Written by Jerry Ratzlaff on . Posted in Structural Engineering

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

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

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

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

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

Symbol English Metric
$$\large{ \theta }$$ = angle enclosed $$\large{deg}$$ $$\large{rad}$$
$$\large{ F }$$ = applied force $$\large{ lbf }$$ $$\large{ N}$$
$$\large{ D_0 }$$ = distance from centeroid of weld group to applied force $$\large{in}$$ $$\large{mm}$$
$$\large{ d_0 }$$ = distance from centeroid of weld group to centerline of weld $$\large{in}$$ $$\large{mm}$$
$$\large{ l }$$ = length of weld $$\large{in}$$ $$\large{mm}$$
$$\large{ \tau_{max} }$$  (Greek symbol tau) = maximum shear stress in weld $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ I }$$ = polar moment of interia $$\large{in^4}$$ $$\large{mm^4}$$
$$\large{ l_r }$$ = radial distance to farthest point on weld $$\large{in}$$ $$\large{mm}$$
$$\large{ \tau_{shear} }$$  (Greek symbol tau) = shear stress in weld due to shear force $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ \tau_{torsion} }$$  (Greek symbol tau) = shear stress in weld due to torsion $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ d }$$ = throat depth of weld $$\large{in}$$ $$\large{mm}$$