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

## Nomenclature

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

## Summary of Formulas

${\displaystyle F_{R||}=0.6Af_{wd}}$

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

Where:

${\displaystyle f_{wd}=\phi {\frac {\sqrt {f_{uc}f_{euc}}}{1.2\gamma _{n}}}}$ ;if ${\displaystyle f_{uc}
or,

${\displaystyle f_{wd}=\phi {\frac {f_{euc}}{1.2\gamma _{n}}}}$ ;if ${\displaystyle f_{uc}>=f_{euc}}$

Interaction formula:

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

## Partial Coefficients

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

${\displaystyle \gamma _{n}=1.0,1.1}$ or ${\displaystyle 1.2}$ depending on whether failure repercussions are regarded as mild, severe or very severe.