Pipe and Tube Welds

Axial Force on CJP Buttweld formula Complete Joint Penetration - Weld completely fills the gap between the two pieces.
\( \sigma \;=\; \dfrac{ P }{ A } \) \( \sigma \;=\; \dfrac{ 4 \cdot P }{ \pi \cdot \left( D^2 - d^2 \right) } \) \( d \;=\; D - 2 \cdot t \)
Symbol	English	Metric
\(\large{ \sigma }\) (Greek symbol sigma) = stress in weld	\(lbf\;/\;in^2\)	\(Pa\)
\(\large{ \pi }\) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\(\large{ d }\) = pipe/tube inside diameter	\(in\)	\(mm\)
\(\large{ D }\) = pipe/tube outside diameter	\(in\)	\(mm\)
\(\large{ P }\) = total axial force	\(lbf\)	\(N\)
\(\large{ A }\) = weld throat area	\(in^2\)	\(mm^2\)
\(\large{ t }\) = weld throat thickness	\(in\)	\(mm\)

Shear Force on CJP Buttweld formula Complete Joint Penetration - Weld completely fills the gap between the two pieces.
\( \tau \;=\; \tau_p \;=\; \dfrac{ V }{ A } \) \( \tau \;=\; \tau_p \;=\; \dfrac{ 4 \cdot V }{ \pi \cdot \left( D^2 - d^2 \right) } \) \( d \;=\; D - 2 \cdot t \)
Symbol	English	Metric
\(\large{ \tau }\) (Greak symbol tau) = shear stress	\(lbf\;/\;in^2\)	\(Pa\)
\(\large{ \tau_p }\) (Greak symbol tau) = shear stress parallel to weld direction	\(lbf\;/\;in^2\)	\(Pa\)
\(\large{ \pi }\) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\(\large{ d }\) = pipe/tube inside diameter	\(in\)	\(mm\)
\(\large{ D }\) = pipe/tube outside diameter	\(in\)	\(mm\)
\(\large{ V }\) = total shear force	\(lbf-ft\)	\(N-m\)
\(\large{ A }\) = weld throat area	\(in^2\)	\(mm^2\)
\(\large{ t }\) = weld throat thickness	\(in\)	\(mm\)

Bending Moment on CJP Buttweld formula Complete Joint Penetration - Weld completely fills the gap between the two pieces.
\( \sigma \;=\; \dfrac{ M }{ E } \) \( \sigma \;=\; \dfrac{ 32 \cdot M }{ \pi \cdot D^3 \cdot \left[ 1 - \left( \dfrac{ d }{ D } \right)^4 \right] } \) \( d \;=\; D - 2 \cdot t \)
Symbol	English	Metric
\(\large{ \sigma }\) (Greek symbol sigma) = stress in weld	\(lbf\;/\;in^2\)	\(Pa\)
\(\large{ \pi }\) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\(\large{ d }\) = pipe/tube inside diameter	\(in\)	\(mm\)
\(\large{ D }\) = pipe/tube outside diameter	\(in\)	\(mm\)
\(\large{ M }\) = bending moment	\(lbf\)	\(N\)
\(\large{ E }\) = modulus of weld section	\(lbf\;/\;in^2\)	\(Pa\)
\(\large{ t }\) = weld throat thickness	\(in\)	\(mm\)

Torsion Moment on CJP Buttweld formula Complete Joint Penetration - Weld completely fills the gap between the two pieces.
\( \tau_p \;=\; \dfrac{ T }{ E } \) \( \tau_p \;=\; \dfrac{ 16 \cdot T }{ \pi \cdot D^3 \cdot \left[ 1 - \left( \dfrac{ d }{ D } \right)^4 \right] } \) \( d \;=\; D - 2 \cdot t \)
Symbol	English	Metric
\(\large{ \tau_p }\) (Greak symbol tau) = shear stress parallel to weld direction	\(lbf\;/\;in^2\)	\(Pa\)
\(\large{ \pi }\) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\(\large{ d }\) = pipe/tube inside diameter	\(in\)	\(mm\)
\(\large{ D }\) = pipe/tube outside diameter	\(in\)	\(mm\)
\(\large{ T }\) = torque force	\(lbf-ft\)	\(N-m\)
\(\large{ E }\) = modulus of weld section	\(lbf\;/\;in^2\)	\(Pa\)
\(\large{ t }\) = weld throat thickness	\(in\)	\(mm\)