# Steel Beam Design (AISC 360-16)

**Symbols**

**C _{b} :** The lateral-torsional buckling modification factor

* Z_{x}* = Plastic section modulus about the x-axis, in.

^{3}(mm

^{3})

**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

**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 _{n} :** The nominal flexural strength

**M _{p} :** Plastic bending moment

**S _{x} :** Elastic section modulus taken about the x-axis, in.

^{3}(mm

^{3})

### 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 M

_{n}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 M

_{n}, the change due to L_{b}and the effect of the moment correction coefficient C_{b}are shown in the figure below.

a) If L_{b} ≤ L_{p} , this limit situation need not apply.

b) If L_{p} <L_{b} ≤ L_{r} , the characteristic bending moment strength M_{n} is calculated by equation F2-2.

c) If L_{b} > L _{r} , the characteristic bending moment strength M_{n} shall be determined by equation F2-3.

C

_{b}: 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.

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