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One support too many — page 3

Essays 49 to 52 of 52 on this thread, in the same order.
hook100 kN57.7 kN57.7 kN60°57.7 kN of compression, in the load2040608000.511.52sling angle (degrees)leg force ÷ load30° Equilibrium

The angle that doubles the force

A crane hook takes the weight and nothing else. What holds the load is a set of legs running down to it at an angle, and each leg is a two-force member — so at thirty degrees from the horizontal each of two legs carries the entire load, and the difference goes into the thing being lifted as compression.

800 kN1.091.010.960.940.940.961.011.09an equal share490 mm = 24.5 dworst bolt 109 kN against a nominal 100 kN Connections

The bolts that do not share

Every bolted connection in this collection has divided a force by a number of bolts. That is right for a short joint and wrong for a long one, and the reason has nothing to do with the bolts — it is that the plates they join are elastic, and stretch by different amounts at different points along the lap.

0123400.20.40.60.81period (s)spectral acceleration (g)fixed baseisolatedbase shear ÷ 10.20123400.050.10.150.20.25period (s)spectral displacement (m)fixed baseisolatedmovement × 2.5five per cent damped, faint; 20 per cent damped, bold Dynamics

Made weaker on purpose

Everything else in this collection resists a load by being stiff or strong enough for it. A base-isolated building resists an earthquake by refusing to hear it — a layer of bearings under the whole structure with a lateral stiffness a twentieth of the frame's, bought with almost no strength at all.

36 × 36210 non-zerosof 1296 entriesbandwidth 13nullity 3before the supports go indense solve 16kbanded 6ka member reaches only its own two nodes Deflection

The matrix that replaced the hand methods

Moment distribution passes moments round a frame until they stop moving. Virtual work computes one deflection at a time. Both are exact and both stop scaling in the low tens of members. What replaced them adds no physics at all — the whole of the invention is the bookkeeping.

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