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.