Tools · Fabrication

Distortion, Shrinkage & Camber Estimator

For a fillet-welded T (stiffener, T-beam, or built-up flange), estimate flange angular distortion, longitudinal camber, shrinkage forces, and the pre-set or pre-camber needed to end up straight.

⚠ Disclaimer: Use at Your Own Risk This tool is provided "as is," for general engineering reference and educational purposes only, with no warranty of any kind. It combines classic empirical and simplified analytical distortion formulas developed mainly for steel fabrication. Real distortion also depends on welding sequence, tack spacing, fit-up, prior plate stresses, and the stiffness of the whole assembly, and restraint factors are indicative only. Jeffrium and Jeffrey Sowards assume no liability for decisions, designs, procedures, or outcomes based on this tool's output. Confirm on a mock-up or by finite-element analysis for critical parts. Use of this tool is entirely at your own risk.

Member geometry (mm)

Welding

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Pre-set angle, each side
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Flange tip deflection
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Midspan camber (tendon force)
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Camber, Blodgett check
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Longitudinal shrinkage force
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Transverse shrinkage
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Longitudinal shortening
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Heating to yield when restrained
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End view: flange rotation

Dashed: as fitted. Solid: after welding.

Side view: camber

The welded side shortens, so the member bows concave toward the welds.

Recommendations and flags

    How it works

    Why welds distort, and how much

    Metal next to a weld heats, expands against cold surroundings, yields in compression, and then shrinks as it cools. That locked-in shrinkage pulls the flange into a vee and bows the member along its length.

    The math

    Flange tipΔ = 0.02·W·ω1.3 / t²  (inches)
    Shrink forceF = 0.335·α·E·Q / (ρc)
    Camberδ = F·e·L² / (8·E·I)
    Transverses = α·Q / (ρ·c·t)
    W, t, ωflange width, thickness, fillet leg
    Qheat input per unit length
    e, Iweld offset from neutral axis, second moment

    Worked example

    GivenSteel T, 300×16 flange, 400×10 web, 6 m long, 8 mm fillets both sides at 1.2 kJ/mm
    Shrink force2 × 263 kN = 525 kN
    SectionI = 1.48×108 mm⁴, e = 84 mm
    Flange3.4 mm tip drop, 1.3° per side
    Result6.5 mm camber over 6 m

    Blodgett's empirical camber formula gives the same 6.5 mm, a useful check that the two approaches agree.

    More detail

    Assumptions used in this calculator
    • Fillet-welded T: the web is centered under the flange, with continuous fillets along the full length at the flange-web junction.
    • Flange angular distortion uses Blodgett's empirical steel formula for fillets on both sides. It is scaled to other metals by α/(ρc) and halved for a single fillet.
    • Longitudinal shrinkage force is 0.335·α·E·Q/(ρc) per pass (Okerblom), acting at the weld centroid (t + leg/3). Passes add linearly, which is conservative.
    • Elastic beam bending with uniform curvature: camber = κL²/8, measured at midspan relative to the ends.
    • Transverse shrinkage ≈ αQ/(ρc·t), taken across the flange thickness.
    • Restraint factors (clamped 0.5, rigid 0.2) are indicative rules of thumb, and are not applied to camber.
    • Room-temperature properties. Welding sequence, tack spacing, fit-up, and prior plate stresses are not included.
    Where the formulas come from

    The flange formula is Blodgett's empirical fit to steel T-sections. For aluminum and stainless, the tool scales it by the thermal distortion parameter α/(ρc) relative to steel. Aluminum's is about three times steel's and stainless's about 1.4 times.

    The longitudinal shrinkage force follows Okerblom's analysis, and agrees with White's rule of thumb of about 0.2 kN per J/mm for steel. Applied at the welds' offset from the neutral axis, it bends the member like an eccentric prestress.

    Pre-setting and pre-cambering

    Pre-setting means bending or tilting the parts by the expected distortion in the opposite direction before welding, so shrinkage pulls them straight. For flanges, that can be a pre-bent flange or wedges under the flange tips. For camber, the member is bowed against the expected curvature, or the welds are balanced about the neutral axis. Clamping reduces angular distortion, but some springback occurs on release and the residual stress stays.

    Ways to reduce distortion
    LeverEffect
    Smaller fillet legAngular ∝ ω1.3; don't over-weld
    Lower heat inputShrink force ∝ Q
    Balanced weldingWeld both sides alternately about the neutral axis
    Intermittent weldsLess total heat where full length isn't needed
    Back-step sequenceSpreads shrinkage, limits locked-in bow
    Higher-energy-density processLaser or EB put far less heat per length
    References
    • O.W. Blodgett, Design of Welded Structures, James F. Lincoln Arc Welding Foundation, 1966, Section 7.7.
    • N.O. Okerblom, The Calculations of Deformations of Welded Metal Structures, HMSO, 1958.
    • J.D. White, R.H. Leggatt and J.B. Dwight, “Weld shrinkage prediction,” Welding and Metal Fabrication, 1980, 587–596.
    • K. Masubuchi, Analysis of Welded Structures, Pergamon, 1980.
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