Design procedure for single angles (Angles and tees: AISC 360)

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 (w, z) bending except where the provision for bending about geometric axis is permitted.

Geometric axis bending permitted:

If single angles without continuous lateral torsional restraint and legs of angles are equal and there is no axial compression and bending about one of the geometric axis only

Note: Design on the basis of geometric axis bending should also be permitted if single angles without continuous lateral torsional restraint but with lateral torsional restraint at the point of maximum moment only and legs of angles are equal and there is no axial compression and bending about one of the geometric axis only. However this is beyond scope of the current release of the program.

Geometric axis design

Nominal flexural strength Mnx – about X axis (major geometric axis)
Nominal flexural strength Mny – about Y axis (minor geometric axis)

Check:

IF LRFD

a. M_rx ≤ φ_b * M_nx , where φ_b = 0.9

b. M_ry ≤ φ_b * M_ny , where φ_b = 0.9

IF ASD

M_rx ≤ M_nx /Ω_b , where Ω_b = 1.67

M_ry ≤ M_ny /Ω_b , where Ω_b = 1.67

Principal axis design

Required flexural strength M_rw – about W axis
Required flexural strength M_rz – about Z axis
Nominal flexural strength M_nw – about W axis (major principal bending axis)
Nominal flexural strength M_nz – about Z axis (minor principal bending axis)

Check:

IF LRFD

a. M_rw ≤ φ_b * M_nw , where φ_b = 0.9

b. M_rz ≤ φ_b * M_nz , where φ_b = 0.9

IF ASD

a. M_rw ≤ M_nw /Ω_b , where Ω_b = 1.67

b. M_rz ≤ M_nz /Ω_b , where Ω_b = 1.67

The principal axes moments are calculated from the following formulas for both LRFD and ASD:

M_rw = M_rx cosα + M_ry sinα

M_rz = -M_rx sinα + M_ry cosα

In the case of biaxial bending, or bending and axial force the combined stress ratio must be checked using the provisions of AISC, section H2.

For the three points of the angle A, B, C the combined ratio check should be performed.

Single Equal Angles - Sign of Moments

Single Unequal Angles - Sign of Moments

If the interaction of stresses at each point is seen to be less than 1.0 the member is adequate to carry the required load.

Check:¹

Abs (f_ra / F_ca + f_rbw / F_cbw + f_rbz / F_cbz) ≤ 1.0

Note: In axial tension when the sum of the moment ratios about the major and minor axis bending is greater or equal to 0 then the axial stress ratio is taken as 0.0 in order to give conservative results and the axial stress ratio is renamed “effective”.