Calculation
τw = F / (a · leff)
The force is carried across the throat area a·leff; a thinner or shorter weld raises stress proportionally.
DIN EN 1993-1-8
Fillet weld shear stress
The force is carried across the throat area a·leff; a thinner or shorter weld raises stress proportionally.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Weld shear stress τw — Nominal shear stress in the throat section.
- Force F — Force transmitted across the weld.
- Throat thickness a — Throat thickness of the inscribed triangle in the weld cross-section.
- Effective weld length leff — Load-carrying weld length after deducting end craters.
Example
10 kN across a = 5 mm and leff = 80 mm give τw = 25 MPa.
Assumptions and limits
Simplified method per DIN EN 1993-1-8: resultant stress in the throat section, uniform along the weld length; notch effects and residual stress are excluded.
Understand Fillet weld shear stress
This calculator finds the nominal shear stress in a fillet weld from the transmitted force, the throat thickness a and the effective weld length leff, using the simplified method.
What does this quantity describe?
In the simplified method per DIN EN 1993-1-8, the entire force acting on the weld is treated as uniformly distributed over the throat area a·leff: τw = F/(a·leff). The actual stress distribution along the weld and across the oblique throat section is less uniform; the simplified method gives a conservative, easy-to-follow design value instead.
Picture the fillet weld as a thin, angled web carrying the entire load from one plate to the other. The thinner (smaller a) or shorter (smaller leff) that web is, the more force the same area must carry and the higher the stress — just like a thinner rope carrying the same load.
Formula and variables
τw = F / (a · leff)
τw = F / (a · leff)F = τw · a · leffa = F / (τw · leff)
| Symbol / input | Meaning |
|---|---|
| Weld shear stress τw | Nominal shear stress in the throat section. |
| Force F | Force transmitted across the weld. |
| Throat thickness a | Throat thickness of the inscribed triangle in the weld cross-section. |
| Effective weld length leff | Load-carrying weld length after deducting end craters. |
Choose the inputs correctly
F is the force to be transmitted across the weld, a is the throat thickness (the height of the inscribed isosceles triangle in the weld cross-section), and leff is the effective weld length after deducting end craters at both ends.
How to use the calculator
Enter F, a and leff to get τw. For sizing, instead enter τw as the allowable value and two of the other three quantities to find the third (usually a).
Worked example
F = 10 kN, a = 5 mm and leff = 80 mm give τw = 10,000 N / (5 mm · 80 mm) = 25 MPa.
Understand the result and units
τw = 25 MPa is the nominal, uniformly assumed shear stress in the throat section. Compare it against the weld's allowable stress, e.g. via the weld safety factor calculator.
F is usually given in N or kN, a and leff in mm, and the resulting stress in MPa (N/mm²).
Why throat thickness a is not the leg length
For a symmetric 45° fillet weld with leg length s, the throat thickness is a = s·cos(45°) ≈ 0.7·s, because a is the height of the inscribed right triangle from the root point to the weld surface — the shortest path along which the weld can fail in the governing section. Mistakenly using the leg length instead of a overstates the weld's capacity by about 40%.
Typical applications
The formula is used for preliminary sizing of fillet welds on steel structures, machine frames, brackets and welded gusset connections.
Assumptions, limits and common mistakes
The simplified method neglects the split into longitudinal and transverse shear stress in the oblique throat section, as well as notch effects and residual stress from welding. Highly loaded or fatigue-critical joints require the more detailed DIN EN 1993-1-8 method (items 30–33).
Common mistake: A common mistake is using the plate thickness t instead of the actual throat thickness a — for a symmetric 45° fillet weld, a is noticeably smaller than the leg length. End craters at the weld ends are also sometimes forgotten, overstating the effective length.
Frequently asked questions
What is the difference between a and the leg length?
a is the throat thickness (height of the inscribed triangle); the leg length is the visible side length of the weld; at 45° a ≈ 0.7 · leg length.
How do I choose the effective weld length leff?
Subtract twice the throat thickness a from the actual weld length l for end craters at both ends, unless the weld runs fully around a closed shape.
Is the simplified method enough for every fillet weld?
For preliminary sizing, yes; for a code-compliant DIN EN 1993-1-8 check, the more detailed directional method with an equivalent stress is usually required.
What force direction does this assume?
The formula treats the resultant force per unit length as pure shear in the throat section; combined tension and shear needs an equivalent stress from the more detailed method.
How does this relate to the safety factor calculator?
The resulting τw feeds directly into that calculator as the actual stress σ/τ, to determine the safety factor against the allowable stress.