## Info

• Ei is the mean value of the modulus of elasticity of element, i (see also 8.6);

• Ai is the cross-sectional area of element i, i.e. = bi x hi.

• Ii is the second moment of area of element i about its axis of bending, i.e.

• Yi is the connection efficiency factor, where y2 = 1 and for i = 1 or 3, then;

Yi = [1 + n2EiAisi/ (KiI2)]-1 (EC5, equation (B.5)) (8.3)

where:

- si is the spacing of the fasteners in connection i. Where a variable spacing is used to suit the shear force distribution and smax < 4sm;n, it is proposed by Ceccotti [2] that an effective spacing, sef = 0.75smin + 0.25smax can be used.

- Where a flange consists of two elements connected to a single web (e.g. Figure 8.4c) or a web consists of two elements connected to a single flange (e.g. Figure 8.4e), si will be 1/2 the fastener spacing per unit length used in each of the joining planes. In other words, the stiffness used for the connection will be twice the fastener stiffness in each of the joining planes.

- Ki is the stiffness of fastener i per joining plane and equates to Ku i for calculations relating to the ULS (see also 8.6).

- I is the length of the column.

- It is to be noted that for a glued interface, i.e. Ki = to, Yi will equal 1 and the effective bending stiffness will equate to that derived for a fully composite section. When Ki is 0, y i will also be 0, equating to a section in which the elements are unconnected.

• ai is the distance from the centre of area of element i to the neutral axis of the composite section.

In Figure 8.4, for profiles (e) and (f), a2 = 0 and for profiles (a)-(d), a2 it will be obtained from:

Y1E1 A1(h1 + h2) - Y3E3As(h2 + hs) a2 =-5- (EC5, equation (B.6)) (8.4)

2E 3=1 YiEiAi

The other distances can be calculated from the geometry of the section and for the T-section in profile (d), h3 will equal 0 in equation (8.4). All measurements are to be taken as positive except for a2, which will be positive when as shown in Figure 8.4.

Applying equations (8.2)-(8.4), the effective bending stiffness about the y-y axis for profiles (a)-(f) inclusive will be as given in Table 8.1. It is to be noted that the equations in Table 8.1 (and 8.2) incorporate the effect of the reduction in fastener spacing where a flange consists of two elements connected to a single web.

8.4.2 The effective bending stiffness of built-up sections about the z-z axis

When due to the geometry of the built-up section or the combination of material properties being used the section is asymmetrical about its y-y axis, as in the case of profiles (a)-(d) in Figure 8.4, irrespective of whether the interfaces are glued or joined by mechanical fasteners, it is proposed that the elements of the section are treated as individual members.

Table 8.1 Effective bending stiffness about the y-y axis

Profile in Figure 8.4

Effective bending stiffness about y-y axis, (E/f

bih3 b2h\ b3h\ -, (E)ef,y = Ei—2 + E2-j-2 + + yiEl (bihi)a\

where for section (a)

Built-up section (c)

Built-up section (d)

Built-up section (e)

Built-up section (f)

and for section (b)

2Kj i2 b2h2

2K3 i2

b3h3

i2 i2 i2

where

2K1 i2

2K3 i2

where

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