Square And Rectangular HSS and Box Sections Flexural Design per AISC 360-16 with ideCAD

How does ideCAD calculate the flexural strength of square and rectangular HSS and box sections according to AISC 360-16?

Symbols

b : Width of compression flange as defined in AISC 3610-16 Table B4.1b
C_b : The lateral-torsional buckling modification factor
E : Modulus of elasticity of steel = 29,000 ksi (200 000 MPa)
F_cr : Lateral-torsional buckling stress for the section as determined by analysis, ksi (MPa
F_y : Specified minimum yield stress of the type of steel being used, ksi
I_ts : Effective radius of inertia
J : Torsional constant
h : depth of web, as defined in AISC 3610-16 Table B4.1b
h_o : Distance between the flange centroids, in. (mm)
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
r_y : Radius of gyration about the y-axis
S : elastic section modulus about the axis of bending, in.3 (mm3)
S_x : Elastic section modulus taken about the x-axis, in.³ (mm³)
Z = plastic section modulus about the axis of bending, in.3 (mm3)
Z_x = Plastic section modulus about the x-axis, in.³ (mm³)

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

Yielding Limit State

Flange Local Buckling Limit State

• The limit state of flange local buckling does not apply to compact sections.

• The nominal flexural strength, M_n, is calculated below for sections with noncompact flanges.

• The nominal flexural strength, M_n, for sections with slender flanges;

S_e is the effective section modulus determined with the effective width, b_e, of the compression flange taken as given below.

• For HSS

• For Box sections

Web Local Buckling Limit State

• The limit state of web local buckling does not apply to compact sections.

• The nominal flexural strength, M_n, is calculated below for sections with noncompact webs.

• The nominal flexural strength, M_n, is calculated below for sections with noncompact webs.

  • Compression flange yielding
    

  • Compression flange local buckling
    

Lateral Torsional Buckling Limit State

• 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

Laterally unbraced length for the limit state of yielding, L_p, is calculated below.

Laterally unbraced length for the limit state of inelastic lateral torsional buckling, L_r, is calculated below.