9. Web bearing and buckling tables

9.1 UB sections and UC sections: bearing, buckling and shear capacities for unstiffened webs

Values have been calculated as follows:

(a) Bearing

The bearing capacity P_w, of the unstiffened web is given by:

where:

b1	is the stiff bearing length
n	= 5, for continuous over bearing
	= 2 + 0.6 be / k , for end bearing
	= 2, for end bearing (be taken as zero in the tables)
be	is the distance to the nearer end of the member from the end of the stiff bearing
k	= (T + r) for rolled sections
t	is the thickness of the web
T	is the thickness of the flange
r	is the root radius
pyw	is the design strength of the web.

(i) Bearing factor C1 is due to the beam alone

(ii) Bearing factor C2 is equal to t p_yw and must be multiplied by b₁ to give the stiff bearing contribution.

(b) Buckling

Generally the buckling resistance, P_x, of the unstiffened web is given by:

Combining with (a), this can be re-written as:

if ae ≥ 0.7d	then K = 1
if ae < 0.7d	then K =

where:

d	is the depth between fillets
t	is the web thickness
Pw	is the web bearing capacity from (a) above.
ae	is the distance from the centre of the load or reaction to the nearer end of the member.

(i) Buckling factor C4 is the same for end bearing and continuous over bearing,

(c) Shear

The shear capacity of the section is given by:

where:

D	= Total depth of section.

Note: Since none of the rolled sections have d/t > 70ε, there is no need to check for shear buckling of the web.

9.2 Parallel flange channels: bearing, buckling and shear capacities for unstiffened webs

The nominal cross-section dimensions of parallel flange channels give a square heel, but the tolerances include a small heel radius (see Corus brochure Structural sections^[11]), based on BS EN 10279:2000^[7]. The heel radius can be between zero and 0.3 times the flange thickness.

In most cases the loads and reactions are applied directly to the web (by angle cleats, end plates or fin plates), so this is usually of no significance.  However, if a force from a load or reaction is applied to the channel through the flange, the presence of a heel radius may produce eccentricity of this force relative to the web, so reduction factors, K_b for bearing and K_w for buckling to allow for this have been included in the tables.

The use of these reduction factors will provide acceptable design, but if necessary the eccentricity can be eliminated.  A simple method is to use a continuously welded flange plate local to the stiff bearing, extending at least to the back of the channel.  Depending on details, other methods may be appropriate.

Values have been calculated as follows:

(a) Bearing capacity, P_w

Where

Kb	is a reduction factor to allow for heel radius.
All other notation as in Section 9.1.

(b) Buckling resistance, P_x

where

Kw	is a reduction factor to allow for heel radius.
All other notation as in Section 9.1.

(c) Shear capacity

9.3 Square and rectangular hollow sections: bearing, buckling and shear capacities for unstiffened webs

Values have been calculated as follows:

(a) Bearing

The bearing capacity, P_W, of the unstiffened web is given by:

where:

b1	is the stiff bearing length (see figures below)
n	= 5, for continuous over bearing
	= 2, for end bearing
k	= t, for hollow sections
t	is the thickness of the web
pyw	is the design strength of the web.

Figure illustrating examples of stiff bearing length, b₁

(i) Bearing factor C1 is due to the beam alone, for both webs.

(ii) Bearing factor C2 is equal to 2tp_yw for both webs and must be multiplied by b₁ to give the stiff bearing contribution.

(b) Buckling

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

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
pc	is the compressive strength based on: Web slenderness, λ =  Strut curve (c).

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.

(i) Buckling factor C1 is the portion of (n₁ t p_c) due to the beam alone.

where:

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

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

For non‑welded flange plates, the equivalent eccentricity of loading from the centreline of the web is given by:

This expression has been derived from research ^[14] and is also applicable to cold‑formed hollow sections ^[15]

The loading P creates a fixed end moment of

and thus the moment at the centreline of the web can be found as follows ^[16]:

where:

a

= D/B

Using the interaction expression 

The limiting value of P is given by substituting for M_y and rearranging:

(ii) Buckling factor C2 is the stiff bearing component factor and is equal to C1/D and must be multiplied by b1 to give the stiff bearing contribution.

(c) Shear

The shear resistance capacity of the section is given by:

where:

A	is the cross‑sectional area.