B. TECHNICAL

8. Load carrying capacity of webs and flanges

Transverse force load carrying capacity of webs

It is possible to calculate the transverse force load carrying capacity of corrugated web beams in accordance with DASt-Ri.015 [4] by substituting a trapezoidal form for the actual corrugated form. However, this leads to inappropriately conservative results. The reason for this is that the interaction between global and local buckling upon which [4] is based does not occur with the corrugated web and the buckling coefficients kt are set too low.

On the basis of tests [8, 11] and finite element calculations, the following design procedure has been suggested by Pasternak in [12]:

The corrugated web is regarded as an orthotropic plate with rigidities Dx and Dy . According to [13], the following formula therefore applies to the corrugated web:

       for D_x << D_y

w ... length of corrugation = 155 mm
s ... uncoiled length
I_y ... moment of inertia of one corrugation

s and I_y are determined by numerical integration of the actual shape of the corrugation.

With transverse buckling stress in accordance with DASt-Ri.015 ([4],Eq.

415) the resulting specific slenderness parameter is

With the buckling coefficient kt in accordance with [12]

the transverse force load carrying capacity for the corrugated web finally results in:

The evaluation for the current geometrical dimensions and strength values of the corrugated web is summarized in Table 1.

Normal force load carrying capacity of flanges In determining the normal bearing force of the flanges, a distinction must be made between tensile and compressive stresses. In the case of tensile stress, the load carrying capacity of the flange is derived as follows:

In the context of compressive stress, the stability of the flange must be taken into account. A distinction must be made here between local buckling of the flange and its global stability (buckling transverse to the axis of the girder = torsional-flexural buckling).

Local buckling is demonstrated via the limit values lim(b/t) in accordance with DIN 18 800 Teil 1, Table.13. In order to take into account the elastic restraining effect of the web, the flange width, reduced by half the height of the web, is used for the width of the plate strip b.

Reformulation of the expression for y = 1 (Table 13, line 4) leads to the following elastic limit stress:

and therefore the reduced normal force on the flange:

if b > 12.9.tg for f_yk = 240 N/mm²
b > 10.5.t_g for f_yk = 355 N/mm²

Global failure of stability - lateral buckling of the flange - is equivalent to the verification against torsional-flexural buckling . If the restraining effect of the web is ignored, the torsional-flexural verification is carried out as the buckling verification for the "isolated" flange in accordance with DIN 18 800 Teil 2, clause 3.3.3, El (310).

By reformulating eqs. (12) and (13), the following condition for the distance between lateral supports is obtained:

k_c ... Compressive force factor in accordance with Table 8, DIN 18 800 Teil 2
c ..... Distance between lateral mountings
or

        with f_yk in [kN/cm²] and b_g , t_g and c in [cm].

In the case of compressive stress, the load bearing capacity of the flange is therefore

Table 2 lists the load bearing capacities of the flanges for steel quality S235 (St 37), related to the distance of lateral supports for a constant normal force (y = 1). For the mentioned flange cross sections act. (b/t) < lim. (b/t) in accordance with DIN 18 800 Teil 1, Table 13 applies. The application limits are elaborated as follows: