Beams of Special Moment Frames: Seismic Reinforcement & Design Requirements

Beams of Special Moment Frames

Contents

1.0General / Scope 2.0Dimensional Limits 3.0Longitudinal Reinforcement 4.0Transverse Reinforcement 5.0Shear Strength 6.0Key Takeaways

1.0

General / Scope

What counts as a "special moment frame beam," and how much geometric freedom the code allows.

• This section governs beams that are part of a special moment frame's seismic-force-resisting system, where the beam's primary job is to resist bending and shear.
• These beams must connect into columns that themselves satisfy the special moment frame column provisions.
• The code assumes a "frame" made of horizontal beams and vertical columns joined at beam-column joints, but allows some flexibility:
  • Beams and columns can be inclined, as long as lateral resistance still comes from moment transfer at the joints rather than from strut/brace action.
  • Beams can be designed for combined moment and axial force when they also serve as diaphragm chords or collectors.
  • A beam is allowed to extend as a cantilever past a column, but that cantilevered length is excluded from the seismic-force-resisting frame itself.
  • A special moment frame beam may connect into a structural wall boundary, provided that boundary element is detailed like a special moment frame column.
• A concrete braced frame — one that relies mainly on axial forces in beams and columns rather than moment transfer — does not qualify as a recognized seismic-force-resisting system under this section.

2.0

Dimensional Limits

Why it matters

For members with a length-to-depth ratio under 4, seismic behavior — especially in shear — departs significantly from the behavior of slender members, so ordinary design rules don't transfer directly. The width limits also control how effectively a beam can deliver force into the beam-column joint.

2.1Beams must satisfy all of the following

• Clear span: the clear span, ℓₙ, must be at least 4 times the effective depth, d — keeps the member "slender enough" for standard seismic design rules to apply.
• Minimum width: the beam width, b_w, must be at least the larger of:
  • 0.3h (30% of overall beam depth), or
  • 10 inches
• Maximum projection beyond the column: where the beam is wider than the column below it, the beam's overhang on each side is capped at the smaller of:
  • c₂ (column dimension transverse to the beam), or
  • 0.7c₁ (70% of the column dimension parallel to the beam)
  This limit exists so the wide beam can still effectively deliver its forces into the confined core of the joint — illustrated in the code's Fig. R18.6.2, which also shows how transverse reinforcement must pass through the column to confine longitudinal bars that fall outside the column core.

Fig. — Maximum effective width of wide beam and required transverse reinforcement.

Figure — General requirement for flexural members of special moment frames. Source: BNBC

3.0

Longitudinal Reinforcement

3.1Continuous bars and reinforcement ratio limits

• At least two continuous bars are required at both the top and bottom faces of the beam, at all sections.
• Minimum reinforcement at any section (top or bottom) must meet the general flexural minimum below:
  • A_s,min is the larger of (a) and (b). For a statically determinate beam with a flange in tension, b_w in these formulas is taken as the smaller of the flange width, b_f, and 2b_w. Also, f_y is capped at a maximum of 80,000 psi for purposes of this calculation (ACI 318).

A_s,min = larger of (a), (b)  ·  f_y ≤ 80,000 psi

(a) 3√f꜀′f_y  b_w × d

(b) 200f_y  b_w × d

• This A_s,min check can be waived at any section where the actual reinforcement provided is at least one-third greater than what analysis requires.
• Maximum reinforcement ratio, ρ:
  • 0.025 for Grade 60 reinforcement
  • 0.02 for Grade 80 reinforcement

Why it matters

These caps exist to preserve ductility and deformation capacity, avoid reinforcement congestion, and indirectly limit shear stresses in beams of typical proportions.

3.2Moment strength distribution along the beam

• Positive moment capacity at the joint face must be at least half of the negative moment capacity at that same face.
• At any section along the beam, both positive and negative moment strength must be at least one-fourth of the maximum moment strength provided at either end (joint face) — ensuring continuous flexural capacity along the beam's length, not just at the ends.

Figure — Flexural requirements for flexural members of special moment frames. Source: BNBC

3.3Lap splices

• Lap splices are only allowed where hoop or spiral reinforcement is provided over the lap length, with transverse spacing enclosing the spliced bars not exceeding the lesser of d/4 or 4 inches.

Prohibited locations

Lap splices are not permitted — because splices are unreliable under cyclic inelastic loading — within:

• a) the beam-column joint
• b) a distance of twice the beam depth from the joint face
• c) twice the beam depth of any critical section where flexural yielding is expected under lateral displacement

Figure — Lap splice requirements for flexural members of special moment frames. Source: BNBC

3.4Mechanical and welded splices

• Mechanical splices must comply with the following Section:
  • Mechanical splices must be either Class G or Class S, with the following restrictions:
  • (a) Splices must be classified as Class G or Class S.
  • (b) Class S mechanical splices are permitted at any location, except as restricted by -. For beam reinforcement specifically, mechanical splices must be Class S and located no closer than h/2 (half the beam depth) from the joint face.
  • (c) Class G mechanical splices in special moment frames are prohibited:
    • Within the beam-column joint itself
    • Within a distance equal to twice the member depth from the column or beam face
    • Within twice the member depth of any critical section where reinforcement yielding is likely under lateral displacement beyond the linear range
  • (d) Class G mechanical splices in special structural walls are prohibited:
    • Anywhere lap splices are already prohibited in boundary regions [according to structural wall provisions by code]
    • Within coupling beams
    • Within twice the member depth of critical sections where yielding is likely under lateral displacement beyond the linear range
• Welded splices must comply with Section.
  • Welded splices are not permitted at all in special moment frames or in special structural walls (including coupling beams).
  • Welding stirrups, ties, inserts, or other similar elements onto longitudinal reinforcement required by design is not permitted.

4.0

Transverse Reinforcement

In a special moment frame, a beam is intended to yield in a controlled, ductile manner during a strong earthquake, rather than fail in shear before its flexural capacity can be developed. This subsection specifies where confinement is required and how conventional detailing governs elsewhere.

4.1Where hoops are required

Two locations within a seismic beam are treated as critical, since flexural yielding is expected to concentrate there under strong ground motion. Both are governed by the same characteristic length, 2h — twice the overall beam depth.

• Zone A — Beam Ends
  • Measured 2h from the face of the supporting column
  • Extends toward the beam midspan
  • Present at both ends of every seismic beam
• Zone B — Plastic Hinge Regions
  • 2h on both sides of any section where yielding is expected
  • May occur away from the column face — for example, beneath heavy concentrated loads
  • Identified from the governing moment diagram rather than assumed by default

Maximum hoop spacing

Within the 2h regions, hoops must be spaced closely enough to confine the concrete core and restrain longitudinal bars against buckling after cover spalling. The limit is the smallest of four values:

Limit	Value	Reasoning
Effective depth ratio	d/4	Ties spacing to member size
Fixed limit	6 in.	Keeps confinement tight regardless of depth
Bar diameter, Grade 60	6·db	Restrains buckling of the smallest primary bar
Bar diameter, Grade 80	5·db	Tighter — higher-strength bars buckle at lower confining demand

where d = effective beam depth, and d_b = diameter of the smallest primary longitudinal flexural bar.

First hoop

The first hoop must be located not more than 2 in. from the face of the supporting column — the reference point from which subsequent spacing is measured.

Fig. — Transverse reinforcement requirements: hoop spacing limits, confinement at both beam ends, and lateral support of longitudinal bars in Section A-A.

4.2Lateral support of longitudinal bars

• Within the hoop regions, every primary top and bottom longitudinal bar must be laterally supported — by a hoop leg or a crosstie — to prevent outward displacement following damage to the surrounding concrete.
• The transverse spacing between adjacent supported bars shall not exceed 14 in.
• Skin reinforcement, along the side faces of the beam, is exempt and does not require lateral support.
• Beams frequently require one or more interior crossties solely to satisfy the 14 in. spacing limit.

4.3Constructing a closed stirrup

A closed stirrup need not be fabricated from a single bent bar. The code permits construction from one or more U-stirrups with 135° seismic hooks, closed by a crosstie — a detailing option that eases field placement in regions of congested longitudinal reinforcement.

• Where consecutive crossties engage the same longitudinal bar, their 90° hooks shall be placed on opposite sides of the beam, distributing the confining force rather than concentrating it on one face.
• Where a slab frames into only one side of the beam, all 90° hooks shall be placed on the slab side, where the slab provides added restraint against outward displacement of the hook.

Fig. — Overlapping hoops and closed-stirrup crosstie detailing, including 6d_b hook extensions and the 14 in. maximum spacing between restrained bars.

4.4Outside the hoop regions

Beyond the 2h zones, the beam is no longer expected to yield, and detailing requirements relax — though they are not eliminated.

• Ordinary stirrups replace seismic hoops throughout the remaining beam length.
• Each stirrup is still required to have 135° seismic hooks at both ends.
• Maximum spacing is limited to d/2 throughout this region.

Why it matters

This provision maintains adequate shear capacity and member integrity without imposing the stringent confinement required in the vicinity of a plastic hinge.

4.5High axial load condition

• If factored axial compressive force exceeds A_gf꜀′/10, hoops meeting the transverse reinforcement requirements for columns of special moment frames are required over the lengths defined in 2h.
• Along the rest of the beam, hoops according to the transverse reinforcement requirements for columns of special moment frames (ACI 318, Section 18.7.5.2) apply, with spacing not exceeding the least of:
  • 6 in.
  • 6d_b (Grade 60)
  • 5d_b (Grade 80) of the smallest enclosed bar
• If concrete cover over the transverse reinforcement exceeds 4 in., additional transverse reinforcement is required with cover ≤ 4 in. and spacing ≤ 12 in.

5.0

Shear Strength

Governing philosophy

Unless a beam's moment capacity is 3–4 times its design moment, engineers should assume it will yield in flexure during a major earthquake — so shear design ties to the beam's actual flexural strength, not just the shear from a lateral-load analysis.

5.1Design shear force, V_e

• V_e is computed by considering the forces on the beam segment between joint faces.
• Moments of opposite sign, both equal to the probable flexural strength (M_pr), are assumed to act at each joint face simultaneously.
• The beam is simultaneously loaded with factored gravity loads and vertical earthquake effects, as generally required by the general building code — e.g., ASCE/SEI 7's 0.2S_DS vertical component.
• M_pr is based on a steel stress of at least 1.25f_y, accounting for strain hardening and the likelihood that actual yield strength exceeds specified yield strength.
• Both directions (clockwise and counterclockwise end moments) must be checked, since the shear diagram — and even the direction of shear — depends on the relative magnitude of gravity load versus end-moment-generated shear.

Fig. — Design shears for beams and columns. Source: ACI 318

5.2Transverse reinforcement for shear (V_c = 0)

• Over the [lengths identified as (a) twice the beam depth measured from the face of the supporting column toward midspan, at both ends of the beam, and (b) twice the beam depth on both sides of a section where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior], transverse reinforcement must be designed assuming the concrete contributes zero shear resistance (V_c = 0) when both of the following are true:
  • The earthquake-induced shear force, calculated according to the design shear force method described in the section above, represents at least half of the maximum required shear strength in that region, and
  • The factored axial compressive force (including earthquake effects) is less than A_gf꜀′/20.

Why it matters

This conservative assumption reflects experimental evidence that cyclic, alternating nonlinear displacements demand more shear reinforcement to still achieve a ductile flexural failure mode, especially with low or no axial load. It doesn't mean the concrete core provides zero shear resistance in reality — the confined core is understood to still contribute — but the design equation intentionally doesn't rely on it where flexural hinging is expected.

6.0

Key Takeaways

• Ductility first. Dimensional limits, reinforcement ratio caps, and confinement requirements all exist to ensure the beam can undergo large inelastic rotations without losing capacity.
• Plastic hinge regions get the strictest treatment. No lap splices, mandatory closed hoops, tight spacing, and a conservative V_c = 0 shear design assumption near the joints and any other yielding sections.
• Capacity design runs throughout. Beam shear demand is derived from the beam's own probable flexural strength (using 1.25f_y), not simply from lateral analysis forces — ensuring shear failure doesn't precede a ductile flexural mechanism.

Reference : ACI 318, BNBC 2020