1. Loading by axial force F x

Resultant Shear Stress

where:

	F x	axial force [N, lb].
	A	throat area of the weld group [mm 2 , in 2 ].

2. Loading by bending moment M

Shear stress in the weld investigated point

where:

	u	constant
		- for calculation in metric units u = 1000
		- for calculation in English units u = 12
	M	bending moment [Nm, lb ft]
	r	radius vector of investigated weld point related to the weld group center of gravity [mm, in]
	J	polar moment of inertia of weld group [mm 4 , in 4 ]

3. Loading by bending force F Y

In any weld point, a stress caused by shearing force F Y and bending moment M F originates. Its size determines the formula:

M F = F Y r F [Nmm, lb in]

where:

	F Y	bending shearing force [N, lb]
	r F	arm of bending force to the weld group center of gravity [mm, in].

Shear stress caused by shearing force

where:

	F Y	bending shearing force [N, lb]
	A	throat area of the weld group [mm 2 , in 2 ].

Shear stress caused by bending moment

- stress x-component

- stress y-component

where:

	M F	bending moment [Nmm, lb in]
	r Y	distance of investigated weld point to the weld group center of gravity in the y-axis direction [mm, in]
	r X	distance of investigated weld point to the weld group center of gravity in the x-axis direction [mm, in]
	J	polar moment of inertia of weld group [mm 4 , in 4 ]

Resultant shear stress in the investigated point of weld

where:

	τ XM	x-component of shear stress caused by bending moment [MPa, psi]
	τ Y	shear stress caused by shearing force F Y ' [MPa, psi]
	τ YM	y-component of shear stress caused by bending moment [MPa, psi]

4. Loading by common force F

In any weld point, a common force F causes adequate stress to the stress which would arise by combined loading from bending moment M F and the pair of shearing forces F X ', F Y ' with action point in the weld group center of gravity, while applies:

M F = F r F [Nmm, lb in]

F X' = F cos φ [N, lb]

F Y' = F sin φ [N, lb]

where:

	F	acting force [N, lb]
	r F	arm of bending force to the weld group center of gravity [mm, in]
	φ	direction angle of acting force [°]

Shear stress caused by shearing force F X'

Shear stress caused by shearing force F Y'

where:

A

throat area of the weld [mm 2 , in 2 ]

Shear stress caused by bending moment

- stress x-component

- stress y-component

where:

	M F	bending moment [Nmm, lb in]
	r Y	distance of investigated weld point to the weld group center of gravity in the y-axis direction [mm, in]
	r X	distance of investigated weld point to the weld group center of gravity in the x-axis direction [mm, in]
	J	polar moment of inertia of weld group [mm 4 , in 4 ]

Resultant shear stress in the investigated point of weld

where:

	τ X	shear stress caused by shearing force F X' [MPa, psi]
	τ XM	x-component of shear stress caused by bending moment [MPa, psi]
	τ Y	shear stress caused by shearing force F Y ' [MPa, psi]
	τ YM	y-component of shear stress caused by bending moment [MPa, psi]

5. Calculation of comparative stress σ S

Comparative stress is determined from calculated partial stresses according to the formula:

while for the x-component of stress that actuates in the investigated point of weld, perpendicularly to the weld direction, the α X = α 3 formula is applied. In the opposite case α X = α 4 . The same applies for the y-component of the stress actuating perpendicularly to the weld direction, that is α Y = α 3 or α Y = α 4 .

where:

	τ X	shear stress caused by shearing force F X' [MPa, psi]
	τ XM	x-component of shear stress caused by bending moment [MPa, psi]
	τ Y	shear stress caused by shearing force F Y ' [MPa, psi]
	τ YM	y-component of shear stress caused by bending moment [MPa, psi]
	α 3	conversion factor of weld joint for fillet end weld [-]
	α 3	conversion factor of weld joint for fillet end weld [-]