For axial compression and bending both the web and flange (Leg 1 and Leg 2) are classified as Class 1, Class 2, Class 3 or Class 4 and the worst of the two is the resultant classification for that cross section.

The rules from Table 5.2 (sheet 2 of 3) of EC3 are used for tee sections. In particular the rules of “Part subject to compression” are used to classify the tee section since these are more conservative compared to the limits of “Part subject to bending and compression”.

For double angles and single angles the rules from Table 5.2 (sheet 3 of 3) of EC3 are used.

Section 6.2.3 of EC3 is used for this design check.

An axial compression capacity check is performed according to clause 6.2.4.(1)

Section 6.2.6 of EC3 is used for this design check.

Moment capacity for Class 4 slender sections:

Class 4 sections are designed as Class 3 effective sections.

Hence, additional moments are induced in the member due to the shift of the centroid of the effective cross-section compared to that of the gross section when under axial compression only.

Thus:

ΔM_Ed,y = e_y × N_Ed,max

ΔM_Ed,z = e_z × N_Ed,max

Where:

N_Ed,max is the max compressive force in the span.

For tees and double angles e_y = 0. Hence, total minor design moment = minor design moment.

Where:

e_y and e_z = the shift of the centroid of the effective area A_eff relative to the centre of gravity of the gross cross section

e_y = abs(cy_new – c_y)

e_z = abs(cz_new – c_z)

So finally, a total moment is obtained for which the moment design check is performed:

M_{total y} = Abs(M_Ed,y) + Abs(ΔM_Ed,y)

M_{total z} = Abs(M_Ed,z) + Abs(ΔM_Ed,z)

Single angles - asymmetric sections:

Single angles with continuous lateral – torsional restraint along the length are permitted to be designed on the basis of geometric axis (y, z) bending.

Single angles without continuous lateral – torsional restraint along the length are designed using the provision for principal axis (u, v) bending since we know that the principal axes do not coincide with the geometric ones.

ΔM_u = ΔM_y × cosϑ + ΔM_z × sinϑ

ΔM_v = -ΔM_y × sinϑ + ΔM_z × cosϑ

Note that when principal axis design is required for single angles and the classification is Class 4, all moments are resolved into the principal axes (total moment in the principal axes u-u and v-v).

Section 6.2.9 of EC3 is used for this design check.

For Class 3 - Equation 6.42 is applied:

Abs (N_Ed / A) + abs (M_y,Ed /W_el,min,y) + abs (M_z,Ed/W_el,min,z) ≤ f_y / γ_M0

For Class 4 - Equation 6.43 is applied:

Abs (N_Ed/A_eff) + (abs (M_y,Ed) + abs (ΔM_y,Ed)) / W_eff,min,y + abs (M_z,Ed) + abs (ΔM_z,Ed)) / W_eff,min,z ≤ f_y / γ_M0

Note that total moments are used when the section classification is Class 4.

For Class 4 cross section capacity - Equation 6.44 is applied.

EC3 is completely silent on LTB check for asymmetric sections such as single angles and mono-symmetric sections such as double angles and tees.

Hence we follow the approach of the Blue Book (Ref. 10):

Firstly we calculate the equivalent slenderness coefficient (φ) (From Blue book) and the equivalent slenderness λ_LT (BS approach).

Then we find the non-dimensional slenderness in order to follow the EC design approach.

Conservatively we have taken:

Section 6.3.1.1 of EC3 is used for this design check.

Effective length:

The value of effective length factor is entirely at the user’s choice. The default value is generally 1.0 although for truss members, there are special settings for the effective length depending upon the type of section and its position in the truss.

Different values can apply in the major and minor axis. Coincident strut restraint points in these two directions define the length for torsional and torsional flexural buckling and this can also have an effective length factor (this is assumed to be 1.0 and cannot be changed).

There is no guidance in EC3 on the values to be used for effective length factors for beam-columns although Annex BB does contain some information on the effective lengths to be used in trusses but not for single, double angles and tees.

It is the responsibility of the user to adjust the value from 1.0 (for the effective length factor) and to justify such a change on the compression page.

For tees:

For single and double angles:

Check:

1. the buckling length in the major axis – Use L_yy = L * major factor
2. the buckling length in the minor axis – Use L_zz = L * minor factor
3. the buckling length for the torsional mode – Use L_xx =1.00 * L
   1. Double angles – Check as single angle
      • Use L_y = L_yy/ 3
      • Use L_z = L_zz/ 3
      • Use L_x = L_xx/ 3
   2. Double angles – Check as double angle
4. the buckling length for the principal axis, v-v – Use L_vv = 1.00 * L
   • Double angles – Check as single angle
     • Use L_v = L_vv/3

For double angles for (4) & (3a) minor principal axis buckling & torsional buckling respectively – half of the axial force and half of the double angle area is used.

In the current version this check is beyond scope for single angles, double angles and tees.

If a single angle is continuously restrained the major geometric moment and major geometric section properties are used in the general equation governing the beam deflection.

Single angle deflections (continuously restrained, unrestrained)

However, because single angle geometric axes are not coincident with the principal axes; a different procedure is required if the angle is not continuously restrained, the procedure being as follows:

1. External loads are transposed from the geometric axes to the principal axes.
2. The deflection equations are used to calculate deflections in the principal axes.
3. These principal axis deflections are then transposed to geometric axes again.