How are EBF links classified as shear, intermediate, or flexural per AISC 341?

AISC 341-22 Section F3.5b classifies EBF links by length e (distance between brace connection points) relative to the shear-flexure boundary ratios. First compute the plastic shear capacity Vp = 0.6 × Fy × (d − 2tf) × tw (the web's full shear yield capacity) and plastic moment Mp = Fy × Zx. Then classify: Short (shear) link when e ≤ 1.6 × Mp/Vp — yielding is pure shear across the full web, rotation capacity 0.08 rad, the most ductile and preferred type. Intermediate link when 1.6×Mp/Vp < e < 2.6×Mp/Vp — combined shear + flexural yielding, rotation capacity linearly interpolated between 0.08 and 0.02 rad. Long (flexural) link when e ≥ 2.6×Mp/Vp — flexural hinging at the link ends (similar to a moment frame beam plastic hinge with an added shear demand), rotation capacity 0.02 rad, least ductile. Worked example: W18×50 (d=18.0", tf=0.570", tw=0.355", Zx=101 in³), Fy=50 ksi. 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. 1.6×Mp/Vp = 1.6×5050/179.6 = 45.0". 2.6×Mp/Vp = 73.1". If e = 36" 73.1) → long flexural link. Short shear links are strongly preferred because: (a) the web yields uniformly, distributing damage across the entire web for superior energy dissipation, (b) the 0.08 rad rotation is 4× the IMF limit, and (c) the link shear is the controlling quantity for capacity design of surrounding elements, making brace force prediction more reliable.

What stiffener spacing is required for EBF link beams per AISC 341?

AISC 341-22 Section F3.5b(4) requires full-depth web stiffeners on both sides of the web for all link types, with spacing dependent on link classification and rotation demand. For short shear links (e ≤ 1.6Mp/Vp) at the maximum rotation γ ≤ 0.08 rad: stiffener spacing s ≤ 30×tw − d/5. For W18×50 (tw=0.355", d=18.0"): s = 30×0.355 − 18.0/5 = 10.65 − 3.60 = 7.05", use 7" maximum. For short links with γ ≤ 0.02 rad (less demand): s ≤ 52×tw − d/5 = 52×0.355 − 3.60 = 18.46 − 3.60 = 14.86", use 14" max. For intermediate links: interpolate linearly between the short-link (0.08 rad) and long-link (0.02 rad) stiffener requirements. For long flexural links (e ≥ 2.6Mp/Vp): stiffeners required only at the link ends (at brace connection points), with a maximum spacing of 1.5×bf measured from each end — no intermediate stiffeners needed since the link yields in flexure, not shear. Stiffener geometry per AISC 341 F3.5b(4)(ii): thickness t_st ≥ max(tw, 3/8"); width w_st ≥ bf/2 − tw (for one-sided stiffeners) or ≥ bf/2 − tw for pairs; fillet welds to the web sized to transfer the stiffener force (typically matching the stiffener thickness). For W18×50: t_st ≥ max(0.355, 0.375) = 0.375" (3/8"); w_st ≥ 7.50/2 − 0.355 = 3.40" → use 3-1/2". Stiffeners must extend the full depth from flange to flange and be welded to both flanges and the web — CJP or fillet per design. The stiffener-to-flange welds transfer the stiffener force into the flanges to restrain web buckling, so full weld development is required.

How does capacity design work for elements outside the EBF link?

Capacity design ensures that all elements outside the designated yielding link remain elastic when the link reaches its fully strain-hardened capacity. Per AISC 341-22 Section F3.3, braces, beam segments outside the link, and columns must be designed for the amplified forces: the link nominal shear strength Vn is amplified by the overstrength factor Ry (ratio of expected to specified yield stress) and a strain-hardening factor of 1.25. Design link shear V_design = 1.25 × Ry × Vn. For A992 steel (Ry = 1.1) and W18×50 link (Vn = 179.6 kips): V_design = 1.25 × 1.1 × 179.6 = 246.9 kips — a 38% amplification above the plastic shear capacity. The brace axial force is derived from link equilibrium: for a single-diagonal EBF where the brace connects at one end of the link with angle α between brace and beam: P_brace = V_design × (L_beam / e) × (1/sin α). For a 25 ft beam with 36" link at α = 45°: P_brace = 246.9 × (300/36) × (1/0.707) = 246.9 × 8.33 × 1.414 = 2,908 kips — this is a massive brace force requiring a heavy brace section (W14×233 or larger). The beam segment outside the link must resist the link end moment M = V_design × e/2 plus axial force from the brace horizontal component. For the same link: M = 246.9 × 36/2 = 4,444 kip-in = 370 kip-ft. The beam must pass P-M interaction at this combined loading. The column at the EBF junction must resist the brace's vertical and horizontal components plus gravity loads — the seismic force often dominates the column size. This capacity design chain (link → brace → beam → column → connection) ensures that yielding is isolated to the link, which is detailed for the required rotation capacity.

How does link rotation relate to story drift in EBF design?

The link rotation γ is NOT equal to the story drift ratio — it's amplified by the ratio of beam length to link length, a geometric multiplier that can be 6-10×. The analytical relationship per AISC 341 Commentary F3: γ = (Δ_e × Cd / h) × (L / e) where Δ_e is the elastic story drift under design seismic forces, Cd is the deflection amplification factor (Cd = 4 for EBF per ASCE 7 Table 12.2-1), h is story height, L is beam length, and e is link length. For a 13 ft story with Δ_e = 0.40" (from elastic analysis), Cd = 4, L = 25 ft, e = 36": γ = (0.40 × 4 / 156") × (300/36) = (1.60/156) × 8.33 = 0.0103 × 8.33 = 0.085 rad. This exceeds the 0.08 rad shear link limit — the link length must be increased or the beam length decreased. Shortening e to 30": γ = 0.0103 × (300/30) = 0.0103 × 10 = 0.103 rad — worse! Lengthening e to 42": γ = 0.0103 × (300/42) = 0.0103 × 7.14 = 0.074 rad ≤ 0.08 — OK. Counterintuitively, a LONGER link reduces rotation (lower geometric multiplier) but may change the link classification to intermediate or flexural (lower rotation capacity). The optimum link: as long as possible while staying below the shear link boundary (e ≤ 1.6Mp/Vp), giving the best combination of shear yielding mechanism and low geometric amplification. For the W18×50 example, the optimum e = 42" (still shear, since 42 < 45), with γ = 0.074 rad < 0.08 rad limit.

What are the advantages and disadvantages of EBF vs SCBF and SMF?

Eccentrically braced frames (EBF) combine features of concentrically braced frames (SCBF, high elastic stiffness) and moment frames (SMF, high ductility). Advantages over SCBF: (1) Architectural flexibility — the link provides a zone where braces can meet the beam away from the beam-column intersection, allowing doorways and corridors to pass through the braced bay (the braces connect to the beam away from the column). SCBF braces must meet at the beam-column work point, blocking the braced bay. (2) Energy dissipation through shear yielding in the link web is more stable and repeatable than brace buckling in SCBF — link yielding doesn't degrade in successive cycles the way a buckled brace does. (3) Drift control — EBF is stiffer than SMF at equivalent strength, reducing drift and nonstructural damage. Disadvantages vs SCBF: (a) More steel tonnage — the beam must be substantially heavier to serve as the link (W18×50+ for the link vs W12× column for SCBF brace), and the beam outside the link is heavier to resist capacity-design forces. (b) Link replacement after a major earthquake is difficult (the link is an integral part of the floor beam, unlike a brace which can be unbolted and replaced). (c) Complex capacity design chain requires careful engineering — more design hours than SCBF or SMF. EBF R = 8 (same as SMF), SCBF R = 6 — meaning EBF reduces seismic forces by 25% vs SCBF for the same building. EBF is the system of choice for: 6-20 story buildings where architectural openness competes with SCBF brace congestion; buildings with stiff drift requirements; and regions where SCBF brace fracture concerns (from full-scale testing) favor shear-yielding EBF links.

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

Q: What stiffener spacing is required for EBF link beams per AISC 341?

AISC 341-22 Section F3.5b(4) requires full-depth web stiffeners on both sides of the web for all link types, with spacing dependent on link classification and rotation demand. For short shear links (e ≤ 1.6Mp/Vp) at the maximum rotation γ ≤ 0.08 rad: stiffener spacing s ≤ 30×tw − d/5. For W18×50 (tw=0.355", d=18.0"): s = 30×0.355 − 18.0/5 = 10.65 − 3.60 = 7.05", use 7" maximum. For short links with γ ≤ 0.02 rad (less demand): s ≤ 52×tw − d/5 = 52×0.355 − 3.60 = 18.46 − 3.60 = 14.86", use 14" max. For intermediate links: interpolate linearly between the short-link (0.08 rad) and long-link (0.02 rad) stiffener requirements. For long flexural links (e ≥ 2.6Mp/Vp): stiffeners required only at the link ends (at brace connection points), with a maximum spacing of 1.5×bf measured from each end — no intermediate stiffeners needed since the link yields in flexure, not shear. Stiffener geometry per AISC 341 F3.5b(4)(ii): thickness t_st ≥ max(tw, 3/8"); width w_st ≥ bf/2 − tw (for one-sided stiffeners) or ≥ bf/2 − tw for pairs; fillet welds to the web sized to transfer the stiffener force (typically matching the stiffener thickness). For W18×50: t_st ≥ max(0.355, 0.375) = 0.375" (3/8"); w_st ≥ 7.50/2 − 0.355 = 3.40" → use 3-1/2". Stiffeners must extend the full depth from flange to flange and be welded to both flanges and the web — CJP or fillet per design. The stiffener-to-flange welds transfer the stiffener force into the flanges to restrain web buckling, so full weld development is required.

Q: How does capacity design work for elements outside the EBF link?

Capacity design ensures that all elements outside the designated yielding link remain elastic when the link reaches its fully strain-hardened capacity. Per AISC 341-22 Section F3.3, braces, beam segments outside the link, and columns must be designed for the amplified forces: the link nominal shear strength Vn is amplified by the overstrength factor Ry (ratio of expected to specified yield stress) and a strain-hardening factor of 1.25. Design link shear V_design = 1.25 × Ry × Vn. For A992 steel (Ry = 1.1) and W18×50 link (Vn = 179.6 kips): V_design = 1.25 × 1.1 × 179.6 = 246.9 kips — a 38% amplification above the plastic shear capacity. The brace axial force is derived from link equilibrium: for a single-diagonal EBF where the brace connects at one end of the link with angle α between brace and beam: P_brace = V_design × (L_beam / e) × (1/sin α). For a 25 ft beam with 36" link at α = 45°: P_brace = 246.9 × (300/36) × (1/0.707) = 246.9 × 8.33 × 1.414 = 2,908 kips — this is a massive brace force requiring a heavy brace section (W14×233 or larger). The beam segment outside the link must resist the link end moment M = V_design × e/2 plus axial force from the brace horizontal component. For the same link: M = 246.9 × 36/2 = 4,444 kip-in = 370 kip-ft. The beam must pass P-M interaction at this combined loading. The column at the EBF junction must resist the brace's vertical and horizontal components plus gravity loads — the seismic force often dominates the column size. This capacity design chain (link → brace → beam → column → connection) ensures that yielding is isolated to the link, which is detailed for the required rotation capacity.

Q: How does link rotation relate to story drift in EBF design?

The link rotation γ is NOT equal to the story drift ratio — it's amplified by the ratio of beam length to link length, a geometric multiplier that can be 6-10×. The analytical relationship per AISC 341 Commentary F3: γ = (Δ_e × Cd / h) × (L / e) where Δ_e is the elastic story drift under design seismic forces, Cd is the deflection amplification factor (Cd = 4 for EBF per ASCE 7 Table 12.2-1), h is story height, L is beam length, and e is link length. For a 13 ft story with Δ_e = 0.40" (from elastic analysis), Cd = 4, L = 25 ft, e = 36": γ = (0.40 × 4 / 156") × (300/36) = (1.60/156) × 8.33 = 0.0103 × 8.33 = 0.085 rad. This exceeds the 0.08 rad shear link limit — the link length must be increased or the beam length decreased. Shortening e to 30": γ = 0.0103 × (300/30) = 0.0103 × 10 = 0.103 rad — worse! Lengthening e to 42": γ = 0.0103 × (300/42) = 0.0103 × 7.14 = 0.074 rad ≤ 0.08 — OK. Counterintuitively, a LONGER link reduces rotation (lower geometric multiplier) but may change the link classification to intermediate or flexural (lower rotation capacity). The optimum link: as long as possible while staying below the shear link boundary (e ≤ 1.6Mp/Vp), giving the best combination of shear yielding mechanism and low geometric amplification. For the W18×50 example, the optimum e = 42" (still shear, since 42 < 45), with γ = 0.074 rad < 0.08 rad limit.

Q: What are the advantages and disadvantages of EBF vs SCBF and SMF?

Eccentrically braced frames (EBF) combine features of concentrically braced frames (SCBF, high elastic stiffness) and moment frames (SMF, high ductility). Advantages over SCBF: (1) Architectural flexibility — the link provides a zone where braces can meet the beam away from the beam-column intersection, allowing doorways and corridors to pass through the braced bay (the braces connect to the beam away from the column). SCBF braces must meet at the beam-column work point, blocking the braced bay. (2) Energy dissipation through shear yielding in the link web is more stable and repeatable than brace buckling in SCBF — link yielding doesn't degrade in successive cycles the way a buckled brace does. (3) Drift control — EBF is stiffer than SMF at equivalent strength, reducing drift and nonstructural damage. Disadvantages vs SCBF: (a) More steel tonnage — the beam must be substantially heavier to serve as the link (W18×50+ for the link vs W12× column for SCBF brace), and the beam outside the link is heavier to resist capacity-design forces. (b) Link replacement after a major earthquake is difficult (the link is an integral part of the floor beam, unlike a brace which can be unbolted and replaced). (c) Complex capacity design chain requires careful engineering — more design hours than SCBF or SMF. EBF R = 8 (same as SMF), SCBF R = 6 — meaning EBF reduces seismic forces by 25% vs SCBF for the same building. EBF is the system of choice for: 6-20 story buildings where architectural openness competes with SCBF brace congestion; buildings with stiff drift requirements; and regions where SCBF brace fracture concerns (from full-scale testing) favor shear-yielding EBF links.

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)

| Link type — Length criterion — Yielding mode — Rotation limit | | --------------- — ------------------------- — ------------------------ — -------------------- | | Short (shear) — e ≤ 1.6 Mp/Vp — Pure shear yielding — 0.08 rad | | Intermediate — 1.6 Mp/Vp < e < 2.6 Mp/Vp — Combined shear + flexure — Linear interpolation | | Long (flexural) — e ≥ 2.6 Mp/Vp — Flexural hinging at ends — 0.02 rad |

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:

| Link rotation — Maximum stiffener spacing | | ---------------- — ------------------------- | | gamma ≤ 0.08 rad — 30tw - d/5 |

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

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.
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.
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.
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.

Link beam classification detail (AISC 341-22 Section F3.4)

The link beam is the fuse element in an eccentrically braced frame (EBF). Its behavior is controlled by the ratio of the link length e to the plastic shear and moment capacities. Understanding the three classification types is essential for proper EBF design.

Short links (e <= 1.6 Mp/Vp)

Short links yield primarily in shear. The entire web engages in uniform shear yielding, producing a stable hysteretic response with excellent energy dissipation. The rotation capacity of 0.08 rad is the highest of any steel seismic fuse element, exceeding even SMF beam plastic hinges (0.04 rad). The uniform shear strain distribution means that the web yields along its full length, maximizing the plastic energy dissipation volume.

Design shear strength: phi × Vn = phi × Vp = 0.90 × 0.6 × Fy × (d - 2tf) × tw

The 0.90 resistance factor for shear yielding is appropriate because the shear yield strength (0.6Fy) is well-characterized and the web is a compact element in W-shapes.

Intermediate links (1.6 Mp/Vp < e < 2.6 Mp/Vp)

Intermediate links experience combined shear and flexural yielding. The rotation limit varies linearly between 0.08 rad (at e = 1.6 Mp/Vp) and 0.02 rad (at e = 2.6 Mp/Vp). This interpolation accounts for the gradual transition from shear-dominated to flexure-dominated behavior.

Interpolated rotation limit: gamma_limit = 0.02 + (0.08 - 0.02) × (2.6Mp/Vp - e) / (2.6Mp/Vp - 1.6Mp/Vp)

Intermediate links require careful detailing because the yielding mechanism is less predictable than for short or long links. The designer cannot assume pure shear or pure flexure behavior.

Long links (e >= 2.6 Mp/Vp)

Long links yield primarily in flexure, with plastic hinges forming at each end of the link. The rotation capacity is limited to 0.02 rad — the same as an IMF moment connection. The energy dissipation is concentrated at two discrete hinge locations rather than distributed along the link length.

Design moment strength: phi × Mn = phi × Mp = 0.90 × Fy × Zx

Long links are generally avoided in high-seismic regions because they provide limited ductility compared to short links. They may be used in low-seismic regions or when architectural constraints prevent a shorter link.

Link rotation angle requirements

The link rotation angle gamma is not the same as the story drift ratio. The relationship depends on the EBF geometry:

gamma_link = (delta_story / h_story) × (L_beam / e_link)

This amplification factor (L_beam / e_link) is the fundamental reason why link rotations are much larger than story drifts. For a typical EBF with L_beam = 30 ft and e_link = 3 ft, a 2% story drift produces:

gamma = 0.02 × (30 × 12) / (3 × 12) = 0.02 × 10 = 0.20 rad

This exceeds the 0.08 rad limit for short links, which is why EBF link lengths must be carefully selected to keep link rotations within the allowable range. In practice, link lengths are often 3-5 ft for typical bay widths of 25-35 ft.

Link stiffener spacing rules

AISC 341-22 Section F3.5b prescribes stiffener requirements based on link type and rotation demand:

Link Type	Stiffener Spacing	Stiffener Location
Short (gamma <= 0.08 rad)	<= 30tw - d/5	Both sides of web, full depth
Intermediate	Linear interpolation between short and long	Both sides
Long (gamma <= 0.02 rad)	At link ends only	At brace connection points

Minimum stiffener dimensions:

Stiffener thickness: >= max(tw, 3/8 in)
Stiffener width: >= (bf/2 - tw)
Stiffener must be fillet-welded to both flanges (minimum 2-filet weld)
For short links, stiffeners are required on both sides of the web

Stiffener purpose: Full-depth web stiffeners prevent the web from buckling at high shear strains. Without properly sized stiffeners, the web buckles locally, creating a pinched hysteretic loop and drastically reducing energy dissipation capacity. Testing has shown that unstiffened short links lose up to 40% of their strength by the second loading cycle.

Link-to-column connection requirements

Link-to-column connections are subject to the most stringent requirements in EBF design because they combine high shear, axial force, and moment in a compact region. AISC 341-22 Section F3.6c requires one of the following:

Prequalification by testing: The connection must have been demonstrated through cyclic testing to achieve the required link rotation without fracture. This follows the same protocol as AISC 341 Section K3 for moment connections (a minimum of 4% story drift for SMF-equivalent performance).
Use of verified connection types: Currently, AISC 358 does not include prequalified EBF link-to-column connections. The designer must rely on published test data or project-specific testing.
Link configuration that avoids column connections: Where possible, the link is positioned between two braces (split-link or V-brace configuration) so that neither end of the link frames into a column. This avoids the link-to-column connection issue entirely.

Link overstrength factor:

All elements outside the link (braces, beam segments, columns, and connections) must be designed for the amplified forces corresponding to the fully strain-hardened link:

Design force = 1.25 × Ry × Vn_link    (for shear links)

The factor 1.25 accounts for strain hardening beyond the expected yield stress (Ry × Fy). For A992 steel, Ry = 1.1, so the total amplification is 1.25 × 1.1 = 1.375 — meaning the braces and beam outside the link must resist 137.5% of the link's nominal shear capacity. This capacity design approach ensures that inelastic action is confined to the link, and all other elements remain elastic.

Worked example: EBF link beam design (short shear link)

Given: EBF bay with W21x57 beam (A992), story height = 14 ft, bay length L = 30 ft. Link length e = 42 in (3.5 ft). Seismic story shear Vu = 200 kips. Expected story drift ratio = 1.8%.

Step 1 — Section properties: W21x57: d = 21.1 in, tw = 0.405 in, tf = 0.650 in, Zx = 129 in³, bf = 6.56 in.

Step 2 — Plastic capacities: Vp = 0.6 × 50 × (21.1 - 2 × 0.650) × 0.405 = 0.6 × 50 × 19.8 × 0.405 = 240.6 kips Mp = 50 × 129 = 6,450 kip-in = 537.5 kip-ft

Step 3 — Classification: 1.6 × Mp/Vp = 1.6 × 6450/240.6 = 42.9 in. 2.6 × Mp/Vp = 2.6 × 6450/240.6 = 69.7 in. e = 42 in < 42.9 in — short shear link (just barely). gamma_limit = 0.08 rad.

Step 4 — Shear capacity check: phi × Vn = 0.90 × 240.6 = 216.5 kips > 200 kips (OK, 92% utilization).

Step 5 — Link rotation check: gamma_link = 0.018 × (30 × 12) / 42 = 0.018 × 8.57 = 0.154 rad. 0.154 > 0.08 rad limit — FAILS. The link is too short for this bay length at this drift level.

Step 6 — Adjust: Increase link length to 60 in (5 ft): Reclassify: e = 60 in > 42.9 in and < 69.7 in — **intermediate link**. gamma_limit = 0.02 + 0.06 × (69.7 - 60) / (69.7 - 42.9) = 0.02 + 0.06 × 9.7/26.8 = 0.02 + 0.0217 = 0.042 rad. gamma_link = 0.018 × 360/60 = 0.108 rad > 0.042 rad — still FAILS.

Step 7 — Final adjustment: Increase to W21x68 (thicker web): W21x68: d = 21.3, tw = 0.430, tf = 0.685, Zx = 153. Vp = 0.6 × 50 × (21.3 - 1.37) × 0.430 = 0.6 × 50 × 19.93 × 0.430 = 257.1 kips. 1.6Mp/Vp = 1.6 × (50 × 153) / 257.1 = 47.7 in. e = 60 in is intermediate. gamma_limit = 0.02 + 0.06 × (77.6 - 60) / (77.6 - 47.7) = 0.02 + 0.06 × 17.6/29.9 = 0.055 rad. gamma_link = 0.018 × 360/60 = 0.108 rad — still over limit. Need to reduce drift (stiffer structure) or use a split-link configuration.

This example illustrates a common EBF design challenge: for moderate seismic drifts and typical bay widths, achieving the link rotation limit can be difficult. The solution often involves a stiffer lateral system (reducing story drift), a longer link, or a split-link configuration that halves the amplification factor.

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Beam Design Methods

Lateral-Torsional Buckling

For beams that are not adequately braced against lateral movement and twist, the nominal moment capacity is governed by lateral-torsional buckling (LTB). The resistance depends on the unbraced length (Lb) relative to limit states:

Plastic hinge (Lb ≤ Lp): The full plastic moment can be developed
Inelastic LTB (Lp < Lb ≤ Lr): Reduced capacity based on linear interpolation
Elastic LTB (Lb > Lr): Capacity governed by elastic buckling

Shear Design

Web shear strength depends on the panel aspect ratio and stiffener configuration. For unstiffened webs, the nominal shear capacity is:

AISC: Vn = 0.60FyAwCv (Cv = web shear coefficient)
EN 1993: Vb,Rd = Vbw,Rd + Vbf,Rd (for stiffened panels with tension field action)

Compact sections with low web slenderness (h/tw) can develop full shear yielding. Slender webs may require transverse stiffeners to develop adequate shear capacity.

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Frequently Asked Questions

What is the recommended design procedure for this structural element?

The standard design procedure follows: (1) establish design criteria including applicable code, material grade, and loading; (2) determine loads and applicable load combinations; (3) analyze the structure for internal forces; (4) check member strength for all applicable limit states; (5) verify serviceability requirements; and (6) detail connections. Computer analysis is recommended for complex structures, but hand calculations should be used for verification of critical elements.

How do different design codes compare for this calculation?

AISC 360 (US), EN 1993 (Eurocode), AS 4100 (Australia), and CSA S16 (Canada) follow similar limit states design philosophy but differ in specific resistance factors, slenderness limits, and partial safety factors. Generally, EN 1993 uses partial factors on both load and resistance sides (γM0 = 1.0, γM1 = 1.0, γM2 = 1.25), while AISC 360 uses a single resistance factor (φ). Engineers should verify which code is adopted in their jurisdiction.

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