Module 16 · Level 3 · which impossible
An influence line versus a bending-moment diagram What does an influence line for the mid-span moment of a beam actually plot?
Predict first, then reveal Reason from the supports, the movement and equilibrium — not from what looks familiar.
A The mid-span moment as a unit load moves to each position along the beam — one response point, load position along the axis. B The bending moment at every point along the beam for a fixed load. C The deflected shape of the beam under its load.
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Module 16 · Level 3 · reactions and load path
Where to put a single moving load You have the influence line for a response, and a single moving point load. Where do you place the load to make that response as large as possible?
Predict first, then reveal Reason from the supports, the movement and equilibrium — not from what looks familiar.
A At the position where the influence line has its peak (maximum ordinate) — that position gives the largest response. B At the nearest support, because reactions are largest there. C At mid-span every time, regardless of what response you are after.
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Module 16 · Level 4 · change and sensitivity
A distributed moving load A distributed live load can cover any part of the span. To maximise a response, which parts of the span should carry it?
Predict first, then reveal Reason from the supports, the movement and equilibrium — not from what looks familiar.
A Only the parts where the influence line has the sign you want (say positive); leave the opposite-sign parts unloaded, since loading them would reduce the response. B The whole span, always — more load means more response. C Only the supports, since that is where reactions build.
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Module 16 · Level 4 · change and sensitivity
Loading a continuous beam for the worst span moment To maximise the sagging moment in one span of a two-span continuous beam, should you load both spans or just one?
Predict first, then reveal Reason from the supports, the movement and equilibrium — not from what looks familiar.
A Just that span — loading the neighbour actually reduces the span's sagging moment, because the influence line for it is negative over the other span. B Both spans, because more load always means more moment. C Neither — the moment is the same however you load it.
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Module 16 · Level 4 · deflected shape
The shape of an influence line By Müller-Breslau's principle, how can you find the shape of an influence line without moving a load step by step?
Predict first, then reveal Reason from the supports, the movement and equilibrium — not from what looks familiar.
A Release the restraint corresponding to that response and impose a unit movement there; the resulting deflected shape IS the influence line. B Draw the bending-moment diagram for a central load; that is the influence line. C There is no shortcut — you must move the load point by point.
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