How is the shear capacity of a steel beam web calculated per AISC 360?

The nominal shear strength of an I-shaped member with an unstiffened web is Vn = 0.6 * Fy * Aw * Cv1 per AISC 360-22 Section G2.1. Here Aw = d * tw is the total web area, and Cv1 is the web shear buckling coefficient. For the vast majority of rolled W-shapes at Fy = 50 ksi, Cv1 = 1.0 because h/tw 53.9, Cv1 = 1.10 * sqrt(k_v * E / Fy) / (h/tw) where k_v = 5.34 for unstiffened webs. For a W30x90 with h/tw = 56.7, Cv1 = 1.10 * sqrt(5.34 * 29,000 / 50) / 56.7 = 1.10 * 55.6 / 56.7 = 0.96, and phi_v drops to 0.90. The practical implication: for standard rolled W-shapes, shear rarely governs design. A W21x44 at 30 ft span with 50 psf LL and 65 psf DL at 10 ft spacing produces Vu = w_u * L/2 = 2.28 * 30/2 = 34.2 kip. phi*Vn = 1.0 * 0.6 * 50 * 20.7 * 0.350 = 217 kip. Utilization = 34.2/217 = 15.8%. Shear typically governs only in three scenarios: (a) heavily loaded transfer beams supporting columns, (b) short-span beams with large point loads near supports where M_u is low but V_u is high, and (c) coped beams where the reduced web depth significantly reduces shear capacity. For plate girders with thin webs (h/tw = 100-200), Cv1 drops to 0.22-0.53, and intermediate stiffeners are required to develop tension field action for adequate shear capacity.

What web failure checks are required at concentrated load points?

At every point where a concentrated load is applied to a steel beam (support reactions, column base plates bearing on beams, or point loads from equipment), four distinct web limit states must be checked per AISC 360-22 Section J10. (1) Web local yielding (J10.2): Rn = Fyw * tw * (2.5k + lb) for interior loads or (1.0k + lb) for end reactions, with phi = 1.00. k is the distance from the outer face of the flange to the web toe of the fillet — typically 0.75 to 1.5 inches for W-shapes. lb is the bearing length. (2) Web crippling (J10.3): a buckling failure of the web adjacent to the loaded flange. For interior loads: Rn = 0.80 * tw^2 * [1 + 3*(lb/d)*(tw/tf)^1.5] * sqrt(E * Fyw * tf / tw). For end reactions: Rn = 0.40 * tw^2 * [1 + 3*(lb/d)*(tw/tf)^1.5] * sqrt(E * Fyw * tf / tw). The 0.40 vs 0.80 factor reflects that end reactions are more susceptible because the load is applied at only one side of the web panel. Phi = 0.75. (3) Web sidesway buckling (J10.4): applies when the compression flange is not laterally restrained at the load point and the load is compressive. The web buckles out of plane together with the compression flange. Rn depends on the flange slenderness and the web depth — typically governs for crane runway beams and monorails where the concentrated wheel load is applied to the unbraced compression flange. (4) Web compression buckling (J10.5): applies when a pair of opposing concentrated compressive forces acts on both flanges (e.g., a column bearing on a beam with a stiffener opposite). Rn = (24 * tw^3 * sqrt(E * Fyw)) / h. In practice, web local yielding and web crippling govern 80% of the time for standard building beams. The bearing length lb is the single most effective parameter for increasing all four capacities — doubling lb from 3 to 6 inches roughly doubles the available strength. This is why base plates and bearing plates are typically sized for web bearing rather than for concrete bearing. If any of these checks fail, bearing stiffeners must be provided per AISC 360 J10.8.

How do you design a steel beam web opening for MEP services?

Web openings in steel beams for mechanical, electrical, and plumbing (MEP) services must be carefully sized and located to avoid compromising beam capacity. The fundamental principle: an opening in the web reduces the shear capacity (by removing web area) and creates secondary Vierendeel bending moments in the tee sections above and below the opening. The design procedure per AISC Design Guide 2: (1) Opening location — locate openings in zones of low shear and low moment. The ideal location is near mid-span for simply supported beams (where shear is low) but away from the mid-span where moment is highest. For a uniformly loaded beam, the best location is at the quarter-point (L/4 from support) where both V and M are moderate. Avoid openings within d of supports, within d of concentrated loads, and within 2d of the beam mid-span for long openings. (2) Maximum opening depth — the web opening depth ho should not exceed 0.7d for rectangular openings or 0.8d for circular openings. The remaining tee section depth above and below the opening should be at least 0.15d each. For a W21x44 (d = 20.7 in), the maximum circular opening diameter is 0.8 * 20.7 = 16.6 inches, and the tee depth must be at least 0.15 * 20.7 = 3.1 inches. (3) Opening width — for rectangular openings, the length-to-depth ratio should not exceed 2.5 to avoid excessive Vierendeel bending in the tees. Circular openings naturally avoid the sharp corner stress concentration. (4) Reinforcement — if the opening reduces the beam capacity below the demand at that location, reinforcement plates are welded around the opening. Typically, horizontal reinforcement bars or plates are added above and below the opening to restore the lost flange area, and sometimes vertical stiffeners are added at the sides of rectangular openings. (5) Limit state checks at the opening: (a) Net section flexure at the opening (reduced plastic modulus Z_net), (b) Net section shear (Aw * tw reduced by ho*tw), (c) Vierendeel bending in the tees (M_vierendeel = V * e / 2 * L/ho ratio), and (d) web post buckling between adjacent openings if two or more openings are in close proximity. For circular openings in standard W-shapes with ho/d <= 0.6 and located in the middle third of the span (low shear), reinforcement is often not required because the tee sections can carry the Vierendeel moments.

What is coped beam design and what failure modes apply?

A coped beam has the top (and sometimes bottom) flange cut away at the end to allow the beam to fit between the flanges of the supporting girder or column. Coping is extremely common in steel framing — nearly every beam-to-girder shear connection involves a coped beam. The cope removes flange material, reducing the beam's flexural and shear capacity at the reduced section, and creates a re-entrant corner that concentrates stress. The three primary failure modes for coped beams: (1) Block shear at the coped end — the bolt group in the web shear tab or double angle connection creates a potential block shear failure path that combines tension on the net section and shear on the gross/net area. AISC 360 J4.3: Rn = 0.60 * Fu * Anv + Ubs * Fu * Ant, but not greater than 0.60 * Fy * Agv + Ubs * Fu * Ant. Ubs = 1.0 for uniform tension stress (typical for coped beam connections with a single row of bolts). For a W21x44 coped top and bottom with 2 rows of 3 bolts (3/4 inch diameter), the block shear check typically governs the connection design when the cope is deep and the bolt spacing is tight. (2) Flexural strength at the coped section — the cope removes the flanges, reducing the section to a rectangular web. The plastic section modulus Z_net = tw * (d - c_top - c_bot)^2 / 4. For a coped depth of 2 inches top and bottom: Z_net = 0.350 * (20.7 - 2 - 2)^2 / 4 = 0.350 * 279 / 4 = 24.4 in^3, compared to Z_x = 95.4 in^3 for the full section — a 74% reduction. The flexural capacity at the cope is phi * Fy * Z_net = 0.90 * 50 * 24.4 = 1,098 kip-in = 91.5 kip-ft. (3) Lateral-torsional buckling of the coped region — the cope removes the compression flange, eliminating the lateral restraint at the end of the beam. The unbraced length for LTB is the cope length plus the distance to the first brace point. If the cope is long (c > 2d) and the beam is unbraced, LTB at the cope may govern. The AISC 360 commentary provides guidance for checking LTB at coped ends, but in practice, the cope length is kept short (c <= 2d) and the connection is detailed to provide lateral restraint. The re-entrant corner at the cope termination must have a minimum radius of 1/2 inch per AISC J1.6 to reduce stress concentration. For fatigue-sensitive beams, a drilled hole at the cope termination point is preferred over a simple radius.

When do web stiffeners become required instead of optional?

Web stiffeners transition from optional to mandatory when the unstiffened web fails to meet the capacity requirements for the applied loads. The specific triggers are: (1) Bearing stiffeners (J10.8): required when the concentrated load or reaction exceeds the capacity from any of the web local yielding (J10.2), web crippling (J10.3), web sidesway buckling (J10.4), or web compression buckling (J10.5) checks. This is the most common trigger — perhaps 30-40% of beam reactions require bearing stiffeners, especially for heavy beams or where the bearing length is limited by the support width. (2) Transverse intermediate stiffeners (G2.2): required when the required shear strength Vu exceeds phi_v * 0.6 * Fy * Aw * Cv1 (the unstiffened web shear capacity). Since Cv1 = 1.0 for almost all rolled W-shapes, Vu would need to exceed 0.6 * Fy * Aw for stiffeners to be triggered — this is rare for beams but common for plate girders with thin webs (h/tw > 100). Stiffeners are also required when a/h exceeds 3.0 or 260/(h/tw)^2, whichever is greater — this is a detailing requirement to ensure the aspect ratio of the web panel is not so large that the tension field cannot develop. (3) Longitudinal stiffeners: required when h/tw exceeds 5.70 * sqrt(E/Fy) = 137 for Fy = 50 ksi, per AISC 360 G2.4. This applies only to deep plate girders — the deepest rolled W-shape (W44x335) has h/tw of about 58, well below the limit. (4) Continuity plates at moment connections: required per AISC 358 when the column flange thickness is less than the beam flange thickness plus the weld leg size, or when the column web fails the J10 checks for the beam flange force. (5) Web stiffeners at large concentrated loads: AISC 360 does not explicitly mandate stiffeners at all concentrated loads, but engineering judgment requires them when the load is applied to an unbraced compression flange or when the web depth exceeds 42 inches and the load is significant. In practice, fabricators often request stiffeners at lifting points and temporary support locations even when calculations show they are not required, because the beam is handled in the shop and field without the full bracing assumed in the final condition.

Beam Web Design — Shear, Crippling, Local Yielding & Web Openings

The web of a steel beam resists shear force and transfers concentrated loads to the flanges. Four distinct limit states govern web design: shear yielding, shear buckling, web local yielding under concentrated forces, and web crippling. Failing to check any one of these can result in a beam that passes flexural checks but fails locally at a support or load point.

Shear strength of beam webs

AISC 360-22 Section G2 provides the shear capacity for I-shaped members with unstiffened webs. The nominal shear strength is:

Vn = 0.6 * Fy * Aw * Cv1

Where Aw = d _ tw (total web area), and Cv1 is the web shear buckling coefficient. For most rolled W-shapes with h/tw <= 2.24 _ sqrt(E/Fy), Cv1 = 1.0 and phi_v = 1.00 (no buckling reduction). This threshold equals h/tw <= 53.9 for Fy = 50 ksi steel, which covers nearly every standard rolled W-shape in the AISC Manual.

For slender webs where h/tw exceeds 2.24 * sqrt(E/Fy), Cv1 drops below 1.0 and phi_v reduces to 0.90. This typically only applies to plate girders or very deep built-up sections.

Shear capacity table — common W-shapes (Fy = 50 ksi)

Section	d (in)	tw (in)	h/tw	Cv1	phiVn (kip)	Notes
W12x26	12.2	0.230	47.6	1.00	84.3	Compact web
W14x22	13.7	0.230	54.8	0.99	94.5	Near limit
W16x40	16.0	0.305	47.1	1.00	146	Compact web
W18x35	17.7	0.300	53.5	1.00	159	Compact web
W18x50	18.0	0.355	45.2	1.00	192	Compact web
W21x44	20.7	0.350	53.4	1.00	217	Compact web
W21x62	21.0	0.400	47.3	1.00	252	Compact web
W24x76	23.9	0.440	48.9	1.00	316	Compact web
W24x131	25.4	0.605	37.8	1.00	462	Heavy section
W27x94	26.7	0.490	49.1	1.00	393	Compact web
W30x90	29.5	0.470	56.7	0.96	396	Slightly slender
W33x118	33.3	0.550	54.5	0.99	551	Near limit
W36x135	35.6	0.600	53.4	1.00	641	Compact web

Nearly all standard W-shapes have Cv1 = 1.0 at Fy = 50 ksi, meaning full shear capacity is available without stiffeners.

Cv1 values for non-compact and slender webs (Fy = 50 ksi)

h/tw	Cv1	phi_v	Category
<= 53.9	1.00	1.00	Compact
60	0.94	0.90	Non-compact
80	0.71	0.90	Slender
100	0.53	0.90	Slender
120	0.41	0.90	Very slender
150	0.31	0.90	Plate girder
200	0.22	0.90	Very thin web

For h/tw > 53.9, Cv1 = 1.10 * sqrt(29000/50) / (h/tw). The reduction is significant for thin-web plate girders.

Web local yielding (AISC 360-22 Section J10.2)

When a concentrated force is applied to the flange (from a beam reaction or point load), the web must resist the force over a limited bearing length.

Interior locations (force > d from end):

Rn = Fy * tw * (5k + lb)     phi = 1.00

End locations (force within d of end):

Rn = Fy * tw * (2.5k + lb)   phi = 1.00

Where k = distance from outer face of flange to web toe of fillet, lb = bearing length.

Web local yielding capacity — common sections (Fy = 50 ksi, lb = 0)

Section	tw (in)	k (in)	Rn interior (kip)	Rn end (kip)
W12x26	0.230	0.625	36.1	18.0
W16x40	0.305	0.825	63.1	31.6
W18x50	0.355	0.875	77.5	38.8
W21x62	0.400	1.000	100	50.0
W24x76	0.440	0.980	108	54.0
W24x131	0.605	1.270	192	96.1

Interior capacity is exactly 2x end capacity (5k vs 2.5k). This is why bearing stiffeners are often needed at end reactions but not at interior loads.

Web crippling (AISC 360-22 Section J10.3)

Web crippling is a localized buckling failure of the web directly under a concentrated force. It differs from web local yielding because it involves stability, not material strength.

End location (lb/d <= 0.2, N/d <= 0.2):

Rn = 0.40 * tw^2 * [1 + 3(lb/d)(tw/tf)^1.5] * sqrt(E * Fy * tf/tw)
phi = 0.75

The low phi factor (0.75) reflects the sudden, brittle nature of web crippling failure. When Rn is insufficient, bearing stiffeners must be provided.

Web crippling vs local yielding — which governs?

Section	WLY end (kip)	WC end (kip)	Governs
W12x26	18.0	15.8	Crippling
W16x40	31.6	38.2	Local yielding
W18x50	38.8	46.3	Local yielding
W21x62	50.0	60.2	Local yielding
W24x76	54.0	68.7	Local yielding

For lighter sections with thin webs, crippling governs. For heavier sections, local yielding governs.

Worked example — shear check for W18x50

Given: W18x50, A992 steel (Fy = 50 ksi), Vu = 120 kips.

Step 1: d = 18.0 in, tw = 0.355 in, h/tw = 45.2

Step 2: 2.24 * sqrt(29000/50) = 53.9. Since 45.2 < 53.9, Cv1 = 1.0 and phi_v = 1.00.

Step 3: Vn = 0.6 _ 50 _ (18.0 _ 0.355) _ 1.0 = 191.7 kips

Step 4: phiVn = 1.00 * 191.7 = 191.7 kips > 120 kips OK

Worked example — web crippling at end reaction

Given: W18x50, A992, end reaction Ru = 80 kips, bearing length lb = 4", at end of beam.

Web local yielding: Rn = 50 _ 0.355 _ (2.5 _ 0.875 + 4.0) = 50 _ 0.355 _ 6.188 = 109.8 kips. phiRn = 1.00 _ 109.8 = 109.8 kips > 80 OK.

Web crippling: Rn = 0.40 _ 0.355^2 _ [1 + 3*(4/18)*(0.355/0.570)^1.5] _ sqrt(29000 _ 50 _ 0.570/0.355) = 0.40 _ 0.126 _ 1.079 _ 1524 = 82.7 kips. phiRn = 0.75 * 82.7 = 62.0 kips.

62.0 kips < 80 kips -- WEB CRIPPLING FAILS. Need bearing stiffeners or increase bearing length.

Fix: With lb = 6" (longer bearing plate): Rn = 0.40 _ 0.126 _ [1 + 3*(6/18)*(0.623)^1.5] * 1524 = 92.0 kips. phiRn = 69.0 kips. Still insufficient.

Fix with stiffeners: Add full-depth bearing stiffeners (2 plates, each 3" x 1/4"). Stiffener column check: As = 2 _ 3 _ 0.25 = 1.50 in^2. Effective web strip = 12 _ 0.355 = 4.26 in^2. Total Ae = 5.76 in^2. phiRn = 0.75 _ 50 * 5.76 = 216 kips >> 80 kips. OK.

Bearing stiffeners

When web local yielding or web crippling capacity is exceeded, full-depth bearing stiffeners are welded to the web at the concentrated load point. Per AISC 360-22 Section J10.8, bearing stiffeners are designed as columns using an effective cross-section consisting of the stiffener plates plus a strip of web (25tw for interior stiffeners, 12tw for end stiffeners).

Minimum stiffener width: bst >= bf/3 - tw/2.

Minimum thickness: tst >= bst/(0.56 * sqrt(E/Fy)) to prevent local buckling of the stiffener itself.

Bearing stiffener sizing table (A36, Fy = 36 ksi)

Beam	Min bst (in)	Min tst (in)	Typical Stiffener
W12x26	2.17	0.18	2-1/2" x 1/4"
W16x40	2.33	0.19	2-1/2" x 1/4"
W18x50	2.56	0.21	3" x 1/4"
W21x62	2.58	0.22	3" x 1/4"
W24x76	2.89	0.24	3" x 5/16"

Web openings

Web openings for ductwork and piping are common in floor beams. AISC Design Guide 2 addresses both rectangular and circular openings. Key rules:

Circular openings: diameter <= 0.67d, centered on the neutral axis
Rectangular openings: height <= 0.5d, length <= 3 * opening height
Minimum distance between openings: clear distance >= greater of d or the opening length
Location: openings must be away from high-shear zones (keep opening centerline at least d from supports)
Reinforcement: horizontal plates welded above and below the opening, required when Vierendeel bending at the tee sections exceeds capacity

Maximum web opening sizes for common beams

Section	d (in)	Max Circle Dia (in)	Max Rect Height (in)	Min Clear Between
W16x40	16.0	10.7	8.0	16.0
W18x50	18.0	12.0	9.0	18.0
W21x62	21.0	14.0	10.5	21.0
W24x76	23.9	16.0	12.0	23.9

Reduced shear capacity with circular web openings

A circular opening removes web area and creates stress concentrations. The reduced shear capacity is approximately:

Vn_reduced = Vn * (1 - 1.15 * do/d) for do/d <= 0.5

do/d	Vn_reduced / Vn	Shear Remaining
0.0	1.00	100%
0.2	0.77	77%
0.3	0.66	66%
0.4	0.54	54%
0.5	0.43	43%
0.67	~0.25	25% (max ratio)

A 50%-depth opening retains only 43% of the beam's shear capacity. This is why openings must be placed in low-shear regions (near midspan of simply supported beams).

Sidesway web buckling (Section J10.4)

When a concentrated compression force is applied to one flange and the other flange is not braced laterally, the web can buckle as the compression flange displaces sideways. This is checked per AISC J10.4 and is critical for crane runway beams and beams with hanging loads.

Multi-code comparison

AISC 360-22 uses the Cv1 approach for shear and separate checks for web local yielding (J10.2), web crippling (J10.3), sidesway web buckling (J10.4), and compression buckling of the web (J10.5). Phi factors range from 0.75 to 1.00.

AS 4100-2020 Section 5.11 checks web bearing yield and web bearing buckling as separate limit states. Bearing buckling uses an effective web compression member with phi = 0.90. Bearing yield uses phi = 0.90 and a dispersion length of bbf + 5tf at interior locations. AS 4100 does not distinguish "crippling" from "buckling" the way AISC does.

EN 1993-1-5 Section 6 addresses transverse forces on webs using the resistance to transverse forces method. The effective loaded length is determined from a dispersion model, and the buckling coefficient is calculated from web slenderness. gamma_M1 = 1.00.

Cross-code web local yielding comparison: W18x50 end reaction, lb = 4"

Code	phiRn (kip)	Method
AISC 360	110	Rn = Fytw(2.5k+lb), phi=1.00
AS 4100	~100	Bearing yield, phi=0.90
EN 1993-1-5	~105	Transverse force, gamma_M1=1.00

Common mistakes

Forgetting to check web crippling at beam ends. A beam that passes shear and flexure may fail web crippling at a short bearing seat. Always check J10.2 and J10.3 at every concentrated load point.
Using the wrong k-distance. The k-value in AISC Tables is the distance from the outer face of the flange to the web toe of fillet, not the fillet radius alone.
Placing web openings in high-shear zones. Openings near supports create Vierendeel bending in the tee sections above and below. If the tee cannot resist this moment, the beam fails prematurely.
Undersizing bearing stiffeners. Stiffeners must be checked as compression members (columns) using an effective length of 0.75h. Simply welding thin plates to the web without checking column buckling is a frequent error.
Ignoring web sidesway buckling for crane beams. Concentrated loads on the bottom flange of laterally unbraced beams can cause sidesway web buckling (J10.4), a limit state many engineers overlook.
Not checking web crippling for short bearing lengths. When lb is small (e.g., bearing on a narrow seat angle), web crippling capacity drops significantly. Use a bearing plate to increase lb.

Frequently asked questions

When do I need bearing stiffeners? When the required reaction exceeds phiRn for web local yielding or web crippling. For typical connections, W18 and smaller sections often need stiffeners at end reactions. W21 and larger usually do not.

What is the difference between web crippling and web local yielding? Web local yielding is a material strength limit (phi = 1.00), while web crippling is a stability/buckling limit (phi = 0.75). Crippling is more dangerous because it is sudden and brittle. Both must be checked.

Can I put an opening in a beam web without reinforcing it? Yes, if the opening is small enough (typically do < 0.33d for circular, h < 0.25d for rectangular) and located in a low-shear region. For larger openings, reinforcement is required per AISC Design Guide 2.

Do I need to check shear for every beam? Yes, but for most standard W-shapes at Fy = 50 ksi, shear capacity far exceeds the demand. Shear typically governs only for short, heavily loaded beams or beams with web openings.

What is the h/tw limit for compact webs? h/tw <= 2.24 * sqrt(E/Fy). For Fy = 50 ksi, this is 53.9. Nearly all standard W-shapes meet this limit. Plate girders and very deep built-up sections may not.

How do bearing stiffeners attach to the beam? Full-depth stiffeners are typically fillet-welded to the web on both sides. At the loaded flange, they must have full bearing (milled to fit) or be welded to the flange. At the unloaded flange, they may be fit tight or welded.

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