The hole that goes oval, and the one that tears to the edge

Two pieces of plate, overlapped, with a bolt through both. Pull them apart.

Something has to give, and there are more candidates than the obvious one. The bolt can shear across the interface between the plates. The plate can tear across its net section. A block can come out along the bolt line. Or — and this is the one that usually happens first — the bolt can simply push its way through the plate, locally, without anything else in the connection noticing.

Two failures with one variable between them #

The corner in that curve separates two genuinely different things, and the useful move is to think of each as its own mechanism rather than as two branches of a formula.

Tear-out. The bolt is close to the end of the plate. The material between the bolt and the end is a short block, bounded by two shear planes running from the sides of the hole to the edge, and the bolt shoves it out. This is block shear at the smallest possible scale: one bolt, no tension plane, and a block a few tens of millimetres long. The capacity is proportional to the amount of material in front, and therefore to the end distance.

Bearing. The bolt is far from the end. There is no block to push out, so the plate has to fail by crushing: the material immediately in front of the hole is compressed until it yields, flows sideways, and the hole ovalises. That capacity does not depend on the end distance at all, because the material doing the work is right at the hole.

One geometric variable — the end distance — decides which. And it is worth noticing what is not on the list of things that decide it: the bolt grade appears nowhere in either mechanism. This is a failure of the plate, and a stronger bolt in a weaker plate simply makes a neater hole.

Where the numbers actually land #

The reason this essay comes early in the field is that bearing is usually the limit, and the usual expectation is that bolts are.

An M20 grade 8.8 bolt in single shear carries about 94 kN. The plate calculation, for the same bolt in a 10 mm plate:

At the minimum end distance the plate gives at a third of what the bolt could carry. It takes 72 mm of end distance for the plate to catch the bolt up, and by then the connection is considerably longer than anybody would have drawn it.

That inversion — plate first, bolt second — is the normal case in ordinary steelwork, and it is why bearing-type connections are so often controlled by plate thickness and edge distances rather than by bolt selection. Choosing a higher bolt grade in a connection that is bearing-critical does nothing whatever.

Two plates, and which one is being checked #

There is a bookkeeping trap in this check that is worth naming before the mechanics, because it catches people who understand the mechanics perfectly well.

A bolt passes through two plates, or three. Every one of them bears, and every one of them has its own thickness, its own steel grade, its own end distance and its own edge distance. The bearing check is a check on each ply separately, and the connection’s bearing capacity is the smallest of them.

That sounds obvious and it is routinely got wrong in one specific way: the plies are usually different. A beam web is 8 mm and the fin plate it bolts to is 10 mm; a bracing member’s leg is 12 mm and the gusset is 15 mm. Checking the thicker one, because it is the one the connection is named after, misses the governing ply by exactly the ratio of the thicknesses.

The end distances differ too, and they differ in a direction that is easy to invert. On a fin plate the end distance is measured to the edge of the plate; on the beam web it is measured to the end of the beam, which may be a long way away — so the same bolt can be a tear-out case in one ply and a bearing case in the other, at the same instant, under the same load.

There is a saving grace, and it is the load path. In double shear the bolt bears on the middle ply once with the whole load and on the two outer plies with half each, so the outer plies are usually comfortable even when they are thinner. In single shear there is no such relief, and single shear is what most beam-to-column connections use.

Where the corner comes from #

The plateau in the curve is a cap on a coefficient, and the cap is not arbitrary.

Write the capacity as

$$P = \alpha\, f_u\, d\, t \qquad\text{with}\qquad \alpha = \min\!\left(\frac{e_1}{3(d+2)},\ 2.5\right)$$

The first branch is the tear-out mechanism reduced to a coefficient. The second is a cap, and the cap exists because past a certain end distance the tear-out block has become long enough that shearing it out costs more than crushing the material at the hole — so the crushing mechanism takes over and the capacity stops rising.

The number 2.5 is where those two costs cross, measured. There is no reason it should be a round number and it is one because it has been rounded; what matters is that it is a crossover between mechanisms rather than a limit on either.

The $3(d+2)$ in the denominator is the hole diameter times three, which is the length over which the tear-out block’s shear planes are taken to act. So the corner lands at $e_1 = 2.5 \times 3 \times (d+2) = 7.5 d_0$ — 165 mm for a 22 mm hole, which is eight bolt diameters and far beyond any end distance anybody details.

Which means the plateau is almost never reached. Real connections live on the ramp, at $\alpha$ between about 0.4 and 1.0, and the mechanism is tear-out rather than bearing in nearly every case where the calculation is called a bearing check. The name of the check is about the branch nobody uses.

Why the end distance is a minimum rather than a choice #

A table of minimum edge and end distances is one of the first things a steelwork detailer learns and one of the least examined. The minimum is usually $1.2 d_0$ — 26.4 mm for a 22 mm hole — and the reason it exists is not the capacity calculation above.

It exists because the calculation stops being trustworthy below it. The tear-out model assumes the block has enough material to shear rather than to split, and assumes the plate edge has not been damaged by the flame cut or the shear that made it. Below about $1.2 d_0$ neither assumption is safe, and the failure becomes a splitting one whose capacity is not a straightforward function of anything.

So the minimum is a validity limit on the model, not a design capacity. Detailing to the minimum is not detailing to a rule; it is detailing to the last point at which there is a rule.

That distinction has a practical edge. When a connection at minimum end distance fails a bearing check, the instinct is to add a bolt. Increasing the end distance is usually cheaper — a longer plate rather than an extra hole — and the capacity is linear in it right up to 165 mm, which is the best exchange rate available anywhere in this field.

The one connection failure that is reliably ductile #

Bearing has a property that almost nothing else here has, and it is worth more than its capacity.

When a plate bears, it does not fracture. The hole ovalises: the material in front of the bolt yields, flows, and the bolt moves. That movement can reach several millimetres before anything separates, and while it is happening the bolt continues to carry its load.

Which makes bearing the mechanism that supplies the ductility everything else in this field quietly depends on:

• the instantaneous centre method for eccentric bolt groups assumes bolts redistribute as they deform, and bearing deformation is where most of that deformation comes from;
• the block shear equation adds two planes at different strains, which needs the connection to deform without coming apart;
• any plastic distribution of forces between bolt rows in a moment end plate needs the same thing.

So a connection designed to be bearing-critical is designed to fail gently, and one designed to be bolt-shear-critical is not — a bolt shears suddenly, with no warning and no redistribution. That is a deliberate design choice available in this field and rarely stated as one: make the ductile mechanism the weakest, exactly as a plastic hinge is preferable to a buckle in a member.

What ovalling costs, and why it is checked twice #

The ductility above comes at a price, and the price is a displacement rather than a strength.

A hole that has gone oval is a joint that has moved. A bearing-type connection detailed to its minima can accumulate several millimetres of slip per joint at working load — clearance first, since a 20 mm bolt sits in a 22 mm hole and has 2 mm to travel before it touches anything, then ovalling on top of that.

For a beam-to-column connection that is invisible. For a bracing system it is not: a brace that has to take up 2 mm of clearance at each end before it does anything has a stiffness far below what its cross-section says, and a frame relying on it to control sway may not be doing so. That is the same failure of intuition the deflection field warns about throughout — a member with ample strength and inadequate stiffness — arriving through the connection rather than through the member.

Which is why the same joint is checked twice, at two limit states, and the two checks look at different things:

• at the ultimate limit state, whether the plate has the capacity computed above;
• at the serviceability limit state, whether the movement is acceptable — and if it is not, whether the joint should be preloaded so that it does not slip at all.

Long joints, and where the equal-share assumption breaks #

There is a second-order effect worth knowing because it is invisible in every calculation above.

A row of bolts in a long lap joint does not share load equally, even under a concentric load. The plates stretch between bolts, so the bolts at the ends of the row take more than those in the middle — the same shear lag logic as an angle connected through one leg, applied along a joint rather than across a section. For a joint under about 15 bolt diameters long, bearing deformation redistributes the difference away and equal sharing is a good assumption. Past that, it does not, and codes apply a reduction factor.

The redistribution that saves the short joint is exactly the hole-ovalling above. The end bolts reach their bearing capacity, their holes deform, and load transfers inward. So the ductile mechanism is doing structural work that the equal-share assumption takes credit for without naming.

That is worth holding on to as a general shape: an assumption of equal sharing is always a claim about ductility, whether it is bolts along a joint, bolt rows up an end plate, or fibres across a section.

The one place a stronger steel helps #

Almost every essay on this site so far has found geometry beating material, and this one has been no exception: the bolt grade is absent from both mechanisms, and the end distance is worth more per millimetre than anything else available.

There is one exception in the formula and it is worth flagging because it runs the other way. The capacity is $\alpha f_u d t$, and the strength in it is the ultimate strength rather than the yield strength. Both mechanisms are failures of separation rather than of first yield — a channel shears out, or the material in front of the hole is crushed past yielding until it flows — so it is $f_u$ that appears, and $f_u$ is a property a higher grade genuinely improves.

That is a rarer situation than it sounds. Deflection is governed by $E$, which no grade changes. Buckling is governed by $EI/L^2$, which no grade changes. Fatigue is governed by a detail category, which no grade changes. Bearing is one of the few checks on a steel structure where specifying S355 instead of S275 buys a proportionate improvement — 14% here, from 430 to 490 N/mm² — and it does so without the usual catch.

The catch it does have is elsewhere: a higher grade raises the yield-to-ultimate ratio, which moves the net section check towards governing. The connection gets better at bearing and worse at rupture, in the same change.

What to take from it #

One geometric variable decides between two mechanisms. Below the corner the bolt tears a channel to the end and the capacity is proportional to the end distance; above it the plate crushes and the end distance is irrelevant. Real connections are always below the corner.

The plate is usually the limit, not the bolt. A third of the bolt’s shear capacity at minimum end distance, in the commonest configuration in steelwork.

The minimum end distance is a validity limit rather than a capacity. It marks where the model stops being trustworthy, not where the plate stops being adequate.

And this is the ductile one. A hole that goes oval is a connection giving warning and redistributing load, and several of the calculations elsewhere in this field are quietly relying on it having done so.