Steel Beam with Web Openings Calculator
Free Steel Beam with Web Openings Calculator. Check unreinforced and reinforced circular or rectangular web openings per AISC Design Guide 2. Vierende
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Steel Beam with Web Openings Calculator AISC DG2
Verify circular or rectangular web openings in steel I-beams — unreinforced or reinforced — with full Vierendeel bending, shear-moment interaction, tee-column buckling, and deflection checks.
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1. Beam Section & Material
W-Shape Selection
Select to auto-fill, or enter manually below
Section Dimensions (auto-fills from selection)
2. Span & Applied Loads
LRFD factored combination: 1.2D + 1.6L applied automatically. ASD: D + L. Shear and moment at the opening location are calculated from the UDL.
3. Opening Geometry
Shape & Dimensions
⚠ h₀ exceeds 70% of beam depth (limit: 0.70d)
Must be ≤ 0.70 × d per AISC DG2
Aspect ratio a₀/h₀ displayed in results
Position & Eccentricity
Opening centroid location along span
+ = above NA, − = below NA (0 = centered)
Distance between lateral braces for LTB check
4. Opening Reinforcement
Reinforcement Option
Minimum fillet weld: Use w = tR/2 ≥ 3/16". Horizontal shear demand: q = VQ/I along bar length.
Accuracy notice: Results follow AISC Design Guide 2 (3rd ed.) procedures. Always verify with a licensed structural engineer for construction use. This tool is for feasibility and preliminary design only.
Beam Diagram (Live)
Beam elevation • Opening shown to scale • SFD below
Opening Not Yet Calculated
Tee Section Properties
| Top Tee Depth tt | — |
| Bottom Tee Depth tb | — |
| Top Tee Area At | — |
| Bottom Tee Area Ab | — |
| Top Tee It | — |
| Bottom Tee Ib | — |
| Top Tee Zxt | — |
| Bottom Tee Zxb | — |
| Shear at Opening Vu | — |
| Moment at Opening Mu | — |
| Aspect Ratio ao/ho | — |
Design Check Results (DCR)
| Check | Demand | Capacity | DCR | Status |
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Sensitivity — Opening Height Effect
Governing DCR as opening height h₀ increases by 10% / 20% / 30% from current:
Current
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+10%
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+20%
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+30%
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Optimal Loc.
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Min DCR Loc.
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📄 Formulas Used in Calculations (AISC Design Guide 2)
▼1. Tee Section Depths
$$t_t = \frac{d - h_o}{2} - e \qquad t_b = \frac{d - h_o}{2} + e$$where $d$ = beam depth, $h_o$ = opening height, $e$ = eccentricity (+ above NA)
2. Plastic Shear Capacity of Unperforated Beam
$$V_p = 0.6\,F_y\,A_w = 0.6\,F_y\,(d - 2t_f)\,t_w$$Opening must satisfy: $V_u \leq \tfrac{2}{3}V_p$ (preliminary limit check)
3. Maximum Shear Strength at Opening (Tee Contributions)
$$V_{mt} = \frac{4\,M_{pt}}{a_o}\bigl(1 - V_u^2/V_{pt}^2\bigr)^{1/2} \qquad V_{mb} = \frac{4\,M_{pb}}{a_o}\bigl(1 - V_u^2/V_{pb}^2\bigr)^{1/2}$$ $$V_m = V_{mt} + V_{mb}$$where $M_{pt} = F_y Z_{xt}$, $M_{pb} = F_y Z_{xb}$, $V_{pt} = 0.6 F_y t_w t_t$, $V_{pb} = 0.6 F_y t_w t_b$
4. Maximum Moment Strength at Opening
$$M_m = M_{pt}\left(1 + \frac{A_{wt}}{A_{ft}}\right) + M_{pb}\left(1 + \frac{A_{wb}}{A_{fb}}\right) - V_{mt}\frac{a_o}{2} - V_{mb}\frac{a_o}{2}$$Simplified (DG2): $M_m \approx F_y\bigl(Z_{xt} + Z_{xb}\bigr) - V_{mt}\dfrac{a_o}{4} - V_{mb}\dfrac{a_o}{4}$
5. M–V Interaction (Governing Limit State)
$$\left(\frac{M_u}{M_m}\right)^2 + \left(\frac{V_u}{V_m}\right)^2 \leq 1.0 \quad \text{(LRFD: } M_u = \phi_b M_m,\; V_u = \phi_v V_m\text{)}$$Interaction ratio $R = \sqrt{(M_u/M_m)^2 + (V_u/V_m)^2}$ must be $\leq 1.0$
6. Vierendeel (Secondary) Bending
$$M_{vt} = V_u\,\frac{a_o}{4}\cdot\frac{I_t}{I_t + I_b} \qquad M_{vb} = V_u\,\frac{a_o}{4}\cdot\frac{I_b}{I_t + I_b}$$ $$\text{DCR}_{Vt} = \frac{M_{vt}}{\phi_b\,M_{pt}} \leq 1.0 \qquad \text{DCR}_{Vb} = \frac{M_{vb}}{\phi_b\,M_{pb}} \leq 1.0$$7. Tee-Column (Web Post) Buckling Check
$$\frac{KL}{r} = \frac{1.2\,a_o}{r_{y,tee}} \qquad F_{cr} \text{ per AISC Chapter E}$$ $$P_c = \phi_c\,F_{cr}\,A_t \qquad \text{DCR} = P / P_c \leq 1.0$$Compression force: $P = (M_u - \phi_b M_m^{0}) / (d - t_t/2 - t_b/2)$ when moment governs
8. Additional Deflection at Opening (Vierendeel Shear Deformation)
$$\delta_{opening} = \frac{V_u\,a_o^3}{12\,E\,(I_t + I_b)}$$ $$\delta_{total} = \delta_{primary} + \sum \delta_{opening} \leq \frac{L}{360} \text{ (live load)}$$9. Compactness Check (Flange Local Buckling)
$$\frac{b_f}{2t_f} \leq \lambda_p = 0.38\sqrt{E/F_y}$$For reinforcement flat bar: $\dfrac{b_R}{2t_R} \leq 0.38\sqrt{E/F_y}$
Frequently Asked Questions
How large can a web opening be in a steel beam?
Per AISC Design Guide 2, the opening height h₀ must not exceed 70% of the beam depth (0.70d). The edge of the opening must be at least one beam depth (d) from the face of the support. For service openings with reinforcement, openings approaching this limit are achievable, but expect elevated DCR values — especially for Vierendeel bending. The opening length a₀ has no specific code limit, but aspect ratios a₀/h₀ greater than about 3 significantly increase secondary (Vierendeel) bending demands. Circular openings are treated as equivalent rectangular shapes per DG2 §3.7b4.
What is Vierendeel bending and why does it govern?
When a shear force acts on a beam at an opening, the upper and lower tee sections must transfer that shear across the opening length like a small portal frame — a mechanism called Vierendeel action. The horizontal shear generates secondary bending moments at the four corners of the opening. These local moments are proportional to V×(a₀/4) and are distributed between the top and bottom tees in proportion to their moments of inertia. This check is most critical when the opening is in a high-shear zone (near supports) or when the opening is wide (large a₀). Placing openings in low-shear midspan regions significantly reduces Vierendeel demands.
When is flat-bar reinforcement required around a web opening?
Reinforcement is required when any of the DCR checks exceed 1.0 for the unreinforced case. The most common trigger is the M–V interaction check or the Vierendeel DCR exceeding unity. Flat bars welded along the top and bottom edges of the opening increase the plastic section modulus of each tee, directly raising Vmt, Vmb, Mm, and Mpt/pb. As a rule of thumb: openings in the outer third of the span (high-shear zone) almost always require reinforcement for h₀ > 50% of d. Openings in the middle third at midspan typically pass unreinforced for h₀ up to 60% of d.
Does AISC Design Guide 2 cover circular openings?
Yes. AISC DG2 §3.7b4 specifies that a circular opening of diameter D₀ may be treated as an equivalent rectangular opening with height h₀ = D₀ and length a₀ = 0.9D₀. This calculator applies that conversion automatically when "Circular" is selected. For very large-diameter openings (approaching 0.70d), the circular shape does offer a slight advantage over a square opening because corner stress concentrations are lower, but the code method conservatively uses the same rectangular equivalent checks.
Can I put an opening near the beam support?
AISC DG2 prohibits the edge of the opening within one beam depth (d) from the face of a support. This calculator flags this violation with a warning. Near-support zones have both high shear and high web shear stress, making Vierendeel demands extremely large. Even with reinforcement, openings closer than 1d to supports are structurally inefficient. If MEP routing requires a near-support penetration, consider deepening the beam, using a stub-girder, or using a castellated/cellular beam system designed for that configuration.
What is the difference between castellated and cellular beams?
Both are expanded steel beams with regularly-spaced web openings created by splitting a parent section along a cut pattern and re-welding. Castellated beams use a hexagonal cut pattern, producing hexagonal or sinusoidal openings. Cellular beams use a circular cut pattern, producing circular openings at regular intervals. Both achieve a deeper section (typically 40–60% deeper than the parent) with the same steel weight, giving higher bending efficiency. The web-post buckling check between adjacent openings is especially critical for these beam types. This calculator handles individual unreinforced or reinforced openings; for full castellated/cellular beam design, a specialized tool with web-post interaction is recommended.