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ELSEVIER

J. Construct. Steel Res. Vo l . 46 No s . I- 3 pp. 146-148 paper number 121; 199801998 Elsevier Science Ltd. All rights reservedPrinted in Great Britain

PII: so143-974xx(9@ooo64-9 0143-974X/98 17.00 + 0.00

Design of Tapered Com pression M embers According toEurocode 3

A. M. Baptista and J. P. M uzeau 2Laboratk io National de Engenharia Civil LN EC), Avenida do Brasil, 101-1799 Lisboa

Codex, PortugalLERM ES, UniversitC Blake Pascal de Clermont-Ferrand, BP 206, 63174 Aubiike Cedex,

FrancePaper Number 121

Full paper on enclosed CD ROM

Tapered members for beams and columns are an interesting solution for thedesign of steel structures. They allow a gain of material which, for someparticular cases, should not be neglected. However, there are no specific rulesfor the design of such elements yet, and the Eurocode 3 allows the designersto choose the method for the verification of the safety of these members.

Instability phenomena, such as global buckling for example, are usuallythose that raise more difficulties to this verification. These elements must bechecked using second-order analysis or simplified methods based on modifi-cations of the basic procedure for uniform members.

This paper presents a formulation for the design of such members, Baptistaet al. (1995). According to Eurocode 3, the buckling resistance of a uniformmember is given by the following relationship:

1)In order to enlarge the field of application of this formula to tapered members,it is proposed to express the design resistance of tapered columns accordingto equation (2):

Nb m p . R d = k N b m i n . R d = k X PA 4ninfvlYM1 2)where: Nb, + , s the buckling resistance of the tapered member,

N b m i n .R d is the buckling resistance of a uniform memberwith the same boundary conditions, whose cross-sectioncorresponds to the smallest tapered member cross-section,k is a coefficient taking into account the effect of taperingon the member buckling resistance.

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Design of Tape red Com pressi on M em bers A cco rd i ng t o Eu rocode 147

In this relationship, Nb,mi,,Rds chosen as a reference value because, in thecase of a stocky column (without buckling), the resistance of the memberdepends on the geometrical and mechanical characteristics of its smallestcross-section. The coefficient k may be expressed by analytical relationships,which are found by means of mathematical fitting to the results of a largenumber of numerical simulations. These analytical relationships may bepresented under the form of various abacuses for the different boundary con-ditions, as shown in Figure 1.

The second-order non-linear mechanical model used on the numerical stud-ies, Baptista (1994), able to take into account the tapered shape of the com-pressed members, is presented in a first step. Then, an application example ispresented to validate its results.

The parametrical study was developed taking into account the variations inthe height of the cross-sections, the slenderness of the members and variousboundary conditions. The differences between the mechanical behaviour ofuniform and tapered compressed columns, with I shape cross-sections andhinged on both ends, are described for the two cases of buckling over theirstrong and weak axes of inertia.

An explanation of these differences is given for the different domains ofelastic and elastic-plastic evolution of their behaviours, depending on theirreference slenderness (A,,) values. 0 I998 Elsevier Science Ltd All r i g h t sreserved

KEYWORDSTapered column, non-uniform member, compressed element, design bucklingresistance, strong-axis buckling, weak-axis buckling, non-linear behaviour,elastic-plastic analysis, buckling rules, Eurocode 3.

k Member hinged at both ends

4 0 s 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8 3 0Fig 1 k coefficients or a tapered mem ber hinged at both ends and bent over its strong ax is.

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148 A. M. Bnptista and J. P. Muzea uREFEREN ES

Baptista, A. M . 1994), ModtYe non linkaire gt ometrique et materiel fond6 sur 1 ana-lyse des dkfoonnations globules des sections, Thkse de Doctorat, Blake Pascal Univer-sity, Clenno nt-Ferrand, 480 pp.Baptista, A. M . and Ribeiro, A. 1995), Resisthcia ao varejamento de pilares deinercia vuriavel em ago, LNEC , L isboa, Nota Tknica No 23/95 - NCE, 234 pp.