4.5MechanicsStretch

Tilting

When a beam on two supports is about to tilt, it is on the point of rotating about one support — and the reaction at the other support becomes zero. This key idea unlocks tilting problems.

24 min Video by Zeeshan Zamurred Moments

Edexcel A Level Maths: 4.5 Tilting (Moments, Resultant Force)Watch the full walkthrough before the notes below.

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What you'll be able to do

Recognise the condition for tilting
Set a support reaction to zero
Take moments about the pivot support
Find limiting loads or positions

On the point of tilting

When a beam is about to tilt about a support, the reaction at the $other$ support is zero. Set that reaction to $0$ and take moments about the pivot support to find the limiting case.

R_{other support} = 0 at the point of tilting

The far reaction vanishes.

1On the point of tilting about B, the beam lifts off A.

2So

R_{A} = 0

Answer

R_{A} = 0

Tip — About to tilt about one support ⇒ the reaction at the OTHER support is zero.

Formula recap

R_{far support} = 0

Condition for tilting.

\sum M_{pivot} = 0

Take moments about the pivot.

Common mistakes to avoid

Setting the pivot support’s reaction to zero.

It is the OTHER (far) support whose reaction is zero.

Forgetting which support the beam tilts about.

Identify the pivot, then zero the far reaction.

Key takeaways

On the point of tilting, the far support’s reaction is zero.
Take moments about the pivot support.
Use this to find limiting loads or positions.

Test yourself

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