Welding
Weld shrinkage calculator
In short
The transverse shrinkage of a butt joint is estimated by S = 0.2·Aw/t + 0.05·g, with Aw the deposited weld area, t the thickness and g the root gap. The longitudinal shrinkage is ΔL = 0.025·Aw·L/Ap, with L the weld length and Ap the resisting section of the plates.
Calculation
Example calculated with the tool’s default values.
Inputs
- Joint
- Single V groove
- Thickness
- 10 mm
- Groove angle (included)
- 60°
- Root face
- 2 mm
- Reinforcement
- 2 mm
- Root gap
- 2 mm
- Weld length
- 1000 mm
- Total width of the joined plates
- 400 mm
- Number of joints in series
- 1
Results
- Transverse shrinkage
- 1.54 mmplates draw together
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Transverse shrinkage, one joint
- 1.54 mm
- Longitudinal shrinkage
- 0.45 mmover 1000 mm of weld
- Longitudinal shrinkage per metre
- 0.45 mmper metre of weld
- Deposited area Aw
- 71.9mm²
- Suggested pre-setting
- +1.5 mmCut parts 1.5 mm longer (or set plates 1.5 mm further apart per joint before tacking), tack firmly, weld back-step or alternate sides. Pre-bend a V groove by the angular distortion measured on a trial.
- Order of magnitude only: textbook empirical relations, with no thermal or mechanical analysis. Restraint, welding sequence, pass count and heat input change the result significantly; validate on a sample.
- The Spraragen-Ettinger relation is established for a single-pass butt joint; in multi-pass welding shrinkage keeps growing with deposited metal, so the result is a low estimate.
- Angular distortion not computed: no verified public constant was found. An asymmetric or single-V groove (one-side welding) rotates the plates: consider a symmetric X or a trial check.
- Indicative values: they do not replace the qualified WPS or a sample trial.
Step-by-step calculation
Deposited weld area
Aw = g·t + d²·tan(α/2) + (2/3)·W·h
57.0 + 15.0 = 71.9 mm² (d = 8.0 mm, W = 11.2 mm)
Transverse shrinkage (Spraragen-Ettinger)
S = 0.2·Aw/t + 0.05·g
0.2 × 71.9 / 10.0 + 0.05 × 2.0 = 1.54 mm
Resisting section
Ap = width × t
400 × 10.0 = 4000 mm²
Longitudinal shrinkage (area form)
ΔL = 0.025·Aw·L/Ap
0.025 × 71.9 × 1000 / 4000 = 0.45 mm
How to use it
- Pick the joint: single V groove, double V groove, or known Aw section.
- Enter the thickness, the included groove angle, the root face and the reinforcement.
- Enter the root gap, the weld length and the total width of the joined plates.
- Set the number of joints in series, then read the transverse shrinkage.
Frequently asked questions
What is the weld shrinkage formula?
Transverse shrinkage follows the empirical relation of the Spraragen-Ettinger / Blodgett family: S = 0.2·Aw/t + 0.05·g, in mm. Longitudinal shrinkage follows the area form: ΔL = 0.025·Aw·L/Ap, with Ap = width × t. With several joints in series, transverse shrinkage adds up: S_total = n × S.
How much does a 10 mm single V butt weld shrink?
With a 10 mm plate, a 60° V, a 2 mm root face, a 2 mm root gap and 2 mm reinforcement, the deposited area is Aw = 71.9 mm². The transverse shrinkage is 0.2 × 71.9 / 10.0 + 0.05 × 2.0 = 1.54 mm. Over 1000 mm of weld and 400 mm of plate width (Ap = 4000 mm²), the longitudinal shrinkage is 0.45 mm.
What weld shrinkage allowance should I add?
The calculation suggests cutting the parts longer by the total transverse shrinkage (+1.5 mm in the example), or setting the plates further apart before tacking by the shrinkage of one joint, per joint, then tacking firmly and welding back-step or on alternate sides.
Does it give angular distortion?
No: no verified public constant was found for angular distortion. A single V welded from one side rotates the plates: consider a symmetric double V, or pre-bend by the angular distortion measured on a trial.
Limits
Indicative results, order of magnitude only: textbook empirical relations, with no thermal or mechanical analysis. Restraint, welding sequence, pass count and heat input change the result significantly; validate on a sample. The transverse relation is established for a single-pass butt joint: in multi-pass welding the result is a low estimate. Below 3 mm, buckling dominates and these relations underestimate distortion.
Sources
- Relation de la famille Spraragen-Ettinger / Blodgett : S = 0,2·Aw/t + 0,05·g : Diapositive 18 (retrait transversal, bout à bout une passe) et 14 (retrait longitudinal 25·Aw/Ap) (link)
- Therness : Welding distortion estimator: Δt = 0,2·Aw/t + 0,05·g ; ΔL = 0,025·Aw·L/Ap (famille Blodgett) (link)
- EZ Virtual Tools : Weld Shrinkage Calculator : Ordres de grandeur : bout à bout en V 1,5 à 3 mm en transversal (link)
- Applied Welding Engineering, 2e éd. (2016) : Chap. 5, Stresses, Shrinkage, and Distortion in Weldments, p. 201-238 (référence générale) (link)