectives. SEAOC-Vision 2000 (1995) and FEMA 273 (1996) docu-ments proposed four performance levels expressed in terms of interstorey drift limits (Table 1).

Table 1. Performance level limits __________________________________________________ Performance level Damage state Drift IDDR [3 – 5] [%] __________________________________________________ Fully operational, No damage 0.2 1 Immediate occupancy __________________________________________________ Operational, Damage Reparaible 0.5 0.3 Control, Moderate __________________________________________________ Life safe-Damage state Irreparable 1.5 0.6 __________________________________________________ Near collapse, Severe <2.5 0.8 Limited safety, Hazard reduced, >2.5 1.0 Collapse __________________________________________________

For comparison, in Eurocode 8 (1994) the allow-able drift takes values between 0.004h and 0.00h, while UBC 97 allows for values between 0.02h and 0.025h; h is the height of the storey. Alternatively, SEAOC-Vision 2000 defines the structural perform-ance in terms of displacement ductility demand, measured by the Inelastic Displacement Demand Ratio (IDDR). The values are also shown in Table 1: IDDR=0 corresponds to an elastic performance; IDDR=1.0 corresponds to an instability limit state and which the useable ductility is fully expended; IDDR=0.6 corresponds approximately to the upper limit for “life safe” level.

The IDDR criterion can be used in Displacement Design approach (Court & Kowalsky, 1998), while drift criterion is a target for Capacity Design ap-proach actually included in available design codes.

The design and analysis procedures (Ghabarah, 2001) play a very important role in the correct pre-diction of robustness parameters. Foutch et al (1998) shown that the calculated drifts at any specific storey in MRS frames can differ by more than 50% de-pending on the analysis method used and the ground motion considered. Also the computation models used for members and joints may significantly affect the structural response. In a recent study by Ciutina et al (2001), the influence of correct modeling of members and joints capacities is analyzed. The seismic response of a three bay-four story SCWB frame, subjected to far- and near-field seismic ac-tions is studied. The columns are X shaped welded steel sections, while beams are double T welded sec-tions. Beam-to-column joints are of bolted extended end plate, their performance being experimentally established (Dubina et al, 2001).

Two different sets of computation models for members and joints have been used in DRAIN 2DX analysis, i.e.:

- Elastic-plastic bilinear M-φ models and - Nonlinear inelastic fiber models for members,

calibrated for given sections with DUCTROT program (Gioncu & Petcu, 1999)

- Multilinear M-φ models for beam-to-column joints calibrated with test results (Figure 1).

-300

-200

-100

0

100

200

-0.035 -0.025 -0.015 -0.005 0.005 0.015 0.025 0.035

Rotation [rad.]

Mom

ent [

kNm

]

300

ExperimentalDRAIN 2DX model

Figure 1. Calibration of joint model

Figure 2 shows the difference in capacities of mem-bers and joints, corresponding to the two modeling techniques.

The increase of capacity is on about 40-50%, which lead to a 30% increase of capacity in push-over analysis.

Obviously, the robustness supply of a given struc-ture is significantly dependent by the design meth-odology, including both analysis procedure and quality of models used in computation

Columns

0

100

200

300

400

500

600

0 0.01 0.02 0.03 0.04 0.05 0.06

rot [rad.]

Mom

ent [

kNm

]

Fiber elementPerfect el-pl model

Beams

0

50

100

150

200

250

300

350

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

rot [rad.]

Mom

ent [

kNm

]

Fiber elementPerfect el-pl model

Joints

0

50

100

150

200

250

300

0 0.01 0.02 0.03 0.04 0.05 0.06

rot [rad.]

Mom

ent [

kNm

]

Perfect el-pl model

Multilinear model – experim.

Figure 2. M-φ curves used in DRAIN 2DX simulation models

4.3 Design criteria and Detailing Structural robustness of steel structures must be

based on proper design criteria and accurate detail-ing, in accordance with material properties and type

of loading effects (high strain rate, fatigue etc.). If discussion remains in the field of MRS frames (but the problems are of similar type for braced and dual steel frames), then the robustness depends on the performance of (SAC Phase II Project, Sanders, 1998):

- SCWB design principle - Panel zone strength - Connection strength and degradation charac-

teristics - P-∆ effects - Member local buckling The detailing analysis must mainly focus the

joints. The following design conditions are consid-ered to be generic irrespective the connection type: - Welded joints:

1. through-thickness strength 2. base material notch-toughness 3. weld wire notch-toughness 4. weld backing and run out tabs 5. reinforcing fillet welds 6. cope hole size, shape, workmanship

- Bolted joints: 1. Bolt sizing, hole type, tightening 2. Net section strength

In Europe a large COPERNICUS Project, called “RECOS”, focused the above mentioned problems and others, like influence of loading asymmetry, strain rate effect and the global performances of MRS frames accounting for connection behaviour. The results have been summarized in a book edited by the coordinator of international research team, Prof. F.M. Mazzolani (2000).

Connected to this subject the special issue of the Journal of Structural Engineering (2000), entitled “Steel Moment Frames After Northridge, must be also referred.

Robustness of steel structures is function of struc-tural redundancy, overstrength and ductility and is a matter of design processus. It depends on the quality of conceptual design, design philosophy and per-formance criteria. Design methodology, analysis and modeling play a very important role in correct evaluation of robustness parameters. Design detail-ing and material properties are also key factors of robustly designed structures.

5 STEEL-CONCRETE COMPOSITE

STRUCTURES

5.1 Introduction The behaviour of steel-concrete composite joints,

compared with the bare steel structures, has enhanced resistance and stiffness, besides other non-structural advantages and improved fire resistance. In this para-graph some examples of these facts are reported for steel and composite structures under monotonic and cyclic loading.

In seismic design composite frame structures are designed to provide dissipative zones in the regions of maximum bending moments. This implies the ap-plication of high behaviour factors taking account of the amount of energy dissipated by the structure when forming plastic hinges to achieve the full plas-tic chain. Thus, members and connections have to be prevented from sudden failure as buckling or crack-ing which is covered by the so-called capacity de-sign such that dissipative zones are mainly located in the beam cross-sections. Considering recent research results in the field of composite it can be stated that composite members and semi-continuous connections generally have ca-pability to perform quite well in static and cyclic loading. This aspect affects current capacity design which excludes connections and columns from con-tributing to the global behaviour.

5.2 Minor axis joints 5.2.1. Experimental behaviour and analitycal model of semi-rigid minor axis composite seat and web site plate joints

The activities of Rzeszow University of Technol-ogy in the field of composite joints are described be-low. Collection of tested composite minor axis speci-me s was shown in Table 1. n Table 1. Collection of test specimens SPECIMEN COLUMN BEAM REINFORCEMENTCP-1 HEB 200 IPE 240 6T10; ρ = 0,5 % CP-2.1 HEB 200 IPE 240 10T10; ρ = 0,8 % CP-2.2 HEB 200 IPE 240 10T10; ρ = 0,8 % CP-3 HEB 200 IPE 240 14T10; ρ = 1,1 %

Fig. 1 shows a general view of the tests, and Fig. 2 shows the comparison of bare steel and composite joints behaviour.

Fig. 1. General view of test An analytical joint model based on component

method has been developed for prediction of the

moment resistance (Fig. 3), initial stiffness (Fig. 4) and rotation capacity.

0

20

40

60

80

100

120

0 10 20 30 40 50 6φ [mrad]

M[k

Nm

]

0

bare steelCP-1CP-2CP-3

Fig. 2 - M-φ curves for composite and bare steel specimen

Fig. 3. Model of joint for predicting the moment resistance

Fig. 4. Spring model of joint for predicting the initial stiffness

Initial joint stiffness prediction was developed in the form of Equation 1.

E

kkkkkk

kkkh

khh

kkh

S

ccbcrt

bctv

cvr

cbr

inij ⋅−+++

+++−+=

2

22

. 1)11)(111(

111(12)11( (1)

5.2.2. Experimental behaviour of minor axis semi-rigid steel and composite end plate joints

Tests of semi-rigid minor axis steel and compos-ite end plate joints, performed at the University of Coimbra are referred below. Two column and two beam types were consid-ered, in two different joint configurations. Each of

these configurations was tested in monotonic load-ing under positive and under negative moment, and under cyclic loading, for the bare steel structure in a total of six tests. Six more similar tests were per-formed adding concrete to the structure to obtain the composite joint of Figure 6, and thus evaluating the composite action in this particular joint layout – Ta-ble 2 Table 2. Collection of test specimens TEST COLUMN BEAM TYPE LOADING E1 Monotonic M+E2 Monotonic M-E3

HEA 220 IPE 200 STEEL Cyclic

E4 Monotonic M+E5 Monotonic M-E6

IPE 330 IPE 240 STEEL Cyclic

E7 Monotonic M+E8 Monotonic M-E9

HEA 220 IPE 200 COMPOSITE Cyclic

E10 Monotonic M+E11 Monotonic M-E12

IPE 330 IPE 240 COMPOSITE Cyclic

p1a r

t r bw

h wh v

r

a

t s

a8

a6 a4

a9a104 M16 (5.8) IPE 240

Fc

Fb

Fr

X tw

2 M16 (5.8)

hr

h v

As in the previous paragraph, joint stiffness and re-sistance are strongly enhanced by the addition of concrete (Figure 7). The plastic moment of the steel joint in Figure 4 (ob-tained for a rotation of 20 mrad) is about 18 kN.m. A final moment of 50 kN.m is attained for a large rota-tion of 200 mrad (limited by the stroke of the hy-draulic jack). This rotation clearly shows the excel-lent ductility of this joint component and the importance of membrane action.

Fig. 5 – Geometry of the joints

φ

Fr kr

kt

kb

kc

∆c

∆b

∆t

∆r

Fc

Fb Ft

Ft

h r

h v

φ

Fig. 6 – Test layout In the equivalent composite joint, the maximum moment attained was 90 kN.m, and the critical com-ponent was not the column web loaded out of the plan. Yielding and instability of the compressed flange in the beam (IPE 220) led to the collapse of the joint. It is to be noted, however, that in cyclic tests the degradation of joint characteristics is much stronger in composite joints than in the bare steel joints with the same geometry, with the former tend-ing to the characteristics of the bare steel configura-tion after a significant number of cycles. This behav-iour is illustrated in Figure 5. It is to be noted, however, that in cyclic tests the degradation of joint characteristics is much stronger in composite joints than in the bare steel joints with the same geometry, with the former tending to the characteristics of the bare steel configuration after a significant number of cycles. This behaviour is illus-trated in Figure 8.

0

10

20

30

40

50

60

70

80

90

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

rot (rad)

Mom

ento

(kN

.m)

E7 - mistoE1 - metálico

H

IPE

20 0

t=1 5

Beam collapse

steel composite

Mom

ent (

kN.m

)

Fig. 7 – Comparison steel and composite behaviour

-100

-80

-60

-40

-20

0

20

40

60

80

100

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12

rot (rad)

E9 - mistoE1 - metálicosteel

composite

Mom

ent (

kN.m

)

Fig. 8 – Comparison between steel and composite behaviour under cyclic loading

5.3 Major axis joints under static and cyclic loading

In the current ECSC research-project “Applicability of composite structures to sway frames” addresses these aspects. Beside a static and cyclic full scale frame test a test series on composite joints is being performed. The series comprises static and cyclic joint tests taking account of the geometries and the distribution of internal forces of the reference full scale tests.

Supplemented with numerical analysis based on the component method guidance can be developed to evaluate the available robustness of a given joint in a certain load situation.

Figure 9. Setup for static test on unsymmetrically loadad beam to column joints

Figure 10. Setup for cyclic test on beam to column joints

Therefore ductility assessment developed for some joint components (AiF-Project: Komponeten-verformung steifenloser Anschlüsse) and already verified for steel joints in static loading (SIF- Pro Table 3. Collection of test specimens

TEST NODE TYPE LOADING E1 Monotonic M- / M- E2 Monotonic M+ / M- E11

INTERNAL STEEL Cyclic

E3 Monotonic M+ E4 Monotonic M- E9

EXTERNAL STEEL Cyclic

E7 Monotonic M- / M- E8 Monotonic M+ / M- E12

INTERNAL COMPOSITE Cyclic

E5 Monotonic M+ E6 Monotonic M- E10

EXTERNAL COMPOSITE Cyclic

Figure 11 - Internal node, composite column (Tests E7, E8 (monotonic) and E12 (cyclic))

Figure 12 - External node, composite column (Tests E5, E6 (monotonic) and E10 (cyclic))

-ject: vorhande Rotationskapazität wirtschaftlicher Anschlußkonstruktionen) will be taken into account and checked for their applicability for composite joints.

Experimental work was also carried out at the University of Coimbra (Simões, 2000) on steel and composite structures with rc slab. As explained in table 3, four main geometries were considered: external node and internal node (Figures 11 and 12) both for the bare steel and for the composite structure. In addition, each of these geometries was loaded under monotonic and cyclic conditions. Figure 13 reports the behaviour of the internal node under (a) monotonic and (b) under cyclic loading. Figure 14 reports the correspondent behaviour in external joints

-250

-200

-150

-100

-50

0

50

100

150

-50 -40 -30 -20 -10 0 10 20 30 40 50

Rotation φTotal (mrad)

Ben

ding

mom

ent (

kNm

)Test E1

Test E2

Test E7

Test E8

Figure 13a - Moment-rotation curves in monotonic tests E1, E2, E7 and E8

-200

-150

-100

-50

0

50

100

150

200

-50 -40 -30 -20 -10 0 10 20 30 40 50

Rotation (mrad)

Mom

ent (

kNm

)

Test E11Test E12

Figure 13b - Moment-rotation curves in cyclic tests E11 and E12

-250

-200

-150

-100

-50

0

50

100

150

200

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70

Rotation φTotal (mrad)

Ben

ding

mom

ent

(kN

m)

Test E3

Test E4

Test E5

Test E6

Figure 14a - Moment-rotation curves in monotonic tests E3, E4, E5 and E6

-250

-200

-150

-100

-50

0

50

100

150

200

250

-50 -40 -30 -20 -10 0 10 20 30 40 50

Rotation (mrad)

Mom

ent

(kN

m)

Test E9Test E10

Figure 14b - Moment-rotation curves in cyclic tests E9 and E10 6 MASONRY STRUCTURES

6.1 Introduction Masonry is a composite, heterogeneous, nonlinear structural material. As with other composite materi-als, also with masonry the mechanical properties are conditioned with the properties of composite com-ponents, their volume ratio and the properties of bond between the bricks and the layers of mortar – joints.

The type of the masonry within the Europe strongly differs in dependence from the most unfa-vorable thermal and loading conditions that could be expected (Figure 1). From that point of view the tra-dition of bricklaying in particular region has been established. Most natural loading condition for the masonry is compressive loading, nevertheless when exposed to accidental loading (Fig. 1.), masonry structural elements has to have enough resistance to prevent sudden collapse of the whole structure.

Compressive loading

Flexuralloading

Shear loading

Shear loading(normal to the direction of the wall)

Figure 1. Types of loading conditions in masonry.

6.2 Robustness of masonry elements In loadbearing masonry buildings, whether they are single or multistory, the walls serve as structural elements to support or resist loads, as architectural elements to divide or enclose space, or as a finish material. According to EC 6 (Eurocode 6 1995), the main types of structural walls are distinguished as:

single-leaf wall, double-leaf wall, cavity wall and grouted cavity wall.

When defining the term 'robustness' most design-ers assume the structure's ability not to suffer a ma-jor collapse due to minor accidental damage. Fac-tors, which are influencing the robustness of masonry buildings, are primarily the elevation, plan, wall layout as well as connections (wall to roof, wall to floor, wall to wall, ties etc.).

There are two main aspects of determination of the robustness of masonry elements: - due to the blast, impact forces, gas explosions,

traffic accidents (flexural loading) and - due to the earthquakes (shear loading).

6.2.1 Out of plane loaded masonry Most common way of designing masonry walls

imposed to lateral loading is by taking into account its flexural strength both parallel (fx1) and perpen-dicular (fx2) to the direction of the bed joints. In the case of accidental loading (ultimate state) it is much more advisable to design the masonry elements ac-cording to the predicted mechanism of failure (Fig. 2.).

Edge supports

First crack

Mechanismor failure

Load

Deflection at center

Diagonal crack

First crack

Permissibleload

Maximumload

Workingload

Ultimateload

Figure 2. Flexural loaded masonry structural element.

6.2.2 In-plane loaded masonry

a) b)

c) d)

e f) Figure 3. Shear tests for masonry structural elements.

There is no standardized test method for determi-

nation of the robustness and shear resistance of the masonry elements due to the earthquake loading (shear loading). Some of the most frequent ways of testing the large masonry elements are presented in Figure 3.

Neither of them can be considered as the one which response to the reality, but they are all chosen because they reproduce undoubted static or kinemat-ics boundary conditions which are easy to be inter-preted. According to our experience and the analysis of the results of other authors, only the test set-up presented in Figure 2a & 2f, with cyclic loading his-tory can give us all the behavioral parameters such are: global forces, global displacements, deforma-tions and response characteristics (mode of failure, shape of hysteresis (Fig. 4), cracking patterns, duc-tility capacity, energy absorption, damage evolution etc.) for the seismic assessment of the masonry structural elements.

-120

-90

-60

-30

0

30

60

90

120

-25 -15 -5 5 15 25

Displacement [mm] For

ce [k

N]

LV2

+Hf

+Hdt

C

σ0H

h

l

Hf

Hdt

-Hf

-Hmax-Hu

Figure 3. Shear tests for masonry structural elements. 7 TIMBER STRUCTURES

7.1 Generalities

This chapter deals with wood as a structural ma-terial. Engineers and architects are often critical of its material properties particularly with respect to strength, anisotropy and durability.

Research has to focus on these three characteris-tics to enhance the acceptance of wood for structural applications. The objective of this chapter is to show a perspective for building with wood where draw-backs can be overcome using wood modification and new technologies. Figure 1. Mechanical characteristics of clear spruce, densified spruce and oil heated densified spruce.

7.2 Modification of wood properties - densification and heat treatment

The design of a structure is decisively determined by the properties of the building material. Therefore the modification of the properties of the building material has the strongest impact on the structure. The above mentioned detrimental characteristics - strength, anisotropy and durability - can be im-proved by means of existing technologies and knowledge. Strength, for instance, can be increased using better grades or species with better mechanical characteristics [Holzbauatlas]. Durability depends to a great extent on the natural resistance of the spe-cies, which is very good for topical hardwood for in-stance[Sell]. Chemical preservation [Willeitner, Schwab] provides good results for outdoors applica-tions, however, the toxicity has a harmful effect on the usual environmental friendliness of wood.

For a further improvement of strength and dura-bility various techniques have been proposed in the past [Kollmann]. It is well known that wood is a po-rous material that can be easily compressed at a temperature of about 140°C. The density of domes-tic softwood, mostly spruce and pine, is increased in this process from about 450 kilogram per cubic me-ter to a value of over 1000, which results roughly in a doubling of the mechanical characteristics.

The application of densified wood has been re-cently investigated in structural connections [Haller, Wehsener] (figure 2). The joints from densified wood showed a significant improvement of the load bearing capacity.

Heat also affects the hygroscopic stability and du-rability. Heat treatments - also in natural oil - at about 200°C result in a dimensionally stable mate-rial with excellent biological resistance. The combi-nation of a simple heat treatment and densification [Rapp,Haller] leads to a new material which is in many cases better suited than ordinary wood (figure 1).

Figure 2. Connection made of densified wood.

7.3 Anisotropy and reinforcement

Anisotropy of wood results in an excellent ratio of strength and weight that surpasses metals, miner-als and plastics to a great extent. However, it may get even experienced designers into trouble because many details in timber construction require high strength in more than one direction.

Today's wood based materials represent a devel-opment where the ratio of anisotropy in the longitu-dinal and transversal direction is reduced. This re-duction leads to a compromise for strength and stiffness in both directions.

Solid wood is characterized by low strengths in shear and parallel to grain . Unlike bending stresses in the fibre direction, the corresponding loadings cannot be transferred economically by choosing a larger cross section. Therefore various techniques have been developed in order to reinforce wood per-pendicular to grain by means of glued-in rods, wood based panels for instance. These measures demand a profound knowledge from the designer and are lim-ited to a few specific problems.

As the design for high shear stresses and stresses parallel to grain cannot be done economically by a wider section the strength has to be increased by means of reinforcement techniques. Technical tex-tiles represent an effective and versatile technology to reinforce timber structures [Haller, Birk]. The re-inforcement can be applied locally or entirely to the construction element where the textile fibres may be oriented towards the occurring stresses and the shape. Moreover, the textile layer protects wood from weathering and hence affects its durability to a great extent.

As stresses are difficult to control within connec-tions e.g. at the vicinity of dowel type fasteners the load bearing behaviour can be tailored according to stiffness, strength and ductility. The influence of stress oriented textile reinforcements can be seen from (figure 3). It also appears that knitted textile placements behave best with an increase of the load bearing capacity for the single dowel of about 4 times.

Holz unverstärkt

Schlaufe gefächert

Auge ungestützt

Auge gestütztGlas-Komplex

Schlaufe gekreuzt

Schlaufe parallel

SternJojo

Flachgestricke

20

25

30

35

40

45

50

55

60

65

f h [N

/mm

2 ]

Lochleibungsfestigkeit (händische Strukturen)Lochleibungsfestigkeit (Flachgestricke)

Figure 3. Tailor made reinforcements of dowel type fasteners.

7.4 Material efficiency

In wood construction solid rectangular cross sec-tions predominate. These sections dispose of a very low material efficiency compared to technical pro-files which need less than 20% of the wooden sec-tion to achieve the required moment of inertia. If one further considers the low yield of about 50% for the saw milling of the logs, it is evident that the material efficiency is dramatic and that wood construction loses competitiveness at this stage.

The condition for the manufacturing of technical profiles is a plastic material behaviour to permit roll-ing or extrusion. Wood is regarded as an easy workable material. Quite the reverse! Wood can only be worked by cutting processes which are more expensive than forming processes. However, if one consider the above thermal densification of wood as a result of a compression strain of about 50%, it be-comes obvious that wood is very deformable. In deed, a tensile strain of 100% can be reached on densified wood by pulling it in hot and moist atmos-phere to its original, undensified state.

With this principle it becomes possible to manu-facture open and closed prismatic sections, the mate-rial efficiency of which is not inferior to technical profiles (figure 4). The availability of such cross sections on the market would promote wood as a structural material in civil engineering and other dis-ciplines to a great extent.

Figure 4. Thermo-mechanically formed cross section.

7.5 Wood compounds Wood can be combined with other materials to

compound elements. If one disregards here the com-pounds of two or more wood cross sections any load bearing building material could be used for a suit-able mixed compound.

Timber concrete composites have been success-fully used in the past for residential houses, bridges and in rehabilitation due to load bearing perform-ance, fire resistance and sound insulation etc. This compound has been mentioned in the literature of the 40's and rediscovered and investigated in the 80's [Hoeft, Natterer] (figure 5).

Figure 5. Example of a wood concrete cross section for floors.

The compound of wood and fibre reinforced plas-tic or technical textiles is recent. First unidirectional fibre reinforced plastic was used to increase the bending moment of gluelam beams. However, this method do not solve a severe design problem as the load bearing capacity can be efficiently increased by choosing a higher cross section where the height is raised to a power of two or three respectively.

Compounds between thermo-mechanically formed wood profiles and textiles are much more in-teresting since the ratio of the areas wood and textile is much better than in the example above. Theoreti-cal considerations show that such compounds have extremely good structural and economical character-istics (figure 6) [Ziegler]. Figure 6. Comparison of columns made of different materials. 8 ALUMINIUM AND STAINLESS STEEL

STRUCTURES

8.1 Aluminium members and connections

In the field of aluminium alloy structures the need for adopting special calculation methods for evaluat-ing the structural integrity of members and connec-tions is felt, especially owing to the necessity to take into account the actual mechanical features of the material (Mazzolani 1995). This is due to several reasons, such as: (1) the complex mechanical behav-iour of the material in post-elastic range, which ex-hibits continuous hardening and limited available ductility; (2) the great variety of aluminium alloys having mechanical features substantially different from each other; (3) the possibility to combine dif-ferent basic materials with different types of me-chanical fasteners (for instance, in case of bolted connections, both aluminium and steel bolts are used in the current practice); (4) the strong effect of weld-ing on the mechanical features of heat treatable alu-minium alloys. As a result, the direct application to aluminium structures of design rules calibrated for steel and other traditional materials is often inappro-priate.

Many of these aspects have being discussed within the activity of the CEN-TC250/SC9 Committee chaired by Prof. F.M. Mazzolani, which has worked out the first edition of Eurocode 9 "Aluminium Al-loy Structures" (Mazzolani 1999), which includes many methods and procedures accounting for the above features of the material. On the other hand, several research programs are ongoing in order to verify and extend the validation range of the existing procedures. Among many others, some of these pro-jects are dealing with stability problems (Landolfo 2000, Rasmussen & Rondal 1999), plastic design (Mazzolani et al. 1999), cross-sectional classifica-tion (De Matteis et al. 2001, Faella et al. 2000).

In particular, as far as structural joints are con-cerned, a large research project has been recently carried out at the University of Naples Federico II, sponsored by the Italian Ministry of University and Scientific and Technological Research (MURST). It is mainly concerned with the behaviour of bolted T-stub joint components, which has been deeply exam-ined under analytical, numerical and experimental points of view. Therefore, firstly, an analytical method to determine both the collapse mechanism type and the corresponding load bearing capacity of aluminium T-stubs based on the existing formula-tions adopted into EC3-Annex J has been proposed, emphasizing that for aluminium the joint collapse mechanism cannot be so easily predicted as for steel, it being strongly conditioned by the actual mechani-cal features of flange and bolt materials, namely strain hardening and available ductility (De Matteis et al. 2000). Then, a wide experimental campaign has been carried out aiming at validating the above model. Such experimental investigation, which represents the largest developed activity in the field of aluminium bolted connections in tension and bending, comprises 26 different specimens tested under monotonic and cyclic loading and allows many of the major influencing parameters to be worked out (De Matteis et al. 2001a). In particular, 4 different T-stub types (varying in-plane dimensions, plate thickness, number and location of bolts), 3 dif-ferent aluminium alloys as flange material, 3 differ-ent bolt materials and two different types of cou-pling systems have been considered. The obtained results allow the influence of the above parameters to be pointed out in terms of initial stiffness, ulti-mate strength, deformation capacity as well as ob-served failure plastic mechanisms (De Matteis et al. 2001b). Another research project, which has as scope the definition of deformation and load-carrying capacity of aluminium riveted connections, was recently car-ried out at the Institute of Steel Structures of the De-partment of Civil Engineering, Aristotle University of Thessaloniki (Zygomalas et al. 2001). In particu-lar, aluminium strips of 1 mm thickness, 60mm

width and 250 mm length have been tested. For each experiment two pieces were connected by applying 8 rivets &4mm. The obtained results of the tests in-clude a linear part of deformation and a part where the deformation is almost constant. The latter “pla-teau” phenomenon is due to the rotation of the rivets during the experiment, a behavior that changes the static response of the connection. Further experi-ments have been just started to be performed aiming to define the deformation in both aluminium pieces and the whole connection as a continuous unit within an aluminium structure and to clarify the pre-vious phenomenon. In parallel to the aforementioned laboratory testing, the behavior of butt-welded alu-minium joints have been numerically studied by ap-plying the F.E.M. aiming to investigate in details the HAZ effect and the ultimate tension strength of such welds (Kontoleon et al. 2000). As far as members are concerned, an extended pa-rametric nonlinear numerical study of the structural response of the structural members of a typical alu-minum structure having as scope to investigate their serviceability and strength were recently performed at the Institute of Steel Structures of the Department of Civil Engineering, Aristotle University of Thessa-loniki (Preftitsi et al. 1998). Concerning the material law of the investigated aluminium members, the Ramberg-Osgood isotropic stress-strain law and the nonlinear evolution law proposed by F. Mazzolani have been both used. At the nonlinear folded thin-shell structural model applied, the aluminium mem-bers were subjected to a variety of loading condi-tions (as dictated by Eurocode 1 and 9) that corre-spond to the loading conditions of a typical aluminium structure (as is e.g. an aluminium curtain-wall system). The computer software CASTEM 2000 has been used for the treatment of the struc-tures under investigation. All the results obtained are presented in (Preftitsi et al. 1998, Baniotopulos et al. 1999). In the forthcoming months, the obtained nu-merical results are to be checked by performing at the laboratory of the Institute of Steel Structures in Thessaloniki an already started program of tests on aluminium members of the same geometry and elas-ticity characteristics as those of the numerical ex-perimentation.

8.2 Stainless steel members and connections Stainless steel used for structural applications is

covered by ENV 1993-1.4. The austenitic steel is the most widely used in construction. Its stress-strain curve shows a non-linear and ductile behaviour with a high ultimate to yield strength ratio. This gives a large capacity of resistance and deformation which let suppose a good dissipation of energy under cyclic loading and a good redistribution of plastic loads without failure (ASCE 1990, NidL-EuroInox 1994). It has a good fire resistance and large possibilities of

strain hardening. However, for bolted connections, a design for the ULS loads may not be sufficient to avoid unacceptable plastic deformations in the SLS. In fact, the available design codes are focused on structural carbon steel. The formulas and design ap-proaches must be modified to take into account the non-linear behaviour of stainless steel. This non-linear behaviour is usually modelled by the Ram-berg-Osgood law using a conventional elastic limit (0.2% plastic deformation). A ECSC project, cover-ing all major aspects of the design of stainless steel elements in buildings, was initiated in 1998. One of its principal objectives was to verify, and propose improvements to the EC3-1.4. An experimental study for the cover-plate joints, was conducted at Clermont Ferrand and the results were compared to the predictions of EC3-1.4 (Bouchair et al. 2001). The tests show that the various ultimate state joint strengths are safely predicted with a very large duc-tility of all the joints under static loads. This will be a good guarantee of safety under cyclic or dynamic loads. The study is now being complimented by the use of finite element modelling in order to better un-derstand joint behaviour. It should also help to ex-tend the study to the design of other geometrical configurations and other types of joints (beam-to-column joints for example). Also, the evaluation of a beam deflections and a plastic loads redistribution needs to be more analysed. For the members, the se-cant modulus could be used in substitution to the elastic modulus (Van Den Berg 2000). Also, atten-tion has to be made to ensure that calculated plastic moment transmitted to the connections do not ex-ceed their own strength.

9 CONCLUSIONS

This paper presents a state-of-the-art in the

evaluation of ductility in view of ensuring adequate robustness of mixed structures under exceptional loading. It focuses on the contributions from within the COST C12 project and highlights the research needs for a comprehensive treatment of this subject.

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statsich und dynamisch belasteter Träger. Dissertation, RWTH Aachen.

Kuhlmann, U. 1986. Rotationskapazität biegebeanspruchter I-Profile unter Berücksichtigung des plastischen Beulens. Mitteilung Nr. 86-5, Dissertation, Ruhr-Universität Bo-chum.

Kuhlmann 1987a. Rechnerische Ermittlung der Rotationska-pazität biegebeansprichter I-Profile. Der Stahlbau. 56: 321 – 327.

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Spangenmacher, R. 1992. Zum Rotationsnachweis von Stahlk-onstruktionen, die nach dem Traglastverfahren berechnet werden. Dissertation, RWTH Aachen.

Stranghöner, N. 1995. Untersuchungen zum Rotationsverhal-ten von Trägern aus Hohlprofilen. Dissertation, RWTH Aachen.

General methodology: connections COST C1 1999. Recent advances in the field of structural steel

joints and their representation in the building frame analy-sis and design process. Brussels/Luxembourg.

COST C1 1992. Semi rigid behaviour of civil engineering structural connections. Proceedings of the 1st state of the art workshop, Straßbourg.

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