Block shear is a tear-out. The bolt group drags a block of steel with it — shearing along the bolt line and pulling apart across the end — and on a coped beam it is the limit state that governs more often than any other, because the cope takes away exactly the material the block needs. This page does the AISC 360 Section J4.3 arithmetic for the common case, one vertical line of bolts in a coped beam web, a shear tab or a plate, and draws the block it is checking so you can see whether the geometry on screen is the geometry on your drawing.
R_n = 0.60 F_u A_nv + U_bs F_u A_nt ≤ 0.60 F_y A_gv + U_bs F_u A_nt — Equation J4-5, with
φ = 0.75 for LRFD and Ω = 2.00 for ASD. The left side is shear rupture on the net area; the right side caps it
at shear yielding on the gross area. The tension term is the same in both.
| Area | For one vertical bolt line |
|---|---|
| A_gv — gross shear | t × [(n−1)s + L_ev] |
| A_nv — net shear | t × [(n−1)s + L_ev − (n−0.5) d_h] |
| A_gt — gross tension | t × L_eh |
| A_nt — net tension | t × [L_eh − 0.5 d_h] |
d_h in every one of those net areas is the nominal hole plus 1/16 in. Section B4.3b: "the width of a bolt hole shall be taken as 1/16 in. greater than the nominal dimension of the hole." So a 3/4" bolt in a standard 13/16" hole deducts 7/8", not 13/16". Several block-shear examples published online use the nominal hole and land about 3% high — on the unconservative side, on the limit state most likely to govern. This page uses the spec's allowance and shows it on the first line of the tape.
The nominal holes themselves are the current Table J3.3 values, which for bolts 1 in. and larger are d + 1/8 — that changed in the 15th edition, and a chart printed before it shows d + 1/16.
U_bs is 1.0 where the tension stress across the block is uniform: a plate in tension, or a coped beam web with one vertical line of bolts. It drops to 0.5 where the stress is non-uniform — most commonly a coped beam web with two vertical lines. This page computes one line; the 0.5 option is there because the same block occasionally sits in a non-uniform field, but a genuine two-line group also changes the tension plane geometry, and that is not what this page draws.
A coped W16×26 web, t = 0.25, four 3/4" bolts at 3", L_ev = 1.5, L_eh = 1.25, A992: A_gv = 2.625 in², A_nv = 1.859 in², A_nt = 0.203 in², rupture path 85.7 kips against a yield path of 92.0, so R_n = 85.7 and φR_n = 64.3 kips (LRFD) or 42.9 kips (ASD). If this page says otherwise, do not use it — tell us.
Equation J4-5, φ = 0.75, the area expressions and the U_bs rule were each confirmed in two independent published sources — two connection-design software vendors' own documentation, one of which quotes B4.3b verbatim in both its net-area and block-shear sections. Nothing here is recalled from memory. Where a source disagreed with the specification, the specification won, and the difference is written into the page above rather than quietly resolved.