# Design procedures (Angles and tees: BS 5950)

This section includes key notes and assumptions made for the British Standard design of tees and angle sections.

## Classification checks

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 11 and 12 of BS 5950-1:2000 apply for the classification of these sections.

## Axial tension check

Section 4.6 of BS 5950 is used for this design check.

## Axial compression check

Section 4.6 of BS 5950 is used for this design check.

## Shear check

Section 4.2.3 of BS 5950 is used for this design check.

## Moment check

Section 4.2.5 of BS 5950 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,x} = e_{x} ×
F_{c}

ΔM_{Ed,y} = e_{y} ×
F_{c}

Where:

F_{c} is the max compressive
force in the span.

For tees and double angles
e_{x} = 0. Hence, total minor design moment = minor design moment.

Where:

e_{x} and e_{y} = the
shift of the centroid of the effective area A_{eff} relative to the centre
of gravity of the gross cross section

e_{x} = abs(cx_{new} –
c_{x})

e_{y} = abs(cy_{new} –
c_{y})

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

M_{total x} =
Abs(M_{Ed,x}) + Abs(ΔM_{Ed,x})

M_{total y} =
Abs(M_{Ed,y}) + Abs(ΔM_{Ed,y})

**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 (x, y) 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_{x} × cosϑ
+ ΔM_{y} × sinϑ

ΔM_{v} = -ΔM_{x} ×
sinϑ + ΔM_{y} × 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).

## Combined bending and axial check

Section 4.8.3 of BS 5950 is used for this design check.

For Class 3:

Abs (F_{c} /
A_{g}P_{y}) + abs (M_{x,Ed} /M_{cx}) + abs
(M_{y,Ed}/W_{el,min,y}) ≤ 1.0

For Class 4:

Abs
(F_{c}/A_{eff}p_{y}) + (abs (M_{x,Ed}) + abs
(ΔM_{x,Ed})) / M_{cx} + abs (M_{y,Ed}) + abs
(ΔM_{y,Ed})) / M_{cy} ≤ 1.0

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

## Lateral torsional buckling check

Section 4.3 of BS 5950 is used for this design check.

In the case of a beam with continuous lateral torsional restraint along its length this check is not performed. The lateral torsional resistance is considered adequate.

For beams that are unrestrained, a Lateral torsional buckling (LTB) check is required, either:

- In its own right check for LTB, clause 4.3, and B2.8 for tee sections and B.2.9 for angle sections in BS 5050-1: 2000.
- As part of combined buckling, clause 4.8 “Members with combined moment and axial force”, 4.8.3.3, for single Angles I3 and I4 sections

This check is not performed when bending exists about the minor axis only

## Combined buckling check

**Single angles: **

Clause I.4 - For beam with continuous lateral torsional restraint or for equal single angle sections with b/t ≤ 15ε a combined buckling check is performed according to clause I.4.3 - the simplified method.

For any other case clause 4.8.3.3.1 is used with the moments being resolved into the principal axes u-u and v-v. Two formula are provided in clause 4.8.3.3.1, both are checked

**Tees: **

- If the axial load is tensile, then F is taken as zero
- Only one value of F is used, the worst anywhere in the length being checked
- Class 4 slender sections are allowed