Structural Engineering & Statics
where the load goes
Field

Sections and stress

How a cross-section resists a moment, and why where the material sits matters more than how much there is.
neutral axiscontribution of each striptotal I = 79.86 × 10⁶the outer strips do almost all of the work

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.

 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.

 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

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.

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