Weld Group Stress Calculator

How is stress found in a weld group?

When the load on a connection made of several weld lines does not pass through the centroid of the weld group, the welds carry both the load itself and the twisting moment it creates. The usual hand method pictures the weld as a line whose width is the throat thickness. The load spreads evenly over the throat area, and the moment produces a stress that grows with distance from the centroid and acts at right angles to the radius. The two are added as vectors.

Formula

Direct shear is τ′ = F / A and torsional shear is τ″ = M × r / J. A is the throat area (throat thickness × total length) and J the polar moment of the weld group about its centroid. With one throat size for all lines, J = a × J_u. J_u depends only on the line geometry: (b + d)³ / 6 for an all round rectangle and d (3b² + d²) / 6 for two parallel lines.

Example

A 50 × 50 mm all round weld is made with 5 mm leg fillets, so the throat is 0.707 × 5 = 3.535 mm. A vertical load of 12 kN acts 175 mm from the centroid. Throat area is 3.535 × 200 = 707 mm² and direct shear 12 000 / 707 = 17.0 MPa. J_u = 100³ / 6 = 166 700 mm³ and J = 589 200 mm⁴. At a corner each component of the torsional stress is 12 000 × 175 × 25 / 589 200 = 89.1 MPa. At the corners nearer the load the resultant is √(89.1² + (17.0 + 89.1)²) = 138.5 MPa. The calculator opens with this example and the result agrees with the worked solution in Shigley.

How to use the tool

Enter each weld line by its start point, end point and throat thickness, or pick one of the ready made patterns. Type the load and a point on its line of action. The tool works out the stress at every line end, marks the critical point on the drawing and gives the load per unit length (N/mm) there. The line load is what you need when picking a weld size from a table.

Limits

Only loads in the plane of the welds are covered. For out of plane moments that bend the weld group, the second moment of area is worked out differently. Compare the stress with the weld strength given by your standard. In the simplified method of EN 1993-1-8 that limit has the form f_u / (√3 × β_w × γ_M2): take the factors from the standard. Parent metal strength, weld quality and fatigue are assessed separately.