A member in tension has two ways to fail, and AISC 360 Chapter D makes you check both: it stretches and yields across its whole section, or it tears across the reduced section through the bolt holes. The lower of the two governs. This page does both, in LRFD and ASD, and prints every number with the arithmetic that produced it.
| Limit state | Nominal | LRFD | ASD |
|---|---|---|---|
| Tensile yielding, gross section (D2-1) | Pn = Fy·Ag | φt = 0.90 | Ωt = 1.67 |
| Tensile rupture, net section (D2-2) | Pn = Fu·Ae | φt = 0.75 | Ωt = 2.00 |
Rupture carries the harsher factors on purpose: yielding is ductile and gives warning, rupture does not.
For any net area, the hole is taken as the nominal hole plus 1/16 in. — Section B4.3b. A 3/4" bolt sits in a 13/16" standard hole, and you deduct 7/8". The extra sixteenth accounts for damage to the material around the hole from punching or drilling. Skip it and every net-section number comes out a few percent high, on the unsafe side. This page never skips it, and the tape shows it on the first line.
When the holes zigzag, the tear can run diagonally and cross more holes than a straight line would, but along
a longer path. The correction is Cochrane's, and it is in the Specification: for each diagonal leg of
the path, add s²/(4g) back to the net width, where s is the stagger along the load and
g is the gage across it.
net width = gross width − Σ(holes on the path × d_h) + Σ(s²/4g for each diagonal leg)
Set the number of diagonal legs to zero and you get the straight line across. The critical path is the one that gives the smallest net width, and on a real plate you check every plausible path — this page computes the one you describe, it does not search them for you.
If the connection does not grab every element of the cross-section — one leg of an angle, the flanges of a
W but not the web — the load cannot spread instantly across the whole section, and the effective net area is
smaller than the net area: Ae = U·An. The factor comes from Table D3.1, which is a table
of cases, and picking the wrong case is a wrong answer with a confident face. So this page offers the
two you can state without a case lookup — U = 1.0 when the connection takes hold of every element,
and U = 1 − x̄/l, the general case, where x̄ is the distance from the connection plane to the
centroid of the connected area and l is the length of the connection — and otherwise takes your number.
Two published examples, both reproduced by this page:
If this page disagrees with either, do not use it — tell us.
Worked examples in older texts often show a 1" bolt with a 1 1/8" net-area hole. That is the older arithmetic: nominal hole d + 1/16, plus 1/16 for damage. The 2020 RCSC Specification widened the standard hole for bolts 1 in. and larger to d + 1/8 — carried into AISC 360-22 and the 16th Edition Manual — so the same bolt now takes a 1 1/8" nominal hole and a 1 3/16" deduction for net area. Below 1", nothing changed. If your hand check disagrees with this page by exactly a sixteenth on a big bolt, that is why — and the page is following the current table.
φ and Ω for both limit states, Ae = U·An, the B4.3b hole allowance and the s²/4g stagger
correction were each confirmed in two independent published sources — a university steel-design course
text and an independent code-reference site — with a connection-software vendor's documentation agreeing on
the hole allowance as a third. Nothing on this page is recalled from memory.