Structural Engineering & Statics
where the load goes
Concept

Weak axis — where it appears

The principal axis about which a section has its smaller second moment of area, such as the axis along the web of an I-section. Bending or buckling about it needs far less load, so any load or slew that reaches it governs out of all proportion.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The neutral axis obeys neither the load nor the moment. A 305 × 102 mm I-section carrying a moment 5° out of the plane of its web. The moment vector is the short arrow; the neutral axis is the long line, at 69.7° to the strong axis. They do not line up, and the reason is that the neutral axis follows the moment ratio scaled by the stiffness ratio: tan α = (M_z/M_y)(I_y/I_z), and I_y ÷ I_z is 30.8 here. So a 5° tilt of the load puts the neutral axis 70° over, the corner that ends up furthest from it carries 489 N/mm² against the 258 the straight-down case would give, and the section has lost 47 per cent of its capacity to a misalignment nobody would draw on a detail.

Two moments and a neutral axis that obeys neither

Tilt the load on a rolled beam by five degrees and the neutral axis swings by seventy. The section is doubly symmetric, its product of inertia is exactly zero, and none of that helps — because what decides the axis is the moment ratio multiplied by a stiffness ratio of thirty.

sections · Biaxial bending The road is the harshest stretch of the beam's journey. The worst top fibre, at any corner of any section, of the 12 m pretensioned beam, 300 × 700 mm, with eight strands, its schedule drawn for the bed and for yard bearers 1.0 m in from each end, in N/mm² with tension negative: on the yard's bearers; on the haulier's trailer, 1.5 m and 2.5 m from its ends with a bounce of ±30 per cent; lifted by loops 1.0 m in from each end on slings at 60° with a snatch of ±20 per cent; slewed at 0.10 g; and set down on bearings sloping 1 per cent across it; dashed, the stored concrete's limit of −3.0. Yard bearers, −2.98; trailer, −4.88; lifted, −2.97; slewed, −3.13; set down, −1.79.

The beam hung from its loops

A pretensioned beam is cast in a bed, stored on bearers, hauled on a trailer and then lifted by a crane onto its bearings — and at every stage its top fibre, which the strands put in tension, has to stay inside the limit its debonding schedule was drawn for. The trailer, with a bouncing wheel and supports where the haulier put them, was the harshest stage the yard essays found. The last few metres, from the trailer to the bearings, are gentler: hung from loops at the yard's bearer positions the beam is on its bearers again, set down it is on the support its middle was designed for, and only a slew of the crane pushes it a little past its limit. Where the loops are cast decides how much margin the lift has, and the best place for them is not where the yard put its bearers but where the bed held the beam: at its ends.

sections · Prestress limits

Named alongside it

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

Bending stressBiaxial bendingCantileverDebondingImpact factorInteraction diagramLiftingNeutral axisPlastic modulusPrestressPretensioningPrincipal axes

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