Structural Engineering & Statics
where the load goes
Concept

Centroid

3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
resultant 24.0at x = 5.33, the centroid of the areamomentspread: 24.6replaced: 42.7reactions agree exactly (8.00 and 8.00); the peak moment does not

The load that is spread out, and the force that replaces it

A distributed load can be swapped for a single force at its centroid. The reactions come out identical and the bending moment does not, and knowing which side of the cut the swap is legitimate on is most of the skill.

equilibrium · distributed load 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.

sections · second moment 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

Named alongside it

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

Neutral axisSection modulusDistributed loadElastic limitFree body diagramI-sectionIdealisationLever armLoad pathParallel axis theoremPlane sectionsPlastic moment

All concepts