Calculation
σw = F / (a · leff)
With full penetration, weld stress equals the stress in the weaker connected part; with incomplete penetration, a is smaller than the plate thickness.
DIN EN 1993-1-8
Butt weld normal stress
With full penetration, weld stress equals the stress in the weaker connected part; with incomplete penetration, a is smaller than the plate thickness.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Weld normal stress σw — Nominal normal stress in the weld section.
- Force F — Tension or compression force transmitted across the weld.
- Effective throat thickness a — Equal to plate thickness for full penetration; for partial penetration a = anom1+anom2 = t − c (gap c).
- Effective weld length leff — Load-carrying weld length after deducting end craters.
Example
20 kN across a = 10 mm and leff = 100 mm give σw = 20 MPa.
Assumptions and limits
Per DIN EN 1993-1-8; for fully penetrated butt welds, weld strength is taken as at least equal to base-metal strength and a separate check is usually unnecessary.
Understand Butt weld normal stress
This calculator finds the nominal normal stress in a butt weld from the transmitted force, the effective throat thickness and the weld length.
What does this quantity describe?
For fully penetrated butt welds, weld strength is taken as at least equal to the strength of the weaker connected part, so a separate stress check is usually unnecessary. For partially penetrated butt welds, the effective throat thickness a is smaller than the plate thickness, and the normal stress σw = F/(a·leff) must be checked as for a fillet weld with deep penetration.
A fully penetrated butt weld behaves like a seamless transition — the plate is practically one piece at that location. Without full penetration, a thinner effective section a remains, similar to a narrowed section in an otherwise continuous bar.
Formula and variables
σw = F / (a · leff)
σw = F / (a · leff)F = σw · a · leffleff = F / (σw · a)
| Symbol / input | Meaning |
|---|---|
| Weld normal stress σw | Nominal normal stress in the weld section. |
| Force F | Tension or compression force transmitted across the weld. |
| Effective throat thickness a | Equal to plate thickness for full penetration; for partial penetration a = anom1+anom2 = t − c (gap c). |
| Effective weld length leff | Load-carrying weld length after deducting end craters. |
Choose the inputs correctly
F is the tension or compression force transmitted across the weld, a is the effective throat thickness (equal to plate thickness for full penetration, otherwise a = anom1+anom2 = t − gap c), and leff is the effective weld length.
How to use the calculator
Enter F, a and leff to calculate σw. For full penetration, a equals plate thickness t; for partial penetration, take a from the welding procedure specification or inspection.
Worked example
F = 20 kN, a = 10 mm and leff = 100 mm give σw = 20,000 N / (10 mm · 100 mm) = 20 MPa.
Understand the result and units
σw = 20 MPa is the nominal normal stress in the weld section. Check it against the allowable stress of the weaker base material, e.g. via the weld safety factor calculator.
F in N or kN, a and leff in mm, σw in MPa (N/mm²).
Full versus partial penetration
With full penetration (welded through the entire plate thickness, usually verified by root welding from both sides or a backing weld), a = t and weld strength equals base-metal strength. With partial penetration, an unwelded gap c remains, so a = t − c is correspondingly smaller. The difference can amount to several tens of percent of capacity and must be clearly specified in the welding procedure.
Typical applications
The formula applies to butt joints in plates, pipes and profiles in steel and pressure vessel construction, particularly for partially penetrated welds or a preliminary estimate ahead of a detailed check.
Assumptions, limits and common mistakes
For fully penetrated, notch-free butt welds a separate stress check is usually not governing; the formula matters mainly for partially penetrated welds. It does not capture notch effects at weld transitions or residual stress.
Common mistake: A common mistake for partially penetrated welds is using the full plate thickness instead of the actual effective throat thickness a, overstating the weld's capacity.
Frequently asked questions
Do I need to calculate anything for full penetration?
Usually not separately, since weld strength then equals at least base-metal strength; a check is mainly useful for partially penetrated welds.
How do I determine a for partial penetration?
a = t − c, where c is the unwelded residual gap from the welding process; this value must come from the welding procedure specification or nondestructive testing.
Does the formula apply to compression too?
Yes, σw = F/(a·leff) applies equally to tension and compression, as long as the connected part does not buckle.
How does this differ from a fillet weld?
A butt weld joins parts flush in one plane; a partially penetrated butt weld is analyzed like a fillet weld with deep penetration.
What comes after the stress calculation?
Use the safety factor calculator to check σw against the allowable stress of the weaker base material.