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Steel Beam Web Openings Calculator | AISC DG2 + Eurocode

Steel Beam Web Openings Calculator for circular & rectangular openings. AISC DG2 (Vierendeel, M-V, shear, reinforcement) + Eurocode. LRFD/ASD, US/SI.
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This Steel Beam with Web Openings Calculator is a preliminary-design tool for circular and rectangular openings in W-shapes, informed by the principles of AISC Design Guide 2 (Steel and Composite Beams with Web Openings).

It uses a transparent, mechanics-based four-hinge Vierendeel model with axial–moment (P–M) interaction in the tees, and reports tee properties, tee shear, tee-column buckling, compactness, gross-section flexure/LTB, deflection and edge-distance checks. It supports unreinforced and flat-bar-reinforced openings, LRFD and ASD, and US/SI units. It does not reproduce the Design Guide 2 interaction curves or design equations — results are indicative and must be confirmed against DG2 by a licensed structural engineer.

For preliminary design only — always verify with a licensed structural engineer.

Steel Beam with Web Openings Calculator DG2-based • preliminary

Check circular or rectangular web openings in steel I-beams — unreinforced or flat-bar reinforced — with a four-hinge Vierendeel model, P–M interaction, tee shear, tee-column buckling and deflection checks.

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⚠ Method & limitations: This tool does not reproduce the Design Guide 2 interaction curves or its closed-form equations. It uses an independent, conservative mechanics model (four plastic hinges, linear P–M interaction in each tee, tee centroids as the flange-force couple). Compare against DG2 and your governing code before relying on any result. Reinforcement is assumed fully developed by its welds; weld design is not performed. The 2/3 overall-shear limit is quoted from memory of DG2 and should be confirmed. The DG2 rule limiting point-load distance from an opening is not implemented.
▸ 1. Beam Section & Material
W-Shape Selection
Select to auto-fill, or enter dimensions manually below
Section Dimensions
Ix and Zx fill automatically from the table; leave blank to compute from the dimensions above (typing a dimension clears them).
▸ 2. Span & Applied Loads
Distance between reaction points (e.g. the bolt line at each end, not necessarily the support-member centrelines). Position x is measured from the same left reaction point.
Point Loads (optional — e.g. girder with framing beams)
ⓘ LRFD: 1.2D + 1.6L. ASD: D + L (applied to the uniform and point loads). Shear and moment are the largest values at the two ends and centre of the opening, so shear that varies across the opening is captured. A point load located over the opening fails; the DG2 limit on point-load distance from an opening is not checked. Include beam self-weight in wD. Deflection uses service live load only.
▸ 3. Opening Geometry
Shape & Dimensions
⚠ Opening exceeds 70% of beam depth (limit: 0.70d)
Must be ≤ 0.70 × d
Aspect ratio ao/ho is reported in the results
Position & Eccentricity
Opening centre, measured along the span
+ = opening shifted above mid-depth, − = below (0 = centred)
Used for the gross-section flexure / LTB check (Cb = 1.0)
▸ 4. Opening Reinforcement
Reinforcement Option
Width projecting from the web face, per bar
Distance from the opening edge to the near face of the bar, leaving room for the fillet weld to the web. 0 = bar flush against the edge.
Default 0. Added to the clear-web shear area of each reinforced tee. DG2 does not provide a rule for crediting reinforcement in shear (e.g. an HSS sleeve through the web) — use only with engineering justification.
ⓘ Enter bR/tR within the compact limit 0.38√(E/Fy). Advisory flags (not DG2 requirements) report whether the bar area is at least 50% of the tee web area and whether the tee plastic neutral axis stays within the flange thickness. Reinforcement Fy must be at least the beam Fy. Weld design is not performed. For a round sleeve or ring, enter an equivalent bar area and justify it separately.
⚠ Accuracy notice: Preliminary feasibility tool. Always verify with AISC Design Guide 2 and a licensed structural engineer before construction use.
▸ Beam Diagram (Live)
Enter inputs and click Calculate
Beam elevation • span compressed horizontally; opening drawn in true proportion • SFD below
Opening Not Yet Calculated
▸ Opening & Tee Properties
Equivalent ho / ao used—
Aspect Ratio ao/ho—
Top Tee Depth tt—
Bottom Tee Depth tb—
Top Tee Area At (incl. bars)—
Bottom Tee Area Ab (incl. bars)—
Top Tee It (elastic)—
Bottom Tee Ib (elastic)—
Top Tee Plastic Moment Mpt—
Bottom Tee Plastic Moment Mpb—
Tee Centroid Lever Arm z—
Pure-Moment Strength at Opening Mm (nominal)—
Pure-Shear Strength at Opening Vm (nominal)—
Shear at Opening Vu—
Moment at Opening Mu—
▸ Design Check Results (DCR)
CheckDemandCapacityDCRStatus

Capacities include φ (LRFD) or 1/Ω (ASD). Edge distance: “demand” = required clear distance d, “capacity” = clear distance provided.

▸ Shear–Moment Interaction Envelope

Design envelope of this tool's four-hinge model (not the DG2 curves). The dot is the factored demand; the dashed line extends to the point where demand reaches the envelope.

▸ Sensitivity

Governing DCR as the opening height (or diameter) grows by 10% / 20% / 30%, and the best position found by sweeping x along the span (same opening, same loads):

Current
—
+10%
—
+20%
—
+30%
—
Lowest DCR in sweep
—
At x =
—
✓ Copied to clipboard!

1. Equivalent rectangle for circular openings

$$\text{Unreinforced: } h_o = D_o,\; a_o = 0.9D_o \qquad \text{Reinforced: } h_o = D_o,\; a_o = 0.45D_o$$

The size limit $D_o \le 0.70d$ is checked on the physical diameter.

2. Tee depths (measured from the outer flange face to the opening edge)

$$t_t = \frac{d - h_o}{2} - e \qquad t_b = \frac{d - h_o}{2} + e$$

$e > 0$ shifts the opening above mid-depth. Each tee is built from the beam flange ($b_f \times t_f$), the web stem ($t_w \times (t - t_f)$) and, if selected, a reinforcing bar ($n\,b_R \times t_R$) set back from the opening edge by the offset.

3. Tee axial and plastic bending capacity

$$P_{y,i} = \sum F_{y}A \qquad M_{p,i} = \sum F_y\,A\,|y - y_{PNA}| \qquad z = d - \bar y_t - \bar y_b$$

$y_{PNA}$ is where the force above equals half the total tee yield force; $\bar y$ is the area centroid measured from the outer flange face.

4. Pure-moment strength at the opening

$$M_m = \min(P_{y,t},\,P_{y,b})\; z \qquad P = \frac{M_u}{z}$$

With zero shear the two tees act as a force couple. $P$ is the axial force in each tee caused by the overall moment.

5. Four-hinge shear strength with P–M interaction

$$V_i(P) = \min\!\left(\frac{2\,M_{p,i}\,(1 - P/P_{y,i})}{a_o},\; V_{p,i}\right) \qquad V_m(P) = V_t(P) + V_b(P)$$

Each tee forms two hinges (one at each end of the opening). The linear $P$–$M$ reduction lies inside the true convex interaction surface and is therefore conservative.

6. M–V interaction DCR

$$\text{DCR}_{MV} = \frac{1}{s_{max}},\quad s_{max} = \max\{s:\; s\,V_u \le \phi_v V_m(P_n),\; P_n = \tfrac{s\,M_u}{\phi_b z} \le P_{y,min}\}$$

The demand point $(M_u, V_u)$ is scaled along a ray until it reaches the design envelope plotted in the results.

7. Vierendeel P–M check per tee (elastic shear split)

$$V_i = V_u\frac{I_i}{I_t + I_b} \qquad M_{v,i} = \frac{V_i\,a_o}{2} \qquad \frac{P}{\phi_b P_{y,i}} + \frac{M_{v,i}}{\phi_b M_{p,i}} \le 1.0$$

Each tee is fixed-fixed over $a_o$, so the end moment is $V_i a_o/2$. The elastic split is more conservative than the plastic mechanism in item 5 when the tees differ.

8. Overall shear limit and tee web shear

$$V_p = 0.6F_y(d - 2t_f)t_w \qquad V_u \le \tfrac{2}{3}\phi_v V_p$$ $$V_{p,i} = 0.6F_y\left[t_w(t_i - t_f) + A_{extra}\right] \qquad V_i \le \phi_v V_{p,i}$$

Tee shear uses the clear web only (tee depth minus flange thickness). $A_{extra}$ is zero unless you deliberately credit reinforcement. The 2/3 limit should be confirmed against DG2.

9. Tee-column buckling (weak axis)

$$\frac{KL}{r} = \frac{1.2\,a_o}{r_{y}} \qquad P_c = \phi_c F_{cr} A \qquad P/P_c \le 1.0$$

$F_{cr}$ per AISC 360 Chapter E; $\phi_c = 0.90$. Bars are credited only when placed on both sides of the web. $K = 1.2$ is an assumption of this tool.

10. Compactness

$$\frac{b_f}{2t_f} \le 0.38\sqrt{E/F_y} \qquad \frac{b_R}{t_R} \le 0.38\sqrt{E/F_y}$$

11. Gross-section flexure with LTB (AISC 360 Section F2, Cb = 1.0)

$$M_u \le \phi_b M_n,\quad M_n = \text{per Eqs. F2-1 to F2-3 with } L_p,\,L_r,\,r_{ts},\,J \text{ approximated from the dimensions}$$

An overall-beam check at the opening location, independent of the opening mechanics.

12. Live-load deflection

$$\delta_{prim} = \max\left|\iint \frac{M_L(x)}{E I_x}\,dx\,dx\right| \qquad \delta_{open} = \frac{V_{L}\,a_o^3}{12E(I_t + I_b)} \qquad \delta_{prim} + \delta_{open} \le \frac{L}{360}$$

$\delta_{prim}$ is found by numerical double integration for the actual support condition, uniform and point loads. The opening term is the full relative displacement across the opening, added without a reduction factor (conservative); it uses $I_t + I_b$, which include any reinforcement. The global $I_x$ is not increased by the bars. Service live load only.

Frequently Asked Questions

How large can a web opening be in a steel beam?+
AISC Design Guide 2 limits the opening depth to about 70% of the beam depth (0.70d). This calculator checks that limit, and also flags an opening whose clear distance to either support is less than one beam depth d. Opening length has no hard limit here, but aspect ratios a₀/h₀ above about 3 make Vierendeel demands rise quickly (advisory check included). Other standards (for example the Eurocode-based guidance) use different limits — this tool follows DG2 only.
What is Vierendeel bending and why does it govern?+
At an opening the shear must pass through the top and bottom tees acting like a small frame. Each tee, fixed at both ends over the opening length a₀, develops end moments of V×a₀/2 (V being that tee's share of the shear). At the same time the overall bending moment pushes an axial force P = M/z into each tee, which reduces the tee's remaining bending strength. Near supports shear dominates; near midspan the axial force dominates. Both effects are included here.
When is flat-bar reinforcement required?+
When any DCR exceeds 1.0 for the unreinforced case. Flat bars along the opening edge increase each tee's area, axial yield force and plastic moment, which raises both the pure-moment and the shear strength of the opening. They do not help the overall shear limit, the edge-distance rule or the deflection check much. Bars are assumed to be fully welded; weld design is outside this tool.
How are circular openings handled?+
Circular openings are converted to an equivalent rectangle. Unreinforced: h₀ = D₀, a₀ = 0.9D₀. Reinforced: h₀ = D₀ and a₀ = 0.45D₀ (aspect ratio 0.45). The reinforced length is much shorter, which is why reinforcement improves circular openings so effectively. The physical diameter is checked against 0.70d.
Can I credit a round sleeve or reinforcement in the tee shear capacity?+
By default tee shear uses only the clear web (tee depth minus flange thickness) times tₔ — reinforcement is not credited. DG2 does not give a rule for an HSS sleeve through the web. If you can justify it, enter the additional effective shear area in the “Extra Tee Shear Area” field; it is added to each reinforced tee.
Does this reproduce the DG2 interaction graphs?+
No. DG2 provides closed-form equations and design curves calibrated to tests. This tool uses an independent mechanics-based model and plots its own M–V envelope. It can be more or less conservative than DG2 in particular cases. Treat the results as a screening check and verify against DG2.
Is it valid for castellated or cellular beams?+
No. It checks isolated openings. Regularly spaced openings need a web-post buckling and web-post shear check that is not included. See AISC Design Guide 31 or SCI P355.
SteelSolver.com — User Guide

Steel Beam with Web Openings Calculator

A walkthrough of every input, formula and result in the web opening checker — with a worked example, common mistakes, and an honest description of what the method does and does not cover.

✅ Informed by AISC Design Guide 2 ✅ LRFD & ASD ✅ US Customary & SI ✅ Free & Browser-Based
⚠
What this calculator is — and is not. It is a preliminary screening tool. It does not reproduce the AISC Design Guide 2 closed-form equations or interaction curves. It uses an independent, deliberately conservative mechanics model (four plastic hinges, linear P–M interaction in each tee). Its results can differ from DG2 in either direction for specific cases, so always confirm against DG2 and have a licensed structural engineer review any opening before it is used in construction. The 2/3 overall-shear limit is quoted from memory of DG2 and should be confirmed against your own copy, and the DG2 limit on how close a point load may be to an opening is not implemented.

1. What Is a Steel Beam Web Opening Calculation?

When mechanical, electrical and plumbing (MEP) trades route ducts, conduit or pipes through the floor structure, they often need to pass through the webs of steel beams. The opening removes web material, so the beam must be checked at that location.

Unlike a standard beam check, a web opening adds failure modes that must be checked independently:

  • Vierendeel bending — frame action of the top and bottom tees around the opening
  • Moment–shear (M–V) interaction — the overall moment loads the tees axially and erodes their shear strength
  • Tee shear — the clear web of each tee carrying its share of the shear
  • Tee-column buckling — stability of the compression tee
  • Local buckling and flexure — flange compactness, reinforcement outstand, gross-section LTB
  • Additional deflection — shear deformation across the opening

The governing U.S. reference is AISC Design Guide 2, Steel and Composite Beams with Web Openings, which treats unreinforced and flat-bar-reinforced openings. This calculator is informed by its principles but implements its own simplified model; see the notice above.

2. Where Engineers Apply Web Opening Calculations

🏠
Multi-Story Office & Residential

HVAC ducts and plumbing risers cross structural bays; openings preserve floor-to-floor height.

🏢
Parking Structures

Conduit and drainage pipes cross beams; openings avoid costly reroutes.

🏭
Industrial Facilities

Process piping and cable trays through heavy framing, where vibration and dynamic loads need extra care.

🏥
Healthcare & Labs

Dense MEP coordination where every inch of ceiling space counts.

🔧
Retrofit Projects

Existing beams checked when new services are installed.

3. Who Uses It — and What It Gives Them

How different users can use the calculator
UserTypical NeedWhat the Tool Provides
Structural EngineerA fast first-pass screening of an opening before detailed DG2 calculations.All checks run at once with colour-coded DCRs, the governing check, an M–V envelope plot, and a sweep of positions.
MEP CoordinatorJudge whether a requested opening is plausible before sending an RFI.An indicative pass/marginal/fail verdict — to be confirmed by the engineer of record, never used as approval.
Steel FabricatorA record of the opening and reinforcement assumptions.A copy-able report listing inputs, tee properties and DCRs. Weld design is not included.
EIT / Junior EngineerUnderstand how opening size and position change demand.Visible formulas, sensitivity to opening size, and the effect of moving the opening along the span.

4. Annotated Steel Beam Web Opening Diagram

The figure identifies the geometric parameters used by the calculator.

Annotated steel beam with rectangular web opening Wide-flange beam elevation showing depth d, opening height ho, opening length ao, top tee depth tt, bottom tee depth tb, eccentricity, position x and span L. Flat bar (optional) Flat bar (optional) mid-depth d hₒ aₒ t_t (top tee) t_b (bottom tee) x (to opening centre) L (span) Rectangular opening Vierendeel action Top tee (2 hinges) Bottom tee (2 hinges) Dₒ (diameter) Circular opening Unreinforced: hₒ = Dₒ, aₒ = 0.9Dₒ Reinforced: hₒ = Dₒ, aₒ = 0.45Dₒ

Figure 1. Beam elevation with a rectangular opening. d = beam depth; hₒ, aₒ = opening height and length; tt, tb = top and bottom tee depths measured from the outer flange face; x = distance from the left support to the opening centre; L = span. Right: Vierendeel action and the equivalent rectangles for circular openings.

5. Step-by-Step User Guide

  1. 1
    Select units and design method

    Use the Units toggle for US (in / kips / ksi / ft) or SI (mm / kN / MPa / m). Switching units converts all values already entered. Choose LRFD (φ = 0.90 for bending, shear and compression) or ASD (Ω = 1.67).

  2. 2
    Choose a W-shape or enter dimensions

    Selecting a shape fills d, bf, tf, tw, Ix and Zx. For other sections type the dimensions; Ix and Zx are then computed from them (the fields clear when you edit a dimension).

  3. 3
    Set grade and modulus

    Pick A36, A992/A572-50 or A572-60. Fy fills automatically; E defaults to 29,000 ksi (200,000 MPa).

  4. 4
    Enter span, supports and loads

    Enter the span, the support condition (simply supported, fixed-fixed, or fixed-pinned) and uniform dead and live loads. The span is the distance between reaction points: if the reaction acts at a bolt line, use the bolt-line spacing, and measure x from the same left reaction point. Optionally add up to three point loads (dead and live, with position) for girders. Include beam self-weight in wD. The tool forms 1.2D + 1.6L (LRFD) or D + L (ASD) for strength and uses the live load alone for deflection.

  5. 5
    Define the opening

    Choose rectangular (ho, ao) or circular (Do). Circular openings are converted to an equivalent rectangle that depends on whether reinforcement is selected. Enter the position x, the eccentricity e (positive = shifted up) and the unbraced length Lb. A red warning appears if the opening exceeds 0.70d.

  6. 6
    Choose reinforcement

    Start with None. If it fails, choose flat bars at the top and bottom edges. Enter the outstand width bR, thickness tR, the offset of the bar from the opening edge (default 1/2 in., leaving room for the fillet weld), the bar yield strength (at least the beam Fy) and whether bars are on one or both sides of the web. Leave “extra tee shear area” at 0 unless you can justify crediting reinforcement in shear.

  7. 7
    Calculate

    The tool runs every check, redraws the beam and shear diagram, fills the DCR table and the M–V envelope plot, and sweeps opening size and position for the sensitivity panel.

  8. 8
    Copy or print the report

    Copy Full Report places inputs, tee properties and DCRs on the clipboard; Print Report prints or saves a PDF. Have a licensed engineer review the outcome.

6. Input Parameters, Valid Ranges and Units

Input reference
ParameterSymbolUS UnitSI UnitNotes
Beam depthdinmmMust be positive.
Flange width / thicknessbf, tfinmm2tf must be less than d.
Web thicknesstwinmmControls tee shear.
Yield strength / modulusFy, EksiMPaE default 29,000 ksi / 200,000 MPa.
Moment of inertia / plastic modulusIx, Zxin⁴, in³mm⁴, mm³From the table or blank (computed).
SpanLftmCentre-to-centre of supports.
Dead / live loadwD, wLkips/ftkN/mUniform. Include self-weight in wD.
Opening sizeho, ao, Doinmmho or Do ≤ 0.70d. ao/ho > 3 is flagged.
PositionxftmSupport centreline to opening centre; 0 < x < L.
Eccentricityeinmm+ = above mid-depth. Both tees must be deeper than tf.
Point loads (optional)PD, PL, akips, ftkN, mUp to three. Position a from the left reaction point. A load over the opening fails.
Unbraced lengthLbftmFor gross-section LTB (Cb = 1.0).
Bar outstand / thicknessbR, tRinmmbR/tR ≤ 0.38√(E/Fy).
Bar offset—inmmOpening edge to near face of bar; default 1/2 in. for weld access.
Extra tee shear areaAextrain²mm²Default 0; engineering judgement only.

7. All Formulas Used in the Calculation

The equations below are those implemented in the code. They are a mechanics-based simplification, not the Design Guide 2 equations. All lengths are in inches and forces in kips.

Formula 1 — Equivalent rectangle and tee depths

$$\text{Circular, unreinforced: } h_o = D_o,\ a_o = 0.9D_o \qquad \text{Circular, reinforced: } h_o = D_o,\ a_o = 0.45D_o$$ $$t_t = \frac{d - h_o}{2} - e \qquad t_b = \frac{d - h_o}{2} + e$$

What it means: Reinforcing a circular opening shortens its equivalent length to 0.45Do, which greatly reduces the Vierendeel demand. Tee depths are measured from the outer flange face to the opening edge.

Formula 2 — Tee axial and bending capacity

$$P_{y} = \sum F_y A \qquad M_{p} = \sum F_y A\,|y - y_{PNA}| \qquad z = d - \bar y_t - \bar y_b$$

What it means: Each tee is built from the beam flange, the web stem and (if present) the reinforcing bar, set back from the opening edge by the bar offset. The plastic neutral axis splits the yield force in half; z is the distance between the two tee centroids and is the lever arm of the axial force couple.

Formula 3 — Moment strength at the opening

$$M_m = \min(P_{y,t}, P_{y,b})\,z \qquad P = M_u / z$$

What it means: With no shear the opening can carry the moment by compression in one tee and tension in the other. P is the axial force each tee must carry at the demand moment.

Formula 4 — Four-hinge shear strength with P–M interaction

$$V_i(P) = \min\!\left(\frac{2M_{p,i}(1 - P/P_{y,i})}{a_o},\ V_{p,i}\right) \qquad V_m(P) = V_t + V_b$$

What it means: Each tee has two plastic hinges, one at each end of the opening, so its shear strength is 2Mp/ao. The axial force P uses up part of Mp. The linear reduction is conservative because the true interaction surface is convex.

Formula 5 — M–V interaction DCR

$$\text{DCR}_{MV} = 1/s_{max} \quad\text{where } s_{max} = \max\{s: sV_u \le \phi_v V_m(P_n),\ P_n = sM_u/(\phi_b z) \le P_{y,min}\}$$

What it means: The demand point (Mu, Vu) is scaled outward along a ray until it meets the design envelope shown in the results. A DCR of 1.0 means the demand sits exactly on the envelope.

Formula 6 — Vierendeel P–M check per tee

$$V_i = V_u\frac{I_i}{I_t + I_b} \qquad M_{v,i} = \frac{V_i a_o}{2} \qquad \frac{P}{\phi_b P_{y,i}} + \frac{M_{v,i}}{\phi_b M_{p,i}} \le 1.0$$

What it means: Each tee is fixed at both ends over the opening length, so the end moment is Viao/2. The shear is split by elastic stiffness, which is more conservative than the plastic mechanism when the two tees differ.

Formula 7 — Shear checks

$$V_p = 0.6F_y(d - 2t_f)t_w \qquad V_u \le \tfrac{2}{3}\phi_v V_p \qquad V_{p,i} = 0.6F_y\left[t_w(t_i - t_f) + A_{extra}\right]$$

What it means: Tee shear uses only the clear web between the flange and the opening edge. Reinforcement is not credited unless you enter Aextra. The 2/3 overall limit should be confirmed against DG2.

Formula 8 — Tee-column buckling

$$\frac{KL}{r} = \frac{1.2a_o}{r_y} \qquad P_c = \phi_c F_{cr} A \qquad \text{DCR} = P/P_c$$

What it means: The compression tee is treated as a short column of length ao about its weak axis, with Fcr from AISC 360 Chapter E and φc = 0.90. K = 1.2 is an assumption of this tool. Bars count only when they are on both sides of the web.

Formula 9 — Compactness

$$\frac{b_f}{2t_f} \le 0.38\sqrt{E/F_y} \qquad \frac{b_R}{t_R} \le 0.38\sqrt{E/F_y}$$

What it means: For A992 steel the limit is 9.15. The plastic capacities assume compact elements.

Formula 10 — Gross-section flexure with LTB

$$M_u \le \phi_b M_n \quad (\text{AISC 360 F2},\ C_b = 1.0)$$

What it means: An overall-beam check at the opening location using approximate ry, rts and J computed from the dimensions. It is independent of the opening and is conservative with Cb = 1.0.

Formula 11 — Live-load deflection

$$\delta = \max\left|\iint \frac{M_L}{E I_x}\,dx\,dx\right| + \frac{V_L a_o^3}{12E(I_t + I_b)} \le \frac{L}{360}$$

What it means: The beam deflection is found by numerical integration for the chosen supports, uniform load and point loads (service live load only). The opening term is the full local displacement across the opening, added without reduction, so it is conservative. It uses It + Ib, which include any reinforcement, so bars do stiffen the opening region. The global Ix is not increased by the bars, which is a reasonable simplification because the opening is a short length of the span.

8. Understanding Your Results — DCR Colour Code and Verdict

Each check is a Demand-to-Capacity Ratio (DCR); 1.0 means 100% utilisation. Capacities already include φ (LRFD) or 1/Ω (ASD).

● PASS — DCR ≤ 0.90 ● MARGINAL — 0.90 < DCR ≤ 1.00 ● FAIL — DCR > 1.00
The checks reported and what to do if one fails
CheckWhat Governs ItWhat to Do if FAIL
Opening size (≤ 0.70d)Opening too deep for the beam.Reduce the opening or choose a deeper beam.
Aspect ratio ao/ho (advisory)Long, narrow opening.Shorten the opening or split it.
Edge distanceOpening edge closer than d to either support.Relocate; reinforcement does not cure this.
Overall shear (2/3 φVp)High-shear zone.Move toward midspan or choose a heavier beam.
M–V interactionCombined shear and moment on the tees.Add flat bars or reposition.
Vierendeel P–M (top / bottom)Shear transfer through a long opening plus axial force.Shorten ao, add bars to the weaker tee, or move.
Tee web shearShallow tee with thin clear web.Reduce the opening height or relocate. Crediting reinforcement requires justification.
Tee-column bucklingLong opening in a high-moment zone.Shorten ao, add bars on both sides of the web, or move.
Reinforcement Fy ≥ beam FyWeaker bar steel than the beam.Use bar steel at least as strong as the beam.
Bar area ≥ 50% of tee web; tee PNA within flange (advisory)Practice-based flags, not DG2 requirements. They show whether the bar is wide enough to brace the tee web and whether the plastic neutral axis stays in the flange. They are listed as REVIEW and do not change the verdict.Increase the bar area or reduce it, as appropriate, and apply engineering judgement.
Point load over openingA concentrated load acts within the opening length.Move the opening or the load. The DG2 distance rule for loads near the opening is not checked.
Compactness / bar outstandThin flange or wide thin bar.Use a compact shape; thicken or narrow the bar.
Gross flexure / LTBLong unbraced length.Add bracing or a heavier section.
Deflection (L/360)Flexible beam or large opening near high shear.Use a stiffer beam or smaller opening.
⚠
Edge distance: if the clear distance from the opening edge to either support is less than the beam depth d, the check fails. Reinforcement does not cure this — the opening must be moved.

9. Worked Example — W21×57, 30 ft Span

▶ Floor Beam with an HVAC Duct Penetration

Problem

A W21×57 (A992, Fy = 50 ksi) spans 30 ft between reaction points, simply supported, with wD = 1.0 and wL = 1.5 kips/ft and no point loads. A 10 in. × 14 in. rectangular opening is centred at mid-depth, x = 10 ft from the left reaction. Lb = 5 ft. LRFD, US units. The numbers below are the calculator's output for these inputs.

SectionW21×57 (d 21.06, bf 6.555, tf 0.650, tw 0.405 in)
Opening ho × ao10 × 14 in, e = 0

Step 1 — Demands over the opening

$w_u = 1.2(1.0) + 1.6(1.5) = 3.6$ kips/ft. The calculator takes the largest shear and moment at the two ends and the centre of the opening (x = 10 ft ± 7 in.). The shear is greatest at the end nearer the support: $V_u = 54.0 - 3.6(10 - 0.583) = 20.1$ kips. The moment is greatest at the other end: $M_u = 4{,}439$ kip·in (at the centre it is 4,320).

Step 2 — Tees

$t_t = t_b = (21.06 - 10)/2 = 5.53$ in. Each tee: flange $6.555 \times 0.65 = 4.26$ in² plus stem $0.405 \times 4.88 = 1.98$ in², so $A = 6.24$ in², $\bar y = 1.20$ in, $Z_{pl} \approx 6.0$ in³.

$P_y = 50(6.24) = 311.9$ kips; $M_p = 50(6.01) = 300.4$ kip·in; $z = 21.06 - 2(1.20) = 18.66$ in.

Step 3 — Axial force and shear strength

$P = 4{,}439/18.66 = 237.9$ kips, against $\phi_b P_y = 280.7$ kips (85% used). Pure-shear strength of the opening: $V_m(0) = 2 \times 2(300.4)/14 = 85.8$ kips; with P applied, each tee's bending strength is reduced by 85%, so little shear strength remains.

Step 4 — Vierendeel check

$V_i = 20.1/2 = 10.05$ kips per tee; $M_{v,i} = 10.05(14)/2 = 70.4$ kip·in.

$$\frac{237.9}{280.7} + \frac{70.4}{270.4} = 0.848 + 0.260 = 1.108$$

❌ M–V / Vierendeel DCR = 1.108 — over 1.0 (the verdict banner calls this band MARGINAL), so this opening does not pass unreinforced in this position. Other checks: tee web shear 0.19, tee-column buckling 0.85, gross flexure/LTB 0.77, deflection 0.81, all passing.

Step 5 — Options

Move the opening: at x = 15 ft (midspan) the shear over the opening is only 2.1 kips, Mu = 4,860 kip·in and the governing DCR is 0.955 (Vierendeel / M–V). The position sweep finds this as its lowest value, so for this beam and opening midspan is the best location.

Reinforce: with 2 in. × 1/2 in. flat bars on both sides of the web at the top and bottom edges (1/2 in. from the edge), Mpt rises to about 723 kip·in, Py to 412 kips and z becomes 16.9 in. The M–V DCR falls to 0.82 and tee-column buckling to 0.71. The bar area (2.0 in²) is twice the 50% advisory minimum (0.99 in²), and the tee's plastic neutral axis stays inside the flange (0.63 in. against a flange thickness of 0.65 in.), which leaves the advisory flag at 0.97.

✅ With the reinforcement above the governing DCR is 0.816. Try it in the calculator using the Reinforcement inputs.

Circular comparison: a 12 in. circular opening at the same position gives an equivalent rectangle of 12 × 10.8 in. unreinforced (DCR 1.16, fails) and 12 × 5.4 in. reinforced (DCR 0.81).

10. Common Mistakes

⚠
Mistake 1: entering an opening deeper than 0.70d. This is a geometric limit, not a capacity result. Reinforcement does not extend it.
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Mistake 2: placing the opening within one beam depth of a support. The edge-distance check fails automatically. The tool checks both supports.
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Mistake 3: measuring x from the wrong point. Enter x from the support centreline to the opening centre.
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Mistake 4: ignoring the aspect ratio. Ratios ao/ho above about 3 raise Vierendeel demands sharply; consider more rigorous analysis.
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Mistake 5: assuming reinforcement fixes everything. Bars help the tee capacities but not edge distance, overall shear or deflection. Bars that are too wide or thin fail the outstand check.
⚠
Mistake 6: loads in the wrong units. Loads are kips/ft in US mode and kN/m in SI mode. Switching units converts values you have already entered, but check the labels before calculating.
⚠
Mistake: using centreline-to-centreline spacing of the supporting members. Shear and moment depend on where the reaction acts. If it acts at the bolt line, enter the bolt-line spacing as L and measure x from the same point.
⚠
Mistake: ignoring framing-beam reactions on a girder. Use the point-load inputs. Remember that the DG2 limit on how close a point load may be to an opening is not checked here.
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Mistake 7: forgetting self-weight. It is not added automatically. A W21×57 adds 0.057 kips/ft to wD.
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Mistake 8: crediting a sleeve or reinforcement in shear without justification. The “extra tee shear area” input is for engineers who can justify it; the default of 0 is the recommended starting point.

11. Frequently Asked Questions

DG2 limits the opening depth to about 70% of the beam depth. For a W21×57 (d = 21.06 in.) that is 14.7 in. There is no hard limit on length, but ao/ho above about 3 is flagged. The clear distance from the opening edge to each support must be at least d (about 1.75 ft here). Other standards (for example Eurocode-based guidance, which allows deeper circular openings) use different limits; this tool does not.

It depends on the governing check. Near supports the shear is high and the moment low; at midspan the shear is zero and the axial force in the tees is highest. The sensitivity panel sweeps the span in 2.5% steps and reports the lowest DCR it finds and where. Always confirm the edge distance and overall shear for the location it suggests.

When any DCR exceeds 1.0 unreinforced. Bars along the opening edge increase the area, axial force capacity and plastic moment of each tee, which improves M–V interaction and Vierendeel strength. Bars are assumed to be fully developed by their welds; the weld design is not performed here.

Shear cannot flow through the missing web, so it is carried by the two tees acting as a small frame. Each tee, fixed at both ends over the opening length ao, develops end moments of Viao/2. In the worked example each tee carries 9 kips, giving 63 kip·in at each end of each tee. That secondary moment combines with the axial force produced by the overall bending moment.

They are converted to an equivalent rectangle. Unreinforced: ho = Do, ao = 0.9Do. Reinforced: ho = Do and ao = 0.45Do, so the aspect ratio is 0.45. The physical diameter is checked against 0.70d.

Enter the distance between the points where the reactions act. If the reaction acts at the vertical line of bolts, use the bolt-line spacing, which is shorter than the centreline spacing of the supporting members. Measure x from the same left reaction point. The program does not apply a built-in adjustment for the supports.

Yes. Enter up to three point loads (dead and live, with position) in addition to any uniform load. The tool computes shear and moment across the opening, so shear that is constant or changes at a point load is captured. A point load acting within the opening length fails. The DG2 limit on the distance from a point load to the edge of an opening is not implemented, so verify it manually.

Yes, locally. The bars increase the stiffness of each tee, and the added deflection across the opening uses It + Ib including the bars. The overall beam deflection uses the unmodified Ix, since the bars act over a short length.

Only the clear web: tw times (tee depth − flange thickness), with 0.6Fy and φv = 0.90. Reinforcement is not included unless you enter an extra area. DG2 does not give a rule for crediting an HSS sleeve or ring through the web, so any credit is the engineer's judgement.

No. It plots and checks its own M–V envelope derived from a four-hinge mechanism with linear P–M interaction. Results may be more or less conservative than DG2 depending on the case. Use it for screening and verify against DG2.

No. It checks isolated openings. Regularly spaced openings need a web-post buckling and web-post shear check that is not included. See AISC Design Guide 31 or SCI P355 and use dedicated software.

No. It assumes non-composite behaviour. Composite beams with web openings need the composite provisions of DG2.

No. It is a preliminary screening tool. Outputs must be reviewed and validated by the licensed structural engineer of record, who takes responsibility for the design.

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