Structural Engineering & Statics
where the load goes
Concept

Balance — where it appears

The state in which the moments of a structure's weight and its counterweight about a pivot cancel, so the support carries their sum and no moment. A balance holds only for the positions it was set for; a load that moves leaves the difference to the support.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as counterweight — the same set of essays touches all of them, so they are one junction rather than several.

Balanced, and four times as heavy on the bearing. A bascule leaf of 900 kN whose centroid is 9 m from the trunnion, balanced by 2700 kN at 3 m on the other side. What balancing achieves is exactly one thing: the moment about the pivot is zero at every opening angle, because both terms carry the same cosine. What it costs is two things that are not zero. The reaction on the trunnion becomes 4.0 times the leaf's own weight, since both weights are still there. And the rotational inertia rises by 33%, so the balanced leaf is the hardest one to start and to stop — which is why the counterweight is put as close to the pivot as it will fit, at the price of being heavy: the same balance at twice the radius weighs 1350 kN and carries 1.25 times the inertia.

Balanced, and four times as heavy

A counterweight cancels a moment about a pivot, and that is the only thing it cancels. The bearing beneath carries both weights, the inertia rises as the square of the radius, and a load that moves cannot be balanced at more than one position at all.

equilibrium · Counterweight A counterweight that follows the jib leaves only the payload, halved. The moment in the mast of a crane whose 50 m jib weighs 300 kN and luffs between 15° and 85°, lifting 60 kN at its tip, against the luffing angle, with a counterweight linked to the luff so that it balances the jib and half the payload at every angle: 1,449 kN·m loaded and −1,449 empty at 15°, 131 and −131 at 85°. What is left is the payload's moment less the half the counterweight was set for, plus or minus 1,449 kN·m at most, against 4,744 with a fixed counterweight.

The counterweight that follows the jib

A counterweight that stays put balances one position and leaves the mast a moment at every other. Make it move and it can balance anything that moves slowly enough to be followed. On a luffing crane the thing that moves most is not the payload but the jib itself, whose own moment about the mast changes more than twice as much through its luff as the payload's ever is — and a counterweight linked to the luff cancels that change exactly. What it cannot cancel is the payload, which leaves the ground in a second. The best any counterweight can do with that is wait halfway, and the mast is left with half the payload's moment at the longest radius, whatever else the counterweight does.

equilibrium · Counterweight

Named alongside it

The objects these essays reach for when they reach for this one.

CounterweightEquilibriumLever armLoad reversalMoving loadOverturningBearingCentre of gravityDead loadFree bodyMomentReaction

All concepts