--------------------- | :-: | :-: | :---------------- | :-----------------------------: | | Moderately Ductile (MD) | 3.0 | 1.3 | Seismic zones 3-5 | 60 m (higher in Vancouver) | | Limited Ductility (LD) | 2.0 | 1.3 | Seismic zones 2-4 | 40 m | | Conventional (no seismic) | 1.0 | 1.0 | Low seismic | No limit |

Ductility-Related Force Modification Factor

Rd accounts for the ability of the frame to dissipate seismic energy through inelastic deformation:

• MD (Rd = 3.0): Braces can undergo compression buckling and tension yielding cycles
• LD (Rd = 2.0): Limited inelastic deformation expected
• Conventional (Rd = 1.0): Elastic response — no ductility relied upon

Brace Member Design

Per CSA S16 Table 27 — Brace Slenderness Limits:

Maximum KL/r

Section Classification

For MD CBF braces, the HSS width-to-thickness limit:

b/t ≤ 145/sqrt(Fy) for HSS in axial compression (Class 1 or 2)

For 350W: b/t ≤ 7.75 (applied to flat width). For HSS 127×127×10: (127 - 4×10)/10 = 8.7. This does NOT satisfy Class 1. Need HSS 127×127×13 (if available) or 350WT with same thickness.

For W-shape braces: b/2tf ≤ 145/sqrt(Fy) (flange Class 1) and h/w ≤ 670/sqrt(Fy) (web Class 1/2 in axial compression).

Capacity Design

Per CSA S16 Clause 27.5.3, the capacity design principle requires:

1. Brace member: Ductile fuse — designed for factored seismic loads
2. Brace connection: Designed for 1.25 × brace factored resistance
3. Beam and column: Design for forces from the expected brace capacity (including overstrength)
4. Gusset plate: Designed for brace capacity with 2tp clearance

Brace Overstrength Factor

Expected brace strength = 1.25 × brace factored resistance (Clause 27.5.3.2)

This accounts for:

• Actual yield strength exceeding minimum specified (typically 15-20% for 350W)
• Strain hardening at large deformations
• Dynamic effects

Horizontal Brace Distribution

Per NBCC 2020 Clause 4.1.8.11, braces must be distributed:

1. Torsional resistance: Braces arranged to resist torsional effects (at least 2 braced bays per line for MD frames)
2. Vertical regularity: No abrupt changes in brace stiffness between storeys
3. Load path: Continuous load path to foundation
4. Diaphragm: Horizontal diaphragms must transfer lateral loads to brace locations

Brace Configuration Types

Worked Example — 4-Storey MD CBF

Given: 4-storey MD braced frame (Rd = 3.0, Ro = 1.3). Storey height = 4.0 m. Bay width = 8.0 m. Total base shear V_base = 1,200 kN (NBCC 2020). Brace angle = 45°.

Step 1 — Brace Force (first storey): Storey shear (first) = 30% of base = 360 kN Brace axial force (two braces, tension/compression): P = 360 / (2 × cos(45°)) = 255 kN Factored brace force from seismic = 255 kN Factored from gravity + seismic combination = 1.0 × D + 1.0 × E = ~400 kN per brace

Step 2 — Brace Selection (MD): KL = 1.0 × 4.0 / cos(45°) = 5.66 m (brace length) For MD: KL/r ≤ 100 → r ≥ 5660/100 = 56.6 mm Try HSS 178×178×8: r = 69.2 mm, A = 5,110 mm^2, b/t flat = (178-32)/8 = 18.3 But Class 1 limit for MD: b/t ≤ 145/sqrt(350) = 7.75. 18.3 > 7.75. NOT OK for MD. Try HSS 178×178×12.7: b/t flat = (178-50.8)/12.7 = 10.0. Still > 7.75. NOT OK.

For MD CBF, HSS 178×178 requires grade 350WT or higher thickness. Alternatively, use a W-shape brace: W310×39 (r_y = 36.7 mm — too low for KL/r = 100). Need W360×51 (W-shape, check flange/web Class 1 limits).

Step 3 — Connection Design: Brace capacity (HSS 178×178×12.7, 350W MD-qualified if Class 1): Cr = 0.90 × 7,910 × 350 × (1 + λ^4.48)^(-0.446) from column check Assume Cr = 1,200 kN (after buckling reduction) Connection design force = 1.25 × 1,200 = 1,500 kN

Gusset plate per gusset plate design: Required Whitmore section: A_g ≥ 1,500 × 1000 / (0.90 × 350) = 4,762 mm^2 L_w = 350 mm (assume), t = 4,762/350 = 13.6 mm → use 16 mm plate.

Step 4 — Beam Design for Chevron Frame: The beam at the chevron apex must resist the unbalanced vertical force from the tension-compression brace pair: P_tension = 1.25 × Cr_tension (yielding tension brace) P_compression = 0.30 × Cr_compression (post-buckling residual capacity, per CSA S16) Unbalanced force = (P_tension - P_compression) × sin(θ) = (1200 - 360) × 0.707 = 594 kN vertical at midspan

The beam must be designed for this unbalanced vertical force plus gravity loads, with continuous lateral bracing at the apex.

Result: MD CBF requires careful section selection to meet Class 1 limits. HSS braces often need 350WT grade or thick walls. Beam at chevron apex must resist unbalanced force per CSA S16 Clause 27.5.5.2.

Detailing Requirements

Per CSA S16 Clause 27.5.4:

1. Gusset plate 2tp clearance: Required between brace end and beam/column face
2. Brace-to-gusset connection: Weld or bolt designed for 1.25 × brace capacity
3. Gusset fold line: Yield line forms at the edge of gusset-to-beam/column weld
4. Stiffeners on beam and column: At gusset connection points, check web yielding and crippling

Frequently Asked Questions

What is the difference between MD and LD braced frames in CSA S16? MD (Rd = 3.0) braces can undergo significant inelastic deformation through cyclic tension yielding and compression buckling. LD (Rd = 2.0) braces are limited in ductility — they rely more on the elastic stiffness of the frame. The key differences: MD has stricter KL/r limits (100 vs 120 for HSS), requires Class 1 sections (vs Class 2 for LD), mandates 2tp gusset clearance, and requires beam design for unbalanced brace forces.

What are the KL/r limits for MD concentrically braced frames? Per CSA S16 Table 27: HSS braces: KL/r ≤ 100. W-shape braces: KL/r ≤ 120. Angle braces: KL/r ≤ 150. These limits ensure the brace is stocky enough to sustain inelastic buckling cycles without fracture. For LD frames: HSS KL/r ≤ 120, W-shape ≤ 150, angle ≤ 200.

How is the beam designed for a chevron braced frame? Per CSA S16 Clause 27.5.5, the beam must resist the unbalanced vertical force from the braces. When one brace is in tension (yielding at 1.25 × capacity) and the other is in compression (post-buckling at ~0.30 × capacity), the vertical component at the midspan connection is: V_unbalanced = (1.25×Cr_tension - 0.30×Cr_compression) × sin(θ). The beam must be laterally braced at the apex and designed for this vertical force plus gravity loads.

When does a brace need to be Class 1 for seismic design? For MD (moderately ductile) braced frames per CSA S16 Clause 27.5.2, the brace must be Class 1 to sustain cyclic inelastic deformations without local buckling. For LD (limited ductility) frames, the brace must be Class 2. For conventional frames (non-seismic), Class 3 is acceptable. The b/t limit for Class 1 is 145/sqrt(Fy). For 350W: this means HSS flat width-to-thickness ≤ 7.75 — requiring heavy wall sections.

Related Pages

• CSA S16 Brace Connection Design
• CSA S16 Gusset Plate Design
• CSA S16 Moment Frame Design
• Canadian Seismic Design
• Canadian HSS Section Properties
• Steel Column Buckling Calculator
• All Canadian References

This page is for educational reference. CBF design per CSA S16:24 Clauses 27.4-27.5 and NBCC 2020. Verify brace ductility category and seismic design requirements with project structural engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.

Design Resources

Calculator tools

• Bolted Connection Calculator
• Weld Capacity Calculator
• End Plate Moment Connection Calculator
• Fin Plate Shear Connection Calculator
• Gusset Plate Calculator

Design guides

• Bolted Connection Worked Example
• Bolted Connection Checklist
• Steel Connection Calculator Guide
• Weld Design Checklist
• EN 1993-1-8 Bolted Connection Worked Example

Reference pages

• CA Shear Tab
• UK Moment Connection