EngineerBenchCalculating stress in a rectangular weld group
An in-plane force applied away from a weld group's center creates both direct shear and a moment. This model distributes the moment around a rectangular perimeter weld and combines it with the direct components. The highest resultant occurs where those vector contributions reinforce one another.
Describe the actual welded perimeter
Enter the rectangle dimensions, fillet leg size, force components, and moment using a consistent sign convention. The model assumes the specified perimeter is welded and participates in the load. Intermittent welds or an open-sided group need a different geometric model.
Interpret the peak stress within the model
Compare the calculated stress with an appropriate design allowance. The result does not evaluate out-of-plane bending, prying, base-metal failure, or fatigue. It also cannot establish whether the welds were made to the required quality or effective size.
Locating the largest resultant stress
The direct shear components are combined with the moment-induced components at positions around the rectangular perimeter. A point farthest from the center can have a large torsional contribution, but the direct-force direction determines whether the contributions reinforce or oppose each other. The governing resultant therefore requires a vector calculation rather than selecting separate maximum X and Y stresses from different locations.
Keep rectangle width and height aligned with the coordinate axes used for the force components. A change in orientation can change which corner governs even when the total weld length stays the same. Increasing perimeter size changes the group's resistance to moment as well as its throat area. Increasing fillet leg size changes throat area but does not alter the centerline layout. Compare these changes using the full calculation rather than a single proportional rule. The elastic line-weld model assumes the perimeter participates as described; gaps, variable weld size, flexible plates, or out-of-plane loading require a method that represents those conditions.
Formula
Line polar inertia J = (w³+h³)/6 + wh(w+h)/2; torsional line forces = M(−y,x)/J.