# Castellated Beam Design with 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

**F _{cr} : **Critical stress

**K : **Effective length factor

**L: **Laterally unbraced length of the member

**P _{r}: **Required axial force resistance for LRFD or ASD load combinations

**P _{c}: **Strength of axial compressive force available according to Section E

**M _{r}: **Required bending moment strength for LRFD or ASD load combinations

**M _{c}: **current bending moment strength according to Section F

**r: **Radius of gyration

**λ: **Width-to-thickness ratio for the element as defined in Section B4.1

**λ _{r} : **Limiting width-to-thickness ratio as defined in Table B4.1a

**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})

### Castellated Beam Sections

Castellated hexagonal, castellated circular, castellated octagonal and angelina sections can be defined. Castellated hexagonal and castellated circular sections are designed.

### Biaxial Bending and Axial Force

#### Yielding Limit State

For the yield limit state, the characteristic bending moment strength of the web is found M_{n} in accordance with AISC 360-16.

**In the case of L**_{b}<L_{p}

This limit situation need not apply.

**In the case of L**_{p}<L_{b}<L_{r}

The characteristic bending moment strength M_{n} is calculated by equation F2-2.

**In the case of L**_{b}> L_{r}

The characteristic bending moment strength M_{n} shall be determined by equation F2-3.

### Axial Force

The axial compression capacity for the web part of the castellated beam is calculated as follows.

### Combined Forces

### Shear Control

#### Gross and Net Area Shear Control

Shear control with the gross area is the full web part of the castellated beam while the shear control with the net area is calculated as follows by taking into account the hollow section of the castellated beam.

#### Horizontal Shear Control

The shear force on the castellated beam web is calculated using the balance equation and compared with the shear strength.

### Vierendeel Bending Control

#### Axial Force and Biaxial Bending

The effects on the T section on the castellated beam spaces are found with the equation of equilibrium. While calculating these forces, internal force diagrams in the static analysis are used. The bending moment and axial force on the T section are calculated by the equation of equilibrium. Then the combined effects are considered by finding the bending and axial force strengths of the T-section.

### Web Post Buckling Control

#### Forces Acting on the Web

The bending moment values at the upper and lower boundaries of the web section between the castellated beam spaces are found and lateral-torsional buckling is checked according to the rectangular section.

#### Web Post Buckling Strength

The web section between the castellated beam is calculated according to AISC 360-16 Section F.