Structural Engineering & Statics
where the load goes
Concept

Column — where it appears

A member carrying load along its length to a support below. Its capacity is decided by whichever arrives first of squashing and buckling, so its section is chosen for a radius of gyration as much as for an area, and its length is the one property it does not choose for itself.

Named by 5 essays across 4 fields — each of them below, with the objects they name alongside it.

A column that has nothing on it but itself. A 30 m column carrying no load except its own weight, with its buckled shape and the axial force that produced it. The force is zero at the top and largest at the base, which is why the answer is not Euler's: the eigenvalue is a load intensity and comes out as q_cr L³/EI = 7.835, a number with no π in it, computed here as the smallest eigenvalue of the same stiffness and geometric-stiffness matrices that give a tip-loaded column its Euler load. It is equivalent to a tip load of 3.18 times as much total weight — a column carries its own weight better than it carries somebody else's, because most of the weight is near the base where the buckle is not. The height limit that follows is a cube root, so a section of radius of gyration 80 mm falls over on its own at 52 m and one of twice that reaches only 82.

Too tall for nothing but itself

Every critical load on this site so far has been applied at the top of a column. A mast carries a load that is zero at the top and largest at the base, the governing equation stops being harmonic, and the answer comes out as a number with no π in it — along with a maximum height that is almost the same for steel, aluminium and wood.

stability · Self-weight buckling Where two buildings touch, and what is there when they do. Closure between an 8-storey building 24 m tall and a 4-storey one 15 m tall, drawn against height, with the 50 mm gap between them. The two swaying out of phase close on each other more the higher up they are, so they first touch at 7.6 m and are in contact above it. The dots are the taller building's floors: its storeys are 3.00 m and the other's are 3.75, so two of them arrive part way up a column rather than at a slab. A blow at mid-height of a column asks it for a shear of half the impact and an end moment of Fh/8, neither of which is a demand any part of the design contains.

The floor that arrives at a column

The gap between two buildings is computed from their roof displacements, which is where each of them moves most. It is not where they touch, and it is not what is there when they do — a slab edge meeting a column part way up its height is a different event from two slabs meeting, and it is the one that appears in the photographs.

dynamics · Pounding 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 Squeeze an I-section and it loses its corner. Moment against curvature for an I-section of 3,000 mm² and 200 mm depth in mild steel, the moment over its unloaded plastic moment and the curvature over its unloaded first-yield curvature, at axial compressions of 0, 30, 60 per cent of its squash load (dots: first yield). At 0 per cent it first yields at 0.92 and reaches 98 per cent of its plastic moment, 1.00, at 1.2 times the unloaded first-yield curvature; at 30 per cent it first yields at 0.64 and reaches 98 per cent of its plastic moment, 0.75, at 2.3 times the unloaded first-yield curvature; at 60 per cent it first yields at 0.37 and reaches 98 per cent of its plastic moment, 0.44, at 6.4 times the unloaded first-yield curvature. Unloaded, the I-section turns its corner almost at once; squeezed, its web is yielding in compression before any moment arrives and its flanges have to be strained far past yield to carry what is left.

The hinge a squeezed section has to work for

Unloaded, a rectangle carries half again its first-yield moment once it is fully plastic and an I-section only a little more, and the I-section gets there almost at once while the rectangle has to bend four times further. Put a column's axial load on them and both rankings move. The rectangle's reserve grows as 1.5(1 + n), to nearly three times its first-yield moment under heavy compression; the I-section's barely moves. And the I-section loses the thing that made it the beam everyone uses: under three-fifths of its squash load it needs more than five times the curvature to develop its plastic moment that it needs as a beam, because the compression has yielded its web before any bending began.

materials · Moment-curvature

Named alongside it

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

Base plateBearing stressDetailingEffective areaFoundationPlate bendingT-stubAxial forceBeam-columnBucklingCantileverCollapse mechanism

All concepts