EBF Link Beam Design — Shear Links, Rotation Limits & Stiffener Requirements

In an eccentrically braced frame (EBF), the link beam is the short segment of the beam between the brace connection point and either the column face or an opposing brace connection. The link is the designated energy-dissipating element — it yields in shear and/or flexure during seismic events while the braces, columns, and beam segments outside the link remain essentially elastic. This makes EBFs uniquely valuable: they combine the high stiffness of braced frames with the ductility of moment frames.

Link classification

The link length e (measured between the ends of the brace connections) determines the yielding mechanism. AISC 341-22 Section F3.5b uses the ratio e to the shear-flexure boundary:

Vp = 0.6 × Fy × (d - 2tf) × tw    (plastic shear capacity)
Mp = Fy × Zx                        (plastic moment capacity)

Short shear links are preferred because they provide the highest ductility (0.08 rad rotation) and the most predictable force distribution. The shear yielding mechanism involves the entire web uniformly, producing excellent energy dissipation. Long flexural links are limited to 0.02 rad — the same as an IMF moment connection — and concentrate damage at the link ends.

Worked example — link design for EBF

Given: EBF with W18x50 beam (A992), link length e = 36 in, story height = 13 ft, story shear Vu = 180 kips (from seismic analysis with R = 8).

Step 1 — Plastic shear and moment: d = 18.0 in, tf = 0.570 in, tw = 0.355 in, Zx = 101 in³. Vp = 0.6 × 50 × (18.0 - 2 × 0.570) × 0.355 = 0.6 × 50 × 16.86 × 0.355 = 179.6 kips Mp = 50 × 101 = 5,050 kip-in = 420.8 kip-ft

Step 2 — Link classification: 1.6 × Mp/Vp = 1.6 × 5050/179.6 = 45.0 in. 2.6 × Mp/Vp = 2.6 × 5050/179.6 = 73.1 in. e = 36 in < 45.0 in — short shear link. Rotation limit = 0.08 rad.

Step 3 — Link shear demand: The link resists the story shear through shear yielding: Vu,link = Vu × (Lbeam / e) × geometry factor. For a typical single-diagonal EBF configuration, the link shear is approximately equal to the story shear (depending on geometry). Vu,link = 180 kips. phi × Vn = 0.90 × 179.6 = 161.6 kips.

180 > 161.6 — link is slightly overloaded. Increase to W18x55 or adjust link length. With W18x55: tw = 0.390 in, Vp = 0.6 × 50 × 16.66 × 0.390 = 195.1 kips. phi × Vn = 175.6 kips — still tight. Try W18x60 or shorten e.

Step 4 — Link rotation check: Link rotation gamma = story drift × (Lbeam / e). For story drift = 2% = 0.02 × 13 × 12 = 3.12 in. Beam length = 25 ft. gamma = 0.02 × (25 × 12 / 36) = 0.02 × 8.33 = 0.167 rad? This is incorrect — the actual relationship depends on the EBF geometry. The correct formula per AISC 341: gamma_link = (story drift / story height) × (Lbeam / e) = (delta_s / h) × (L / e). For delta_s = Cd × delta_e = 4 × (first-order drift). If elastic drift delta_e = 0.40 in: delta_s = 4 × 0.40 = 1.60 in. gamma_link = (1.60 / 156) × (300 / 36) = 0.01026 × 8.33 = 0.085 rad > 0.08 rad limit. Marginally exceeds — increase beam size or shorten e to 30 in.

Link stiffener requirements (AISC 341-22 Section F3.5b)

Short links (e ≤ 1.6 Mp/Vp): Full-depth web stiffeners on both sides of the web at regular intervals:

For W18x50: spacing = 30 × 0.355 - 18.0/5 = 10.65 - 3.60 = 7.05 in. Use 7 in spacing. Stiffener thickness ≥ max(tw, 3/8 in) = 3/8 in. Stiffener width ≥ (bf/2 - tw) = (7.50/2 - 0.355) = 3.39 in. Use 3-1/2 in wide.

Intermediate links: Stiffener spacing transitions between the short-link and long-link requirements by linear interpolation.

Long links (e ≥ 2.6 Mp/Vp): Stiffeners required only at the link ends (at the brace connection points) to prevent web buckling at the plastic hinge locations. No intermediate stiffeners needed.

Capacity design for elements outside the link

Everything outside the link must resist the forces generated when the link reaches its fully strain-hardened capacity. AISC 341-22 Section F3.3 requires:

Design force for brace and beam outside link = 1.25 × Ry × Vn,link    (adjusted for link equilibrium)

For the W18x50 link: 1.25 × 1.1 × 179.6 = 246.9 kips (amplified link shear). The braces and beam segments must resist the moments and axial forces associated with this amplified shear. The 1.25 factor accounts for strain hardening beyond Ry × Fy.

Code comparison

AISC 341-22 Section F3 (USA): Defines short, intermediate, and long links. Link rotation limits: 0.08 rad (short) to 0.02 rad (long). R = 8 for EBF. Stiffener requirements per Section F3.5b. Link-to-column connections require testing per AISC 341 Section K3 or must use a pre-qualified detail. Column links are not permitted.

NZS 3404:1997 Clause 12.11 (New Zealand): Pioneered EBF design in building codes. NZ practice typically uses shear links with e/d ratios of 1.0–1.6. Overstrength factor for link = 1.5 × Vy (higher than AISC's 1.25 × Ry × Vn). NZ requires the link-to-column CJP weld to be a complete penetration butt weld with proven toughness.

EN 1998-1 Section 6.8 (Eurocode 8): EBF design for DCM and DCH ductility classes. Short links e ≤ es = Mp/(Vp) (note: no 1.6 factor — Eurocode's threshold is more conservative). Link rotation capacity: 0.08 rad for short links. Connection overstrength factor gamma_ov = 1.25. Eurocode requires that the link cross-section be Class 1 (fully compact) to develop full plastic resistance.

CSA S16-19 Clause 27.7 (Canada): EBF design similar to AISC 341. Link rotation limits match AISC. Overstrength factor = 1.30 × Ry × Vy (slightly higher multiplier). CSA uses Rd = 4.0 and Ro = 1.5 for ductile EBF.

Common mistakes engineers make

1. Choosing a long flexural link instead of a short shear link. Long links seem simpler (no intermediate stiffeners), but their 0.02 rad rotation limit means the EBF provides only moderate ductility — equivalent to an IMF, not an SMF. The full R = 8 benefit of EBF requires short shear links.

2. Undersizing web stiffeners in shear links. Shear links develop very high web shear strains (up to 8% shear angle). Without properly sized and spaced stiffeners, the web buckles and the link loses strength before reaching the expected rotation. Stiffeners must be full-depth, on both sides, and fillet-welded to both flanges.

3. Not checking link rotation from amplified drift. The link rotation is much larger than the story drift ratio because the link concentrates the entire bay's inelastic deformation into a short segment. A 2% story drift with a 25 ft bay and a 36 in link produces a link rotation of approximately 0.08 rad — right at the limit. Small drift increases push it over.

4. Using link-to-column connections without testing qualification. AISC 341-22 Section F3.6c requires that link-to-column connections be demonstrated by testing to achieve the required rotation capacity, similar to SMF moment connections. Standard welded flange connections are not pre-qualified for link-to-column use.

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Related references

• Beam Sizes
• Beam Formulas
• How to Verify Calculations
• SCBF brace design
• seismic force-resisting systems
• gusset plate connection
• steel beam capacity calculator
• Seismic Detailing

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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.