Tees and Double Angles Flexural Design per AISC 360-16 with ideCAD

How does ideCAD calculate the flexural strength for Tees and double-angles according to AISC 360-16?

Symbols

d: depth of tee or width of web leg in. (mm)
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
h: Distance as defined in AISC 360-16 Table 4.1b
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)
L_p: The limiting laterally unbraced length for the limit state of yielding, in. (mm)
L_r: The limiting unbraced length for the limit state of inelastic lateral-torsional buckling, in. (mm),
M_n: The nominal flexural strength
M_p: Plastic bending moment
M_y: Yield moment about the axis of bending, kip-in. (N-mm)
S_x: elastic section modulus, in.³ (mm³)
S_xc: elastic section modulus referred to the compression flange, in.³ (mm³)
S_y: elastic section modulus taken about the y-axis, in.3 (mm3)
t_f: the thickness of the flange, in. (mm)
Z_y = Plastic section modulus about the y-axis, in.³ (mm³)
λ_p: Limiting slenderness for a compact flange, defined in Table B4.1b
λ_r: Limiting slenderness for a noncompact flange, described in Table B4.1b

The nominal flexural strength, M_n, should be the lower value obtained according to the limit states of yielding (plastic moment), lateral torsional buckling, flange local buckling, and local buckling of tee stems and double-angle web legs.

Yielding Limit State

• The plastic bending moment, M_p, for tee stems and web legs in tension is calculated as shown below.

The yield moment about the bending axis, M_y, is calculated as shown below.

• The plastic bending moment, M_p, for tee, stems in compression is calculated as shown below.

• The plastic bending moment, M_p, for double angles with web legs in compression is calculated as shown below.

Lateral Torsional Buckling Limit State

The lateral torsional buckling limit state is calculated for stems and web legs in tension.

• When L_b ≤ L_p, the limit state of lateral-torsional buckling does not apply.

• When L_p < L_b ≤ L_r

• When L_b > L_r

Limiting laterally unbraced length for the limit state of yielding, L_p is calculated as shown below.

Limiting unbraced length for the limit state of inelastic lateral-torsional buckling, L_r is calculated as shown below.

The elastic lateral-torsional buckling moment, M_cr is calculated below.

where

d: depth of tee or width of web leg in tension, in. (mm)

For tee stems and web legs in compression, the elastic lateral-torsional buckling moment, M_cr, and The nominal flexural strength, M_n, are calculated below.

where

d: depth of tee or width of web leg in compression, in. (mm)

The nominal flexural strength, M_n, is calculated for double-angle web legs given the title.

Flange Local Buckling Limit State of Tees and Double-Angle Legs

• The limit state of flange local buckling does not apply for tee flange sections with compact flanges in flexural compression.

• The nominal flexural strength, Mn, is calculated as shown below for tee flange sections with noncompact flanges in flexural compression.

• The nominal flexural strength, Mn, is calculated as shown below for tee flange sections with slender flanges in flexural compression.

The nominal flexural strength, M_n, is calculated for double-angle web legs given the title.

Local Buckling Limit State of Tee Stems and Double-Angle Web Legs in Flexural Compression

The nominal flexural strength, M_n, for tee stems is calculated as shown below.

The critical stress, F_cr, for tee stems is calculated as shown below.

The nominal flexural strength, M_n, is calculated for double-angle web legs given the title.