Concept

Self weight

6 essays name this object, across 3 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
cable: pure tensionreflected herearch: pure compression

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.

structures · funicular
0.511.52050100150200250300depth of the truss2501671251007150the same moment, resisted by a longer lever arm

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.

structures · span to depth
0.60.811.21.41.61.8200.511.5span, relative to the firstthey cross heredeflection runs out at 1.40strength runs out at 1.54the limitstrengthdeflection

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.

deflection · serviceability
11.522.533.54050100150200250300span, relative to the first16×81×256×moment: the squareload: the first powerdeflection: the fourth

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.

deflection · span scaling
00.020.040.060.080.10.120.1400.20.40.60.81sag at the middle of the baywater depth ÷ critical depthλ = 1.00, approached and never reachedreversed construction camber: δ₀ = 0.01

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.

deflection · serviceability

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

All concepts