Block Shear Failure — Tension + Shear Tear-Out Path
Block shear failure is a limit state in bolted steel connections where a block of material — typically rectangular or U-shaped — tears out from the connected member through a combination of tension fracture on one face and shear yielding or fracture on parallel faces. It is the governing limit state for many short, wide bolted connections and must be checked alongside net section tension rupture and bolt bearing.
Failure surface:
┌────────────────────────────┐
│ Shear plane (Agv, Anv) │ ← bolt holes along this line
│ █████████████████████████ │
├────────────────────────────┤
│ Tension plane (Ant) │ ← material fractures here
│ █████████████████████████ │
└────────────────────────────┘
(Block tears out in direction of load →)
PRELIMINARY — NOT FOR CONSTRUCTION. All content is for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.
The Failure Mechanism in Detail
Block shear is fundamentally a combined stress failure — neither pure shear nor pure tension alone governs. The failure path consists of:
- Shear face(s): One or two planes parallel to the applied load, passing through the bolt holes along the bolt lines. These faces resist shear.
- Tension face: One plane perpendicular to the applied load, at the end of the bolt group. This face resists tension.
The block separates from the member when the combined shear resistance on the parallel planes plus the tension resistance on the perpendicular plane is exceeded. The controlling mechanism is the smaller of:
- Shear fracture on net shear area + tension fracture on net tension area
- Shear yielding on gross shear area + tension fracture on net tension area
Why Two Mechanisms?
Shear yielding (0.6×Fy×Agv) represents the maximum force the gross cross-section can carry before the entire length yields in shear. Once the gross section yields, load cannot be redistributed to the remaining material — so even if the net-section fracture calculation suggests higher capacity, the yielding upper bound caps it.
AISC 360-22 J4.3 — Complete Formula with Derivation
The nominal block shear strength:
Rn = 0.60 × Fu × Anv + Ubs × Fu × Ant ≤ 0.60 × Fy × Agv + Ubs × Fu × Ant
Where:
| Symbol | Meaning | Units |
|---|---|---|
| Fu | Specified minimum tensile strength | ksi |
| Fy | Specified minimum yield stress | ksi |
| Anv | Net area subject to shear | in² |
| Agv | Gross area subject to shear | in² |
| Ant | Net area subject to tension | in² |
| Ubs | Non-uniform stress factor (0.5 or 1.0) | — |
| φ | Resistance factor = 0.75 (LRFD) | — |
Term 1 — 0.60×Fu×Anv: Shear fracture on the net shear area. The 0.60 converts tensile strength Fu to shear strength per von Mises criterion (τ = F/√3 ≈ 0.577F, rounded to 0.60).
Term 2 — Ubs×Fu×Ant: Tension fracture on the net tension area, modified by Ubs to account for uneven stress distribution.
Upper bound — 0.60×Fy×Agv: Limits total capacity to gross-section shear yielding plus tension fracture. This prevents the formula from predicting a capacity higher than what the gross section can deliver before the entire shear plane yields.
Design Strength (LRFD and ASD)
LRFD: φ × Rn = 0.75 × Rn
ASD: Rn / Ω = Rn / 2.00
Area Calculations
Gross Shear Area Agv
Agv = n_planes × (Le + s × (n_bolts_per_plane − 1)) × t
where:
n_planes = number of parallel shear failure planes (typically 1 or 2)
Le = edge distance from center of outermost bolt to plate edge (in)
s = bolt spacing center-to-center along shear plane (in)
n_bolts_per_plane = number of bolts along one shear plane
t = plate thickness (in)
Net Shear Area Anv
Anv = Agv − n_planes × n_bolts_per_plane × (dh + 1/16") × t
where:
dh = nominal bolt hole diameter (in)
1/16" = allowance for hole damage per AISC 360
The additional 1/16" accounts for damage caused by punching or drilling — the effective hole diameter for net area calculations exceeds the nominal bolt hole diameter.
Net Tension Area Ant
Ant = (g − n_holes_in_tension × (dh + 1/16")) × t
where:
g = gage distance — perpendicular distance between bolt lines (in)
n_holes_in_tension = number of bolt holes intersecting the tension plane
Ubs — Non-Uniform Stress Factor
The Ubs factor is the most judgment-dependent parameter in block shear design:
| Ubs = 1.0 (uniform tension stress) | Ubs = 0.5 (non-uniform tension stress) |
|---|---|
| Multiple bolt rows distributing tension | Single bolt row in tension |
| Short, wide bolt patterns | Coped beam flanges |
| Symmetric bolt layout | Gusset plates with eccentric tension |
| Mid-length spliced plates | End connections where tension path is disrupted |
| Tension members with staggered bolt pattern | Single angle leg with bolts in one row |
AISC 360 Commentary guidance: The default Ubs = 1.0 for most bolted connections. Use Ubs = 0.5 when the tension stress cannot redistribute uniformly across the net tension area — the canonical example is a coped beam where the coped flange disrupts the tension load path and prevents stress from equalizing across the tension face.
Worked Example — Gusset Plate Block Shear
Problem: A 1/2" thick A36 gusset plate (Fu = 58 ksi, Fy = 36 ksi) is connected with two rows of three 3/4" A325 bolts. Bolt gage = 4.0", spacing = 3.0", end distance = 1.5", edge distance = 1.5". Determine block shear capacity.
Step 1: Compute geometric parameters
t = 0.500 in
dh = 3/4 + 1/16 = 13/16 = 0.8125 in
n_planes = 2 (both sides of the tension face)
n_bolts_per_plane = 3 (three bolts along each shear line)
s = 3.0 in (bolt spacing)
Le = 1.5 in (end distance)
g = 4.0 in (gage between bolt lines)
n_holes_in_tension = 2 (one hole per bolt line intersecting tension face)
Ubs = 1.0 (multiple bolt rows, symmetric pattern)
Step 2: Compute areas
Gross shear area (both planes):
Agv = 2 × [(1.5 + 3.0 + 3.0) × 0.500] = 2 × [7.5 × 0.500] = 2 × 3.750 = 7.500 in²
Net shear area (both planes):
Anv = 7.500 − 2 × [3 × 0.8125 × 0.500] = 7.500 − 2 × 1.219 = 7.500 − 2.438 = 5.062 in²
Net tension area:
Ant = [4.0 − 2 × 0.8125] × 0.500 = [4.0 − 1.625] × 0.500 = 2.375 × 0.500 = 1.188 in²
Step 3: Block shear strength
Rn1 = 0.60 × 58 × 5.062 + 1.0 × 58 × 1.188
= 176.2 + 68.9 = 245.1 kips
Upper bound:
Rn2 = 0.60 × 36 × 7.500 + 1.0 × 58 × 1.188
= 162.0 + 68.9 = 230.9 kips
Rn = min(245.1, 230.9) = 230.9 kips
Step 4: Design strength
LRFD: φRn = 0.75 × 230.9 = 173.2 kips
ASD: Rn/Ω = 230.9 / 2.00 = 115.5 kips
Block Shear vs Net Section Tension — Which Governs?
| Connection Type | Likely Governing Limit State | Why |
|---|---|---|
| Short, wide (2 bolts × 3 rows) | Block shear | Large tension face, compact shear area |
| Long, narrow (8 bolts × 1 row) | Net section tension rupture | Long bolt line, narrow gage, large net area reduction |
| Coped beam end | Block shear (Ubs likely 0.5) | Cope disrupts tension path, creates U-shaped block |
| Tension member splice | Check both (varies with geometry) | Symmetric loading, both mechanisms possible |
A practical rule: calculate both φRn_block_shear and φRn_net_tension. The smaller one governs. Never assume one controls without checking the other.
Frequently Asked Questions
How does block shear differ from tearout? Tearout (bolt bearing) is a localized failure where the bolt bears against the plate edge and shears out a narrow strip of material — it involves one bolt at one edge. Block shear involves the entire bolt group tearing out a large block — the failure encompasses all bolts along the shear plane. Block shear capacity is typically much larger than tearout capacity for a single bolt.
Why is the 1/16" hole allowance used? The additional 1/16" accounts for hole wall damage from the punching or drilling process. Punching creates a slightly oversized, irregular hole with a damaged heat-affected zone. The 1/16" allowance makes the effective net area calculation conservative for both punched and drilled holes. AS 4100 uses a similar 2 mm allowance.
Does block shear apply to welded connections? Block shear is primarily a bolted connection limit state, but the same mechanism can occur in welded connections at gusset plates and coped beam ends. The weld line replaces the bolt line as the shear plane. For coped beams with welded end connections, the block comprises the web between the cope and the weld — check using the welded length as the shear plane and the web depth as the tension face.
International Code References
- AISC 360: Section J4.3 — Block Shear Strength. φ = 0.75. Ubs per Commentary J4.3.
- AS 4100: Clause 9.1.10 — Tension and shear interaction. Similar mechanism, φ = 0.75 for bolted connections.
- EN 1993-1-8: Clause 3.10.2 — Block tearing. Veff,1,Rd and Veff,2,Rd for symmetric and asymmetric bolt groups.
- CSA S16: Clause 13.11 — Block shear. φ = 0.75, Ubs = 1.0 or 0.5 matching AISC.
Related Terms and Pages
- Block Shear — Definition & Failure Mode
- Shear Lag — Definition & Design Effect
- Prying Action — Definition & Bolt Force
- Tensile Strength (Fu) — Definition & Values
- Bolted Connection Calculator — Free Online Tool
- Bolt Bearing & Tearout — Full Guide
Educational reference only. Block shear must be checked per the governing design code for all bolted connections in structural applications. All designs must be independently verified by a licensed Professional Engineer.
Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.