Structural Engineering & Statics
where the load goes
Concept

Limit analysis — where it appears

Bounding a collapse load without solving for the path to it, by finding either an admissible set of internal forces or an admissible mechanism. The first is a lower bound and the second an upper one, and neither claims to describe what the structure actually does.

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

-150-100-505010015000.20.40.60.811.21.4the redundant — horizontal reaction at the right base (kN)load factorbeam 1.00sway 1.25combined 0.71best lower bound 0.714every mechanism is at or above the answer; every admissible field is at or below it

Two ways of being wrong

Plastic analysis has two theorems and they point in opposite directions. Any equilibrium field that nowhere exceeds the plastic moment gives a load at or below the collapse load; any mechanism gives one at or above it. Only one of those errors is safe.

equilibrium · bound theorems T = 40 kN at 25°no pinnaclee = 0.503 moutside the middle thirdthe line stays in the stone · σ = 351 kPa at the toe

The weight that makes it safer

Every load in this collection makes a structure worse. A pinnacle does not. A masonry pier fails when the line of compression leaves the stonework, and adding weight at the top rotates that line back towards the vertical without adding anything the pier cannot carry — so the stone is not being strengthened, it is being aimed.

structures · buttress

Named alongside it

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

EquilibriumThrust lineArchBearing stressButtressCollapse mechanismDuctilityEccentricityFree bodyFrictionKernLoad factor

All concepts