Composite columns and composite compression members

6.7.1. General

Scope

A composite column is defined in clause 1.5.2.5 as ‘a composite member subjected mainly to

compression or to compression and bending’. The title of clause 6.7 includes ‘compression

members’, to make clear that its scope is not limited to vertical members but includes, for example, composite members in triangulated or Vierendeel girders. These girders may also have composite tension members, for which provisions are given in EN 1994-2.

In this guide, references to ‘columns’ includes other composite compression members, unless noted otherwise, and for buildings, ‘column’ means a length of column between adjacent lateral restraints; typically, a storey height.

Design rules for columns sometimes refer to ‘effective length’. That term is not generally used in clause 6.7. Instead, the ‘relative slenderness’ is defined, in clause 6.7.3.3(2), in terms of Ncr, ‘the elastic critical normal force for the relevant buckling mode’.

This use of Ncris explained in the comments on clause 6.7.3.3.

Clause 6.7.1(1)P

Clause 6.7.1(1)P refers to Fig. 6.17, in which all the sections shown have double symmetry; but clause 6.7.1(6) makes clear that the scope of the general method of clause 6.7.2 includes members of non-symmetrical section.84

The bending moment in a column depends on the assumed location of the line of action of the axial force, N. Where the cross-section has double symmetry, this is the intersection of the axes of symmetry. In other cases the choice, made in the modelling for global analysis, should be retained for the analysis of the cross-sections. A small degree of asymmetry (e.g. due to an embedded pipe) can be allowed for by ignoring in calculations concrete areas elsewhere, such that symmetry is restored.

No shear connectors are shown in the cross-sections in Fig. 6.17, because within a column length the longitudinal shear is normally much lower than in a beam, and sufficient interaction may be provided by bond or friction. Shear connectors should be provided for load introduction, following clause 6.7.4.

The minimum compression for a member to be regarded as a column, rather than a beam, is not stated. As shown in Example 6.11, the use of the cross-sections in Fig. 6.17 as beams without shear connectors is usually prevented by the low design shear strengths due to bond and friction (clause 6.7.4.3).

Clause 6.7.1(2)P The strengths of materials in clause 6.7.1(2)P are as for beams, except that class C60/75 and lightweight-aggregate concretes are excluded. For these, additional provisions (e.g. for creep, shrinkage, and strain capacity) would be required.85,86

Clause 6.7.1(3) Clause 6.7.1(3) and clause 5.1.1(2) both concern the scope of EN 1994-1-1. They appear to exclude composite columns in high-rise buildings with a reinforced concrete core. For these ‘mixed’ structures, additional consideration in the global analysis of the effects of shrinkage, creep, and column shortening may be needed.

Clause 6.7.1(4) The steel contribution ratio (clause 6.7.1(4)), is essentially the proportion of the squash load of the section that is provided by the structural steel member. If it is outside the limits given, the member should be treated as reinforced concrete or as structural steel, as appropriate.

Independent action effects Clause 6.7.1(7)

The interaction curve for the resistance of a column cross-section to combined axial force N and uniaxial bending M is shown in Fig. 6.19, and, as a polygon, in Fig. 6.38 of this guide. It has a region BD where an increase in NEdincreases MRd. Clause 6.7.1(7) refers to a situation

where at ultimate load the factored bending moment, γFMEk, could co-exist with an

‘independent’ axial force that was less than its design value, γFNEk. It says that verification

should be based on the lower value, 0.8γFNEk.

Discussion of this rule is illustrated in Fig. 6.34, which shows region BDC of the interaction curve in Fig. 6.19, which is symmetrical about the line AD. If

Npm, Rd/2 gFNEk 0.8gFNEk B 0 D C N M E MRd Mpl, Rd A

γFNEk< Npm, Rd/2 (D6.37)

then MRdshould be found for an axial force of 0.8γFNEk, as shown by point E. The reduction

in MRdis usually small.

A simpler but more conservative rule is given in ENV 1994-1-1, with a clearer definition of ‘independent actions’: if MRdcorresponding to γFNEkis found to exceed Mpl, Rd, MRdshould

be taken as Mpl, Rd. It is applicable unless the bending moment MEd is due solely to the

eccentricity of the force NEd. Its effect is to replace the curve BDC in Fig. 6.34 with the line

BC.

Local buckling

Clause 6.7.1(8)P

The principle of clause 6.7.1(8)P is followed by its application rules. They ensure that the concrete (which will be reinforced in accordance with EN 1992-1-1) restrains the steel and prevents it from buckling even when yielded.

For partly encased sections, the encasement prevents local buckling of the steel web, and prevents rotation of the steel flange at its junction with the web, so that a higher bf/t ratio may

be used than for a bare steel section. Table 6.3 gives the limit as 44ε, compared with about 22ε (from EN 1993-1-1) for a Class 2 flange. (In EN 1994, as in EN 1993, ε = ÷(235/fy), in units of

newtons per square millimetre.)

For concrete-filled rectangular hollow steel sections (RHS), the limit of 52ε compares with about 41ε for a steel RHS. For a concrete-filled circular hollow section, the limiting d/t of 90ε2_{compares with 70ε}2_{for Class 2 in EN 1993-1-1.}

6.7.2. General method of design

Clause 6.7.2

Designers of composite columns will normally ensure that they fall within the scope of the simplified method of clause 6.7.3; but occasionally the need arises for a non-uniform or asymmetric member. The ‘general method’ of clause 6.7.2 is provided both for this reason, and to enable advanced software-based methods to be used.

Clause 6.7.2(3)P Clause 6.7.2 is more a set of principles than a design method. Development of software

that satisfies these principles is a complex task. Clause 6.7.2(3)P refers to ‘internal forces’. These are the action effects within the column length, found from those acting on its ends, determined by global analysis to Section 5. At present, such an analysis is likely to exclude member imperfections and second-order effects within members, but comprehensive software may become available.

Clause 6.7.2(3) also refers to ‘elastic-plastic analysis’. This is defined in clause 1.5.6.10 of

EN 1990 as ‘structural analysis that uses stress/strain or moment/curvature relationships consisting of a linear elastic part followed by a plastic part with or without hardening.’

As the three materials in a composite section follow different non-linear relationships, direct analysis of cross-sections is not possible. One has first to assume the dimensions and materials of the member, and then determine the axial force N and bending moment M at a cross-section from assumed values of axial strain and curvature φ, using the relevant material properties. The M–N–φ relationship for each section can be found from many such calculations. This becomes even more complex where biaxial bending is present.87

Integration along the length of the column then leads to a non-linear member stiffness matrix that relates axial force and end moments to the axial change of length and end rotations.

6.7.3. Simplified method of design

Scope of the simplified method

Clause 6.7.3.1 Clause 6.7.3.1(1)

The method has been calibrated by comparison with test results.88_{Its scope (clause 6.7.3.1) is}

limited mainly by the range of results available, which leads to the restriction £ 2 in clause 6.7.3.1(1). For most columns, the method requires second-order analysis in which explicit account is taken of imperfections. The use of strut curves is limited to axially loaded members.

Clause 6.7.3.1(2)

The restriction on unconnected steel sections in clause 6.7.3.1(1) is to prevent loss of stiffness due to slip, which would invalidate the formulae for EI of the column cross-section. The limits to concrete cover in clause 6.7.3.1(2) arise from concern over strain softening of concrete invalidating the interaction diagram (Fig. 6.19), and from the limited test data for columns with thicker covers. These provisions normally ensure that for each axis of bending, the flexural stiffness of the steel section makes a significant contribution to the total stiffness. Greater cover can be used by ignoring in calculation the concrete that exceeds the stated limits.

Clause 6.7.3.1(3) The limit of 6% in clause 6.7.3.1(3) on the reinforcement used in calculation is more liberal than the 4% (except at laps) recommended in EN 1992-1-1. This limit and that on maximum slenderness are unlikely to be restrictive in practice.

Clause 6.7.3.1(4) Clause 6.7.3.1(4) is intended to prevent the use of sections susceptible to lateral–torsional buckling. The reference to hc< bcarises because hcis defined as the overall depth in the

direction normal to the major axis of the steel section (Fig. 6.17). The term ‘major axis’ can be misleading, because some column sections have Iz> Iy, even though Ia, y> Ia, z.

Resistance of cross-sections

Clause 6.7.3.2(1)

Calculations for composite sections, with three materials, are potentially more complex than for reinforced concrete, so simplifications to some provisions of EN 1992-1-1 are made in EN 1994-1-1. Reference to the partial safety factors for the materials is avoided by specifying resistances in terms of design values for strength, rather than characteristic values; for example in equation (6.30) for plastic resistance to compression in clause 6.7.3.2(1). This resistance, Npl, Rd, is the ultimate axial load that a short column can sustain, assuming that the

structural steel and reinforcement are yielding and the concrete is crushing.

For concrete-encased sections, the crushing stress is taken as 85% of the design cylinder strength, as explained in the comments on clause 3.1. For concrete-filled sections, the concrete component develops a higher strength because of the confinement from the steel section, and the 15% reduction is not made; see also the comments on clause 6.7.3.2(6).

Resistance to combined compression and bending

Clause 6.7.3.2(2) The bending resistance of a column cross-section, Mbeam in Class 1 or 2 (clause 6.7.3.2(2)). Points on the interaction curve shown in Figs 6.18 andpl, Rd, is calculated as for a composite

6.19 represent limiting combinations of compressive axial load N and moment M which

correspond to the plastic resistance of the cross-section.

The resistance is found using rectangular stress blocks. For simplicity, that for the concrete extends to the neutral axis, as shown in Fig. 6.35 for resistance to bending (point B in Fig. 6.19 and Fig. 6.38). As explained in the comments on clause 3.1(1), this simplification is unconservative in comparison with stress/strain curves for concrete and the rules of EN 1992-1-1. To compensate for this, the plastic resistance moment for the column section is reduced by a factor αMin clause 6.7.3.6(1).

0.85fcd fyd fyd fsd fsd Mpl, Rd – + + Reinforcement Steel Concrete

As axial compression increases, the neutral axis moves; for example, towards the lower edge of the section shown in Fig. 6.35, and then outside the section. The interaction curve is therefore determined by moving the neutral axis in increments across the section, and finding pairs of values of M and N from the corresponding stress blocks. This requires a computer program, unless the simplification given in clause 6.7.3.2(5) is used. Simplified expressions for the coordinates of points B, C and D on the interaction curve in Fig. 6.34 are given in Appendix C. Further comment is given in Examples 6.10 and C.1.

Influence of transverse shear

Clause 6.7.3.2(3) Clause 6.7.3.2(4)

Clauses 6.7.3.2(3) and 6.7.3.2(4), on the influence of transverse shear on the interaction curve, are generally the same as clause 6.2.2.4 on moment–shear interaction in beams. One assumes first that the shear VEdacts on the structural steel section alone. If it is less than

0.5Vpl, a, Rd, it has no effect. If it is greater, there is an option of sharing it between the steel and

reinforced concrete sections, which may reduce that acting on the steel to below 0.5Vpl, a, Rd. If

it does not, then a reduced design yield strength is used for the shear area, as for the web of a beam. In a column, however, the shear area depends on the plane of bending considered, and may consist of the flanges of the steel section. It is assumed that shear buckling does not occur.

Simplified interaction curve

Clause 6.7.3.2(5)

Clause 6.7.3.2(5) explains the use of the polygonal diagram BDCA in Fig. 6.19 as an