EngineeringMechanical EngineeringPart 14 of 15
Welded Joint Design
Treat a fillet weld as a line with no thickness and the algebra collapses. Section properties become geometry alone, and the weld size falls out at the end instead of being guessed at the start.
- Butt vs fillet
- Throat = 0.707 s
- Weld as a line
- Vector combination
Executive summary
A butt weld made at full penetration, running the full width of the plate, with a rod at least equal in strength to the parent metal and executed by a competent welder to correct procedure, can be assumed to be at least as strong as the unwelded plate. A good butt weld will break in the plate, not the weld — so there is nothing separate to design, and the assembly is treated as one continuous plate.
A fillet weld is different. Its size need not match the plate, it need not run the full length, and it is designed on the assumption that it fails in shear across the throat for any direction of applied load.
Fillet weld geometry and allowable stress
- s
- leg length — this is what is specified on the drawing
- t
- throat thickness — this is what carries the stress
- Weld both sides wherever access permits. A single-sided fillet on a plate in bending doubles the stress and introduces an eccentricity that was never in the calculation.
- For long joints, intermittent welds are preferable to a continuous run — less heat input, less distortion and often less weld metal for the same capacity.
Two methods, one preferred
Conventional method
The weld is treated as a component with a stress area equal to throat thickness multiplied by weld length. Stress is force divided by that area. Simple for direct loads, awkward for everything else, because the section properties change with every trial weld size.
Weld as a line
The weld is treated as a line of zero thickness. Line stress is force divided by weld length, in newtons per millimetre. Section properties become pure geometry, independent of weld size — and the throat thickness falls out at the end by dividing line stress by allowable stress.
For simple direct loads the two methods are equivalent and give the same answer. The line method earns its keep the moment bending or torsion appears, because the second moment of area or polar moment would otherwise change with every trial weld thickness — forcing a trial-and-error solution where a direct one is available.
Because the weld is treated as a line, the section modulus of a weld group has units of mm2 rather than mm3, and the polar moment has units of mm3 rather than mm4. Line stress is not a true stress — it is force per millimetre of weld length.
Bending and torsion by the line method
- Z
- section modulus of the weld group treated as a line, mm2
- J
- polar moment of the weld group treated as a line, mm3
- r
- distance from the weld group centroid to the point being checked
- L
- total weld length, mm
Line section properties for standard weld configurations — a single line, parallel lines, a rectangle, an L shape, a channel shape, a full box — are published as closed-form expressions in terms of the weld lengths b and d. They are used directly; nothing is integrated at the desk.
Locating the centroid
The centroid of a weld group is found exactly as for any area: break the shape into components, take moments about a reference axis, and equate to the total area moment. Treating each weld as a narrow line of unit thickness, an individual weld contributes no moment about its own longitudinal axis.
For b = 50 mm and d = 30 mm this gives a centroid 5.625 mm down and 15.625 mm across from the corner — and it is that point, not the geometric corner, about which the bending or torsional moment must be taken.
Worked example
A steel bar is welded all round to a base plate. A variable load of maximum 10 kN acts vertically upward at the centre of the bar. The steel yields at 220 MPa in tension and a safety factor of 3 is required.
By the line method
The conventional method gives an identical throat thickness, as it must for a direct load. The calculated leg of 1.15 mm is well below the smallest practical fillet, so the weld is specified at a preferred size — the joint is governed by minimum practical weld size, not by stress.
Now tilt the load
If the same 30 kN design load acts at 30 degrees to the horizontal, it resolves into vertical and horizontal components of 15 kN and about 26 kN. Each produces a direct line stress. The horizontal component also produces a bending moment about the weld group centroid, and the resulting bending line stress — obtained from the appropriate line section modulus — can be several times the direct stresses.
The critical point is the corner of the weld group furthest from the centroid on the tension side, where bending line stress is maximum and adds directly to the direct stress. Combine the stresses vectorially at that point — not at the centroid, and not by averaging around the group.
Design checklist
- Butt welds confirmed as full penetration, full width, with matching or overmatching electrode.
- Fillet weld size specified as leg length, not throat thickness.
- Calculated leg rounded up to a preferred size.
- Allowable stress derived from the electrode class, with a design factor added for dynamic loading.
- Welds placed on both sides where access allows.
- Intermittent welds considered for long joints to limit heat input and distortion.
- Weld length calculated excluding weld thickness at corners.
- Weld group centroid located before taking moments.
- Line section modulus and polar moment taken from the correct configuration.
- Line stresses combined vectorially at the most highly stressed point in the group.
- Weld symbol, size, length and intermittent pitch fully detailed on the drawing.
- Welding procedure and welder qualification specified for load-bearing joints.