The hole made bigger so the steel would fit

A hole is made larger than the bolt because the steel has to go together. The pieces were cut to a tolerance, the frame was erected to another, and the bolt has to pass through both plates as they actually arrived rather than as they were drawn. That is a fabrication problem, and it is solved by enlarging the hole.

In an ordinary bolted joint that costs almost nothing. In a joint that carries its load by friction it costs a fixed fraction of the resistance, and the fraction is not derived from anything about the plate.

The hero above is the baseline: four M20 bolts preloaded to 172 kN each, one blasted friction face at μ = 0.5, standard clearance holes. The friction plateau is 344 kN and the joint slips into bearing at 362. The two numbers are close, which is normal and is the whole reason the hole factor matters — a joint designed to slip at 95 per cent of its ultimate load has no room to lose fifteen per cent of anything.

The coefficient that is not a calculation #

The slip resistance is a product of four things and a fifth:

$$F_s = n \cdot \mu \cdot F_p \cdot k_s \cdot \text{faces}$$

Four of those are physical. The number of bolts is a count. The preload is a force the tightening put in and the coating slowly takes out. The friction coefficient belongs to the surface. The face count is geometry.

The fifth is $k_s$, and it is a number from a table. Standard clearance gives 1.0. An oversize hole, or a short slot perpendicular to the load, gives 0.85. A short slot parallel to the load gives 0.76. A long slot perpendicular gives 0.7, and a long slot parallel gives 0.63.

There is no free body behind that 0.85. It is not the ratio of two contact areas, and it does not fall out of any equilibrium statement — which is unusual on a site where a figure is a calculation and every number in one is solved rather than looked up.

What it encodes is a spread rather than a mean. A bolt in an oversize hole sits somewhere in that hole, and where it sits decides how the preload cone reaches the faying surface, how evenly the pressure is distributed across it, and how much of the clamped area is actually in contact. The test data on oversize and slotted joints is not much lower on average than the standard-hole data — it is wider, and a characteristic value taken from a wider distribution is lower. The factor is a statement about scatter dressed as a statement about geometry.

That is worth knowing, because it changes what the factor is doing. It is not describing a mechanism that could be improved by understanding it better. It is pricing an uncertainty that the detail introduced and that nothing on site will resolve.

How the hole was made, which the factor does not ask #

The table has one entry for an oversize hole and does not care how it got that way, and the three ways differ.

A drilled hole is round, its edge is clean, and its axis is normal to the plate. A punched hole is made by shearing a slug out, so it is slightly tapered — larger on the exit face — and its edge carries a zone of cold-worked, torn material a millimetre or two deep. A subpunched and reamed hole is punched undersize and then cut to size, which removes the damaged edge and leaves something close to a drilled hole.

For a bearing joint that distinction matters, because the bolt bears against the edge and a torn edge crushes sooner. For a slip-resistant joint it should not matter at all: the load crosses the interface between the plates, nowhere near the hole.

Except that the punching disturbs the faying surface around the hole. The slug is sheared out with a die pressed against one face, the plate dishes locally, and the region immediately around the hole — which is where the preload’s pressure cone is most concentrated — is no longer flat. On a thick plate the dishing is small; on a thin one it can lift the surfaces apart over a ring several diameters across.

That is a real effect on the quantity the joint depends on, and $k_s$ does not contain it, because $k_s$ is indexed on the hole’s shape and not its manufacture. Codes handle it elsewhere and bluntly — by limiting punching to plates below a thickness, or by requiring subpunching and reaming above one — which is a rule about fabrication standing in for a term that was never written into the resistance.

The long slot, and what it actually buys #

The 37 per cent looks like a penalty for nothing. It is not: the slot buys the ability to assemble the structure at all, and the alternative is not a standard hole — it is a member that cannot be erected.

Where a slot is genuinely load-bearing as a design device is in accommodating movement that is expected. A long span whose supports must take thermal expansion, a cladding rail on a frame that will sway, a bracing member that has to be tuned during erection — each of these needs a connection that is adjustable at one moment and fixed at every moment after.

And that is precisely what a preloaded slotted joint is. It is adjustable while it is snug and fixed once it is preloaded. The slot does not remain a movement allowance in service; the friction closes it.

Which produces the trap this essay exists for. A slotted joint that is preloaded is not a sliding joint, and a designer who has drawn a slot in order to allow movement has drawn a joint that will not move. If movement is wanted, the joint must not be preloaded — which means it is a bearing joint, with the hole factor irrelevant and the oval hole as the governing check instead.

What the slot costs after it slips #

The slip resistance is only half of what the slot changes.

A standard clearance hole slips 2 mm and finds bearing. A long slot in a 20 mm bolt is around 2.5 diameters, so a joint that slips travels perhaps 30 mm before the bolt touches the far end of its slot and starts to carry in shear.

Thirty millimetres of a frame is not a serviceability detail. It is a floor that has stepped, a cladding panel out of line, a crane rail that no longer runs true, and it happens on one load event with no warning and no way back — a joint that has slipped does not slip back, because the plates find a new resting position and the preload holds them there.

So the slot has two costs that are usually quoted as one. The first is 37 per cent of the resistance, which the calculation sees. The second is the consequence of exceeding it, which the calculation does not see at all: the same overload that causes 2 mm of movement in one joint causes 30 in the other, and neither appears anywhere in a slip check.

The face count, which beats the hole #

That figure is the answer to the objection that the hole factor makes slotted preloaded joints impractical. It does not: the arrangement of the plates is a stronger variable than the shape of the hole, and it is free.

A double-lap joint costs one extra plate. In return it doubles the slip resistance, doubles the shear planes so the bearing capacity roughly doubles too, and removes the eccentricity that makes a single-lap joint bend as it loads. It is one of the few changes in connection design that improves every limit state at once.

It also changes which check governs, and that is the part worth reading carefully. In the standard-hole single-face joint the friction plateau at 344 kN sat just under the 362 kN bearing capacity, so slip governed by a hair. In the two-face slotted joint the plateau is above the bearing capacity, so the joint reaches its ultimate limit state without ever slipping — which means the slip calculation, having been the governing check, has become irrelevant.

A designer who adds a cover plate to fix a slip problem may find they have made the slip check redundant rather than satisfied. Those are not the same outcome and the second is better: a joint that cannot slip before it fails has no serviceability limit state to check.

Two checks at two different loads #

The slip check and the bearing check are not two calculations on one load; they are two calculations on two different loads, and the gap between the plateau and the bearing line in every figure here is smaller than it looks for that reason.

The slip check is done at serviceability. Its load combination has no partial factors on the actions worth speaking of, because the question is whether the structure behaves as intended under the loads it will actually see. The bearing check is done at ultimate, where the same actions arrive multiplied by 1.35 and 1.5.

So a joint whose friction plateau is 344 kN and whose bearing capacity is 362 is not a joint with a 5 per cent margin between behaving and failing. The applied load on the left-hand side of those two inequalities differs by roughly 40 per cent, and a joint that just passes its slip check at serviceability will usually be comfortable in bearing at ultimate — or, read the other way, a joint sized for its ultimate load will often fail its slip check by a wide margin.

This is what makes the hole factor bite. Fifteen per cent off the resistance in a check whose applied load is already the unfactored one is fifteen per cent off a margin that was never generous, on the check that governs. The bearing capacity — the number the hole factor does not touch — is the one with the headroom.

It also explains a shape that turns up repeatedly in real design: a joint gets more bolts than the ultimate check needs, and the extra bolts are there for the slip check, which is to say they are there to stop the structure moving rather than to stop it falling down. That is not a strength argument at all, and treating it as one is how the extra bolts get value-engineered out.

The surface still beats the hole #

Set the two variables against each other and the ranking is unambiguous. A long slot on a blasted face carries 216.72 kN. A standard hole on an untreated face carries 137.6. The worst hole with the best surface beats the best hole with the worst surface by 58 per cent.

And the two differ in how they are controlled. The hole is on a drawing, cut by a machine to a stated size, and visible to anybody who looks at the steel before it goes together. The surface class is a specification, achieved by a process, protected between blasting and erection, and invisible once the joint is closed — which is the workmanship risk the rung below this one is about, and it is not made smaller by getting the holes right.

The order to attack a slip problem in, then, is the reverse of the order the code presents it in. Fix the surface first, because it is the largest term and the least reliable. Add a friction face second, because it doubles everything at the cost of a plate. Adjust the preload third. And argue about the hole factor last, because it is the one term in the product that was chosen for a reason that has nothing to do with structure.

Preload, which the hole factor is multiplying #

Every factor in that product multiplies every other, which means the losses compound rather than add. A joint with a long slot, a surface one class below what was specified and a preload that has relaxed by a quarter is not carrying 63 + 60 + 73 per cent of anything; it is carrying 0.63 × 0.6 × 0.73 = 28 per cent of what a nominally identical joint on the drawing was credited with.

That compounding is the argument for treating slip resistance as a serviceability quantity and never as a strength one. The ultimate capacity of this joint is 362 kN whatever happens to the preload, because bearing does not care how tight the bolt is — the shear plane through the bolt and the crushing of the plate in front of it are unchanged.

So the honest statement of what the hole factor does is narrow: it changes the load at which the joint stops behaving as designed, and it does not change the load at which it fails. That is exactly the distinction between the two limit states, and the hole factor lives entirely on one side of it.

What to carry away #

The hole factor prices scatter, not steel. An oversize hole removes almost no material and costs 15 per cent of the slip resistance, because the characteristic value comes from a wider distribution of test results rather than from a smaller contact area.

A slotted preloaded joint does not move. The slot is a fit-up device that the friction locks. What it changes is the distance travelled after slip — 30 mm rather than 2 — and no slip calculation contains that number.

The face count and the surface class both beat the hole. Two faces recover a long slot’s loss and 26 per cent besides; the worst hole on a blasted surface beats the best hole on an untreated one.

And the terms multiply. A slot, a surface one class low and a relaxed preload leave 28 per cent of the design resistance, with the joint looking exactly as drawn.

Where the model stops #

The rising branch is drawn, not solved. Every curve here has an elastic ramp before the plateau that represents the shear stiffness of the plates and the bolts together; nothing on this site computes it, and the figures say so.

Slip is drawn as a single event and it is not. A real joint with four bolts slips progressively as each bolt’s local clamping is overcome, and the plateau is a slightly ragged descent rather than a corner — which is also why a long joint’s bolts do not all reach their limit together.

The friction coefficient is a design class, not a measurement. Class A at 0.5 is a blasted surface tested to a procedure; a real faying surface is somewhere between classes and is not sampled.

External tension is not modelled. A preloaded joint carrying tension as well as shear loses slip resistance as the interface decompresses, roughly as $\mu(F_p - 0.8F_t)$, and the prying force a flange develops is exactly the sort of tension that is not on any drawing.

And fatigue is a separate subject with the opposite conclusion. A preloaded joint is excellent in fatigue precisely because the bolt sees almost no stress range below decompression, so the detail category improves for reasons the slip check never mentions.

The ladder from here #

Later rungs on this anchor: how a preload is actually delivered and measured, and why torque is the worst of the four available methods. The decompression calculation for a joint in combined shear and tension. Slip-resistant joints in seismic design, where the slip is the energy dissipation and the hole is a friction damper. Packing and its effect on the shear plane’s position. And the long-term question — a coated faying surface whose friction coefficient is a property of a paint system that will be reformulated before the structure is thirty.

The hole factor is one of the oldest numbers in bolted connection design and one of the least derived. It entered the American specifications in the 1970s from tests on joints with oversize and slotted holes carried out because fabricators wanted the tolerance and nobody could say what it cost. The answer that came back was a ratio of characteristic values, and it has been a ratio of characteristic values ever since — a number that says how much less certain a result became, written in the same table as numbers that say how much force something carries.