According to EN1993-1-3, formula (10.1b), the shear stiffness of trapezoidal sheeting connected to a purlin may be calculated as :

With:

• t : thickness of sheeting (in mm)
• b_roof: width of the roof (in mm) (roof dimension parallel to the direction of the panel ribs)
• s: spacing between purlins
• h_w: profile depth of sheeting

Assume a purlin connected to the following trapezoidal sheeting, at each rib:

Roof width : 6,00m

Distance between purlins : 2,50m

This result sin a shear stiffness of 8361 kN.

Formula (10.1b) assumes the purlin is connected at each rib to the trapezoidal sheeting :

In case the purlin is not connected at each rib but at every other rib, only a small portion (20%) of this S stiffness can be considered :

If this value exceeds a certain value (S_min), the purlin may be regarded as laterrally restrained in the plane of the sheeting.

Assume an IPE140 purlin:

I_w = 1980 cm⁶ (warping constant of the purlin)

I_t = 2,45 cm⁴ (torsion constant of the purlin)

I_z = 44,92 cm⁴ (minor axis inertia of the purlin)

h = 140 mm (height of the purlin)

L = 6,00m (span of the purlin)

In Advanced Design, such a purlin may have its ‘Continuous restraint along flange’ property enabled on the upper flange :

For more complex cases, when the member is prone to torsional effects (Channel or Z section for example), a more sophisticated calculation may be required (2^nd order calculation with warping).

In this case, the shear stiffness (S) may be taken into account as the ‘Shear field’ parameter from the ‘Advanced stability’ dialog :