Structural Engineering & Statics
where the load goes
Concept

Base plate — where it appears

The plate that spreads a column's load into its foundation, in bearing over part of its area and in tension through holding-down bolts over the rest. Where the resultant sits inside the kern the plate bears everywhere; past it the plate lifts, the contact shortens, and the bolts begin to work.

Named by 12 essays across 4 fields — each of them below, with the objects they name alongside it.

A base plate, and when the bolts start working. A 500 × 400 mm plate carrying 600 kN and 90 kN·m, so the resultant sits 150 mm from the centre against a kern of 83.33 mm. The plate is in partial contact: bearing over 300 mm at a peak of 10 N/mm², with the holding-down bolts carrying 0 kN. The plate lifts at 50 kN·m and crushes at 120 kN·m, and the bolts are not needed until 150 kN·m.

Where the structure meets the ground, and when the bolts start working

Push a base plate off its middle third and it lifts off the foundation. The holding-down bolts then carry exactly nothing, and go on carrying nothing until the plate has crushed the concrete underneath it.

connections · Base plate A force may be moved anywhere, at the price of a couple. A 80 kN force applied 250 mm off the centreline of a body, and the same force applied ON the centreline together with a couple of 20 kNm. The two systems are equivalent: they have the same resultant force and the same moment about every point in space, so no equilibrium equation written about the body can tell them apart. What they are not is the same loading — the stresses inside the body differ, and they differ over a distance of about the body's own depth. The offset is drawn to a scale that keeps the arrow on the body; the number beside it is the real one.

The moment the beam left behind

A beam reaction is drawn arriving on a column's centreline. It arrives on a cleat a hundred millimetres out from the face, and the difference is a couple that goes into the column and has to be shared between the lengths above and below it. Nothing about it appears in a frame model whose members meet at nodes.

internal-forces · Column eccentricity A base plate, and when the bolts start working. A 500 × 500 mm plate carrying 600 kN and 180 kN·m, so the resultant sits 300 mm from the centre against a kern of 83.33 mm. The plate is in bolts engaged: bearing over 150.88 mm at a peak of 20 N/mm², with the holding-down bolts carrying 154.42 kN. The plate lifts at 50 kN·m and crushes at 126 kN·m, and the bolts are not needed until 150 kN·m.

The failure that is in the concrete

An anchor bolt is a steel component and its capacity is usually decided by something else entirely — a cone of concrete pulled out around it, failing in tension, in a material every other calculation on the project has assumed cannot take tension at all. The exponent in the capacity says so: it is not the square the geometry implies.

connections · Anchor breakout A base plate, and when the bolts start working. A 550 × 450 mm plate carrying 900 kN and 140 kN·m, so the resultant sits 155.56 mm from the centre against a kern of 91.67 mm. The plate is in partial contact: bearing over 358.33 mm at a peak of 11.16 N/mm², with the holding-down bolts carrying 0 kN. The plate lifts at 82.5 kN·m and crushes at 192.95 kN·m, and the bolts are not needed until 247.5 kN·m.

The pinned base that is not pinned

A column base drawn as a pin is a plate bearing on grout, and a plate in contact over its whole length resists rotation whether anybody wanted it to or not. The stiffness it delivers depends on the axial load, so the assumption is one a frame can leave and re-enter as its loads change.

stability · Sway stability The part of a base plate that is delivering anything. A plan of the plate: the 260 × 260 column in the middle, and the shaded region it can reach — its own outline grown by 43 mm, which is t√(f_y/3f_jd) for a 20 mm plate on grout at 20 N/mm². That is 78176 mm² of a 200000 mm² plate, or 39 per cent of it. The corners are outside it and are carrying nothing: a plate cantilevers from the column's perimeter and runs out of bending capacity at c, so making it larger in plan beyond that changes nothing at all, and making it thicker changes everything.

The plate that is only as big as it is thick

A base plate's design is presented as a bearing calculation: an area, a bearing strength, and a check that the pressure fits. The area in that calculation is the plate, and the plate cannot deliver it — a 20 mm plate on a 500 square reaches 43 mm past the column and the corners carry nothing at all.

connections · Base plate The compression is under the flange, not at the edge of the plate. A 500 × 400 mm base plate, 20 mm thick, under a 260 mm column carrying 300 kN and 120 kN·m, with holding-down bolts 60 mm from the tension edge. A plate this thick can deliver bearing only 43 mm past the compressed flange, so the compression sits under that flange, 124 mm from the column's centre, and the lever arm to the bolts is 314 mm: the bolts carry 264 kN and the flange zone 564 kN. The dashed block is the rigid-plate answer, 54 mm deep at the plate's far edge with its resultant 223 mm out, which needs only 128 kN in the bolts. Both satisfy equilibrium; only one is a plate that can carry the pressure where it is drawn.

The compression that stays under the flange

Put a moment on a base plate and a pressure-block calculation pushes the compression out to the plate's edge, where the lever arm to the holding-down bolts is longest. A plate that is not rigid cannot put it there. The compression stays within a few tens of millimetres of the compressed flange, the lever arm shrinks, and the bolts carry twice what the pressure block said.

connections · Base plate What the frame notices. An 8 m by 4 m portal whose columns stand on bases of every rotational stiffness, in units of the column's EI/L on a logarithmic scale: solid, the portal's sway under a load at the knee as a multiple of the fixed-based portal's; dashed, the columns' effective length factor in sway (fixed bases 1.13, pinned 2.26). Bolts sleeved 300 mm, 5.3 EI/L: 1.45 times the fixed portal's drift, an effective length factor of 1.30 and 75 per cent of its buckling load; as detailed, 9.1 EI/L: 1.28 times the fixed portal's drift, an effective length factor of 1.23 and 83 per cent of its buckling load; rigid by EN 1993-1-8, 30.0 EI/L: 1.09 times the fixed portal's drift, an effective length factor of 1.16 and 94 per cent of its buckling load.

The fixed base the bolts decide

A column base drawn as fixed is a spring, and the component method says what it is made of: the grout squeezed under the flange, the plate bending under the bolt row, and the anchor bolts stretching over their free length. For a 500 mm plate on two M24 bolts the bolts are three fifths of its flexibility, so the base comes out at nine times the column's EI/L — under a third of what EN 1993-1-8 calls rigid — and no thickness of plate can lift it above fifteen. Leave the bolts free in sleeves for erection tolerance and it falls to five. The frame on it drifts 28 per cent more than a fixed-based one and buckles at 83 per cent of the load.

connections · Base plate 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 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 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 Pinned bases: weaker, and nothing lost to repetition while gravity leads. For a portal 10 m wide and 5 m high, plastic moment 200 kNm in the columns and 200 in the beam, in the plane of the gravity load's peak V·L/Mp and the reversing wind's H·h/Mp: the shakedown boundary (solid) and the collapse boundary under the loads applied once (dashed), on fixed bases and on pinned ones. On pinned bases the two coincide wherever gravity leads, along the beam and combined mechanisms, until the wind reaches about H·h/Mp = 1.6; past that a knee alternates and shakedown falls inside collapse, meeting it again at H·h/Mp = 2 with the wind alone. On fixed bases collapse reaches 8 and 4 and shakedown sits inside it except where the beam's mechanism meets the gravity axis. The dot is 160 kN of gravity at midspan that comes and goes with 60 kN of wind that reverses: its shakedown factor is 0.88 on fixed bases and 0.73 on pinned ones, where it is also the collapse factor.

The base that sends the wind to the knees

A fixed-base portal loses 12 per cent of its load to a wind that reverses, because each knee takes its worst moment from a different storm. Pin the bases and the loss disappears — not because the pinned frame is better, but because its collapse load already contains it. What the bases decide is where the moment goes, and a base that is merely weaker than its column can cost nothing at all, or be made into the part that yields every storm so that nothing else does.

materials · Shakedown 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

Named alongside it

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

ConnectionEccentricityJoint stiffnessPreloadShakedownAnchor boltComponent methodFoundationLoad pathPryingRatchetingStiffness

All concepts