Structural Engineering & Statics
where the load goes
Concept

Weld group — where it appears

A set of weld runs treated as one section resisting a force and a moment about their own centroid. The throat stress is a distribution round the group rather than a total divided by a length, and the peak is at the greatest radius from the centroid.

Named by 8 essays across one field — each of them below, with the objects they name alongside it.

Throat stress round a fillet weld group. A c shape weld group carrying 100 kN at 150 mm from its centroid. The peak throat stress is 0.88 kN per mm of throat, at (79.5, -100); the worst point at maximum radius from the centroid carries 0.88. Checking by radius is right here, and points at identical radius differ by a factor of 1.

The corner that is not the worst point

Check the point furthest from the centroid. It is the standard rule for a weld group under an eccentric load, it is exactly right for some shapes, and for others it misses the peak by sixteen per cent — or picks one of four points it cannot tell apart whose stresses differ by two thirds.

connections · Weld group The end bolts do the work and the middle ones very nearly nothing. A lap of 10 bolts at 75 mm pitch transferring 800 kN between two plates, with the force each bolt actually carries drawn above it and the flat line a division by the bolt count would have given drawn behind. The end bolts carry 1.16 of their nominal share and the middle ones 0.89. The reason is not in the bolts: at the leading end the first plate is carrying everything and the second nothing, so the two strain at different rates and the slip between them is largest there. In the middle they strain alike, there is almost no slip, and a bolt with no slip across it transfers almost no force. The mean over the worst is 0.861, and the end bolt has to slip 1.16 mm before the rest catch up.

The joint that has to be as good as the member

A splice exists because members come in lengths and structures do not. It has to deliver the same force, at the same stiffness, in the same distribution across the section, through a discontinuity — and each of those three requirements is met by a different feature of the detail, with the third one usually left to look after itself.

connections · Splice Throat stress round a fillet weld group. A l shape weld group carrying 150 kN at 200 mm from its centroid. The peak throat stress is 2.17 kN per mm of throat, at (139.53, 100); the worst point at maximum radius from the centroid carries 1.99. Checking by radius is wrong here by 9.17%, and points at identical radius differ by a factor of 1.

The radius rule, and where it fails

A weld group under an eccentric load is checked at the point furthest from its centroid, on the reasoning that the stress from the twist grows with the radius. That reasoning ignores the direction the two stresses point in, and for one common shape it misses the peak by nine per cent.

connections · Weld group Force and capacity round a weld group, which do not vary together. Utilisation round the c shape group under 100 kN at 150 mm, walked from one end of the weld to the other, with the force scaled onto the same axis for comparison. The capacity is 1460 N/mm where the force runs along the weld and 1789 where it runs across it — √1.5 more — so the utilisation is not simply the force in different units. The worst point is at 47 degrees to the weld, where the capacity is 1612 N/mm, and the group carries 182 kN against the 165 the along-the-weld value would allow.

The weld that is stronger where it is pulled

A fillet weld pulled across its axis is √1.5 stronger than the same weld pulled along it. On a group under an eccentric load the direction of the pull varies from point to point, so the capacity does too — and the gain that follows is worth twenty per cent at one eccentricity and nothing at all at another.

connections · Weld strength The whole line works, and the axis is not a choice. A weld group 200 mm deep carrying 15 kNm about an axis in its own plane, together with 100 kN of vertical shear. The bending force per unit length runs linearly from 1125 N/mm at one extreme to the same the other way at the other, through zero at the group's own centroid — and the centroid is where the neutral axis is because a weld carries compression across its throat as readily as tension. The 250 N/mm of shear runs along the weld and is uniform over the whole 400 mm, so the two components are perpendicular to one another and are combined on the throat rather than added as vectors in the plane.

The eccentricity at right angles to the drawing

A bracket's load stands off the plane of its welds as well as being offset within it, and the second eccentricity produces a completely different object — bending about an axis through the group rather than torsion about a point in it. The weld line has no compression zone to argue about, so its neutral axis is its own centroid, and the whole length works.

connections · Weld group Three fasteners, three completely different clocks. What each of three shear fasteners carries against how far the joint has moved. A 400 kN fillet weld is linear to 0.4 mm and then gone — it is stiff and it is not ductile. A 380 kN bolt in a hole 2 mm larger than itself carries nothing until the hole closes and then rises over several millimetres of hole elongation. A 250 kN preloaded bolt is at its slip resistance in under a tenth of a millimetre and holds it until it slips. Two of these in one joint are at the same displacement, so the one that gets there first carries the load — and the weld gets there 23 times sooner than the bearing bolt does.

Two fasteners that never arrive together

Every steel code forbids adding a weld's capacity to a bolt's in one shear joint, and states it as a rule rather than deriving it. It is derivable. Two fasteners in parallel are at the same displacement rather than the same force, and a weld has ruptured at four tenths of a millimetre while a bolt in a standard hole has not yet touched the side of it.

connections · Weld group Where each check bites. The c shape group with a 5.0 mm throat drawn to scale, loaded 1 mm from its vertical run. Offset from each weld, the use of each point: solid for the static directional check, dashed for fatigue at 2 × 10⁶ cycles, each scaled to its own worst point, which is marked. The static check's worst point is where the force runs most nearly along a weld; the fatigue check's is where it runs most nearly across one. Here the two checks are governed at different points, and a fatigue check made only at the static peak allows a load range 2.25 times the group's.

Strongest across, and first to crack across

A fillet weld pulled across its length is √1.5 stronger than one pulled along it, and every static check of a weld group uses that. In fatigue the same two directions are rated the other way round: the part of the force across the weld is checked against a detail category of 36 and the part along it against 80. The point of a group that governs the static check need not govern the fatigue one, and checking fatigue there can allow more than twice the load range the weld will take.

connections · Weld group A plate pulled off an unstiffened flange. Looking down the column at a 250 × 20 mm plate on a 300 × 19 mm flange with a 11 mm web and 27 mm root radii, the plate pulled away from the flange. Shaded on the plate's welded edge: the force per millimetre of weld while everything is elastic, 47% of it entering over the web and its root radii and peaking at 2.67 times the uniform value at the toe of the radius. Dotted: the uniform force P/bp a rigid flange would give. Dashed: the same force spread over the effective width EN 1993-1-8 gives the joint, 191 mm — a plastic width, 2.8 times the 69 mm the elastic share fits at the web's average.

A quarter of the weld takes half the pull

A beam flange welded straight on to an unstiffened column flange is checked with an effective width of 191 mm out of 250. While the joint is elastic the plate's force does not use anything like that width: 47 per cent of it goes through the 65 mm over the web, and the flange has already yielded at 30 per cent of the force the rule allows. The rule's width is a plastic width, and the full-strength weld it insists on is what lets the joint get there.

connections · Weld group

Named alongside it

The objects these essays reach for when they reach for this one.

Fillet weldEccentricityBolt groupConnectionDuctilityPlastic redistributionThroat stressCentroidFree bodyPolar second momentPreloadTorsion

All concepts