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made from the same material, the method will also apply. The value of the effective bending stiffness of these profiles about the z-z axis is given in Table 8.2.

### 8.4.3 Design procedure

When a built-up section is subjected to an axial compression design force, Fcd, the stress in the section will depend on the effective axial stiffness of the composite section, (EA)ef, which is:

i=i where n represents the number of members in the cross-section, and Ei is the mean modulus of elasticity of member i parallel to the grain and Ai is the cross-sectional area of member i .

In EC5 it is assumed that under the action of the axial design force the section will be subjected to a uniform strain and there will be no shear stress along the interfaces between the members. This will be achieved when the axial force is applied as a rigid body force over the section and its resultant acts through the centroid of the EA diagram of the section. Under this condition, the axial stress in each member i in the section will be:

Z.i=i EiAi where the symbols are as described above and ac,0,d,i is the axial stress in member i of the built-up section.

If the modulus of elasticity is the same for all members in the section, equation (8.6) reduces to:

Fc d

Atot i.e. the axial stress will be the same in all members and Atot is the total cross-sectional area of the built-up section.

The buckling strength of a built-up section about each axis of bending is dependent on the effective slenderness ratio of the section, A.ef, and, for a built-up column section having a pin jointed length t, it will be:

There will be a value for A.ef about the y-y axis and the z-z axis, and the value of the effective bending stiffness, (EI)ef, for each axis will be determined in accordance with the requirements of 8.4.1 and 8.4.2.

In EC5, to simplify the design procedure the effective axial stiffness of the built-up section as given in equation (8.5) is replaced by an axial stiffness based on the average E value of the members forming the section, Emean, as follows:

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