Structural Engineering & Statics
where the load goes
Concept

First moment of area

3 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
neutral axispeak 0.4stressflow, q = VQ ÷ Imean stress 0.19 — the value a shear divided by an area would givepeak 2.15× that, and in the place bending ignoresthe flow is continuous; the stress jumps wherever the width does

The shear nobody draws

A stack of loose planks slides at its ends when it is loaded. Glue them and the sliding stops — and whatever the glue is now carrying is a stress that no bending calculation contains.

sections · shear flow x = 1371200 mm² of steel, n = 7.5b = 30018.0 N/mm²371 kN in the steelz = 404C = T = 371 kN · C·z = 150.0 kNm = the applied momentcracked I 1139×10⁶ mm⁴ against uncracked 3422×10⁶ — 67% of the stiffness gone

When half the section has given up

Bending theory puts the neutral axis through the centroid. That is a consequence, not a rule — and when the tension side cracks, the same reasoning moves the axis somewhere else entirely.

sections · bending stress neutral axispeak 82.8stressflow, q = VQ ÷ Imean stress 38.46 — the value a shear divided by an area would givepeak 2.15× that, and in the place bending ignoresthe flow is continuous; the stress jumps wherever the width doesq = 820.0connectors of 20000 each, at 24 centres, are what make this one section

The section made of pieces

Two plates bolted together are twice as strong as one plate. Two plates made to act as one section are eight times as stiff. The difference is entirely in the joint, and the joint has a calculable spacing.

sections · second moment

Named alongside it

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

Neutral axisDelaminationSecond moment of areaShear connectionShear flowBuilt up sectionCracked sectionI-sectionLever armModular ratioParallel axis theoremShear stress

All concepts