Written by Jerry Ratzlaff on . Posted in Structural

$$\large{ \tau_{shear} = \frac{ F }{ 2 \; d \; l } }$$

$$\large{ I = 2\; \left( \frac{ l \; d^3 }{ 12 } + \frac{ d \; l^3 }{ 12 } + l \; d \; d_0^2 \right) }$$

$$\large{ l_r = \sqrt{ \left( \frac{ l }{ 2 } \right)^2 + d_0^2 } }$$

$$\large{ \tau_{torsion} = \frac{ F \; D_0 \; l_r }{ I } }$$

$$\large{ \theta = tan^{ -1 } \left( \frac{ 0.5 \; l }{ d_0 } \right) }$$

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