Stability, mechanisms and determinacy exercises

Module 3Level 2stable or mechanism

A pin-jointed rectangle under sideways load

A rectangle of four bars with pinned corners is pushed sideways at the top. Is it stable, or a mechanism?

Predict first, then reveal

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

AA mechanism — the bars keep their length while the rectangle racks into a parallelogram, so it cannot resist the sideways load.BStable — four bars is plenty to hold a rectangle together.CStable, because the corners are connected all the way round.

Module 3Level 2change

Add one diagonal

A single diagonal bar is added across the racking rectangle. What is the effect?

Predict first, then reveal

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

AIt becomes stable: the diagonal triangulates the panel, so racking would have to change the diagonal's length, which it resists.BNo change — it still racks, because the diagonal is only one bar.CIt becomes a mechanism in the other direction.

Module 3Level 3stable or mechanism

Three vertical rollers — enough restraint?

A beam rests on three vertical rollers. A plane body needs three restraints, and there are three reactions. Is it stable?

Predict first, then reveal

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

ANo — all three reactions are vertical (parallel), so nothing restrains horizontal movement and the beam can slide sideways.BYes — three reactions for a plane body is exactly enough, so it is stable and determinate.CYes, because rollers are supports and supports make things stable.

Module 3Level 3stable or mechanism

A portal with four pins

A rectangular portal has pinned bases and pinned beam-to-column joints — every connection is a pin. It is pushed sideways at the top. Stable or a mechanism?

Predict first, then reveal

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

AA mechanism — with every joint pinned, the rectangle sways as a four-bar linkage; nothing resists the sideways movement.BStable, because the columns are fixed to the ground by the bases.CStable, because a portal is inherently rigid.

Module 3Level 4stable or mechanism

A panel with two diagonals

A rectangular panel has both diagonals as well as its four sides, on a pin and a roller. What is the best description of it?

Predict first, then reveal

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

AStable and indeterminate: either diagonal alone would triangulate it, so with both present one is redundant — extra stiffness and an alternative path, not extra stability.BA mechanism, because two diagonals over-constrain it and it cannot move.CUnstable, because the diagonals cross and interfere.