Structural Engineering & Statics
where the load goes
Concept

Tapered member — where it appears

A member whose depth varies along its length, so that neither the demand nor the capacity is constant along it. The governing section is where their ratio peaks rather than where the moment does, and for a tip-loaded cantilever that station is exactly where the depth has doubled.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

30 kNwhat it can carrywhat it carriesworst at 3.00 mfree endroot79% used at the governing station · 70% at the root

The section that changes along the span

A prismatic beam is checked where the moment is largest, and everyone knows where that is. A tapered one is not, because the capacity is moving too — and for a cantilever with a load at its tip the governing station is exactly where the depth has doubled, with no length, no load and no material in the answer.

sections · tapered member 00.20.40.60.8100.20.40.60.81along the memberdensity ÷ its peak, and running sharewhere it comes fromrunning totalhalf nearest the root: 87.5% of it · worth 7.0× stiffening the other half

Where a deflection comes from

The unit-load method gives a deflection as an integral, and this collection has treated that integral as a number to evaluate. It is not a number. It is a density, and it says which millimetres of the member produced the answer — which is not the same map as where the moment is largest.

deflection · deflection distribution

Named alongside it

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

DeflectionHaunchMoment diagramSecond moment of areaBending momentCurvatureFully stressed designInfluenceOptimisationReciprocitySection modulusServiceability

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