Castellated & Cellular Beam Design — Geometry, Limit States & Sizing
Castellated beams are fabricated by cutting a rolled W-shape along a zigzag pattern, then re-welding the two halves offset to create a deeper section with hexagonal web openings. Cellular beams use a similar process but produce circular openings. Both types increase the beam depth by roughly 50% without adding steel weight, dramatically improving flexural stiffness for long-span floor and roof applications.
How castellated beams are made
A standard W-shape is flame-cut along the web in a zigzag (castellated) or sinusoidal (cellular) pattern. The two halves are separated and re-welded with the peaks aligned, producing a beam approximately 1.5d deep (where d is the original section depth). For example, a W18x35 becomes a CB27x35 -- same weight, 50% deeper, with significantly higher moment of inertia.
The key geometric parameters per AISC Design Guide 31:
| Parameter | Castellated (hexagonal) | Cellular (circular) |
|---|---|---|
| Opening height | typically 0.5 _ dt to 0.75 _ dt | diameter Do = 0.6 _ dt to 0.8 _ dt |
| Web post width (e) | >= ho/3 for strength | >= Do/4 |
| Spacing (S) | e + opening width | center-to-center = Do + e |
| Overall depth (dt) | ~1.5 * d_original | ~1.5 * d_original |
Common castellated beam profiles
| Parent Section | Castellated Depth (in) | Opening Height (in) | Weight (plf) | Ix Increase |
|---|---|---|---|---|
| W16x26 | 24 | 12 | 26 | ~2.0x |
| W18x35 | 27 | 14 | 35 | ~2.0x |
| W21x44 | 32 | 16 | 44 | ~2.0x |
| W24x55 | 36 | 18 | 55 | ~2.0x |
The moment of inertia approximately doubles because I is proportional to depth cubed for the flanges.
Castellated beam weight efficiency
| System | Span (ft) | Weight (plf) | Reason |
|---|---|---|---|
| W18x50 rolled | 30 | 50 | Solid web |
| CB27x35 castellated | 30 | 35 | 30% lighter, same I |
| W21x44 rolled | 40 | 44 | Solid web |
| CB32x44 castellated | 40 | 44 | Same weight, more I |
| W24x55 rolled | 45 | 55 | Solid web |
| CB36x40 castellated | 45 | 40 | 27% lighter |
For spans 30-50 ft, castellated beams typically save 25-35% of steel weight compared to rolled sections.
Limit states unique to castellated beams
Standard beam checks (flexure, shear, deflection) still apply, but castellated beams introduce additional failure modes:
1. Vierendeel bending -- At each opening, the beam acts like a Vierendeel truss. The tee sections above and below the opening resist the shear force through local bending. The Vierendeel moment in each tee is approximately:
Mv = Vglobal * S / 4
Where Vglobal is the global shear at the opening and S is the opening spacing. Each tee must resist Mv with its own plastic moment capacity (Mp,tee = Fy * Zx,tee). This check typically governs near supports where shear is highest.
2. Web post buckling -- The narrow web post between adjacent openings can buckle horizontally under the horizontal shear transferred between tee sections. Web post buckling is checked using the method in AISC Design Guide 31 Section 5.3, which treats the post as an effective strut.
3. Web post flexure (horizontal bending) -- The web post bends about its vertical axis due to the difference in axial forces between adjacent tee sections. The interaction of this bending with the vertical shear determines whether the post is adequate.
4. Lateral-torsional buckling of tee sections -- The compression tee at an opening is laterally unbraced across the opening width. For large openings with high compression, the tee can buckle laterally.
5. Compression flange yielding -- At points of high moment, the reduced cross-section through the opening must still resist the global bending moment.
Complete design checklist
For every castellated or cellular beam, check ALL of the following:
- Global flexure at critical sections (through openings and through solid web posts)
- Global shear at supports
- Vierendeel bending at each opening (top and bottom tees)
- Web post buckling between adjacent openings
- Web post flexural capacity
- Lateral-torsional buckling of compression tee
- Deflection (consider reduced stiffness at openings)
- Floor vibration (special consideration for long-span cellular beams)
- Connection capacity at ends (reduced web area)
- Composite action (if applicable)
Worked example -- Vierendeel check at opening
Given: CB27x35 (from W18x35), Fy = 50 ksi. Opening height ho = 14 in, spacing S = 18 in, web post e = 4 in. Global shear at the opening Vu = 30 kips.
Step 1: Vierendeel moment: Mv = 30 * 18 / 4 = 135 kip-in per tee.
Step 2: Tee section properties: Top tee: flange = 6.00 _ 0.425 in, stem depth = (27 - 14)/2 = 6.5 in, tw = 0.300 in. Approximate Zx,tee = 0.425 _ 6.00 _ (6.5 - 0.425/2) + 0.300 _ 6.075^2 / 4 = 16.0 + 2.77 = 18.8 in^3.
Step 3: phiMp,tee = 0.90 _ 50 _ 18.8 / 2 = 423 kip-in >> 135 kip-in OK.
Worked example -- web post buckling
Given: Same CB27x35, web post width e = 4 in, web thickness tw = 0.300 in, post height = ho = 14 in.
Step 1: Web post slenderness: kl/r = 0.5 _ 14 / (sqrt(12) _ 4/(2*0.300)) -- treating the post as a fixed-fixed column of height ho and cross-section e x tw.
Step 2: Post area: Ap = 2 _ e _ tw = 2 _ 4 _ 0.300 = 2.40 in^2 (post includes web on both sides of the opening).
Step 3: Horizontal shear through post: Vh = change in tee axial force between adjacent openings. For uniform load: Vh = w _ S / 2 = 2.5 _ 18 / 2 = 22.5 kips per post.
Step 4: phiVh = 0.90 _ 2.40 _ 0.6 * 50 = 64.8 kips > 22.5 kips OK.
For closely spaced openings (e < ho/3), web post buckling often governs and may require infill plates.
Span-to-depth ratios
Castellated beams excel at long spans. Typical span-to-depth ratios:
| Application | Span/depth (composite) | Span/depth (non-composite) |
|---|---|---|
| Office floors | 20-24 | 16-20 |
| Parking garages | 18-22 | 14-18 |
| Roof beams | 22-28 | 18-24 |
| Industrial | 18-22 | 14-18 |
A cellular beam spanning 45 ft with dt = 27 in gives span/depth = 20 -- efficient for a composite office floor.
Maximum economic span by section type
| Beam Type | Economic Span Range (ft) | Weight Efficiency |
|---|---|---|
| Rolled W-shape | 15-35 | Baseline |
| Castellated beam | 25-50 | 25-35% lighter |
| Cellular beam | 25-55 | 25-40% lighter |
| Plate girder | 40-120 | Custom |
| Steel truss | 60-150 | Lightest |
Castellated beams fill the gap between rolled shapes and plate girders for medium to long spans.
When to infill openings
Not all openings can remain open. Infill plates are welded to fill openings when:
- Near supports where shear is high (typically first 1-2 openings from each end)
- At concentrated load points where local effects are severe
- When web post buckling governs and increasing post width is not practical
- At connections where the reduced section cannot develop the required capacity
Infill plate design
| Opening Type | Infill Plate | Weld |
|---|---|---|
| Hexagonal | Cut from same web | Fillet weld, both sides |
| Circular | Circular plug | Full-penetration or fillet |
| Rectangular | Flat plate | Fillet weld, all sides |
The infill restores the full section properties at the opening location.
Floor vibration considerations
Castellated and cellular beams have reduced mass compared to solid-web beams, which can affect floor vibration performance. AISC Design Guide 11 and AISC DG31 provide guidance:
- Minimum natural frequency: 3 Hz for offices, 5 Hz for rhythmic activities
- Castellated beams have 15-20% lower mass than equivalent rolled sections
- The reduced mass partially offsets the reduced stiffness, so vibration performance is often similar
- For sensitive occupancies (operating rooms, laboratories), check floor acceleration per DG11
Multi-code comparison
AISC Design Guide 31 (USA): The primary US reference for castellated and cellular beam design. Provides detailed procedures for Vierendeel bending, web post buckling, and horizontal shear. Uses LRFD with phi = 0.90 for flexure and phi = 0.90 for the web post checks.
SCI P355 (UK/Europe): The Steel Construction Institute publication P355 covers design of composite beams with large web openings per EN 1993. Uses the Vierendeel mechanism approach with Eurocode partial safety factors (gamma_M0 = 1.00, gamma_M1 = 1.00).
AS 4100-2020 (Australia): No specific castellated beam provisions exist in AS 4100. Australian practice follows SCI P355 or first-principles Vierendeel analysis using AS 4100 capacity reduction factors (phi = 0.90 for flexure, phi = 0.90 for shear).
Cross-code Vierendeel capacity comparison
| Code | phiMp,tee Basis | Safety Factor | Result |
|---|---|---|---|
| AISC DG31 | phi _ Fy _ Zx,tee | phi = 0.90 | ~423 kip-in |
| EN 1993/SCI | fy * Wel,tee/gamma | gamma = 1.00 | ~410 kip-in |
| AS 4100 | phi _ fy _ Zx,tee | phi = 0.90 | ~423 kip-in |
All codes produce similar results for the Vierendeel check.
Common mistakes
Placing openings in high-shear zones near supports. Vierendeel bending is proportional to global shear. Openings in the end quarter of the span, where shear is highest, frequently fail the Vierendeel check. Infill the first one or two openings near each support.
Ignoring web post buckling for closely-spaced openings. Reducing the web post width (e) to fit more openings increases the risk of web post buckling. Minimum e >= ho/3 (castellated) or Do/4 (cellular) is a practical floor.
Using non-composite section properties for deflection when the slab is composite. Castellated and cellular beams are almost always designed as composite with the concrete slab. Using non-composite stiffness overestimates deflection by 40-60%.
Forgetting to check the net section at openings for axial load. When castellated beams carry axial force from diaphragm action, the reduced net section at each opening must be checked for combined axial and bending demand.
Not accounting for floor vibration. The lighter weight of castellated beams can lead to objectionable floor vibrations. Check per AISC Design Guide 11.
Specifying castellated beams for short spans. Below about 25 ft, the fabrication cost of cutting and re-welding exceeds the material savings from using a lighter section. Stick with rolled shapes for short spans.
Frequently asked questions
What is the difference between castellated and cellular beams? Castellated beams have hexagonal openings; cellular beams have circular openings. Both are made by cutting and re-welding a standard W-shape. Cellular beams are more common in modern practice because circular openings are easier to analyze and provide better stress distribution.
How much weight do castellated beams save? Typically 25-35% compared to a rolled W-shape of equivalent stiffness. The savings increase with span length.
What is the maximum opening size? Hexagonal openings: up to 0.75 _ dt. Circular openings: up to 0.8 _ dt. Larger openings require special analysis and often need reinforcement.
Do castellated beams cost more than rolled sections? Yes, fabrication cost is higher due to cutting and re-welding. However, the material savings and reduced foundation loads often make the total project cost lower, especially for spans over 30 ft.
Can I use castellated beams for moment frames? Generally not recommended. The web openings reduce the beam's ability to develop full plastic hinging at connections. Special analysis is required if castellated beams are used in moment-resisting frames.
How do I handle connections at castellated beam ends? The end connection must be designed for the reduced web area. Options include: infilling the end openings, using thicker end plates, or providing a short solid-web transition section at each end.
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Castellated Beam Types
Castellated beams are produced by cutting a standard wide-flange section longitudinally along a predetermined pattern, offsetting the two halves, and welding them back together. The resulting beam has a deeper cross-section with regularly spaced openings (castellations) in the web. The cutting pattern determines the opening geometry.
| Type | Opening Shape | Depth Increase | Max Opening Depth | Key Advantage | Common Application |
|---|---|---|---|---|---|
| Hexagonal (standard) | Regular hexagon | 1.5× parent depth | ~0.6× finished depth | Highest moment capacity gain | Office buildings, parking structures |
| Octagonal | Elongated octagon | 1.3–1.5× parent depth | ~0.55× finished depth | Smoother stress distribution | Industrial mezzanines, long-span floors |
| Sinusoidal (Angelina) | Sinusoidal wave | 1.3–1.5× parent depth | ~0.5× finished depth | Lowest stress concentration | Architectural applications, exposed steel |
| Diamond (custom) | Diamond/rhombus | 1.3–1.4× parent depth | ~0.45× finished depth | Aesthetic appeal | Feature structures, canopies |
| Circular (cellular) | Circular holes | 1.3–1.6× parent depth | ~0.65× finished depth | Best for services penetration | Modern multi-service buildings |
Castellated Beam Design Considerations
Designing castellated beams requires checks beyond those for standard I-sections. The web openings introduce additional limit states that must be evaluated individually. Per AISC 360-22 and design guides, the following must be checked.
Vierendeel bending occurs at the web openings when shear force causes secondary bending in the top and bottom tees above and below the opening. The tees act as short beams spanning between solid web posts. This is often the governing limit state for heavily loaded beams with large openings.
Web post buckling occurs at the narrow solid section between adjacent openings. The web post is subjected to combined shear and bending and can buckle laterally if the post width is insufficient relative to its depth. This limit state is particularly critical for closely spaced hexagonal openings.
Horizontal shear in web post — The web post transfers horizontal shear between the top and bottom tees. The post must have sufficient cross-sectional area to resist this shear without yielding.
Lateral-torsional buckling — Castellated beams are more susceptible to LTB than their parent sections because the deeper cross-section has different lateral stiffness characteristics. The effective length for LTB should account for the reduced torsional rigidity at openings.
Web Post Buckling Check
The web post between openings is the most critical design element. The following simplified procedure is based on the AISC Design Guide 31 approach for cellular and castellated beams.
Web post buckling check (simplified):
1. Determine web post width: wp = s - d_o (opening pitch minus opening depth)
2. Calculate web post shear: V_post = V_u × (d_o / s)
3. Check post slenderness: λ = wp / (tw × √(k_s))
4. If λ ≤ λ_p: φVn = φ × 0.6 × Fy × tw × wp (yielding governs)
5. If λ > λ_p: φVn = φ × 0.6 × Fy × tw × wp × (λ_p / λ)² (buckling governs)
where:
d_o = opening depth
s = opening pitch (center-to-center)
k_s = shear buckling coefficient (typically 5.34 for rectangular posts)
λ_p = limiting slenderness for compact posts
Vierendeel Bending Check
Vierendeel bending is the secondary bending that develops in the top and bottom tees at each opening due to the global shear force. The check involves treating each tee as a fixed-end beam spanning the opening length.
Vierendeel moment at opening:
M_v = V_u × e_o / 4 (for point load at mid-opening)
where:
V_u = factored shear at opening centerline
e_o = opening length (clear horizontal dimension)
Check each tee:
M_u,tee = M_v ≤ φ × M_n,tee = φ × Fy × S_tee
If V_u is high and e_o is large, stiffener plates may be required
at the opening corners to reduce vierendeel bending stresses.
Typical Castellated Beam Span Ranges
The table below provides practical span ranges for castellated beams by finished depth, assuming typical office floor loads (50 psf live + 20 psf superimposed dead).
| Parent Section | Finished Depth (in) | Typical Span Range (ft) | Max Opening Depth (in) | Opening Pitch (in) | Weight (plf) |
|---|---|---|---|---|---|
| W12x26 → castellated | 18 | 25–35 | 10 | 24 | 26 |
| W14x30 → castellated | 21 | 30–40 | 12 | 28 | 30 |
| W16x36 → castellated | 24 | 35–50 | 14 | 32 | 36 |
| W18x46 → castellated | 27 | 40–55 | 16 | 36 | 46 |
| W21x57 → castellated | 32 | 45–65 | 19 | 42 | 57 |
| W24x68 → castellated | 36 | 50–70 | 21 | 48 | 68 |
| W27x84 → castellated | 40 | 55–80 | 24 | 52 | 84 |
| W30x99 → castellated | 45 | 60–90 | 27 | 58 | 99 |
| W33x118 → castellated | 50 | 70–100 | 30 | 64 | 118 |
| W36x135 → castellated | 54 | 75–110 | 32 | 70 | 135 |
Note: Actual span capacity depends on loading, bracing conditions, opening geometry, and serviceability requirements (L/360 for floors, L/240 for roofs).
Related references
- Beam Sizes
- Beam Formulas
- Beam Web Design
- Composite Beam Design
- Deflection Limits
- Floor Vibration
- Serviceability Design
- Lateral-Torsional Buckling
- How to Verify Calculations
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This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.
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