# Castellated Beam Design

### Castellated Beam Sections

Hexagonal, circular, octagonal-shaped hollow, and Angelina sections can be defined. Hexagonal and circular hollow sections are designed.

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### Biaxial Bending and Axial Compression Control

**Yielding Limit State**

For the yielding limit state, the solid element's characteristic bending moment strength Mn is found in accordance with ÇYTHYEDY.

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

The element is safe against the lateral-torsional buckling limit state and the bending moment strength can be calculated according to Equation 9.2.

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

Considering the lateral-torsional buckling limit state, the bending moment strength M_{n} can be calculated as follow:

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

Considering the elastic-buckling of the element, the bending moment strength M_{n} can be calculated as follow:

### Axial Compression

The axial compression capacity for the solid element part of the castellated beam can be calculated as follow:

### Combined Effects

### Shear Control

**Gross and Net Area for Shear Control**

The gross shear area is the full web part of the castellated beam and the net shear area is calculated by taking into account the hollow parts of the castellated beam as follow:

**Horizontal Shear Control**

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

### Vierendeel Control

**Biaxial Bending and Axial Compression Effects**

The loads on the T section that is above of the castellated beam hollow are found with the assistance of equilibrium equations. 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 equilibrium equations. Then the combined effects are considered by finding the bending and axial force strengths of the T-section.

### Web Buckling Control

**Forces Acting on the Web**

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

**Web Buckling Strength**

The solid web section between the castellated beam hollows is calculated according to ÇYTHYEDY 9.11.