Beam with web openings

Rectangular or circular openings through the web of a W-shape, steel or composite, unreinforced or with bars along the opening edges, by AISC Design Guide 2 (Darwin, 1990, revised 2003), Chapter 3. The result is the moment and shear strength at each opening, their interaction R, the proportioning rules of the guide, the bar welds, and the range of the span where the opening may sit. Use it for duct and pipe penetrations. The beam away from its openings is a separate calculation (steel beam or composite beam).

Inputs of the beam with web openings #

• Beam: a W-shape and its steel, Fy up to 65 ksi. Construction: steel or composite. On a composite beam the composite expressions apply in positive moment; the steel expressions and the steel resistance factor apply in negative moment (section 3.3).
• Openings: up to 6. Each has its centerline position, length ao, depth ho, and eccentricity e (positive upward, as the guide takes it on composite beams; on steel beams it enters as a size). A circular opening uses ho as its diameter Do, with the equivalent sizes of Eqs. 3-29 and 3-30. N and No count studs on a composite beam: N completely between the high moment end of the opening and the support, No completely over the opening. A stud on the edge of the opening is not counted (section 3.6).
• Required strengths: from the beam and its loads (each ASCE 7-22 combination, at the opening's centerline), or entered at each opening. Under ASD, the guide's section 3.8 multiplies the required strengths by 1.7 and uses the expressions with φ = 1.00. The guide names dead and live load; other load types take the same 1.7 here, which is our reading.
• Reinforcement: openings marked Bars take the bar entered, on one or both sides of the web. Ar counts both bars when on both sides. The bars are taken within the tee, against the opening edge, as Example 2 places them, and at least as strong as the beam.
• Slab and studs: solid slab, or deck with ribs across or along the beam; thicknesses, effective width, f'c. Qn is your value, with the rib reduction, by AISC 360-22 I8.2a. The guide's examples use the 1986 rules (no Rg and Rp as today), and today's rules usually give less per stud. The slab reinforcement ratio and studs per foot near the opening are entered and checked against the guide's values (section 3.7c). An unshored beam is checked as a steel beam under the construction loads entered.
• Stability (steel): the K of the tee as a column, which the guide does not state: 1.0 is prefilled and it is your value. If the compression flange is not braced throughout, enter Lb and Cb.

Auto-design varies the W-shape, lightest first, with optional depth limits, and the steel when unlocked. The openings, their bars, the loads and the studs stay as you entered them.

Checks performed #

The key results also give the range of the span where each opening may sit: R at most 1 and the edge at least d from a support, for that opening's size and its studs as entered. On a composite beam, N changes along the span, so move the opening and re-enter N to confirm the ends of the range.

Limitations #

• W-shapes only: the guide is for compact rolled sections. Its web slenderness rules are applied as written.
• The guide's load and resistance basis is LRFD of 1986; its factors and equations are applied as written, with ASCE 7-22 combinations. Its compact flange and web limits (65/√Fy, 420/√Fy, 520/√Fy) are in ksi as printed.
• The tee column force (the moment over the distance between the tee centroids) and the condition "high moment" for reinforced openings (above 90 % of φMm) are our reading: the guide says the tee must be checked and "only for large openings in regions of high moment", without a number. The stem's local slenderness is noted, not applied.
• Bars on a composite beam's reinforced top tee follow Eqs. 3-14 and 3-20 as written. Bar shear rupture is not computed; the guide says the limit on Pr covers the steel section, and Example 2 checks the bar.
• Deflection with openings, fatigue (section 5.7 advises against openings under significant fatigue loading), and the beam away from the openings are not covered. Bars welded to one side need the bracing note of section 3.7a4.
• Concentrated loads over an opening are not allowed: the expressions assume constant shear through it.

Verification examples #

Verification status: 82 values compared in 13 examples (13 published, 0 hand calculations from the cited equations): 78 within tolerance, 4 recorded deviations. Code basis: the provisions it uses were read in the target edition.

AISC Design Guide 2, Examples 1, 1A, 2, 3 and 4, all parts. The tables and values are on the Verification page, each with its page. Four values are recorded as deviations, each traced to the guide's older shape table, its rounding or its own slips, as below.

• The guide's load factors match today's (1.2 D + 1.6 L; ASD 1.7 on D + L), so every required strength compares directly.
• Shapes: the guide uses the 1986 tables, this calculation the 16th Edition (W24X55 d = 23.57 in. against 23.6 in.).
• Slips in the guide, documented on the Verification page: Example 4's μ of the reinforced top tee is 8.35 on p. 34 and 9.05 on p. 35. The first follows from its own numbers; both give the same Vmt, limited by Eq. 3-21. Example 3 takes Qn as 21.0 and later 21.3 kips.
• R by the guide is read from a chart to two digits; this calculation computes it.
• No published example: circular openings, the section 5.5 equilibrium, the tee column, lateral buckling with reduced J and the spacing rules are by hand from the equations (tests/test_beam_web_opening.py).