Structural Engineering & Statics
where the load goes
Connections

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.

Assumes The corner that is not the worst point, The bolt that carries more than its share and The joint that carries nothing until it slips.

15 min read 7 figures The load must go somewhereWhich failure arrives firstDrawing as calculation

A bracket is welded on. Somebody adds two bolts through it, because the fabrication drawing had them and nobody took them off, or because a repair put them there. The connection now has 400 kN of weld and 380 kN of bolt in it, and the obvious question is whether it carries 780.

It carries 400.

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.
Fig. 1 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. A 380 kN bolt in a hole 2 mm larger than itself carries nothing until the hole closes and then rises over several millimetres. A 250 kN preloaded bolt is at its slip resistance in under a tenth of a millimetre. Two of these in one joint are at the same displacement, so the one that gets there first carries the load.

The rule against adding them is in every steel code and it is almost always stated as a rule. It has a derivation, the derivation is a compatibility problem, and the three curves above are the whole of it.

Same displacement, not same force

Two fasteners in parallel across one joint are attached to the same two plates. When the plates move relative to one another, both of them move by that amount. Neither has any say in it.

So the question how much does each carry is not a question about capacities. It is a question about what each curve gives at one displacement, and the answer depends on the shape of the curves rather than on their heights.

That is the same statement this collection makes wherever two things resist in parallel — a wall beside a frame, a stiff spandrel beside a long one, two bolts at different distances from a centroid — and it is usually phrased as stiffness attracts load. Here it goes one step further than that, because one of the two systems has a stiffness of exactly zero over the range that matters.

The sum of two capacities that are never both available. The load a 400 kN weld and a 380 kN bearing bolt carry together, against how far the joint has moved, with the two capacities added marked across the top. Two fasteners in parallel are at the same displacement rather than at the same force, so each carries whatever its own curve gives there. The pair peaks at 400 kN at 0.40 mm, which is 51 per cent of the 780 kN the addition promises — and is the weld's own capacity exactly, because the bolt is still crossing its 2 mm of clearance when the weld lets go.
Fig. 2 The load a 400 kN weld and a 380 kN bearing bolt carry together, against how far the joint has moved, with the two capacities added marked across the top. The pair peaks at 400 kN at 0.4 mm — the weld’s own capacity, exactly — which is 51 per cent of what the addition promises. The bolt is still crossing its clearance when the weld lets go.

The peak of that curve is at the instant before the weld ruptures, and its value is the weld’s capacity plus whatever the bolt has managed to reach by then. That is the general statement, and on a standard hole the second term is zero.

What happens after

The curve does not stop at the peak, and what it does next is the second half of the argument.

Past 0.4 mm the weld is gone and the whole load transfers to the bolt in one step. The bolt is at nothing, so the connection is momentarily carrying nothing at all — which physically means the joint snaps open by the remaining clearance and lands on the bolt, dynamically, with whatever kinetic energy that fall gave it.

A connection whose two fasteners are both fully stressed is not a connection with a reserve. It is a connection with a step in it. The bolt then has to catch a load that has been travelling, and the calculation for whether it can is not a shear check.

That is why the rule is a prohibition rather than a reduction factor. A code could perfectly well say take the weld plus a third of the bolt; what it says instead is that the joint is designed for one system or the other, and the reason is that the failure sequence is not something a partial factor describes.

Removing the clearance does not fix it

The obvious response is that the clearance is the problem, and a fitted bolt in a reamed hole would share properly.

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 0 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 21 times sooner than the bearing bolt does.
Fig. 3 The same three curves with the bolt hole reamed to a fit. The bearing curve now starts at the origin and rises steeply — but it rises over millimetres, because what it is measuring is the bolt shank yielding and the plate crushing locally around it, and neither of those happens in tenths.
Even a bolt with no clearance at all does not catch up. How much of the arithmetic sum of a 400 kN weld and a 380 kN bearing bolt the pair actually reaches, against the clearance in the bolt hole. At the 2 mm a standard hole gives, the pair reaches 51 per cent — which is the weld's capacity and nothing else, because the hole has not closed when the weld ruptures at 0.4 mm. Take the clearance to nothing and it reaches 68 per cent, with the bolt at 35 per cent of its own capacity: a fitted bolt in a reamed hole still cannot reach its strength inside the deformation a weld allows. The clearance makes the rule obvious; removing it does not make the rule wrong.
Fig. 4 How much of the arithmetic sum the pair reaches, against the clearance in the hole, and how much of its own capacity the bolt has reached when the weld ruptures. At 2 mm the pair reaches 51 per cent and the bolt has reached nothing. At zero clearance it reaches 68 per cent and the bolt has reached 35. The clearance makes the rule obvious; removing it does not make the rule wrong.

Sixty-eight per cent, with a fit no ordinary fabrication achieves. The clearance is not the mechanism — it is what makes the mechanism visible. The mechanism is that a bolt reaches its strength through deformation and a weld does not tolerate deformation, and the two are separated by an order of magnitude in the quantity they are both measured in.

This is worth holding onto because it generalises past this pair. Any two load paths whose deformation capacities differ by an order of magnitude do not share, whatever their strengths, and the one that is stiff and brittle governs. A bolt group’s own instantaneous-centre method is the same argument at a smaller scale, and it is why that method is available for bolts and not for welds.

The exception the rule half admits

Preloaded bolts are different, and the difference is exactly the quantity above.

A preloaded bolt does most of what adding the two would claim. The load a 400 kN weld and a 250 kN preloaded bolt carry together, against how far the joint has moved, with the two capacities added marked across the top. Two fasteners in parallel are at the same displacement rather than at the same force, so each carries whatever its own curve gives there. The pair peaks at 587 kN at 0.40 mm, which is 90 per cent of the 650 kN the addition promises — because a preloaded joint reaches its slip resistance in under a tenth of a millimetre, which is inside what a weld will tolerate.
Fig. 5 A 400 kN weld and a 250 kN preloaded bolt. The pair reaches 587 kN of the 650 the addition promises — 90 per cent — because a preloaded joint reaches its slip resistance in under a tenth of a millimetre, which is comfortably inside what a weld tolerates. The two arrive at almost the same time.

A slip-critical joint carries load by friction between clamped plates, and friction needs no movement to develop. The pre-slip stiffness is the elastic shear of the plates themselves, which is very high, so the joint is at its slip resistance almost immediately.

That puts a preloaded bolt on the weld’s own clock rather than on the bearing bolt’s, and the sharing is nearly complete: 90 per cent of the arithmetic sum, against 51 for the bearing case.

Several codes permit exactly this combination and forbid the other, which is the strongest evidence available that the rule is a mechanical statement rather than a blanket caution. What is permitted is a weld sharing with a slip-resistant connection, checked at the serviceability limit where slip is the criterion, and even then with care about the order in which the two were made — because a joint welded after it was preloaded has had heat put into the faying surfaces, and a joint preloaded after it was welded is being clamped across a shrinkage that is pulling the plates together already.

The order of assembly, which is the other half

That last point deserves its own paragraph, because it is the practical version of everything above and it is decided by a person on site rather than by a calculation.

Weld first, then bolt: the weld shrinks as it cools, pulling the plates along the joint, and the bolts are then fitted into holes that have moved. On a long connection they may not line up at all, and the fitter’s response is to ream them — which restores the fit and removes the preload’s faying surface at the same time.

Bolt first, then weld: the bolts are carrying whatever the weld shrinkage wants to do, before any load has been applied. On a preloaded joint that is a locked-in force nobody computed; on a bearing joint the plates simply take up their clearance in the direction the weld pulled, which means the clearance is now on one side and the bolt is already in contact.

That last case is the one where a bolt might genuinely be in bearing from the start, and it is entirely an accident of assembly. It is not a basis for a calculation, and the reason the codes do not offer a partial factor for it is that the factor would be a property of a sequence nobody records.

The same joint doing the other job

None of this applies to a connection where the two systems carry different actions rather than the same one.

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.
Fig. 6 A welded bracket carrying 100 kN offset 150 mm within the plane of its welds. The weld group takes the whole of this — a direct shear and a torsion about its own centroid — and every point of it carries a force in the plane of the plate.

The same bracket also carries a moment about an axis in the plane of its welds, which is a different object again and is resisted by the same weld metal doing something else.

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.
Fig. 7 The same bracket under the out-of-plane eccentricity, where the weld group is in bending about an axis through its centroid. A connection can have both of these and a set of bolts doing something else again — holding a cover plate, resisting an uplift — and nothing above forbids that.

The rule is about two systems resisting one action along one path. A weld carrying a bracket’s vertical shear and bolts holding a horizontal tie in the same connection are two load paths, they are checked separately, and each is complete on its own. What is forbidden is dividing one force between them.

The distinction is easy to state and not always easy to apply, because a connection detailed for one action usually ends up carrying a bit of another. The safe reading is the one the codes take: if a force could go either way, it goes down the stiff path entirely, and the flexible one is not counted at all.

The arithmetic of the three fractions

It is worth putting the three fasteners’ states at one displacement side by side, because the numbers are the argument in its shortest form.

At 0.4 mm of joint movement — the instant before the weld goes — the weld is at 100 per cent of its capacity, the bearing bolt at nothing, and the preloaded bolt at 75 per cent.

Three fasteners, one displacement, three fractions with no relation to one another. Nothing about their capacities produced those numbers; nothing about their materials did either. What produced them is the shape of three curves near the origin, and that shape is set by three completely different mechanisms — elastic shear of weld metal, a hole closing, and friction between clamped plates.

The design consequence is a habit rather than a calculation. When two things resist in parallel, ask what displacement each needs before asking what force each can take. The second question is the one on the drawing and the first is the one that decides.

There is a version of this in nearly every field of the subject and it is usually met as a surprise. A bolt group’s furthest bolt reaches its capacity while the others are at a fraction of theirs, and the group’s real strength depends on whether that bolt will wait. A long bolted joint’s end bolts carry more than its middle ones for the same reason and by the same arithmetic. A cracked reinforced section’s steel and its concrete reach their limits at strains an order of magnitude apart. In each case the question that resolves it is the deformation one.

What a repair does about it

Adding bolts to a cracked weld is a common repair, and the argument above says it does not work as usually imagined.

If the weld is still there and the bolts are added beside it, the bolts are inert until the weld fails. If the weld is cracked and the bolts are added, the bolts are the connection and the weld’s remaining ligament is inert — a small, stiff, brittle path across a joint that now moves millimetres, which will crack the rest of the way on the first significant load.

So the honest versions of the repair are the two extremes. Remove the weld entirely and bolt the connection, sizing the bolts for the whole force. Or repair the weld and leave the bolts out. The middle is not a stronger connection than either end; it is one of the two ends with something extra in it that will break.

Why the rule reads as arbitrary

It is worth asking why a rule with this clean a derivation is almost never derived where it is stated.

Part of it is that the derivation needs a load-deformation curve for each fastener, and load-deformation curves are not what a code carries. A code carries capacities — one number per fastener, obtained by dividing a test result by a factor — and the whole apparatus of design is built on comparing forces with those numbers. A rule about deformation has nowhere to live in a document written entirely in forces, so it arrives as a prohibition with no reason attached.

Part of it is that the reason was known before the curves were measured. The prohibition is older than Crawford and Kulak’s bolt curve, older than any published measurement of a fillet weld’s rupture deformation, and it came out of observing that riveted-and-welded repairs failed in the weld at loads the addition said they should have survived. It was an empirical rule first and became derivable afterwards, which is the usual order.

And part of it is that the rule is nearly always applied in the safe direction anyway. A designer who does not add the two capacities designs the joint for one of them and gets a connection that works. The cost of the rule being unexplained is not usually a failure — it is that the exception gets missed, and the exception is the preloaded case where 90 per cent of the sum was genuinely available and nobody used it.

Four single numbers that are not single numbers

The weld’s rupture deformation is a single number and it is not. A fillet weld’s ductility depends on the direction of the force on it: loaded along its length a weld is roughly three times more deformable than loaded across, at the price of being weaker. So a weld group loaded at an angle has a rupture displacement varying round it, and 0.4 mm is a representative value for a group of the size drawn rather than a property of welds.

The bearing curve is Crawford and Kulak’s fit and it has no derivation. It is a curve fitted to tests, stated in inches, and every bolt-group calculation on this site rests on it. Its shape is what makes the argument here, and its shape is empirical.

The plates are treated as rigid between the two fasteners. They are not: a weld at one end of a plate and a bolt at the other are separated by a length of plate that stretches, so the two are not strictly at the same displacement. On a long connection that is a real effect and it moves the sharing — in the direction of less sharing, because the plate’s stretch adds to the bolt’s displacement demand and not to the weld’s.

And nothing here is a fatigue argument. Under repeated load the question is not which fastener reaches its capacity but which one accumulates damage, and a weld beside a bolt is a stress concentration beside a hole with an entirely different S-N category. That is a different check with a different answer.

A clearance is crossed in an instant, not over a range

The curves are drawn as though the joint moved smoothly, and a bearing bolt’s traverse of its clearance is not smooth. It is a slip: the plates jump, they land on the bolt, and there is a sound. Everything between 0 and 2 mm on those plots happens in an instant under load, and drawing it against a displacement axis makes it look like a process.

The other absence is the sequence. Every one of these figures is a snapshot of a joint at one displacement, and the argument is about what happens as the displacement grows past the weld’s limit — which is a fall rather than a curve, and is the part of the story a load-deformation plot is least able to tell.

The assumption underneath the whole rule

Everything here assumes the two fasteners are in parallel — same two plates, same relative movement, one force divided between them.

That assumption is the thing to check before applying any of it, and it is checked by drawing the free body rather than by looking at the connection. Two fasteners are in parallel if a cut that severs one severs the load path of the other; they are in series if the force goes through both. A weld and a bolt in series share perfectly, because they carry the same force and their deformations add — which is the ordinary case of a bracket welded to a plate that is bolted to a column, and is exactly why that arrangement is the one that gets built.

The one place the sum is allowed

There is a case where a weld’s capacity and a bolt’s may be added, and it is worth naming because it looks like a contradiction and is not.

If the two fasteners are on different planes of the same connection, each carrying the whole force across its own plane, then the connection’s capacity is the smaller of the two rather than the sum — that is series, not parallel, and it is the ordinary case. But if the force is genuinely divided by geometry rather than by compatibility — a bracket welded on one side of a web and bolted to the other, with a load that is delivered half to each by where it sits — then each side carries a known share and each is checked for it.

The distinction is whether the division is known from statics or decided by stiffness. A load delivered half to each face by symmetry is a statics division and the two halves are separate problems. A load delivered to a joint with two fasteners in it is a stiffness division and the stiffer one takes it.

Getting that wrong in the safe direction costs a connection that is twice the size it needed to be. Getting it wrong the other way produces the joint this essay is about, and the failure is not gradual.

Two paths are not two capacities

Later rungs on this anchor: weld group fatigue, where the peak point rather than the average decides the category and where the direction argument disappears. The connected plate’s own flexibility, which is the largest omission in every model above. Welds combined with bolts under a moment rather than a shear, where the two are at different lever arms and the compatibility is a rotation rather than a displacement. And the general shape of all of it — two paths of very different ductility across one joint — which turns up again wherever a stiff repair is added to a flexible structure or a new element is tied into an old one.

The rule has been in the codes since bolted connections replaced riveted ones, and it has been derived considerably less often than it has been quoted. What is worth carrying out of the derivation is not the rule but its reason, because the reason applies in places the rule does not reach: two load paths are not two capacities unless they are ductile enough to wait for one another.

Where this goes next

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. 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. A preloaded joint, before and after it slips. Two preloaded bolts at 137 kN each, on one friction face at μ = 0.5. The joint carries 137 kN by friction with the bolts in tension and not in shear at all; past that it slips into bearing and carries 188 kN with the bolts now in shear. Two different mechanisms, one joint. The joint that carries nothing until it slips Tighten the bolts hard enough and the plates are clamped together with a force nothing applied. The joint then carries shear by friction, the bolts are in tension and not in shear at all, and the load path has nothing in common with the joint it looks identical to. A bolt group under an eccentric load. A 3 by 2 bolt group carrying 100 kN at 150 mm from its centroid, with the resultant force on each bolt drawn to scale, by the elastic vector method. The load is shared equally and the torque is not, so the worst bolt carries 50.37 kN against 16.67 kN of direct shear alone — 3.02 times as much. The bolt that carries more than its share Six bolts, one hundred kilonewtons, and a worst bolt carrying fifty. The load is shared equally and the torque is not, and the second one is invisible on any drawing where the connection is a point. The end bolts do the work and the middle ones very nearly nothing. A lap of 8 bolts at 70 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 1.09 of their nominal share and the middle ones 0.94. 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 0.918, and the end bolt has to slip 1.36 mm before the rest catch up. The bolts that do not share Every bolted connection in this collection has divided a force by a number of bolts. That is right for a short joint and wrong for a long one, and the reason has nothing to do with the bolts — it is that the plates they join are elastic, and stretch by different amounts at different points along the lap.

Named alongside this one

Essays reaching for the same objects. Nobody chose these; they are what the concept index makes visible.

The objects this essay names

Each one links to every other essay that touches it.

BearingBolt groupConnectionDuctilityFillet weldLoad deformationPlastic redistributionPreloadSlip resistanceStiffness attracts loadToleranceWeld group