Teaching basis and review status

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

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Module 2 · Exercises

Equilibrium

Predict before you reveal — the explanation compares your choice against the structural model.

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Module 2Level 3reactions and load path

Which way does the far support push?

A beam runs on a pin and a roller, with a downward load out on the overhang beyond the roller. What is the direction of the reaction at the pin (the support away from the load)?

Predict first, then reveal

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

ADownward — a hold-down. Removing the pin would let that end spring up, so the reaction must pull it back down.BUpward, because supports always push up.CThere is no reaction at the pin, because the load is not above it.

Module 2Level 2reactions and load path

Where does the load path end?

Tracing a floor load, an engineer follows it from the slab into a beam and then into a column, and stops there, satisfied the path is complete. Is it?

Predict first, then reveal

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

ANo — the path is not complete until the load is balanced by the ground. The column must carry it through its foundation into bearing.BYes — reaching the column is the end of the structural path.CYes, provided the column is strong enough.

Module 2Level 3reactions and load path

Can a support end up carrying tension?

A continuous beam has only its central span loaded. A bearing at one far end is a simple pad that can push up but cannot pull down. What can happen there?

Predict first, then reveal

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

AThe end can lift off: continuity pulls that end upward, and a pad that cannot hold down simply loses contact, changing the structural system.BNothing unusual — the end reaction is a normal upward force.CThe bearing develops a downward reaction and holds the beam down.

Module 2Level 3reactions and load path

Balancing forces but not moments

A support arrangement makes the upward reactions add up to exactly the applied downward load. Does that guarantee the structure is in equilibrium?

Predict first, then reveal

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

ANo — force balance is necessary but not sufficient. The moments must close too; an eccentric load can leave an unbalanced turning effect.BYes — if the vertical forces balance, the structure is in equilibrium.CYes, because a moment cannot exist if the forces balance.

Module 2Level 2reactions and load path

The quickest way to a reaction's direction

You need the direction (not the magnitude) of a reaction. What is the fastest reliable method?

Predict first, then reveal

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

AImagine removing that support: the direction that would push the structure back to its place is the reaction's sense.BAssume it points up; reactions almost always do.CCalculate the magnitude first; the sign will tell you the direction.

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