Residual Stresses in Structural Steel — Sources, Patterns, and Design Effects

Residual stresses are internal stresses that exist in steel members without any applied external load. They arise from non-uniform cooling during manufacturing (hot rolling, welding, flame cutting) and from cold working (bending, punching). Residual stresses do not affect the ultimate plastic capacity of a cross-section (they self-equilibrate), but they significantly reduce the inelastic buckling resistance of columns and beams and affect fatigue life. All design code column curves implicitly account for typical residual stress patterns.

Sources of residual stress

Hot rolling

When a W-shape exits the rolling mill, the thin flange tips and web cool faster than the thick web-to-flange junction. The parts that cool first contract first and develop residual compression. The junction region, constrained by the already-cooled extremities, cools last under restraint and develops residual tension.

Typical pattern for hot-rolled W-shapes:

This pattern means the flange tips, which are farthest from the neutral axis and most critical for buckling resistance, start with compressive residual stress. Under applied compression, these fibers reach yield first, reducing the effective stiffness of the cross-section and initiating inelastic buckling at loads below the Euler load.

Welding

Weld metal shrinks as it cools, producing very high tensile residual stresses (up to Fy) in the heat-affected zone (HAZ). Balancing compressive stresses develop in the surrounding parent metal.

Typical pattern for welded I-sections:

Welded sections have higher residual stresses than hot-rolled sections, which is why Eurocode 3 assigns them less favorable buckling curves (curves c and d vs. curves a and b for hot-rolled shapes). AISC uses a single column curve calibrated primarily to hot-rolled shapes.

Flame cutting

Flame-cut edges develop tensile residual stresses (approaching Fy) along the cut edge, with compensating compression in the interior. Universal mill plates (sheared edges) have lower residual stresses than flame-cut plates. For plate girder flanges, the edge condition affects the residual stress pattern and thus the LTB resistance.

Cold working

Cold bending, press-braking (for HSS), and bolt-hole punching introduce residual stresses through plastic deformation. Cold-formed HSS sections have through-thickness bending residual stresses at the corners, which are different from the membrane-type stresses in hot-rolled sections. This is why AS 4100 and Eurocode 3 use different buckling curves for hot-formed vs. cold-formed hollow sections.

Effect on column buckling

Residual stresses reduce column capacity in the inelastic buckling range (intermediate slenderness). The mechanism:

  1. Applied compression adds to residual compression at flange tips
  2. Flange tips yield first (at applied stress = Fy - sigma_rc, where sigma_rc is the compressive residual stress)
  3. The yielded zones no longer contribute to bending stiffness
  4. The effective moment of inertia decreases, lowering the tangent modulus
  5. Buckling occurs when the tangent-modulus load equals the applied load

For a typical hot-rolled W-shape with sigma_rc = 0.3Fy, early yielding begins at an applied stress of 0.7Fy. This is why the AISC column curve begins to deviate from the squash load at relatively low slenderness ratios.

Quantified effect: At KL/r = 80 (moderate slenderness), residual stresses reduce column capacity by approximately 15-25% compared to the ideal Euler curve. At KL/r < 30 (stocky) and KL/r > 150 (slender), the effect is minimal because yielding or elastic buckling dominates respectively.

Effect on lateral-torsional buckling

Residual stresses affect beam LTB similarly to column buckling. The compression flange tips yield early, reducing the torsional and warping stiffness of the beam. This effect is captured in the AISC Chapter F LTB equations through the inelastic zone (Lp < Lb < Lr), where the capacity transitions linearly from Mp to 0.7FySx. The 0.7 factor directly reflects the expected onset of yielding due to residual stresses (Fy - 0.3Fy = 0.7Fy).

Post-weld heat treatment (PWHT) and stress relief

Thermal stress relief (PWHT)

Heating the fabricated member to 600-650 degC (1100-1200 degF) and holding for 1 hour per inch of thickness relaxes residual stresses by allowing creep deformation. Controlled cooling (typically in the furnace or under insulation) prevents re-introduction of thermal stresses.

Vibratory stress relief (VSR)

An alternative to PWHT that uses mechanical vibration to redistribute residual stresses. Less effective than PWHT (30-50% reduction) and not accepted by all codes. Sometimes used for large fabrications that cannot fit in a furnace.

Effect on fatigue

Tensile residual stresses from welding are particularly harmful for fatigue because they keep the weld detail in tension even when the applied load is compressive. This means the full applied stress range contributes to fatigue damage, regardless of the minimum stress in the cycle. AISC 360 Appendix 3 fatigue provisions account for this by basing the fatigue check on the full stress range (f_SR), not the stress amplitude.

Important: Improving the weld detail category (e.g., grinding weld toes, using TIG-dressed welds) improves fatigue life more than stress relief because it reduces the stress concentration factor at the weld toe.

Practical tip: when to worry about residual stresses

For most building structures, residual stresses are already accounted for in the design code column and beam curves. No additional calculation is needed. However, explicitly consider residual stresses when:

Common mistakes

  1. Ignoring residual stresses in FEA. Linear elastic analysis inherently misses the early-yielding effect. Nonlinear FEA of columns and beams must include initial residual stress patterns to match experimental behavior.
  2. Assuming PWHT eliminates all residual stresses. PWHT reduces stresses by 70-90%, not to zero. Some residual stress always remains.
  3. Specifying unnecessary PWHT. PWHT for standard building connections adds cost and schedule without structural benefit -- the design codes already account for residual stresses through the column and beam curves.
  4. Neglecting welding sequence effects. Welding sequence affects the residual stress pattern and distortion. For large fabrications, a welding sequence plan (balanced welding, back-step technique) reduces distortion and peak residual stresses.
  5. Confusing residual stress effects with material defects. Residual stresses reduce buckling capacity but do not reduce ductility or toughness (unless they cause cold cracking, which is a separate issue related to hydrogen, restraint, and preheat).

Run this calculation

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 the applicable standard and project specification. The site operator disclaims liability for any loss arising from the use of this information.