Steel Web Local Yielding and Crippling (AISC 360 J10)
Where a column bears on a beam or a beam lands on a plate, the web itself can fail before the member does.
Example
You enter
- Yield stress Fy (ksi) 50
- Web thickness tw (in) 0.355
- Flange thickness tf (in) 0.57
- k distance kdes (in) 1.25
- Member depth d (in) 18
- Bearing length lb (in) 4
- Force location interior
You get
- Wly rn 181.94
- Wc rn 204.2
- ASD (kip) 102.1
- Governing LRFD capacity 153.2 kip
Checked against published worked examples from: AISC.
Details, formula, and sources
ScopeJ10.2 web local yielding Rn = Fy tw (5k + lb) interior or (2.5k + lb) at an end, and J10.3 web crippling with its sqrt(E Fy tf/tw) term. Because their safety factors differ (1.50 vs 2.00), the governing limit can flip - a W18x50 on a 4 in interior bearing is crippling-governed at 102.1 kip ASD, but move the same bearing within d/2 of the end and the 0.40 end coefficient (J10-5) halves crippling, which governs at 51.5 kip; between d/2 and d from the end, yielding takes over at 84.3 kip. The check that decides a bearing stiffener. A design aid, not the engineer of record's stamped design.
Formula or tableWLY Rn = Fy tw (5k + lb) interior, Fy tw (2.5k + lb) end (Omega 1.50 / phi 1.00); WC Rn = 0.80 tw^2 [1 + 3(lb/d)(tw/tf)^1.5] sqrt(E Fy tf/tw) interior; within d/2 of the end WC Rn = 0.40 tw^2 [1 + 3(lb/d)(tw/tf)^1.5] sqrt(E Fy tf/tw), with [1 + (4 lb/d - 0.2)(tw/tf)^1.5] when lb/d > 0.2 (Omega 2.00 / phi 0.75); governing = min of the factored pair. (E = 29,000 ksi)
Source and editionThe AISC 360-22 J10.2 web local yielding and J10.3 web crippling limit states under a concentrated transverse force, with the interior/end coefficients and their differing resistance/safety factors, by name.
Free accessAISC 360 is free to read at aisc.org (Specification for Structural Steel Buildings); the J10 provisions are in the published specification.
What governsEstimate. AHJ and licensed professional govern.
API field namesfy, tw, tf, k_in, d_in, lb_in, location, wly_rn, wc_rn, asd_kip, lrfd_kip
- Web local yielding Fy tw (5k + lb) interior; (2.5k + lb) within a member depth of the endAISC 360-22 J10.2
- Web crippling 0.80 tw^2 [1 + 3(lb/d)(tw/tf)^1.5] sqrt(E Fy tf/tw) for an interior forceAISC 360-22 J10.3
- Differing factors Omega 1.50 vs 2.00 (phi 1.00 vs 0.75) - the governing limit state can flip between ASD and LRFDAISC 360-22 J10