Fillet Welds Loaded Perpendicular to the Plane of Part Joins
Standard Calculation Procedure
1. Common solution for combined loading
Loading in the plane perpendicular to the weld plane induces a tensile or pressure stress σ in the weld.
Normal stress caused by axial force F Z
where:
F Z | axial force [N, lb]. | |
A | throat area of the weld group [mm 2 , in 2 ]. |
Normal stress caused by bending moment M
where:
Total normal stress
σ = σ F ± σ M [MPa, psi]
where:
σ F | normal stress caused by the axial force F Z [N, lb] | |
σ M | normal stress caused by the bending moment M [mm, in] |
Loading in the weld plane induces a shear stress τ in the weld:
Shear stress caused by shearing force F Y
where:
F Y | shearing force [N, lb] | |
A | throat area of the weld group [mm 2 , in 2 ] |
Shear stress caused by torsion moment T
- x-component of stress
- y-component of stress
where:
Total shear stress
for circular weld:
for other welds:
where:
τ XT | x-component of shear stress caused by torque T [MPa, psi] | |
τ Y | shear stress caused by shearing force F Y ' [MPa, psi] | |
τ YT | y-component of shear stress caused by torque T [MPa, psi] |
Resultant shear stress in the investigated point of weld
where:
| σ | total normal stress [MPa, psi] | |
| τ | total shear stress [MPa, psi] |
2. Loading with bending force F Y
For calculation purposes, the bending force can be substituted by the combination of shearing force F Y acting in the weld plane and the bending moment M acting in the plane perpendicular to the weld plane. Then the stress in the weld can be calculated using the previously mentioned procedure.
The bending moment is defined by a formula:
where:
F Y | shearing force [N, lb] | |
e | arm of bending force [mm, in] | |
u | constant | |
- for calculation in metric units u = 1000 | ||
- for calculation in English units u = 12 |
3. Loading with common force F Y
For calculation purposes, the common force F can be substituted by the combination of shearing force F Y acting in the weld plane with the axial force F Z and the bending moment M acting in the plane perpendicular to the weld plane. Then the stress in the weld for so defined loading can be calculated using the above mentioned procedure.
The particular components of the loading are defined by formulas:
- bending moment
- axial force
F Z = F cos φ [N, lb]
- shearing force
F Y = F cos φ [N, lb]
where:
Method of Comparative Stresses
1. Common solution for combined loading
Compared with the standard calculation method, the method of comparative stresses approaches a different way to calculate stresses caused by the axial force or bending moment that actuate in the plane perpendicular to the weld plane. Generally the stress in fillet welds has normal and tangential components. The method of comparative stresses is based on the fact that the shear strength of weld metal is lower than the tensile strength. To simplify the calculation, weld joints are only checked for shear stresses. But the calculation method is the same as in the standard calculation method. Used calculation formulas are also similar.
Loading in the perpendicular plane to the weld plane:
Shear stress caused by axial force F Z
where:
F Z | axial force [N, lb]. | |
A | throat area of the weld group [mm 2 , in 2 ]. |
Shear stress caused by bending moment M
where:
Loading in the weld plane:
Shear stress caused by shearing force F Y
where:
F Y | shearing force [N, lb] | |
A | throat area of the weld group [mm 2 , in 2 ] |
Shear stress caused by torque T
- stress x-component
- stress y-component
where:
Total shear stress in the investigated point of weld
where:
2. Calculation of comparative stress σ s
The 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 .