3D behaviour — exercises | Queensferry

Module 9Level 3reactions and load path

A wheel near one edge of a deck

A two-girder bridge deck carries a wheel load close to one girder. How is the load shared, in plan?

Predict first, then reveal

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

AThe nearer girder attracts more of the load; the cross-members transfer some load and twist across to the far girder, so both participate.BThe nearer girder carries all of it; the far girder does nothing.CThe two girders share it equally, because they are the same size.

Module 9Level 4change and sensitivity

Wind that misses the stiffness centre

A rigid floor diaphragm is pushed by a lateral wind load whose resultant does not pass through the building's centre of stiffness. What does the floor do?

Predict first, then reveal

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

AIt translates and rotates in plan — plan torsion — so the resisting frames take unequal shares, the ones further from the stiffness centre working harder.BIt only translates sideways; a rigid floor cannot rotate.CNothing — a rigid diaphragm is too stiff to move.

Module 9Level 4deflected shape

A load through the centroid of a channel

A transverse load is applied through the centroid (at the web) of an open channel section. Does the member simply bend?

Predict first, then reveal

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

ANo — it bends and also twists, because the shear centre of a channel is not at the centroid; the load misses the shear centre.BYes — a load through the centroid never causes twist.CIt twists only, without bending.

Module 9Level 3change and sensitivity

Move the load to the shear centre

The transverse load on the channel is moved out to act through its shear centre. What changes?

Predict first, then reveal

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

AThe twist disappears — the member now bends only. The shear centre is exactly the point through which a transverse load causes no torsion.BNothing changes — the load is the same magnitude.CThe twist doubles, because the load is now further out.

Module 9Level 3software check

Trusting a rendered member's strong axis

In a 3-D model, a beam is drawn deep in the vertical direction on screen. A colleague reads its bending result assuming that on-screen deep direction is its strong (major) axis. Is that safe?

Predict first, then reveal

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

ANo — the rendered depth is a display choice; bending must be read in the member's declared local axes, which may not line up with how it looks on screen.BYes — the deep direction on screen is always the strong axis.CYes, provided the render looks realistic.

Module 9Level 2reactions and load path

A wheel on the centreline

The same two-girder deck now carries the wheel load exactly on its centreline. How is the load shared, and is there any twist?

Predict first, then reveal

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

ABoth girders share the load equally and there is no net twist — the symmetric load on a symmetric deck gives a symmetric response.BThe load still goes mostly to one girder, as before.CThe deck twists strongly because the cross-members are loaded.

Module 9Level 3reactions and load path

Wind through the stiffness centre

A lateral wind load on a rigid floor diaphragm passes exactly through the building's centre of stiffness. How does the floor move, and how do the frames share the load?

Predict first, then reveal

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

AThe floor simply translates without rotating, and each frame carries a share in proportion to its own stiffness.BThe floor rotates in plan, loading the frames unequally.CThe stiffest frame carries everything and the others carry nothing.

Module 9Level 5change and sensitivity

A stiff core on one side

A building has a symmetric plan but a stiff lift-core wall on one side only. A wind load acts through the geometric centre of the plan. Does the floor twist?

Predict first, then reveal

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

AYes — the stiff core pulls the centre of stiffness towards it, so a load through the geometric centre is offset from the stiffness centre and twists the floor.BNo — the load is through the geometric centre, so by symmetry it cannot twist.CNo — only an off-centre LOAD can cause twist, and this load is central.

Module 9Level 3reactions and load path

Which way does a long slab span?

A rectangular slab is supported on all four edges but is much longer in one direction than the other. Which way does most of the load span?

Predict first, then reveal

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

AAlmost all the load spans the SHORT way, across to the nearer pair of supports — the slab behaves essentially one-way.BMost of the load spans the LONG way, to make use of the longer edges.CThe load splits equally in both directions regardless of the proportions.

Module 9Level 3internal force diagram

How a square slab collapses

A square slab is supported on all four edges and loaded to failure. What collapse (yield-line) pattern would you expect?

Predict first, then reveal

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

ADiagonal yield lines running from the corners to a central region — the slab folds up along these lines as a two-way mechanism.BA single straight hinge across the middle, like a one-way slab.CNo pattern — a slab supported on all edges cannot form a mechanism.

Module 9Level 4change and sensitivity

Which section resists twist better?

Two beams carry the same twisting moment: one is an open channel, the other a closed rectangular box of similar size. Which twists far less, and why?

Predict first, then reveal

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

AThe closed box twists far less — a closed section carries torsion as a smooth shear flow around the perimeter, which is enormously stiffer than an open section's thin-walled twisting.BThe open channel twists less, because it has more corners to grip the load.CThey twist the same, because they are similar in size.

Module 9Level 3reactions and load path

Two beams of different depth share a load

A load sits on a deck carried by two parallel beams connected by the deck: one beam is much deeper (stiffer) than the other. How is the load shared?

Predict first, then reveal

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

AThe deeper, stiffer beam attracts the larger share of the load, in proportion to its stiffness — load follows stiffness.BThe two beams share equally, because they carry the same deck.CThe shallower beam carries more, because it deflects more.

Module 9Level 4reactions and load path

Balancing all six directions

A three-dimensional structure is in equilibrium. Beyond the three familiar force balances, what else must hold — and why does it matter for reading behaviour?

Predict first, then reveal

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

AAll three moment balances must hold too — about each axis — so an eccentric load that leaves a net moment about a vertical axis must be resisted by torsion somewhere.BOnly the three force balances matter; moments look after themselves.CNothing else — three equations are enough in three dimensions.