8 Resistance to transverse forces tables

EN 1993-1-5 does not cover the resistance to transverse forces for hollow sections. Therefore in this software the approach previously presented in Steelwork Design Guide to BS 5950-1:2000, Volume 1 - Section properties member capacities (SCI publication P202)[8] has been adopted and is presented below in terminology consistent with EN 1993-1-1.

8.1Bearing resistance

The bearing resistance, FRd,bearing, of the unstiffened web may be calculated using the factors C1 and C2 in the tables, using:

FRd,bearing = (b 1 + n k)2 t fy / γM0  
  = b 1 C2 + C1 (Resistance table notation)

where:

b1 is the effective bearing length (see figures below)
n = 5, for continuous web over bearing
  = 2, for end bearing
k = t for hollow sections
t is the wall thickness
fy is the yield strength.

 

Figure 8.1 Figure illustrating examples of stiff bearing length, b1

 

The bearing factor C1 represents the contribution from the flanges, adjacent to both webs, and is given by:

C1 = 2 n k t fy / γM0 Generally
C1 = 2 × 5 t 2 fy / γM0 For a section continuous over the bearing
C1 = 2 × 2 t 2 fy / γM0 For end bearing

The bearing factor C2 is equal to 2 t fy / γM0 representing the stiff bearing contribution for both webs.

8.2 Buckling resistance

The buckling resistance FRd,buckling of the two unstiffened webs is given by:

FRd,buckling = (b1 + n1) 2 t χ fy / γM1
  = b1 C2 + C1 (Resistance table notation)

where:

b1 is the stiff bearing length
n1 is the length obtained by dispersion at 45° through half the depth of the section
t is the wall thickness
χ is the reduction factor for buckling resistance, based on the slenderness as given in Section 6.2.

Unless loads or reactions are applied through welded flange plates, the additional effects of moments in the web due to eccentric loading must be taken into account, which will result in lower buckling values.

The buckling factor C2 is the stiff bearing component factor and is equal to C1 / h

The buckling factor C1 is the portion of (n1 t χ fy / γM1) due to the beam alone.

C1 = 4 D t χ fy /2 γM1 for welded flange plates
C1 = 4 F for non-welded flange plates

where:

F is the limiting force in each web (derived below).

The factor of 4 allows for two webs and dispersion of load in two directions and applies to a member that is continuous over a bearing or an end bearing member with a continuously welded sealing plate.

For non–welded flange plates, the limiting force F depends on the equivalent eccentricity of loading from the centreline of the web given by:

e = 0.026 b + 0.978 t + 0.002 h

This expression has been derived from research [9] and is also applicable to cold-formed hollow sections [10].

If the flange is considered as a fixed-ended beam of length b - t, the two forces F create a fixed end moment M;

M =

and thus the moment at mid-height of the web Mz can be found as follows [11]:

where:

a = h / b

Using the interaction criterion

The limiting value of F is given when the left hand side of this criterion = 1.

If the length of the wall resisting F and M is h / 2, given by a 45° dispersal in one direction, A = h t /2 and Wel,z = h t 2 / 12. Substituting these values, introducing k = Mz / F, and rearranging, the limiting value becomes:

F =

where:

nb =
k is given by the expression for Mz / F above

8.3 Shear resistance

6.2.6(2)

The shear resistance is determined in accordance with Section 7.1, 7.2 and 7.3.