# Advanced Structural Analysis/Part I - Theory/Failure Modes/Plastic Failure/Special Members/Welds/Fillet Welds

## Nomenclature

$f_{uc} =$ characteristic ultimate stress of parent material
$f_{euc} =$ characteristic ultimate stress of electrode material
$f_{wd} =$ dimensioning ultimate stress of joint
$\gamma_n =$ application partial coefficient
$\phi =$ reduction factor that corresponds to the weld class
$F_{\alpha} =$ transverse load
$F_{||} =$ longitudinal load
$A =$ surface area of investigated cross section
$\alpha =$ angle between transverse load and the investigated cross section

## Summary of Formulas

$F_{R||} = 0.6 A f_{wd}$

$F_{R\alpha} = A \frac{f_{wd}}{\sqrt{2 + cos(2 \alpha)}}$

Where:

$f_{wd} = \phi \frac{\sqrt{f_{uc} f_{euc}}}{1.2 \gamma_n}$ ;if $f_{uc} < f_{euc}$
or,

$f_{wd} = \phi \frac{f_{euc}}{1.2 \gamma_n}$ ;if $f_{uc} >= f_{euc}$

Interaction formula:

$(\frac{F_{S||}}{F_{R||}})^2 + (\frac{F_{S\alpha}}{F_{R\alpha}})^2 <= 1$

## Partial Coefficients

$\phi = 0.9$ in most cases. $\phi = 1$ is acceptable for high quality butt welds.

$\gamma_n = 1.0, 1.1$ or $1.2$ depending on whether failure repercussions are regarded as mild, severe or very severe.