on . Posted in Structural Engineering

$$\tau_{shear} = F \;/\; ( 2 \; d \; l )$$

$$I = 2\; [\; ( l \; d^3 \;/\; 12 ) + ( d \; l^3 \;/\; 12 ) + l \; d \; d_0^2 \;]$$

$$l_r = \sqrt{ ( l \;/\; 2 )^2 + d_0^2 }$$

$$\tau_{torsion} = ( F \; D_0 \; l_r ) \;/\; I$$

$$\theta = ( tan^{ -1 } \; 0.5 \; l ) \;/\; d_0$$

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