Influence lines — exercises | Queensferry

Module 16Level 3which 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.

AThe mid-span moment as a unit load moves to each position along the beam — one response point, load position along the axis.BThe bending moment at every point along the beam for a fixed load.CThe deflected shape of the beam under its load.

Module 16Level 3reactions 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.

AAt the position where the influence line has its peak (maximum ordinate) — that position gives the largest response.BAt the nearest support, because reactions are largest there.CAt mid-span every time, regardless of what response you are after.

Module 16Level 4change 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.

AOnly 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.BThe whole span, always — more load means more response.COnly the supports, since that is where reactions build.

Module 16Level 4change 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.

AJust that span — loading the neighbour actually reduces the span's sagging moment, because the influence line for it is negative over the other span.BBoth spans, because more load always means more moment.CNeither — the moment is the same however you load it.

Module 16Level 4deflected 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.

ARelease the restraint corresponding to that response and impose a unit movement there; the resulting deflected shape IS the influence line.BDraw the bending-moment diagram for a central load; that is the influence line.CThere is no shortcut — you must move the load point by point.