How this calculation works
An in-plane force applied away from a weld-group centroid creates both direct shear and a twisting moment. The elastic line method combines those vector contributions along straight weld segments. This page exposes the centroid, throat area and endpoint stresses.
A = tΣL; qx = Fx/ΣL − M(y−cy)/Jline; qy = Fy/ΣL + M(x−cx)/Jline; τ = |q|/tA worked example
Two vertical weld lines, each 100 mm long and separated by 100 mm, have centroid (50, 50) mm. With a 5 mm throat their total effective area is 1000 mm². A direct 10000 N y force and zero centroid moment give 10 MPa everywhere.
Good to know
Uniform throat and straight-line elastic group theory only. Overlapping lines should not be entered twice. Out-of-plane loads, weld defects, fatigue, local plate behavior and code resistance checks are excluded; this page does not choose weld size.
Reference: Union College — eccentric weld shear lecture (opens in a new tab) ↗
What this model answers
An in-plane force applied away from a weld-group centroid creates both direct shear and a twisting moment.
The elastic line method combines those vector contributions along straight weld segments. This page exposes the centroid, throat area and endpoint stresses.
The Plane stress principal stresses and Mohr circle calculator transforms local stress components. First obtain the correct weld-group force and moment distribution before interpreting a local state.
Keep the input conventions consistent
Coordinates describe weld centre lines in one plane.
Throat thickness is the effective throat, not the fillet leg dimension. Enter the signed moment about the computed group centroid; if the force is eccentric, calculate and include its moment rather than assuming the page knows its application point.
Read the result carefully
The polar line moment includes both each segment’s offset from the centroid and its own length contribution.
Uniform direct shear is then added vectorially to moment-induced shear. The largest endpoint resultant is the maximum on a straight segment in this affine model.
Work through the numbers
Two vertical weld lines, each 100 mm long and separated by 100 mm, have centroid (50, 50) mm.
With a 5 mm throat their total effective area is 1000 mm². A direct 10000 N y force and zero centroid moment give 10 MPa everywhere.
Where the calculation stops
Uniform throat and straight-line elastic group theory only.
Overlapping lines should not be entered twice. Out-of-plane loads, weld defects, fatigue, local plate behavior and code resistance checks are excluded; this page does not choose weld size.
A few questions, answered
Does the page add an eccentric moment automatically?
No. Enter the complete signed moment about the group centroid, including force eccentricity where applicable.
What should I change in the comparison?
Add a centroid moment and inspect endpoint force-vector combinations.