Structural Engineering & Statics
where the load goes
Concept

Propping — where it appears

Supporting a member temporarily so that a load is carried by a different structure from the one that will carry it afterwards. It changes which section carried which load, so a propped member and an unpropped one of identical size have different stresses and different deflections at the same finished state.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

The props decide where the stress ends up. Bottom-fibre stress in the steel of a 12 m composite beam carrying 12 kN/m of wet concrete and 18 kN/m afterwards. Unpropped, the bare steel takes the first stage alone and reaches 292 MPa; propped, the finished composite section takes everything and reaches 186 MPa — a ratio of 1.57. 62% of the unpropped beam's final stress was locked in before the slab was structural at all. The deflections differ by 1.73 times for the same reason, and no drawing of the finished beam distinguishes the two.

The structure that was never complete

Every analysis in this collection is of a finished structure loaded once. Real ones are built in pieces, and each piece carries whatever was present at the moment it became structural — so the stress in a member depends on when it arrived, which appears nowhere on any drawing.

structures · Construction sequence Four camber rules, and what each leaves on the finished beam. The same 12 m composite beam, cambered against four different things, followed through its own load history. Positive is a sag and negative a hog, and the point at the left of each line is the shape it was fabricated to. Cambering against the wet concrete leaves 12.7 mm of sag at the end and a flat beam on the day the slab is poured; cambering against the total load leaves the beam dead flat when fully loaded and hogged 37.9 mm — one part in 316 of the span — before anything is on it at all.

Built to the wrong shape on purpose

A cambered beam is fabricated curved upward so that load bends it down to something like straight. Nothing in the analysis changes, no stress anywhere is altered, and almost every mistake made with it is a bookkeeping mistake about which loads count.

deflection · Camber The check that depends on a date. Total deflection and the deflection occurring after the brittle finishes are built, for one 12 m beam, against the day those finishes go up. The total barely moves — the beam ends up where it ends up. The increment falls from 32 mm at a week to 14 mm at a year, because creep is fast at first and slow later and a partition built early inherits nearly all of it: 44% of the final creep has already happened by day 28. The span/500 limit is 24 mm and the span/250 limit is 48; this beam passes the first only after day 25. Camber subtracts from both terms of the difference and therefore changes the upper curve and not the lower one, which is the reason a cambered beam can satisfy every total-deflection check and still crack the wall.

The limit that depends on a date

Total deflection can nearly always be met, and on a long span it is met with camber. The limit that actually decides the member is the other one — the deflection occurring after the brittle finishes are built — and camber does nothing for it whatever, because it is subtracted from both terms of a difference. The same beam passes or fails on the day the partitions went up.

deflection · Incremental deflection More props, heavier slabs — unless they go in after the weight. The heaviest load any slab carries during construction, as a multiple of its own weight, against the number of levels of props under the slab being cast. Every level a shore that carried the wet concrete and moves up with the formwork: 2.00, 2.25, 2.37, 2.44 w for one to four levels. One level of shores and the rest backprops, put in snug after the formwork is struck: 2.00, 1.50, 1.33, 1.25 w. The same number of props, differently timed: a shore enters the load path before the weight it carries and passes it down, and a backprop enters after and shares only what arrives later.

Loaded twice over before it is a month old

A concrete floor in a building going up a storey a week carries, in its first weeks, the wet weight of the floors being cast above it, handed down through the props. By Grundy and Kabaila's arithmetic that is twice its own weight on a single level of shores, and more with more levels — 2.25 on two, 2.37 on three — because every prop that carried wet concrete passes its load down the stack. The same props put in after the formwork is struck carry nothing until something new arrives, and the peak falls to 1.5, 1.33, 1.25. The heaviest day of a floor's life is decided by when its props went in, not how many there are.

materials · Maturity

Named alongside it

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

Construction sequenceComposite actionCreepDeflection limitServiceabilitySuperpositionBackproppingCamberContinuityDeflectionDifferential settlementEarly age strength

All concepts