Tension Member Design — AISC 360 Chapter D Reference
Tension members carry axial tensile force: bracing, truss bottom chords, hangers, and tie rods. Design is governed by yielding of the gross section and rupture of the effective net section per AISC 360-22 Chapter D.
Two governing limit states
Yielding on gross section (ductile): phiPn = 0.90 _ Fy _ Ag [Eq. D2-1]. Ensures the member does not elongate excessively. Ductile failure with significant warning.
Rupture on effective net section (brittle): phiPn = 0.75 _ Fu _ Ae [Eq. D2-2], where Ae = U * An. Checks whether the member fractures through bolt holes. Brittle failure, hence lower phi = 0.75.
Design strength = min(yielding, rupture). For most practical bolted members, rupture governs because Ae < Ag and the lower phi factor.
Quick check: Rupture governs when Ae/Ag < 1.20Fy/Fu. For A992 (Fy/Fu = 50/65 = 0.77): threshold = 0.92. Rupture governs when Ae < 0.92Ag -- almost always with bolted connections.
Net area (An)
An = Ag - sum(dh*t), where dh = hole diameter + 1/16" (damage allowance for punched holes).
Staggered holes -- s^2/4g rule: For zigzag paths, net width = gross width - sum(dh) + sum(s^2/(4g)), where s = longitudinal pitch, g = transverse gage. Check all possible failure paths; minimum governs.
Effective net area (Ae)
Ae = U * An, where U = shear lag factor from AISC Table D3.1. See the Shear Lag Factor reference for complete details and worked examples.
Block shear rupture
In addition to yielding and rupture, block shear must be checked:
phiRn = 0.75 * (0.60*Fu*Anv + Ubs*Fu*Ant)
<= 0.75 * (0.60*Fy*Agv + Ubs*Fu*Ant)
Where Anv/Agv = net/gross shear area, Ant = net tension area, Ubs = 1.0 (uniform tension) or 0.5 (non-uniform). Block shear frequently governs for short connections and coped beams.
Worked example — WT8x25
Given: WT8x25, 4 bolts (2x2), 3/4" A325, 3" gage/pitch. A992 (Fy=50, Fu=65 ksi). Ag = 7.37 in^2, tf = 0.630 in.
Net area: 2 holes in flange: An = 7.37 - 2*(7/8)*0.630 = 7.37 - 1.10 = 6.27 in^2.
Shear lag: bf/d = 7.07/8.13 = 0.87 > 2/3, U = 0.90 (Case 3).
Effective net area: Ae = 0.90*6.27 = 5.64 in^2.
Yielding: phiPn = 0.90507.37 = 332 kips. Rupture: phiPn = 0.75655.64 = 275 kips. Governing: 275 kips (rupture).
Common tension member shapes
| Shape | Typical Use |
|---|---|
| W-shapes | Truss bottom chords, heavy bracing |
| WT-shapes | Truss chords, bracing |
| Double angles | Bracing, truss diagonals |
| Single angles | Light bracing, secondary framing |
| Round HSS | Bracing, hangers |
| Rods | Hangers, sag rods, tie rods |
| Plates | Splice plates, gussets, hangers |
Common mistakes
- Checking only one limit state. Both yielding, rupture, AND block shear must be checked.
- Using bolt diameter instead of hole diameter for An. Hole deduction uses dh + 1/16", not bolt diameter.
- Forgetting shear lag factor U. Using Ae = An when U < 1.0 overestimates capacity.
- Not checking all paths for staggered holes. The zigzag path may govern.
- Applying L/r <= 300 as a strength limit. It is a serviceability recommendation, not a hard limit.
Frequently asked questions
Yielding vs. rupture? Yielding occurs across the full gross section (ductile, with warning). Rupture occurs at the weakest net section through bolt holes (brittle, sudden). Rupture typically governs for bolted members.
Why is phi lower for rupture? Rupture is brittle with no redistribution capability. The lower phi = 0.75 (vs 0.90 for yielding) provides additional safety for the more dangerous failure mode.
Must I check block shear for every connection? Yes. Block shear is a potential failure mode for virtually all bolted tension connections, especially with short connections or thin elements.
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Related references
Disclaimer
This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against AISC 360-22 Chapters D and J and the governing project specification. The site operator disclaims liability for any loss arising from the use of this information.