Tensile Strength (Fu) — Definition, Stress-Strain Curve & Design Use
Tensile strength (Fu) is the maximum engineering stress that a material can withstand while being stretched before necking occurs. On the engineering stress-strain curve, Fu is the peak stress — the highest ordinate reached. Beyond this point, localized reduction in cross-sectional area (necking) concentrates deformation in one region, and the engineering stress drops until fracture.
Engineering stress: ÃÂÃÂ_eng = P / A0 (based on original area)
True stress: ÃÂÃÂ_true = P / Ai (based on instantaneous area, continues to rise)
Fu = max(ÃÂÃÂ_eng) — the peak of the engineering curve
PRELIMINARY — NOT FOR CONSTRUCTION. All content is for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.
The Stress-Strain Curve — Key Regions
- Elastic region (0 to Fy): Linear, governed by E = 200 GPa. Deformation is fully recoverable.
- Yield plateau (Fy to ÃÂõ_sh): Constant stress, Lueders bands propagate. Strain hardening begins at ÃÂõ_sh.
- Strain hardening (ÃÂõ_sh to Fu): Stress rises as dislocations multiply. The tangent modulus Et decreases progressively.
- Peak (Fu): Considere's criterion satisfied — the point where strain hardening can no longer compensate for area reduction.
- Necking (Fu to fracture): Localized reduction in area. Engineering stress drops; true stress rises.
- Fracture (ÃÂõ_f): Ductile cup-and-cone fracture surface. Typical elongation at fracture: 20-30% for structural steel.
Common Tensile Strength Values
| Steel Grade | Fu (ksi) | Fu (MPa) | Fu/Fy | Notes |
|---|---|---|---|---|
| A36 | 58-80 | 400-550 | 1.6-2.2 | Wide range; 58 ksi typical |
| A992 | 65 | 450 | 1.30 | Minimum Fu; Fy/Fu âÃÂä 0.85 req |
| A572 Gr 50 | 65 | 450 | 1.30 | Minimum Fu |
| S275 | 410-560 | 410-560 | 1.49-2.0 | Per EN 10025-2 |
| S355 | 470-630 | 470-630 | 1.32-1.8 | Per EN 10025-2 |
| G300 | 440 | 440 | 1.47 | AS/NZS 3679.1 minimum |
| G350 | 480 | 480 | 1.37 | AS/NZS 3679.1 minimum |
Key rule: A992 requires Fy/Fu âÃÂä 0.85. This prevents excessively high yield-to-tensile ratios, ensuring ductile behavior and adequate strain-hardening reserve. Seismic applications (AISC 341) impose additional requirements.
Design Use of Fu — Rupture Limit States
While Fy governs yield limit states, Fu governs rupture (fracture) limit states where the ultimate resistance against tearing is critical:
| Limit State | Formula | Fu Role |
|---|---|---|
| Tension rupture | Pn = Fu * Ae | Net section fracture (AISC D2) |
| Block shear rupture | Rn = 0.6FuAnv + UbsFuAnt | Tension plane rupture |
| Bolt shear | Rn = Fnv * Ab | Fnv = 0.563*Fu (Group A, threads excluded) |
| Fillet weld rupture | Rn = 0.60*FEXX * Aw | FEXX = electrode tensile strength |
| Base metal at welds | Rn = 0.60*Fu * An | Base metal shear rupture near weld |
Frequently Asked Questions
What is the difference between engineering stress and true stress? Engineering stress uses the original cross-sectional area A0: ÃÂÃÂ_eng = P/A0. True stress uses the instantaneous area: ÃÂÃÂ_true = P/Ai. After necking begins (at Fu), true stress continues to rise while engineering stress drops, because the actual load-bearing area decreases faster than the load. Design standards use engineering stress (Fu) for simplicity and conservatism.
Why is the Fu/Fy ratio important? The Fu/Fy ratio (also called the yield ratio) indicates ductility reserve. A low ratio (e.g., 0.6-0.7 for A36) means significant strain hardening before fracture — highly ductile. A high ratio (e.g., 0.85 for A992) means less plastic reserve but still adequate. AISC 360 limits Fy/Fu âÃÂä 0.85; seismic provisions per AISC 341 may impose stricter limits (Fy/Fu âÃÂä 0.80 for R > 3 systems).
Does cold forming change tensile strength? Yes. Cold forming (bending, rolling HSS, punching) increases both Fy and Fu in the worked region due to strain hardening, but reduces ductility. AISC 360 permits using increased Fy and Fu for cold-formed HSS (per A500), averaging Fy = 46 ksi and Fu = 58 ksi for Grade C, but not for design at the cold-worked corner regions (AISC B4.2).
International Code References
- AISC 360: Fu per ASTM product standards. Rupture checks in Chapter D (tension), J3 (bolts), J4 (block shear). ÃÂÃÂt = 0.75 for tension rupture (ÃÂét = 2.00 for ASD).
- EN 1993-1-1: fu per EN 10025. Net section rupture in EN 1993-1-1 Clause 6.2.3. Partial factor ÃÂóM2 = 1.25 for tension fracture checks.
- AS 4100: fu per AS/NZS 3679.1. ÃÂÃÂ = 0.90 for gross yield, ÃÂÃÂ = 0.75 for net section fracture (Table 3.4).
- CSA S16: Fu per CSA G40.21. ÃÂÃÂu = 0.75 for rupture limit states. Tension member fracture: Tr = ÃÂÃÂu _ Fu _ Ane.
Educational reference only. Tensile strength values must be confirmed from certified mill test reports (MTRs). All structural designs must be independently verified by a licensed Professional Engineer.
Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.