Structural Engineering & Statics
where the load goes
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The load must go somewhere — page 20

Essays 457 to 458 of 458 on this thread, in the same order.
A helix puts the bore's rest state on the long axis of the yield ellipse. The hoop and axial stress at the bore of a closed tube of a 100 mm bore, a 15 mm steel liner yielding at 900 N/mm² and a jacket of balanced carbon fibres 30 mm thick, at rest and at its highest pressure, on the yield ellipse of the liner at 900 N/mm². At ±54.7°, wound at 978, it rests at −1,045 and −609 and works at 688 and 59 N/mm², a pressure of 352. As hoops, wound at 710, it rests at −908 and −7 and works at 228 and 778, a pressure of 265. Materials

The angle that forgets the liner

Every filament-wound pressure vessel is laid at about 55 degrees, because a closed tube pulls twice as hard round its hoop as along its axis, and a fibre at that angle carries the two in exactly that ratio. Wrap those fibres over a steel liner and the ratio has stopped being the fibres' business, because the steel is carrying a share of each. Wound slack, the best angle is nearly a hoop and 55 degrees is the second-worst sensible choice. Wind it tight enough to squeeze the bore to its floor, though, and the helix returns, for a reason the fibres had nothing to do with: it is the only winding that also presses the steel along its length.

 The wrong energy moves load towards the cable furthest along its curve. Each cable's share of 50 kN, by compatibility and by minimising the strain energy. With lengths of 30, 22, 16 and 12 m and one pretension: 0.08, 0.14, 0.27, 0.51 against 0.04, 0.07, 0.22, 0.67. With one length of 20 m and pretensions of 20, 60, 120 and 240 kN: 0.16, 0.20, 0.26, 0.38 against 0.33, 0.28, 0.21, 0.18. Deflection

The load goes to the cable furthest along

Applied to one stiffening member, Castigliano's theorem halves or thirds its deflection and leaves its force alone, since there is only one member to carry it. A net has many, each at its own place on its own curve, and when the wrong energy has to divide a load among them it hands it to whichever is furthest along. The peak cable force comes out a fifth too high on one net and a quarter too low on another, by the same mistake. Only a net with no pretension at all gets the force right, and even that one gets the deflection wrong by a factor of three.

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