Doubly Symmetric Compact I-Shaped Members and Channels Flexural Design Bent About Their Major Axis per AISC 360-16 with ideCAD

How does ideCAD calculate the flexural strength for compact I-shaped members and Channels according to AISC 360-16?

Symbols

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_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_max : absolute value of maximum moment in the unbraced segment, kip-in. (N-mm)
M_A : absolute value of moment at quarter point of the unbraced segment, kip-in. (N-mm)
M_B : absolute value of moment at centerline of the unbraced segment, kip-in. (N-mm)
M_C : absolute value of moment at three-quarter point of the unbraced segment, kip-in. (N-mm)
M_n : The nominal flexural strength
M_p : Plastic bending moment
r_y : Radius of gyration about the y-axis
S_x : Elastic section modulus taken about the x-axis, 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) and lateral-torsional buckling.

Yielding Limit State

It is a situation where the beam's cross-section is dimensioned to remain stable until it becomes plastic above the effect of bending if the local buckling of the compression flange and the lateral torsional buckling are prevented. In this case, the characteristic moment strength can be considered equal to the plastic moment strength. If these elements are compact, the nominal flexural strength, M_n, equals to plastic bending moment strength.

Lateral Torsional Buckling Limit State

The part of the beam in the compression flange area acts like an axially loaded compression frame. The beam section cannot reach its full bending capacity if the compression flange's stability is insufficient. Similar to the compression elements, global buckling or loss of stability in cross-sectional parts that may occur with local buckling determines the collapse limit state. This type of buckling of the compression flange is called lateral torsional buckling.

• When L_b ≤ L_p

• When L_p < L_b ≤ L_r

• When L_b > L_r

The lateral-torsional buckling modification factor, C_b, is calculated below.

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

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

• For doubly symmetric I-shapes,
  

• For channels
  

For doubly symmetric I-shapes with rectangular flanges, C_w = I_yh_o² / 4 and r_ts is calculated below.