# 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?**

The flexural strength of steel elements is calculated automatically according to

**AISC 360-16**.

The nominal flexural strength limit states yielding, and lateral-torsional buckling are controlled automatically according to

**AISC 360-16**.

For design members for flexure, sections are automatically classified as compact, non-compact, or slender-element sections, 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

*Radius of gyration about the y-axis*

**r**_{y}:

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

^{3}(mm

^{3})

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

**Z**_{x}^{3}(mm

^{3})

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*and

_{y}h_{o}^{2}/ 4*r*is calculated below.

_{ts}