The joint that has to be as good as the member

A structure is continuous and its members arrive on lorries. Somewhere along every long member there is a place where two pieces were joined, and the job of that place is to be invisible: to deliver the same force, in the same distribution, at the same stiffness, as the material it replaces.

Three requirements, and they are met by three different features of a detail — a division that a connection which is not a point makes for joints in general and that a splice makes unusually sharply, because a splice has no other job. The first is what gets designed. The second is what gets assumed. The third is what nobody writes down, and the order in which they are usually discovered is the reverse of the order in which they matter.

Which free body produced the number #

Cut across the splice and take one plate. The force in it has to be handed to the other plate through the fasteners, and how much each fastener hands over is decided by compatibility rather than by equilibrium — equilibrium only says the total.

Follow the two plates along the lap. At the leading end, the first plate carries the whole force and the second carries nothing, so the first is stretched and the second is not, and the relative slip between them is at its largest. In the middle both plates carry about half, they strain alike, and the slip between them is nearly zero. A fastener transfers force in proportion to the slip across it, so the end fasteners work hard and the middle ones barely work at all.

How badly depends on how long the lap is, and the shortest lap is the control that says so. Four bolts at the same pitch is a joint 225 mm long, and over 225 mm the two plates have barely had room to strain differently at all.

That is the bolts that do not share and it is the single most important fact about a splice. It makes the connection’s efficiency a function of its length, which is a quantity no member calculation contains.

At ninety diameters of joint length the end bolt carries 2.19 times its nominal share. The reduction that standards actually apply is milder than the elastic curve, and the gap between the two is exactly the ductility the connection is being asked for: the end bolt yields in bearing, stops taking more, and passes its share inwards. A splice made with fasteners that cannot do that — a fitted bolt, a bonded joint, a brittle weld — has to live on the elastic curve.

The section that is left #

The second requirement a splice has to meet is that the pieces it is made of are weakened by the holes it needs.

The tear that goes diagonally is the essay about that construction. Its consequence for a splice is a familiar tension: staggering the holes recovers net area and lengthens the joint, which costs efficiency by the argument above. The two effects pull in opposite directions and the optimum is short and staggered — which is also the arrangement hardest to fit a spanner into.

The third reduction is the one that is really about distribution. Connect an angle through one leg and the force arrives on one side of the section; the other leg only picks up its share after the force has spread into it, and over a short connection it never fully does. On a 150 × 90 angle bolted through its long leg the centroid sits 20.65 mm from the connected face, so over a 150 mm connection the shear lag factor is $1 - 20.65/150 = 0.862$ and 13.77% of the net area is not working. The remedy is a longer connection, which costs efficiency again — the same trade an angle that uses half of itself is about.

Three reductions, all geometric, all interacting, and none of them a property of the member being spliced. Together they mean a splice made of the same material and the same thickness as the member it joins is not as strong as it, and the shortfall is between a tenth and a third depending on nothing but how the holes were arranged.

Matching the section, not the force #

The requirement that gets least attention is that a splice should deliver the force to the same parts of the section it came from.

A beam’s moment is carried mostly by its flanges. A splice made with a single deep web plate carrying the whole moment delivers it to the web instead, and the force then has to travel from the web into the flanges through a length of member — a redistribution over about a member depth, with shear stresses in the web that the member calculation never contained.

The usual detail therefore splices flange to flange and web to web, with the flange plates sized for the flange’s own share of the moment ($M I_f/I$, roughly $M$ times 0.85 on a rolled beam) and the web plate for the shear plus the web’s small share. That looks like a decomposition made for convenience and it is a requirement: a splice reproduces a stress distribution, not just a resultant.

The same argument decides how a welded splice is made. A full-penetration butt weld reproduces the parent section exactly and needs no argument at all; a fillet-welded lap does not, and its stress distribution has to be checked round the group rather than divided by a length.

There is a version of the same failure the lap itself can be made to show. Every distribution above assumed the two plates either side of the joint were equally stiff, which is what makes the bolt forces symmetric about the middle. Splice plates half the axial stiffness of the member are perfectly ordinary — a single cover plate on one face, or covers sized for the force rather than for the section — and that asymmetry goes straight into which bolt is worst.

That is the distribution requirement showing up inside the strength check rather than beside it. A splice plate chosen by area has changed the load path within the joint, and the bolt that fails first is at the end nobody was watching.

Slip, which is the stiffness requirement #

The second of the three requirements is that the splice should not change how the member behaves, and for a bolted joint that is a question about slip.

A joint in clearance holes has to travel the clearance before its bolts bear. Two millimetres per joint sounds negligible and is not, because a bracing system may contain several in series and the slip is a rigid-body movement that no stiffness calculation contains. A joint that carries nothing until it slips is the essay about the mechanism.

The two mechanisms are worth reading as a pair. Preloaded, a joint of eight bolts at a friction coefficient of 0.5 carries 688 kN by friction, with the bolts in tension and not in shear at all. Slipped, the same eight bolts carry 250 kN in bearing, now in shear — a different mechanism, a different capacity, and a different stiffness. One joint, two structures, with the transition at a load that depends on a coefficient of friction and a bolt tension nobody will ever measure again. Which of the two the structure is in at any moment is not recorded anywhere, and the only way to find out is that it has already happened.

There is a second slip in the same joint and it is not a clearance. The bolt forces even themselves out only because the fasteners themselves deform: on the ten-bolt lap the end bolt has to move 1.16 mm relative to the plates before the middle bolts pick up their share. A fastener that will not move that far does not get an even distribution. It gets the elastic one.

That figure is the reason a splice is not made stiffer by making its fasteners stiffer. Stiffness across the joint is bought with preload and fit, which act on the whole faying surface; stiffness in the fasteners is bought at the cost of the sharing, and the two are opposite operations that a drawing does not distinguish between.

What a splice costs, counted properly #

The three requirements have three prices, and it is worth putting them beside each other because they are paid to different people.

Strength is paid in bolts and plate — the visible cost, and usually the smallest. A flange splice on a rolled beam is a few kilograms of plate and a dozen bolts.

Stiffness is paid in preload and in fit. Preloading eight bolts means torque control or turn-of-nut, an inspection regime, and faying surfaces prepared to a specified condition — which is site labour rather than material, and which is where most of a splice’s real cost sits.

Distribution is paid in the arrangement, and it is nearly free. Splicing flange to flange rather than through a single deep plate costs nothing but the decision to do it.

The ordering explains a persistent pattern in construction. Splices get value-engineered by removing preload, because preload is the expensive part and the strength check passes without it. What is lost is the stiffness requirement, which appears in no calculation that was checked and shows up later as a drift that is larger than predicted or a joint that is heard slipping.

The same reasoning, run the other way, is why a welded splice is often cheaper in the end for a member that has to be stiff. A butt weld satisfies all three requirements at once, by being the member — and it costs more per joint and nothing at all in inspection of a mechanism that might not have been achieved.

Where to put it #

Splices are placed where the member’s force is smallest, and the usual instruction is to put them near a point of contraflexure.

Three cautions come with that. The moment is zero for one arrangement of load, and it moves as soon as the load is patterned — which is guaranteed, because imposed load can be absent. The shear is not small there; on a continuous beam it is near its largest. And the stiffness requirement does not care where the splice is at all: a joint that rotates changes the member’s behaviour wherever it sits.

The third caution deserves its own sentence, because it is the one that survives every change of location. A splice is a rotational spring inserted into a member, and a spring softer than the member sheds moment away from itself — safe for the splice and unsafe for wherever the moment went. Between a rigid joint and a pinned one the end moment of a beam runs from 80% of its fixed-end value to 20%, and every splice stiffness in between produces a redistribution nobody chose.

What counts as soft is not an absolute stiffness but a multiple of $EI/L$, which means it is a property of the member as much as of the detail. The same splice is rigid in a short deep beam and semi-rigid in a long shallow one, so a detail carried unchanged from one job to the next can change classification without a single dimension changing.

The column splice, which is a different problem #

Everything above is about a member in tension or bending. A column splice is governed by something else entirely and is worth separating, because the reasoning inverts.

A column carries compression, and compression can cross a joint by bearing — the two ends in contact, force passing directly from one to the other with the splice plates carrying almost nothing. Where the ends are prepared for contact, a column splice is nominal for the compression it was ostensibly made for.

What it is not nominal for is everything else. It has to carry the tension that arises under wind uplift or a reversed moment; it has to carry the shear at the splice level; and it has to hold the two lengths in line, because a splice that allows a kink has introduced an eccentricity into a member whose whole design is an eccentricity check. That last requirement is a stiffness one and it is why a column splice’s plates are sized for a notional force rather than for a computed one.

The other consequence is about erection. Between the moment the upper length is landed and the moment its splice is bolted up and its bracing connected, the column is a cantilever from the splice, carrying its own weight and whatever wind is blowing — which is the most dangerous day and a load case in which the splice is the only structure there is.

The splice that is designed for no force in particular #

Everything above sizes a splice for the force crossing it. Codes then require something else on top, and the requirement looks arbitrary until the reasons are separated: a splice must develop a stated fraction of the member’s own capacity — commonly a quarter, sometimes a half — whatever the computed force.

There are three reasons and they are genuinely different from one another.

The computed force belongs to one arrangement. The section on placement above already says so: a splice put where the moment is zero is at a station where the moment is zero for one pattern of load and not for the others. A rule expressed as a fraction of capacity does not care which arrangement was analysed.

The member is often not sized by the force at the splice. A column is sized by buckling over its whole length, a beam by deflection, a tie by a minimum slenderness or by what the fabricator had. So the member’s capacity can be several times the force it will ever carry, and a splice designed for the force is a splice several times weaker than the thing it interrupts. Everything the structure might do that the analysis did not contain — a reversal, an impact, a settlement, a load applied during erection — arrives at the member’s capacity, not at its computed force, and finds the splice.

And a splice interrupts a tie. Robustness rules require a structure to have continuous tension paths through it, so that if a column is removed the floor above can hang from what is left. Those tie forces are horizontal and vertical, they are specified as forces rather than derived from an analysis, and a splice is exactly where a tie is most likely to be broken — because a compression splice designed by bearing may have no tension capacity at all. A column splice with prepared ends in contact and nominal plates carries its compression beautifully and its tie force not at all.

Which is why the minimum is written against capacity rather than against force. It is not a safety factor on the computed answer; it is a different requirement in the same units, and it is the one that keeps a splice from being the place a structure comes apart in a scenario nobody analysed.

The practical form is short. A splice’s computed force says what it does on an ordinary day. The member’s capacity says what it might be asked for on the day the analysis did not describe — and the second number is the one the detail has to survive.

Where the model stops #

The bolt distribution above is elastic. The tanh expression assumes every fastener is a linear spring, which is right until the end one yields. Past that the connection redistributes and the ultimate capacity is very nearly the sum of the individual capacities — so the length effect is a serviceability and fatigue problem, and only a strength problem for fasteners that cannot yield.

The extreme is worth drawing, because it is where the elastic model and the plastic one are furthest apart. Twenty bolts at 75 mm pitch is a lap 1,425 mm long — longer than any ordinary beam splice, and the length of a bridge cover plate or a long tie.

Fatigue does not forgive. A splice is a discontinuity in a stress field, so it is a fatigue detail — several classes below the parent member — and in a member that sees repeated load the splice may be the whole design.

Nothing here is about erection. A splice exists to allow a member to be delivered and lifted, so its position is decided by lorry lengths, crane capacity and where a temporary support can go, and the structural argument is applied to a location chosen for other reasons.

And the member may be spliced in more than one plane. A beam spliced in its web and its flanges has three bolt groups with three different eccentricities from the section’s own centroid, and the small residual moments they leave on one another are the reason a splice is checked as a group rather than as a set of parts. The same is true of the moment an eccentric reaction leaves behind: a force delivered off a centreline is a force plus a couple, and a splice has several centrelines to miss.

What the picture cannot show #

A splice drawing shows plates and bolts and says nothing about which of the three requirements each feature is meeting. The flange plates are there for the distribution, the bolt count for the strength, the preload for the stiffness, and the arrangement for the fatigue class — and a detail simplified by removing one feature usually loses one requirement silently.

Nor does any drawing show the fit. A splice with a gap between the member ends is a splice whose plates carry the compression too; a splice with the ends in contact is one where they may not. Which of those was built is decided on site, by a saw cut, and it changes which mechanism carries the compression flange.

The generalisation #

The habit worth carrying is that continuity has three separate meanings, and a detail can supply one without the others.

Continuity of force is a strength requirement and is what gets designed. Continuity of stiffness is what keeps the analysis true, and it is met or not by features — preload, fit, plate thickness — that the strength calculation does not mention. Continuity of distribution is what keeps the member’s own behaviour intact, and it is met by which parts of the section are connected to which.

The same triple appears elsewhere. A moment connection can be strong and soft, which changes the frame’s drift. A repair can restore strength and not stiffness, which redistributes load away from it. A bearing can carry a reaction and not allow a rotation, which puts a moment into a member designed as simply supported.

In every case the calculation that was done answers the first question, the analysis quietly assumed the second, and the third is a matter of where the pieces were attached. A splice is the clearest example because it has no other purpose: it exists solely to be as good as the thing it interrupts, which makes every way of failing to be a design decision rather than an accident.