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, F_{Rd,bearing}, of the unstiffened web may be calculated using the factors C_{1} and C_{2} in the tables, using:
F_{Rd,bearing} | = (b 1 + n k)2 t f_{y} / γ_{M0} | |
= b 1 C_{2} + C_{1} | (Resistance table notation) |
where:
b_{1} | 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 |
f_{y} | is the yield strength. |
Figure 8.1 Figure illustrating examples of stiff bearing length, b_{1 }
_{}
The bearing factor C_{1} represents the contribution from the flanges, adjacent to both webs, and is given by:
C_{1} = 2 n k t fy / γ_{M0} | Generally |
C_{1} = 2 × 5 t ^{2} f_{y} / γ_{M0} | For a section continuous over the bearing |
C_{1} = 2 × 2 t ^{2} f_{y} / γ_{M0} | For end bearing |
The bearing factor C_{2} is equal to 2 t f_{y} / γ_{M0} representing the stiff bearing contribution for both webs.
8.2 Buckling resistance
The buckling resistance F_{Rd,buckling} of the two unstiffened webs is given by:
F_{Rd,buckling} | = (b_{1} + n_{1}) 2 t χ f_{y} / γ_{M1} | |
= b_{1 }C_{2} + C_{1} | (Resistance table notation) |
where:
b_{1} | is the stiff bearing length |
n_{1} | 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 C_{2} is the stiff bearing component factor and is equal to C_{1} / h
The buckling factor C_{1} is the portion of (n_{1} t χ f_{y} / γ_{M1}) due to the beam alone.
C_{1} = 4 D t χ f_{y} /2 γ_{M1} | for welded flange plates |
C_{1} = 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:
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;
and thus the moment at mid-height of the web M_{z} 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 W_{el,z} = h t ^{2} / 12. Substituting these values, introducing k = M_{z} / F, and rearranging, the limiting value becomes:
where:
n_{b} | = |
k | is given by the expression for M_{z} / F above |
8.3 Shear resistance
The shear resistance is determined in accordance with Section 7.1, 7.2 and 7.3.