Yield-line — exercises | Queensferry

Module 15Level 2reactions and load path

How a square slab spans

A roughly square slab is supported on all four edges. In how many directions does it carry its load?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

ATwo — it spans in both directions at once, sharing the load between them by stiffness (the shorter span, being stiffer, takes more).BOne — a slab always spans the short way only.CNone — a slab carries load in shear, not spanning.

Module 15Level 3internal force diagram

What is a yield line?

At collapse a slab develops yield lines. What is a yield line, and what does the pattern of them represent?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

AA line along which the slab hinges plastically; a valid pattern of them divides the slab into rigid regions that rotate about their supports, folding it into a collapse mechanism.BA line of zero bending moment, like a point of contraflexure.CA crack that forms randomly with no relation to collapse.

Module 15Level 4software check

Is an assumed yield-line pattern safe?

You calculate a slab's collapse load from an assumed yield-line pattern. Can you rely on that value as a safe estimate of capacity?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

ANo — yield-line analysis is an upper-bound method: an assumed pattern gives a load at or above the true collapse load, so it can be unsafe. You must find the pattern giving the lowest load.BYes — any yield-line pattern gives a safe, conservative answer.CYes, provided the pattern looks symmetric.

Module 15Level 3change and sensitivity

When does a slab span one way?

A slab is supported on all four edges but is long and narrow — much longer in one direction than the other. How does it span?

Predict first, then reveal

Reason from the supports, the movement and equilibrium — not from what looks familiar.

AEssentially one way — across the short direction, like a series of beams; the long-direction span is too flexible to attract much load.BStill equally two ways, because it has four supported edges.COnly the long way, because that is the main span.