Structural Engineering & Statics
where the load goes
Concept

Energy balance — where it appears

A way of finding a response by setting the work a load delivers against the energy the structure can store and dissipate. It suits a falling weight, whose force is not known in advance and whose energy is.

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

Spread over the span, the rotation gathers at the supports every drop shares. The plastic rotation each station of a 6 m beam fixed at both ends (EI 42,000 kN·m², plastic moment 200 kN·m) struck 20 times by a weight of 4.9 kJ has gathered by the last drop, for drops always at mid-span, at 0.3 and 0.7 of the span in turn, and at random. Always at mid-span, the worst station holds 0.193 radians, at 3.0 m, and 3 stations more than a milliradian; at 0.3 and 0.7 in turn, the worst station holds 0.104 radians, at a support, and 4 stations more than a milliradian; at random, the worst station holds 0.128 radians, at a support, and 15 stations more than a milliradian.

The weight that lands somewhere else

A beam that yields under a falling weight takes a permanent set from every drop, and if the weight always lands in the same place the set grows by the same amount every time. Let the weight land somewhere different each time — rocks on a canopy, crates on a deck — and the set still grows: the weight's energy fixes how much plastic work every drop does, wherever it lands. What the landing point decides is where the work goes. Half of every drop's hinge rotation goes under the weight and half to the supports, so wandering drops spread the first half along the span and leave the second half where it always was: the worst hinge turns half as fast, and it is at a support.

dynamics · Impact factor A weaker joint spends less per radian, so every hinge turns further. The plastic rotation each further drop adds, once the beam has settled into its mechanism, at each joint and under the load, against the joint's resistance as a share of the beam's plastic moment. At a share of 1, 3.2 and 6.4 mrad; at 0.5, 5.6 and 11.3; at 0.2, 6.8 and 13.7.

The fuse that makes the span work harder

A rock-fall canopy's beams hang on connections weaker than themselves, so it seems natural to let those connections be fuses: let them take the blows, replace them after a bad winter, and keep the beam clean. A falling weight is an energy, though, and a mechanism fixes how far its hinges turn relative to each other. Weaken the ends and each drop's energy has less moment to spend itself against, so every hinge turns further, and the one under the weight turns furthest. Under a big rock the fuse is the part of the beam that does less of the work, and it takes the span a third sooner to its limit. It keeps its promise only for the rocks too small to bend the span at all.

dynamics · Impact factor

Named alongside it

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

Impact factorPlastic hingeShakedownDuctilityLow-cycle fatigueMechanismMoment connectionRatchetingResidual stressRotation capacitySelf-stress

All concepts