Cb : The lateral-torsional buckling modification factor

Zx = Plastic section modulus about the x-axis, in.3 (mm3)

E: Modulus of elasticity of steel = 29,000 ksi (200 000 MPa)

Fy : Specified minimum yield stress of the type of steel being used, ksi

Its : Effective radius of inertia

J: Torsional constant

ho : Distance between the flange centroids, in. (mm)

Lb : Length between points that are either braced against lateral displacement of the compression flange or braced against twist of the cross section, in. (mm)

Lp : The limiting laterally unbraced length for the limit state of yielding, in. (mm)

Lr : The limiting unbraced length for the limit state of inelastic lateral-torsional
buckling, in. (mm),

Mn : The nominal flexural strength

Mp : Plastic bending moment

Sx : Elastic section modulus taken about the x-axis, in.3 (mm3)

Bending Member Definition

  • Members that are affected by bending moment around any of their principal axes. In the members with effect of bending, the loads should act in the plane parallel to the principal axis passing through the shear center or the member should be supported against torsion at the load impact points and supports.

Yielding Limit State

  • It is a situation where the cross section of the beam 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 is prevented. In this case, the characteristic moment strength can be taken equal to the plastic moment strength.

  • The yield moment is that the upper fiber of the section above the influence of bending moment reaches the yield stress.

  • Plastic moment is the moment value when all fibers of the section above the effect of bending moment reach the yield stress.

Lateral Torsional Buckling Limit State

  • The part of the beam in compression flange area acts like an axially loaded compression frame. If the stability of compression flange is not sufficient, the beam section cannot reach its fully bending capacity. In this case, 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.

Design with AISC 360-16

9.2.1 - Yielding Limit State

  • The characteristic bending moment strength Mn for the yield limit state is calculated by equation F1-2.

9.2.2 Lateral Torsional Buckling Limit State

  • For the lateral torsion buckling limit state, the characteristic bending moment strength for 3 different failure limit conditions, the laterally unsupported length of compression flange Mn, the change due to Lb and the effect of the moment correction coefficient Cb are shown in the figure below.

a) If Lb ≤ Lp , this limit situation need not apply.

b) If Lp <Lb ≤ Lr , the characteristic bending moment strength Mn is calculated by equation F2-2.

c) If Lb > L r , the characteristic bending moment strength Mn shall be determined by equation F2-3.

  • Cb : It is the positive contribution of bending moment propagation along the length between the points supported by the lateral stability connection in the case of lateral torsional buckling limit.

Design for Combined Forces

  • It is the strength calculation made by taking into account the combined stresses created in the elements above bending and axial force.

  • Account details are available at Design of Members for Combined Forces.