Concept

Lever arm

4 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
25.0the cut — three members, three unknowns47.06-52.947.72moments about here kill two of the threesolved without touching any of the other 18 members

Answering one question without solving the rest

A truss of fifty members can be interrogated about one of them. Cut through three, take moments about the point where two of them meet, and the third falls out in a single line.

equilibrium · method of sections
0.511.52050100150200250300depth of the truss2501671251007150the same moment, resisted by a longer lever arm

Depth is the cheapest strength there is

Doubling the depth of a truss halves its chord forces without adding a gram of material to the chords. Nothing else in structural design is that cheap, and almost every structure has already spent it.

structures · span to depth
neutral axiscompressiontensionI = 29.97 × 10⁶Z = 299.7 × 10³peak stress 200.2σ = M y ÷ I, at every height

Bending is a pair of forces, pushing and pulling

A bending moment is not a mysterious twisting. It is a push near the top of a section and a pull near the bottom, separated by a lever arm — a couple, made out of stress.

sections · bending stress
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

Named alongside it

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

Chord forceNeutral axisSecond moment of areaStress blockBucklingCentroidCracked sectionEfficiencyElastic limitFirst moment of areaFree body diagramMethod of sections

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