------------------------ | ----------------------- | --------------------- | ------------------- | ----------- | --------------------- | | W-shape (hot-rolled, moderate) | Hot rolling | Compression | Tension | Near zero | 10-15 (0.2-0.3 Fy) | | W-shape (hot-rolled, heavy) | Hot rolling | Compression | Tension | Compression | 12-18 (0.25-0.35 Fy) | | HSS (hot-formed) | Hot forming | Compression (outside) | Tension (corners) | Variable | 5-12 (0.1-0.25 Fy) | | HSS (cold-formed) | Cold forming | Tension (corners) | Compression (flats) | Variable | 15-25 (0.3-0.5 Fy) | | Built-up I (welded, fillet) | Welding | Compression | Tension (near weld) | Variable | 15-25 (0.3-0.5 Fy) | | Built-up plate girder | Welding + flame cutting | Tension (cut edge) | Tension (near weld) | Compression | 20-30 (0.4-0.6 Fy) | | Double angle | Hot rolling | Compression (toe) | Tension (heel) | N/A | 8-12 |

The key insight: hot-rolled shapes have lower residual stresses than welded built-up sections because the entire cross-section cools more uniformly. This is why Eurocode 3 assigns more favorable buckling curves (curves a, b) to hot-rolled shapes and less favorable curves (curves c, d) to welded sections.

Residual stress distribution in a typical W12x65

For a W12x65 (A992), the residual stress distribution across the flange width is approximately parabolic:

Flange tip (compression):     -12 ksi  (0.24 Fy)
Quarter-point:                -6 ksi   (0.12 Fy)
Flange center (web junction): +12 ksi  (0.24 Fy, tension)

The sign convention is: negative = compression, positive = tension. Under applied axial compression of 30 ksi, the flange tips reach yield at 30 + 12 = 42 ksi (below Fy = 50 ksi), while the web-flange junction remains elastic at 30 - 12 = 18 ksi. This non-uniform yielding pattern reduces the effective flexural stiffness of the cross-section.

Welding residual stress distribution

Welding introduces the highest magnitude residual stresses in structural steel members. The distribution depends on weld type, sequence, and joint geometry:

Longitudinal residual stresses (parallel to weld)

Region Stress state Approximate magnitude Width of affected zone
Weld centerline Tension, up to Fy 40-50 ksi (A992) Equal to weld width
Heat-affected zone (HAZ) Tension, 0.5-0.8 Fy 25-40 ksi 2-3x weld width
Transition zone Tension to compression gradient 0-20 ksi 3-5x weld width
Far field (base metal) Compression (balancing) 5-15 ksi Remainder of cross-section

Transverse residual stresses (perpendicular to weld)

Transverse residual stresses are typically 30-50% of longitudinal values. At the weld start and stop points, transverse stresses can approach Fy due to the triaxial restraint condition. This is why weld defects (cracks, porosity) are most common at weld terminations.

Through-thickness residual stresses

In thick welded joints (> 1 in.), residual stresses vary through the thickness of the weld. The last-deposited pass has the highest tensile residual stress at the surface, while the root pass may be in compression. This through-thickness variation is why UT inspection of thick CJP welds requires scanning from both surfaces.

Thermal cutting effects

Flame cutting and plasma cutting introduce residual stresses different from those caused by rolling or welding:

Cutting method Cut edge stress Affected depth Typical magnitude Mitigation
Oxy-fuel (flame cutting) Tension 3-6 mm (1/8-1/4 in.) 30-50 ksi (up to Fy) Grinding cut edge, stress relief
Plasma cutting Tension 2-4 mm 25-40 ksi Grinding, or specify universal mill plate
Laser cutting Tension 1-3 mm 15-30 ksi Generally acceptable as-is
Mechanical shearing Compression + tension 1-2 mm 10-20 ksi Edge condition varies by machine

For plate girders, the flange edges produced by flame cutting have tensile residual stresses that reduce the local buckling resistance of the compression flange. AISC 360-22 Section F4 accounts for this indirectly through the plate buckling coefficient. For heavy plate girders (flanges over 2 in. thick), some specifications require grinding the flame-cut edges to remove the heat-affected zone.

Stress relief methods

Thermal stress relief (PWHT)

Parameter Typical range Notes
Temperature 1100-1200F (595-650C) Must not exceed tempering temperature for Q&T steels
Soak time 1 hour per inch of thickness Minimum 1 hour regardless of thickness
Heating rate 400F/hr maximum (200C/hr) Faster rates cause thermal gradients and new stresses
Cooling rate 400F/hr maximum to 600F, then air cool Controlled cooling in furnace or under insulation
Resulting reduction 70-90% of original residual stress Never eliminates 100% of residual stress
Applicable steels A36, A992, A572 (all grades) A514 (Q&T) requires special temperature limits (max 1150F)

Mechanical stress relief

Method Reduction achieved Cost Applicability Code acceptance
Vibratory stress relief (VSR) 30-50% Low ($500-2000 per member) Large fabrications, simple shapes Not universally accepted; AWS D1.1 does not recognize VSR as equivalent to PWHT
Shot peening 40-60% (surface only) Moderate Small components, fatigue-critical surfaces Used in aerospace and mechanical components, not typical for structural steel
Mechanical stretching 50-70% High (requires specialized equipment) Plates, simple tension members Not typical for building construction
Thermal cycling (multiple PWHT cycles) 80-95% High (multiple furnace cycles) Critical applications Required for some nuclear and pressure vessel applications

Practical guidance on stress relief selection

Situation Recommended approach Rationale
Standard building connections (A992) No stress relief needed Design codes account for residual stresses
Thick welded joints (t > 2 in.) PWHT per AWS D1.1 Reduces hydrogen cracking risk and improves toughness
Fatigue-critical structures (crane runways) PWHT for critical joints Reduces mean stress and improves fatigue life
Large built-up members (no furnace available) VSR as supplementary measure Better than nothing, but not equivalent to PWHT
Seismic moment frame connections No stress relief (not practical) Design detailing (RBS, etc.) manages the issue

Impact on column buckling: AISC Commentary perspective

AISC 360-22 Commentary Chapter E provides the theoretical background for the single column curve used in US practice. The commentary explains that the AISC column curve (Equation E3-1/E3-2) was calibrated against approximately 100 column tests covering a range of shapes, residual stress patterns, and initial out-of-straightness values.

Comparison with multiple column curve approaches

Code Number of curves Basis for curve selection AISC equivalent (approximate)
AISC 360-22 1 curve Calibrated average of all shapes Single curve for all
Eurocode 3 EN 1993-1-1 5 curves (a0, a, b, c, d) Based on shape type, manufacturing, and residual stress level Curve b for hot-rolled W-shapes
AS 4100-2020 5 curves (1-5) Based on section type and residual stress category Curve 2-3 for hot-rolled sections
CSA S16:24 3 curves (1, 2, 3) Based on shape type and manufacturing Curve 2 for W-shapes

The AISC single-curve approach was deliberately chosen for simplicity. The curve is positioned to be safe for all common structural shapes, meaning it is slightly conservative for hot-rolled W-shapes (which have lower residual stresses) and slightly unconservative for heavy welded built-up sections (which have higher residual stresses). The overall safety is maintained by the resistance factor phi = 0.90.

Measurement methods for residual stress

Method Principle Accuracy Destructive? Cost Typical application
Sectioning (hole drilling) Release strain measured by strain gauges when material is removed +/- 5-10% of Fy Yes (small hole) Moderate Research, quality control of critical members
X-ray diffraction Measures lattice strain at the surface +/- 3-5% of Fy No (surface only) High Aerospace, research
Neutron diffraction Measures lattice strain through the thickness +/- 3-5% of Fy No Very high (requires neutron source) Research, nuclear applications
Ultrasonic (acoustoelastic) Correlation between wave velocity and stress state +/- 10-15% of Fy No Low-Moderate Field screening, large structures
Barkhausen noise Magnetic domain wall motion correlates with stress Qualitative to semi-quantitative No Low Surface stress mapping on ferromagnetic steel

For structural engineering practice, residual stress measurement is rarely required. The most common application is in research validating finite element models of column and beam behavior. However, forensic investigations of unexpected failures may employ hole-drilling or ultrasonic methods to determine whether residual stresses contributed to the failure.

Mitigation strategies table

Strategy Description Effectiveness Cost impact When to apply
Preheat before welding Reduces cooling rate, lowers residual stress magnitude Moderate (10-20% reduction) Low (labor and fuel) Always per AWS D1.1 minimums
Controlled welding sequence Balanced welding, backstep technique Significant (20-40% reduction in peak stress) Low (planning and supervision) All multi-pass welds and large fabrications
Interpass temperature control Maintains consistent thermal state Moderate Low (monitoring) All multi-pass welds
PWHT (furnace) Heats to 1100-1200F, holds, controlled cool High (70-90% reduction) High (furnace, schedule) Thick joints, fatigue-critical, per specification
VSR (vibratory) Mechanical vibration during and after welding Low-Moderate (30-50% reduction) Low Large fabrications where PWHT not practical
Weld toe grinding Removes stress concentration at weld toe High for fatigue life (not for residual stress) Moderate (labor) Fatigue-critical details
Peening (hammer or shot) Plastic deformation at surface introduces compression Moderate (surface only) Low-Moderate Fatigue-critical surfaces, not a substitute for PWHT
Use hot-rolled shapes instead of welded built-up Lower residual stresses in mill-produced shapes Significant May reduce cost (less fabrication) Always prefer standard rolled shapes when available

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This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification. The site operator disclaims liability for any loss arising from the use of this information.

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Frequently Asked Questions

What is the recommended design procedure for this structural element?

The standard design procedure follows: (1) establish design criteria including applicable code, material grade, and loading; (2) determine loads and applicable load combinations; (3) analyze the structure for internal forces; (4) check member strength for all applicable limit states; (5) verify serviceability requirements; and (6) detail connections. Computer analysis is recommended for complex structures, but hand calculations should be used for verification of critical elements.

How do different design codes compare for this calculation?

AISC 360 (US), EN 1993 (Eurocode), AS 4100 (Australia), and CSA S16 (Canada) follow similar limit states design philosophy but differ in specific resistance factors, slenderness limits, and partial safety factors. Generally, EN 1993 uses partial factors on both load and resistance sides (γM0 = 1.0, γM1 = 1.0, γM2 = 1.25), while AISC 360 uses a single resistance factor (φ). Engineers should verify which code is adopted in their jurisdiction.