Fillet Weld Under Axial Torsional Loading

Fillet Weld Under Axial Torsional Loading formulas

\(\large{ \tau_{shear} = \frac{ F }{ 2 \; d \; l }   }\)
\(\large{ I = 2\; \left(  \frac{ l \; d^3 }{ 12 }  +  \frac{ d \; l^3 }{ 12 }  + l \; d \; d_0^2  \right)  }\)
\(\large{ l_r =   \sqrt{ \left( \frac{ l }{ 2 } \right)^2 + d_0^2  }  }\)
\(\large{ \tau_{torsion} = \frac{ F \; D_0 \; l_r }{ I }   }\)
\(\large{ \theta = tan^{ -1 }   \left(  \frac{ 0.5 \; l }{ d_0 }   \right)  }\)

Where:

\(\large{ \theta }\) = angle enclosed

\(\large{ F }\) = applied force

\(\large{ D_0 }\) = distance from centeroid of weld group to applied force

\(\large{ d_0 }\) = distance from centeroid of weld group to centerline of weld

\(\large{ l }\) = length of weld

\(\large{ \tau_{max} }\)  (Greek symbol tau) = maximum shear stress in weld

\(\large{ I }\) = polar moment of interia

\(\large{ l_r }\) = radial distance to farthest point on weld

\(\large{ \tau_{shear} }\)  (Greek symbol tau) = shear stress in weld due to shear force

\(\large{ \tau_{torsion} }\)  (Greek symbol tau) = shear stress in weld due to torsion

\(\large{ d }\) = throat depth of weld