Single Angles Flexural Design per AISC 360-16 with ideCAD

How does ideCAD calculate the flexural strength for single angle members according to AISC 360-16?

Symbols

A: cross-sectional area of angle, in.² (mm²)
b: width of leg, in. (mm)
C_b: The lateral-torsional buckling modification factor
E: Modulus of elasticity of steel = 29,000 ksi (200 000 MPa)
F_y: Specified minimum yield stress of the type of steel being used, ksi
L_b: Length between points that are either braced against lateral displacement of the compression flange or braced against twist of the cross-section, in. (mm)
M_cr: The elastic lateral-torsional buckling moment
M_n: The nominal flexural strength
M_y: Yield moment about the axis of bending, kip-in. (N-mm)
S_c: elastic section modulus to the toe in compression relative to the bending axis, in.³ (mm³).
t: thickness of angle leg, in. (mm)
β_w: section property for single angles about major principal axis, in. (mm).

The nominal flexural strength, M_n, should be the lower value obtained according to the limit states of yielding (plastic moment), lateral torsional buckling, and leg local buckling.

The nominal flexural strength of single-angle members is calculated by considering the geometric axis and principal-es cross-sectional properties. Only the limit states of yielding and leg local buckling apply for bending about the minor principal axis.

Yielding Limit State

Lateral Torsional Buckling Limit State

The nominal flexural strength, M_n, for single angles without continuous lateral-torsional restraint along the length is calculated as shown below.

The elastic lateral-torsional buckling moment, M_cr, for bending about the major principal axis of single angles is calculated as shown below.

The elastic lateral-torsional buckling moment, M_cr, for bending about one of the geometric axes of an equal leg angle with no axial compression of single angles is calculated as shown below.

With no lateral-torsional restraint:

• With maximum compression at the toe, M_cr is calculated as shown below.

• With maximum tension at the toe, M_cr is calculated as shown below.

M_y should be taken as 0.80 times the yield moment calculated using the geometric section modulus.

With lateral-torsional restraint at the point of maximum moment only:

The elastic lateral-torsional buckling moment, M_cr, is calculated as 1.25 times M_cr computed using Equations F10-5a or F10-5b. M_y should be calculated using the geometric section modulus as the yield moment.

Leg Local Buckling Limit State

• The limit state of leg local buckling does not apply when the toe of the leg is in compression with compact section in compression.

• The nominal flexural strength, M_n, is calculated as shown below for sections with noncompact legs

• The nominal flexural strength, M_n, is calculated below for sections with slender legs.