How to calculate block shear

Block shear is the limit state nobody draws but everybody has to check at a bolted end connection. A wedge of base metal — bounded by the bolt holes — tears out: it shears along the plane parallel to the load and ruptures across the tension plane at the end of the group, simultaneously. It governs exactly where you'd least like it to: coped beam webs, gusset plates and angle legs with bolts crowded near a free edge.

The AISC equation

Rₙ = 0.6·Fu·Anv + Ubs·Fu·Ant  ≤  0.6·Fy·Agv + Ubs·Fu·Ant

Two failure paths add up. The shear term runs along the plane(s) parallel to the load; the tension term (Ubs·Fu·Ant) tears across the end. Because the tension term is common to both sides of the inequality, in practice you take the lesser of net-section shear rupture 0.6·Fu·Anv and gross-section shear yield 0.6·Fy·Agv, then add the tension rupture. Ubs = 1.0 when the tension stress is uniform (most connections) and 0.5 when it is nonuniform, the classic case being a coped beam with two bolt lines. The block shear capacity calculator runs the equation from your areas and reports which shear limit governs.

Worked example — coped beam web

A992 steel (Fu = 450 MPa, Fy = 345 MPa), tear-out block Agv = 1800 mm², Anv = 1200 mm², Ant = 400 mm², uniform tension (Ubs = 1.0):

shear: min(0.6·450·1200 = 324, 0.6·345·1800 = 372.6) = 324 kN · tension: 1.0·450·400 = 180 kN

Rₙ = 324 + 180 = 504 kN · φRₙ = 0.75·504 = 378 kN (LRFD) · Rₙ/Ω = 504/2.00 = 252 kN (ASD)

Net-section rupture (324 kN) is smaller than gross yield (372.6 kN), so it sets the shear term. The connection carries 378 kN factored (LRFD) or 252 kN service (ASD) in block shear — if, and only if, no other limit state is smaller.

Where it connects

Block shear is one of several limit states sharing the same bolt group, and the connection capacity is the smallest of all of them. Check the fasteners with the bolt shear strength calculator, the material at each hole with the bolt bearing & tearout calculator, and the load share on an eccentric group with the bolt pattern force calculator.

Common mistakes

• Using gross area for the rupture term. The 0.6·Fu term acts on the NET shear area Anv — deduct the holes the shear plane crosses (hole = bolt + 2 mm clearance + 2 mm damage per AISC).
• Forgetting the yield cap. 0.6·Fy·Agv is an upper bound on the shear term; skip it and you can over-predict on planes with few holes.
• Defaulting Ubs to 1.0 on a coped beam with two bolt lines. That case is nonuniform — Ubs = 0.5 — and 1.0 is unconservative there.
• Stopping at block shear. It is one check among bolt shear, bearing/tearout, and member net-section rupture; the governing connection strength is the minimum.

Frequently asked questions

How do you calculate block shear?

AISC 360 Eq. J4-5: Rn = 0.6·Fu·Anv + Ubs·Fu·Ant, not to exceed 0.6·Fy·Agv + Ubs·Fu·Ant. The tension term Ubs·Fu·Ant is common to both, so the shear term is the lesser of net-section rupture (0.6·Fu·Anv) and gross-section yield (0.6·Fy·Agv). For Fu = 450 MPa, Fy = 345 MPa, Agv = 1800 mm², Anv = 1200 mm², Ant = 400 mm², Ubs = 1.0: shear rupture 324 kN governs, plus 180 kN tension, so Rn = 504 kN.

What is block shear failure?

It is a tear-out: a block of the connected base metal pulls free, shearing along the plane(s) parallel to the load while rupturing across the tension plane at the end of the bolt group — both at the same time. It commonly governs at coped beam ends, gusset plates and short angle connections where the bolts sit close to a free edge.

Why take the lesser of shear rupture and shear yield?

Net-section shear rupture (0.6·Fu·Anv) uses the ultimate strength on the holed area; gross-section shear yield (0.6·Fy·Agv) uses the yield strength on the full area. AISC caps the rupture term at the yield term so the equation never predicts more shear than the gross section can yield — a safeguard on lightly-perforated planes. On ordinary connections rupture is the smaller and governs.

Is block shear checked with LRFD or ASD?

Both are in AISC 360. The same nominal Rn is multiplied by φ = 0.75 for LRFD (compare φRn to the factored load) or divided by Ω = 2.00 for ASD (compare Rn/Ω to the service load). For Rn = 504 kN that is φRn = 378 kN (LRFD) or Rn/Ω = 252 kN (ASD).