Structural Engineering & Statics
where the load goes
Concept

Preload — where it appears

A tension put into a bolt before any load arrives, clamping the plies so that the joint carries shear by friction rather than in bearing. It is what removes slip from a connection, and a joint that has slipped past it is a different mechanism with a different capacity and a different stiffness.

Named by 16 essays across 3 fields — each of them below, with the objects they name alongside it.

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.

connections · Slip-critical 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 The reaction lies inside the cone, so the block stands. A block of 48 on a plane at 22°, against a coefficient of friction of 0.6. Resolving across and along the plane gives a normal force of 44.5 and a friction demand of 18.0, against a capacity of μN = 26.7 — a ratio of 0.67. Added together the two make one contact reaction leaning 22.0° from the normal, and the admissible reactions fill a cone of half-angle arctan μ = 31.0°. Equilibrium is possible exactly when the demanded reaction lies inside that cone, which here it does. The weight enters neither the cone nor the lean: a block of any weight on this slope leans its reaction by the same 22.0°, which is why the angle of repose is a material property and the size of a heap of sand is not.

The area that is not in the equation

Friction is proportional to the force pressing two surfaces together and independent of how large they are, which sounds like an approximation and is not. The area is absent because the contact that carries the load is a tiny fraction of the contact that is drawn, and that fraction grows in exact proportion to the load.

equilibrium · Friction A preloaded joint, before and after it slips. Eight preloaded bolts at 100 kN each, on two friction faces at μ = 0.35. The joint carries 560 kN by friction with the bolts in tension and not in shear at all; past that it slips into bearing and carries 900 kN with the bolts now in shear. Two different mechanisms, one joint.

The force that is capped on purpose

Everywhere else in this collection friction is a nuisance whose value nobody controls, checked with a coefficient known to one figure. In a friction damper the inequality is the design intent — the device is specified so that a member behind it can never be asked for more than a stated force.

equilibrium · Friction A preloaded joint, before and after it slips. Four preloaded bolts at 172 kN each, on one friction face at μ = 0.5. The joint carries 344 kN by friction with the bolts in tension and not in shear at all; past that it slips into bearing and carries 362 kN with the bolts now in shear. Two different mechanisms, one joint.

The hole made bigger so the steel would fit

A preloaded joint carries load by friction, and the friction is reduced by the shape of the hole the bolt passes through — not by how much steel the hole removes, but by a coefficient in a table. An oversize hole costs fifteen per cent of the resistance; a long slot costs thirty-seven. Both are provided because the steel would not otherwise line up.

connections · Slip-critical 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 Nine-tenths of a tightening torque stretches nothing. Where the torque applied to the nut of an M20 grade 10.9 bolt goes, against the coefficient of friction in its thread and under its nut, taken as equal. The bottom band is the thread's lead — the only part of the work that stretches the bolt — the middle band is friction in the thread and the top band is friction under the nut. At μ = 0.14 the lead takes 11% of the torque, the thread 39% and the nut face 50%. At μ = 0.06 the lead's share is 22% and at 0.24 it is 6%, so a coefficient nobody measured decides how much of a specified torque arrives in the bolt as preload.

The torque that goes into the thread

A preload specified as a torque is a preload specified through two coefficients of friction that nobody measures. Nine-tenths of the torque on a bolt is spent turning against its own thread and the face of its nut, so a change in the grease moves the clamping force by half — and the one method that escapes it does so by yielding the bolt on purpose.

connections · Slip-critical Preload makes the base rigid, until the bed lets go. Moment against rotation at the base of a 500 × 400 × 20 mm base plate under a 260 mm column, with two M24 holding-down bolts in each of two rows 60 mm from its ends: with no preload (dashed), 58,609 kN·m per radian, 9.8 times the column's EI/L; with bonded anchors whose free length is 136 mm (dotted), 13.9 EI/L; preloaded to 150 kN a bolt (solid), 45.6 EI/L until the bed under the plate lets go at its tension edge at about 57 kN·m, then softening toward the unpreloaded base. Faint: the slope of EN 1993-1-8's rigid boundary, 30 EI/L.

The base that is rigid until the bed lets go

A column base drawn as fixed is a spring about a tenth as stiff as the rule for "rigid" requires, and most of its softness is the holding-down bolts stretching. Shortening the bolts helps less than it seems: even 60 mm of free length leaves the base below two thirds of the rigid boundary. Preloading them works completely — the base becomes half as stiff again as the boundary asks — but only while the grout under the plate stays in compression. The preload is spent at a definite moment, the same moment the column's own weight would buy for free, and the shorter the bolt the faster creep of the grout takes the preload away.

connections · Base plate The preload lifts the young slab and lands on the one below it. The load on one slab of a frame of 250 mm slabs on a 7.5 m grid cast a floor every 7 days at 20 °C, on one level of shores and one of backprops, as a multiple of its own weight, from the day it is struck at 7 days to 28 days, with creep. With its backprops put in snug (dashed) it takes 1.52 w at the cast above it, creeps down to 1.29 by the end of the week, takes 1.48 w when the slab above it is struck and cast on in turn, and creeps up to 1.71. With every backprop jacked to 0.30 w (solid) the young slab starts its week at 1.22 w and ends it at 1.14; a week later the preload of the backprops above lands on it, and it takes 1.78 w, creeping to 1.86.

The backprop jacked tight lands on the floor below

A backprop put in snug shares only the load that arrives after it, and creep then pushes the young slab above onto it anyway. Jack it to a preload instead and the young slab is lifted at once — but the preload survives the week, so the lift lands on the slab below the moment the next level is struck, and about half of it is load creep would have moved within the week regardless. The best preload balances the week-old slab against the fortnight-old one, and with creep it is small: a fourteenth of a slab's weight, about six hundred newtons a prop. Anything over a fifth leaves the frame worse than snug. What a small preload does buy completely is immunity to slack.

materials · Maturity The base comes back to a different joint. Moment against rotation at the base of a 500 × 400 × 20 mm base plate with two M24 holding-down bolts in each of two rows, preloaded to 150 kN a bolt, through four cycles to ±170 kN·m. It is stiff until the bed lets go at 57 kN·m, softer past it, and near 170 kN·m the bolts on the tension side yield and stretch for good. Coming back through zero the base is not the base it was: its bolts have kept 83 per cent of their preload, and it lets go at 46.0 kN·m instead of 56.6. After the first full cycle the loops lie on top of one another.

The base that lets go and closes again

A column base whose holding-down bolts are preloaded is rigid until the moment on it lifts the plate off its bed, and then softer. Under a storm the moment goes one way and then the other, many times, and the question is whether the preload survives. It does, entirely, as long as no bolt yields — and on an ordinary base the bolts do not yield until the moment is three times what first lifts the plate. Past that the yielded bolts lose part of their preload once, and the loss stops within a cycle or two: the base settles rather than ratchets. What decides how much is lost is how close to its yield the bolt was tightened, so that past a point a larger preload leaves less after the storm.

connections · Base plate Slackening a backprop gives the young slab back more than the preload. The load on one slab of a frame of 250 mm slabs cast a floor every 7 days at 20 °C, on one level of shores and one of backprops, as a multiple of its own weight, from the day it is struck at 7 days to 21 days, with creep. Snug, it takes 1.52 w at the cast above it. With its backprops jacked to 0.15 w it takes 1.37. Slackened to snug 1.0 day later, the backprops give it back everything they carry — the preload, their share of the slab cast above and what creep has added — and its load jumps from 1.19 to 2.00 w. Let down by the preload alone, it goes from 1.23 to 1.38. A week after it is struck the slab becomes the slab below, and the backprops jacked above it land on it whatever is done to its own.

The preload that cannot be taken back

A backprop jacked tight under a young slab relieves it and loads the slab below by the same amount at the same instant. The obvious repair is to slacken the backprop once the young slab is past its worst, so that the preload never reaches the slab below. It cannot work. Slackened to snug, a backprop lets go of everything it carries, not only its preload, and the young slab's load jumps from 1.19 to 2.00 times its weight. Let down by the preload alone, it gives back a load the slab below has already carried at its worst.

materials · Maturity Every day taken off the cycle is paid for in the youngest slab. For a frame of 250 mm slabs on a 7.5 m grid at 20 °C, on one level of shores: the largest use of strength of any slab against the floor cycle, with one level of backprops snug or jacked to its best preload, and with two levels snug or jacked to theirs; dotted, a seven-day cycle on snug backprops. On one level of snug backprops the worst use is 1.95 at seven days, 2.14 at five and 2.53 at three. With the best preload, 1.87, 2.01 and 2.30. With two levels, 1.79, 1.95 and 2.31; with two levels and their best preload, 1.67, 1.78 and 1.99.

The day taken off the floor cycle

A frame cast a floor a week loads its slabs with the same multiples of their weight whether the cycle is seven days or four. What a shorter cycle changes is how strong each slab is when its load arrives, and it changes that unequally, costing the youngest slab more than the one below it. That is why a faster cycle makes a jacked backprop more useful rather than less, and why a frame that wants four days needs both a second level of backprops and a preload to be as safe as a week on one.

materials · Maturity Retightened after every storm, the bolts stretch in every storm. The permanent stretch in the worse bolt row of a 500 × 400 × 20 mm base plate with two M24 holding-down bolts in each of two rows, accumulated over ten storms of four cycles to ±170 kN·m, with the nuts retightened after every storm to 200 kN, to the 150 kN they were first given, to the 124 kN the first storm left, or left alone. Left alone, the bolts stretch 0.12 mm in the first storm and not at all after it. Retightened to 150 kN they add 0.12 mm in every storm, 1.25 mm after ten; to 200 kN, 0.43 mm a storm. Retightened only to what the first storm left, they stretch no more than if they had been left alone.

The nut turned after the storm

A preloaded column base that has been through a storm has lost some of its preload, and the obvious repair is to retighten its bolts. Left alone, the bolts stretched once in the first storm and never again; the base settled. Retightened, they are given back the preload the storm could not live with, and the next storm takes it away again by stretching them again. Retightening after every storm turns a base that settles into one that ratchets, a tenth of a millimetre at a time, and the count of storms it has in it is set by the bolt's elongation.

connections · Base plate The preload a storm can live with, raised by a spring under the nut. The largest preload the bolts of a 500 × 400 × 20 mm base plate with two M24 holding-down bolts in each of two rows can be given and come out of a storm without stretching, against the stiffness of a stack of disc springs under each nut, for storms to ±165, ±170, ±175 kN·m; dashed, the same for the bare base; dotted, the bolt's yield of 226 kN. To ±170 kN·m the bare base keeps at most 128 kN; with a stack of 500 kN/mm, 150; 100 kN/mm, 187; 20 kN/mm, 214; 5 kN/mm, 223.

The spring under the nut

Retightening a column base after every storm makes its bolts ratchet, because a storm can only live with 128 kN of preload and the spanner keeps putting back 150. A stack of disc springs under each nut changes what the storm can live with. Soft enough, the bolts never reach their yield: the compression side keeps its preload, the bed's resultant moves out to the plate's edge, and the moment rides on lever arm rather than on bolt force. A stack as stiff as the bolt itself keeps 150 kN through every storm. Much softer, and the storm the bolts no longer feel lands on the grout.

connections · Base plate The pair holds its clamp longer than the stub it is checked by. The tension a bolt at which the clamp lets go, as a share of the 110 kN preload, against the end plate's lever arm from web to bolt, for an end plate 18 mm thick on a column flange 14 mm thick at 30 mm: the pair (solid), the end plate's stub (dashed) and the column flange's (dotted). With the end plate's bolt at 30 mm the pair and the stubs nearly agree. At 45 mm the pair lets go at 88.2 kN and the end plate's stub already at 81.1, the pair holding 9 per cent more; at 60 mm, 82.0 against 71.2, 15 per cent more.

The clamp the pair holds longer

A preloaded bolt clamps an end plate to a column flange, and the joint stays closed until the tension relieves the clamp. The joint diagram says that happens at the preload over one minus the bolt's share — 122 kN for a 110 kN preload — but prying adds to the tension at the bolt line and the clamp lets go at 88. A component model checks each flange as a stub on a rigid base and lets the joint go when its weaker stub does, at 81 kN. The real pair, its tips leaning on a column flange that gives way, pries less than the end plate alone would, and holds its clamp nine per cent longer — fifteen when its lever arms are two to one.

connections · Prying An old joint passes the bolts that have lost their preload. The chance that an M20 grade 10.9 bolt holds the inspection torque of 647 N·m without its nut turning, against the tension actually in it as a fraction of the minimum preload, for a joint new and 1 year old, 5 years old and 20 years old. New, a bolt at half the minimum preload passes 0% of the time and one at the minimum 83%; 20 years old, the bolt at half passes 80% of the time and one at a quarter 9%.

The wrench that reads the rust

The obvious check on a preloaded joint that has been in service for years is a wrench on the nut, and it measures the wrong thing. The nut holds against the bolt's tension times a friction bracket, and twenty years of rust raise the bracket until a bolt with half its preload passes four times in five. The washer that could have said more remembers only the day it was crushed.

connections · Slip-critical

Named alongside it

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

ConnectionSlip resistanceFrictionCoefficient of frictionBase plateBolt tensionCreepDuctilityJoint stiffnessLimit stateLoad sharingTolerance

All concepts