How to use this calculator
- Pick LRFD or ASD. Match the rest of your design — LRFD compares φPn to the factored load; ASD compares Pn/Ω to the service load.
- Enter the areas and strengths. Gross area Ag, net area An (deduct bolt holes), Fy and Fu of the steel.
- Set the shear-lag factor U. U = 1.0 if all cross-section elements are connected; ~0.8–0.9 for an angle/tee bolted through one element, or 1 − x̄/L. Ae = An·U.
- Read the governing capacity. The tool returns gross yielding, net rupture and the lesser of the two — the member tension capacity. Then verify the connection (block shear, bolt shear, bearing).
How it works
A tension member has two ways to fail, and AISC 360 Chapter D makes you check both. It can yield along its length on the full gross section — ductile and gradual — or it can rupture suddenly across the bolt holes on the net section. The design strength is the lesser of the two:
gross yielding: Pₙ = Fy·Ag · net rupture: Pₙ = Fu·Ae, Ae = An·U
The effective net area Ae = An·U folds in shear
lag: when the member is connected through only part of its
section (an angle bolted through one leg), the net area cannot fully
mobilize, so U < 1. LRFD applies φ = 0.90 to yielding and 0.75 to
rupture; ASD divides by Ω = 1.67 and 2.00. The lower rupture factor
reflects that a net-section tear is brittle. The
calculator runs both
and names which governs.
The gross area comes from the section property calculator, and once the member is sized the same bolt group must pass its own limit states — the block shear capacity calculator and the bolt shear strength calculator. The connection capacity is the smallest of the lot.
Worked example
Verified against the live calculator
An A992 member (Fy = 345 MPa, Fu = 450 MPa),
Ag = 3000 mm², net An = 2500 mm² after the
holes, connected through part of the section so U = 0.8, by
LRFD:
Ae = 2500·0.8 = 2000 mm²
gross yield φPy = 0.90·345·3000 = 931.5 kN · net rupture φPr = 0.75·450·2000 = 675 kN
Net-section rupture (675 kN) is the smaller, so it governs —
the member can take a 675 kN factored tension load. The
shear lag did it: with U = 1.0 the rupture strength would be
0.75·450·2500 = 844 kN and gross yielding (931.5 kN) would no
longer be the larger — so improving the connection (more elements
engaged, longer weld) raises U and the capacity.
Frequently asked questions
How do you calculate tension member capacity?
AISC 360 Chapter D gives two limit states and you take the lesser. Gross-section yielding: Pn = Fy·Ag. Net-section rupture: Pn = Fu·Ae, where Ae = An·U and U is the shear-lag factor. Apply LRFD factors (φ = 0.90 yield, 0.75 rupture) or ASD factors (Ω = 1.67, 2.00). For Fy = 345 MPa, Fu = 450 MPa, Ag = 3000 mm², An = 2500 mm², U = 0.8 (LRFD): gross yield 931.5 kN vs net rupture 675 kN, so the member capacity is 675 kN.
Why are there two limit states for a tension member?
A tension member can fail two ways. It can yield along its whole length on the gross section (a ductile, gradual failure — Fy·Ag), or it can tear suddenly across the bolt holes on the net section (a brittle failure — Fu·Ae). AISC checks both and the smaller design strength governs; the lower φ on rupture (0.75 vs 0.90) reflects its brittleness.
What is the shear lag factor U?
When a tension member is connected through only some of its cross-section elements — an angle bolted through one leg, say — the stress cannot spread uniformly at the connection, so the effective net area is less than the geometric net area: Ae = An·U. U comes from AISC Table D3.1: 1.0 when all elements are connected, around 0.8–0.9 for typical bolted angles and tees, or computed as U = 1 − x̄/L.
Does net rupture or gross yielding usually govern?
It depends on the hole loss and shear lag. With light hole loss and U near 1.0, gross yielding (the ductile mode) governs, which is preferred. Heavy hole loss or a low U (connection through one element) drops the net-rupture strength below gross yield, so rupture governs — and AISC wants you to confirm adequate ductility when it does.
Method & assumptions
- AISC 360 Section D2: design tensile strength = lesser of gross-section yielding (Fy·Ag) and net-section rupture (Fu·Ae). LRFD φ = 0.90 (yield) / 0.75 (rupture); ASD Ω = 1.67 / 2.00.
- Effective net area Ae = An·U. You supply the shear-lag factor U (AISC Table D3.1) — this tool does not embed the table. U = 1.0 when all elements are connected; lower for one-element connections.
- Net area An deducts the bolt-hole material on the critical chain (standard hole = bolt + 2 mm + 2 mm). For staggered holes apply the s²/4g rule to An before entering it; for welded members with no holes, An = Ag.
- Member check only — the connection (bolt shear, bearing, block shear) and any slenderness/serviceability limits are separate. The governing strength is the smallest of all of them, and a licensed engineer owns the final design.