Structural Engineering & Statics
where the load goes
Series

Second moment — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Every strip counts by the square of its distance. A rectangular section divided into equal strips, with each strip's contribution to the second moment of area drawn beside it. The strips are identical in size; only their distance from the neutral axis differs.

    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.

    part 1 · sections
  2. Shear stress across a section. The distribution of shear stress over an I-section, computed as VQ/It by accumulating the first moment of the area above every height. The peak is 82.77 against a mean of 38.46 — a ratio of 2.15 — and it falls at the neutral axis, where the bending stress is zero. At the junction between flange and web the flow is 820.0 per unit length, so connectors of 20000 each have to be spaced no further apart than 24 — which is what turns two pieces into 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.

    part 2 · sections

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