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Module 13 · Exercises

Moment distribution

Commit a prediction before you reveal the answer — the explanation checks it against the structural model.

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Module 13Level 3change and sensitivity

Sharing the out-of-balance

Two members of equal EI meet at a rigid joint, both with fixed far ends: one is 6 m long, the other 4 m. How is an out-of-balance moment shared between them?

Predict first, then reveal

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

ABy distribution factors DF = K/ΣK: the 4 m member (stiffer, 4EI/4) takes 0.60 and the 6 m member takes 0.40 — the shorter member takes more, and the two sum to 1.0.BEqually, 0.5 each, because the EI is the same.CThe 6 m member takes more, because it is longer.

Module 13Level 3reactions and load path

The carry-over to a fixed end

A moment is distributed into a member at one end. Its far end is fully fixed. What fraction of that distributed moment appears at the fixed far end?

Predict first, then reveal

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

AOne half — the carry-over factor to a fixed far end is ½.BAll of it — the whole moment carries over.CNone — moment never carries across a member.

Module 13Level 3change and sensitivity

A pinned far end

The far end of the member is a pin instead of a fixing. What now carries over to it, and what happens to the member's stiffness?

Predict first, then reveal

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

ANothing carries over — the carry-over factor to a pin is 0 — and the member's stiffness drops from 4EI/L to 3EI/L.BHalf carries over, the same as a fixed end.CThe full moment carries over, because a pin is weak.

Module 13Level 2reactions and load path

Where moment distribution starts

What quantities does a moment-distribution analysis start from, before any balancing?

Predict first, then reveal

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

AThe fixed-end moments — the joints are locked first, making each member fixed-ended, and its end moments are the standard results.BThe final balanced moments, read straight off.CZero everywhere, then moments are added.

Module 13Level 3software check

What is moment distribution, really?

How does moment distribution relate to the matrix stiffness method used by software?

Predict first, then reveal

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

AIt is the same physics — it solves the joint rotations of the stiffness method by iterating (balancing joints one at a time) instead of solving the matrix directly.BIt is a completely different method that gives a different answer.CIt is the flexibility (force) method under another name.

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