Plastic collapse — exercises | Queensferry

Module 14Level 3internal force diagram

What is a plastic hinge?

A plastic hinge forms in a ductile beam. What is the moment there while it rotates?

Predict first, then reveal

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

AA constant moment equal to the plastic moment Mp — the section is fully yielded and rotates at that moment, unlike a real pin which carries zero moment.BZero moment, exactly like a real pin.CAn ever-increasing moment as it rotates.

Module 14Level 3change and sensitivity

Does the first hinge mean collapse?

In an indeterminate beam, the first plastic hinge forms. Has the beam collapsed?

Predict first, then reveal

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

ANo — an indeterminate structure redistributes moment and carries on, forming further hinges until it becomes a mechanism.BYes — any plastic hinge means immediate collapse.CYes, because a hinge is a release and releases cause mechanisms.

Module 14Level 4stable or mechanism

How many hinges to collapse?

A fixed-ended beam is indeterminate to the second degree. How many plastic hinges must form for it to collapse?

Predict first, then reveal

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

AThree — one more than the degree of indeterminacy. Hinges form at both fixed ends and at mid-span, turning the beam into a mechanism.BOne — the first hinge collapses it.CTwo — the two fixed ends.

Module 14Level 3stable or mechanism

A simply supported beam at first hinge

A simply supported beam is loaded until a plastic hinge forms at mid-span. What is its state?

Predict first, then reveal

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

AIt has collapsed — being determinate, its first hinge (at mid-span) immediately makes it a mechanism.BIt carries on, redistributing to the supports.CIt needs two more hinges at the supports first.

Module 14Level 3change and sensitivity

Collapse load versus first-yield load

For a ductile indeterminate beam, how does the collapse load compare with the load at first yield?

Predict first, then reveal

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

AThe collapse load is higher — often significantly — because redistribution lets the structure keep carrying load after the first section yields.BThey are the same — first yield is collapse.CThe collapse load is lower, because yielding weakens the beam.