Self weight
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.
The shape that carries itself, and the arch that is its reflection
Hang a chain and it takes the one shape that carries its load in pure tension. Turn the shape upside down and it carries the same load in pure compression. That is what an arch is.
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.
Stiffness is not strength, and usually it is the one that governs
A beam can be nowhere near failure and still be unusable, because it has moved too far. For most long-span members that limit arrives first, and stronger steel does not help at all.
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.
The water that will not run off
A flat roof deflects, the deflection makes room for water, the water deepens the deflection. It is the same equation as a buckling column, with rain in place of the axial load.
Named alongside it
The objects these essays reach for when they reach for this one.
StiffnessDeflection limitLimit stateSecond moment of areaServiceabilityAmplification factorBucklingCatenaryCentroidChord forceCritical loadDistributed load