Steel Tension Member: Yield and Rupture with Shear Lag (AISC 360 D2/D3)
The axial tension capacity of a brace, hanger, or truss diagonal.
Example
You enter
- Gross area Ag (in²) 3.75
- Yield stress Fy (ksi) 36
- Tensile stress Fu (ksi) 58
- Thickness at the holes (in) 0.5
- Hole diameter (in, bolt + 1/8) 0.875
- Hole lines across the section (0 if welded) 1
- Connection eccentricity xbar (in, 0 => U = 1) 1.18
- Connection length L (in) 6
You get
- An (in²) 3.3125
- Shear lag factor U 0.8033
- Ae (in²) 2.661
- P ASD (kip) 77.17
- P LRFD (kip) 115.76
Details, formula, and sources
The lower of gross yielding Fy Ag and net rupture Fu U An, where the shear-lag factor U = 1 - xbar/L punishes a member connected through only some of its elements. An L4x4x1/2 bolted through one leg draws U = 0.80 and flips the governing limit from yielding to rupture - the penalty a straight Fy Ag estimate misses; weld the full section and it flips back. Single hole line, no stagger. A design aid, not the engineer of record's stamped design.
An = Ag - nh dh t; U = U_override or 1 - xbar/L (capped at 1.0); Ae = U An; Pn_yield = Fy Ag (ASD /1.67, LRFD x0.90); Pn_rupture = Fu Ae (ASD /2.00, LRFD x0.75); capacity = min of the two limit states.
The AISC 360-22 Chapter D tension-member provisions -- D2 yielding on the gross section and rupture on the effective net area, with the D3 shear-lag factor U = 1 - xbar/L (Table D3.1 Case 2) and the net-area hole deduction -- by name; the paired resistance/safety factors are named constants.
AISC 360 is free to read at aisc.org (Specification for Structural Steel Buildings); Table D3.1 and the Chapter D provisions are in the published specification.
Estimate. AHJ and licensed professional govern.
Field names used by the API: ag_in2, fy, fu, t_in, dh_in, nh, xbar_in, l_in, an_in2, u, ae_in2, p_asd_kip, p_lrfd_kip
- Two limit states gross-section yielding (Fy Ag) and effective-net-section rupture (Fu U An); the lower factored capacity governsAISC 360-22 D2
- Shear lag U = 1 - xbar/L for a member connected through only some elements (Case 2); entered U overrides; capped at 1.0AISC 360-22 Table D3.1
- Net area Ag minus nh holes at the entered diameter and thickness, one transverse line, no staggerAISC 360-22 B4.3 / D3