How to play Plank Bridge
- Choose a load and read the span, the weights, and their positions on the card.
- Use ΣF = 0, R_A + R_B = W + w, and ΣM = 0 about one support to find the other reaction.
- Type the rating or the distance and press Load. The crane lowers the crate, or the truck or walker sets off.
- Watch the reaction bars against the ratings. A support cracks at its rating; the plank tips when R_A reaches zero.
What are the two conditions for equilibrium?
An object stays at rest only if two conditions hold. The forces cancel, ΣF = 0, so it does not start moving; and the moments cancel about any point, ΣM = 0, so it does not start turning. For a plank on two supports, ΣF = 0 says R_A + R_B = W + w. Taking moments about A, where R_A has no turning effect, gives R_B·L = W·x + w·x_c in one step. The nearer a load is to a support, the more that support carries. If the load moves past a support, the far support's reaction can fall to zero: then nothing holds that end down, and the plank tips.
A focused learning model
The plank is rigid and uniform, so its weight acts at its centre, and the supports only push up. The crane lowers crates slowly, and the truck and walker move slowly, so the plank is in equilibrium at every moment. A support cracks exactly when its reaction reaches its rating; the plank tips exactly when R_A reaches zero. A rating within 0.05% of the reaction counts as holding, so a rounded answer does not crack. Plays in real time.