on . Posted in Structural Engineering

$$\large{ \sigma_{butt} = \frac{T}{l\;d} }$$

$$\large{ \tau_{butt} = \frac{V}{l\;d} }$$

$$\large{ \sigma_{avg} = \frac{\sigma_{butt} }{ 2 } }$$

$$\large{ \tau_{max} = \sqrt{ \sigma_{avg}^2 + \tau_{butt}^2 } }$$

$$\large{ \sigma = \sigma_{avg} \;+\; \tau_{max} }$$

Symbol English Metric
$$\large{ \sigma_{avg} }$$  (Greek symbol sigma) = average stress of weld $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ l }$$ = length of weld $$\large{in}$$ $$\large{mm}$$
$$\large{ \tau_{max} }$$  (Greek symbol tau) = maximum shear stress $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ \sigma_{butt} }$$  (Greek symbol sigma) = normal stress of weld $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ V }$$ = shear force $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ \tau_{butt} }$$  (Greek symbol tau) = shear stress of weld $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ \sigma }$$  (Greek symbol sigma) = principle stress $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ T }$$ = tensile force $$\large{lbf}$$ $$\large{N}$$
$$\large{ d }$$ = throat depth of weld $$\large{in}$$ $$\large{mm}$$ 