Structural Engineering & Statics
where the load goes
Generator

The parallel-axis generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
Moving the flanges apartThe second moment of area of an I-section against its depth, with the flange and web areas held constant. The growth is close to quadratic, because the parallel-axis term dominates everything the flanges contribute about their own centres.1001502002503000M10M20M30M40M50M60Moverall depth1.0×2.6×4.9×7.9×13.8×21.3×same steel, moved apart

5 essays call parallel-axis. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

0.511.52050100150200250300depth of the truss2501671251007150the same moment, resisted by a longer lever arm Structural form

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.

 neutral axiscontribution of each striptotal I = 79.86 × 10⁶the outer strips do almost all of the work Sections and stress

The material far from the middle does nearly all the work

A strip of steel contributes to bending stiffness in proportion to the square of its distance from the centre. Move the same steel outward and the section gets stiffer for nothing.

 the same, laid flatI = 0.06 × 10⁶1.0× the firstsquareI = 0.75 × 10⁶13.3× the firsttall rectangleI = 10.00 × 10⁶177.8× the firstI-sectionI = 24.29 × 10⁶431.8× the firstevery section here has an area of 3000 — only the shape differsthe bar is the second moment of area, to scale Sections and stress

The same steel in a different shape, and a factor of forty

Four sections of identical area, identical weight and identical cost. The stiffest is dozens of times the stiffest of the flattest, and the only thing that changed was the arrangement.

 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 Sections and stress

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.

 11.522.533.54050100150200250300span, relative to the first1×5×16×81×256×moment: the squareload: the first powerdeflection: the fourth Deflection

Span to the fourth, which is why spans are short

Doubling a span multiplies its deflection by sixteen. No other relationship in ordinary structural work is that steep, and it is the reason long spans are always a different kind of structure.

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